Andrés Carmona

Carlo Felice Manara

Cláudio Melo

Fátima López-Martinez

Gösta Gahm

Juan Manuel Alcalá

Nestor Sanchez

Peter Petrov

Sérgio Sousa

Sílvia Alencar

Véronique Cayatte

Adriana Ferreira

Ana Catarina Leite

Ana Marta Pinho

Andressa Ferreira

Benard Nsamba

Gil Marques

João Camacho

Loïc Chantry

Michel- Andrès Breton

Sandy Morais

Solène Ulmer-Moll

A special

Keywords: Accretion, Classical T Tauri stars, Ejection, Star formation, Young Stellar Objects iii Accrétion, Étoiles T Tauri classiques, Éjection, Formation stellaire, Objets Stellaires Jeunes vii

The interplay between accretion and outflow processes in young stellar objects (YSOs) constitutes one of the big challenges in the field of star formation. We can better understand their evolution not only by a proper derivation and analysis of stellar and activity parameters through spectra, but also by modelling and simulating accretion and outflow mechanisms. In order to take a step further towards a better understanding of these phenomena, we started by carrying out a detailed study of the spectra of some YSOs and explored different tools that can be used to better understand these stars. We then proceeded to perform detailed simulations of the environment around such a YSO, where both accretion and outflows are at play, using existing numerical tools and self-similar semi-analytical magnetohydrodynamic solutions as initial conditions. Thus, to accomplish the goals of this project, we first test available software for main-sequence stars that has the potential to characterize pre-main sequence stars through their main stellar parameters.

Second, we characterize a sample of YSOs using ultraviolet to near-infrared spectra plus available photometry. Third, we explore a long-term monitoring of two variable classical T Tauri stars, through both spectroscopy and photometry, in order to characterize their circumstellar environment. Fourth, we actually simulate the circumstellar environment of one of these objects and evaluate if it is compatible with what is observationally expected.

Our simulations are able to reproduce the general behaviour expected for the environment around such a YSO. Also, we can derive from those simulations mass accretion and mass loss rates that agree well with the ones we could obtain from the corresponding spectra and with those available in the literature. Furthermore, we have simulations that could not only represent the bimodal behaviour of RY Tau, characterized by active and quiescent periods, but also the ceasing of accretion activity in YSOs. The work presented in this thesis, shows how the synergy between an observational and a numerical approach can improve our knowledge towards the study of low-mass YSOs.

Resumo

A interação entre processos de acreção e ejeção em objetos estelares jovens (YSOs) constitui um dos maiores desafios na área de formação estelar. Podemos compreender melhor a sua evolução não só através de uma derivação e análise adequadas dos seus parâmetros estelares e de atividade por meio de espectros, mas também através da modelação e simulação de mecanismos de acreção e ejeção. De forma a darmos um passo em frente para uma melhor compreensão destes fenómenos, começámos por realizar um estudo detalhado de espectros de alguns YSOs e explorámos diferentes ferramentas que podem ser utilizadas para melhor compreender estas estrelas. Em seguida, procedemos à realização de simulações detalhadas do ambiente em torno de um YSO, onde tanto a acreção como a ejeção estão em jogo, usando ferramentas numéricas já disponíveis e soluções em magneto-hidrodinâmica auto-similares e semi-analíticas como condições iniciais. Assim, para atingir os objetivos deste projeto, primeiro testamos software disponível para estrelas da sequência principal que tem o potencial de caracterizar estrelas da pré-sequência principal através dos principais parâmetros estelares. Segundo, caracterizamos uma amostra de YSOs usando espectros do ultravioleta ao infravermelho próximo, além de fotometria disponível. Terceiro, exploramos uma longa monitorização de duas estrelas T Tauri clássicas variáveis, com fotometria e espectroscopia, a fim de caracterizar os seus ambientes circum-estelares. Quarto, simulamos o ambiente circum-estelar de um desses objetos e avaliamos se é compatível com o que é esperado observacionalmente. As nossas simulações são capazes de reproduzir o comportamento geral esperado para o ambiente em torno de um YSO. Também podemos derivar dessas simulações taxas de acreção e perda de massa que estão de acordo com os valores disponíveis na literatura. Além disso, temos simulações que podem representar não só o comportamento bimodal de RY Tau, caracterizado por períodos ativos e quiescentes, mas também a cessação da acreção nos YSOs. O trabalho apresentado nesta tese mostra como a sinergia entre uma abordagem observacional e uma abordagem numérica pode melhorar o nosso conhecimento em relação ao estudo de YSOs de baixa massa.

Palavras-chave: Acreção, Estrelas T Tauri Clássicas, Ejeção, Formação estelar, Objetos Estelares Jovens v Résumé L'interaction entre les processus d'accrétion et d'éjection dans les objets stellaires jeunes (YSOs) constitue l'un des plus grands défis dans le domaine de la formation stellaire.

Nous pouvons mieux comprendre leur évolution non seulement par une dérivation et une analyse appropriées des paramètres stellaires et d'activité à travers des spectres, mais aussi à travers la modélisation et la simulation des mécanismes d'accrétion et d'éjection.

Pour approfondir la compréhension de ces phénomènes, nous avons commencé par faire une étude détaillée des spectres de certaines étoiles jeunes et nous avons exploré différents outils qui pouvaient être utilisés pour mieux comprendre ces étoiles. Nous avons ensuite fait des simulations détaillées de l'environnement autour d'une étoile jeune de classe II, où l'accrétion et l'éjection sont en jeu, en utilisant les outils numériques existants et des solutions magnétohydrodynamiques semi-analytiques et auto-similaires comme conditions initiales. Ainsi, pour atteindre les objectifs de ce projet, nous avons testé, premièrement, des logiciels disponibles pour les étoiles de la séquence principale qui pouvant potentiellement caractériser les étoiles de pré-séquence principale à travers des leurs paramètres stellaires principaux. Deuxièmement, nous caractérisons un échantillon d'YSOs utilisant les spectres de l'ultraviolet à l'infrarouge proche ainsi que la photométrie disponible. Troisièmement, nous avons effectué un suivi à long terme de deux étoiles T Tauri classiques variables, en spectroscopie et en photométrie, afin de caractériser leur environnement circumstellaire.

Quatrièmement, nous avons fait des simulations de l'environnement circumstellaire de l'un de ces objets et nous avons comparé nos résultats avec les observations. Nos simulations sont capables de reproduire le comportement général attendu pour l'environnement autour des YSOs. Nous pouvons également déduire de ces simulations des taux d'accrétion et d'éjection qui concordent bien avec ceux que nous pourrions obtenir à partir des spectres correspondants et avec ceux disponibles dans la littérature. De plus, nous avons fait des simulations qui pourraient non seulement représenter le comportement bimodal de RY Tau, caractérisé par des périodes actives et quiescentes, mais également expliquer les phases d'absence d'activité d'accrétion dans les YSOs. Le travail présenté dans cette thése montre comment la synergie entre une approche observationnelle et une approche numérique peut améliorer nos connaissances en vue de l'étude des YSOs de faible masse. -Antoine de Saint-Exupéry, Le Petit Prince

List of Tables

One of the astonishing facts we learn during our childhood is that the Sun is the closest star to planet Earth. As we grow up, we start asking ourselves how did it form? What were the physical processes involved in the formation of the Sun? What impact the evolution of the Sun had on the formation of the planets as we know nowadays? Is there any other way we can look backwards in time to better understand all the mechanisms involved?

Are there any other stars similar to the Sun? All the answers are hidden in low-mass Pre-Main Sequence (PMS) stars called T Tauri stars (TTSs). These Young Stellar Objects (YSOs) can be seen as teenage Suns that are still forming and contracting towards the Main Sequence (MS). By observing and studying them, we are getting a step closer towards the understanding of the formation of our own Solar System.

In this chapter, we briefly describe the formation and evolution of low-mass stars. In addition, we characterize these objects through their spectral features and explore accretion an outflow processes enrolled in their evolution. Finally, we mention the goals of the present thesis and describe how is it structured.

A closer look on T Tauri stars

T Tauri stars were named after the prototype T Tauri was found by the astronomer John Russel Hind (Hind 1856;Cox 2008). This group of low-mass stars were first studied by Joy (1945) and Herbig (1962), and have been characterized as variable Sun-like stars. TTSs have stellar masses that can go up to 2-3 M ⊙ and ages ranging between 1 and 10 Million years (Myr). In the HR diagram, these objects are located at the right side of the main sequence, as shown in Fig. 1.2 for TTSs observed in the Taurus-Auriga star-forming region (Stahler 1988). Iben (1965) and Grossman & Graboske (1971), for pre-main sequence stars, along with the corresponding stellar masses in M ⊙ . The heavy solid line represents the birthline of Stahler (1983). From Stahler (1988).

TTSs mark a particular evolutionary phase in low-mass stars. Their emission spectra resemble the one from the solar chromosphere (Joy 1945). Their spectral types vary between F and M. This evolutionary stage corresponds to the time at which these PMS stars become optically visible and they can be classified in two types. Classical T Tauri stars (CTTSs) are known for having strong ultraviolet and optical emission lines, namely Balmer lines, neutral and ionized metals. In addition, their spectra can also show traces of chromospheric activity. One particular emission is the Hα line, characteristic in YSOs and which can be easily identified in Fig. 1.3 at 6563 Å. CTTSs also show the lithium line in absorption at 6708 Å, which is characteristic of young stellar objects. In addition, they are surrounded by accretion disks, which are responsible for the infrared excess fingerprinted in their spectra. Conversely to CTTSs, Weak line T Tauri stars (WTTSs) lack strong emission lines, as shown in Fig. 1.3 for V830 Tau spectrum. This evolutionary stage is usually outflow/accretion activity, the corresponding absorptions will get stronger and go below the continuum. In that case, we are in the presence of a P Cygni profile, for the blueshifted absorption, or a Inverse P Cygni (IPC) in case of a redshifted absorption (e.g Edwards et al. 1994;[START_REF] Reipurth | [END_REF]. In Fig. 1.5 both profiles are shown. et al. (1996).

On the other hand, narrow emission lines such as He I, should be created near the accretion shock region (Hartmann et al. 2016). Besides accretion tracers, the spectra of CTTSs can also show blueshifted emission of low-excitation lines formed in outflows, namely forbidden lines such as [OI] (Herbig 1962). Forbidden lines originate from rarefied gas flows and form at large distances from the YSO higher than 1 Astronomical Unit (AU) and have two components, a High-Velocity Component (HVC) and a Low-Velocity Component (LVC). While the HVC has been associated with the presence of a stellar jet, the LVC is probably linked with slower outflows, namely disk winds.

Besides showing a very rich emission line spectrum, CTTSs have also been characterized by irregular light variability and variable accretion and outflow activity detected through emission line profiles. The time scale variability can be daily, or even take place in only few hours (e.g. Chou et al. 2013;Petrov et al. 2019). According to Herbst et al. (1994), irregular variability in TTS can be explained by three reasons. First, the presence of cold spots due to magnetic activity that is mainly observed in WTTSs. Second, accretion of circumstellar material and, consequently, the presence of hot spots on the stellar surface due to on-going accretion in CTTSs. Hot spots have a shorter life-time compared to cold spots. Third, obscuration of the central star by circumstellar dust that leads to an increase of visual extinction in the line of sight seen in both CTTSs and WTTSs.

The presence of circumstellar disks is due to the angular momentum conservation all along the collapse of the protostellar core, which lead to the settling of gas and dust in a disk (Shu 1977). Disks can be detected through the presence of infrared excess emission in the spectra of TTSs. Depending on the distance to the star, circumstellar material will have different temperatures. Warmer material will have higher temperatures if it is closer to the YSO, while cooler material will be further away in the disk (Williams & Cieza 2011).

This IR excess can be quantified through the infrared spectral index given by

α IR = d log νF ν d log ν , (1.1)
where ν corresponds to the frequency and νF ν is the flux density. Different ranges of the α IR index will correspond to a different class, according to the works of [START_REF] Lada | [END_REF]; [START_REF] Lada | IAU Symposium[END_REF]; [START_REF] Andre | [END_REF] and Greene et al. (1994) (see Fig.1.6). According CHAPTER 1. INTRODUCTION accretion through the disk (Balbus 2003). Bertout et al. (1988) applied for the first time the accretion disk theory to TTSs by using a model with an active PMS star and an accretion disk similar to the one in Lynden-Bell & Pringle (1974). According to the authors, between the star and the disk there is a boundary layer, i.e. a shock front, at the equatorial plane. The emerging radiation from this region could explain the excess emission observed at ultraviolet wavelengths.

The magnetospheric accretion model has been generally accepted by the scientific community in order to characterize the way accretion is processed in a low-mass pre-main sequence star. Originally conceived for neutron stars by Ghosh & Lamb (1979), it was later adapted for CTTSs by Uchida & Shibata (1984), Camenzind (1990) and Koenigl (1991). This model suggests that the circumstellar disk is truncated in its inner region close to the star, thanks to the presence of strong magnetic fields, around 1-3 kG (e.g.

Johns-Krull 2007)1 . In this inner edge of the disk, the stellar magnetosphere is strong enough to funnel the disk material onto the stellar surface through accretion columns. In these funnel flows, the gas can reach temperatures around 8000 K. It is thought that in these same columns the Hα line is emitted. The corresponding emission will translate into broadened velocity profiles (Muzerolle et al. 1998b(Muzerolle et al. , 2000)). When the material falls onto the surface of the star, near the star's magnetic poles, with a velocity between 200 and 300 km s -1 , it creates a shock region. The shock region can reach temperatures near 10 6 K, but the average temperature of spot is about 10 4 K (Kenyon et al. 1994;Hartmann et al. 2016). Romanova et al. (2004) discovered through 3D simulations that hot spots have an inhomogeneous structure and their shape depends on the magnetic axis inclination. The smaller the tilt, the bigger the shape. Higher tilts imply spots with bar shapes. In Kulkarni & Romanova (2013), simulations were made to study the shape and structure of these shock regions. They found out that the density and temperature of a hot spot increases towards its interior. This implies that the central region of the spot will be responsible for emission in the X-rays waveband, while the surrounding regions will emit in the ultraviolet, optical and infrared. In this region, temperatures can increase up to 10 6 K and the release of ultraviolet energy will be responsible for adding a continuum excess emission in the spectra of CTTSs (Valenti et al. 1993;Calvet & Gullbring 1998). This emission will make the photospheric absorption lines appear less deep when compared to non-accreting YSOs of the same spectral type. This effect is known as veiling, which tends to be stronger towards shorter wavelengths (Hartmann et al. 2016).

In order to enable the formation of accretion columns in the star-disk system, magnetic braking is needed [START_REF] Bouvier | Protostars and Planets V[END_REF]. This is only possible if the truncation radius, R t , is less than the co-rotation radius, R co , as illustrated in Fig. 1.10.

On average, accretion processes in CTTSs can last for 2 to 3 Myr. A typical value for the average accretion rate in these low-mass YSOs has been estimated to be around 10 -8 M ⊙ yr -1 (Hartmann et al. 2016), as shown in Fig. 1.11. Typical ratios between the jet mass loss and accretion rates range between 1% and 10% (Hartigan et al. 1995;White 1.1. STATE OF THE ART

Outflows

It has been debated that the disk-locking paradigm could give a plausible explanation for the spin-down of YSOs, as proposed for neutron stars in Ghosh & Lamb (1979). If the disk and the star are trapped by the magnetic field, this should be responsible for slowing down the rotation of the star. The stellar rotation is higher than the rotation of the disk.

If a strong magnetic field connects the star to the disk, this will imply the deceleration of the star.

Nevertheless, there are new studies that suggest that there should be other angular momentum removal mechanisms responsible for slowing down these objects efficiently, namely outflow mechanisms (see Fig. 1.13). As mentioned previously, outflows can be detected through forbidden emission lines or blueshifted absorptions present in the profiles of permitted emission lines [START_REF] Bouvier | Protostars and Planets V[END_REF]. Those outflows can be shaped as stellar winds (Matt & Pudritz 2005), disk winds (Blandford & Payne 1982), X-winds (Shu et al. 1994), conical winds (Romanova et al. 2009), or even Magnetospheric Ejections (MEs) (Goodson et al. 1997;Zanni & Ferreira 2013). According to Ferreira (2013), the Ghosh & Lamb (1979) model, X-winds, conical winds and the accretion powered stellar winds cannot spin-down the star, contrary to magnetospheric ejections. Indeed, it seems very difficult that only one mechanism is responsible for the angular momentum removal observed in CTTSs. Most likely, the spin-down is processed by a combination of different outflows jointly with the contribution of magnetospheric accretion processes.

Stellar winds

Stellar winds could give an explanation for slowing down the stellar rotation. We know that for the Sun, the angular momentum removal is due to stellar winds (e.g. Parker 1958).

One of the promising works is given by the accretion-powered stellar winds models by Matt & Pudritz (2005). These outflows would be sustained by a fraction of energy released by accretion processes. According to the authors, if the mass loss rate in the stellar winds is around 10% of the accretion rate, it should be enough to break the spin-up of the star.

Assuming that stellar winds are powered by accretion, Matt & Pudritz (2008) suggest that the mass loss rate of the wind should be equal to or less than 60% of the accretion rate.

Above this value accretion is not possible to power the wind.

The modelling performed in Sauty et al. (2011) shows that jets can efficiently brake a CTTS. One of the presented solutions suggests that close to the star, with a dipolar CHAPTER 1. INTRODUCTION magnetic field configuration, the wind is more efficient concerning the extraction of angular momentum.

Disk winds

Extended disk winds are magneto-centrifugally accelerated from the corresponding Keplerian disk (e.g. Blandford & Payne 1982). This kind of outflows may be sufficient to spin-down the disk, but is not enough to decelerate the star [START_REF] Cabrit | IAU Symposium[END_REF]Ferreira 2013).

1.1.4.3 X-winds X-winds are a product of the interaction between the star's magnetosphere and the circumstellar disk. The X-region separates two regions at a co-rotation radius R X . The disk material close to the inner region of R X rotates at sub-Keplerian velocities favouring accretion. The disk material close to the exterior region of R X rotates at super-Keplerian velocities enabling the escape of the disk material through a wind. At R X the stellar angular velocity equals the Keplerian velocity of the disk (Ω = GM * /R 3 X ). In this process there is angular momentum that is transported from the accretion flow to the interior region of R X . In addition, and outside R X , the X-wind transports angular momentum from that region towards the interstellar medium. The angular momentum transfer from the accretion column to the outflow regulates the spin-up of the star. et al. (2009) have simulated a different shape of winds for slowly rotating stars named conical winds, which are driven by magnetic pressure (see Fig.1.14). The outflows are conically-shaped, have a half-opening angle between 30 and 40 • and are composed by 10 to 30% of the inner disk material, up to 0.3 AU from the star. Besides the conical winds, Romanova et al. (2009) managed to simulate also a jet inside the conical wind region. The launching mechanism of these outflows results from compression of the magnetosphere by the radial velocity of the material in the circumstellar disk, as shown in Fig. 1.15. There are some differences between the X-wind and the conical wind models. First, the X-wind model requires that the truncation radius coincides with the co-rotation radius, while in conical winds the truncation radius can be smaller than the co-rotation radius. This means that, in the second model, the star can rotate more slowly than the inner disk. Second, the X-winds are driven by the centrifugal force, while the conical winds are magnetically pressure driven (Romanova & Owocki 2015). Due to the star-disk differential rotation, the magnetic field lines will inflate as illustrated in Fig. 1.16 . In the work of Romanova et al. (2009), this leads to the release of winds, from the inner disk region, with a conical shape.

Conical winds

Romanova

Jets

The origin and structure of jets has been under debate since many decades. Ferreira et al. (2006) mention that outflow processes in CTTSs should result from a mixture of different processes, namely a disk wind, a coronal stellar wind and hot material ejected CHAPTER 1. INTRODUCTION

Goals and structure of the thesis

The purpose of the current thesis is to show that we can improve our knowledge on Classical T Tauri stars by joining both observational and numerical perspectives. Since a few decades ago, the physical mechanisms involved in the formation and evolution of YSOs can be more easily explored through models and numerical simulations constrained by observational data. In view of this, the aim of this thesis is to explore not only observational data of CTTSs, but also numerical simulations aiming to reproduce what we see. By shaping numerical tests with observational constraints and playing with the main physical quantities, we intend to model accretion and outflow phenomena that could characterize the circumstellar environment of a well known CTTS, RY Tau. This could be fruitful to understand what low-mass YSOs are experiencing in the early stages of their evolution.

The thesis is divided in four parts, followed by the conclusions and three appendices including supplementary information and results through tables and/or plots.

Chapter 2 concerns a sample of CTTSs for which we have tested the determination of stellar parameters with available software. Since in a previous work the mass accretion rates and accretion velocities for these objects were explored, in this work we examine outflow activity parameters. Some of the computed values will be used in Chapter 5 to re-scale numerical simulations aiming to portrait the circumstellar environment of a YSO.

Chapter 3 deals with a sample of five low and very-low mass YSOs belonging to the Orion Nebula Cluster. The observations were taken by the X-shooter instrument installed at the VLT. Throughout the chapter is explained how the data reduction was performed and how did we determine their corresponding stellar parameters. We also searched for evidence of accretion activity in the spectra and looked for the presence of circumstellar disks through available on-line photometry.

Chapter 4 is the product of a project developed with P. P. Petrov concerning the analysis of the variability of two CTTSs, RY Tau and SU Aur. Spectroscopic variability is studied through spectral measurements, which are compared with photometric data. Chapter 5, gathers numerical simulations of the circumstellar environment of CTTSs, based on observational constraints of RY Tau. We give an overview of the outflow model and the analytical solution that rule the simulations, as well as the initial and boundary conditions. Several tests were performed and the most interesting cases are discussed. The numerical results will be compared with the ones we derived for RY Tau in Chapter 4. In addition, we try to extend these results to other objects than RY Tau, but we will see that there are some limitations in doing so.

Finally, Chapter 6 summarizes all the main conclusions from the previous chapters, but also pinpoints which are the limitations found, as well as future perspectives based on the work developed in this thesis.

2

Deriving stellar parameters for CTTSs

Emission and absorption lines of a spectrum contain information that can be decoded into stellar parameters, which are fundamental to characterize stars. In particular, optical emission profiles can be analysed in order to detect signatures of outflow processes. These are some of the steps taken towards the understanding of the circumstellar dynamics of each YSO.

In this chapter, a sample of 35 CTTSs spectra is analysed. The data were taken by A. Pedrosa in November 1998 and collected with the Utrecht Echelle Spectrograph (UES), installed at the 4.2m William Herschel Telescope, La Palma, before being de-commissioned in 2002. The used slit was 6" long and 1.20" wide, corresponding to a resolution of 51 000.

The average signal-to-noise ratio was estimated to be above 40.

Although the spectra were taken more than 20 years ago, the data were never published before. Table 2.1 lists all the targets and corresponding stellar parameters available in the literature and relevant for this work, while Fig. 2.1 shows the distribution of the spectral types in the sample. Around 83% of the CTTSs composing the sample are K-type stars, 11% correspond to G-type stars, while only 6% are M-type stars.

From this sample, we determined some typical stellar parameters as effective temperature, projected rotational velocity and veiling. Some outflow parameters were also derived, namely the projected terminal velocity of the jet and mass loss rate, whenever we had in emission a well known outflow tracer, the forbidden line of [OI] at 6300 Å. This emission was corrected with Molecfit (Kausch et al. 2015;Smette et al. 2015) by S. Ulmer-Moll, who removed the telluric absorptions that were contaminating this particular wavelength region (Ulmer-Moll et al. 2019).

Table 2.1: Stellar parameters available in the literature. All the targets are listed in the first column followed by the corresponding spectral type (SpT), stellar luminosity (log L * ), stellar mass (M * ), stellar radius (R * ), inclination (i), projected rotation velocity (v sin i), veiling measured at 5700 Å (r 5700 ) and 6300 Å (r 6300 ). The last column lists all the references from which the parameters were taken. The main challenge concerning the measurement of equivalent widths is that it is a very time consuming task. Each spectrum has a multiple number of lines that can be measured manually. This number increases if we deal with a wide wavelength coverage, plus the fact that the sample may include tens, hundreds or even thousands of stars. One way to automatize this tedious measuring process is through ARES (Sousa et al. 2007(Sousa et al. , 2015)). This is a code able to measure automatically the equivalent widths of absorption lines. According to Sousa et al. (2010), the measurements of the equivalent widths can be affected from errors coming from the continuum determination. That is why the line-ratio calibrations consider lines that are separated by less than 70 Å. This is also an important detail if we take into account that the spectrum may have veiling. This ultraviolet and optical excess continuum emission should not affect the estimation of the effective temperature. Veiling should be approximately constant when considering line ratios with lines relatively close to each other. Let us consider that the veiling for a certain line (r λ ) is expressed by

Object SpT log L * M * R * i v sin i r 5700 r 6300 References (L ⊙ ) (M ⊙ ) (R ⊙ ) (
r λ = F λ veil F λ phot = F λ * -F λ phot F λ phot = F λ * F λ phot -1 , (2.2)
where F veil is the veiled flux, F λ phot corresponds to the flux of the undisturbed photosphere and F λ * is the measured flux of the star. We can re-write the previous equation as

r λ + 1 = F λ * F λ phot , (2.3)
which is equivalent to

r λ + 1 = F 0 + F E F 0 , (2.4)
where F 0 is the flux at the continuum level and F E corresponds to the flux of the line with 2.1. DETERMINING STELLAR PARAMETERS WITH ARES AND TMCALC the continuum excess. We assume that F E is the same for the entire line. From Eq.2.1, the equivalent width of a line with veiling is given by

W E λ = line = F 0 + F E -F λ -F E F 0 + F E dλ = 1 F 0 + F E line (F 0 -F λ ) dλ = F 0 F 0 + F E W λ . (2.5)
This last equation can be re-written as

W λ = (1 + r λ )W E λ . (2.6)
If we consider the ratio of the equivalent widths of two veiled lines separated by less than 70Å, W E λ1 and W E λ2 , veiling should be approximately the same (r λ1 ∼ r λ2 = r). Thus, the ratios of the equivalent width of veiled or non-veiled absorption lines should be conserved if they are separated by less than 70 Å,

W E λ1 W E λ2 = W λ1 /(1 + r) W λ2 /(1 + r) = W λ1 W λ2 . (2.7)
Once the equivalent widths are measured with ARES from a given line list, this output will become the input of TMCalc (Sousa et al. 2012). The selected lines should depend mostly on effective temperature and metallicity. The line list used contains 388 lines and it was provided by S. G. Sousa. This list contains more chemical elements than the one provided with the software installation. In case the spectrum does not have a sufficient number of photospheric lines due to strong veiling, the software may not be able to compute the T eff and the metallicity will deviate more from its true value. In this case, the program automatically asks the user to give a temperature so it can choose the appropriate synthetic spectra and proceed after with the template fitting to derive veiling and v sin i. This situation happened only once for DR Tau, whose spectrum was very rich in emission lines and veiling was stronger.

In Table 2.2 we list the effective temperatures available in the literature and computed with TMCalc. To simplify the comparison between the values in this work and the literature ones, the top plot in Fig. 2.5 shows the comparison between these two sets. We computed the Pearson correlation coefficient as well, which quantifies the linear relation between two

given variables. In order to do it, we use the function pearsonr 3 . We can see that TMCalc is overestimating the T eff towards the coolest stars in the sample. This is confirmed in the bottom plot, where the differences between the computed T eff in this study for each star and the ones from the literature are shown. The cooler the star, the more overestimated will be the effective temperature computed by TMCalc. Nevertheless, if we go towards effective temperatures higher than 5000 K, we still see few stars whose T eff starts to deviate a few hundreds of K. Sousa et al. (2012) mention that TMCalc is optimized for stars with effective temperatures varying between 4500 and 6000 K. Indeed, the biggest differences start for T eff below 4500 K, which correspond to spectral types cooler than a K4. In our sample, 49% of the ). The number of line ratios used is also shown jointly with the surface gravity (log g) of the best fitted template, the rotation velocity (v sin i), the veiling computed at 6263 Å (r 6263 ) and the chi-square value (χ 2 ).

Target

T lit eff a metallicity for the star? Very briefly, TMCalc computes the metallicity for each line and makes a selection of the calibrated lines. The metallicity of the star is then given by the weighted average of all the individual iron abundances.

T temp eff T TMCalc eff Line ratios log g v sin i r 6263 χ 2 (K) (K) (K) (dex) (km
If the calibration for the [Fe/H] determination is based on individual lines from the entire wavelength range, how can we ensure that we are retrieving the correct metallicity for the star if its spectrum is veiled? One way to test this is by adding veiling to mainsequence spectra for which the metallicity is well known. In order to add veiling for a given spectrum, we assume that the veiled flux (F veil ) will have the shape of an exponential function given by

F λ veil = Ce kλ , (2.9)
where C and k are constants and λ is the wavelength. The veiling at a certain wavelength is expressed by Eq.2.2. We can re-write this last equation considering the expression in Eq.2.9 as

r λ = Ce kλ F λ phot .
(2.10)

The exponential function, which will simulate veiling in a given spectrum, will be shaped by two points where we assign a veiling value at a corresponding wavelength λ in the format P = (λ, r λ ). For each pair of points given as input, the constants k and C are determined from equation (2.10).

We considered HD4208, a main-sequence star classified with spectral type G7. We used the corresponding spectrum provided by S. G. Sousa from the HARPS GTO planet search program 4 (Sousa et al. 2008). The effective temperature and metallicity for this star are well known and we use the corresponding spectrum to apply a veiling contamination, to recreate a veiled CTTS spectrum, and compute the corresponding stellar parameters. In order to veil HD4208 spectrum with this continuum excess emission, we will assume two different ways of veiling the spectrum by adding a constant or an exponential veiling. In Table 2.3, all the tests for different veilings are listed. For comparison, we also include the no_veil test that corresponds to the original spectrum without veiling contamination.

The remaining tests identified with suffix letters A to F, concern spectra contaminated with different veilings fixed at 4000 and 6500 Å. The reference values from Sousa et al. (2008), hereafter quoted as "reference" and the computed effective temperatures (T eff )

and metallicities ([Fe/H]) by TMCalc are shown jointly with the corresponding errors and number of line ratios used by the software.

In order to add a constant veiling in test HD4208_A, for instance, we considered the following points, where we indicate in brackets a wavelength (in Å) and the veiling we want to impose there: P A1 = (4000, 1.5) and P A2 = (6500, 1.5). For the exponential case in test HD4208_B, we assumed the following points, P B1 = (4000, 1.5) and P B2 = (6500, 0.01). In Fig. 2.6, we show a spectrum with (a) constant and (b) exponential veiling. The original spectrum is represented in blue, the veiled flux in red, the veiled spectrum in cyan and the normalized one in green. The previous points given will add in the main-sequence star spectrum constant and exponential veilings between 4000 and 6500 Å. Nevertheless, we notice in the figure that, due to the strong veiling, the metallicity is always below the real one. In contrast, when adding an exponential veiling as shown in Fig. 2.7b, besides seeing a trend, we can also see that in the wavelength regions of the spectra with low veiling (near 6000 Å), the metallicities computed by TMCalc (blue dots)

tend to be closer to the reference value for the metallicity (red line), while the reverse happens when considering shorter wavelengths (close to 4500 Å). If the veiling is very small, the equivalent widths do not change much. Thus, the metallicity should be close to its real value. The reference value for the metallicity of -0.28 ± 0.01 for HD4208 was taken from Sousa et al. (2008). This metallicity was determined using the B -V colour index implemented in a calibration that is different from the one presented in Eq.2.8. As expected, for both constant and exponential veiling tests, the dispersion in metallicity is higher for wavelength regions where the veiling is stronger. In Table 2.3, the metallicities computed from tests B to F differ quite a lot compared with the reference value.

When comparing the effective temperatures obtained with TMCalc, the values seem to be reasonable taking in account the error bars of each measurement. Contrary to the metallicity, the computed effective temperature does not vary as much according to stronger or weaker veiling values. The constant veiling imposed in test HD4208_A has the least amount of line ratios to compute T eff returning a higher value than the reference one. The reason for this is that, when we increase the veiling, the photospheric lines depth decreases and makes it difficult to measure their equivalent widths. In general, photospheric lines in the red are weaker than photospheric lines in the blue. So this effect is stronger for the red part of the spectrum. In addition, test HD4208_A has such a strong veiling that TMCalc cannot compute a value for the metallicity. With exception of test HD4208_no_veil, all the remaining ones return metallicities that can differ almost 0.5 dex from the reference one. The worst values correspond to the cases where there are CHAPTER 2. DERIVING STELLAR PARAMETERS FOR CTTSS Allard et al. (2012) with solar metallicity (commonly used for YSOs), log g varying between 3.0 and 5.0 (in steps of 0.5), and temperature ranging from 3000 to 6000 K (in steps of 100 K).

Each template is degraded in resolution and rebinned according to the corresponding target. In order to decrease the template resolution, we used a function from PyAstronomy that makes the convolution with the instrumental profile named instrBroadGaussFast.

This profile is a gaussian produced from the resolution of the target.

Later, the script varies simultaneously the values of v sin i and veiling in the template spectra and compares them with the target through a non-linear least squares minimization routine 5 , in a specific wavelength range. We found that the region between 6220 to 6270 Å is quite reasonable to test the code in HD4208, while 6253 and 6273 Å is the best suited one for CTTSs spectra. Although veiling is wavelength dependent, we assume these small wavebands and consider that the veiling is constant in these regions. At the same time that v sin i is adjusted to the template, veiling is added and fitted as a constant value in one of those wavebands. In those wavelength regions we found a minimum amount of emission features and more photospheric absorptions. The spectral region between 6000 and 6500 Å is one of the best suited ones to perform this kind of fitting in cool stars since there is not too much line blending as in other regions of the spectrum [START_REF] Gray | The Observation and Analysis of Stellar Photospheres Gray[END_REF].

In order to adjust a rotational velocity, rotational broadening is applied with rotBroad function from PyAstronomy. This function was written according to the formulae given in [START_REF] Gray | The Observation and Analysis of Stellar Photospheres Gray[END_REF], where the rotation profile G(∆λ) is given by the following expression 2.11) where c 1 and c 2 constants expressed by

G(∆λ) = c 1 [1 -(∆λ/∆λ L ) 2 ] 1/2 + c 2 [1 -(∆λ/∆λ L ) 2 ] , (
c 1 = 2(1 -ǫ) π∆λ L (1 -ǫ/3) , c 2 = ǫ 2∆λ L (1 -ǫ/3) , (2.12)
where ∆λ is the shift from the line centre, ∆λ L is the maximum shift, corresponding to the disk points on the limb at the equator and ǫ is the limb-darkening coefficient. In this study we assumed ǫ = 0.6 used for the Sun. The maximum shift relates to the projected rotational velocity through the expression,

∆λ L λ c = v sin i c , (2.13)
where λ c is the central wavelength of the line, v is the equatorial velocity, i is the inclination of the stellar rotation relatively to the observer, and c the speed of light.

The output given by the script is a text file that contains all the fits made sorted by crescent value of the χ 2 value given by χ 2 = λband (F λ target -F λ template ) 2 , determined between 6253 and 6273 Å for the CTTSs spectra, and between 6220 to 6270 Å for HD4208.

Additionally, the output lists also the name of the fitted template, the effective temperature 2.1. DETERMINING STELLAR PARAMETERS WITH ARES AND TMCALC and corresponding error, the number of line ratios considered by TMCalc, the surface gravity of the fitted template, the projected rotational velocity and associated error, the veiling computed for the selected band and corresponding error.

We have tested the routine first for HD4208 and after for the entire sample of CTTSs.

In Table 2.4 we show the computed values for veiling and projected rotational velocity for HD4208, with and without veiling contamination. We also list the theoretical veiling values at 6245 Å (r t 6245 ). The remaining columns show the following variables: fitted veiling at 6245 Å (r 6245 ) and corresponding error, projected rotational velocity and associated error, χ 2 value provided by the fit, a reference value for the surface gravity (log g) taken from Sousa et al. (2008) and the corresponding value of the best fitted template.

For HD4208 we could confirm that if no veiling is incremented, no veiling is detected.

Nevertheless, it appears that veiling is underestimated, as well as the corresponding error, comparatively to the theoretical value we should expect at 6245 Å. Concerning v sin i, the stellar sample analysed by Sousa et al. (2008) are slow rotating stars (v sin i < 10 km s -1 ) and in the specific case of HD4208, the v sin i is between 1.8 and 3.0 km s -1 (Soto & Jenkins 2018). In view of this, tests B and F are the ones that fit within that range of velocities, besides the control test without veiling. Nevertheless, the remaining velocities are not so different from the correct one, but the errors seem to be underestimated, similarly to the veiling. Concerning the log g of the best fitted templates, the values are close to the one in Sousa et al. (2008).

Table 2.4: Veiling and projected rotational velocity computed for HD4208. The first column lists all the tests performed followed by the veiling values imposed at 4000 Å and 6500 Å, the expected veiling at 6245 Å (r t 6245 ) and the best fitted values for veiling measured at 6245 Å (r 6245 ), rotation velocity (v sin i) and chi-square value (χ 2 ). The reference value (Ref.) for the surface gravity taken from Sousa et al. (2008) is also listed as well as the log g value of the best fitted template for each test. After testing the script on a main-sequence star, we used the code to determine stellar parameters in spectra of CTTSs. In Table 2.2 the effective temperatures computed for each CTTS with the software TMCalc (T TMCalc eff ), as well as the number of lines used by the software to compute this parameter (line ratios) are listed. Additionally, the effective temperatures available in the literature (T lit eff ) are shown. We converted these values from the spectral type listed in Table 2.1 with the temperature scale from Kenyon & Hartmann (1995)

Outflow activity parameters

The interest of outflows in accreting stars has been increasing in the past few decades.

One way to analyse these outflowing structures is through forbidden emission lines. These low-excitation and optically thin lines are a useful tool not only to dissect the outflow components of a star-disk system and their kinematics, but also to explore their morphology.

OUTFLOW ACTIVITY PARAMETERS

Some of the useful parameters that can be derived from these lines include mass loss rates, outflow velocities, as well as densities and temperatures (Hartigan et al. 1995). Pioneer works involving the study of forbidden lines showed to the scientific community that it was possible to derive mass flux rates and infer about the outflow geometries based on the emission of forbidden emission lines (Edwards et al. 1987;[START_REF] Cabrit | [END_REF]).

Projected terminal velocities

One way to characterize the outflow dynamics of CTTSs is through the emission line of

[OI] at 6300 Å. This emission tends to be blueshifted in these young objects [START_REF] Cabrit | [END_REF]Hartigan et al. 2004;Rigliaco et al. 2013) and has its origin in a low-ionization flow (Edwards et al. 1987). It has been suggested that this forbidden line can be decomposed in two components associated with different densities and temperatures, the low-velocity component (LVC) and the high-velocity component (HVC). These two components have been confirmed and characterized in several studies (Hamann 1994;Hartigan et al. 1995;Hirth et al. 1997;Simon et al. 2016;Fang et al. 2018). Furthermore, it has been suggested that the LVC and the HVC trace different physical environments with different extensions from few AU to few hundreds of AU.

Although the origin of the LVC is still not clear, it has been discussed that it may come from slow and dense disk winds, within a few tens of AU of the star (Hartigan et al. 1995(Hartigan et al. , 2004;;Natta et al. 2014;Bai et al. 2016;Ercolano & Owen 2016;Simon et al. 2016).

According to Hartigan et al. (1995), this component is blueshifted to 5 km s -1 and is present whenever the star shows a near-infrared excess. The authors do not discard also the possibility that this component is created in the accretion columns. [START_REF] Acke | [END_REF] proposed that the origin of the LVC emission of [OI] at 6300 Å comes from photodissociation of OH and H 2 O molecules. More recently, Simon et al. (2016) suggested that the broad component of the LVC traces a magnetohydrodynamic (MHD) driven wind, while the narrow component could be tracing a thermal photoevaporative wind.

Concerning the HVC, it has been proposed that is originated in an extended collimated jet characterized by low densities and high temperatures (Lavalley-Fouquet et al. 2000;Bacciotti et al. 2000). Typically, this emission is blueshifted by 30 to 200 km s -1 .

Although the mechanism responsible for this outflow is not completely understood, it is probably connected with angular momentum extraction processes in the star-disk system and magnetized MHD winds (Ferreira et al. 2006).

Whenever observations are made from Earth-based telescopes, the spectra is contaminated with atmospheric absorptions due to the presence of molecules that compose our atmosphere. These features are the so called telluric lines. The [OI] emission is affected by these absorptions from the Earth's atmosphere. Therefore, the spectra needed to be corrected from telluric absorptions before being analysed. Since we did not have the telluric standards (hot stars) observed at the time of the observations, the alternative was to use the software package Molecfit (Smette et al. 2015;Kausch et al. 2015). The correction was based in the method of Ulmer-Moll et al. (2019), where the authors compare Molecfit with other telluric correction methods in the near-infrared. In this work, they found 2.2. OUTFLOW ACTIVITY PARAMETERS difficult to distinguish both components, since they appear to be blended due to a low SNR and weaker emissions. We did not correct these profiles with photospheric templates, for that reason the equivalent widths measured for [OI] are underestimated. The reason why the photospheric correction was not performed is due to two main issues. First, and since we cannot ensure that we determined the correct effective temperature with TMCalc, we could not select the best suited photospheric templates to perform the correction. Second, there are some issues concerning the continuum normalization of the spectra. We tried to perform the correction on RY Tau spectrum with a photospheric template matching the effective temperature available in the literature. It turns out that, since the continuum normalization is not the best one, there are regions that, instead of being at the continuum level, they show an excess emission that is not real after the correction is performed.

We have also detected a different kind of issue in one of the CTTSs spectra. If we look to DG Tau plot in Fig. 2.10, we can see a sharp emission very close to 0 km s -1 . We suspect that this is a strong terrestrial emission line at 6300 Å that passed through the sky subtraction, but does not affect our measurements in this study. This emission is produced at altitudes higher than 200 km in the Earth's atmosphere and is designated as an airglow line emission (Noll et al. 2012). This feature has been previously detected in other CTTSs in the work of Hartigan et al. (1995) and Simon et al. (2016).

Among the [OI] line profiles for the different targets, we found some interesting emis- In Fig. 2.11n, a redshifted absorption in RY Tau spectrum is shown. This strong feature is present for the same star in Hartigan et al. (1995), even after performing a correction with a photospheric template. More recently, Chou et al. (2013) show in their work the same profile with a similar redshifted absorption.

Mass loss rates

Once we have the projected terminal velocity of the jet, it is possible to determine the corresponding mass loss rate following Comerón et al. (2003) procedure, based on the original method of Hartigan et al. (1995). Very briefly, the method relies on measuring the equivalent width of [OI] (EW [OI] ), convert it to line luminosity (L 6300 ) and then to mass loss rate ( Ṁloss ).

In order to properly account for the continuum excess emission, we added the term in blue in Eq.2.15 to include a veiling correction, similarly to what has been done in Simon et al. (2016). The line luminosity can be derived from the equivalent width of the emission line with the following expression,

L 6300 (L ⊙ ) = 6.71 × 10 -5 D 2 EW [OI] (1 + r 6200 )10 -0.4R 0 , (2.15)
where D is the distance star-observer of 140 pc for the Taurus-Auriga molecular cloud (Elias ) and logarithmic mass loss rates ( Ṁ lit loss ) were taken from the literature. The measured parameters are the terminal velocity of the jet (V term ), the equivalent width of the forbidden line of [OI] (EW [OI] ) and the logarithmic mass loss rate ( Ṁloss ). We included also the veiling values (r 6200 ) derived by J. F. Gameiro and the accretion rates derived in de Albuquerque (2015) ( Ṁacc ) for the same spectra. 1978; Kenyon et al. 1994), EW [OI] is the equivalent width of [OI] measured with the splot task from Image Reduction and Analysis Facility (IRAF)7 , R 0 is the derredened magnitude of the object and r 6200 is the veiling estimated near 6200 Å by J. F. Gameiro. We decided to use these values because the ones determined in this chapter are underestimated. The veiling values determined by J. F. Gameiro were computed by comparing interactively the target spectra with templates of the same spectral type from the high-resolution ELODIE stellar library (Prugniel & Soubiran 2001). After re-sampling to the appropriate spectral resolution and spectral bins, the best fit of the rotationally broadened veiled spectrum of the template to the target spectrum in the spectral region centred at 6200 Å and 50 Å wide was determined, as in Gameiro et al. (2006). The derredened magnitudes were taken from Hartigan et al. (1995) for the common stars in the sample. These are approximate values, since the magnitude variability of CTTSs is one of the largest sources of uncertainty. All of these parameters are listed in Table 2.6. Once the luminosity is determined, we derived the mass loss rates ( Ṁloss ) following the equation in Comerón et al. (2003): .16) where N c is the critical density of 2 × 10 6 cm -3 for [OI], as assumed by the authors, and N e is the electronic density in the emitting volume of 7 × 10 4 cm -3 , as Hartigan et al.

Star R 0 r 6200 V term EW [OI] log Ṁloss log Ṁ lit loss Ref. log Ṁacc (km s -1 ) (Å) (M ⊙ yr -1 ) (M ⊙ yr -1 ) (M ⊙ yr -
Ṁloss (M ⊙ /yr) = 3.03 × 10 7 1 + N c N e × L 6300 (L ⊙ )V (km/s) l(cm) , ( 2

CONCLUSIONS

constant and high veiling, although not realistic, was to push the tests to an extreme case and see how the software would handle it. From these tests, we concluded that metallicity cannot be estimated from high veiled spectra. Unless the spectra is previously corrected from this excess, the user cannot trust the calibration for the metallicity performed by TMCalc, which is performed for each individual line. Concerning the effective temperatures, higher veilings will imply a smaller number of photospheric lines detected by ARES, which leads to a deviating value of the T eff determined by TMCalc. For both metallicity and effective temperature determination, stronger veiling will make the photospheric lines weaker and difficult to disentangle from the noise. When computing the veiling added to the spectra, it seems that this can be slightly underestimated. Concerning the v sin i , it was in agreement with the literature.

Regarding the stellar parameters derived for the sample of CTTSs, the effective temperatures are overestimated towards cooler (late-type) stars. Although the software was conceived for FGK stars, TMCalc is optimized for stars with T eff between 4500 and 6000 K.

For that reason, we cannot fully trust the temperatures derived for the stars in the sample that have a spectral type of K5 and later. The computed rotational velocities appear to correlate reasonably with the literature. The problematic cases are DR Tau and DG Tau due to the template selected by the code and some issues fitting broad photospheric lines, correspondingly. Concerning the veiling determination, if the effective temperature of the target is not well determined, then the veiling cannot be correct.

In Section 2.2, the forbidden line of [OI] at 6300 Å was analysed. From this well known outflow tracer, we measured the terminal velocities of the jet associated to the high-velocity component of this emission in 16 out of 35 CTTSs. Consequently, we could derive the corresponding mass loss rate for each CTTSs. According to our results, we concluded that DG Tau and RW Aur are the YSOs with the strongest mass loss rates, with values of 10 -6.5±0.3 and 10 -6.6±0.3 M ⊙ yr -1 , respectively. The differences between these values and the corresponding ones in Hartigan et al. (1995) could be due to the absence of a photospheric correction, but also the variability of the forbidden emission line. RW Aur showed already evidence of daily variability in the [OI] emission line at 6300 Å (Alencar et al. 2005). Concerning DG Tau, previous studies have detected strong variability in the emission of [OI] (Mundt et al. 1987;Hartigan et al. 1995;Solf & Boehm 1993). Dougados et al. (2002) studied this CTTS and observed a perturbed jet, suggesting a strong interaction with the circumstellar environment or even a variation of the jet axis.

When Dougados et al. (2002) compare spectro-imaging data with the work of Lavalley et al. (1997), the morphology and kinematics of the outer not, with a proper motion of 200 km s -1 , are indicative of variable ejection. Most likely, the variability observed in these two YSOs has an impact on the geometry of the forbidden line emission, which will affect both terminal velocities and mass loss rates estimated. Additionally, the observational epochs of our data are different from the cited works, which makes the comparison task even more difficult.

3

Accretion activity among low-mass YSOs in the Orion Nebula Cluster

Low-mass YSOs have been widely studied in these last decades. They are relevant objects, helping us to understand some mechanisms associated with the formation and early evolution of stars and how they can potentially lead to planets.

The Orion Nebula Cluster (ONC), also known as M42 or NGC 1976, has been extensively studied due to its young stellar population (Kounkel et al. 2017), which makes it a promising place to characterize low-mass YSOs. Such young stellar members represent a big opportunity to study accretion processes. If a YSO is accreting, it is very likely that it is surrounded by an accretion disk, where the circumstellar material is expected to move towards the inner edge of the truncated disk. Here, the gas will be transported from the disk to the stellar surface through accretion columns shaped by the presence of strong magnetic fields (Koenigl 1991;Shu et al. 1994).

In the previous work of [START_REF] Biazzo | [END_REF], they studied around 90 very low-mass members belonging to the ONC, with the multi-fibre spectrograph FLAMES. One of the conclusions was that none of those 90 objects were accreting according to White & Basri (2003) accretion criterion. According to this work, a YSO is an accretor if the Hα width at 10% of peak intensity is greater than 270 km s -1 . Nevertheless, this criterion did not fully convinced [START_REF] Biazzo | [END_REF] since some of the stars show the Hα 10%-width larger than the median of the sample, slow rotation rates, Li I (670.8 Å) in absorption proving their youth and evidence of infrared excess in some objects indicating the presence of circumstellar disks.

In the following sections we will infer from a sample of five very-low mass YSOs, if the objects are accreting or not. Besides searching for and quantifying accretion activity through emission line profiles for each object, we also searched for the presence of accretion disks through available photometry. The work described in this chapter was carried out in 3.2. OBSERVATIONS AND DATA REDUCTION

JW 2MASS d

(1) * (pc) SpT (2) RV (3) (km s -1 ) v sin i (4) (km s The X-shooter instrument offers a wide wavelength coverage, ranging between 300 and 2500 nm, approximately. Thus, this instrument covers three arms in different wavebands, Ultraviolet (UVB), Visible (VIS) and Near-Infrared (NIR). The UVB arm extends from 300 to 550 nm, while the VIS arm ranges between 550 to 1050 nm and the NIR arm goes from 1050 to 2500 nm (Vernet et al. 2011).

Although the nodding 1 mode was requested in the observational proposal, the targets were observed in stare2 mode with slit widths of 1.3"/1.2"/1.2", corresponding to a resolution of 4000/6700/3900 for the UVB/VIS/NIR arms, respectively. The stare mode made it difficult to perform the sky subtraction, in particular in the NIR arm.

The spectra of all arms were reduced with version 2.7.1 of X-shooter pipeline [START_REF] Modigliani | Observatory Operations: Strategies, Processes, and Systems III[END_REF]. The 2D outputs were later extracted with the IRAF task apall. The resulting 1D spectra needed two additional corrections. First, we needed to correct the NIR spectra from telluric lines. One way to correct the spectra from these unwanted features is to use telluric standards, which correspond to spectra of hot stars that present few photospheric lines in the location of the telluric lines [START_REF] Modigliani | X-Shooter Pipeline User Manual[END_REF]. In order to correct the 1D spectra from telluric absorptions in the NIR arm, we used IRAF task telluric and gave as inputs the target spectra and the corresponding standard tellurics, observed before or after each ONC member, as listed in Table 3.3.

The final correction involved the flux of the NIR arm. If we had not applied a flux shift, the ending of the spectrum in the VIS arm would not overlap with the beginning of the NIR arm. A similar issue was verified in the spectra of Alcalá et al. (2014). According to the authors, this shift in flux could be due to a small misalignment of the NIR slit relatively to the VIS and UVB arms.

Results

Extinction and spectral type

The correction of the visual extinction (A V ) for each star should be taken into account, specially when dealing with objects that are embedded in nebular structures such as the ONC. Nebulae are rich in gas and dust. This means that the light emitted by the star can be absorbed and scattered, leading to the reddening of the spectra. In order to correct this effect, we measured the extinction for each target.

In order to perform the correction, we used the spectra of the VIS arm and compared the targets with templates selected from the library of non-accreting class III YSOs from Manara et al. (2013) and Manara et al. (2017). We selected the templates according to the original classification of the targets listed in Table 3.1 and we used the nearby spectral types as our first guess. The spectral types were rectified more ahead in this subsection, and when we checked major differences with the original classification, the extinctions were corrected according to the spectral type derived in this work. We had to perform an additional veiling correction before computing A V only for JW647, as we explain more ahead in this chapter.

Although the interstellar medium is not uniform, we assume the same extinction law for all the targets and consider two reddening parameters. Amongst the literature, some authors have been deriving different values for the reddening parameter R V , which models the extinction law. For the ONC, we can find values starting at 3.0 and going beyond 5.5 (Lee 1968;Walker 1969;Cardelli et al. 1989;Da Rio et al. 2010[START_REF] Rio | [END_REF]. As mentioned in Hasenberger et al. (2016), it has been accepted that higher R V values are related with bigger sizes of dust grains. Furthermore, this range of values should be a result of a nonuniform grain size distribution in the molecular cloud, as previously suggested by Baade & Minkowski (1937). Most authors have been using the 3.1 value when working with ONC members (e.g. Da Rio et al. 2012;Manara et al. 2012;Hillenbrand et al. 2013). This value corresponds to the one used for the diffuse interstellar medium in the Milky Way. Da (2007), which are independent of reddening and nebular emission. While for K and early M-type stars, we used spectral indices from Herczeg & Hillenbrand (2014). Additionally, we computed the TiO (7140 Å) spectral index by Jeffries et al. (2007) that is valid for stars with spectral types K5 and later. The selected indices and spectral validity range are displayed in Table 3.4. After computing the spectral indices, we took the average spectral type for each target. The results obtained are listed in Table 3.5 (2nd to 4th columns).

In order to confirm the estimated SpT from the spectral indices, we compared each target with a template of similar spectral type taken from the library of non-accreting class III YSOs (Manara et al. 2013(Manara et al. , 2017)). To ease the comparison process, we normalized VIS spectra at 750 nm and applied a gaussian instrumental broadening with the function broadGaussFast3 to the templates. This way, we ensure that the template resolution matches the one of the target. In Table 3.6 we list the best suited templates used in this study.

Table 3.4: Spectral indices used to determine the spectral type of the targets. All spectral indices are calculated from the ratio between the average flux of the numerator (N) and denominator (D), except the following cases: (a) F (N ) The targets JW180, JW293 and JW908 were fitted reasonably well with the corresponding templates, conversely to JW647 and JW847. Although we computed an average

F (D) F line (4650) F line (5100) ; (b)log( F (N ) F (D) -1).

RESULTS

Table 3.6: List of templates selected for this work taken from the library of non-accreting class III YSOs (Manara et al. 2013(Manara et al. , 2017)). The 2MASS name was included, as well as the distance estimated from Gaia DR2 parallaxes (d * ) and the spectral type (SpT) for each template.

Template 2MASS d

(1) * (pc) SpT (2) Par-Lup3-2 J16083578-3903479 166 ± 3 M5 SO797 J05385492-0228583 354 ± 16 M4.5 TWA13B J11211745-3446497 60 ± 0.1 M1 RX J1543.1-3920 J15430624-3920194 166 ± 7 K6 (3) References: spectral type of approximately M2.0 for JW647, an M1 template fits better the target spectrum. As mentioned previously, JW647 was the only star in the sample showing a reasonable veiling value. This was taken into account and the spectrum was corrected from this excess before computing the extinction and the spectral type. In the case of JW847, the R5150 index suggests a spectral type of K1.2, but the TiO index indicates that this star should be a K6.6. According to Tripicchio et al. (1997) empirical relation for the Na I doublet, the spectral type of JW847 should be a K0 or a K1. However, when we compare the target spectra with other templates from the template library, the best match corresponds to a K6. We had to discard the possibility of a K0 and K1 templates because they are too hot to fit the target and a K7 template has stronger molecular features. In view of this, we adopt for both stars the spectral classes obtained from template comparison.

In Table 3. Hillenbrand (2014) (HH14) and the adopted spectral type which corresponds to the best matched template. To convert from spectral type to temperature, we used the temperature scale obtained by Kenyon & Hartmann (1995) and Luhman et al. (2003) for earlierand M-type stars, respectively. The corresponding effective temperatures for each star are shown as well.

Stellar luminosity, radius, mass and age

In order to measure the stellar luminosity, we started by determining the stellar flux following the procedure of Manara et al. (2013). First, we integrate the flux of the entire X-shooter spectrum from 350 to 2450 nm, excluding the first and last 50 nm of noisy data and substituting the two strongest H 2 O telluric regions in the NIR (at 1330-1550 nm and 1780-2080 nm) by straight lines linearly interpolated. Second, BT-Settl synthetic spectra from Allard et al. (2012) are used to extend the target spectrum, shortward of 350 nm and longward of 2450 nm. The synthetic patches are scaled to the flux values at these two last wavelengths. Then, the "synthetic flux" is integrated and added to the observed one.

The synthetic spectra chosen have a compatible effective temperature and solar metallicity with the targets (D'Orazi et al. 2009), and we assume a log g = 4, a common value adopted for low-mass YSOs. We performed a flux correction whenever the excess continuum is not negligible. The determination of the veiling is explained more ahead in this chapter.

CHAPTER 3. ACCRETION AMONG YSOS IN THE ONC

The stellar flux (F * ) is then converted into luminosity (L * ) through L * = 4πd 2 * F * , where d * is the distance to the star. In this work, we derived the distances from the Gaia DR2 parallaxes (Gaia Collaboration et al. 2016[START_REF] Rei | [END_REF]Luri et al. 2018), which are listed in Table 3.1, and we estimated the stellar radius (R * ) through the equation

R * = F * d 2 * σT eff 4 1/2 , (3.1)
where σ is the Stephan-Boltzmann constant. The luminosities and stellar radii derived are shown in Table 3.5.

In Fig. 3.4a we plot the position of our targets in the HR diagram and include the Siess et al. (2000) pre-main sequence evolutionary tracks for several masses and isochrones, from 1 to 10 Myrs, considering a solar metallicity (Z = 0.020, X = 0.703 and Y = 0.277). In Fig. 3.4b we replot the same results, but this time we use the evolutionary tracks and isochrones for pre-main sequence stars from Baraffe et al. (2015). The circles correspond to the effective temperatures and stellar luminosities determined in this work and listed in Table 3.5. The squares correspond to the values of Hillenbrand (1997), whose fluxes were rescaled to distances derived from the Gaia DR2 parallaxes. Although the stellar masses between both HR diagrams do not differ that much, Baraffe et al. (2015) evolutionary model reveals younger ages. In particular, JW847 is younger than 1 Myr according to Baraffe et al. (2015) isochrones.

Conversely to this later model, Siess et al. (2000) has an on-line tool to estimate the stellar mass and age, and respective errors, by giving as inputs the effective temperature and stellar luminosity. We assume for the effective temperature an error of one subclass, which corresponds to approximately 100 K. For the stellar luminosity and radius, we estimated the uncertainties through error propagation considering the uncertainties associated with the distances, stellar flux and effective temperature. In Table 3.5 we list the stellar masses and ages derived with this tool for each target with the corresponding errors. The stellar mass of the targets varies between 0.17 and 0.90 M ⊙ and we conclude that only JW180, JW293 and JW908 are very low-mass stars. Most of the targets have ages around 3 Myr, with the exception of JW847 with 1 Myr.

According to both HR diagrams, JW647 and JW847 are the stars that deviate the most from the original classification of Hillenbrand (1997). For the case of JW647, this star seems to be hotter and older. Conversely, JW847 appears to be colder and younger.

The remaining stars do not diverge too much on stellar mass, but there are some differences concerning their ages. We will discuss these discrepancies more ahead in Sect.3.4.

Accretion analysis

In our sample, we have detected veiling only for JW647 (see Table 3.5). J. F. Gameiro measured this excess at 610 nm (r 610nm ) through the same method explained in Chapter 2, as in Gameiro et al. (2006), and got a veiling of 0.5. The only differences between this determination and the one in Chapter 2 concern the wavelength at which the veiling was measured and the templates used, which correspond to the ones from the library of Manara 2015) evolutionary tracks and isochrones. In plot (a), we show the evolutionary tracks from 0.2 to 1.8 M ⊙ (dashed lines) and the isochrones corresponding to 1, 2, 3, 4, 5 and 10 Myrs (solid lines). In plot (b), we show the evolutionary tracks from 0.15 to 1.4 M ⊙ (dashed lines) and the isochrones corresponding to 1, 2, 3, 5 and 10 Myrs (solid lines). The circles correspond to the values determined in this work and the squares to the values of Hillenbrand (1997), rescaled to the distances derived from the Gaia DR2 parallaxes.

et al. ( 2013) and Manara et al. (2017).

Besides the detection of this continuum excess emission, JW647 is the target showing the strongest Balmer jump in the sample, near 364.6 nm (see Fig.3.5). This is another evidence that this YSO has on-going accretion activity. One way to quantify the strength of the Balmer jump in the current sample is through the determination of the ratio between the flux at 360 nm and 400 nm (Calvet & Gullbring 1998), known as the observed Balmer jump (BJ obs ). According to the accretion criterion suggested in Herczeg & Hillenbrand (2008), a mid-M dwarf should be considered as an accretor if it has a Balmer jump higher than 0.5. The values measured for the BJ obs can be found in Table 3.5 for all the targets.

According to this criterion, the only star that is clearly accreting is JW647, with a BJ obs of 1.1.

JW847 was classified as a K6, and for that reason we should be cautious when using this criterion since this is not an M-type star. Nevertheless, we can find in the literature recent studies as the one from Rugel et al. (2018), who used this criterion from K6 to M6 type stars in the η Chamaeleontis association. Comparatively to the remaining spectra, Fig. 3.5d for JW847 does not show significant Balmer emission lines characteristic in accreting YSOs in the UVB arm. This lack of accretion tracers in emission also applies for the VIS and NIR arms. According to the accretion criterion from Herczeg & Hillenbrand (2008), JW180, JW293 and JW908 could be accreting or not, since the observed Balmer jump matches the threshold value of 0.5. Maybe this could mean that the targets are ceasing accretion activity and transiting from CTTS to WTTS evolutionary stage.

Besides the presence of the Balmer jump, we have found several accretion tracers in emission among the target's spectra, except for JW847. The remaining YSOs show several Balmer lines in emission, as well as He I lines. JW647 has additional emissions in the NIR arm for the Paschen and Brackett lines. The existence of these emissions is already indicative of on-going accretion in these YSOs. In the particular case of JW647 spectrum, we found in the Balmer emission lines from H4 (486.1 nm) to H10 (379.8 nm) an IPC absorption present in all the profiles (see Fig.3.6). The red edge of this redshifted absorption falls around 300 km s -1 , which is the typical value found for infalling material that is accreting onto the star (e.g. Edwards et al. 1994). Such IPC profiles are also observed in the Na I D lines and He I at 667.8 nm and 1082.9 nm (see Fig. 3.7). In Fig. 3.7a, the IPC is not as strong as for the other lines and seems to coincide with a photospheric absorption when we compare with the corresponding template represented with the black solid line.

In Fig. 3.7b, the velocity of the IPC detected for He I at 1082.9 nm is around 300 km s -1 , as seen previously for the Balmer lines. These redshifted absorptions were first detected in active T Tauri stars by Walker (1972), and characterize the class of YY Orionis stars.

High velocity redshifted absorptions come from photons emitted near the shock region that are absorbed by the infalling gas in the accretion columns, with high velocity with respect to our line of sight (Edwards et al. 1994). Besides the detected veiling, this is another indication that JW647 is an accreting star.

Accretion can be detected through spectral features, but how can we quantify this inflow of material into the star? One solution is given by the measurement of line fluxes, f line ,

RESULTS

that can be converted to line luminosities, L line , and corresponding accretion luminosities, L acc (e.g. Alcalá et al. 2014). By knowing the later of these parameters, plus the stellar mass, M * , and radius, R * , we estimate the mass accretion rates, Ṁacc .

First, we start by checking the accretion tracers in emission from the UVB to the NIR arm, for each YSO. A list of the emission lines used to compute Ṁacc can be found in Table 3.7. Among the accretion tracers, we include Paβ and Brγ lines in the NIR that, according to Alcalá et al. (2014), are less contaminated by chromospheric activity when compared to other lines in the visible waveband. Although the emission line of Hα is a well known accretion tracer, we discard this line to measure the mass accretion rates because it is very likely contaminated with nebular emission [START_REF] Muench | Star Formation in the Orion Nebula I: Stellar Content[END_REF]. We also discarded the emission of He I at 1082.9 nm, since we were not sure that the sharp absorption in the IPC was real or a feature from the data reduction.

Second, we measure the line fluxes of all the previous lines and we convert them to line luminosities by assuming the stellar distances listed in Table 3.1. The accretion luminosity was estimated using the empirical relations obtained by Alcalá et al. ( 2014)

log(L acc /L ⊙ ) = a log(L line /L ⊙ ) + b , (3.2)
where the coefficients a and b are listed in Table 3.7. From the accretion luminosities we derive the mass accretion rates with the following equation

M acc = 1 - R * R in -1 L acc R * GM * ≈ 1.25 L acc R * GM * , (3.3)
where R in is the star inner-disk radius, which corresponds to the truncation radius of the disk. As in Gullbring et al. (1998) and Alcalá et al. (2014), we assume R in = 5R * . The measured Ṁacc for the different lines are listed in Table 3.8, where the last row gives the average mass accretion rate. According to the previous table, JW647 is the star with the highest average accretion rate, with a value of 10 -8.6 M ⊙ yr -1 . Since we had only three very weak accretion tracers in emission for JW847, we could not estimate the accretion rate for this star. Additionally, we suspect that the Ca II emission lines in the UVB arm have included some chromospheric emission that affect the Ṁacc determination. As shown in Fig. 3.8, the Ca II emission profiles are embedded in the absorption on the same lines.

For the remaining targets, ten accretion tracers in emission were available and returned an average Ṁacc around 10 -10.0 M ⊙ yr -1 , which are within the expected values for this range of stellar masses.

Circumstellar disks

The SED of a YSO is a useful tool to detect the presence (or absence) of circumstellar disks. If the SED has an infrared excess emission, it is very likely that the star still has a circumstellar disk. Usually, class II objects have infrared excess emission revealed through their SEDs when compared with the corresponding SED of a black body. After 2µm, the energy distribution can show flat or negative slopes [START_REF] Lada | IAU Symposium[END_REF]. For class III objects, 3.3. RESULTS these have SED features of a stellar photosphere (Whitney et al. 2003).

In Fig. 3.9, we compare the SED of each YSO with synthetic spectra and photometric data. The grey line corresponds to the synthetic BT-Settl spectra (Allard et al. 2012) with the closest temperature to the one we derived in this work for each target. The red dots correspond to photometric data available at Vizier (Ochsenbein et al. 2000), which gathers data from several surveys, namely, Gaia DR1 and DR2 (Gaia Collaboration et al. 2016[START_REF] Rei | [END_REF], 2MASS (Cutri et al. 2003), WISE (Cutri & et al. 2012), Pan-STARRS (Chambers et al. 2016), SkyMapper Southern Sky Survey (Wolf et al. 2018) and VISTA Hemisphere Survey (McMahon et al. 2013). The blue, green and red solid lines correspond to the X-shooter spectra in the ultraviolet, visible and near-infrared, respectively. The synthetic spectra were scaled according to the J-band value (∼ 1.25 µm) of the star. The photometric data and flux calibrated spectra are in good agreement, except for JW647 and JW847, in which we observed a larger spread on photometric values.

According to [START_REF] Lada | IAU Symposium[END_REF] classification, JW908 resembles the SED of a class III object, but this is not clear since we do not have photometry beyond 10 µm. The remaining YSOs show an infrared excess characteristic of class II objects. The plots show also a dip just before 10 µm for JW180, JW293, JW647 and JW847, which is usually associated to a silicate emission feature from the disk (e.g. [START_REF] Furlan | [END_REF]). The equivalent width of this emission can be used to identify objects with disks that started to develop gaps.

Although we do not have infrared spectroscopy beyond 2.5 µm, from the SED profiles of JW180, JW293, JW647 and JW847, we suspect that we might have some transition disks among them (e.g. Williams & Cieza 2011), as we explain after. These circumstellar disks

DISCUSSION

which inner regions were partially cleared from dust, can be related to planet formation or disk dispersal around pre-main sequence stars (Espaillat et al. 2014). Strom et al. (1989) and Skrutskie et al. (1990) were the pioneers of transition disk detection through NIR and Mid-Infrared (MIR) photometry. These objects show in their SEDs a small excess emission at NIR wavelengths (1-5µm) followed by an excess at the MIR (5-20µm). This can be understood as the presence of a hole in the disk without dust, scarcity of dust particles in the inner disk or even a change in the dust particle size (e.g. Carmona 2010). Furthermore, it has been suggested that these disks result from the transition from Class II to Class III objects, where optically thick disks evolve towards optically thin ones with progressive dissipation of its gas and dust. The evolution and dispersion of the material in the circumstellar disk could be due to the contribution of disk winds, as suggested in Simon et al. (2016).

In Espaillat et al. (2014), three types of disks are distinguished, as shown in Fig. 3.10: a full disk, a pre-transitional disk and a transitional disk. A full disk corresponds to a continuous disk without significant gaps. A transitional disk corresponds to a disk with an inner disk hole, while a pre-transitional disk has a gap that separates an inner dust ring from an outer one.

In Fig. 3.10, when comparing the SED from a full disk with a pre-transitional disk or a transitional disk, the dip at the left of 10 µm silicate emission feature gets deeper as the warm dust in the inner region of the disk starts do disappear. One of the main differences on the SEDs between the pre-transitional and transitional phase is the significant NIR excess that pre-transitional disks show comparatively to their corresponding stellar photospheres, which is not as pronounced for transitional disks. This can be explained by the presence of an optically thick inner disk close to the star, that corresponds to the residuals of the inner portion of the original disk. Once this inner ring starts to dissipate, there is much less NIR excess in the SED.

Looking at the four top plots in Fig. 3.9, we can see that JW647 shows a pronounced NIR excess emission comparatively to JW180, JW293 and JW847. Taking into account Espaillat et al. (2014) classification and the SEDs of these four objects, we suggest that JW647 has a pre-transitional disk, while JW180, JW293 and JW847 have a transitional disk. Concerning JW908, since we do not have MIR photometry available, we cannot infer if this star hosts a transitional disk or not.

Discussion

The study of accretion activity among the very low-mass members of the ONC has not been fully addressed. Although this work has quite a small sample, we make here the effort to get a step closer towards the big picture. [START_REF] Biazzo | [END_REF] studied 91 very low-mass stars of the ONC and by using the accretion criterion of Hα width at 10%, they did not find any accreting stars with masses less than 0.2 M ⊙ . Nevertheless, they found that some of those stars were locked to their disks by showing slow rotation periods and infrared excess. The evidence that the YSOs studied in [START_REF] Biazzo | [END_REF] have, apparently, no on-going accretion but they seem to be locked to their disks, suggests that disk-locking 3.4. DISCUSSION had operated extremely fast and early in their evolution. If this is confirmed, it can bring implications for the time-scale of the angular momentum evolution in low-mass stars.

A short sample of possible accreting stars has been selected and 6 out of 8 were observed.

Additional problems concerning the observation mode and saturation issues decreased the sample down to the 5 objects presented in this study. It turned out that only 3 of those 5 targets are very low-mass stars. But do they have on-going accretion? In order to disentangle all the findings, in the following subsections we discuss some of the main results found for each target.

JW180

JW180 was classified as an M5 and shows the lowest luminosity, stellar mass and radius computed and has an estimated age of 3.5 Myr. This star has quite a few accretion tracers in emission, most of them being Balmer lines, which were translated in a Ṁacc of 10 -10.1

M ⊙ yr -1 . According to the corresponding SED, there is a significant MIR excess indicative of the presence of a disk which inner region has been cleared. We suggest that this star should be accreting and hosting a transitional disk.

JW293 and JW908

These two objects were classified with the same spectral type of M4.5. They have very similar luminosity, stellar mass, radius and age around 3 Myr, according to Siess et al. (2000) model. These two YSOs have the same lines in emission as JW180, returning an average Ṁacc of 10 -10.0 and 10 -9.8 M ⊙ yr -1 for JW293 and JW908, respectively. The SED of JW293 has a similar MIR excess to JW180. Unfortunately, we do not have photometry in the MIR for JW908. As it is, the SED looks like a class III object, but we think that this is not the case given all the accretion tracers in emission and so we conclude that both stars are accreting.

Our results partially agree with the classification given by Fűrész et al. (2008), who classified JW293 as probably a CTTS, but could be a WTTS and JW908 as a WTTS.

JW647

JW647, originally classified as an M5 in Hillenbrand (1997), was recently changed to an M0.5 in Hillenbrand et al. (2013). According to our work, we suggest a spectral type of M1 for this YSO, which is quite similar to the second classification done by Hillenbrand et al. (2013). This is what explains the big shift in effective temperature in the HR diagram.

Concerning the shift in luminosity, the flux for JW647 was corrected from veiling in this work, while Hillenbrand (1997) could not correct the spectral types from this additional contribution. That should be the reason why the luminosity slightly drops in the same diagram. Comparing with the previous targets, JW647 has a higher stellar mass of approximately 0.5 M ⊙ and an age about 3 Myr. However, this age estimate is highly dependent on the flux correction due to the continuum excess emission determined through the veiling of photospheric lines.

This was the only star in the sample that showed significant veiling, with an average value of 0.5 measured at 610 nm. A stronger Balmer jump was observed in the UVB arm, comparatively to the remaining targets, which leads to the highest observed Balmer jump measured in the sample. Additionally, we have also detected several accretion tracers for this YSO, and many emission lines present inverse P Cygni profiles. Taken all the line luminosities into account, we got for this star the highest Ṁacc with a value of 10 -8.6

M ⊙ yr -1 , which is a typical mass accretion rate for CTTS (Hartmann et al. 2016). This result is in agreement with Fűrész et al. (2008) work, who classified this star as a CTTS.

The SED of this object stands out from all the others, with the presence of a significant NIR excess which suggests the presence of a thick inner ring close to the star. This suggests that JW647 should have a pre-transitional disk, which means that this star is going through an earlier evolutionary stage comparatively to the remaining YSOs. We discard the possibility of a full disk, because in that case we would not have the 10µm silicate emission feature as pronounced. This idea can be supported by the mass accretion rate, which is the highest in the sample. Once the YSO is closer from turning into a class III object, accretion rates decrease as the star cleans its disk and there is less and less material to be accreted.

JW847

According to this work, JW847 is the earliest-type star in the sample with a spectral type of a K6. Previously, Hillenbrand (1997) classified this star as a K3/G8, which explains such a big temperature shift in the HR diagram. This is supported by template comparison, in which the target spectrum fits best a late K-type template rather than an early K-type.

Besides being the most luminous object with an age of only 1 Myr, it also presents the highest value for stellar mass and radius. The spectrum has no significant accretion tracers in emission and there are signs of chromospheric emission when we analyse the Ca II K and H lines at 393.4 and 396.8 nm, correspondingly. These line profiles show an emission feature embedded in the line absorption.

We think that this star has no on-going accretion, but the corresponding SED indicates that there is still an outer disk. If true, this star hosts the youngest transition disk of the sample with only 1 Myr. It could be that JW847 is already transiting from class II to class III. Hernández et al. (2008) plotted the disk frequency of late-type stars (mid-K and later) as a function of age, through NIR excess emission from the disk for several stellar groups.

According to their results, at 1 Myr, 80% of the stars have disks, but 20% do not. Some stars loose their disks quite early and this may happen due to several reasons, namely the proximity of high mass stars, binary companions, or even strong interactions with other stars in early star formation.

3.5. CONCLUSIONS

Conclusions

We have analysed X-shooter spectra of low and very low-mass YSOs belonging to the ONC.

These objects were suspected of carrying accretion activity in a previous work from [START_REF] Biazzo | [END_REF]. The main goal of this chapter was to infer if those objects are accretors or not.

First, we classified the spectral type of the stars through spectral indices and determined the corresponding stellar parameters. Second, we looked for accretion features in the spectra and measured accretion rates in all three arms (UVB, VIS and NIR) of the suspicious accretors. Third, we looked for the presence of circumstellar disks through available photometry.

We conclude that JW647 is a CTTS and has on-going accretion activity supported by its mass accretion rate, IPC profiles present among Balmer emission lines and measured Balmer jump. The SED for this star has a considerable NIR excess that suggests the presence of a thick inner disk as found in stars with pre-transitional disks.

JW180, JW293 and JW847 show photometric evidence of hosting a transitional disk.

The two first stars are quite similar to each other, not only among the computed stellar parameters but also concerning the measured mass accretion rates. JW847 is a different case. This K6 star contrasts in both stellar parameters derived as well as the lack of emission lines characteristic of accreting stars. Most likely, JW847 is not accreting and could be transiting from class II to class III. Additionally, it seems that this star hosts the youngest disk in the sample with 1 Myr.

Although we do not have enough photometry to ensure that JW908 has a circumstellar disk, this star has quite a few accretion tracers in its spectrum that support on-going accretion.

Taking all into account, we have detected accretion in 4 out of the 5 targets with Ṁacc values that are in agreement with the corresponding stellar masses (Hartmann et al. 2016). Among the 4 accretors, 3 of them belong the the very low-mass range with stellar masses below 0.25 M ⊙ .

Although we cannot retrieve a robust conclusion from only few YSOs, it seems that the accretion criterion of White & Basri (2003) does not work for stars in the very low-mass range. According to this work, 4 of the targets show spectral evidence of on-going accretion that was not detected by the previous criterion in [START_REF] Biazzo | [END_REF]. A new accretion threshold for such low-mass YSOs should be studied in a future work. In addition, if disk-locking is operating, it means that it should occur in an even early stage for very low-mass stars. A more quantitative analysis would be useful in order to confirm if either disk-locking or any other angular momentum evolution model fit within the time-scale observed for the ONC members. Additionally, we would like to characterize more deeply the transition disks of these YSOs with data from instruments that can give us information not only about the disk mass (IRAM/NOEMA), but also to understand the disk structure (SPHERE) and magnetic topology to understand the star-disk interaction (SPIRou). As in any star-disk system, these objects have an inclination in our line of sight. We can see YSOs edge-on or pole-on oriented, if their inclination is close to 90 • or 0 • , respectively.

Depending on their inclination it can favour the observation of accretion and/or outflow phenomena. In the case of RY Tau and SU Aur, these are two edge-on systems with high inclination angles. According to Isella et al. (2010), RY Tau has an inclination of 66 • . Concerning SU Aur, an inclination of 62 • has been determined (Akeson et al. 2002).

The main advantage of dealing with such high inclination systems is that our line of sight intersects the disk winds, enabling the study of the variability of these outflowing structures and how they interact with the circumstellar medium.

RY Tau is a CTTS with approximately 4.7 Myr, and has been monitored since quite a few decades due to its irregular light variability, with documented magnitudes in the Vband varying between 9.5 to 11.5 (see Petrov et al. (2019) and references therein). It has been also characterized for having negligible veiling values in the optical (Basri et al. 1991;Hartigan et al. 1995;Petrov et al. 2019). Although the brightness of the star is variable, the veiling remains negligible. Additionally, this star has a high projected rotational velocity of approximately 50 km s -1 (Petrov et al. 1999), which makes it difficult to determine the spectral type. For example, previous works classified this star as a G1-G2 (Petrov et al. 1999), but also as a K1 (Güdel et al. 2007).

SU Aur is a low-mass YSO with approximately 6.6 Myr (Petrov et al. 2019) and has also been documented as a variable star in the V-band. Previous works have reported 4.1. DATA FOR RY TAU AND SU AUR V-band magnitudes that can go from 9 to 11 magnitudes (Herbst & Shevchenko 1999;DeWarf et al. 2003) and variations up to 0.5 magnitudes on time-scales of days (Unruh et al. 2004). SU Aur was classified as a G2 by Herbig (1960) with no evidence of veiling in its spectra (Johns & Basri 1995b;Petrov et al. 2019) and, similarly to RY Tau, is a rapid rotator with a v sin i between 60 and 66 km s -1 (Petrov et al. 1996;[START_REF] Nguyen | [END_REF]).

In the following sections we explore some results concerning these two last CTTSs that are a product of a collaboration with P. P. Petrov. The study of spectroscopic and photometric variability of RY Tau and SU Aur will shed a light on the structure of their inner disks, as well as the physical processes involved in the circumstellar environment.

Data for RY Tau and SU Aur

In All the collected spectra were obtained from the following observatories: Crimean Astrophysical Observatory (CrAO), Nordic Optical Telescope (NOT) at Observatorio del Roque de Los Muchachos, Centro Astronómico Hispano-Alemán (CAHA), Thai National Observatory (TNO) and Kourovka Astronomical Observatory of the Ural Federal University (UrFU). More details concerning the telescope diameter, instrument used, spectral resolution and slit or fibre sizes can be found in Table 4.1.

The data reduction was done by each observer and the data collection performed in CrAO. This data collection takes in account only spectra with SNR above 100 in the wavelength range of Hα and includes the resampling of all spectra to the same resolution.

All the spectra are corrected for the radial velocity. The log of the observational surveys can be found in Table B.1 and B.2 for RY Tau and SU Aur, respectively. Notes: (a) A slit was used in this instrument; (b) A fibre was used in this instrument.

Results

Photometric variability

In order to fully analyse the photometric variability of our targets, we gathered all the V-magnitudes available from CAS, CrAO and AAVSO. In the case we have no photometry available for a day of spectroscopic observations, we interpolate a value only if the time difference to the nearest photometry is not larger than ±3.0 days. Otherwise we cannot ensure that the accuracy of the interpolated V-mag is ±0.10 mag, as estimated in Petrov Once we gather all the magnitudes, we plot the light curves to examine the photometric behaviour of the stars throughout the observational seasons. In Fig. 4.1a, we can see that the brightness of RY Tau is decaying since season 2013-2014, when we start observing the star, until 2016-2017. During the first two seasons, the large variations in photometry are connected with high Hα variability. Then the brightness starts to increase more significantly during 2017-2018. In the literature, previous brightening events were reported for RY Tau during the 80's and the 90's (e.g. Herbst & Stine 1984;Herbst et al. 1994;Zajtseva 2010). For the case of SU Aur, we can see in Fig. 4.1b that the variability of SU Aur for the first two observational seasons does not seem to be as pronounced as for RY Tau. Although we have only three observational epochs for SU Aur, 2015-2016 and 2016-2017 periods are less variable when compared with 2017-2018, where we start to see sharp brightness decays.

In 2017-2018, V-band measurements can go fainter than 11 magnitudes.

Usually, irregular light variability can be linked with stochastic accretion events and circumstellar dust. We will see later in this chapter that we cannot make any robust conclusions on brightness variability based on the mass accretion rates measured for RY Tau through the Hα emission line. Nevertheless, there is evidence that the dust from the disk wind is always obscuring this star.

First, in Petrov et al. (2019), colour-magnitude diagrams of RY Tau show that this stars gets bluer colours towards higher extinction values. This behaviour is typical in UX Ori-type stars. UX Ori type variable stars, also known as UXors, are intermediate-mass

YSOs known for their variability due to circumstellar extinction. The amplitude in the Vmagnitude can range between 2 and 3 magnitudes, approximately. Whenever these objects are fainter, they show higher polarization values (e.g. Davies et al. 2018). This variable phenomenon is associated with optically thick dust from the circumstellar disk that blocks part of the light emitted by the star. As dust, in our line of sight, absorbs and scatters light while decreasing stellar brightness, the polarization will increase. When there are no dust clumps in the line of sight, the stellar brightness increases and polarization decreases (Grinin et al. 1994). In Pereyra et al. (2009) work, RY Tau is confirmed to have UXor characteristics through near-infrared polarimetry measurements in the H-band.

Second, colour-magnitude diagrams V /(B -V ) and V /(V -Rj) in Petrov et al. (2019) show a curved track for RY Tau rather than a linear relation, as seen for SU Aur. One hypothesis raised is that RY Tau could be permanently obscured by circumstellar dust even when the star gets brighter.

In order to analyse the variability of the intensity of the Hα emission line and how it correlates with the brightness of each target, we made diagrams for all the collected Hα profiles in velocity, showing the amplitude of the profile variability. Later, we computed the Pearson correlation coefficients of Hα intensity, for each velocity bin, with stellar brightness (V-magnitude).

In Fig. 4.2, we are considering the data including all the observational epochs. In the bottom plots, a positive correlation means that the intensity of the emission increases with brightness decreasing. The False Alarm Probability (FAP) is also plotted (dashed lines)

and it was taken from [START_REF] Bevington | Data reduction and error analysis for the physical sciences[END_REF], according to the number of observations. For instance, when the correlation is above the level FAP=0.1%, it means that the probability of non-correlation is less than 0.1%. These plots in Fig. Additionally, we find a negative correlation linked with the blueshifted absorption centred around -50 km s -1 . In this case, a negative correlation means that the intensity of the emission increases with the decrease of V-mag (increase of brightness). This means that the depth of the absorption, associated with the presence of an outflow, is linked with a decrease of the brightness of the star. This suggests that the circumstellar extinction is higher for moments of enhanced outflow activity, which is the opposite situation inferred for RY Tau.

But there is something else we should take into account which is, what if the magnetosphere of SU Aur is tilted relatively to the rotation axis, as suggested by Johns & Basri (1995b) (see Fig. 4.5)? This could mean that sometimes, along the line of sight, the observer can see alternately the accretion columns or the dusty disk winds. As we will see in the following section, this could explain why sometimes we detect redshifted absorptions in the profile, but also why the blueshifted absorption correlates with higher circumstellar extinction. Maybe this inclined configuration enables the outflow to sweep more efficiently the dust from the inner circumstellar region. This dust will intersect the line of sight of the observer and the star will be obscured by the dusty disk wind, whose presence was recently confirmed by Labdon et al. (2019). In the case of RY Tau, it could be that the outflows clean the dust in our line of sight. But for the case of SU Aur, the hypothesis is that maybe the inclination of the star-disk system enables the outflow to blow the dust of the inner region of the circumstellar disk towards our line of sign.

Spectroscopic variability

In this subsection we analyse the evolution of the Hα emission profiles throughout the different observational epochs. Besides being one of the strongest emission lines in the optical wavelength range, it is also a reliable accretion and outflow tracer.

It is quite common to find in CTTSs spectra either blueshifted or redshifted absorptions, superposed on broad emission lines, whenever these stars are experiencing outflow and/or accretion activity, respectively. On one hand, the absorptions located on the blue wing correspond to a stellar wind signature. These features can evolve towards stronger absorptions that go below the continuum and are known as P Cygni profiles (e.g. Beals (1953)). This is the observational evidence that the star is experiencing a more intense outflow activity. On the other hand, redshifted absorptions are linked to accretion activity.

If there is enhanced accretion activity and the material infall is in the line of sight of the observer, inverse P Cygni profiles can be found. These profiles are shaped as redshifted absorptions that go below the continuum and were first observed by Walker (1972). where the Hα10% width is given in km s -1 and Ṁacc in M ⊙ yr -1 . The Hα10% is an accretion indicator that can be used qualitatively for very low-mass objects, but also to estimate the Ṁacc from TTSs to brown dwarfs (Natta et al. 2014). Nevertheless, we are aware that some authors consider the Hα10% as a reasonable accretion indicator to do statistics for a large sample of stars, but it can be considered unreliable when used for single stars. In this study, we could only use the Hα emission line as accretion indicator.

There is also another issue we should mention, which is the effect of a blueshifted absorption or P Cygni profile in the measurement of the Hα10% width. In these cases, the regions that are being considered to compute this parameter are the ones marked with the green solid line in Fig. 4.8.

In Fig. 4.9, we show the correlation plots for the following parameters: magnitude in the V-band, EQW Hα, EQW blue Hα / EQW red Hα and Ṁacc . Each symbol corresponds to a different observational season. The left panels correspond to the results of RY Tau, while the right panels concern the plots for SU Aur. In Tables 4.4 and4 For SU Aur we see a similar trend for the correlation between the EQW Hα with the stellar brightness, but stronger than RY Tau when we consider the three observational seasons. The main difference is that the points are more concentrated towards smaller equivalent widths of the Hα emission line with lower V-magnitude, i.e. higher stellar brightness. Overall, the correlation coefficient is about 0.6. What has been suggested, is that SU Aur is occasionally obscured by the dust, while the star light is permanently blocked for RY Tau (Petrov et al. 2019). The presence of a dusty disk wind has been confirmed recently, for SU Aur, through NIR interferometry and disk wind models (Labdon et al. 2019).

In Fig. 4.9c and 4.9d, we can see that the correlations between the asymmetry ratio EQW blue Hα / EQW red Hα and the stellar brightness are quite distinct for RY Tau and SU Aur. While for RY Tau the ratio increases with higher magnitudes, particularly for the epoch 2014-2015, we found the opposite trend for SU Aur if we consider 2015-2016 and 2016-2017 seasons with stronger correlations. Although with some dispersion, higher asymmetries in the profiles of RY Tau are associated with higher brightness values, as seen in Petrov 4.2. RESULTS et al. (2019) for observations made between 2013 and 20152 . Therefore, the main source of photometric variability is due to extinction rather than stellar variability, since veiling is constant and the V-magnitude is varying. The asymmetry of the Hα emission profile is correlated with V-magnitude and so the line asymmetry should be related with the extinction variation.

Finally, in Fig. 4.9e and 4.9f the correlations between V-magnitude and the mass accretion rate measured from the Hα emission line are rather low, in both stars, and considering the complete samples. Nevertheless, we should mention that the error bars are quite large and even if any correlation exist it would be very difficult to identify. The fact that there is no correlation between Ṁacc and V-magnitude agrees with the constant veiling, which is very weak in all seasons for both stars. Table 4.4: Correlation coefficients between stellar V-magnitude and other parameters obtained from the Hα emission line for RY Tau. The parameters include the equivalent width of the Hα emission line (EQW Hα), the ratio between the equivalent width of Hα measured for the blue and red side of the profile (EQW blue Hα / EQW red Hα ) and the mass accretion rate ( Ṁacc ).

All epochs 2013-2014 2014-2015 2015-2016 2016-2017

Periodogram analysis

The photometric variability observed in T Tauri stars has revealed to be a complex task.

We should take into account not only a variety of physical processes, namely enhanced accretion/outflow activity, circumstellar extinction or even the presence of cold/hot spots, but also a variety of timescales in which these phenomena may occur. If periodic variability is detected, it should be due to the presence of either cool or hot spots or even obscuration due to dust in the circumstellar disk (Percy et al. 2006).

RY Tau has been known in the literature as a CTTS with irregular brightness variations. As we saw previously, the V-magnitudes for RY Tau have an amplitude of around 1 magnitude for each season and if we consider all the five years of observations we get an amplitude of almost 2 magnitudes. According to Beck & Simon (2001), this star can reach amplitudes of more than 2 magnitudes.

RESULTS

The measurement of the periodicity related with the brightness variation of RY Tau reveals to be quite challenging since a few decades ago. When looking into the literature, the periodicities detected for the brightness variations of this star can assume different values. Herbst et al. (1987) found periodicities of 5.6 and 66 days. Chugainov et al. (1991) retrieved values of 5.6 and 7.25 days, while [START_REF] Bouvier | [END_REF] determined a periodicity of 24 days. Interestingly, in the work of [START_REF] Strassmeier | [END_REF] and Percy et al. (2006) they found no significant periods for RY Tau. Years later, Zajtseva (2010) and Ismailov et al. (2011) inferred a periodicity of 7.5 and 23.26 days, respectively. Although no periods are confirmed, RY Tau shows two sets of periods, short and long ones. It is very likely that both periods are real, but they should be related with different regions, probably the short ones are relative to the surface rotation of the star, while the long ones are associated with the disk. Petrov et al. (1999) did not find any relevant periodicity, but suggested that the variability of RY Tau brightness could be caused by circumstellar dust clouds rather than by the presence of startspots or even irregular accretion events. The authors reach this conclusion due to several reasons. First, RY Tau has no significant veiling, which suggests that accretion activity should not be the cause of brightness variability. Second, is very likely that RY Tau shows no cold spots since no significant periodicities are found through the light variations. Third, the authors confirm that there are no major changes in the photospheric lines of RY Tau, which suggest that the light variability is not due to any kind of phenomenon occurring at the stellar surface. Fourth, the authors detected an increase of polarization values along a brightness decrease of RY Tau, which is typical in UX Ori-type stars. Therefore, is very likely that the fading events are caused by obscuration of the star due to the circumstellar dust.

Years later, a new idea popped out. Babina et al. (2016), after monitoring RY Tau for 2 years, suggested that the dusty disk-wind close to the star seems to be affected by irregular magnetospheric ejections, which modify the wind geometry and consequently its opacity leading to brightness variations. This idea is still supported through our results published in Petrov et al. (2019).

For SU Aur, the periodicities associated with the brightness variations and measured along the years seem to be more consistent, although there are a few outliers. Herbst et al. (1987) detected periods of 1.55 and 2.73 days, while in Herbst & Koret (1988) were not found any periodicities. During the 90's, more periodicities (in days) are determined with values of 18.7 (Gahm et al. 1993), 2.78 (Bouvier et al. 1993), 2.98 (Giampapa et al. 1993) and 3.03 (Petrov et al. 1996). Years later, Unruh et al. (2004) inferred a periodicity of near 2.7 days for the same star. Overall, most of the values presented here range between 2.7 and 3 days. The periodicities that differ the most are 1.55 and 18.7 days.

In Petrov et al. (1996) it is also suggested that the line profile variability should be associated with circumstellar instabilities in SU Aur, rather than other phenomenon occurring at the stellar surface. This is inferred from simultaneous U BV photometric with spectroscopic data, which show significant changes in the intensity of Balmer, He I and Na D lines while the stellar continuum flux was practically constant. According to the authors, the daily variability observed for the blueshifted absorptions present in the Balmer emis-sion lines suggests that the outflow is ejected in a pulsating way. Other explanation given for the variable behaviour of the Balmer emission lines in SU Aur is proposed by Johns & Basri (1995b). They suggest that this star has its magnetosphere tilted relatively to the rotation axis, as shown previously in Fig. 4.5. This could possibly explain why spectral evidence of accretion and high-velocity outflows alternate with one another. Percy et al. (2006) found through self-correlation technique, periods of multiples of 16 days for SU Aur.

The method used is a time-series analysis tool able to measure cycle-to-cycle behaviour of the star, averaged over all the data. According to the authors, this is a high value for the stellar rotation period. It is possible that it refers to the periodicity of an inhomogeneity in the inner region of the circumstellar disk.

One way to search for periodicities in the intensity of the emission lines is through the construction of a periodogram (e.g. Johns & Basri 1995b;Alencar et al. 2005). Very briefly, a periodogram is a tool able to calculate the spectral density of a given signal. In this work we show the periodograms made from the Hα emission profiles for RY Tau and SU Aur. Preliminary tests within the collaboration for Petrov et al. (2019) showed that no significant periods are found for periodograms based on photometric data.

In a first step we selected all the data from all observational seasons and plotted the periodograms shown in Fig. 4.10 and 4.11 for RY Tau and SU Aur, respectively. By performing the periodograms for all the seasons of both stars, we can search for longer periodicities.

In order to do it, we used Astropy function LombScargle3 , based on the work of Van-derPlas et al. (2012) andVanderPlas &[START_REF] Vanderplas | [END_REF], which computes the Lomb-Scargle periodogram (Scargle 1982). The latest is a useful tool in frequency analysis to detect periodicities in unevenly spaced data, as we have for RY Tau and SU Aur. How do we get a 2D periodogram? First, we start by joining all the velocity profiles of Hα for each target.

Second, a 1D periodogram is computed for each velocity bin. Third, the 1D periodograms for all the velocity bins are concatenated (and interpolated) in order to retrieve the 2D periodogram.

In Fig. 4.10 and 4.11, for RY Tau and SU Aur, respectively, plot (a) shows the 2D

periodogram obtained for all the observational seasons. In plot (b), we show a zoom-in of plot (a) towards lower frequencies, where we find the most intense peaks of the power spectrum, which are above a FAP of 0.5%. Still in plot (b), we mark with white dashed lines the velocities that intersect the regions with the most significant peaks and in plots (c) we extract the corresponding 1D periodograms.

Considering the entire sample for both targets, the periodograms trace only few and narrow intense regions towards lower frequencies. Some of these regions, shown in red, remain in plots (b) for a FAP of 0.5%. In Fig. 4.10b, the most intense peaks in RY Tau are centred near -52 and 58 km s -1 with a corresponding period of 72 days. There is an additional secondary peak appearing at -146 km s -1 with a period close to 28 days. The highest periods found for RY Tau correspond to 24 days, measured in [START_REF] Bouvier | [END_REF], and 23 days, determined by Ismailov et al. (2011). So far, they are no detected periods higher than these values. In the 2D periodogram of SU Aur in Fig. 4.11b, we find very

RESULTS

small peaks for a FAP of 0.5%, at -38 and -8 km s -1 , corresponding to 20 and 18 days, approximately. In the literature, Gahm et al. (1993) found a period of approximately 19 days for SU Aur.

If the v sin i of both stars are high, we should expect small periods. In order to search for such periodicities we performed the same periodograms by selecting the spectra according to each observational season, as shown in we can see that the significant peaks fall at periods of nearly 4, 5, 10 days and beyond.

Interestingly, the intensity of the significant peaks declines towards the 2015-2016 season, the quiescent epoch of RY Tau. In 2017-2018, there is an increase of the peak intensity for periods higher than 10 days. If the extinction is variable and does not relate with star/disk rotation in RY Tau, it makes it difficult to measure the stellar rotation period.

For the case of SU Aur, One issue that could be affecting our results, for both RY Tau and SU Aur, is the insufficient number of observations that we have available and that we use to plot the periodograms. Another problem concerns the number of observations that we use to plot the periodograms for each season. The number of available spectra is not the same from one observational epoch to another and maybe this could have an impact on the true results and when comparing different observational seasons.

Conclusions

Daily and irregular variabilities were observed in the lightcurves for the V-magnitude and in Hα emission profiles of RY Tau and SU Aur. Taking into account the photometry collected for all the observational seasons, the amplitude of the V-magnitude is approximately 2 magnitudes for both targets. We also observe in these two stars that the large variations in photometry are linked with higher variability of the Hα emission profile. The profiles of this emission are mostly characterized by the presence of absorptions in the blue wing, but we also detect weaker absorptions in the red wing. These features are indicative that both outflow and accretion mechanisms are active. In addition, the presence of P Cygni profiles in both YSOs is a proof that these CTTSs are experiencing periods of enhanced outflow activity.

From the diagrams with Hα profile in velocity and its correlation with V-magnitude, for each observational season for RY Tau and SU Aur, we can take some conclusions.

First, the quiescent periods of RY Tau and SU Aur are seasons 2015-2016 and 2016-2017, respectively. Second, the confident correlation for the absorption in the blue wing of Hα for RY Tau in four seasons suggests that outflow activity is connected with an increase of stellar brightness. One possible scenario is that RY Tau has a dusty wind curtain in our line of sight that is blown up by enhanced outflow activity. This additional outflows will clean the dust in the line of sight and the star will appear brighter. In Petrov et al. ( 2019) is suggested that these additional outflows could be magnetospheric ejections. Third, the negative correlation found for the blue wing of Hα for SU Aur is quite intriguing. This correlations suggests that the outflow is connected with a decrease of the brightness of the star, which is the opposite case of what we see for RY Tau. Although we do not have a robust conclusion for SU Aur, there is at least one possible (and maybe remote)

hypothesis. If SU Aur has its magnetosphere tilted relatively to the rotation axis (Johns & Basri 1995b), it could be that the dust blown by additional outflow activity goes towards our line of sight. Thus, the star will appear fainter due to the increase of circumstellar extinction.

In Petrov et al. (2019), veiling is very weak for different activity phases of both stars, which means that the photometric variation is not due to phenomena occurring at the stellar surface. As a matter of fact, we found no correlation between stellar brightness and mass accretion rates for both targets, suggesting that accretion is not responsible for the light variability in both YSOs. Nevertheless, a correlation could exist but our accuracy in mass accretion rate is small and depends only on the Hα emission line observed.

In RY Tau and SU Aur, the equivalent width of the Hα emission increases with decreasing stellar brightness, meaning that both stars are being obscured by dust. Within the work presented in Petrov et al. (2019), colour-magnitude diagrams support the idea that RY Tau could be permanently obscured by circumstellar dust even when the star appears brighter. But SU Aur seems that is not occulted by dust all the time. In view of this, we conclude that the stellar variability is essentially related with extinction variations.

Concerning the asymmetry measured through EQW blue Hα / EQW red Hα , we find different trends between the two targets. RY Tau shows smaller ratios, i.e. higher asymmetry, towards 4.3. CONCLUSIONS higher brightness. This effect is more evident if we analyse each season separately. In particular, the 2014-2015 season presents the highest correlation so far. As discussed in Petrov et al. (2019), this result supports the idea that lower circumstellar extinction is caused by enhancement of Hα activity. For the case of SU Aur, the profile asymmetry tends to accentuate towards lower brightness values. Maybe this could be an effect of the inclination of the star-disk system.

The determination of periodicities for RY Tau and SU Aur reveals to be a complex task. Although we cannot make any strong conclusions from this frequency analysis due to the insufficient number of observations per observational epoch, the 2D periodograms for each observational season show different periodicities for both stars, and most of the times they are not constant from one epoch to another. For RY Tau, we do not find any matching periodicities with the ones in the literature. It is very likely that a variety of physical processes are involved in the irregular variability of RY Tau making it hard to extract a period. In the case of SU Aur, we found a period close to 3 days around 150-200 km s -1 present in all of the three observational seasons at a FAP of 0.5%. This period was found multiple times in the literature since the late 80's. Curiously, this periodicity is still detected in the 2016-2017 season, the quiescent period of this star characterized by weaker blueshifted absorptions in the Hα emission profile.

Simulating the circumstellar environment of CTTSs

In this chapter we explore 2.5 dimensional Magnetohydrodynamics (MHD) time-dependent simulations. In other words, 3D simulations assuming axisymmetry. The MHD numerical simulations were performed with PLUTO1 , a modular code for fluids in astrophysics (Mignone et al. 2007). Part of the results concerning these MHD simulations started at LUTh (Laboratoire Univers et Théories, Observatoire de Paris) under the supervision of V. Cayatte who is collaborating to this project.

The goal of this numerical work is to simulate the surrounding environment of a star with the same characteristics as RY Tau. We selected this star because it had some relevant observational structures and parameters available in the literature. These parameters were essential to conceive the analytical solution presented in Sauty et al. (2011) for a lowmass TTS. From the measurements of the radius, mass, period of the star, mass loss rate and terminal velocity of the jet, the model parameters have been constrained using the self-similar model of Sauty & Tsinganos (1994), where the outflows are pressure driven.

In this work, the analytical solution provided in Sauty et al. (2011) for TTSs is used as initial condition for the simulations presented in this chapter, both for the stellar jet and magnetospheric accreting regions, and also partially for the boundary conditions.

This study aims to analyse not only the behaviour of the stellar jet region with time, but also the closed magnetospheric region where accretion is expected to take place. We focus on how the stellar jet may influence the magnetospheric ejection, with a weak disk wind.

After multiple attempts, we analyse and discuss some of the most interesting simulations performed in this study.

IDEAL MHD EQUATIONS FOR ASTROPHYSICAL PLASMAS

Ideal MHD equations for astrophysical plasmas

Probably the most traditional and finest way to introduce astrophysical plasmas is by presenting the set of ideal MHD equations that describe the hydrodynamic interaction of a conducting fluid with a magnetic field. These equations can be deduced from Maxwell's equations and Ohm's law, together with the fluid equations, and are crucial to characterize the circumstellar environment of a CTTS, which is governed by inflows and outflows of ionized gas.

Starting with the set of Maxwell's equations, they are given by the following expressions (in their differential form and in c.g.s.):

• Gauss' law for magnetism

∇ • B = 0 , (5.1)
where B is the magnetic field.

• Ampère's law

∇ × B = 1 c 4πj + ∂E ∂t , (5.2)
where j is the current density, c the speed of light, E is the electric field and t the time. In ideal MHD, the second term on the right-side of Eq.5.2 is negligible since the bulk speed of the flow is much less than the speed of the light (V ≪ c). Therefore, we can re-write the previous equation as

∇ × B = 4π c j . (5.3)
• Gauss' law

∇ • E = 4πρ elec , (5.4)
where ρ elec is the electric charge density, which is almost zero.

• Faraday's induction law

∇ × E = - 1 c ∂B ∂t . (5.5)
The last electromagnetic equation is given by Ohm's law (in c.g.s.

)

j = σ(E + V c × B) , (5.6)
where σ is the electric conductivity, which is infinite in ideal MHD, and V is the bulk flow speed.

CHAPTER 5. SIMULATING THE CIRCUMSTELLAR ENVIRONMENT OF CTTSS

The set of ideal MHD equations enumerated below allow the characterization of the hydrodynamic interaction in astrophysical plasmas, which are ionized.

• Continuity equation

∇ • ρV + ∂ρ ∂t = 0 , (5.7)
where the density is represented by ρ, the bulk flow speed by V and time by t. This equation is an expression of mass conservation.

• Equation of motion

ρ ∂V ∂t + (ρV • ∇)V = -∇P + j × B -F G , (5.8)
where P corresponds to the pressure, j is the current density, B is the magnetic field and F G is the gravitational force density. This equation describes the momentum conservation, in which the inertial term is given by the sum of the pressure gradient, the Lorentz force and the gravitational force.

• Induction equation

∂B ∂t = ∇ × (V × B) . (5.9)
Since we are dealing with high conducting plasma, the induction equation is only left with the convective term.

• Energy equation in the co-moving frame

q = ρ ∂h ∂t - ∂P ∂t + ρV • ∇h - ∇P ρ , (5.10)
where q is defined as the volumetric rate of thermal energy, h denotes the specific enthalpy of the gas given by

h = Γ Γ -1 P ρ , (5.11)
where Γ = c p /c v corresponds to the ratio of specific heats in the gas. The enthalpy function h works as an energy reservoir, which provides thermal energy to the outflow gas to be converted into kinetic energy. q can also be written as q = H -Λ, where H is the rate of volumetric heating and Λ is the rate of volumetric cooling.

An outflow model as a starting point

The origin of outflows, their shape, how they are accelerated and how these structures influence the evolution of the angular momentum in pre-main sequence stars have been some of the main questions addressed in star formation since many decades. Although plenty of observational data are available and a very broad range of studies have been published, models are needed to understand the physical processes involved.

AN OUTFLOW MODEL AS A STARTING POINT

The need for outflow models triggered the development of several studies. Some pioneer works started by developing steady-state models for the solar wind. One example is given by Parker (1958), who introduced a thermally driven non-rotating wind to explain the Sun's outflow. This model suggests that the outflowing material is accelerated outwards from the Sun by a pressure gradient. Years later, Weber & Davis (1967) proposed a model where they added a magnetic field and rotation. In this case, the acceleration of the magnetically driven outflow depends on the pressure gradient of the magnetic field.

Another steady model is the one from Blandford & Payne (1982), where accretion-power disk winds were introduced. In this model, the outflows are magnetocentrifugally accelerated from the disk, if the field line inclination is < 60 • relatively to the disk. Uchida & Shibata (1985) were pioneers in time-dependent simulations. They suggested that jets are shaped by twisted magnetic field lines anchored to the disk, which has a Keplerian rotation. However, their numerical code failed to ensure solenoidality (∇ • B = 0). Other outflow models include the X-wind model from Shu et al. (1994), which suggests a new kind of disk winds originated from the disk-magnetosphere boundary that could be responsible for the deceleration observed in CTTSs. Later, Matt & Pudritz (2005) introduced the accretion-powered stellar winds, which suggests that the energy released by accretion could be channelled to stellar winds. These outflows could have a significant contribution for spinning-down the star. Romanova et al. (2009) simulated a new kind of outflows named conical winds. According to the authors, these winds can be composed up to 30% of inner disk material and are the product of magnetospheric compression by the material in the circumstellar disk. Another example includes the simulations from Zanni & Ferreira (2013) in which the stellar winds are neglected. They simulate magnetospheric ejections, where plasma is ejected to the interstellar medium through repeated disconnections and re-connections of magnetic field lines along time, as shown previously in Fig. 1.19, Chapter 1. They suggest that these outflowing structures have an important role concerning the extraction of angular momentum in the star.

In this work, the simulations are based on the model of Sauty & Tsinganos (1994). This

analytical model makes use of self-similarity, which means that a mathematical approach was used to convert the partial MHD differential equations into nonlinear ordinary ones. In order to accomplish this, variables are separated and functions are scaled with one spatial coordinate (Sauty et al. 1998). This analytical solution incorporates magnetic rotation forces, plus a non polytropic heating, that generate pressure driven outflows. What this model suggests is that the initial cylindrical shape of a stellar jet in a YSO evolves towards a conical shaped wind as the star looses angular momentum towards the main sequence.

Four of the main physical quantities that govern the meridional self-similar model of Sauty & Tsinganos (1994) are velocity (V), magnetic field (B), pressure (P ) and density (ρ). Using spherical coordinates, velocity and magnetic field can be decomposed in their radial (r), polar (θ) and azimuthal (ϕ) components and expressed with the following equations: F (R) is a logarithmic expansion factor that measures the angle that the projection of a field line makes on the poloidal plane with the radial direction and can be written as .25) According to this last equation, radial field lines will correspond to F = 0 and cylindrical field lines will be associated to F = 2 (Sauty & Tsinganos 1994).

V r = V * M 2 (R) G 2 (R) cos θ 1 + δα(R, θ) , ( 5
F (R) = ∂ ln α(R, θ) ∂ ln R = 2 1 - d ln G d ln R . ( 5

The analytical solution and the initial setup

The boundary conditions on the star and the disk rely on the RY Tau micro jet model presented in Sauty et al. (2011). The solution used reproduces fairly well the observational constraints, namely the mass loss rate and the asymptotic speed, on the micro jet seen in UV spectral lines derived by Gómez de Castro & Verdugo (2001, 2007), as well as in the optical by St-Onge & Bastien (2008) and Agra-Amboage et al. (2009).

As previously mentioned, we used the analytical solution for a low mass accreting T Tauri star derived in Sauty et al. (2011), which considers some stellar parameters of RY Tau, namely the mass loss rate, stellar radius and mass, of Ṁloss = 10 -8.5 M ⊙ yr -1

(Gómez de Castro & Verdugo 2001), R * = 2.4R ⊙ (Hartigan et al. 1995) and M * = 1.5M ⊙ , respectively. The observed mass loss rate is used to fix the boundary mass density on the star. The density at the base of the flow is kept constant so later on in the simulations the asymptotic mass loss rate may vary due to changes in the outflow geometry and velocity.

The analytical solution deduced from observational constraints gives a stellar dipolar magnetic field of order 1 kG, which is typical for a T Tauri star (e.g. Johns-Krull 2007). The UV electron density at various distances observed fits within the error bars the obtained solution. Although the density used in the model corresponds to the proton density, it is still compatible with the electron density as long as the medium is ionized. The analytical solution also gives as an output an equatorial rotational velocity of 8.6 km s -1 (Sauty et al. 2011). This value is close to the lower limit of measured velocities for RY Tau [START_REF] Bouvier | [END_REF], but this may be rather low for actual values of 50 km s -1 (e.g. Petrov et al. 2019).

Initially, the Sauty & Tsinganos (1994) meridional self-similar model was developed only for the stellar driven jet. Later, it was adapted in order to include an accreting region inside the closed magnetosphere of the star (Sauty et al. 2017;[START_REF] De Albuquerque | Master's thesis[END_REF][START_REF] De Albuquerque | JET Simulations, Experiments, and Theory: Ten Years After JETSET[END_REF]. In this region, we impose a reversal of the sign of the poloidal velocity in order to induce accretion. Furthermore, the azimuthal component of the magnetic field was also reversed to keep consistency with the isorotation law and to keep the magnetic confinement.

5.5. PLUTO SETUP

PLUTO setup

PLUTO is a modular code written in C programming language. In order to run a simulation with this software, first, the user needs to configure the following input files:

• definitions.h

The header file, where the user can choose the fluid equations to be solved, the adopted geometry, the number of dimensions, some user defined parameters and any additional constants.

• makefile

The executable file needed to compile PLUTO.

• pluto.ini This is the file where the user defines the grid, time step, output files and any additional parameters.

• init.c Probably one of the most important files, where we have implemented the model of Sauty & Tsinganos (1994) with the corresponding initial and boundary conditions retrieved from the analytical solution for CTTS presented in Sauty et al. (2011). The additional changes mentioned in Sect.5.4 were implemented here as well.

• cooling.c This is the file where the energy equation is solved. The heating rate is currently implemented in this file and will be adjusted according to the velocity of the flow, as explained in a previous section in this chapter.

In this work we have adopted spherical coordinates and the set of MHD equations is solved assuming axisymmetry. Concerning the grid size, the radial component varies between 0.16 and 250, where from 0.16 to 1.8 we assume an uniform grid with 512 cells, and from 1.8 to 250 a stretched grid with 256 cells. In the co-latitude direction, the values range from 0 to π/2 within an uniform grid composed by 128 cells. Integration ends when the simulation time reaches 100 PLUTO time units.

The self-similar model is implemented in PLUTO simulations through the input file init.c, jointly with an accreting region. In this closed magnetospheric region, a reversal of the flow direction gathered with an enhancement of the mass accretion rate will generate the accreting region we aim to simulate.

When all the details are set, how does PLUTO work? The simulations run based on the outflow model given and use the analytical solution as initial condition. For each time t, PLUTO computes density, pressure, velocity and magnetic field through the MHD equations.

The software then uses the last four quantities to calculate P + dP = P (t + dt) followed by ρ(t + dt), V (t + dt) and B(t+dt) from the energy equation. All the calculations in PLUTO are made in spherical coordinates (r, θ, ϕ).

Conversion factors

The conversion factors to transform PLUTO units into physical units take into account a set of parameters determined in Sauty et al. (2011), specifically for low mass accreting T Tauri stars. The parameters are δ = 0.0778, κ = 0.021 and λ = 0.775 mentioned previously. An additional parameter is ν = 1.5. This parameter depends on the gravitational field and is

given by .31) where G is the gravitational constant and M the mass of the central object.

ν = 2GM r * V 2 * , ( 5
Below, we list the conversion factors for time, distance, velocity, mass flux and density.

• Time PLUTO time is given by (5.32) and we can write the stellar angular velocity as .33) Therefore, the stellar rotation period is given by

t pluto = r * /V * ,
Ω * = λ V * r * = λ t pluto . ( 5
2π λ t pluto ≈ 8.1 t pluto , (5.34)
which means that one stellar rotation is completed every 8.1 PLUTO time units. In other words, 1 t pluto corresponds to approximately 0.12 stellar rotations.

• Distance

According to the analytical solution proposed in Sauty et al. (2011), one Alfvén radius is equivalent to r * = 0.104 AU .

(5.35)

• Velocity

In order to retrieve V * in physical units, we can re-write Eq.5.31 as

V * = 2GM ν 2 r * ≈ 106.8 km s -1 .
(5.36)

•

Mass flux

In order to estimate the mass loss and accretion rates, we need the conversion factor for the mass flux. According to Sauty & Tsinganos (1994), we can write the free function Ψ A (α) assuming the Alfvén density, ρ * , as

Ψ A (α) = 4πρ * V * B * √ 1 + δα .
(5.37)

RESULTS

The poloidal mass flux can be determined through the stream function Ψ. Therefore, from the last equation, we can write the following expression where the mass is conserved (5.38) According to Sauty & Tsinganos (1994), the mass loss rate Ṁ per each stellar hemisphere is given according to the equation (5.39) where α out is the dimensionless magnetic flux value for the last field line connected to the star. In other words, α out corresponds to the last field line of the stellar jet.

Ψ = 2πρ * r 2 * V * α 0 √ 1 + δα ′ dα ′ .
Ṁ = S ρV p • dS = πρ * r 2 * V * αout 0 √ 1 + δα ′ dα ′ ,
By integrating the previous expression, the mass loss rate can be written as,

Ṁ = πρ * r 2 * V * 2 3δ
(1 + δα out ) 3/2 -1 .

(5.40)

As in Sauty et al. (2011), we assume a stellar radius, stellar mass and mass loss rate of 2.4 R ⊙ , 1.5 M ⊙ and 3.1×10 -9 M ⊙ yr -1 , respectively. Consequently, the conversion factor for the mass flux will be given by

πρ * r 2 * V * = 3δ Ṁ 2 (1 + δα out ) 3/2 -1 ≈ 3.1 × 10 -9 M ⊙ yr -1 .
(5.41)

• Density From Eq.5.41 we can easily derive the conversion for density as it follows

ρ * = Ṁ πr 2 * V * ≈ 2.4 × 10 -15 g cm -3 .
(5.42)

We use these conversion factors to rescale the simulations for other stars, besides RY Tau, as discussed below in Sect.5.7.2.3.

Results

Preliminary tests

First, we perform several simulations with different combinations of multiplying factors for the velocity and the density inside the closed magnetospheric region. Second, and taking into account the previous combinations, we include in the simulations dead zones with different sizes and a Keplerian rotation profile in the disk wind region. We also test different density thresholds to prevent the crash of the simulations and verify that they do not affect the end result of the simulation.

A complete list of all the tests performed can be found in Table C.1. In this table, Tests A, B, C, C+, D and D+ are our best simulations and we analyse them in detail below.

What distinguishes one set of tests from another is the combination of multiplying factors for density and velocity. For instance, for all tests C we multiply density and velocity by a factor of 5 and -1.5, respectively. While for tests D we choose for these two quantities factors of 10 and -2.0, correspondingly. Additionally, we list the total time needed to run each simulation and the status of the test: Finished, Cancelled, Crashed or Terminated.

Finished corresponds to a simulation that ran until 100 PLUTO time units. Cancelled corresponds to a simulation that was intentionally interrupted by the user. Crashed concerns a simulation that stopped at PLUTO time 0. Terminated regards a test that PLUTO stopped running after PLUTO time 0. In the following columns we show the multiplying factors imposed for density, ρ, and velocity, V . We also identify the simulations, which include a dead zone, DZ, and corresponding α max to define the accreting region, Keplerian rotation, KR, and a density threshold, DT.

The criterion to make the selection of the best simulations rely on the stability of the test. A simulation with a stable configuration is able to run completely without crashing due to small time steps. When PLUTO is not able to converge to a value of density, pressure, velocity or magnetic field, the dt will decrease in order to converge to a value. If it is still not enough, PLUTO will systematically reduce the time step until that dt is so small that PLUTO by itself stops the simulation. In many of our tests, the simulations stop due to very small density values. Hence, the density thresholds are, in some tests, a key-factor to allow the simulation to evolve until the end of the running time.

Some of the preliminary tests can be found in Fig. 5.3. We show TestC_03 in plots (a) and (b), where we have a considerable dead zone defined with α max = 1.0, which will imply a small accretion column. We have not implemented here a Keplerian rotation nor a density threshold. As the simulation evolves, the thin column disrupts. After the disruption event, the simulation conserves quite a steady configuration until the end of the running time.

A similar case can be found in TestC_08, shown in plots (c) and (d), still with no Keplerian rotation in the disk region, nor a density threshold. Although the size of the dead zone is slightly decreased, by setting α max = 1.05, the accretion column is not strong enough to avoid a disruption. This was one of the many simulations that did not went until the end. Simulations with big dead zones, imply weak accretion columns that can easily break throughout the simulation. This implies the cease of accretion and only the disk wind remains. These simulations could be an illustrative case of what happens during the transition of a CTTS to a WTTS evolutionary stage. This could be the situation of JW847, a low-mass star discussed previously in Chapter 3. When a YSO is transiting from

Class II to Class III, the circumstellar disk starts to disperse and there is less and less material to be accreted by the star. Eventually, the accretion columns will weaken until they disrupt and accretion is ceased.

Later, we induce the creation of a smaller dead zone in TestC_12, as shown in plots (e) and (f), where we set α max = 1.4. This leads to the creation of a wider accretion column 5.7. RESULTS that does not disrupt. This structure is pushed down by the presence of a low density corridor on top of the column. At a certain point, the densities reach such small values that lead to very small time steps and the simulation stops.

Plots (g) and (h) correspond to TestC_14, where we implement a Keplerian rotation in the disk wind region and we define α max = 1.7. Similarly to TestC_12, the accretion column is strong enough to avoid a disruption event. This was one of the tests where we start to implement the density threshold, but we detected later on that it was not working at all because the INTERNAL_BOUNDARY parameter was not enabled in the definitions.h file.

This parameter allows the user to control the solution inside the computational domain.

Nevertheless, we got a complete run for this test with a quasi-steady configuration.

Among all the simulations performed, we got interesting perturbations in some of the tests. One of those cases is TestD_02_04, where we start with a small dead zone, set by α max = 1.7, and we include a Keplerian rotation and a density threshold. This configuration did not last longer than 1 PLUTO time, and in its last frame shown in Fig. 5.3j, we see the formation of shear instabilities, probably due to a velocity shear produced in the frontier between accretion and outflow regions.

Another interesting simulation is TestC_07, where we have defined α max = 1. & Ferreira (2013) or even the conical winds produced in Romanova et al. (2009) tests.

Nevertheless, we show below few remarkable stable solutions that represent a new set of solutions without this kind of outflowing activity (Tests C and C+).

We perform some additional runs through the sets of tests E, F, G and H, listed in Table C.1. In these simulations we explored not only higher multiplying factors for density and velocity, but also the implementation with dead zones of different sizes. More than a half of those simulations did not go beyond 1 PLUTO time unit and the ones that did showed some issues related with sharp decreases in the density values and/or additional perturbations. For all of these reasons, we do not analyse these tests in detail. 5.7. RESULTS

Mass fluxes

In this chapter we analyse the simulations in terms of mass flux variations, namely mass loss ( Ṁloss ) and accretion rates ( Ṁacc ). In Fig. 5.8 we plot these two last quantities between -8.4 and 10 -7.3 M ⊙ yr -1 , which is in agreement with the typical values found for RY Tau around 10 -7.4±0.4 M ⊙ yr -1 (e.g. Hartigan et al. 1995;Calvet et al. 2004;Mendigutía et al. 2011;Costigan et al. 2014). Concerning the stellar mass loss rates, we get approximately the same mean value in time for most of the simulations of 10 -8.6

M ⊙ yr -1 at MF Jet. This value does not differ too much from the one fixed initially by the analytical solution, 10 -8.5 M ⊙ yr -1 , and agrees with the range of values found in the literature around 10 -8.0±0.9 M ⊙ yr -1 (e.g. Kuhi 1964;Edwards et al. 1987;Hartigan et al. 1995;Gómez de Castro & Verdugo 2001;Agra-Amboage et al. 2009;Skinner et al. 2018).

RY Tau is a CTTS known for its variability. As we saw already in the previous chapter, this star has epochs of enhanced outflow activity (Petrov et al. 2019), which support the high variability of the Ṁloss measured along the years.

We can confirm through Fig. At the moment, it is not possible to achieve a simultaneous agreement among all the parameters for any CTTS. One possibility to extend the analytical solution used in the simulations to other range of stellar radius and masses is to re-iterate the model parameters of Sauty et al. (2011) according to the stellar parameters of each star. This way, each personalized solution should be better adjusted for each YSO. Nevertheless, we can have a better agreement with the observations if we take into account the uncertainties of the observed quantities, but we would always have a problem in order to fit the rotational velocities.

Discussion

Preliminary tests

The preliminary set of simulations shows us that the α max parameter, needed to define the accretion columns, needs to be high enough to avoid the disruption of the funnel flow. On one hand, when α max < 1.4, the accretion columns are very thin and are easily disrupted.

On the other hand, when α max ≥ 1.4, the funnel flow is thick enough to resist against possible outflowing events from the star.

The weak accretion columns generated through α max < 1.4 could be representative cases of the transition phase from a Class II to a Class III object. CTTS are Class II objects, which are actively accreting from their disks. As soon as the disk starts to disperse, due to either photoevaporation, planet formation or even interaction with other stars, the lack of material should lead to the weakening of the funnel flow and, consequently, to the cease of accretion activity. At this stage we have a WTTS, which corresponds to a Class III object.

Although the initial goal of this set of simulations was to recreate the circumstellar environment of an accreting star, it would be interesting to extend and improve these simulations to study in detail the transition phase between Class II and Class III objects.

Selected tests

In the literature we can find many values for the mass loss and accretion rates determined with different methods along the years for RY Tau. Concerning the mass accretion rates for this star, the values vary from 10 -7.7 to 10 -7.0 M ⊙ yr -1 (Hartigan et al. 1995;Calvet et al. 2004;Mendigutía et al. 2011;Costigan et al. 2014), while the mass loss rate oscillates between 10 -8.8 and 10 -7.1 M ⊙ yr -1 (Kuhi 1964;Edwards et al. 1987;Hartigan et al. 1995;Gómez de Castro & Verdugo 2001;Agra-Amboage et al. 2009;Skinner et al. 2018).

The mass loss rates for all of the tests performed do not deviate significantly from the initial value of 10 -8. the ratio for the same star is 0.06. When looking to Test C, C+, D and D+, these simulations show ratios of 0.12, 0.22, 0.05 and 0.11, respectively, which are consistent with the previous references. As expected, due to the lower mass accretion rates measured for Tests A and B, the mass loss-accretion ratio is higher than the observed values.

The maximal accretion velocities measured for Tests C+, D and D+ are within the range of velocities mentioned by Edwards et al. (1987), between 200 and 300 km s The remarkable and unexpected steadiness of Test C may be related to the presence of a low static force free region. In this region, the magnetic pressure dominates over the plasma pressure and leads to the formation of a low density channel (see Fig. 5.4o) with no evidence of outflowing material. Conversely, Test D and D+ show a more perturbed configuration with magnetospheric ejections released by the disconnection of the magnetic field lines, and boosted by the increase of the accretion rate. These results somehow resemble the time-dependent MHD simulations performed by Zanni & Ferreira (2013), which focus on magnetospheric ejections resulting from the interaction between the accretion disk and the dipolar magnetosphere of the star. Our simulations seem to be more stable than the ones in Zanni & Ferreira (2013) and we achieve a steady configuration sooner, around 2.5 stellar rotations in the case of Test C. Nevertheless, the mass loss rate of the magnetospheric ejections in our simulations is not as strong as the ones measured in Zanni & Ferreira (2013). While in our simulations we reach, at most, a mass flux for the magnetospheric ejections of 7.4% Ṁacc , Zanni & Ferreira (2013) can go up to 18% Ṁacc .

The steadiness of Test C and C+ contrasting with the perturbed configuration of Test D and D+ suggests two possible behaviours for RY Tau. Previously in Chapter 4, we analysed and discussed simultaneous spectroscopic and photometric observations of RY Tau carried for 5 years, and we found that RY Tau has a bimodal behaviour (Petrov et al. 2019). This monitoring of RY Tau showed that most of the time the star shows a variable outflow, although a period of quiescence was also detected.

Conclusions

In this chapter, we used the analytical solution proposed by Sauty et al. (2011) in 2.5D

MHD simulations based on the pressure driven outflow model of Sauty & Tsinganos (1994).

In order to recreate the accretion environment of RY Tau, we started by performing initial tests where we imposed accretion inside the entire closed magnetospheric region. In a second stage, we made more realistic simulations by adding a dead zone and a Keplerian rotation outside the anchor point of the accretion column.

In a set of preliminary tests, we got solutions that can be useful to explain the transition from CTTS to WTTS evolutionary stage. It could be that, as the material in the disk starts to disappear, the accretion column gets thinner and weaker. This will lead to the disruption of the accretion funnel, accretion activity is ceased, and only outflows corresponding to the stellar jet region and the disk winds remain.

The increase of velocity and density from Test A to Test D+ enables to obtain higher accretion rates compatible with the observed ones for RY Tau. Furthermore, when we compute the ratios between ejected and accreted material, the values of Tests C, C+, D and D+ are quite consistent with the literature and supporting the observational evidence that accretion is dominant over ejection. Nevertheless, it seems that velocity and density cannot be increased arbitrary in the simulations. In other words, there is a correspondence between the combination of multiplying factors for velocity and density. If these two 5.9. CONCLUSIONS parameters are increased randomly, the simulation can evolve towards a more perturbed configuration.

Additional perturbations to the system were observed after adding a dead zone and implementing a Keplerian rotation in the circumstellar region. Nevertheless, Tests C+ and D+ represent the best configurations reached so far.

We have also managed to achieve a steady configuration for the first time with Test C in 2. The re-scaling of the outputs of Tests C and D is quite limited. In order to achieve a better match between the simulated values and the ones from the literature, there should be an analytical solution iterated for each YSO.

6

Conclusions

In this chapter, the main conclusions of this study on low-mass young stellar objects are summarized. It is highlighted not only what has been done, but also some limitations of this work and what can be done to overcome them.

What has been done

The derivation of stellar parameters for Classical T Tauri stars spectra from the Utrecht Echelle Spectrograph, with ARES and TMCalc, was carried out and is described in Chapter 2. We have performed some preliminary tests for a main-sequence star in which a continuum excess emission, veiling, is added to its spectrum. Our conclusion is that ARES and TMCalc cannot be used to derive metallicity for high veiled spectra. Higher veiling values make the photospheric lines appear less deep and hard to identify in spectra with lower signal-to-noise ratios. In order to ARES estimate properly the equivalent widths and to TMCalc compute realistic metallicities in PMS stars, the spectra need to be previously corrected from veiling. Otherwise, the equivalent widths will be always underestimated since the photospheric lines will appear less deep due to this excess emission. Concerning the effective temperature, the preliminary tests have shown that is possible to determine it with those two codes, but we need better SNR and likely higher resolution to get good results. The poor results retrieved for the UES data are related with the small SNR of the spectra. Whenever the photospheric lines are too weak the noise will distort their profiles.

From the forbidden line of [OI] at 6300 Å, available in the spectra of 16 YSOs, the corresponding terminal velocities of the jet and the mass loss rates were derived. Since the profiles were not corrected with photospheric templates, it is very likely that the equivalent widths measured for [OI] are underestimated. In general, the terminal velocities range from a few tens to a few hundred of km s -1 . DG Tau and RW Aur show the highest velocities with 352 and 335 km s -1 , respectively. The low-velocity and high-velocity components are M ⊙ yr -1 , but they seem to be overestimated relatively to the values of Hartigan et al. (1995). The two outstanding mass loss rates belong to DG Tau and RW Aur with values of 10 -6.1 and 10 -6.6 M ⊙ yr -1 , respectively. The observed differences between the values in this work and the ones from the literature could be due not only to the absence of a photospheric correction of the [OI] line, but also to the strong variability in this emission line at different observing epochs.

In Chapter 3, the accretion activity in five likely very low-mass YSOs belonging to the Orion Nebula Cluster was studied. This has been done by combining X-Shooter data with the available photometry, which also allow us to infer about the presence of circumstellar disks. First, we have started by characterizing the stars in the sample through the corresponding stellar parameters. Second, accretion was quantified through the accretion tracers available from ultraviolet to near-infrared wavelengths. Third, the presence of circumstellar disks was explored through archival photometry.

From the five objects studied in this work four of them are accreting. Furthermore, three out of these four accretors are very low-mass stars with stellar masses below 0.25M ⊙ .

JW647, besides being the YSO with the highest accretion rate of the sample, shows evidence of hosting a pre-transitional disk. From the spectral energy distributions for JW180, JW293 and JW847, it seems that these stars host a transitional disk. JW847 shows no evidence of accretion activity, but seems to host the youngest transitional disk of the sample with an age of only 1 Myr.

In Chapter 4, was studied the spectroscopic and photometric variability spanning over 5 and 3 year period of the CTTSs RY Tau and SU Aur, respectively. The V-magnitude changes approximately 2 orders of magnitude in both targets and the large variations in photometry are related with higher variability of the Hα emission line. In addition, the brightness variability is related with variations in the circumstellar extinction. The presence of strong P Cygni profiles in both stars suggests that these YSOs are experiencing periods of enhanced outflow activity. Although irregular variability is common in both stars, we have found quiescent phases for RY Tau and SU Aur during the period 2015-2016 and 2016-2017, respectively In RY Tau, the outflow activity is correlated with an increase of stellar brightness. One of the plausible scenarios discussed for this object is that, due to the high inclination of the system, during an epoch of enhanced outflow activity, the dusty disk wind is blown up and the star appears brighter. In SU Aur, was found the opposite scenario where enhanced outflows are connected with a decrease of the stellar brightness. Although we cannot make any robust conclusion on this YSO, it could be that if the magnetosphere of the star is indeed tilted relatively to the rotation axis, the outflow will sweep the dust from the inner region of the disk towards our line of sight. In view of this, the increase of the circumstellar extinction will make the star appear fainter. The periods of enhanced outflow activity do not seem to be correlated with an increase of the mass accretion rates in both RY Tau and SU Aur. This is supported by previous veiling measurements that indicate the continuum CHAPTER 6. CONCLUSIONS excess is very weak. We conclude it is very likely the variability observed for these YSOs is due to circumstellar extinction rather than other phenomena occurring at the stellar surface.

In Chapter 5, were performed 2.5D simulations of the circumstellar environment of RY Tau using the analytical solution for T Tauri stars proposed in Sauty et al. (2011).

Since the simulations are based on the pressure driven model of Sauty & Tsinganos (1994), accretion was implemented in the closed magnetospheric region.

As soon as we have retrieved the most stable tests, a dead zone was included as well as a density threshold and a Keplerian rotation in the disk wind region. Among our simulations, there are solutions where the dead zones are too big and accretion columns disrupt. Although this point needs further analysis and we cannot make strong conclusions at the moment, this could somehow illustrate the transition phase of a class II to a class III object, in which the circumstellar disk starts to disperse and accretion activity ceases.

Limitations and perspectives

ARES and TMCalc are useful codes regularly used for main-sequence stars to derive effective temperature and metallicity. Although it cannot be used to the derive the metallicity in PMS stars, as we have seen in Chapter 2, it can be adapted. The adaptation should include, at least, two points. First, veiling should be previously measured and corrected for PMS spectra before being delivered to ARES. But in order to measure veiling we need to know the effective temperature and log g of the target. One possibility could be to develop an iterative method, which would converge to a solution. Second, it could be that the current line list optimized for main-sequence stars and used by ARES needs to be adjusted for PMS stars. Therefore, it would be worth testing if these two implementations could improve significantly the results or not.

In Chapter 3, we have mentioned that the accretion criterion from White & Basri (2003), that has been widely used in the study of YSOs, is not well suited for stars in the very-low mass range. Since there is this new generation of instruments that are able to retrieve data from fainter sources, it could be useful to work on an accretion criterion with a suitable threshold for stars in the very-low mass range. In view of this, such tool could provide to the scientific community a fast and trustworthy way of classifying these objects as accretors on non-accretors.

In Chapter 5, we have attempted extending Tests C and D to other Classical T Tauri 6.2. LIMITATIONS AND PERSPECTIVES stars studied in Chapter 2. We conclude that the re-scaling is very limited, in the sense that is very hard to find an agreement among all the derived parameters with the ones available in the literature. In order to retrieve suitable results, the parameters of the model derived in Sauty et al. (2011) should be re-iterated according to the corresponding stellar parameters of each individual star.

Taking all into account, this thesis shows us the relevance and interconnectivity of the different subjects studied throughout the chapters, but can also give us some perspectives on what can be done in the future. Observations of CTTSs from the ultraviolet to the near-infrared and long-term monitoring of CTTSs are key-factors not only to understand the activity and dynamics of the circumstellar medium, but also to retrieve stellar and activity parameters useful to constrain models and numerical simulations. Observations in the NIR using high-resolution spectroscopy will be important to analyse regions with higher extinction, but also to unravel and characterize the circumstellar disks of YSOs.

Another challenging topic in star formation is probably the evolution of angular momentum in low-mass YSOs. On one hand, there are defenders of the disk-locking theory.

On the other hand, there are more recent studies suggesting that outflows can have a significant role in decelerating these objects. To make matters worse, very little is known about angular momentum removal mechanisms operating in very-low mass stars. In order to disentangle all the mysteries, a more quantitative analysis in such objects would be useful to confirm if either disk-locking or any other angular momentum evolution model fits for such objects in the very low-mass range.

Finally, and concerning the numerical simulations, there are some extensions discussed, namely the inclusion of an accretion disk and a disk wind. A self-similar disk wind solution that can be used is the one from Vlahakis et al. (2000), which is based on the Blandford & Payne (1982) model for the magneto-centrifugal acceleration of a disk wind.

This solution can be implemented in the disk wind region as initial condition in the current PLUTO simulations.

2. 1

 1 Stellar parameters available in the literature . . . . . . . . . . . . . . . . . . 20 2.2 Stellar parameters derived with ARES and TMCalc . . . . . . . . . . . . . . . 25 2.3 Stellar parameters derived with TMCalc for HD4208 . . . . . . . . . . . . . . 29 2.4 Veiling and projected rotational velocity computed for HD4208 . . . . . . . 32 2.5 Comparison between the veiling determined in this study and the one in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 Outflow parameters derived for the targets . . . . . . . . . . . . . . . . . . . 41 3.1 Stellar parameters available in the literature for the ONC targets . . . . . . 48 3.2 Observation log of VLT/X-shooter spectra . . . . . . . . . . . . . . . . . . . 48 3.3 Observation log of VLT/X-shooter standard tellurics . . . . . . . . . . . . . 49 3.4 Spectral indices used to determine the spectral type of the targets . . . . . . 51 3.5 Stellar parameters derived for the ONC targets . . . . . . . . . . . . . . . . 51 3.6 List of templates selected for this work. . . . . . . . . . . . . . . . . . . . . 52 3.7 Coefficients needed to determine the mass accretion rates . . . . . . . . . . 59 3.8 Logarithmic mass accretion rates derived for the ONC targets . . . . . . . . 60 4.1 Details on the telescopes/instruments for the spectroscopic observations . . 68 4.2 Variability of the V-magnitudes for RY Tau . . . . . . . . . . . . . . . . . . 69 4.3 Variability of the V-magnitudes for SU Aur . . . . . . . . . . . . . . . . . . 69 4.4 Correlation coefficients between stellar V-magnitude and other parameters obtained from the Hα emission line for RY Tau . . . . . . . . . . . . . . . . 80 4.5 Correlation coefficients between stellar V-magnitude and other parameters obtained from the Hα emission line for SU Aur . . . . . . . . . . . . . . . . 80 5.1 Configuration of the simulations. . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 Re-scaling the simulations to other CTTSs . . . . . . . . . . . . . . . . . . . 119 B.1 Observational log for RY Tau spectra . . . . . . . . . . . . . . . . . . . . . . 147 B.2 Observational log for SU Aur spectra . . . . . . . . . . . . . . . . . . . . . . 151 C.1 Complete list of simulations performed with PLUTO . . . . . . . . . . . . . . 162 1 Introduction Les gens ont des étoiles qui ne sont pas les mêmes. Pour les uns, qui voyagent, les étoiles sont des guides. Pour d'autres elles ne sont rien que de petites lumières. Pour d'autres, qui sont savants, elles sont des problèmes.

Figure 1 . 2 :

 12 Figure 1.2: Hertzprung-Russel diagram for TTSs in the Taurus-Auriga molecular cloud. The solid lines correspond to the evolutionary tracks fromIben (1965) andGrossman & Graboske (1971), for pre-main sequence stars, along with the corresponding stellar masses in M ⊙ . The heavy solid line represents the birthline ofStahler (1983).From Stahler (1988).

Figure 1 . 5 :

 15 Figure 1.5: Illustration of P Cygni (left) and inverse P Cygni (right) profiles. From Reipurth et al. (1996).

Figure 1 . 13 :

 113 Figure 1.13: Outflow mechanisms in low-mass stars. From Romanova & Owocki (2015).

Figure 2 . 4 :

 24 Figure 2.4: Illustration of the conservation of the equivalent width with stellar rotation in theoretical line profiles. All the lines have the same equivalent width. The labels on the profiles correspond to v sin i in km s -1 . From Gray (2005).

CHAPTER 2 .

 2 DERIVING STELLAR PARAMETERS FOR CTTSS

  . The effective temperature (T temp eff ) and corresponding surface gravity (log g) of the best fitted template are also shown. The minimized values for the projected rotational velocity (v sin i) and veiling measured at 6263 Å (r 6263 ) are also listed with the corresponding errors. Finally, in the last column we show the χ 2 values of the best fit for each CTTS. The corresponding plots for each target can be found in Fig.A.1 in Appendix A. CHAPTER 2. DERIVING STELLAR PARAMETERS FOR CTTSS important, and by using the wrong fitted template the result will not correspond to the real value.

  sions. The plots for DF Tau and RW Aur have more structures, showing an emission with blueshifted and redshifted absorptions in Fig.2.11d and 2.11m, respectively. Similar profiles for the same targets can be found inHartigan et al. (1995) and more recently inSimon et al. (2016), for DF Tau, and inAlencar et al. (2005) andChou et al. (2013), for RW Aur.

  [START_REF] Rio | [END_REF] compared extinction estimates and concluded that R V = 5.5, within the CHAPTER 3. ACCRETION AMONG YSOS IN THE ONC in the optical waveband of the spectrum of each target. The indices are based on ratios of average fluxes and rely upon the strength of specific molecular lines that are sensitive to temperature. For the late M-type stars, we used the spectral indices from Riddick et al.

  (1) Gaia Collaboration et al. (2016, 2018); Luri et al. (2018); (2) Manara et al. (2013); (3) Manara et al. (2017).

  5 we list the spectral types derived with the spectral indices from the following works, Riddick et al. (2007) (RRL07), Jeffries et al. (2007) (J07) and Herczeg &

Figure 3 . 4 :

 34 Figure 3.4: Hertzsprung-Russel diagrams using (a)Siess et al. (2000) and (b)Baraffe et al. (2015) evolutionary tracks and isochrones. In plot (a), we show the evolutionary tracks from 0.2 to 1.8 M ⊙ (dashed lines) and the isochrones corresponding to 1, 2, 3, 4, 5 and 10 Myrs (solid lines). In plot (b), we show the evolutionary tracks from 0.15 to 1.4 M ⊙ (dashed lines) and the isochrones corresponding to 1, 2, 3, 5 and 10 Myrs (solid lines). The circles correspond to the values determined in this work and the squares to the values ofHillenbrand (1997), rescaled to the distances derived from the Gaia DR2 parallaxes.

Figure 3 . 9 :

 39 Figure 3.9: Spectral energy distributions for the ONC targets. The spectra of the stars are shown for different wavebands: ultraviolet (blue), visible (green) and infrared (red). The grey line corresponds to the BT-Settl synthetic spectra from Allard et al. (2012) with effective temperatures of 3100, 3200, 3700, 4200 and 3200 K (for plots a, b, c, d and e, respectively), log g = 4.0, solar metallicity and null chemical index. The red dots correspond to the available photometry at Vizier(Ochsenbein et al. 2000).

4

  Spectroscopic and photometric variability in CTTSsRY Tau and SU Aur are two CTTSs known for their irregular spectroscopic and photometric variability. The brightness variability of CTTSs can be explained through different physical processes, namely starspots, irregular accretion and star obscuration by circumstellar dust clouds (e.g.Petrov et al. 1999).

  et al. (2019). The V-magnitudes we use are listed in Tables B.1 and B.2 with the corresponding error and source. For RY Tau the magnitudes in the V-band vary from 9.71 to 11.65 between 2013 and 2018, while for SU Aur range between 9.15 and 11.50 between 2015 and 2018, as listed in Tables 4.2 and 4.3, respectively.

  figure for each observational season in Fig.4.3 and 4.4 for RY Tau and SU Aur, respectively. In Fig.4.3 for RY Tau, there is always a positive correlation over the FAP level at 0.1%, peaking between -200 and 0 km s -1 and linked with the blue part of the Hα emission profile, where we have an absorption feature, except for the 2015-2016 season. The confident correlations for the 2013-2014 and 2014-2015 periods show the highest correlation values. A positive correlation means decrease of line intensity with increasing brightness of the

CHAPTER 4 .

 4 SPECTROSCOPIC AND PHOTOMETRIC VARIABILITY IN CTTSS measure the width of the Hα line at 10% of the maximum intensity, Hα10%, and the mass accretion rates, Ṁacc , derived with the empirical relation of Natta et al. (2004) expressed by, log Ṁacc = -12.89(±0.3) + 9.7(±0.7) × 10 -3 Hα10% , (4.1)

  .5, we show the computed Pearson correlation coefficients for each individual epoch and taking into account all the seasons. In the top row of Fig.4.9, we compare the EQW Hα with the stellar brightness. For RY Tau in Fig.4.9a, the EQW Hα increases with decreasing stellar brightness. Although the correlation coefficient is rather low when assuming the complete sample, 2013-2014 (magenta circles) and 2017-2018 (blue inverted triangles) present strong correlation with coefficients of 0.8 and 0.7, respectively.

  Fig.B.1 and B.3 for RY Tau and SU Aur, respectively. The significant peaks at a FAP of 0.5% of the corresponding periodograms are shown in Fig.B.2 and B.4 for both YSOs. In Fig.B.1a we can see the power spectrum for RY Tau for season 2013-2014 with more peaks than the one considering all the observational epochs from 2013 to 2018. If we consider only the values of the power spectrum at a FAP of 0.5%, as shown in Fig.B.2a,

  figure, the peaks spread from shorter to longer periods, starting around 2.5 days and going beyond 10 days. The intensity of the peaks decreases in the 2016-2017 epoch, as we show in Fig.B.4b. This season corresponds to the quiescent epoch of SU Aur, where the blueshifted absorption in Hα almost vanished. Although the position of the peaks in the power spectrum is varying significantly, there is always at least one peak close to the 3 days period around 150-200km s -1 . In the literature, Johns & Basri (1995b) plotted a similar 2D periodogram in velocity for the power spectrum for the Hα emission of SU Aur. The most intense peaks correspond to periodicities of approximately 3 and 8 days. The 3 day period in Hα is centred between -200 and -150 km s -1 . The periodicity of 3 days is also found in the power spectra in velocity of the Hβ emission line for the same star centred at -150 and 150 km s -1 . Finally, in Fig.B.4c we can see peaks with periodicities higher than 10 days present at both blue and red sides of the Hα profile.

  .12) 5.3. THE ANALYTICAL SOLUTION AND THE INITIAL SETUP where the cylindrical cross section of a flux tube is expressed by G 2 (R) and ̟ corresponds to the cylindrical radius given by ̟ = √ αr * G = r * R sin θ .(5.24)

  4, and we have not imposed a Keplerian rotation nor a density threshold. The accretion column shown in plot (k) develops a perturbation seen in plots (m) and (o), similar to a vortex.Finally, TestF_04 shown in plots (l), (n) and (p) has the formation of huge outflowing structures similar to the coronal mass ejection we see in the Sun. This was a result of assuming the multiplying factors of 15 and 1.8, for density and velocity, respectively, as well as α max = 1.6, Keplerian rotation in the disk and a density threshold. Only this last test is comparable to other simulations as the magnetospheric ejections simulated in Zanni

2 Figure 5 . 3 :Figure 5 . 3 :Figure 5 . 4 :Figure 5 . 4 :Figure 5 . 4 :Figure 5 . 5 :Figure 5 . 5 :Figure 5 . 5 :Figure 5 . 6 :

 2535354545455555556 Figure 5.3: Density plots for some preliminary tests with dead zones. Plots (a) to (p) represent the logarithmic density maps in PLUTO units. The velocity vectors are shown through the black arrows and the magnetic field lines are represented by the solid white lines. The distances in the vertical (z) and horizontal (̟) axis are represented in astronomical units, while the time is in t pluto . The caption for each plot mentions the multiplying factors for velocity, V, density, ρ, the parameter responsible for defining the last closed magnetic field line, α max , and the stellar rotation period, P * .

Figure 5 . 7 :

 57 Figure 5.7: Mass flux plots for Test D+. Plots (a) to (f) represent the logarithmic maps in PLUTO units. The velocity vectors are shown through the black arrows and the magnetic field lines are represented by the solid white lines. The distances in the vertical (z) and horizontal (̟) axis are represented in astronomical units. The plots refer different PLUTO time units and the corresponding stellar rotation period, P * , is mentioned in the caption for each plot.

30 and 100

 100 PLUTO time units for the best simulations. The results for Tests A, B, C and D are represented through the black lines, while Tests C+ and D+, which include a dead zone, a Keplerian rotating disk and a density threshold, are represented with the red lines. The blue vertical lines represent the times used to plot Fig.5.4 and 5.5. After near 30 PLUTO time units, or 3.6 stellar rotations, the simulations relax to steady (Test C and C+) or quasi steady states (Test A, B, D and D+) and we measure the mass loss and the accretion rates ( Ṁloss and Ṁacc , respectively). As illustrated in Fig.5.9, the mass fluxes are measured for each PLUTO time in two regions, the stellar jet region (MF Jet) and the closed magnetospheric region (MF Mag). When considering a spherical shell of 0.02 AU, we have the MF Jet at the stellar jet region (in blue) and the MF Mag at the closed magnetospheric region (in red). The mass fluxes were derived by integrating ρV p across the open magnetic field lines of the stellar jet region, for Ṁloss , and across the roots of the closed magnetospheric field lines, for Ṁacc . The mean value in time for the accretion rates measured at MF Mag, vary between 10

  5.8 the conservation of mass flux for Test C and Test C+ for both stellar jet and accreting regions, which correspond to the simulations that reached a steady configuration. The remaining ones show a more oscillating behaviour, specially for Test D and Test D+ in which we detected the reconnection and disconnection of the magnetic field lines that go along the release of magnetospheric ejections into the interstellar medium. Although we do not plot it in the previous figure, we estimated the mass flux rate of the magnetospheric ejections for these two simulations and retrieved a value of 10 -9.1 and 10 -8.9 M ⊙ yr -1 for Test D and D+, respectively. This means that the MEs correspond to approximately 1.5% and 7.4% of the Ṁacc for Test D and D+, correspondingly. If we compare with other works, namely the one fromZanni & Ferreira (2013), their MEs present mass fluxes that can go up to 18% of the Ṁacc , where the accretion rate was measured at the stellar surface. Comparatively withZanni & Ferreira (2013), our simulations present much weaker outflows. The values corresponding to the mass loss in the MEs should strongly depend on the treatment of the dead zone. 5.8. DISCUSSION Tau and GM Aur have quite different values for the measured terminal velocity of the jet. Let us take the example of DS Tau. While the re-scale from Test C and D return a V term of 203 and 197 km s -1 , respectively, the measured velocity from the [OI] emission line in Chapter 2 returns a value of 46 km s -1 . Probably in some stars we could only trace the slow component in the [OI] line and this could explain some of the big discrepancies in velocity. Nevertheless, the v sin i estimated for the simulations has one of the most similar values with the literature, besides DR Tau. Conversely, the projected rotational velocities estimated for DF Tau and UY Aur are strongly different from the ones in the literature. Overall, the re-scaled rotation velocity is always underestimated comparatively to the literature. For most of the stars, the projected terminal velocity is overestimated in respect to the one measured from the forbidden line of [OI]. Concerning the mass accretion rates, they are quite difficult to match, with exception for GK Tau and GM Aur.

5 M

 5 ⊙ yr -1 from Gómez de Castro & Verdugo (2001). Concerning the accretion rates, Tests A and B show values that are lower than the observed ones, while Test C agrees with the value of 10 -7.7 M ⊙ yr -1 of Mendigutía et al. (2011) and Test D and D+ are within the range of values derived by Costigan et al. (2014), 10 -7.6 -10 -7.1 M ⊙ yr -1 . Ratios between mass loss and accretion rates for RY Tau were estimated by Agra-Amboage et al. (2009) varying between 0.02 and 0.4. According to Hartigan et al. (1995),

  -1 . In order to compare properly the terminal velocities of the jet, first we need to project in the line of sight the jet velocities measured in the simulations. We assume the inclination of 66 • for RY Tau, determined byIsella et al. (2010). When projecting the velocities, we retrieve values ranging from 137 km s -1 to 143 km s -1 . In Chapter 2, we derived a projected terminal velocity for the jet of RY Tau of 146 ± 10 km s -1 . Recently,Skinner et al. (2018) determined from the C IV line, the radial velocity for the blueshifted jet, for RY Tau, of 136 ± 10 km s -1 at 39 AU. This means that the values determined in both simulations and observations are quite consistent with the one determined bySkinner et al. (2018).

  The latest was observed for several months, in which this star got fainter and less active in outflowing activity. Conversely, periods of higher brightness (lower circumstellar extinction) of RY Tau are correlated with moments of increased outflow activity observed from the spectral profile of Hα. InPetrov et al. (2019) we suggested that these outflows could be sporadic magnetospheric ejections that modify the dusty disk wind geometry and, therefore, the brightness of the star and spectral footprint. What we propose is that the quiescent epoch of RY Tau could match the steady configuration observed in Test C or C+ and the active stage could fit the configuration of Test D or D+. We could suggest that the increase of the outflow intensity during the episodic plasma ejections is a consequence of an increase in accretion, as shown in Test D. Nevertheless, we saw previously in Chapter 4 that the mass accretion rates for RY Tau do not change significantly from one observational season to another, including the transition from the quiescent to the active regime. For such reason, what is triggering the enhancement of outflowing activity in RY Tau needs further research.

  5 stellar rotations, conversely to all previous simulations. Tests D and D+ present a more perturbed configuration with magnetospheric ejections propagating between the stellar jet and closed magnetospheric regions. However, the magnetospheric mass loss rate does not dominate over the stellar mass loss rate. Much higher accretion rates are needed to have a strong magnetospheric flow. The accretion velocities measured for Tests C, C+, D, and D+ seem to be in agreement with the literature, as well as the terminal velocities determined for the stellar jet.We suggest that the two behaviours observed for RY Tau inPetrov et al. (2019) could match the ones simulated in this study. Tests C and C+ could match the quiescent epoch of RY Tau, characterized by lower brightness, and Test D and D+ link with a more active stage characterized by enhanced outflow activity. For the latest, is still not clear from the observations, which mechanism is responsible for intensifying the outflow activity.

6. 1 .

 1 WHAT HAS BEEN DONE more easily identified in the spectrum of DG Tau, comparatively to the remaining stars of the sample. The mass loss rates vary in the expected range between 10 -9 and 10 -8

  There are remarkable steady configurations namely Tests C and C+, while in Tests D and D+ we have the release of outflows that resemble magnetospheric ejections propagating between the stellar jet and closed magnetospheric regions. Taking all into account, the mass fluxes, accretion velocities and terminal velocities measured for Tests C, C+, D and D+ are in agreement with the literature. Although these simulations are still missing a realistic accretion disk, it seems that we are on the right track towards the simulation of circumstellar environments of YSOs. We suggest that Test C and C+ could illustrate the quiescent period of RY Tau analysed in Chapter 4, while the active epochs could be represented by Tests D and D+ with enhanced outflow activity.

Table 2

 2

	.2: Stellar parameters derived with ARES and TMCalc. All the CTTSs are listed in the
	first column followed by the effective temperature available in the literature (T lit eff ), the one from the best fitted template (T temp eff ) and the one computed by TMCalc (T TMCalc eff

Table 2 . 3 :

 23 Stellar parameters derived with TMCalc for HD4208. The first column lists all the tests performed followed by the veiling values imposed at 4000 Å and 6500 Å. The reference values (Ref.) for the effective temperature (T eff ) and metallicity ([Fe/H]) fromSousa et al. (2008) were included, as well as the values computed in TMCalc with the corresponding number of line ratios used.

	Test	Veiling introduced 4000 Å 6500 Å	Ref.	T eff (K) TMCalc	Line ratios	Ref.	[Fe/H] (dex) TMCalc	Line ratios
	HD4208_no_veil HD4208_A HD4208_B HD4208_C HD4208_D HD4208_E HD4208_F	0.00 1.50 1.50 1.00 0.60 1.50 0.50	0.00 1.50 0.01 0.80 0.50 1.00 0.10	5599 ± 19 5676 ± 15 5687 ± 13 5676 ± 15 5682 ± 13 5681 ± 13 5684 ± 13 5675 ± 15	405 353 397 395 397 395 403	-0.280 ± 0.01 -0.254 ± 0.049 ... -0.322 ± 0.116 -0.714 ± 0.073 -0.603 ± 0.081 -0.762 ± 0.067 -0.387 ± 0.092	113 ... 105 49 72 13 102
	Since the metallicity of the star is determined from the average of individual iron
	abundances, it means that heavily veiled lines will be taken into account and the result
	should not be trustworthy. In order to check the values of the individual metallicities,
	we measured them in the artificially veiled spectra as a function of the corresponding
	wavelength of each line measured previously by ARES. If we consider the spectra of HD4208
	and add a constant veiling, we get the plot of metallicity for each measured line as shown
	in Fig.2.7a. In this figure, we cannot see any trend since the values are very dispersed.

Table 2 . 5 :

 25 Comparison between the veiling determined in this study (r 6263 ) and the one in the literature byHartigan et al. (1995) (r 5700 ) andSimon et al. (2016) (r 6300 ).

	Target	r 6263	r 5700 r 6300
	AA Ori AA Tau AS 353a BM And BP Tau BZ Sgr CI Tau CW Tau DF Tau DG Tau DI Cep DK Tau DL Ori DL Tau DQ Tau DR Tau DS Tau EH Cep GKT au GM Aur LKHA 191 0.36 ± 0.03 0.05 ± 0.02 0.13 ± 0.02 0.63 ... 3.00 ± 0.27 5.10 ... 0.08 ± 0.02 0.88 ± 0.04 0.61 ... 0.05 ± 0.03 1.37 ± 0.07 0.39 0.98 ± 0.05 1.70 0.82 ± 0.07 0.66 1.20 ± 0.08 3.00 ... 0.35 ± 0.02 0.25 ± 0.02 0.49 ... 3.00 ± 0.23 2.19 ± 0.14 1.10 0.00 ± 0.02 0.18 3.00 ± 0.00 9.20 1.38 ± 0.06 0.96 ... 0.44 ± 0.03 0.15 ± 0.03 0.23 0.32 ± 0.02 0.22 ... ... LKHA 330 1.14 ± 0.05 RW Aur 3.00 ± 0.42 1.80 RY Tau 0.02 ± 0.01 0.10 T Tau ... 0.27 ± 0.02 UY Aur 0.44 ± 0.03 0.35 UZ TauE 0.45 ± 0.04 0.73 ... V1079 Tau 0.19 ± 0.02 ... V1305 Ori 0.33 ± 0.03 ... V1980 Cyg 2.94 ± 0.21 ... V466 Ori 0.05 ± 0.02 ... V625 Ori 1.23 ± 0.07 ... V649 Ori 0.07 ± 0.02 ... V828 Cas 0.03 ± 0.02 WY Ari 0.64 ± 0.03 ...	... 0.00 ... ... 0.60 ... 0.60 1.50 1.60 1.00 ... 0.40 ... 1.00 ... 5.60 0.60 ... 0.10 0.60 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

Table 2 . 6 :

 26 Outflow parameters derived for the targets with [OI] 6300Å in emission. The dereddened magnitudes (R 0

Table 3 .

 3 1: Stellar parameters available in the literature for the ONC targets. We list the following parameters: name of the objects according toJones & Walker (1988) (JW) and the 2MASS(Cutri et al. 2003) nomenclature, the distances (d * ) estimated from the Gaia DR2 parallaxes, spectral types (SpT), radial velocities (RV) and projected rotational velocities (v sin i) available in the literature.

Table 3 . 2 :

 32 Observation log of VLT/X-shooter spectra. The objects name is followed by the corresponding right ascension (RA), declination (DEC), observation date and exposition time for each arm of the target spectra.

	-1 )

Table 3 . 3 :

 33 Observation log of VLT/X-shooter standard tellurics. The standard name is followed by the corresponding right ascension (RA), declination (DEC), spectral type (SpT) taken from Simbad, observation date, exposition time for the spectrum of the NIR arm and the corresponding target(s) to correct.

	Object	RA(J2000) DEC(J2000) SpT Obs. Date Exp. time (s) Target to correct
	Hip024618 05:16:48.40	-17:08:32.00	B2	2015-03-05	15	JW847
	Hip025869 05:31:21.00	-06:42:30.60	B3	2015-01-15	9	JW293
	Hip029417 06:11:51.80	-06:32:59.80	B2	2015-02-25	3	JW180
	Hip033703 07:00:08.10	-20:09:30.90	B3	2015-01-25	30	JW647+908

Table 3 . 5 :

 35 Stellar parameters derived for the ONC targets. The spectral types derived in this work through spectral indices of Riddick et al. (2007) (RRL07), Jeffries et al. (2007) (J07) and Herczeg & Hillenbrand (2014) (HH14) are listed, as well as the adopted one. The stellar parameters derived include effective temperature (T eff ), stellar luminosity (L

	JW	SpT derived in this work	T eff (K)	L * (L ⊙ )	R * (R ⊙ )	M * (M ⊙ ) Age (Myr) r 610nm BJ obs
		RRL07 J07 HH14 Adopted
	180 293 647 847 908	M5.0 M4.8 M3.2 ... M4.5	M5.1 M5.0 M4.8 M4.8 M0.6 M2.1 K6.6 K1.2 M4.5 M4.4	M5 M4.5 M1 K6 M4.5	3125 3197 3705 4205 3197	0.11 ± 0.05 1.12 ± 0.24 0.17 ± 0.04 3.53 ± 2.15 0.13 ± 0.05 1.17 ± 0.21 0.21 ± 0.04 3.14 ± 1.02 0.30 ± 0.12 1.32 ± 0.21 0.47 ± 0.07 3.26 ± 2.17 1.93 ± 0.78 2.62 ± 0.21 0.90 ± 0.13 1.03 ± 0.67 0.14 ± 0.06 1.21 ± 0.21 0.21 ± 0.04 2.99 ± 1.10	0.0 0.0 0.5 0.0 0.0	0.5 0.5 1.1 0.6 0.5

* ), stellar radius (R * ), stellar mass (M * ), age, veiling measured at 610 nm by J. F. Gameiro (r 610nm ) and the observed Balmer jump (BJ obs ).

Table 3 .

 3 8: Logarithmic mass accretion rates derived for the ONC targets in M ⊙ yr -1 , for each target and for different emission lines.

	Line	λ (nm) JW180 JW293 JW647 JW908
	H10	379.8	-10.2	-10.1	-8.8 *	-10.2
	H9	383.5	-10.3	-10.2	-8.8 *	-10.2
	H8	388.9	-10.2	-10.2	-8.7 *	-10.3
	Ca II (K)	393.4	-9.8	-9.8	-9.2 *	-9.7
	Ca II (H)	396.8	-9.6	-9.6	-9.2	-9.2
	H7 (Hǫ)	397.0	-10.3	-10.3	-9.0 *	-9.6
	He I	402.6	...	...	-8.7	...
	H6 (Hδ)	410.2	-10.2	-10.1	-8.7 *	-10.2
	H5 (Hγ)	434.0	10.2	-10.1	-8.7 *	-10.2
	He I	447.1	...	...	-8.8	...
	H4 (Hβ)	486.1	-10.3	-10.1	-9.1 *	-10.0
	He I	587.6	-10.1	-9.9	-8.3	-9.6
	He I	667.8	...	...	-8.6	...
	He I	706.5	...	...	-8.6	...
	Pa7 (Paδ)	1004.9	...	...	-8.6	...
	Pa6 (Paγ) 1093.8	...	...	-8.7	...
	Pa5 (Paβ) 1281.8	...	...	-8.0	...
	Br7 (Brγ)	2166.1	...	...	-8.3	...
	Mean		-10.1	-10.0	-8.6	-9.8

Note: (*) This emission line shows an Inverse P Cygni (IPC) profile.

  this work we gather spectral and photometric data from RY Tau and SU Aur, provided

by P. P.

Petrov and published in Petrov et al. (2019)

. For RY Tau, the sample gathers a long-term series of 127 reduced spectra collected in five observational seasons between 2013 and 2018. For SU Aur, we have 101 observations from three observational epochs between 2015 and 2018. For all the observational seasons we have access to photometric data for the targets from the Crimean Astronomical Station (CAS), Crimean Astrophysical Observatory (CrAO) and American Association of Variable Star Observers (AAVSO) 1 .

Table 4 . 1 :

 41 Details on the telescopes/instruments for the spectroscopic observations. The observatory/telescope acronym (see text) is followed by the diameter of the telescope, name of the instrument (whenever available), spectral resolution and the width of the slit/fibre entrance. In the CrAO and UrFU the instrument is an echelle spectrograph.

	Observatory/ Telescope diameter Instrument Spectral resolution Width
	Telescope	(m)			(arcsec)
	CrAO	2.6		27 000	2.0 a
	NOT	2.5	ALFOSC	10 000	0.5 a
	CAHA	2.2	CAFE	58 000	1.2 a
	TNO	2.4	MRES	19 000	2.0 b
	UrFU	1.2		15 000	5.0 b

Table 4 . 2 :

 42 Variability of the V-magnitudes for RY Tau. We list in the table the variance (σ 2 ), the maximum and minimum V-magnitudes followed by the amplitude of these two values for all the observational epochs and for each season.

		All epochs 2013-2014 2014-2015 2015-2016 2016-2017 2017-2018
	σ 2	0.13	0.07	0.12	0.04	0.03	0.08
	Max	11.65	11.05	11.65	11.24	11.34	11.20
	Min	9.71	9.71	10.04	10.34	10.53	9.88
	Max-Min	1.94	1.35	1.61	0.91	0.82	1.32

Table 4 .

 4

		All epochs 2015-2016 2016-2017 2017-2018
	σ 2	0.10	0.02	0.02	0.17
	Max	11.50	9.84	9.80	11.50
	Min	9.15	9.16	9.15	9.28
	Max-Min	2.35	0.68	0.66	2.22

3: Variability of the V-magnitudes for SU Aur. We list in the table the variance (σ 2 ), the maximum and minimum V-magnitudes followed by the amplitude of these two values for all the observational epochs and for each season.

Table 4 . 5 :

 45 Correlation coefficients between stellar V-magnitude and other parameters obtained from the Hα emission line for SU Aur. The parameters include the equivalent width of the Hα emission line (EQW Hα), the ratio between the equivalent width of Hα measured for the blue and red side of the profile (EQW blue Hα / EQW red Hα ) and the mass accretion rate ( Ṁacc ).

	2017-2018

Table 5 . 2 :

 52 Re-scaling the simulations to other CTTSs. In the first column are listed some of the targets from Chapter 2, followed by the rotational velocity re-scaled in this work (v sin i) and the one available in the literature (v sin i lit ), the terminal velocity re-scaled according to Test C (V term C ) and Test D (V term D ), and the one we measured in Chapter 2 from the [OI] emission line (V term ). The accretion ( Ṁacc ) and mass loss rates ( Ṁloss ) re-scaled for Tests C and D are listed, as well as the corresponding values available in the literature ( Ṁacc lit and Ṁloss lit ). In the last column can be found the corresponding references to the values taken from the literature.

	Star	v sin i	v sin i lit	V term	C	V term	D	V term	log Ṁacc

C log Ṁacc D log Ṁacc lit log Ṁloss C log Ṁloss D log Ṁloss lit

  Table C.1: (continued)

		Simulation ID TestC_15 Simulation ID	t f pluto 4 t f pluto	Elapsed time 4d:02h:19m:16s Terminated 5 Status ρ Table C.1: (continued) Elapsed time Status ρ	V -1.5 V	DZ? α max ? KR? Yes, 1.6 Yes DZ? α max ? KR?	DT? Malfunctioning DT?
		TestC_15_02 TestE_04	21.5 14d:05h:17m:41s Cancelled 13 5d:18h:25m:26s Cancelled	5 10 -1.5 -1.5	Yes, 1.6 Yes, 1.6	Yes Yes	Malfunctioning Yes, 0.065 < ρ <
		TestC_15_03 TestF_01	23.5 14d:04h:41m:19s Cancelled 1 20h:43m:02s Terminated 15 -1.8 5 -1.5	Yes, 1.6 Yes, 1.6	Yes No	Yes, ρ > 0.065 Malfunctioning
		TestC_15_04 TestF_02	36.5 13d:22h:56m:16s Cancelled 1 20h:29m:50s Terminated 15 -1.8 5 -1.5	Yes, 1.6 Yes, 1.6	Yes Yes	Yes, ρ > 0.065 Malfunctioning
		TestC_16 TestF_03	18 0.5	8d00h:40m:01s 01h:40m:41s	Cancelled Terminated 15 -1.8 5 -1.5	Yes, 1.1 Yes, 1.6	No Yes	Malfunctioning Yes, 0.25 < ρ < 100
		TestC_17 TestF_04	21 14	8d:00h:56m:06s 1d:09h:47m:30s Terminated 15 -1.8 Cancelled 5 -1.5	Yes, 1.1 Yes, 1.6	Yes Yes	Malfunctioning Yes, 0.065 < ρ <
		TestD TestG_01	100 0	0d:3h:30m:10s 00h:26m:05s	Finished Crashed	10 -2.0 30 -3.6	No Yes, 1.1	No No	No Malfunctioning
		TestD_01 TestG_02	2 0	04h:42m:39s 00h:26m:14s	Terminated 10 -2.0 Crashed 30 -3.6	No Yes, 1.1	No Yes	No Malfunctioning
		TestD_02 TestH_01	2 1	02h:26m:13s 01h:50m:39s	Terminated 10 -2.0 Terminated 7.5 -1.75	Yes, 1.7 Yes, 1.7	Yes Yes	Yes, ρ > 0.065 Yes, ρ > 0.065
		TestD_02_02 TestH_02	2 13	01h:44m:53s 5d:18h:08m:54s	Terminated 10 -2.0 Cancelled 7.5 -1.75	Yes, 1.7 Yes, 1.7	Yes Yes	Yes, 0.065 < ρ < 250 Yes, 0.065 < ρ <
		TestD_02_03 (Test D+) 100	2d:20h:13m:02s	Finished	10 -2.0	Yes, 1.7	Yes Yes, 0.065 < ρ < 950.6
		TestD_02_04	1	01h:03m:35s	Terminated 10 -2.0	Yes, 1.7	Yes	Yes, 0.065 < ρ < 100
		TestD_02_05	28.5	8d:02h:37m:47s	Cancelled	10 -2.0	Yes, 1.7	Yes	Yes, ρ > 0.065
		TestD_03	2	03h:46m:48s	Terminated 10 -2.0	Yes, 1.6	Yes	Yes, ρ > 0.065
		TestD_04	2	03h:28m:58s	Terminated 10 -2.0	Yes, 1.8	Yes	Yes, ρ > 0.065
		TestD_04_02	1	01h:02m:32s	Terminated 10 -2.0	Yes, 1.8	Yes	Yes, 0.25 < ρ < 100
		TestD_05	2	04h:04m:46s	Terminated 10 -2.0	Yes, 1.5	Yes	Yes, ρ > 0.065
		TestD_06	1.5	02h:46m:15s	Terminated 10 -2.0	Yes, 1.4	Yes	Yes, ρ > 0.065
		TestD_07	71.5	5d:16h:14m:26s Terminated 10 -2.0	Yes, 1.9	Yes	Yes, 0.065 < ρ < 250
		TestD_08	86.5	6d:14h:05m:51s Terminated 10 -2.0	No	Yes	Yes, 0.065 < ρ < 250
		TestE_01	0.5	8d:01h:41m:23s	Cancelled	10 -1.5	Yes, 1.6	No	Malfunctioning
		TestE_02	0.5	8d:01h:39m:04s	Cancelled	10 -1.5	Yes, 1.6	Yes	Malfunctioning
	163	TestE_03	0.5	01h:47m:10s	Terminated 10 -1.5	Yes, 1.6	Yes	Yes, 0.25 < ρ < 100

For comparison, the average intensity of the solar magnetic field is less than 4 G and the one from planet Earth ranges between 0.25 and 0.65 G (e.g.Bouvier et al.

2007;Finlay et al. 2010).

More info at: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats. pearsonr.html

More information at: http://www.astro.up.pt/~sousasag/harps_gto_catalogue.html

We used lmfit routine developed by[START_REF] Newville | LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python[END_REF], which includes the implementation of the Levenberg-Marquardt algorithm. The projected rotational velocity and veiling are set as the two free parameters in this routine.

IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

The nodding mode implies several observations of the target at different slit positions.

The stare mode means that the target and the background are observed only once.

More info available at: https://github.com/sczesla/PyAstronomy.

AAVSO website: https://www.aavso.org/

In the study presented inPetrov et al. (2019), the definition of the blue equivalent width of the Hα emission lines is slightly different than the one applied in this work. It is assumed that this parameter is measured only between -200 and -100 km s -1 .

More info at: https://docs.astropy.org/en/stable/api/astropy.timeseries.LombScargle.html

More information available at: http://plutocode.ph.unito.it.

Acknowledgements

Without them this PhD would not be possible. I would also like to express my gratitude to Fundação para a Ciência e a Tecnologia (FCT) for their financial support through the fellowship PD/BD/113745/2015, under the FCT PD Program PhD::SPACE (PD/00040/2012), funded by FCT (Portugal) and POPH/FSE (EC), and Instituto de Astrofísica e Ciências do Espaço for the Research Fellowship CIAAUP-23/2019-BIM. I also acknowledge additional funding from CRUP through the PAUILF cooperation program (TC-16/17), Programme National de Physique Stellaire of CNRS/INSU (France) and FCT/MCTES through the grants UID/FIS/04434/2019; PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/ 2017 & POCI-01-0145-FEDER-028953.

List of Acronyms

2MASS 2Micron All-Sky Survey AAVSO American Association of Variable Star Observers

sin θ 1 + δα(R, θ) , (5.13)

R sin θ 1 + δα(R, θ) , (5.14)

cos θ , (5.15)

)

(5.17)

Finally, pressure and density are given by (5.18) and

where B * and V * are, respectively, the poloidal magnetic field and velocity at the Alfvén surface, which is equivalent to a sphere of radius r * . The Alfvén radius corresponds to the radius at which the kinetic energy is equal to the magnetic energy, both only associated to the poloidal components. R corresponds to the dimensionless radial distance and is given by r/r * . The colatitude is represented by θ. The δ parameter describes the deviations from a spherically symmetric density and λ is responsible for controlling the rotation of the poloidal streamlines at the Alfvén surface. ρ * is the density at the Alfvén radius, Π(R) is the dimensionless pressure and κ is the parameter responsible for controlling the deviations from the spherically symmetric pressure configuration. M 2 (R) is the square of the poloidal Alfvén number as a function of the radial distance R given by

where V p and B p are the poloidal velocity and magnetic field and can be expressed as

and (5.22) respectively. The dimensionless flux function α is expressed as

(5.23) CHAPTER 5. SIMULATING THE CIRCUMSTELLAR ENVIRONMENT OF CTTSS This equation for the angular speed is given by

Additionally, the magnetosphere is surrounded by an infinitely thin accretion disk that is used as a boundary condition. It produces a weak disk wind which mass flux density is negligible. The analytical solution corresponds to a spatially given map of heat rate deposit along the flow. The change in direction and magnitude of the velocity between the simulation and the analytical solution are taken into account in the heat rate at each time step. In a first step, and along the flow, we can rewrite the volumetric rate of thermal energy expressed in Eq.5.10 in its steady version as

( 5.27) This energy equation is given in the co-moving frame with the fluid which explains why it eventually has to be proportional to the velocity. Using Eq.5.27, PLUTO manages to compute iteratively, for each time t, the density, pressure, velocity and magnetic field.

Another way to write the equation for the volumetric rate of thermal energy, is starting by writing q in its vectorial form as q = q r e r + q θ e θ .

(5.28)

If we normalize q by the poloidal velocity we can write

(5.29)

An important detail that we should keep in mind is that the results returned from the simulations (V p = V r e r + V θ e θ ) may differ from the ones in the analytical solution (V p,An = V r,An e r +V θ,An e θ ). In order to account for such vectorial shifts, q was normalized with the poloidal velocity given by the analytical solution using the following relation:

( 5.30) where q An and V p,An correspond to the heat flux and the poloidal velocity, respectively,

given by the analytical solution and used as initial conditions.

In the magnetospheric accretion zone, the magnitude of the velocity and density are increased in order to enhance the accretion rate in the simulations. We multiply the analytical density and velocity in the closed field line region by some given factors (negative for the velocity), reverse the toroidal magnetic field, while keeping the analytical values

Selected tests

We start to present here a selection of four solutions (Test A, B, C and D) that show the most stable configurations. In Table 5.1, we list the factors used to multiply the initial poloidal velocity and density. These two quantities will be increased until we reach a desirable mass accretion rate.

In a second step, we select the solutions with the best matching mass fluxes and velocities with the ones we find in the literature for RY Tau (Tests C and D). In these tests, we implemented a dead zone, a rotating Keplerian disk and a density threshold (Tests C+ and D+), as described previously, and we let the simulations evolve along the time. The initial 30 PLUTO time units correspond to the relaxation time, which corresponds to the time the simulation needs to achieve either a steady or quasi-steady configuration. After this transition period, the simulations get more stable.

In Fig. 5.4 we plot the density maps for Tests A, B, C, C+, D and D+ at PLUTO times 50, 75 and 100, which are equivalent to 6, 9 and 100 stellar rotations, respectively. In Tests D and D+ have very similar outputs and no major differences are detected between these solutions.

Table 5.1: Configuration of the selected simulations. The simulations are identified in the first column followed by the multiplying factors imposed for velocity (V ) and density (ρ). It is also identified which simulations have included a dead zone (DZ), a Keplerian rotating disk (KR) and a density threshold (DT). Are also listed the averaged mass accretion rates ( Ṁacc ) and mass loss rates ( Ṁloss ) in logarithmic scale, as well as the maximal accretion velocities (V acc ) and terminal velocities of the jet (V term ).

Simulation ID V ρ DZ? KR? DT? log Ṁacc log Ṁloss The simulation ID is listed in the first column followed by the final running time in PLUTO time units (t f pluto ), the total time needed to run the simulation and the status of the simulation (Finished, if it went until t = 100; Cancelled; Crashed, if it stopped at t = 0; Terminated, if it stopped after t = 0 and before t = 100). In the following columns are shown the multiplying factors imposed for density (ρ) and velocity (V ). Are also identified which simulations have included a dead zone (DZ) and corresponding α max to define the accreting region, a Keplerian rotating disk (KR) and a density threshold (DT).

Simulation