Caroline Soubiran
email: caroline.soubiran@u-bordeaux.fr

Orlagh Creevey

Nadège Lagarde

Nathalie Brouillet

Paula Jofre

Laia Casamiquela

Ulrike Heiter

Claudia Aguilera Gomez

Sara Vitali

Clare Worley

P Jofré

C Aguilera-Gómez

D De Brito

Gaia FGK Benchmark Stars: fundamental Teff and log g of the third version

Keywords: late-type -stars, fundamental parameters -stars, atmospheres -standards -surveys

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Introduction

The last decade has been marked by a large observational effort aimed at deciphering the history of our Galaxy based on large samples of stars observed by spectroscopic surveys. This has stimulated the development of efficient methodologies for the massive determination of atmospheric parameters (APs). In particular the recent Gaia Data Release 3 (Gaia Collaboration et al. 2023c, Gaia DR3) just delivered T eff , log g and [Fe/H] for millions of stars (Creevey et al. 2023;Fouesneau et al. 2023). In particular two datasets were released that mainly include F, G and K-type stars, one for 5.6 million stars with APs based on medium resolution spectra from the Radial Velocity Spectrometer (Recio-Blanco et al. 2023), the other one for 471 million stars ⋆ The full catalogue is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/?/?

with APs based on low resolution spectra from the blue and red prisms, parallax and integrated photometry (Andrae et al. 2023). The methodologies used for the massive determination of atmospheric parameters rely on stellar models which are not perfect and not able to reproduce exactly real spectra, causing some biases which have to be corrected.

The Gaia FGK Benchmark Stars (GBS) are reference stars to be used for the calibration and the validation of spectroscopic methods of parametrisation. They are chosen to cover the range of F, G, and K spectral types at different luminosities and metallicities, and to have the necessary observations available to determine their effective temperature and surface gravity independently from spectroscopy, at a precision level of 1-2%. The determination of T eff and log g is performed through the fundamental relations implying observable quantities (angular diameters directly measured by interferometry, bolometric fluxes and paral-laxes) and the mass, the only parameter depending on theoretical assumptions.

The first and second versions of the GBS (hereafter V1 and V2, respectively) were presented in a series of papers. Heiter et al. (2015), hereafter Paper I, describe the initial selection of 34 stars, including the Sun, and the determination of their fundamental effective temperatures and surface gravities, resulting in the GBS V1 sample. Blanco-Cuaresma et al. (2014) (Paper II) present the library of high-resolution spectra that was assembled and used to determine metallicities (Jofré et al. 2014, Paper III) and elemental abundances of α-capture and iron-peak elements (Jofré et al. 2015, Paper IV). One limitation of the V1 sample was the small number of targets, in particular in the metal-poor regime. Metal-poor stars are usually distant and faint, which makes them difficult to observe in interferometry. In Paper V, Hawkins et al. (2016) proposed a list of ten metal-poor stars to be included in the GBS sample. The GBS V2 sample summarised by Jofré et al. (2018) includes 36 stars, merged from Paper I and Paper V. The change in number from 34 to 36 comes from the addition of five metal-poor stars from Paper V and the removal of some stars from Paper I because their spectroscopic analysis indicated that they could not be recommended as reference stars. However, V2 was an intermediate version where the fundamental properties of the stars were not redetermined owing to the lack of direct and accurate measurements of angular diameters for some stars.

The material provided in these series of papers consists of accurate APs for stars covering a extensive range of spectral types and metallicities, in addition to a library of high resolution and high signal-to-noise spectra from which line-by-line abundances are also provided. This material can be further exploited in spectroscopic studies. Indeed, Paper VI of the GBS series (Jofré et al. 2017), reports on a collective work using the GBS to investigate the different sources of uncertainties in elemental abundances in order to improve spectroscopic pipelines.

The ultimate goal of the efforts dealing with GBS is to provide to spectroscopic surveys the fundamental T eff and log g scales and an external reference for abundances. Despite their limitation in sample size and parallax precision previous to Gaia data, the GBS have been extensively used in the past years. The Gaia astrophysical parameters inference system (Bailer-Jones et al. 2013;Creevey et al. 2023) made use of GBS for the validation of the stellar parameters published in Gaia DR3. The GBS are also a fundamental source of calibration and validation of the Gaia-ESO Survey (Gilmore et al. 2022;Randich et al. 2022;Hourihane et al. 2023), of the RAVE survey (Steinmetz et al. 2020b,a), and of the GALAH survey (Buder et al. 2021). The OCCASO project (Casamiquela et al. 2019) has systematically observed two GBS giants, Arcturus and µ Leo, to validate chemical abundances of open clusters. Upcoming large projects such as WEAVE (Jin et al. 2022) are also making use of the GBS.

Calibrations based on GBS can help to make surveys more homogeneous and mutually compatible so that they can be combined into the most comprehensive database of chemical measurements for the study of the Milky Way stellar populations (Jofré et al. 2018). The applications of the GBS however can extend far beyond this specific purpose. As for the study presented in Paper VI (see also Blanco-Cuaresma 2019), many spectroscopic studies have benefited from the GBS effort. For example, Adibekyan et al. (2020) used the GBS to assess the performances of the ESPRESSO, PEPSI and HARPS high-resolution spectrographs while Heiter et al. (2021) used some spectra from Paper II to assess the quality of hundreds of spectral lines and the corresponding atomic and molecular data used for the abundance analyses of FGK-type stars carried out within the Gaia-ESO survey (see also Kondo et al. 2019;Fukue et al. 2021, for lines in the Infrared). Amarsi et al. (2022) and Lind et al. (2022) used the GBS to quantify the differences in abundances derived using state-of-the-art 3D non-LTE atmosphere models and the standard 1D LTE models.

In addition to spectroscopy, the GBS help to constrain better stellar evolution models. For example, Sahlholdt et al. (2019) determined ages of the GBS as a way to test the reliability of the determination of stellar ages for various stellar populations; Serenelli et al. (2017) used GBS to validate their asteroseismic analysis performed on dwarfs and subgiants. The GBS have also been used as validation for the PLATO stellar analysis pipeline (Gent et al. 2022). Many of the lessons learnt from the GBS are further discussed in Jofré et al. (2019).

However, we are aware that the current sample of GBS is still imperfect and too small to make a satisfactory interconnection between surveys. This is why an extension of the sample is required. The V1 and V2 GBS samples were also limited by the parallax accuracy needed for a fundamental log g determination. This is not anymore an issue thanks to the exquisite astrometric quality of the Gaia data (Gaia Collaboration et al. 2016).

In this Paper VII of the series, we present the extended sample and third version of the GBS (GBS V3) that includes about 200 stars. We took advantage of recent interferometric studies that provided new measurements of angular diameters for large samples of stars (e.g. Ligi et al. 2016;Baines et al. 2018Baines et al. , 2021;;van Belle et al. 2021) and for metal-poor stars (e.g. Creevey et al. 2015;Karovicova et al. 2018Karovicova et al. , 2020)). As explained in Sect. 2 we selected new GBS candidates based on quality criteria applied on interferometric measurements. Sect. 3 describes the compilation of angular diameters and fluxes that are needed to compute the fundamental T eff . Bolometric fluxes (F bol ) were homogeneously computed by the method of spectral energy distribution (SED) fitting based on a large collection of (spectro)photometric data. Sect. 4 deals with the determination of log g with parallaxes from Gaia DR3 (Gaia Collaboration et al. 2023c), or Hipparcos (van Leeuwen 2007) for the brightest stars, and with masses inferred from a state-of-the-art methodology and stellar tracks. At each of these different steps we assess the uncertainties of the stellar parameters. Sect. 5 provides an overview of the sample properties and shows some comparisons to T eff and log g from different catalogues, before our concluding remarks in Sect. 6. All the compiled and computed parameters of this work are given in the form of a catalogue distributed by the CDS. We note that these parameters still require a last iteration considering [Fe/H] values, needed for the estimation of F bol and masses and here adopted from the literature, that are consistent with our fundamental parameters. This is a necessary step to recommend our parameters for reference (Heiter et al. 2015). The accompanying Paper VIII (Casamiquela et al. in preparation) presents homogeneous determinations of [Fe/H] and of detailed abundances of the GBS V3 derived from a spectroscopic analysis. For this purpose a large dataset of high-resolution, high signal-to-noise spectra was collected from public archives and through our own observing programs. The recommended parameters and abundances of the GBS are appropriately updated at the CDS.

Star selection

In order to determine T eff and log g through the fundamental relations with a minimum of assumptions and theoretical input, our principal criterion was to choose F, G and K stars with a high quality measurement of angular diameter. Ideally we want our GBS sample to homogeneously cover the (T eff ,log g,[Fe/H]) space, which implies a special effort to add metal-poor stars. We have therefore searched the literature for GBS candidates fulfilling these criteria.

First, we considered the GBS from V1 and V2 (Heiter et al. 2015;Jofré et al. 2018). The GBS V1 sample has 29 FGK-type stars (including the Sun), four giants with T eff around 4000 K, corresponding to late K and early M spectral types, and one cooler M giant. The V2 sample was built from the V1 one, with the addition of metal-poor stars. For the V3 list we considered all the 39 V1 and V2 stars including several stars with indirect determinations of angular diameters. For all we searched for new direct determinations of angular diameters as well as other data needed to update their fundamental T eff and log g. We added to this list eight metal-poor stars from Karovicova et al. (2020Karovicova et al. ( , 2022a)), not part of V1 and V2, and two targets recently observed with the CHARA interferometer (Creevey et al. in preparation). This sample of 49 stars was our initial set.

To further extend the GBS sample, we searched for new candidates observed in interferometry. We used the compilation from the Jean-Marie Mariotti Center (JMMC), the JMMC Measured Stellar Diameters Catalogue (JMDC, Duvert 2016). This catalogue, regularly updated, intends to be as exhaustive as possible in listing all the measurements of stellar apparent diameters made with direct techniques. It is therefore a very appropriate resource to extend the GBS sample. The JMDC is a bibliographical catalogue which implies that some stars have multiple entries, resulting from studies with different instruments, in different bands and with different precisions. Deciding which value of angular diameter is the most appropriate for a given star can be challenging, in particular owing to non-homogeneous uncertainties listed in the JMDC. In addition, there are many stars in the JMDC which are not appropriate for our purpose, such as some classes of variable stars, hot stars, spectroscopic binaries, and fast rotators. In addition, some very uncertain measurements of angular diameters could propagate large uncertainties to T eff and should be discarded. Therefore we made a first selection to reject stars and measurements not relevant for our purpose.

To do so, we followed Salsi et al. (2020) who established accurate surface brightness-colour relations for different spectral types and luminosity classes. They applied three types of rejection criteria on the JMDC data. First they examined the stellar characteristics to reject variable and semi-regular pulsating stars, spectroscopic binaries and other multiple stars, fast rotators and stars with a doubtful luminosity class. Second, they used criteria on the quality of the interferometric measurements that we apply similarly (see Sect. 3.1). The third type of criterion is based on the uncertainty of the K magnitude. We considered their list of 106 carefully selected F5 to K7 dwarfs and giants that we added to the initial set (five stars were already there). However, the study of Salsi et al. (2020) does not take into account the metallicity of the stars since their objective is to infer radii of stars and planets in the context of the PLATO mission which mainly focuses on solar-like stars. For us the metallicity is essential since the GBS should be representative of all the Milky Way stellar populations. We aim to improve the sampling of the GBS in T eff and log g but also in [Fe/H] with as many GBS candidates as possible on the metal-poor side. We noticed that the criteria used by Salsi et al. (2020), in particular the photometric one, tend to reject metal-poor stars. The only star with [Fe/H]< -1.0 in Salsi et al. (2020)'s sample is the well-known benchmark star HIP76976 (HD 140283), part of GBS V1, which has [Fe/H]=-2.36±0.10 in Paper IV.

We then searched for additional stars in the September 2021 version of JMDC available at the CDS which includes 2013 measurements of 1062 stars, a significant increase compared to the February 2020 version used by Salsi et al. (2020). In order to find stars in the appropriate range of atmospheric parameters, we used the PASTEL catalogue (Soubiran et al. 2016) and its recent version which provides mean atmospheric parameters for 14 181 FGK stars (Soubiran et al. 2022). We expect PASTEL to be complete for metal-poor stars brighter than V∼8.25, which is the limiting magnitude of FGK-type stars with an interferometric measurement in JMDC. Among the ∼500 stars in common between PASTEL and JMDC, we considered 63 additional stars to include in our sample, because they fill gaps in the AP space, and their interferometric angular diameters fulfill the criteria of Salsi et al. (2020).

The resulting list of selected candidates for GBS V3 includes 201 stars (the Sun is not considered here) They are all members of the Hipparcos catalogue (ESA 1997) and only the ten brightest ones are missing in Gaia DR3 (Gaia Collaboration et al. 2016). We keep the Sun in the GBS V3 since it is an obvious benchmark star, although it is not observable in the same conditions as other stars. We do not discuss the Sun in the present paper, keeping its fundamental T eff and log g determined in Paper I (we also note that a nominal value for the effective temperature of the Sun was adopted at the XXIXth IAU General Assembly, see Mamajek et al. 2015;Prša et al. 2016).

In the following, metallicities [Fe/H] are needed for the determination of F bol from SEDs (to initialize the minimization process, see Sect. 3.4), and for the determination of masses from stellar evolutionary tracks (see Sect. 4.2). We have adopted [Fe/H] from the literature for the 201 stars, mainly from the PAS-TEL catalogue. For a sake of homogeneity, we have not adopted [Fe/H] from Papers III and V for stars in V1 and V2 because they are corrected from non-local thermodynamic equilibrium (NLTE) effects, while for all the other stars the literature values are assuming LTE. It is the purpose of the forthcoming Paper VIII to provide precise and homogeneous abundances of Fe and other elements. This will imply some iterations to get the recommended T eff and log g of our targets.

Fundamental effective temperature

The luminosity L, the radius R, and the effective temperature T eff of a given star are linked through the fundamental relation L = 4πR 2 σT 4 eff , where σ is the Stefan-Boltzmann constant. The fundamental relation can be expressed in a way that gives T eff as a function of the limb-darkened angular diameter θ LD and the bolometric flux F bol which are measurable quantities:

T eff = F bol σ 0.25 (0.5 θ LD ) -0.5 = 2341       F bol θ 2 LD       0.25 (1)
where θ LD is in milliarcseconds (mas) and F bol in 10 -8 erg s -1 cm -2 or 10 -11 W m -2 .

In the following subsections we describe our compilation of measured angular diameters and fluxes. The latter were used to compute F bol by means of SED fitting. Subsequently, Eq. ( 1) was used to obtain T eff for the selected stars.

Compilation of angular diameters

As explained in Sect. 2, the selection of GBS V3 stars was mainly based on the JMDC which provides one or several values of θ LD for each star. In particular, we considered the 106 targets that Salsi et al. (2020) used as calibration stars to define precise surface brightness-colour relations. Salsi et al. (2020) applied interferometric criteria to remove non reliable values of θ LD in the JMDC. They rejected measurements with a relative uncertainty on the angular diameter larger than 8%, and those based on observations in the 8-13 micron band or having a bad observation quality and/or a poor spatial frequency coverage in the visibility curve. They also rejected stars with inconsistent redundancies. We adopted their selected values of θ LD for the 106 stars. For HIP112748 and HIP54539, provided with two values of θ LD differing by less than 1%, we adopted the one with the lowest uncertainty.

For the remaining stars, we queried JMDC and the recent literature in order to retrieve the latest values of θ LD fulfilling the interferometric criteria applied by Salsi et al. (2020). When provided we inspected the visibility curves to evaluate the reliability of the measurement.

We found recent and precise θ LD for ten of the GBS V1 and V2. In particular, for three of the metal-poor benchmark stars new measurements are available, for HD103095 (HIP57939) and HD122563 (HIP68594) by Karovicova et al. (2020), and for HD140283 (HIP76976) by Karovicova et al. (2018). The two components of the binary α Cen were remeasured by Kervella et al. (2017), while four other targets were found in Baines et al. (2018Baines et al. ( , 2021). Among the six stars which had no direct θ LD in Paper I, only one (HIP48455, µ Leo) was observed in interferometry by Baines et al. (2018). Among the five metal-poor stars from Paper V with indirect values of θ LD , one (HIP92167) was observed by Karovicova et al. (2020). Thus, we are left with nine stars from V1 and V2 that are still without any direct measurement of θ LD . We keep them in a separate table for continuity of the samples, but we do not consider them as GBS anymore.

The final version of the GBS V3 includes 192 stars with a direct measurement of θ LD . For each we provide the limb darkened angular diameter with its uncertainty and the corresponding reference in Table A.1 of Appendix A and in the catalogue available at the CDS. The sample includes stars with small angular diameters such as HIP97527 (θ LD =0.231±0.006 mas) and HIP93427 (θ LD =0.289±0.006 mas), both of which are asteroseismic targets observed with the CHARA/PAVO instrument by Huber et al. (2012). The sample also includes Aldebaran (HIP21421) and Arcturus (HIP69673) which have angular diameters as large as ∼20 mas. The median angular diameter of the sample is 1.12 mas.

The relative θ LD uncertainties range from 0.1% (HIP87808) to 7% (HIP25993) with a median value of 1.1% (see histogram in Fig. 1). Two other stars have relative uncertainties larger than 5%, HIP7294 and HIP14838. In absolute values, the largest uncertainties occur for the two giants ψ Phe (HIP8837) and Arcturus (HIP69673), with θ LD =8.0±0.2 mas and θ LD =21.0±0.21 mas, respectively. The two stars do not seem to have been reobserved recently, so that their θ LD is still that of Paper I.

We note that, for a small fraction of stars, we had to make a choice between the two or more values of θ LD fulfilling the adopted quality criteria. As shown in Fig. 2, several small diameters (typically θ LD <1.5 mas) disagree by more than 10%, but in general the agreement is at the 2σ level. We note three stars with estimations of their angular diameters differing by more than 3σ: HIP96441, HIP57939, HIP108870.

HIP96441 has three values of θ LD reported in the JMDC, that fulfill the interferometric criteria of Salsi et al. (2020): 0.861±0.015 mas in the K band (Boyajian et al. 2012a), 0.753±0.009 mas in the R band (White et al. 2013) and 0.749±0.007 mas in the H band (Ligi et al. 2016). The first de- termination is not compatible with the two others, but Boyajian et al. (2013) mention a calibration problem and discarded this star. Between the two other values we adopted the most recent one by Ligi et al. (2016).

HIP57939 (HD103095) is a well-known metal-poor dwarf studied by several authors. We adopted the latest determination, θ LD =0.593±0.004 mas, by Karovicova et al. (2020) who used the combination of two instruments, VEGA and PAVO on the CHARA interferometer giving a high confidence to their result.

For HIP108870 we adopted the value θ LD =1.758±0.012 mas by Rains et al. (2020) which significantly differs from that previously reported by Kervella et al. (2004), θ LD =1.89±0.02 mas. Rains et al. (2020) have analysed this discrepancy, considering that they obtained tighter constraints on the angular diameter by better resolving the star, thanks to the configuration now available at the VLTI.

These cases of disagreement also illustrate the inhomogeneity of uncertainties listed in JMDC, which sometimes only reflect the precision of a fit, or also include systematic effects identified at the calibration level. The dispersion among measurements available for a given star is critical for small angular diameters, typically below ∼1.5 mas, because it corresponds to discrepancies that can reach 10 to 15%. This illustrates the limitations of measuring interferometric diameters in the sub-mas regime. Some inhomogeneity can also arise from different recipes applied for the limb darkening correction. According to Eq. ( 1), a variation of 10% in θ LD translates into a variation of 5% in T eff . Inversely, a 1% precision on T eff implies angular diameters obtained at the 2% level.

Compilation of magnitudes and fluxes

In order to build a SED for each star and measure the corresponding F bol we compiled fluxes using the VOSA tool1 (Bayo et al. 2008). VOSA allowed us to collect all the photometry available in the Virtual Observatory (VO) for our list of 201 stars (including the nine stars from V1 and V2 with an indirect θ LD ) and to convert magnitudes into fluxes thanks to an exhaustive description of all the existing filters. We only kept the photometry from the VO catalogues that contain at least fifty of our targets, namely 2MASS (Cutri et al. 2003), AKARI (Yamamura et al. 2010), Gaia DR3 (Gaia Collaboration et al. 2023c), GALEX (Bianchi et al. 2017), Strömgren photometric catalogues (Hauck & Mermilliod 1998;Paunzen 2015), Johnson UBV (Mermilliod 1987), IRAS (Neugebauer et al. 1984), Hipparcos (ESA 1997), Tycho-2 (Høg et al. 2000) and WISE (Cutri et al. 2021). We note that the components of the bright binary star α Cen A and B are not resolved in the 2MASS catalog2 , and the magnitudes given for α Cen A contain actually the combined flux of both components. We therefore used J, H, and K magnitudes from Engels et al. (1981), which are given for each component separately, and converted them to flux values using the VOSA tool.

An interesting new feature of the latest VOSA version (July 2022 update) is to provide synthetic photometry based on Gaia DR3 BP/RP spectra analysed with the GaiaXPy tool (De Angeli et al. 2023;Gaia Collaboration et al. 2023b). We therefore collected through VOSA the synthetic photometry from Gaia which is provided in 13 passbands corresponding to the filters of the Hubble Space Telescope, Sloan Digital Sky Survey, PanSTARRS1 and Johnson UBVRI systems. Also from Gaia BP/RP spectra and GaiaXPy, VOSA computes fluxes in the 65 bands of the OAJ/J-PAS and OAJ/J-PLUS surveys. However we noticed that a small fraction of the Gaia synthetic photometry was affected by saturation, causing the corresponding SED to be deformed. We had to remove the Gaia spectrophometry, totally or partially, for about thirty bright stars with G≃4. Finally we added to the compilation the fluxes in the range 320-1080 nm from the Pulkovo spectrophotometric catalog (Alekseeva et al. 1996), adopting a homogeneous uncertainty of 1% for each value of flux (this value allowed us to give these data an appropriate weighting in our analysis). The Pulkovo catalogue provides 167 or 305 flux values, depending on the star. The details of the num-An illustration of the obtained SEDs is given for two stars in Fig. 4 in Sect. 3.4. HIP103598 is a K4 giant with a metallicity of -0.36 according to PASTEL, which has a well constrained SED thanks to Gaia and Pulkovo spectrophotometry. HIP50564 is a F6 turn-off star with a metallicity of +0.10 according to PASTEL, having only broad-band photometric observations. We chose these stars to illustrate both the SED shape variations due to different temperatures, and the more or less good coverage of the SED depending on the availability of spectrophotometric data.

Extinction

The extinction towards each of the 201 targets was estimated thanks to the recent 3D maps provided by Vergely et al. (2022), based on the inversion of large spectroscopic and photometric catalogues including Gaia DR3. We chose the closest map, covering a volume of 3 kpc x 3 kpc x 800 pc at a resolution of 10 pc, which is particularly well adapted for our sample of nearby stars.

The extinction is low for most of the stars (90% of them have A V < 0.05) which is not surprising owing to the small distances of the GBS V3 from the Sun. Our GBS span distances from 3 pc to 550 pc (deduced from parallaxes, see Sect. 4.1). Five giants have the highest extinction values, between 0.1 and 0.31 mag. As expected, A V is well correlated to the distance, as shown in Fig. 3.

SED fitting and bolometric fluxes

Although the observed fluxes compiled for the GBS cover a wide range of wavelength, some extrapolation of the SED is needed to integrate the full distribution and measure the total flux from the star received at the Earth, F bol . To do so we followed the SED fitting method previously used by Creevey et al. (2015) and Ligi et al. (2016), based on the BASEL empirical library of spectra (Lejeune et al. 1997), a highly cited library in the astrophysical community. Our choice for these models is based upon the work in Creevey et al. (2015) where one star was analysed in detail using different approaches and models. A 1% flux difference was found using the BASEL and PHOENIX libraries, with the former being in best agreement with other literature results using different methodologies.

The BASEL library covers the following parameter ranges: 3 500 < T eff < 50 000 K, 0.00 < log g < 5.00, and -5.0 < [M/H] < +1.0. It extends to 2 000 K for a subset of the log g and [M/H]. The wavelength range spans 9.1 to 160 000 nm on a non-evenly sampled grid of 1221 points, with a mean resolution of 100 nm in the UV and 200 nm in the visible. Beyond 10 000 nm the resolution is 20 000 nm and to avoid issues with numerical integration we interpolate on a log scale before performing the integration. A Levenberg-Marquardt minimisation algorithm finds the optimal template that fits the observed flux points. F bol is then calculated by integrating the optimal fitted spectrum. Recent improvements of the method include the weighting of the fluxes and the determination of F bol uncertainties through Monte-Carlo simulations.

The parameters of the model are the atmospheric parameters: T eff , log g, [Fe/H], the extinction, and the scaling factor (stellar radius scaled according to the distance). We used the atmospheric parameters from PASTEL to initialise the minimization and the extinction from Sect. 3.3. To account for extinction in our method we implemented the IDL routine ccm_unred3 which dereddens theoretical fluxes, and requires colour-excess on input. To convert extinction to colour-excess we adopted R 0 = 3.1. Most of these stars are nearby and as such have little or no extinction. In order to be complete in our analysis, in the catalogue available at the CDS we also provide F bol for the full sample of stars by assuming zero extinction.

All of the above parameters can be fitted, but in practice due to degeneracies between the parameters, the T eff and the scaling factor are the only free parameters, while log g, [Fe/H], and the extinction are fixed each time a minimization is performed. In order to include the impact of the uncertainties of the parameters log g and [Fe/H], and of the fluxes, we performed a bootstrappedbased method where we (a) perturbed these parameters by their uncertainty multiplied by a random number drawn from a Gaussian distribution, and (b) perturbed the fluxes by their uncertainties using the same approach. These simulations were done 400 times where 400 was a balance between computing time and having a significant sample size (the results with 200 simulations were equivalent within the uncertainties and the standard deviation of the 400 simulations reproduced the uncertainties of the atmospheric parameters). For the fitted parameters, the result is a distribution of stellar parameters that fit the observational data, and from these fitted parameters we integrated the corresponding semi-empirical flux distribution. We therefore obtained a distribution of F bol for each star, and from these distributions we calculated the medians and the symmetric 68% confidence intervals, and report half of the latter as the uncertainty.

Two examples of the data and the best-fitted model SED are shown in Fig. 4, left and right panels. The left is an example of a star with many observational points (in this case HIP103598), while the right panel shows an example where relatively few data points are available; in this case HIP50564. The lower panels show the distribution of the fitted F bol and the individual χ 2 values from the 400 Monte Carlo simulations, along with the value of the adopted median and 16 and 84 percentile confidence levels (dashed lines). We defined the uncertainty as the half of the distance between the upper and lower confidence levels.

The distribution of F bol and relative uncertainties is shown in Fig. 5. The histogram of uncertainties shows a clear peak in the first bin corresponding to uncertainties lower than 0.5%. The relative uncertainties have a median value of 1.4%, and they are lower than 10% except for two stars, namely HIP8837 (ψ Phe) and HIP14135 (α Cet). These two M giants combine a low T eff and a lack of spectrophotometric data which make their SED poorly constrained, resulting in a relative uncertainty of about 21% and 18% respectively. They had uncertain F bol in Paper I as well. We note that the stars with uncertainties larger than 4% have their SED made of broad-band photometry only, while the majority of stars have spectrophotometry from Gaia and/or Pulkovo, resulting in a very precise F bol determination.

In this procedure to determine F bol , we use log g and metallicity from the PASTEL catalog, a compilation of literature work. We have evaluated the impact of not knowing precisely these parameters. To do so, we made two tests. One test is to adopt a large uncertainty of 0.15 on both log g and [Fe/H] inducing a different distribution of the fitted F bol from the 400 Monte Carlo simulations. The other test is to change the literature values of log g and [Fe/H] by an amount of 0.15 dex, in the eight possible configurations, for seven stars selected to cover the parameter space. In this test, the largest effect (<1%) is reached when adding 0.15 dex to [Fe/H] for the hottest stars. Varying log g has more effect on the coolest stars. When combining the variations of log g and [Fe/H] the effect remains at the level of 1% for the coolest and the hottest stars. Interestingly the most metal-poor star chosen for that test, HIP48152, is less affected by a change of log g and [Fe/H]. In the other test, enlarging the log g and [Fe/H] uncertainties in the Monte-Carlo simulations also has a low impact on the derived value of F bol . We note four stars with F bol changed by 1-2%, while 90% of the sample changes by less than 0.5%. We conclude that our procedure weakly depends on the input values of log g and [Fe/H]. A change of 1% in F bol induces a change of 0.2% on T eff . However a more rigorous treatment will be performed through iterations once the spectroscopic analysis of the targets will be performed to derive [Fe/H] homogeneously (Paper VIII in preparation). This will lead to self-consistent parameters.

In Paper I, the F bol values of the V1 stars were compiled from the literature and therefore not as homogeneous as here. This is another important improvement of the GBS V3, in addition to the larger number of stars. We still have a good agreement between V1 and V3, with a slight offset of 1.4%, and a typical dispersion of 2.1% (median absolute deviation, MAD).

Our approach is similar to that of Boyajian et al. R versus F bol for the 400 simulations for the two stars with the 16 th , 50 th (median), and 84 th percentiles indicated by the dashed lines. ric measurements available in the literature, extended by spectrophotometry when available. They also applied the SED fitting method with reference templates taken from the library of Pickles (1998) which is made of observed spectra, whereas we used a hybrid library of synthetic stellar spectra calibrated from observations (Lejeune et al. 1997). Another difference comes from the Gaia spectrophotometry recently made available, which constrains very well the SED shape in the optical range. We have 66 stars in common with Boyajian et al. (2013) and 24 with Baines et al. (2018). The F bol comparison is shown in Fig. 6. The agreement with Boyajian et al. (2013) is very good, with differences within 10%. On average our F bol values are higher than their values by 3.3%, with a typical dispersion of 2.5% (MAD). The offset does not seem correlated with extinction which is lower than 0.03 mag for the stars in common according to our estimations, and that they have not considered given the close distance of the stars. It is likely that the small offset observed between our F bol determinations and those of Boyajian et al. (2013) is related to their use of magnitudes from photometric catalogues, with a maximum of 17 values per star and less than 12 values in most cases, while we have typically ten times more flux values, mostly from Gaia spectrophotometry, providing SEDs of better quality. In addition they did not take photometric uncertainties into account for the fit, while we do. Baines et al. (2018) determine a high extinction for some stars which seems correlated with a larger positive offset. HIP47431 and HIP90344 are the most extreme cases with A V =0.7 mag and A V =0.54 mag respectively in Baines et al. (2018) while we get A V =0.02 mag and A V =0.03 mag from the 3D maps of Vergely et al. (2022), leading to a difference of 50% and 37% on F bol (HIP47431 is not shown in Fig. 6). Considering the 24 stars in common, Baines et al. (2018) find F bol higher than us by 7.6% (median) with a dispersion of 6.6% (MAD).

We also compared our F bol determinations to those of González Hernández & Bonifacio (2009) who implemented the infrared flux method (IRFM) based on 2MASS magnitudes (see Fig. 6). The 61 stars in common generally agree well with an offset less than 1% and a dispersion of 3.9% (MAD). The extinction is low for the majority of these nearby stars.

Finally, we also made a comparison with the catalog of empirical bolometric fluxes and angular diameters of 1.6 million Tycho-2 stars built by Stevens et al. (2017) which has 119 stars in common with us. This work is based on the flux-colour relations of Casagrande et al. (2010) with T eff and A V being determined separately in an iterative way. Their F bol are globally larger than ours by 4.9%, with a dispersion of 7.5% (MAD). Similarly to the tendency observed in the comparison with Baines et al. (2018), the larger differences correspond to stars with the largest values of A V in Stevens et al. (2017) which significantly differ from our lower extinctions. Eight stars do not appear in Fig. 6, given their difference larger than 50%, up to 360% for HIP112731 and HIP96837. They are found highly reddened by Stevens et al. (2017) with A V ≥0.6 mag, up to more than 2 mag for the two most extreme stars HIP112731 and HIP96837. We therefore suspect that some extinctions are overestimated by Stevens et al. (2017) and Baines et al. (2018), leading to overestimated bolometric fluxes.

Assessment of T eff

We computed the fundamental T eff of each star by applying Eq. ( 1) with the values of θ LD and F bol obtained as described above. T eff uncertainties were deduced by propagating the θ LD and F bol uncertainties in Eq. ( 1). We consider here the 192 stars with a direct value of θ LD . The resulting uncertainties on T eff span 5 K to 183 K, with a median value of 43 K (see histogram in Fig. 7). Only four giants present a relative uncertainty larger than 3% (absolute uncertainty larger than 150 K): the two M giants HIP8837 (ψ Phe) and HIP14135 (α Cet) previously mentioned for their large F bol uncertainty resulting in T eff uncertainties of ∼5%, and the K giants HIP25993 and HIP14838 previously mentioned for their large uncertainty on θ LD resulting in T eff uncertainties of ∼3.5%. These four stars clearly stand as outliers in Fig. 8 which shows how the relative uncertainties on θ LD and F bol propagate on T eff . In order to reach a 1% accuracy on T eff one should restrict the sample to stars with measurements better than ∼2% in θ LD and ∼4% in F bol . We have 127 stars fulfilling this condition, while 179 of the 192 stars have T eff uncertainties better than 2%.

In Fig. 9 we compare our values of T eff to other direct determinations from the literature, including those in Paper I. The values of offset (median difference) and dispersion (MAD) are given in Table 2. The dispersion is remarkably low (MAD≃30 K) for the comparison to Paper I and Karovicova et al. (2020Karovicova et al. ( , 2022a,b),b), our determinations being larger by 26 K and 39 K re- spectively. The agreement is therefore at the 1% level in general. The two outliers in the comparison to Paper I (upper left panel of Fig. 9) are the metal-poor benchmark stars HIP57939 and HIP76976 (HD103095 and HD140283). Our new T eff values are about 400 K and 250 K higher than in Paper I, where their sub-mas angular diameters were quoted as very uncertain. Both stars have been remeasured by Karovicova et al. (2018Karovicova et al. ( , 2020) ) leading to more precise θ LD and higher T eff . Our determination for HD103095 (T eff =5235±18 K) is larger by 61 K than that of Karovicova et al. (2020). Since we use their determination of θ LD , the difference is only due to F bol . As noted in Sect. 3.1, the angular diameter of HD103095 measured by Karovicova et al. (2020) from the combination of two instruments is very reliable. For HD140283 we find T eff =5788±45 K, lower by 4 K than their value. Three other stars differ by 2-3% from Paper I: ψ Phe, 61 Cyg B and γ Sge. Only γ Sge has a new angular diameter measured by Baines et al. (2021), while for the other ones we used the same θ LD as in Paper I, indicating that the difference comes from the new determination of F bol , which we expect to be more accurate than the previous determination.

Table 2 and Fig. 9 exhibit larger discrepancies in the comparison to Boyajian et al. (2013) with an offset of 59 K and a scatter of 58 K. We note that we have 66 stars in common but 82 measurements since Boyajian et al. (2013) provide a compilation of their own θ LD together with other values from the literature (we removed discrepant values quoted by them for HD146233 and HD185395). Among the stars that differ by more than 300 K, we have again HD103095 which is the largest outlier. As explained above, the recent θ LD determination by Karovicova et al. (2020) gives a higher T eff which is in better agreement with our value for that star. For HIP61317 Boyajian et al. (2013) give two values of T eff , only one being in significant disagreement with ours. For HIP89348 our values of F bol and θ LD (the latter adopted from Ligi et al. 2016) are larger and smaller, respectively, by ∼10% than those of Boyajian et al. (2013), resulting in a significantly different T eff . Our value of T eff =6569±69 K seems however more consistent with spectroscopic values listed in the PASTEL catalogue than their lower value of T eff =6221±39 K.

The comparison to van Belle et al. (2021) gives an offset of 61 K, this time our values being lower, with a dispersion of 77 K. This relies on 17 giants in common. These large differences could partly be due to disagreement in extinction values for some stars. We note four stars (HIP7607, HIP111944, HIP74666, HIP3031) that van Belle et al. ( 2021) found significantly reddened (A V from about 0.15 to 0.30 mag) while our A V determinations are below 0.05 mag. This possibly explains the T eff differences from 150 K to 220 K. On the other hand, HIP22453 has A V =0.36 mag in van Belle et al. ( 2021) and A V =0.08 mag in our work, but the T eff difference is only 31 K. We note that we use the same determination of angular diameter as in the literature for some of the stars. Hence, the comparison data sets are not completely independent from ours.

Surface gravity

We determined the surface gravity log g with the fundamental relation expressed as:

log g = log        M M ⊙ R R ⊙ -2        + log g ⊙ (2)
where M/M ⊙ and R/R ⊙ are the mass and radius of the star in solar units. For the Sun, we adopt for the surface gravity log g ⊙ = 4.4380 ± 0.0002 dex4 determined in Paper I. The linear radius of each star is deduced from its angular diameter (see Sect. 3.1) and its distance is inferred from its parallax (see below). Masses, which cannot be directly measured, are estimated from evolutionary tracks, using our fundamental T eff , luminosities (from F bol and parallaxes), radii (from θ LD and parallaxes) The parallax of the stars is needed to convert their angular diameter into linear radius, and their bolometric flux into luminosity. All the targets have a Hipparcos parallax, and the majority of them have also an even more precise and accurate Gaia DR3 parallax. Only four stars have a Gaia parallax with an uncertainty larger than 3%, the largest value being 6% for HIP55219. The ten brightest stars not in Gaia DR3 have a precision of their Hipparcos parallax better than 3.5%. With parallaxes π and θ LD we computed linear radii R and their uncertainties, while we used parallaxes and F bol to compute luminosities L and their uncertainties. Adopting the solar radius

R R

⊙ = 1 0.00930093 × θ LD π (3) L L ⊙ = 312.564 × F bol π 2 (4)
with θ LD and π expressed in mas, and F bol in 10 -8 erg s -1 cm -2 .

The radii of the GBS V3 span 0.6 to ∼140 R ⊙ (see Fig. 11). The luminosities span 0.08 to nearly 6000 L ⊙ (see Fig. 12).

Solar-like oscillations provide robust constraints to the radius of G and K dwarfs and giants (Chaplin & Miglio 2013), giving us an opportunity to compare our determinations with others obtained in a different way. We estimated seismic radii using the following scaling relation (e.g. Miglio 2012) when the asteroseismic parameters, the so-called large frequency separation ∆ν and the frequency of maximum oscillation power ν max , were available:

R R ⊙ ≈ ν max ν max⊙ ∆ν ∆ν ⊙ -2 T eff T eff,⊙ 1/2 , ( 5
)
where we adopt the fundamental T eff determined in Sect. 3 and the solar parameters as in Paper I: ∆ν ⊙ = 135.229 ± 0.003 µHz, ν max,⊙ = 3160 ± 40 µHz, T eff,⊙ = 5771 ± 1K. We have compiled ∆ν and ν max from the literature and found determinations of both parameters for 37 stars. The comparison is shown in Fig. 13. There is a small systematic offset, the fundamental radii being larger than the seismic ones by 0.7%, with a typical dispersion (MAD) of 3.3%. Several stars show discrepancies larger than 10%, up to 22% for HIP92984. There is however an ambiguity about the seismic parameters of HIP92984, measured by Mosser et al. (2009) from CoRoT observations, because Huber et al. ( 2012) did not detect solar-like oscillations. The other discrepant stars have error bars that still give an agreement at the 3σ level. We also note that Sharma et al. (2016) and Hon et al. (2022) proposed some corrections to the scaling relations to obtain a better agreement for giants. It is however out of the scope of this paper to apply such corrections. We retain from this comparison the general good agreement, with no systematics, between our values and seismic ones, at the level of ∼4%. 3), and seismic estimations from Eq. ( 5).

Figure 14 shows our derived luminosities compared to those available for 36 stars in the Gaia DR3 Golden Sample of Astrophysical parameters for FGKM stars (Gaia Collaboration et al. 2023a). Gaia luminosities were computed from the parallax, the G magnitude and a bolometric correction (Creevey et al. 2023) and are therefore different from our determinations, although not completely independent. The three most luminous stars in common are found brighter by Gaia by more than 10%, up to 30% for HIP70791, known as a horizontal branch star. Only that star shows a discrepancy significantly larger than 3σ. We note six other stars with Gaia luminosities significantly larger than our values, with differences ranging from 5% to 10%. These discrepancies cannot be explained by the extinction that we find negligible for these nine stars. For the other stars, we find luminosities slightly larger than those from Gaia, by 0.35% (median), with a typical dispersion of 0.9% (MAD).

Masses

Masses were computed with the SPInS code (Lebreton & Reese 2020) implemented with the stellar evolutionary tracks from BaSTI (Pietrinferni et al. 2004(Pietrinferni et al. , 2006)), and from STAREVOL (Lagarde et al. 2012(Lagarde et al. , 2017)). We implemented the two grids in order to make comparisons owing to the different behaviour of the tracks in some parts of the HR-diagram (HRD), like the clump. The determinantion of the logg is less accurate at clump luminosity (logg≃2.2) because this is a point in the HR diagram where the evolutionary tracks of different masses and [Fe/H] overlap. In the following, we detail the main differences between these two grids that may have an impact on the position on the HRD and thus on the mass determination with SPInS. -BaSTI -We use stellar tracks coming from the non-canonical grid covering a mass range between 0.5 M ⊙ and 10.0 M ⊙ and a metallicity range [Fe/H] ∈ [-2.27, +0.40] without αenhancement. This grid takes into account core convective overshooting during the H-burning phase. The overshoot parameter is set to 0.2 for a stellar mass higher than 1.7 M ⊙ , no overshooting is considered for a mass lower than 1.1 M ⊙ , and a linear variation is assumed in-between. The solar mixture comes from Grevesse et al. (1993). We tried the α-enhanced tracks ([α/Fe]=+0.4) for metal-poor stars ([Fe/H]<-0.70 dex) leading to masses higher by 30% on average. However, as explained later, we got a wrong mass for µ Cas, the only metal-poor binary with a reliable dynamical mass. This convinced us to adopt the tracks without αenhancement for the whole sample. The Kroupa initial mass function (Kroupa 2001;Kroupa et al. 2013, IMF) was used as a prior, as well as a truncated uniform star formation rate between 0 and 13.8 Gyr, that is, roughly the age of the Universe. The stellar properties used as an input to SPInS are: (1) our fundamental T eff determinations (Sect. 3);

(2) luminosities deduced from F bol and parallaxes; (3) metallicities from the literature, and (4) radii deduced from θ LD and parallaxes. Radii are not independent of T eff and luminosities, but still add a useful constraint to the mass since the correlations are lost in the way we determined the three parameters. The resulting masses and their uncertainties are shown in Fig. 15. Most of the stars have masses < 2 M ⊙ but STAREVOL finds more stars in the range 2-2.5 M ⊙ than BaSTI. STAREVOL gives a more extended distribution of relative uncertainties with fewer very low values, and five stars within 30-55%.

For the validation of the mass determination, we compared the SPInS results to other determinations. This includes dynamical masses of binary stars, seismic masses, as well as mass determinations based on evolutionary tracks and methods different from those we used.

Dynamical masses are available for four stars, µ Cas, α Cen A & B, and Procyon. We did not consider 61 Cyg A & B since their masses are not well established (Kervella et al. 2022). The comparison to SPInS masses is shown in Fig. 16. The orbit of the binary α Cen has been studied by Akeson et al. (2021) who determined masses of 1.0788±0.0029 M ⊙ and 0.9092±0.0025 M ⊙ for the A (HIP71683) and B (HIP71681) components, respectively. The agreement is at the 0.4% level for the STAREVOL mass and 3.4% for the BaSTI mass, for the component A. Both sets of evolutionary tracks give masses that differ by 5% for the B component, in opposite directions. The dynamical mass of the metal-poor ([Fe/H]=-0.83 dex) visual binary µ Cas (HIP5336) results from an astrometric study with the Hubble Space Telescope by Bond et al. (2020) who determined a value of 0.7440±0.0122 M ⊙ . BaSTI and STAREVOL underestimate it by 4% and 1.3% respectively. Running SPInS with the α-enhanced BaSTI tracks ([α/Fe]=+0.4) for that star led to an overestimation of its mass by 32%. This convinced us not to adopt the α-enhanced tracks for metal-poor stars. Hence, we have opted to exclusively rely on the BaSTI tracks that do not incorporate any alpha-enrichment. This underscores the importance of presenting mass values obtained from both BaSTI and STAREVOL tracks, since it offers an understanding of the inherent errors linked to relying solely on a single stellar evolution model. The orbit of Procyon (HIP37279) based on Hubble Space Telescope astrometry (Bond et al. 2015(Bond et al. , 2018)), yields a dynamical mass of 1.478±0.012 M ⊙ . The BaSTI mass differs by 0.9% while the STAREVOL mass is lower by 2.6%. There is therefore a satisfactory agreement between the SPInS masses and the dynamical masses for these four stars, whatever the set of evolutionary tracks, considering the few constraints we use with the models, and given the inherent model assumptions of e.g. the chemical enrichment law which constrain the position of the tracks in the HRD.

1:0 We estimated seismic masses using the following scaling relation (e.g. Miglio 2012) for the 37 stars having a determination of the asteroseismic parameter ∆ν available in the literature (see Sect. 4.1 for the solar values)

1:5 M dynamic [M ¯]
M M ⊙ ≈ ∆ν ∆ν ⊙ 2 R R ⊙ 3 , ( 6
)
where R is the linear radius computed in Sect. 4.1. The resulting comparison is shown in Fig. 17. Although the agreement between SPInS and seismic masses is good in general in the range 1-1.5 M ⊙ , there is a trend in the sense that SPInS tends to overestimate masses smaller than 1 M ⊙ and to underestimate those larger than 1.5 M ⊙ . This is true for both sets of evolutionary tracks, with more outliers with STAREVOL. However, seismic masses may not necessarily be more accurate than those deduced from evolutionary tracks, given that the range of validity of the scaling relation is not yet clear (e.g. Sharma et al. 2016). We also compared the two sets of SPInS masses to masses from the literature, based on different evolutionary tracks and methods. Figure 18 shows comparisons to masses from Paper I, Baines et al. (2018) and Boyajian et al. (2013). In Paper I masses were determined by visual interpolation in two grids, the Padova grid (Bertelli et al. 2008(Bertelli et al. , 2009) ) and the Yonsei-Yale grid (Yi et al. 2003;Demarque et al. 2004), the adopted value being the average of the two. Baines et al. (2018) used a Bayesian method with the PARSEC isochrones developed by da Silva et al. ( 2006); Bressan et al. (2012). Boyajian et al. (2013) used the Yonsei-Yale isochrones. The resulting comparisons reflect the nature of the stars in common, with a good agreement for dwarfs and a large dispersion for giants. A larger dispersion is expected for giants, in particular at the clump, because of the overlap of the evolutionary tracks of different masses and [Fe/H]. Degeneracies in evolutionary tracks of evolved stars can also lead to different masses for a giant depending on whether it is on the red-giant branch or on the horizontal branch. The sample of Boyajian et al. (2013) is made of dwarfs and exhibits a small dispersion, despite a few outliers with STAREVOL. The sample of Baines et al. (2018) is mostly made of giants and exhibits a large dispersion, while GBS V1 are a mixture of dwarfs and giants. Figure 19 shows our derived masses to those available for 30 stars in the Gaia DR3 Golden Sample of Astrophysical parameters for FGKM stars (Gaia Collaboration et al. 2023a). Gaia masses were derived by comparing Gaia photometric effective temperatures and Gaia luminosities to BaSTI solar metallicity stellar evolution models (Hidalgo et al. 2018;Creevey et al. 2023), and are therefore similar to our determinations. We find an excellent agreement between our two sets of masses and the Gaia ones, except for the three stars in common with the highest masses (≳1.5 M ⊙ ), and one outlier within the STAREVOL set. From the above comparisons, there is no strong evidence that one set of evolutionary tracks is better than the other one. Therefore we provide the two masses and their uncertainties in the catalogue available at the CDS.

In this procedure to determine masses we need metallicities as input for SPInS. We have used [Fe/H] values from the literature which are not homogeneous and therefore we have evaluated their impact on the resulting masses. We made two tests similar to those made for F bol . One test is to adopt a large uncertainty of 0.15 on [Fe/H] for all the stars, much larger than the original ones. The other test is to add or subtract 0.15 dex to the literature values of [Fe/H] for seven stars selected to cover the parameter space. Enlarging the metallicity uncertainty to 0.15 dex affects mainly the clump giants. Based on the BASTI tracks, only 5 stars in our sample have their mass affected by more than 30%, and only 8 stars if we consider the STAREVOL tracks. The most critical stars are not common from one set to the other. This reinforces the interest of considering the masses computed by the two sets of stellar evolution models. Such differences could be explained by different inputs in the computation of the evolutionary tracks (e.g. mass loss, atmosphere models, etc.) which change the position in the HRD. It should be noted that at least 90% of the stars in our sample experience a mass variation less than 10%, while three quarters of the sample remain below 5%, whatever the set of stellar models taken into account. Changing the value of [Fe/H] by ±0.15 dex for seven stars leads to a similar conclusion: the dwarfs are not affected, whatever their metallicity, while changes occur among giants. However, due to the dependency of log g on the logarithm of mass in Eq. ( 2), in the worst cases where the mass is changed by 30%, the impact on log g is limited to 0.11 dex and up to 0.5 dex for the most critical cases.

Assessment of log g

We computed the fundamental log g of each star by applying Eq. ( 2) with the values of mass from SPInS, with both evolutionary tracks BaSTI and STAREVOL, and the radius deduced from θ LD , with the propagation of their uncertainties. We consider here the 201 stars of the sample. The resulting uncertainties on log g span from 0.004 to 0.13 (BaSTI) and 0.23 dex (STAREVOL), with a median value of 0.02 dex. Figure 20 shows the comparison of log g determinations, using the mass from SPInS with BaSTI or STAREVOL. The agreement is excellent for dwarfs with log g>4. Below that value, log g from STAREVOL is systematically larger by 0.06 dex than log g from BaSTI, with an exception around log g STAREVOL =2.3. Following the comparisons made in the previous sections, for radii and masses, we used the seismic data to determine log g in another and independent way, through the relation that gives log g as a function of the maximum of the power spectrum of oscillation frequencies, ν max , available for 42 stars, and the effective temperature:

log g ≈ log ν max + 0.5 log T eff -log ν max,⊙ , -0.5 log T eff,⊙ + log g ⊙ , (7)
The comparison of seismic and fundamental log g is shown in Fig. 21. For dwarfs, typically log g seismic >3.8 dex, the agreement is very good except for one star, HIP92984. For this star we find log g=4.48 dex with BaSTI and STAREVOL masses, while the seismic log g is significantly lower, log g=4.23. We have pointed out the ambiguity about the seismic parameters of that star in the previous section. If this star is excluded, the differences between seismic and fundamental log g of dwarfs have a MAD of 0.02 dex. For giant stars, the dispersion is larger (MAD=0.07 dex), with log g based on BaSTI lying slightly below the seismic values (median offset of -0.06 dex), while the log g based on STAREVOL tend to lie above (median offset of 0.01 dex). A few outliers, reaching nearly 0.5 dex, correspond to stars with one of the two masses giving a disagreement with the seismic log g but not the other one. From that comparison, we cannot say that the agreement is better with BaSTI or with STAREVOL masses.

We also compare our log g determinations with those in Paper I and in Karovicova et al. (2020Karovicova et al. ( , 2022a,b) ,b) in Fig. 22. Offsets are negligible while dispersions (MAD) are 0.04 dex for Paper I, whatever the tracks. The values of log g generally agree 0: 5 1:0 1:5 2:0 2:5 3:0 3:5 4:0 4:5 5: We can draw similar conclusion as for the comparison to seismic log g: a better agreement with one or the other set of evolutionary tracks is not obvious. Therefore, since there is no strong argument to adopt masses from BaSTI instead of STAREVOL and vice versa, we compute the average of the two values as the final log g. This strategy allows us to mitigate some discrepancies among giants while it has no impact for most of the stars which have consistent masses whatever the used tracks. The final log g distribution and uncertainties are shown in Fig. 23. The bottom panel shows separately the uncertainties for dwarfs (log g>3.8) and giants (log g≤3.8), highlighting the lower precision obtained for giants. The median uncertainty is 0.02 dex for dwarfs and 0.06 dex for giants. While 90% of the dwarfs have an uncertainty lower than 0.05 dex, 90% of the giants have an uncertainty higher than 0.03 dex.

The new set of Gaia FGK benchmark stars

The fundamental T eff and log g determined for the 192 GBS V3 stars with a direct value of θ LD are given in Table A.1 of Appendix A while the nine other stars from V1 and V2 with an indirect θ LD are provided in Table 3. The metallicity from the literature is provided for convenience, but will be redetermined homogeneously in the coming Paper VIII. The full catalogue with all the other parameters determined in this work is available in VizieR.

The Kiel diagram with fundamental T eff and log g is shown in Fig. 24 for the full sample of 192 stars and for a selection of the best stars, with an uncertainty on T eff and log g better than 2% and 0.1 dex, respectively. This selection of 165 stars mainly rejects giants with large uncertainties, as discussed in Sect. 4, but still preserves a good distribution across the Kiel diagram.

The metallicity histogram of the GBS V3 is shown in Fig. 25, compared to that of V1 (only considering stars with a direct θ LD ), highlighting a number of new metal-poor stars. This is however more evident in the interval -1.0 <[Fe/H]< -0. One of the main purposes of the GBS is to calibrate or validate atmospheric parameters from spectroscopy. We therefore checked spectroscopic T eff and log g available in different sources, using the subset of 165 most reliable GBS.

Fig. 26 compares our fundamental determinations with those available in the PASTEL catalogue, based on high-resolution, high signal-to-noise spectroscopy. Overall, the agreement on T eff is good with a dispersion of MAD=54 K and a slight offset of 12 K (median), the spectroscopic T eff being larger. Two extreme outliers have differences larger than 400 K. For HIP86614 we suspect an uncertain angular diameter given its noisy squared visibility curve in Boyajian et al. (2012b) while for HIP108535 the only spectroscopic T eff in PASTEL is dubious. For that star we note a good agreement with the determination by Prugniel et al. (2011) based on a medium resolution spectrum.

Concerning log g we can see three regimes of precision, corresponding to dwarfs, clump giants, and cooler giants, with an increasing dispersion. The dispersion among dwarfs is 0.04 dex (MAD). It rises to 0.1 dex among clump giants (2.0<log g<3.5) with no offset, while for red giants there is a tendency of spectroscopic log g to be larger than the fundamental ones by 0.16 dex (median offset) with a significant dispersion of 0.2 dex (MAD). The GBS can therefore be used to better understand and correct the spectroscopic gravities of evolved stars.

Focusing on the best studied stars we selected in the PAS-TEL catalogue the stars which are included in at least 15 spectroscopic studies at high resolution and high signal to noise ratio since 1990. The resulting 16 stars are all dwarfs or subgiants, with some of them also in common with Paper I. In general there is a good agreement, within our uncertainties and the standard deviation from the literature values. Three stars, HIP14954, HIP57939 and HIP8159, exhibit a significant difference in T eff , larger than 150 K. HIP14954 (94 Cet) has been very much studied, with 41 spectroscopic determinations of T eff , likely because of its exoplanet discovered in 2000 (Queloz et al. 2001). The literature values range from 5916 K to 6424 K with a mean of 6176 K and a standard deviation of 84 K. Our determination is lower, T eff =5912±59 K, but still in agreement with the coolest spectroscopic determinations. Our fundamental value is in a very good agreement with that of Boyajian et al. (2013), T eff =5916±98 K, independent from ours since we use the angular diameter from Ligi et al. (2016). It would be important to better understand why spectroscopy gives a higher T eff for that star because it has implications on the parameters of its exoplanet. HIP8159 (109 Psc) also hosts an exoplanet and has several recent T eff from high resolution spectroscopy ranging between 5560 K and 5711 K. The fundamental determinations, from Boyajian et al. (2013) and from us (T eff =5438±61 K) based on the same θ LD , are cooler than the mean spectroscopic value by ∼200 K. This discrepancy requires further investigation. HIP57939 (HD103095) has 57 spectroscopic determinations of T eff after 1990, ranging from 4500 K to 5250 K with a mean of 5057 K and a standard deviation of 18 K. Our fundamental determination T eff =5235±18 K is in agreement with the hottest spectroscopic determinations, e.g. by Luck & Heiter (2005).

We also checked atmospheric parameters massively determined by large spectroscopic surveys against our fundamental determinations of the best GBS. We considered APOGEE DR17 (Majewski et al. 2017;[START_REF] Abdurro'uf | [END_REF], the Gaia-ESO survey (Randich et al. 2022;Gilmore et al. 2022) and GALAH DR3 (Buder et al. 2021) in the comparisons shown in Fig. 27. Table 5 gives the median offsets and corresponding MAD for dwarfs and giants separately. Although GALAH and Gaia-ESO have less stars in common than APOGEE, we see the same trends in the three surveys. Their T eff and log g for dwarfs are smaller on average than the fundamental ones, and vice-versa for the giants. These trends are worth to be investigated and better understood.

Finally we also assessed the photometric and spectroscopic T eff and log g of the Gaia DR3 Golden Sample of Astrophysical Parameters (Gaia Collaboration et al. 2023a) with the best GBS, Table 5. Median difference (MED) and median absolute deviation (MAD) between our fundamental determinations of T eff and log g and the spectroscopic ones from surveys (survey results minus our results), for N stars in common.

Sample

Conclusion

Large spectroscopic surveys usually calibrate or validate their determinations of atmospheric parameters using reference stars. Ideally they should adopt a common T eff and log g scale in order to minimize systematic differences in abundances provided by different instruments and pipelines. The GBS are intended to provide such an anchor to the fundamental T eff and log g. GBS are also suited to help understand any shortcomings in the stellar models.

We have presented determinations of fundamental T eff and log g, based on the Stefan-Boltzmann law and Newton's law of gravitation, for the third version of the GBS. Compared to the previous V1 and V2 versions, a significant improvement is the larger number of stars, 192 instead of ∼40, resulting from our systematic search of high quality angular diameters based on interferometric measurements. More accurate log g were obtained thanks to the higher precision parallaxes which mostly come from Gaia DR3, while the improved T eff are in part a result of the homogenous photometric data from Gaia DR3, which feed into the F bol determination. F bol are now more precise and homogeneous owing to the methodology of SED fitting applied to a combination of photometric and spectrophotometric data including measurements made on BP/RP spectra from Gaia DR3. Better F bol also result from the adopted extinction values deduced from state-fo-the-art 3D maps of the solar neighbourhood. The most difficult part comes from the determination of masses from evolutionary tracks. We have shown that using two different grids can lead to differences of up to more than 50% in masses, giving systematic offsets of about 0.06 dex in log g among giants.

At each stage of the compilation and determination of the parameters, we evaluated the uncertainties that we aimed to keep at the 1-2% level. Our results were assessed by comparing them to other determinations of similar accuracy available in the literature. In general the comparison with literature data is satisfactory, with differences not exceeding 4%. We can explain most of the outliers. We also determined seismic radii, masses and surface gravities for comparisons, using scaling relations and seismic parameters available for ∼40 stars. They show a good agreement for dwarfs but a trend in masses outside the 1-1.5M ⊙ range. From the different comparisons we are confident that our uncertainties in T eff are reliable. We reach the expected 1-2% level in T eff . For log g only dwarfs have such a level of accuracy. Uncertainties for giants are larger and reflect the difficulty to obtain reliable masses for them from evolutionary tracks.

The T eff and log g presented here will be updated. Two steps of our determination process, F bol and masses, depend on [Fe/H] which we took from the literature. This is the subject of the coming paper VIII to determine abundances of the GBS-V3 from a large collection of high quality spectra. Some iterations will be needed to adjust T eff , log g and [Fe/H] in a self-consistent way. In the meantime, we have evaluated the impact of using nonhomogeneous metallicities through tests in which we modified the values of [Fe/H] and uncertainties by 0.15 dex in input of the SED fitting and of SPInS. We found that it has a negligible impact on T eff , and also on log g for most of the stars, although a few giants have their mass affected by more than 30% inducing a change of log g by 0.11 to 0.5 dex.

In order to use the GBS V3 for calibration or validation of atmospheric parameters, we recommend the users to select the 165 stars with uncertainties on T eff and log g lower than 2% and 0.1 dex, respectively. We have used this subsample to assess T eff and log g obtained by high-resolution and high-signal to noise spectroscopy (PASTEL catalogue), by medium-resolution spectroscopy (APOGEE, GALAH and Gaia-ESO surveys), and by Gaia photometry and spectroscopy. This has revealed some issues that need to be investigated to improve the future releases.

Due to the lack of metal-poor stars in the solar neighbourhood the GBS V3 do not yet cover the metallicity range in a uniform way. We still lack angular diameters for stars with [Fe/H]< -1.0 which are important targets in galactic archeology and stellar physics. Interferometric measurements are still limited to stars brighter than V∼8, and larger than θ LD ≃0.2 mas. There are however metal-poor candidates which are bright and large enough to fulfil these criteria. They could be observed with powerful interferometers, such as the new SPICA instrument on the CHARA array [START_REF] Mourard | Optical and Infrared Interferometry and Imaging VIII[END_REF] expected to provide an estimation of the stellar radius of such stars to 1% precision. It would also be useful to remeasure partly or totally the GBS with θ LD <1.2 mas, which show a large dispersion of the current measurements, exceeding the quoted uncertainties.

Fig. 1 .

 1 Fig. 1. Histogram of θ LD (top panel) and its relative uncertainty (bottom panel) for the 192 GBS V3 stars having interferometric measurements.

Fig. 2 .

 2 Fig. 2. Difference between θ LD adopted for this work and other values in JMDC fulfilling the selection criteria by Salsi et al. (2020).

Fig. 3 .

 3 Fig. 3. Extinction A V deduced from 3D maps of Vergely et al. (2022) as a function of distance, for the 201 targets.

  Fig. 4. Example of fits of the observed (reddened) data to the (reddened) semi-empirical spectra for HIP 103598 (left) and HIP 50564 (right). The bolometric flux is calculated by integrating the un-reddened spectrum. The bottom panels illustrate the distribution of χ 2 R versus F bol for the 400 simulations for the two stars with the 16 th , 50 th (median), and 84 th percentiles indicated by the dashed lines.

  10 ¡8 :erg:s ¡1 :cm ¡2 ]

Fig. 5 .

 5 Fig. 5. Histogram of F bol (top panel) and its relative uncertainties (bottom panel).

Fig. 6 .Fig. 7 .

 67 Fig. 6. Comparison of F bol obtained in this work with literature. The colour code relates to the extinction. Several extreme outliers are out of the figure boundaries but they are discussed in the text.

Fig. 8 .

 8 Fig. 8. Propagation of θ LD and F bol relative uncertainties on T eff .

Fig. 9 .Fig. 10 .

 910 Fig. 9. Comparison of our fundamental determinations of T eff with other fundamental determinations from the literature in Paper I and Boyajian et al. (2013); Karovicova et al. (2020, 2022a,b); van Belle et al. (2021).

  For α Cen A & B (HIP71683 & HIP71681) we adopt the high precision determination by Akeson et al. (2021) instead of the Hipparcos one. Figure 10 shows the distribution of the parallax relative uncertainties as a function of the Hipparcos magnitude Hp. The four faintest stars with Hp>8 mag have an indirect θ LD . We applied the zero-point correction derived by Lindegren et al. (2021) to the Gaia parallaxes.

Fig. 11 .

 11 Fig. 11. Histogram of linear radii R (top panel) and their relative uncertainty (bottom panel).

Fig. 12 .

 12 Fig. 12. Histogram of luminosities L (top panel) and their relative uncertainty (bottom panel).

Fig. 13 .

 13 Fig. 13. Linear radius difference between our determination of R from Eq. (3), and seismic estimations from Eq. (5).

Fig. 14 .

 14 Fig. 14. Luminosity difference between our determinations L from F bol and distance, and Gaia DR3 estimations based on G magnitudes and bolometric corrections for 36 stars in common in the Golden Sample of Astrophysical Parameters (Gaia Collaboration et al. 2023a).

  -STAREVOL -This stellar grid covers a mass range between 0.6 and 6.0 M ⊙ and a metallicity range [Fe/H] ∈ [-2.14, +0.51] without α-enhancement, with the exception of [Fe/H]=-2.14 and -1.2 where [α/Fe]=+0.3. Except for convection, additional mixing effects such as rotationinduced mixing are not taken into account. The overshoot parameter is set to 0.05 or 0.10 for stars with masses below or above 2.0 M ⊙ , respectively; no overshooting is considered for masses lower than 1.1 M ⊙ . The stellar grid is constructed using the solar mixture coming fromAsplund et al. (2009).

Fig. 15 .

 15 Fig. 15. Histogram of masses (top panel) and their relative uncertainty (bottom panel), red for BaSTI, for STAREVOL.

Fig. 16 .

 16 Fig. 16. Comparison of masses determined with SPInS (red dots for BaSTI, blue open squares for STAREVOL) to dynamical masses for µ Cas, α Cen B, α Cen A and Procyon, ordered by increasing mass.

Fig. 17 .

 17 Fig. 17. Comparison between masses from SPInS (red dots for BaSTI, blue open squares for STAREVOL) and seismic masses from Eq. (6).

Fig. 18 .

 18 Fig. 18. Comparison of masses determined with SPInS (red dots for BaSTI, blue open squares for STAREVOL) to those available in the literature, also based on evolutionary tracks.

Fig. 19 .

 19 Fig. 19. Comparison between masses from SPInS (red dots for BaSTI, blue open squares for STAREVOL) and masses from the Gaia Golden Sample of Astrophysical Parameters (Gaia Collaboration et al. 2023a).

Fig. 20 .

 20 Fig. 20. Comparison of log g determinations, using masses from SPInS with BaSTI or STAREVOL. The area between the two dashed lines indicates an agreement within 0.1 dex.

Fig. 21 .

 21 Fig. 21. Comparison of our fundamental values of log g to those determined from ν max and our fundamental T eff . Red dots for SPInS masses using BaSTI models, blue open squares for STAREVOL models.

Fig. 22 .

 22 Fig. 22. Comparison of our fundamental values of log g to those determined in Paper I and by Karovicova et al. (2020, 2022a,b). Red dots for SPInS masses using BaSTI models, blue open squares for STAREVOL models.

Fig. 23 .

 23 Fig. 23. Histogram of log g (top panel) and uncertainty (bottom panel). The bottom panel shows the uncertainties for dwarfs (red) and giants (blue).

Fig. 24 .

 24 Fig. 24. Kiel diagram with fundamental T eff and log g. The colour scale is related to metallicities from the literature. The left panel shows the full sample of 192 stars while the right panel shows the stars with uncertainties on T eff and log g better than 2% and 0.1 dex respectively.

Fig. 25 .

 25 Fig. 25. Histogram of [Fe/H] for the 192 fundamental GBS V3 (grey) compared to the V1 version (red).

Fig. 26 .

 26 Fig. 26. Comparison of our fundamental values of T eff (top panel) and log g (bottom panel) to spectroscopic ones available in the PASTEL catalogue.

Fig. 27 .

 27 Fig. 27. Comparison of T eff and log g from this work with the spectroscopic ones in surveys: APOGEE DR17 (blue), Gaia-ESO (red), GALAH DR3 (green).

Fig. 28 .

 28 Fig. 28. Comparison of T eff and log g from this work with the photometric (red dots) and spectroscopic (blue squares) ones from the Gaia DR3 Golden Sample of Astrophysical Parameters (Gaia Collaboration et al. 2023a).

Table 2 .

 2 Median difference (MED) and median absolute deviation (MAD) between direct determinations of T eff from the literature and our values (literature minus this work), for N stars in common.

	Reference	N MED MAD
			(K)	(K)
	Heiter et al. (2015) -Paper I	28	-26	32
	Boyajian et al. (2013)	82	-59	58
	Karovicova et al. (2020, 2022a,b) 21	-39	30
	van Belle et al. (2021)	17	61	77

Table 3 .

 3 T eff and log g determined in this work for stars from V1 and V2 with an indirect value of θ LD . [Fe/H] from the literature is given for indication.

	HIP	HD	T eff	log g	[Fe/H]
			(K)	(dex)	(dex)
	14086	18907 5143± 56 3.53±0.03	-0.63
	17147	22879 5962± 86 4.28±0.04	-0.84
	48152	84937 6484±106 4.16±0.05	-2.12
	50382 298986 6343± 43 4.29±0.02	-1.33
	57360 102200 6205± 45 4.27±0.02	-1.23
	59490 106038 6172± 42 4.28±0.02	-1.33
	60172 107328 4576± 87 1.77±0.22	-0.38
	86796 160691 5974± 60 4.30±0.03 +0.29
	104659 201891 6040± 44 4.34±0.02	-1.02
	log g for these eight GBS V3 stars are presented in Table 4 to-
	gether with the values from Paper I for the four stars in common.

Table 4 .

 4 Fundamental T eff and log g for the eight GBS V3 with [Fe/H]< -1.0 (from the literature), and comparison to the Paper I values, when available.

			HIP		other name	T eff V3	T eff V1	log g V3	log g V1	[Fe/H]
			HIP2413	HD2665		4951±25		2.318±0.029	-1.97
			HIP5445	HD6755		4977±27		2.767±0.027	-1.43
			HIP8837	ψ Phe		3362±183	3472±92	0.438±0.058 0.51±0.18	-1.24
			HIP57939	HD103095	5235±18	4827±55	4.717±0.014	4.6±0.03	-1.33
			HIP68594	HD122563	4642±35	4587±60	1.312±0.029 1.61±0.07	-2.67
			HIP76976	HD140283	5788±45	5522±105 3.750±0.089 3.58±0.11	-2.48
			HIP92167	HD175305	4902±30		2.533±0.017	-1.45
			HIP115949 HD221170	4380±18		1.216±0.023	-2.10
	3500	4000	4500	5000	5500	6000	6500	7000
				Te® [K]

  at CDS, Strasbourg, France, and of NASA's Astrophysics Data System Bibliographic Services. This publication makes use of VOSA, developed under the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. VOSA has been partially updated by using funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement no. 776403 (EXOPLANETS-A). The Stellar Parameters INferred Systematically (SPInS) code is a spin-off of the Asteroseismic Inference on a Massive Scale project, one of the deliverables of the SpaceINN network, funded by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 312844. SPInS was initially created for the 5th International Young Astronomer School Scientific Exploitation of Gaia Data held in Paris, (26 February -2 March 2018), as a simple tool to estimate stellar ages, as well as other stellar properties.

Table A .

 A 1. Fundamental T eff and log g and their uncertainties determined in this work for the 192 GBS V3, with [Fe/H] from the literature and the θ LD adopted measurement.

				A&A proofs: manuscript no. main A&A proofs: manuscript no. main
			Table A.1. continued. Table A.1. continued.
	HIP HIP	HD HD	θ LD θ LD	Reference for θ LD Reference for θ LD	T eff T eff	ru_T eff ru_T eff	log g log g	[Fe/H] [Fe/H]
	HIP HIP27530 HIP96014 HIP101345 HD195564 HD HD39523 HD184293 HIP27621 HD39640 HIP96100 HD185144 HIP10234 HD13468 HIP27913 HD39587 HIP96441 HD185395 HIP102422 HD198149 HIP28011 HD39910 HIP96837 HD185958 HIP103598 HD200205 HIP28139 HD40020 HIP96895 HD186408 HIP104214 HD201091 HIP29575 HD43023 HIP96901 HD186427 HIP104217 HD201092 HIP3031 HD3546 HIP97527 HD187637 HIP106039 HD204381 HIP30565 HD46116 HIP98036 HD188512 HIP108535 HD209369 HIP3093 HD3651 HIP98269 HD189349 HIP108870 HD209100 HIP3137 HD3750 HIP98337 HD189319 HIP109176 HD210027 HIP32362 HD48737 HIP98624 HD188887 HIP109937 HD211388 HIP32851 HD49933A HIP98767 HD190360 HIP11095 HD15248 HIP3456 HD4211 HIP98819 HD190406 HIP111944 HD214868 HIP112440 HD215665 HIP112447 HD215648 HIP112731 HD216174 1.5980 ± 0.0120 θ LD (mas) (mas) (mas) 1.939 ± 0.016 1.548 ± 0.022 0.712 ± 0.03 1.251 ± 0.017 1.254 ± 0.011 0.886 ± 0.01 1.051 ± 0.009 0.749 ± 0.007 2.882 ± 0.088 1.09 ± 0.008 1.764 ± 0.012 2.032 ± 0.043 1.012 ± 0.023 0.539 ± 0.007 1.775 ± 0.013 0.842 ± 0.014 0.490 ± 0.006 1.581 ± 0.022 1.77 ± 0.08 0.231 ± 0.006 1.524 ± 0.017 1.145 ± 0.031 2.079 ± 0.011 0.621 ± 0.017 0.722 ± 0.007 0.417 ± 0.005 1.758 ± 0.012 1.003 ± 0.02 6.089 ± 0.011 1.206 ± 0.053 1.401 ± 0.009 1.595 ± 0.011 3.371 ± 0.049 0.445 ± 0.012 0.698 ± 0.019 0.949 ± 0.019 1.1 ± 0.011 0.584 ± 0.01 2.731 ± 0.02 2.26 ± 0.1 1.091 ± 0.008 HIP112748 HD216131 2.496 ± 0.04 HIP113357 HD217014 0.685 ± 0.011 HIP114622 HD219134 1.106 ± 0.007 HIP114855 HD219449 2.22 ± 0.031 HIP114971 HD219615 2.3400 ± 0.0400 HIP115227 HD220009 2.045 ± 0.034 HIP115620 HD220572 1.092 ± 0.013 HIP115949 HD221170 0.596 ± 0.005 HIP116771 HD222368 1.082 ± 0.009 HIP12114 HD16160 1.03 ± 0.007 HIP12486 HD16815 2.248 ± 0.014 HIP12530 HD16765A 0.497 ± 0.007 HIP12777 HD16895 1.103 ± 0.008 HIP13288 HD17824 1.391 ± 0.015 HIP13328 HD17709 4.056 ± 0.041 HIP14060 HD18784 1.036 ± 0.014 HIP14135 HD18884 12.2 ± 0.04 HIP14632 HD19373 1.246 ± 0.007 HIP14838 HD19787 1.87 ± 0.12 HIP14954 HD19994 0.761 ± 0.01 HIP15457 HD20630 0.936 ± 0.024 HIP15776 HD21019 0.606 ± 0.015 HIP16537 HD22049 2.087 ± 0.011 HIP16852 HD22484 1.081 ± 0.014 HIP1686 HD1671 0.6 ± 0.006 HIP17086 HD22798 0.792 ± 0.021 HIP171 HD224930 0.716 ± 0.007 HIP17378 HD23249 2.343 ± 0.009 HIP17595 HD23526 0.915 ± 0.021 HIP17738 HD23940 1.093 ± 0.021 HIP18859 HD25457 0.582 ± 0.016 HIP19849 1.504 ± 0.006 HIP2021 HD2151 2.257 ± 0.019 HIP21421 HD29139 20.58 ± 0.03 HIP22449 HD30652 1.526 ± 0.004 HIP22453 HD30504 2.803 ± 0.013 HIP22479 HD30814 1.31 ± 0.01 HIP2413 HD2665 0.395 ± 0.004 HIP24813 HD34411 0.981 ± 0.015 HIP25993 HD36848 1.386 ± 0.098 HIP26019 HD36874 1.118 ± 0.011 HIP27435 HD38858 0.572 ± 0.009 HIP671 HD360 0.906 ± 0.015 HIP6592 HD8651 1.228 ± 0.013 HIP65721 HD117176 0.998 ± 0.004 HIP64394 HD114710 1.127 ± 0.011 HIP63608 HD113226 3.318 ± 0.013 HIP63584 HD113337 0.386 ± 0.009 HIP61317 HD109358 1.133 ± 0.034 HIP57939 HD103095 0.593 ± 0.004 HIP57757 HD102870 1.431 ± 0.006 HIP57477 HD102328 1.606 ± 0.006 HIP56997 HD101501 0.91 ± 0.009 HIP56343 HD100407 2.386 ± 0.021 HIP56127 HD99998 3.21 ± 0.02 HIP55219 HD98262 4.561 ± 0.016 HIP5458 HD6833 0.852 ± 0.008 HIP54539 HD96833 4.131 ± 0.007 HIP5445 HD6755 0.369 ± 0.004 HIP544 HD166 0.624 ± 0.009 HIP5336 HD6582 0.973 ± 0.009 HIP51459 HD90839 0.794 ± 0.014 HIP50887 HD90043 0.659 ± 0.009 HIP50564 HD89449 0.731 ± 0.026 HIP49908 HD88230 1.268 ± 0.04 HIP49637 HD87837 3.33 ± 0.04 HIP49081 HD86728 0.771 ± 0.012 HIP48455 HD85503 2.887 ± 0.016 HIP47908 HD84441 2.643 ± 0.015 HIP47431 HD83618 3.462 ± 0.033 HIP47080 HD82885 0.821 ± 0.012 HIP46853 HD82328 1.632 ± 0.005 HIP4587 HD5722 0.995 ± 0.019 HIP45860 HD80493 7.538 ± 0.075 HIP45343 HD79210 0.871 ± 0.014 HIP43813 HD76294 3.196 ± 0.017 HIP43587 HD75732 0.724 ± 0.011 HIP4257 HD5268 0.767 ± 0.035 HIP4151 HD5015 0.865 ± 0.01 HIP40843 HD69897 0.706 ± 0.013 HIP40693 HD69830 0.674 ± 0.014 HIP40526 HD69267 5.03 ± 0.03 HIP3850 HD4747 0.39 ± 0.007 HIP37826 HD62509 8.018 ± 0.043 HIP37664 HD62713 1.446 ± 0.012 HIP3765 HD4628 0.868 ± 0.004 HIP37279 HD61421 5.406 ± 0.006 HIP36732 HD60341 1.19 ± 0.022 HIP36444 HD60060 0.948 ± 0.01 HIP99663 HD192781 1.859 ± 0.002	Reference for θ LD 2018A&A...616A..68G 2016AJ....152...66B 2013ApJ...771...40B 2018A&A...616A..68G 2012ApJ...746..101B 2018A&A...616A..68G 2012ApJ...746..101B 2016A&A...586A..94L 2016ApJS..227....4H 2018A&A...616A..68G 2009MNRAS.394.1925V 2010ApJ...710.1365B 2018A&A...616A..68G 2013MNRAS.433.1262W 5849 ± 39 T eff (K) (K) (K) 4583 ± 80 4336 ± 42 5514 ± 116 4851 ± 41 5289 ± 24 4676 ± 80 5883 ± 63 6914 ± 33 4751 ± 73 4565 ± 33 4990 ± 20 4032 ± 45 4671 ± 59 2008A&A...488..667K 4398 ± 34 2020A&A...639A..67N 5043 ± 43 2013MNRAS.433.1262W 5807 ± 36 2008A&A...488..667K 4174 ± 47 1999AJ....118.3032N 4909 ± 111 2012ApJ...760...32H 6236 ± 81 2018A&A...616A..68G 5079 ± 31 2018A&A...616A..68G 4880 ± 68 2020MNRAS.493.2377R 5155 ± 15 2016A&A...586A..94L 6754 ± 93 2016A&A...586A..94L 5297 ± 31 2022A&A...658A..48K 5175 ± 31 2020MNRAS.493.2377R 4754 ± 35 2018A&A...616A..68G 4610 ± 51 2021AJ....162..198B 3904 ± 30 2009ApJ...694.1085V 6419 ± 141 2012ApJ...746..101B 6537 ± 25 2018A&A...616A..68G 4381 ± 28 2018AJ....155...30B 4258 ± 41 2011A&A...534L...3B 6628 ± 89 2016A&A...586A..94L 5463 ± 75 2018A&A...616A..68G 4721 ± 52 2018A&A...616A..68G 4572 ± 35 2012ApJ...751...97C 5825 ± 50 2010ApJ...710.1365B 4203 ± 34 1999AJ....118.3032N 4848 ± 109 2012ApJ...746..101B 6223 ± 23 2016AJ....152...66B 4297 ± 36 2003AJ....126.2502M 4961 ± 40 2013ApJ...771...40B 5746 ± 72 2012ApJ...757..112B 4800 ± 34 2018AJ....155...30B 4631 ± 69 2015A&A...573A.138B 4970 ± 43 2015A&A...582A..49H 4227 ± 77 2018A&A...616A..68G 4756 ± 41 2020A&A...640A..25K 4380 ± 19 2012ApJ...746..101B 6169 ± 56 2012ApJ...757..112B 4583 ± 76 2018A&A...616A..68G 4720 ± 23 2013ApJ...771...40B 6310 ± 51 2012ApJ...746..101B 6206 ± 23 2018A&A...616A..68G 4980 ± 64 2003AJ....126.2502M 3799 ± 72 2018A&A...616A..68G 4652 ± 80 2006A&A...460..855W 3738 ± 170 2012ApJ...746..101B 5921 ± 17 1999AJ....118.3032N 4703 ± 161 2016A&A...586A..94L 5912 ± 59 2012ApJ...746..101B 5786 ± 87 2013ApJ...771...40B 5259 ± 66 2020MNRAS.493.2377R 5130 ± 30 2012ApJ...746..101B 6000 ± 59 2016A&A...586A..94L 6674 ± 34 2020A&A...639A..67N 4652 ± 88 2020A&A...640A..25K 5445 ± 30 2020MNRAS.493.2377R 5026 ± 38 2018A&A...616A..68G 4763 ± 81 2018A&A...616A..68G 4815 ± 52 2018ApJ...858...71S 6295 ± 91 2012ApJ...757..112B 5181 ± 21 2007MNRAS.380L..80N 5917 ± 25 2005A&A...433..305R 3921 ± 80 2012ApJ...746..101B 6518 ± 35 2009MNRAS.394.1925V 4097 ± 20 2018A&A...616A..68G 4901 ± 27 2020A&A...640A..25K 4951 ± 25 2012ApJ...746..101B 5823 ± 45 2012A&A...539A..58C 4537 ± 163 2018A&A...616A..68G 4616 ± 32 2013ApJ...771...40B 5705 ± 47 2018A&A...616A..68G 4679 ± 79 2018A&A...616A..68G 4685 ± 43 2015ApJ...806...60K 5473 ± 22 2012ApJ...746..101B 5930 ± 30 2018AJ....155...30B 4950 ± 10 2019A&A...627A..44B 6783 ± 79 2018AJ....155...30B 6013 ± 91 2020A&A...640A..25K 5235 ± 18 2012ApJ...746..101B 6093 ± 13 2010ApJ...710.1365B 4450 ± 31 2012ApJ...746..101B 5310 ± 28 2005A&A...436..253T 5034 ± 34 1999AJ....118.3032N 3852 ± 90 2018AJ....155...30B 4187 ± 61 2020A&A...640A..25K 4447 ± 42 2018AJ....155...30B 4543 ± 6 2020A&A...640A..25K 4977 ± 27 2013ApJ...771...40B 5378 ± 40 2008ApJ...683..424B 5358 ± 31 2012ApJ...746..101B 6259 ± 56 2018MNRAS.477.4403W 4801 ± 83 2013MNRAS.434.1321M 6385 ± 120 2001ApJ...551L..81L 4132 ± 72 1999AJ....118.3032N 4106 ± 47 2012ApJ...746..101B 5610 ± 46 2018AJ....155...30B 4519 ± 23 2009MNRAS.394.1925V 5314 ± 17 2018AJ....155...30B 4238 ± 22 2012ApJ...746..101B 5452 ± 46 2012ApJ...746..101B 6217 ± 44 2018A&A...616A..68G 4914 ± 50 2003AJ....126.2502M 3881 ± 20 2012ApJ...757..112B 3997 ± 34 2018AJ....155...30B 4836 ± 14 2016A&A...586A..94L 5169 ± 44 2020A&A...639A..67N 4944 ± 116 2012ApJ...746..101B 6033 ± 37 2013ApJ...771...40B 6203 ± 57 2015ApJ...800..115T 5317 ± 58 1999AJ....118.3032N 4080 ± 15 2019ApJ...873...83W 5351 ± 48 2016ApJS..227....4H 4810 ± 14 2018A&A...616A..68G 4661 ± 32 2012ApJ...757..112B 5093 ± 33 2021AJ....162..198B 6582 ± 5 2018A&A...616A..68G 4563 ± 53 2018A&A...616A..68G 4814 ± 32 2010ApJ...710.1365B 4084 ± 25	ru_T eff (%) (%) (%) 1.7 1.0 2.1 0.8 0.5 1.7 1.1 0.5 1.5 0.7 0.4 1.1 1.3 0.7 0.8 0.9 0.6 1.1 2.3 1.3 0.6 1.4 0.3 1.4 0.6 0.6 0.7 1.1 0.8 2.2 0.4 0.6 1.0 1.3 1.4 1.1 0.8 0.9 0.8 2.2 0.4 0.8 0.8 1.3 0.7 1.5 0.9 1.8 0.9 0.4 0.9 1.6 0.5 0.8 0.4 1.3 1.9 1.7 4.5 0.3 3.4 1.0 1.5 1.3 0.6 1.0 0.5 1.9 0.6 0.8 1.7 1.1 1.5 0.4 0.4 2.0 0.5 0.5 0.6 0.5 0.8 3.6 0.7 0.8 1.7 0.9 0.4 0.5 0.2 1.2 1.5 0.3 0.2 0.7 0.5 0.7 2.3 1.4 0.9 0.1 0.5 0.7 0.6 0.9 1.7 1.9 1.7 1.2 0.8 0.5 0.3 0.5 0.8 0.7 1.0 0.5 0.9 0.3 0.8 2.3 0.6 0.9 1.1 0.4 0.9 0.3 0.7 0.6 0.1 1.2 0.7 0.6	(dex) (dex) log g (dex) 2.36 ± 0.13 1.79 ± 0.05 -0.35 (dex) (dex) [Fe/H] 0.15 (dex) 2.60 ± 0.05 -0.11 4.56 ± 0.02 -0.21 3.95 ± 0.09 0.05 4.47 ± 0.02 -0.03 4.24 ± 0.01 -0.03 2.37 ± 0.09 -0.13 2.50 ± 0.05 0.26 2.20 ± 0.02 0.00 3.15 ± 0.05 -0.13 2.57 ± 0.09 0.13 4.28 ± 0.02 0.08 1.20 ± 0.06 -0.36 2.96 ± 0.08 0.00 4.35 ± 0.02 0.07 4.63 ± 0.01 -0.13 2.44 ± 0.11 -0.62 4.26 ± 0.03 -0.09 4.68 ± 0.02 -0.21 2.53 ± 0.15 -0.32 3.68 ± 0.06 -0.15 2.86 ± 0.04 -0.11 4.52 ± 0.02 0.14 2.39 ± 0.04 -0.59 3.84 ± 0.05 -0.24 2.40 ± 0.13 0.03 1.06 ± 0.04 -0.26 4.62 ± 0.01 -0.13 3.79 ± 0.03 0.14 2.35 ± 0.10 0.11 4.15 ± 0.06 -0.11 4.19 ± 0.04 -0.39 4.26 ± 0.03 0.22 1.39 ± 0.05 -0.05 2.34 ± 0.10 0.01 4.35 ± 0.02 0.05 2.59 ± 0.06 0.06 0.18 0.06 0.08 0.01 0.00 0.09 0.11 0.20 0.04 0.24 0.09 0.10 0.03 0.06 0.19 0.00 2.32 ± 0.11 -0.09 4.43 ± 0.02 -0.22 2.39 ± 0.08 -0.20 2.47 ± 0.10 3.94 ± 0.08 -0.06 2.71 ± 0.13 4.37 ± 0.01 0.06 4.20 ± 0.02 2.72 ± 0.02 0.06 2.32 ± 0.03 -1.97 4.24 ± 0.03 0.17 2.73 ± 0.04 -0.02 4.41 ± 0.04 -0.20 1.32 ± 0.05 -0.34 4.72 ± 0.01 -1.33 4.31 ± 0.01 4.08 ± 0.02 0.13 1.17 ± 0.05 -0.20 2.37 ± 0.08 0.19 3.97 ± 0.04 -0.12 4.42 ± 0.01 -0.05 4.51 ± 0.01 -0.29 2.78 ± 0.07 -0.09 4.39 ± 0.04 0.95 ± 0.06 -0.39 2.43 ± 0.06 -0.34 1.38 ± 0.10 -0.14 2.33 ± 0.15 -0.15 1.83 ± 0.02 -0.86 3.83 ± 0.10 2.12 ± 0.05 -0.11 4.39 ± 0.03 -0.79 2.77 ± 0.03 -1.43 2.40 ± 0.25 4.46 ± 0.02 0.11 3.69 ± 0.04 -0.09 4.49 ± 0.01 -0.83 4.06 ± 0.03 -0.08 4.40 ± 0.02 -0.12 4.63 ± 0.01 -0.08 3.11 ± 0.06 -0.03 3.73 ± 0.12 -0.45 4.12 ± 0.05 0.10 4.50 ± 0.04 4.63 ± 0.04 0.21 4.00 ± 0.04 1.59 ± 0.06 -0.02 2.36 ± 0.23 4.25 ± 0.02 0.20 4.17 ± 0.01 2.43 ± 0.06 0.27 0.66 ± 0.07 -0.24 2.36 ± 0.05 -0.03 2.30 ± 0.12 1.78 ± 0.04 -0.06 0.93 ± 0.06 -0.36 4.44 ± 0.02 0.34 2.89 ± 0.03 -0.02 3.83 ± 0.05 -0.17 4.26 ± 0.01 2.61 ± 0.05 -0.23 4.36 ± 0.02 -0.02 1.06 ± 0.04 -0.26 2.37 ± 0.06 -0.36 4.69 ± 0.02 0.17 4.52 ± 0.01 -0.13 2.49 ± 0.04 -0.05 4.09 ± 0.02 -0.14 4.41 ± 0.02 0.32 1.22 ± 0.02 -2.10 2.36 ± 0.18 -0.35 2.61 ± 0.06 4.03 ± 0.03 0.05 1.66 ± 0.04 -0.66 4.17 ± 0.02 -0.28 2.44 ± 0.12 -0.53 4.45 ± 0.03 -0.03 2.32 ± 0.11 -0.03 1.28 ± 0.05 -0.20 4.55 ± 0.01 4.55 ± 0.03 -0.23 4.33 ± 0.02 2.55 ± 0.03 0.02 2.85 ± 0.03 -0.03 2.29 ± 0.08 0.02 1.75 ± 0.03 -0.55 4.64 ± 0.01 -0.26 3.95 ± 0.04 -0.27 3.98 ± 0.02 -0.02 2.12 ± 0.08 -0.07 2.40 ± 0.08 0.01 1.56 ± 0.06 -0.20 2.59 ± 0.04 -0.08 1.40 ± 0.04 -0.24

http://svo2.cab.inta-csic.es/theory/vosa/

https://www.ipac.caltech.edu/2mass/releases/allsky/ doc/sec4_4a.html ber of stars retrieved in each passband or catalogue are provided in Table1. The number of flux values per star ranges from only 15 for HIP14135 (α Cet) to 404 for HIP7294 (χ Cas). The median number of fluxes per star is 101. Fluxes used for the determination of F bol are available at the CDS.

This routine is distributed as part of the IDL Astronomy User's Library at https://github.com/wlandsman/IDLAstro.

The units of surface gravity g are cm s -2 . However, throughout the article, we omit the unit or use the unit dex when specifying values of log g.

https://www.iau.org/static/resolutions/IAU2015_ English.pdf

Acknowledgements. CS, NL, and LC acknowledge financial support from "Programme National de Physique Stellaire" (PNPS) and from the "Programme National Cosmology et Galaxies (PNCG)" of CNRS/INSU, France. CS, PJ and LC acknowledge financial support from the French-Chilean program of cooperation ECOS C18U02 (ECOS-ANID 180049). We acknowledge support from FONDECYT Regular grant 1231057, 1200703, and Millenium Nucleus ERIS NCN2021_017, Centros ANID Iniciativa Milenio. LC acknowledges the grant RYC2021-033762-I funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR. U.H. acknowledges support from the Swedish National Space Agency (SNSA/Rymdstyrelsen). DDBS acknowledges financial support from Becas-ANID scholar-ship 21220843. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos. esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The preparation of this work has made extensive use of Topcat (Taylor 2005), of the Simbad and VizieR databases