Andrea Catalano

Jean-Michel Lamarre

Daniel Marco

POINTECOUTEAU

Vm trying to bring heaven in my head but the Moon seems to know

Introduction

Planck est le troisième satellite consacré à l'étude du Fond Cosmologique Micro-onde (FCM), après, COBE et WMAP. Il réalisera un relevé complet dans 9 bandes couvrant le domaine spectral compris entre 25 GHz et 1 THz.

Planck fournira la mesure ultime des anisotropies en température du FCM jusqu'à des échelles d'environ 5 minutes d'arc, avec une sensibilité limitée principalement par le bruit de photons et par sa capacité à soustraire les avant-plans. Il mesurera aussi sa polarisation, les modes scalaires (modes E) devant largement sortir du bruit alors que la détection des modes tensoriels (modes B), où l'on peut espérer trouver la signature d'ondes gravitationnelles produites pendant l'inflation, n'est pas assurée. La mesure des avant-plans fournira une riche moisson de données de plusieurs composantes de l'émission du ciel, par exemple des milliers de galaxies et d'amas de galaxies ou le milieu diffus de notre propre galaxie. Le lancement de Planck et de son compagnon Herschel est attendu en d'Avril 2009.

A bord de Planck, l'instrument haute fréquence HFI (High Frequency In strument) comportera 52 bolomètres refroidis à lOOmK. Cet instrument très ambitieux est réalisé par un consortium international piloté par la France (PI : Jean-Loup Puget IAS/Orsay). Mon travail de thèse est consacré es sentiellement à l'étalonnage et au réglage, au sol et en vol, de l'instrument HFI. Il comprend d'un côté une partie expérimentale, c'est-à-dire la réalisa tion de séquences d'étalonnage au sol et le traitement des données obtenues pendant la campagne d'étalonnage PFM (Proto-Flight-Model), et de l'autre un travail de simulation de l'instrument pour interpréter ces données et pour prédire et comprendre son comportement pour la campagne future de réglage et d'étalonnage en vol. Des modèles numériques spécialisés de l'instrument HFI ont été développés, en particulier en ce qui concerne la détermination de sa réponse photométrique et de sa réponse dynamique, qui est essentielle du fait du mode d'observation par balayage du ciel à grande vitesse (6 Deg/s).

Ces modèles sont élaborés à partir d'une description physique de l'instrument et de ses composants. Cela concerne par exemple la transmission totale de l'optique, le rayonnement de l'instrument sur ses propres détecteurs et le Introduction Planck is the third satellite devoted to the study of the Cosmic Microwave Background (CMB) after COBE and WMAP. It will measure the whole sky in 9 spectral bands between 25GHz and ITHz.

Planck will provide the definitive measurement of the CMB température anisotropies down to 5' angular scales with a sensitivity mainly limited by the photon noise and by the contamination of foregrounds. Planck will also measure the polarisation of the sky. The scalar modes (E modes) of the CMB will be measured with a large signal to noise ratio, and the tensor modes (B modes) that should contain signatures of gravitational waves generated during inflation, may be detected. The measurements of the foregrounds will provide a wealth of data on astrophysical components observable in the submillimetre range, such as thousands of galaxies, The Sunyaev-Zeldovich effect of thousands of clusters, or the diffuse émission of our own galaxy. The launch of Planck and its companion satellite Herschel is expected in April 2009.

The High Frequency Instrument of Planck (HFI), with its 52 bolometers cooled at 100 mK, has been designed and developed by a international con sortium headed by France (PI Jean-Loup Puget IAS/Orsay). This work is dedicated to the calibration and the optimal tuning of the HFI on ground and in flight. It reports two types of complementary activities: One is the operation and calibration of the proto-flight model (PFM), including the optimization of the instrument settings, the réduction and the interprétation of the data. The second one is the development of numerical models representing the physics of the instrument to understand and predict its response in a large variety of situations. Specialized models hâve been developed to describe its photometric response and its dynamical behaviour, which is a key point in relation with the chosen observation strategy, based on a 6 Deg/s scanning speed. These models are based on a description of the physical phenomena that take place inside the instrument, especially its self-radiation on its receivers and the physics of the bolometers and their readout electronics.

This document présents the Planck project and the HFI instrument. It describes the calibration sequences to which I directly contributed. It details original measurements methods that we hâve developed, such as the accurate measurement of the linearity of HFI bolometers. It présents also a breakthrough in the theory of the response and noise of bolometers mounted in a

Alternating Current (AC) biased electronics.

In parallel to this experimental work, a study on clusters of galaxy lias been developed. It regards the physics of the intra-cluster medium components. The optical and infrared observations hâve shown the presence of an intra-cluster stellar component in addition to baryon gas and dark matter.

This stellar population is probably related to a spread dust component so it has to be related to cooling and/or heating processes in the cluster medium.

In collaboration with Antonio da Silva, Centro de Astrofisica da Universidade do Porto et Etienne Pointecouteau, Ludovic Montier, Martin Giard (CESR, Toulouse), we hâve utilized a digital model of structure formation, including the radiative cooling of the dust in the intra-cluster medium. My work consisted in analysing results of these digital simulations and in comparing the statistical properties (Lx-M, Y-M and S-M relations) of the cluster population for different models of structure formation (gravitation+radiative cooling and gravitation+ radiative cooling+ dust cooling models). We hâve shown that the radiative cooling has a tangible effect and that accounting for this effect improves the agreement between models and observations.

Chapter 1

The Planck Satellite and its

Science The Précision Cosmology Era

Cosmology is the astrophysical study of the origin, structure, composition and évolution of the Universe.

Ail peoples from prehistory to présent day hâve asked to themselves the reason why there is something instead of nothing, and when and where the first object formed. The technological challenge in answering these ques tions during past centuries has been too great to provide ail but a purely philosophical argument.

The birth of a Scientific Cosmology1 could be set as the work of Alexan der Friedmann in 1922 [START_REF] Friedmann | Uber die Krummimg des Raumes[END_REF] on the cosmological solution of General Relativity for the case of Isotropy and Homogeneity. From this through to the 1950s, many improvements and some observations hâve been made in order to to make this model a satisfactory représentation of reality. This Mathematical framework is based on four principles and a set of équations1 2:

The Dicke Principle: Gravity is a metric phenomenon and the geometry of the Universe is determined by its matter and energy contents;

The Newtonian Paradigm of Dimensions: We live in a universe with three space-like and one time-like dimensions;

1 Considering as Scientific a spéculation following the Galilean scientific method 2This section has been written thanks to the notes I took from the lectures of Prof.

Francesco Melchiorri in 2003.

The Conditional Cosmological Principle: The Universe is Isotropie. If space is analytic, then Isotropy implies Homogeneity3;

The Fluidity Principle: The Universe is filled by one or more idéal fluids (such as a perfect gas) governed by a simple équation of state: P = cap where the state parameter a; is a function of time only, and the speed of light c= 1;

The Einstein Field Equations: The équations of General Relativity relate the properties of the cosmic fluids to that of the space-time geometry;

Rfiu ~]^9hvR ~Ag^u = 87tGT^ (1.1) where g^u is the metric, = diag(p,p,p,p) is the momentum-energy tensor, p is the energy density, p is the pressure of the fluid and R^u is the Riemann tensor (and R its related scalar) and A is a component, as Einstein originally did in his formulation of general relativity, called the Cosmological Constant, which is not diluted with the expansion of the universe. The Riemann tensor dépends on the second dérivatives of the metric and contains information about the considered space curvature.

In general, under the assumptions of Homogeneity and Isotropy allowed by the first two principles, we can obtain the Friedmann-Robertson-Walker met ric which can be expressed as:

d2s = d2t -a2{t)[~--(-r2{d20 + sin2 9d2p)] (1.2) 1 KT
where k can be equal to 0, ±1 and fixes the space-time metric, and a(t) is the scale factor.

At the beginning of the 1950s, George Gamow, by interpreting Hubble's observations [START_REF] Hubble | A relation between distance and radial velocity among exstra-galactic nebulae[END_REF] of the recession of galaxies4, added physics to the model of Mathematical Cosmology, assuming that the primordial Universe was in a phase of high température where light éléments (H, He-4, He-3, D, Li, Be)

were synthetized [START_REF] Gamow | Expanding Universe and the Origin of Eléments[END_REF]; this new idea was called Big Bang Cosmology by Fred Hoyle and opened the Era of Modem Cosmology.

3The term Conditional takes into account the possibility of a fractal Universe which can be Isotropie but not Homogeneous.

4This shift in frequency called Redshift, is proportinal to the distance to the galaxies and it points to the expanding nature of the Universe.

Filling the metric in the general relativity équation we obtain the dynamic équation for a Homogeneous and Isotropie Universe (Friedmann équations): where à = Ha is the Hubble Law (in its linearised form).

Matter and radiation dépend on the scale factor in a different ways: in case of matter the number of particles is preserved so the scale factor decreases as ^5. For radiation (photons and massless neutrinos) results

In order to solve the Friedmann équations we hâve to specify the matter density of the Universe. The Friedmann équations become: ^i) ~+ Qm°(^j)3 + (1~n°)(5y)2 + Qa1 (1.5) where + ^m0 + = -jp and pc is the critical density at which the expansion (of the universe) is constant.

For these reasons the history of the Universe is roughly divided in two eras [START_REF] Padmanabhan | Structure formation in the universe[END_REF]: the Radiation Era and the Matter Era. The Radiation Era dominated the first years; the following ~1010 years, the Matter Era, are characterised by the prevalence of matter. At the beginning of the radiation era, a few minutes after initial singularity, the température of the Universe and the baryonic density were high enough to allow the nucleosynthesis of light éléments to take place. At earlier times the physics of the Universe is almost unknown. It is assumed that the Universe underwent a phase of accelerated expansion, known as Inflation [START_REF] Guth | Inflazionary Universe: a possible solution to the horizon and flatness problems[END_REF]. At redshift equal to 1100 the radiation de-coupled from the matter (de-coupling era). This is the era of the surface of last scattering (LSS) in which the photons are de-coupled from the matter and were free to move in a transparent Universe , eventually to become the présent day Cosmic Microwave Background (CMB) radiation.

The Big Bang model was strongly supported by the discovery of CMB in 1965 by Arno Penzias and Robert Wilson [START_REF] Penzias | A Measurement of Excess Antenna Température at 4080 Mc/s[END_REF].This discovery evidenced that the Universe at very large scale is isotropie and homogeneous. 5R = ya(t) is the product between the comoving distance \ an<l the scale factor parameter a(t).

6The energy density decreases for two reasons: a factor (as for matter) and a factor 4 due to the wavelength stretching. In recent times (two décades) a new era of Précision Cosmology started.

It happened particularly due to the technological improvements of the in struments used to observe the far distance galaxies and the CMB. It is nevertheless necessary to stress that the word Précision is motivated by fact that the final précision dépends only on the sensitivity of the instrument rather than on the difficulty of interpreting the results. In fact, the simplicity of the physical situation makes the interprétation of the data straightforward.

Nevertheless, the Big Bang theory is characterized by a small number (approximately 11) of free parameters at early times, but the complexity of the présent Universe would require an enormous number of parameters to describe. This is why the cosmologists concentrate their efforts in describing the universe at early times rather than trying to understand the évolution and the origin of the Universe starting from présent time.

Some scientists (see for example [START_REF] Eisenstein | Cosmic Complementarity: Joint Parameter Estimation from Cosmic Microwave Background Experiments and Redshift Surveys[END_REF]) conclude that précision cosmology is essentially a x2-kased cosmology. Parameter estimation requires two con ditions being fulfilled: the data set must be free from systematic errors, and Freçuency (CH?)

Figure 1.2: Photometric data from Cobe Satellite compared with a blackbody at T=2.275 ± lmK [START_REF] Smoot | Cobe observation and results[END_REF].

the fitted model must be physically correct. In our cosmology it may be that the fitted data are not clean enough, and that a different set of physical laws applied to a different cosmology would fit the same data set equally well. For this reason an appropriate set of tests must be identified and performed to verify the basic hypothèses. These tests hâve to be model-independent. That is, independent of the values of the cosmological parameters involved. A very important source of model-independent tests is the CMB. For instance, we can check the scaling of the température of the CMB with redshift, which is independent of both the matter density and energy content of the Uni verse [START_REF] Lamagna | S Z constraints on the dependence of the CMB température on redshift[END_REF],

In the following sections I will introduce the CMB and its theoretical framework. In section 1.2 I will describe space-borne missions to observe the CMB prior to the Planck Surveyor Planck satellite which represents the main subject of my PhD thesis.

The Cosmic Microwave Background

The History of the Universe évolution as it has been presented in the last section, is essentially a thermal history because it is determined by the mean energy of the photons through the different epochs and consequently their different interaction with matter.

The expansion of the Universe is an adiabatic process7 in which the tem pérature decreases as T oc a(t)-\ Before redshift 2 ~1100 the température of the Universe was such that protons and électrons were de-coupled and free to move in a primordial plasma. Compton scattering (Fig 1 in relation to the standard scaling with the a parameter, that our Universe is permeated by a radiation of a blackbody at a température of T = 2.725 [START_REF] Mather | Calibrator Design for the COBE Far-Infrared Absolute Spectrophotometer (FIRAS)[END_REF].

From this resuit, using the standard cosmological model we can extrapolate the température of the CMB at any 2 through the law:

Tcmb -2.725(1 + 2) (1.6)

Note that the location of the LSS dépends on the validity of the above redshift law. On the other hand, the précisé location of the LSS is important because the angular extent of the horizon at LSS is a crucial quantity, related to the matter content of the Universe.

The CMB is the most perfect blackbody in nature. Nevertheless, a level of anisotropy in the CMB is necessary in such a way that it could evolve into the strongly non-homogeneous structures we observe in the présent Universe.

The origin of the anisotropies is found in the fluctuations of the quantum inflationary field. This would resuit in fluctuation in the primordial plasma when radiation and matter were tighly coupled. Small différences of the CMB température in different directions are due to several phenomena:

• Photon and matter température différences on the LSS lead to différences in the observed CMB température as a function of the position on the sky; 7we neglect exothermic matter processes such as electron-positron annihilations. In these cases the température increases but not the a parameter. • The same density différences lead to gravitational potential différences:

if photons "climb" a potential well to get to us, they get redshifted (and vice versa), and this decreases the observed température (gravitational potential redshift);

• Gravitational potential différences create forces that cause motions, these motions create shifts in frequency due to the doppler effect;

• If the gravitational potentials are changing with time, the energy of pilo tons changes along the way, leading to the so called integrated Sachs-Wolfe (ISW) effects.

Since CMB is projected onto the sky it is usual to develop the sky maps in spherical harmonies Y as:

AT OO +/ -= EE«(M (i.7) 0 1=2 m=-l
where the coefficients a/m are random variables with an average equal to zéro.

For gaussian fluctuations, the statistical content is encapsulated in the two point température corrélation function, or equivalently, its angular decomposition into Legendre moments Ci.

/A T\2 1 00 (1.8) where we set:

') = crsU'Smm, (1.9) In Fig. 1.3, we show typical prédictions for the Intensity anisotropy power spectrum Ci for different models of Cosmology.

CMB anisotropies and the derived angular power spectrum, can be used to fix the values of many of the key parameters that define our Universe, in particular its geometry, âge, and composition.

The Dipole Anisotropy

The study of CMB anisotropies shows a dipole term associated with the peculiar motion of the observer with respect to the local cosmological standard of rest. This amplitude of distortion can be represented by the following law: T = T0(l + /3cos6) (1-10) The second is a sinusoidal term dominated by the Earth orbital motion. It is a perfectly known in amplitude and direction and corresponds to about 15% of the first term in amplitude.

The kinetic explanation of the dipole requires a peculiar velocity of the observer, which can be explained only as the resuit of a gravitational accél ération integrated in time. We know that the Local Group of galaxies has a peculiar velocity with respect to LSS. From the COBE (see section 1. primordial fluctuations are partially polarised at last scattering they would polarise the CMB anisotropies up to us [START_REF] Hu | A CMB Polarization Primer[END_REF].

Observations of CMB polarisation (CMBP) provide important tools for reconstructing the model of the fluctuations from the observed power spectrum:

• Different sources of température anisotropy (scalar, vector and tensor) give rise to different patterns in polarisation. Thus, by including polarisation in formation, one can provides information complementary to the température power spectrum. This could break parameter degeneracy;

• The polarisation spectrum is sensitive to the presence of gravitational waves at a wider angular scale range than the température spectrum. Inflationary theory predicts in fact the existence of a stochastic gravitational-wave background with a nearly-scale-invariant spectrum. CMB polarisation would thus allow in some way to study the inflationary model and to investigate the pri mordial plasma before the LSS;

• The level of polarisation is a direct measurement of the duration of the last scattering surface period;

We detail the basic argument of génération of CMBP. Thompson scatter ing of the photons with plasma dépends directly on their level of polarisation (Figl.5). The cross-section of this process is:

d&T 3(7t . / // . 2 dQ 8n
Where ar is the total Thompson cross-section, and e , e" represent the inci dent (scattered) polarisation directions.

Thompson scattering does not produce circular polarisation because of its rotational symmetry. Heuristically the incoming radiation shakes an électron in the direction of its electric field vector ~Ê causing it to radiate with an outgoing polarisation parallel to tliat direction. However, since the outgoing polarisation ~É must be orthogonal to the outgoing direction, incoming radiation that is polarised parallel to the outgoing direction cannot scatter, leaving only one polarisation state. If the intensity were completely isotropie the missing polarisation state is supplied by radiation incoming from the di rection orthogonal to the original one. In an isotropie context contributions of polarised radiation scattered by LSS électrons cancel out two by two, leaving (1.17

)
where / is the intensity of the radiation, Q and U the linear polarisation (horizontal and vertical at ±45 degrees ), and V the circular polarisation. In the case of a non-polarised wave Q, U and V are < quai to zéro.

Corning back to Thompson scattering, from a mathematical point of view, after scattering the output Stokes parameters of th ' re-radiated field is given by:

I = 3CTT 8 r-J 4 fW T . 167r[3'/™<00> + 3V5a<20>] (1.18) Q = 3 (Jj1 2TT r
4TT }j 15Real(a( 22)

) (1.19) U = 3crT Fht , 4-rrVl5/m(a<22>} (1.20) V = 0 (1.21)
Both Q and U are generated by the radiation process, but they are due to the quadrupole of the incident radiation. V is not generated through this process, although it can be generated through other processes.

Température perturbations hâve three geometrically distinct sources: the scalar (compressional), vector (vortical) and tensor (gravitational wave) per turbations. The scalar perturbations represent perturbations in the density of the primordial plasma at LSS and are the only fluctuations which can form structure through gravitational instability. Vector perturbations represent vortical motions of the matter. There is no associated density perturbation and the vorticity is damped by the expansion of the Universe as are ail the motions that are not enhanced by gravity.

Tensor fluctuations are transverse perturbations to the metric, which can be viewed as gravitational waves. A plane gravitational wave perturbation represents a quadrupolar stretching of space in the plane of the perturbation.

In order to expand the polarisation pattern in spherical harmonies, it is useful to décomposé it into E modes and B modes (scalar and pseudo-scalar components). This cornes from a linear combination of Q±iU and allows to describe polarisation using two quantities completely determined by linear polarisation which are rotationally invariant: Due to their origin, température fluctuations are expected to be well correlated with E -modes while B -modes power spectrum is expected to be not correlated with température. While the température power spectrum peaks at the same angular scale of the horizon, the polarisation spectrum peaks at angular scales smaller than the horizon at last scattering due to the casuality. Furthermore, the polarised fraction of the température anisotropy is small since only those photons that last scattered in an optically thin région could hâve possessed a quadrupole anisotropy. The fraction dépends on the duration of the last scattering. For a standard thermal history, it is expected to be between 5% and 10% on a characteristic scale of tens of arcminutes. an intensity decrease at frequencies lower than ~217GHz and an increase at higher frequencies (Figl.8). Because of its spectral signature, the ther mal S-Z effect can be separated from the primary CMB anisotropies using observation at several frequencies.

p oo / -?(0-¥>) = E £ ["Ko»(0> v) + *0] io 1=2 m--l 20 (1.22)
The S-Z effect recovers many astrophysical and cosmological informations: first, we can perform a survey of the cluster versus redshift in the sky using CMB. We can recover CMB température at cluster redshift in order to check the brighness-redshift équation 1.6. Finally, CMB observation of clusters can be combined with X-ray observations to dérivé independently the principal cosmological parameters.

• Gravitational Leasing : The General Theory of relativity says a photon follows a géodésie paths rather than a straight line. These géodésie paths in fact represent the shortest line between two points in a gravitationally distorted space-time. Since the Universe today is strongly non-homogeneous, the CMB photons can be used to trace out the large-scale matter distribution thanks to this secondary gravitation effect.

Figure 1.9: The Galaxy Cluster Abell 2218 (NASA): the Gravitational Lensing effect is présent by distortion of the galaxies of the cluster.

• The Integrated Sachs-Wolfe Effect : The Sachs-Wolfe effect is caused by the gravitational redshift (or blueshift) of the CMB photons climbing out of (or falling into) an over-density. If the effect occurs at the surface of the last scattering , it is considered to be a component of the primary anisotropy (Non-Integrated Sachs-Wolfe).

If the same effect occurs between the surface of last scattering and the ob server, so it is not part of the primordial CMB and is called The integrated Sachs-Wolfe effect (ISW). It occurs when the density of the Universe is dominated by something other than matter. If the Universe is dominated by matter, then large-scale gravitational potential wells and hills do not evolve significantly. If the Universe is dominated by radiation, or by dark energy, though, those potentials do evolve, subtly changing the energies of the pho tons passing through them. There are two contributions to the ISW effect.

The "early-time" ISW occurs immediately after the (non-integrated) Sachs-Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough radiation around to affect the Uni versel expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable. The "late-time" ISW effect arises quite recently in cosmic history, as dark energy, or the cosmological constant, starts to govern the Universe's expansion. This linear part of the effect entirely vanishes in a fiat universe with only matter, but dominâtes over the higher-order part of the effect in a universe with dark energy. The full nonlinear (linear + higher-order) late-time ISW effect, especially in the case of individual voids and clusters, is sometimes known as the Rees-Sciama [START_REF] Hubble | A relation between distance and radial velocity among exstra-galactic nebulae[END_REF] effect, since Martin Rees and Dennis Sciama elucidated the following physical picture. Accelerated expansion due to dark energy causes even gentle large-scale potential wells and hills to decay over the time it takes a photon to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get ail of it back upon exiting the slightly squashed potential hill. A signature of the late-time ISW is a non-zero cross-correlation function between the galaxy density (the number of galaxies per square degree) and the température of the CMB, because superclusters gently heat photons, while supervoids gently cool them. This corrélation has been detected at moderate to higli significance.

Foregrounds

Foregrounds are ail the astrophysical sources cause a spurious effect in the CMB observations. In particular, the characterization of polarised fore grounds is a key point for a successful mission. In case of a space mission we do not hâve to deal with foregrounds coming from the atmosphère.

The main astrophysical foregrounds are free -free, synchrotron and dust émission.

Free-Free Emission

Thermal bremsstrahlung from an ionized hydrogen cloud (HII région) is often called free-free émission because it is produced by free électrons scattering off ions without being captured. The électrons are free before the interaction and remain free afterwards. The émission is proportional to:

TBr oc z/~215 (1.28)

Free-Free émission is intrinsically unpolarised but it can be partially po larised by Thomson scattering within the HII région.

The émission is larger at low frequencies but it is not expected to dominate the polarisation at any frequency.

Synchrotron Emission

A charged particle moving in a magnetic field radiâtes energy. At nonrelativistic velocities, this results in cyclotron radiation while at relativistic velocities it results in Synchrotron radiation. Synchrotron radiation is typically generated by galaxies, where relativistic électrons spiral (and hence change velocity) through magnetic fields.

The Synchrotron émission follows the power law:

= Ci/ (1.29)
where C and (3 are determined by the density and energy of électrons and the intensity of the magnetic fîeld in the considered région.

This non-thermal radiation contains a percentage of polarised émission:

Dust Emission

Dust émission is due to the thermal émission from small particles and grains in a local medium. Part of this émission is polarised by its local magnetic field which acts to align elongated grains so that they spin with their long axes perpendicular to the field.

At low Galactic latitudes, thermal émission from dust particles dominâtes the IR spectrum. In general, depending on the shape and the alignment of dust particles, émission from dust can be polarised from 2% to 10% [START_REF] Hildebrand | The Shapes and Alignment Properties of Interstellar Dust Grains[END_REF]. At frequencies higher than 200GHz, dust is the dominant foreground.

This émission results in a linear polarisation that can be also used to measure the direction of the magnetic field.

Due to the different spectral indices, the minimum in the foreground po larisation, as with the température, is near 100GHz (Fig. 1.10). For full sky measurements, because synchrotron émission is more highly polarised than dust, the optimum frequency at which to measure intrinsic (CMB) polari sation is slightly higher than for anisotropy. Over small région of the sky where one or the other of the foregrounds is known a priori to be absent the optimum frequency would clearly be different. However, as with anisotropy measurements, with multifrequency coverage, polarised foregrounds can be removed. Synchrotron (blue square), free-free (green triangle) and anomalous dustcorrelated émission (magenta circles) co-add to the dust (red dotdashed line).

CMB is shown at 70 mK r.m.s. Total foregrounds (black solid curve) show a clear minimum around 70 GHz.

It also interesting to consider how the spatial as well as the frequency signature of the polarisation can be used to separate foregrounds. Using angular power spectra for the spatial properties of the foregrounds is a simple généralisation of methods already used in anisotropy work. For instance, in the case of synchrotron émission, if the spatial corrélation in the polarisation follows that of the température itself, the relative contamination will decrease on smaller angular scales due to its diffuse nature. Furthermore, the peak of the cosmic signal in polarisation occurs at even smaller scales than for température anisotropy [START_REF] Delabrouille | Diffuse source séparation in CMB observations[END_REF].

1.2

The Challenge of Précision Cosmology: Three

Générations of Satellites

As many scientists say, we live in the précision cosmology era. This is possi ble thanks to experiments (space-borne and ground-based) which permitted (as COBE and WMAP) and will permit (Planck) measurements to increased The spectrum of the dipole has been measured by FIRAS and its shape is consistent with the assumption that it is produced by a Doppler shift of the monopole. Its value of (3.372 ± 0.007) mK implies that the Sun's peculiar speed with respect to a comoving frame is (371 ± 1) km/s. Further contrast enhancement reveals a very srnall but significant random anisotropy, i.e., déviations from uniformity, with rms amplitude of (29 ±1) /iK at the angular resolution of 10 degrees ( [START_REF] Bennett | The Microwave Anisotropy Probe (MAP) Mission[END_REF]). Such anisotropies were keenly expected as a major sign that we understood the nature and the origin of the CMBR.

They were expected to be the remnants of quantum fluctuations during the first moments of the Big Bang. And without them, it would hâve been very difficult to understand how such an extremely uniform source could hâve produced the highly structured Uni verse that we can observe now in our neighbourhood. J. The Boomerang ( [START_REF] De Bernardis | Détection of anisotropy in the Cosmic Microwave Background at horizon and sub-horizon scales with the BOOMERanG experiment[END_REF]), Maxima ( [START_REF] Hanany | MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on Angular Scales of 10-5deg[END_REF]) and Archeops ( [START_REF] Benoît | The cos mic microwave background anisotropy power spectrum measured by Archeops[END_REF]) balloonborne experiments hâve shown images of the CMB on fractions of the sky with good signal to noise ratio. Ground based experiments, such as CBI ( [START_REF] Pearson | The Anisotropy of the Microwave Background to 1 -3500: Mosaic Observations with the Cosmic Background Imager[END_REF]; [START_REF] Readhead | Polarization Observations with the Cosmic Background Imager[END_REF]), ACBAR ( [START_REF] Runyan | ACBAR: The Arcminute Cosmology Bolometer Array Receiver[END_REF]; [START_REF] Kuo | High-Resolution Observations of the Cosmic Microwave Background Power Spectrum with ACBAR[END_REF]), VSA ( [START_REF] Scott | First results from the Very Small Array -III. The cosmic microwave background power spectrum[END_REF]), and DASI ( [START_REF] Halverson | Degree Angular Scale Interferometer First Results: A Measurement of the Cosmic Mi crowave Background Angular Power Spectrum[END_REF]) hâve unveiled the highresolution part of the CMB spectrum.

The stationary part of the noise from an instrument can be evaluated by powerful statistical tools, but its non-Gaussian and non-stationary parts, and the other sources of systematics are much more difficult to evaluate and to remove from the data. Their levels hâve to be reduced as much as possi ble. This difficulty has been considered as the major design driver of CMB experiments. In addition, an optimal interprétation of the Ci will rely on full sky maps with a pixel size of less than 0. results as soon as possible, while Planck was designed to perform at the limits set by physics, which required more risky and longer development. In the following subsections I will detail separately the two instruments in terms of orbits and general configuration.

The Wilkinson Microwave Anisotropy Probe (WMAP)

The Wilkinson Microwave Anisotropy Probe (WMAP Fig. 1.12), developed by NASA, was launched on June 30, 2001, and has been mapping the tem pérature and polarisation anisotropies on the full sky in 5 microwave bands [START_REF] Benoît | The cos mic microwave background anisotropy power spectrum measured by Archeops[END_REF][START_REF] Lamarre | Background Limited Infrared and Submillimeter Instruments[END_REF][START_REF] Desert | Private Communications[END_REF][START_REF] Montier | RU Calibration PFM[END_REF]94GHz).

The satellite observes at the Lagrange 2 (L2) point, where émission and magnetic fields of the Earth do not affect the satellite. The differential mea surements with many scans in different orientations per pixel significantly suppress undesired l/f noise and noise corrélations between pixels. the instrument sweeps through the sky at a rate of few per cent day~l. The whole sky will be covered in a little more than 6 months; this operation will be repeated at least twice during the lifetime of the cryogénie System.

The spacecraft

The spacecraft consists of a telescope, a baffle, V-grooves (these three élé ments constitues the Planck Optical System) and the Service Module Houses.

The Planck Telescope consists of two ellipsoidal mirrors with a Gregorian-Dragone-Mitsugushi configuration of 1.5m and 0.64m (circular projected aperture) and the supporting structures and the surrounding baffles. The Telescope unit includes the structure in witch both LFI and HFI instrument are mounted(Figl.l7). Ail the structures and baffles provide to the telescope a stable thermal environment, protect the telescope from sun and earth di rect irradiation and contribute to reduct the radiative power that reaches a detector when it is not originated from a source in the far fields of the beam (iStraylights).

In Figl.18 the distribution of the power of the straylight in the detected signal is presented. The Planck Telescope is designed as an ofï-axis tilted System offering the advantage of an unblocked aperture. The Telescope line of sight lies in the Z,X plane of the spacecraft coordinate System and is at an angle of 85 degrees from the spacecraft's axis. It opérâtes at a température between 40K and 65K and it is optimized to work in a range of frequency between 25 and 1000 GHz. The useful field of view for ail the horns of Planck HFI is equal to 4 degrees in the sky.

The image of the sky in the focal plane of the telescope has a typical distortion produced by the design of the mirrors, that is the reason why the position in space of the horns in the FPU is optimized taking into account this effect (Figl. [START_REF] Bennett | The Microwave Anisotropy Probe (MAP) Mission[END_REF]).

The design of the telescope was based on these criteria :

• Angular resolution should cover the useful range of multipole moment, i.e. provide an angular resolution of 5 arcmin.

• The design should minimize the straylight, which means -No diffracting obstruction (an off-axis Gregorian-like design)

-providing the resolution with a extremely low edge taper (-20 to -30 dB) to minimize spillover.

-Having a low emissivity and a low température. Ref.. ( [START_REF] Lamarre | Background Limited Infrared and Submillimeter Instruments[END_REF])

• fitting in the volume allocated inside the compartment allocated in the Ariane V shroud, that must also accommodate Herschel and the structure supporting it. This requirement is in contradiction with the two previous ones, which led to painful compromises. They resulted in the distorting optical design, whose effect on science may hâve been underestimated. The Sorption cooler are integrated in a complex way in the spacecraft.

I
It relies on the passive cooling provided by the 3 V-grooves and the warm radiator which radiâtes into deep space the power of the sorption cooler.

The sorption coolers hâve been extensively tested at JPL and then in an integrated test with the payload, the warm radiator and a représentative spacecraft in the FMI test at CSL.

The LFI Instrument

The Low Frequency Instrument (Fig. The LFI receivers are sensitive to polarisation. The ratio between the sen sitivity to fluctuations in intensity and polarisation is y/2 because the number of channels per polarisation is half that for intensity. The principal rôle of LFI is the characterisation the foreground (polarised and un-polarised) such as the synchrotron émission and polarised Galactic foreground components which are expected to hâve a strong émission in the LFI spectral bands.

In order to eliminate as much as possible the contribution of 1 // noise a differential pseudo-correlation scheme is adopted. In this scheme the signal from the sky is combined with a blackbody reference load by a hybrid coupler.

The two signais are amplified, in two independent amplifier chains and then separated by a second hybrid. Because the two signais hâve been amplified

with the same gain through the two amplifiers, the true sky power can be recovered. The control of the 1// noise and the recovery of the fluctuation of the sky signal is performed by switching phase shifters at 8kHz in each amplifier. The choice of the reference signal to be used, was made in order to minimise the effects of other systematics by adopting a source as close as possible in température to the sky input signal. For this reason the chosen source was the signal emitted by the 4k stage of the HFI (see section 2.2).

The HFI Instrument

A detailed description of the HFI instrument is postponed to chapter 2.

Introduction

The HFI consists of the focal plane unit, the readout electronics, the Data Processing Unit, the coolers (and their electronics), harness and tubes linking the various subsystems (see Fig2.1). It is designed to use bolometers cooled at 0.1K, that are the most sensitive detectors for wide band photometry in the HFI spectral range (lOOGHz-lTHz).

Cooling the detectors at 0.1K in space is a major requirement that drives the architecture of the HFI. This is achieved, starting from the passively cooled 50K/60K stage of the payload module, by a four-stage cooling System (18K-4K-1.6K-0.1K) detailed in section 2.5. The 18K cooler is common to the HFI and the Low Frequency Instrument (LFI).

In this chapter we shall présent a general view of the instrument from HFI cold optics to the scientific signal in digital units.

The Cold Optics

The coupling of the FPU with the telescope is done by naked corrugated horns (devoid of Windows), designed to minimise the energy taken from outside the telescope (Spill-Over) and to optimise the angular resolution. This horn is attached to the 4K stage and coupled to a back horn by a wave guide section that constitutes the only radiative coupling between the outside and the inside of the 4K box. Filters are attached on the 4K, 1.6K stage, and bolometers on the 0.1K stage, which corresponds to an optimal distribution of heat loads on the different stages.

Since most sources of spurious radiation hâve a steep spectrum, a high spectral rejection is mandatory. In addition, the radiation of the filters them- The number of detectors at the same frequency is determined by the cross scan sampling requirement, the need to measure polarisation and the goal of maximum redundancy. In fact in order to measure polarisation we must hâve at least a measurement of three polar directions at the same point of the sky. For redundancy and because polarisation sensitive bolometer (PSB) can be made by pair, it has been chosen to measure 4 [START_REF] Maffei | Planck-HFI focal plane concept[END_REF].

The location of the different pixel at different frequencies is determined by the requirement to minimise the effect of focal plane aberration, and to measure at short time intervals the different polarisations of a given source on the sky by detectors on the same scan path. The problems to find a sufficient sampling issue is detailed in the chapter 5. and L the horn axial length). However, because of mass restrictions and the limited field of view in the telescope focal plane, sizes of the horns hâve to be minimised. For the higher frequencies (545GHz and 857GHz) the angular resolution requirement does not demand diffraction limited operation for the required spillover levels. Few moded horns hâve been designed for these cases to increase the throughput and coupling to a 5 arcmin beam on the sky [START_REF] Murphy | Corrugated horn design for HFI on PLANCK[END_REF].

Few moded operation is obtained by increasing the waveguide diameter and allowing higher-order waveguide modes to propagate.

the table hereafter shows the nominal resolution for each HFI band:

Frequency (GHz)

Spectral band Sélection: Filters

The sélection of the observation band of each detector is obtained by a sé quence of filters that guarantee the spectral purity of the final measurements.

The spectral bands are defined by a combination of the high pass (cut-on) effect of the waveguide of the back-to-back horns and a low pass métal mesh filter (eut off). Four additional low pass edge fillters minimise the harmonie leaks, which makes an overall rejection factor that exceeds 1010 at higher frequencies. This scheme also allows some flexibility to choose where the unwanted thermal power is dumped (i.e. 4K, 1.6K or lOOmK cryogénie stages).

The interferometric mesh filters are using low-loss metallic grids that provide a very high transmission and a very sharp eut. They produce the effective band sélection of HFI Channels. The working principle of this filter is based on reflection of the unwanted radiation (not on absorption as yoshinaga fil ters). This provide a very low level of backgroung from instrument itself [START_REF] Ade | A review of métal mesh filters[END_REF].

The HFI métal mesh interférence filters hâve been developed by Univer- on ail the 52 channels of HFI [START_REF] Savini | HFI Spectral Calibration report of the IAS measurements[END_REF] sity of Cardiff. They hâve been shown to be durable (embedded in polypropylene) and lightweight (self-supporting) and hâve been qualified for space use by NASA.

To minimise the thermal loading on the lOOmK stage the first low pass filter is placed at the exit of the back-to-back horn pair where there is a beam waist and the incident radiation is at near normal angles to the filter. This ensures that rnost of the unwanted power (wavelength lower band edge) is kept at the 4K stage level. Equally important, this location has been shown

to eliminate the enhanced side lobe response that occurs if the filters are placed in a converging beam in front of the feeds.

The spectral transmission of each HFI channel is derived from PFM cali bration [START_REF] Savini | HFI Spectral Calibration report of the IAS measurements[END_REF]. In Fig 2 .6 the total spectral transmission normalised to 1 for ail 52 channels of HFI is presented. The normalisation factor is one of the measurements performed by LERMA (EFF sequence) and it is showed in Chapter 4.

The Detectors

The Planck HFI bolometric detectors must hâve inhérent NEPs less than or equal photon noise of the background together with a speed of response fast enough to preserve ail of the signal information at the 1 rpm scan rate of the satellite. This is achieved by the CalTech/JPL (California Institute of Tech nology, Jet Propulsion Laboratory, Pasadena, USA) spiderweb bolometers.

Bolometers are broadband thermal detectors optimized to the work from far infrared to the microwave domain. At wavelength larger than 200/ira, photoconductors lose their efficiency . On the other hand in this range of frequency, cohérent detectors are not sensitive enough to be preferred to bolometers (see Fig2.7).

Spiderweb bolometers are manufactured using métal meshes and a doped (NTD) germanium with a résistance strongly dépendent on the température.

The size of meshes is adapted to operate in 6 spectral band of frequency between 100-900 GHz. A detailed theory of a bolometer is postponed to chapter 3. Polarisation Sensitive Bolometers (PSB) are implemented in ail CMB channels (100GHz, 143GHz, 217GHz, 353GHz, 545GHz, 857GHz).

The choice of the spiderweb technology is due to the necessity to reduce the noise produced by cosmic rays. The use of an absorber with a spider web shape in fact reduces strongly the cross section (of the order of 90%less)

for ail the particles coming from the sky. Because of the size of the aperture Wavelength (min) The spectral resolution versus wave length is plotted [START_REF] Lamarre | The High Frequency Instrument of Planck: Design and Perfor mances[END_REF] of the spiderweb mesh, the bolometer hâve an effect of a low frequency pass filter on the incoming radiation.

Because the mechanical résonant frequency of the micromesh bolometers is high (~50 kHz), the devices are insensitive to the relatively low fre quency vibrations encountered during the launch and operation. This type of bolometer has been tested under vibrations 10 times in excess of the expected level. No dégradation in the noise performance has been observed after vibration.

Readout Electronics

The readout electronics (REU) is designed to measure the impédance of the température sensitive element of the bolometer. This is done by injecting a current, and therefore deposing some power in the bolometer which changes its température. In conséquence, the bolometer response and performance strongly dépend on the design of the readout electronics.

The classical method is: a bolometer is polarised with a DC bias voltage through a load résistance Rl, and the voltage Vf, is measured thanks to an amplifier with an high input résistance. The advantage of this architecture is the use of a well established theory of bolometer [START_REF] Jones | The general theory of bolometer performance[END_REF], [START_REF] Mather | Bolometer noise: nonequilibrium theory[END_REF]. The optical power Wopt absorbed by the bolometer and the response of the bolometer can be directly computed.

On the other hand a DC bias polarisation increases the level of low frequency noise like fliker noise making impossible the détection of a faint and slowly varying optical signal. In addition the Johnson noise produced by the load résistance obliges to put this element on the coldest cryogénie stage.

The Electronic chain implemented in HFI instrument initially proposed by A. Benoit [START_REF] Gaertner | A new readout System for bolometers with improved low frequency stability[END_REF], is a évolution of the AC readout developed by Rieke et al., known to improve the law frequency stability of bolometers [START_REF] Rieke | An AC bridge readout for bolometric detectors[END_REF]. In the Fig2.9 a scheme of the principles of read-out System is presented.

Here the load resistor is replaced by two simetric capacitors in order to equilibrate an AC bias polarisation System. The capacitance does not produce any significant heat and is not a source of Johnson noise so it is not more necessary to put this element in the coldest cryogénie stage with any significant advantage in terms of thermal budget and lifetime of the instrument. In addition the capacitance has a large input impédance (for 4.7pF the value of the impédance at 100Hz is equal to ~4.7GQ against a typical value of 40MD for a load résistance).

A Second original feature of this new System is that the AC bias applied is the sum of two differents signais. The output signal is amplified in the Pre-Amplification Unit (PAU), and

Vbai is substracted. After that the signal is amplified a last time according to the programmable gain of amplification Gamp (set to 0.33, 1, 3 or 7. Sphase -is the rank of the first high frequency sampie to be co-added to form a DSN.

They are computed according to the following expressions :

Nsample ^-^~^phase E = E + Sphase Sphase~-1 2Nsampie 1 E= E + E 0 Nsample^Spha, 2.3.1

St ray Capacitance

Any two adjacent conductors can be considered as a capacitor, although the capacitance will be small unless the conductors are close together or long. This (unwanted) efïect is called stray capacitance. Stray capacitance can allow signais to leak between otherwise isolated circuits (an effect called crosstalk), and it can be a limiting factor for proper functioning of circuits at high frequency. Let us consider here the effect of the stray capacitance in the readout circuit.

It is possible to calculate analytically the stray capacitance of the circuit by making some simple assumptions: If we consider a stray capacitance in parallel with the bolometer, the équation of the circuit is:

Vb = ZpZb ZpZb + (Zp -f-Zb)Zi Vo (2.4)
where Zp, Zi and Zb are the impédances of stray capacitance, the load ca pacitance and the bolometer. Vo is the total input voltage (triangular plus square voltage).

To compute how the transient step of Vo is propagated to Vb the bolometer impédance can be considered as very large with respect to that of capacitors Cp and Cl-In this case we obtain from Eq 2.4:

Vb = Cl Vo 2 Cp + CL

In this case Vq = Vrran', from Eq 2.1 and Eq 2.2 we obtain:

Vi Tran = 2- R 50 T, Tran D i r> ymnc ' GPAU20oVbal Ri + R$o 4095
In the readout electronics is balanced it must happen:

Vb = VBal (2.5) (2.6) (2.7)
So it is possible to calculate the stray capacitance from 2.5 as:

Cp = ( 2GPAU2QQ rp Rso Tmn _ .O/ (R7 + i?5o)4095 2 (2.8)
For a typical bolometer if Cl = 4.7pF and T^ran = 2000 (that is nearly the value of the transient during PFM ground calibration) we obtain:

Cp = 150.6pF
The interaction between the bolometers and the REU is therefore complex.

We address in the next chapter various approaches taken to model this in teraction and the response of the instrument.

Sensitivity

The quantity that takes in account the sensitivity of the instrument is the Noise Equivalent Power (NEP). It represents the power producing a signal in a post détection bandwidth of 1Hz integrated for 0.5 sec equal to standard déviation of the noise. This quantity takes into account the response and the noise of the detector (see section 3.2.5). Ail the sources of noise add quadratically the corresponding NEP to produce the total NEP.

In the case of Planck HFI we can separate three type of contributions in terms of noise:

NEP?ot = NEPphotons + £ NEPllo{() + Y. NEPÏthers(i) (2.9) i=1 i-\
where 52ÏLi NEP^olo^corresponds to the contribution in NEP of the noise coming from the bolometer (Johnson noise, phonon noise principally), and

YlïLi NEP^thersii) *s contribution of the rest of source of noise1 (Preamplifier noise principally but also microphone, cross-talk, shot noise and electronic noise). NEPphotons is determined by the corpuscular nature of photon following the Bose-Einstein statistic. So in the best conditions the contri bution of Photon noise is the limit of sensitivity of the instrument and it is taken as a reference for the other ones.

In case of Planck HFI the goal NEP has been defined:

NEPgoal < 2 * NEPphotons (2.10)
To make this happens it has been fixed as nominal spécification:

Y,NEPllo{i)<NEPÏhotlm (2.11) 1=1 and 2 • jr NEP*her4i) < NEPphoton (2.12) i=1
As a guideline for the design of the instrument, it has been required that the proper source of noise of each sub-system had to be less than 0.3 time photon noise.

N EPsub -System -0.3NEPphoton (2.13)

So that the impact on the total NEP is less than 5%.

'A detailed discussion on principal sources of noise is posponed to section 3.2.5

In the table 2

2.5

The HFI Cryogénie System

The sensitivity of the HFI critically dépends on the température of the detectors.

It has been shown [START_REF] Torre | Background Limited bolometers for First and COBRAS/SAMBA[END_REF] that lOOmK or less were needed for the Planck mission called COBRAS/SAMBA at this time.

To obtain such a low température, it is necessary to surround the coldest stage with different cryogénie stages at different températures. In addiction, in order to decrease the photon noise level of the instrument itself, several cryogénie levels are used to cool down the hornes and the mesh filters witch selects the spectral bands (see section 2.3).

A basic technique to reach cryogénie températures is to put the detector in thermal contact with a fluid (or a solid) with a low boiling température (or sublimation température). The évaporation latent heat permits to keep the normal boiling température as a constant even in presence of an heat input from a warm environment, of course wasting part of the fluid.

In the case of Planck HFI the use of cryogénie fluids like Hélium or Nitrogen to make the dilution cooler System working has not been considered as feasible. It has been chosen to use a Joule-Thompson mechanical cooling technique2, in which the reliability dépends only on mechanics of cooling System and so it provides a considérable cost réduction and an increase in lifetime.

The cooling scheme that allows to cool at 0.1K the 52 bolometers and their filters is based on technical solutions that hâve been successfully tested in space borne, balloon borne and ground based instruments. Each cooling System takes advantage of the previous one.

The HFI cryogénie System is composed by a dilution cooler and a 4K The principle of cooling via dilution of 3 He in 4 He atoms is based on the fact that Van der Waals forces between 3He and 4He atoms are higher than between a pair of 3He or a pair of 4He atoms. When we mix of these two isotopes they absorb heat to build stronger bonds ( [START_REF] Benoît | New types of dilution refrigerator and space applications[END_REF]). This commercially available technology uses gravity to mix and separate the 3He rich and 4He dilute phases. Alain Benoit and Serge Pujol hâve invented an original method that allows to use the same principle in a micro-gravity environment ( [START_REF] Benoît | Development of a 0.1 K cryocooler for space applications[END_REF]).

Mixing 3He and 4 He in small capillary tubes in an open cycle has proven to work in any gravity condition testable on the ground.

In the dilution cooler, it is possible to distinguish a low température part in contact with the bolometers plate and a warm part where the gas is stored and its flow controlled (see Fig 2.11).

The low température part of the dilution cooler is linked to the plate that supports 52 bolometer, 2 blind bolometers, their horns and filters, thermometers. Three pipes are used to mix the two isotopes: the first two for isotopes injection and the last one to retrieve the mixture.

The dilution is performed in this pipe and it is used to cool down the lOOmK head. The main components of the 4K System for Planck are:

• The JT compressors which give two stages of compression from about 1 bar to 10 bar.

• Ancillary plumbing which contains part of the gas purification System, a filter, a flow meter and a valve for the JT by pass System.

•The cold température plumbing which incorporâtes countercurrent heat exchangers between the stages and filters and gas purifiers on the stages. The 4K stage contains a réservoir for liquid hélium. cooling température, the 1.6 K JT is then operated in a rather marginal mode implying to use a higher isotope flow rate than the one required by the dilution part. Thus the preferred 4K pre-cooling température is below 4.7K which brings the 1.6-100 mK dilution cooler in the normal régime where the dilution is setting the isotope flow requirement.

The electrical power needed to operate the 4K cooler is 100W. The dura tion of life is fixed by the lifetime of the power supply of about 5105 hours.

Thermometers

There are 16 sensitive NTD germanium thermometers on HFI in order to analyse and attenuate the température fluctuations of the three active coolers. They are placed at ail the cryogénie levels.

Rôle of the Calibrations and Instrument Model

To calibrate an instrument is to détermine its response by comparison with standards. In Astrophysics, this means characterising in detail the sélection of photons (geometry and energy) by the instrument, the détection of these photons and their transformation to data that can be ingested by a computer.

In addition it means identifying and characterizing the spurious signais added in this process.

The way of HFI transforms brightness in digital data dépends on many environmental and REU parameters. This is presented in the idealised view in figure 2.15. First, the optical chain applies spatial and spectral filtering: the image of the sky is convolved with the beam of the System made by the telescope, the horn and the internai optics including the bolometers.

Photons are also selected in frequency by stacks of interférence métal mesh filters at different cryogénie températures and by the spectral transmission of the waveguide sections of the horn Systems. This produces a timeline of optical power in watts (Wopt(t)) to which a nearly constant self-emission signal is added, produced by the thermal émission of the telescope and the cryogénie stages. Optical power is absorbed by the bolometer and its statistical fluctuations produces the photon noise Nph0t• The température changes of the bolometer are detected as a voltage with corresponding noises in the bolometer itself and in the readout electronics. Then the signal is amplified, digitised, compressed and delivered to the telemetry System. This makes a very complex process with a large number of free parameters. Prédiction of the instrument response and of optimal tuning of the readout is not likely to be accurate enough for our scientific goals. The logic has been to develop numerical models to assist instrument tuning and data réduction, to validate these models during the ground based calibrations and to rely on a fine cal ibration based on in-flight observation of known sources. Once this point is clear, let me underline also that a flight calibration cannot answer alone to ail the scientific needs. For instance, the shape of the spectral bands cannot be measured in flight. This measurement is important in order to remove efficiently the contribution of the foregrounds from the cosmological signal since the two signais hâve different spectral indices. So it is necessary during ground calibration, to test every single component making use of a physical model in order to understand the physical processes involved. Then, to check the performances of the instrument as a whole, verify the numerical model of the instrument and détermine its unknown parameters.

Chapter 3

Modelling the Response of HFI

The Models of HFI

The interprétation of the CMB maps that will be obtained by Planck will rely on an accurate knowledge of the transformation of the information operated in the instrument. Important quantities describing the instrumental functions will be calibrated in flight: photometric response to CMB calibrated on the dipole. Effective beams will be calibrated on planets. Others important quantities can be measured on the ground (i.e. spectral bands).

In order to support this calibration activity, numerical models describing the physical processes that take place in the instrument hâve been developed.

They are mainly:

Model of optics: they describe the propagation of waves from the sky to the receivers. They are using classical optics, physical optics or dedicated théories, depending on which one is the most adapted. They are used to describe the beams outside of the domain of measurement (far side lobes).

Thermomechanical distortion model of the telescope: The telescope cooling down from 300K to 50K deforms its mechanical characteristics. Different models takes into account these changes and predict the variation of perfomances.

Thermal Models: It is needed to define the settings for ail the coolers, to monitor their évolution in flight and to anticipate changes in the tuning. It The HFI response models hâve been presented at the Instrument Science Vérification (ISVR) on September 2008 in charge to cover the following tasks:

• To predict the optimal tuning of the instrument.

• To predict the effect of any action that we would hâve to take in-fiight.

• To simulate the response of the instrument in a crédible way for end-to-end test.

• To correct for the effects of some variations that could happen while the data is being taken for in-flight calibration (e.g. changes of Xi0om/c > B7^).

• To extend empirical calibrations outside of the measured range.

• To replace empirical calibration data in domains where the model is believed to be more accurate.

• To interpret some complex test data, such as the Bias Step Low Frequency Response (LFR) measurement.

• To validate the good health of the instrument by showing that the in strument behaves as expected and as shown before.

In this chapter I shall présent a description of the models that I contributed to develop: the SOS model , the analytical static model and the SEB model. A general description of the modelling AC biased bolometers is also described.

SOS Model

The output of this model is the optical power absorbed by bolometers.

Considering the background generated by the instrument itself and a source (planets, our galaxy or laboratory sources), the incident power ab sorbed by detectors is:

1 , r°o Wopt = ( / AÇL(v)tak(v)cak(v)BB{Tak, v)dv+ 1 + F Jo roc roo + / AQ(i/)r1£K(i')ei&K{i')BB(Ti'6Kli/)di/+ AÇl(i/)eTei(v)BB(TTel, v)dv J o J o roc roc + / Att(v)TTei(v)eTei(v)BB(TTei,v)dv + / AÇl(v)TTot{v){v)S(Ts,v)dv) J 0 J 0 (3.1)
Where rxx and exx are the transmission from the source considered to the detector and the emissivity of the considered cryogénie level respectively and Trot is the total optical transmission of the instrument. P is the polarisation factor (P=l for PSBs, P=0 for SWBs). the production of large arrays of bolometers ( [START_REF] Griffin | SPIRE instrument for FIRST[END_REF], [START_REF] Holland | SCUBA-2: A new génér ation submillimeter imager for the James Clerk Maxwell Telescope[END_REF], [START_REF] De Bernardis | Détection of anisotropy in the Cosmic Microwave Background at horizon and sub-horizon scales with the BOOMERanG experiment[END_REF], [START_REF] Hanany | MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on Angular Scales of 10-5deg[END_REF], [START_REF] Benoît | The cos mic microwave background anisotropy power spectrum measured by Archeops[END_REF], [START_REF] Lamarre | Planck high-frequency instrument[END_REF], [START_REF] Piat | Modeling of Planck-high frequency instrument bolometers using non-linear effects in the thermometers[END_REF], [START_REF] Yun | Bolometric detectors for the Planck surveyor[END_REF]). They are now the most sensitive devices for photon détection in wide domains of the electromagnetic spectrum. In the same time, the theory of bolometers was refined and updated to follow the emergence of new technologies and the exploration of new domains of bolometer températures ([51], [START_REF] Piat | Précisé measurement of CMB polarisation from Dome-C: the BRAIN and CLOVER experiments[END_REF]). The readout electronics for semi-conductor bolometers experienced a radical change about two décades ago. Most of them are now using a modulated bias current in order to get rid of low frequency noises that plague DC bias and amplification Systems [START_REF] Rieke | An AC bridge readout for bolometric detectors[END_REF].

The interaction of AC biased readout electronics with semi-conductor bolometers is rather different from that of DC readout polarising the detectors through a load resistor RL as analysed in the founding paper by Jones ([36]). Such différences were evidenced during the calibration of the bolome ter instrument of the project Planck, although the readout electronics had been designed ( [START_REF] Gaertner | A new readout System for bolometers with improved low frequency stability[END_REF]) to mimic, as far as possible, the operation of a DC bi ased bolometric System. This chapter results from the need to be able to predict the real behaviour of AC biased semi-conductor bolometers in an extended range of working parameters. It reports for the first time new results obtained by the LERMA team on this issue.

Model of Bolometers

As pointed out in chapter 2 Planck bolometers are thermal detectors manufactured using métal meshes and a doped semiconductor résistance strongly dépendent on the température.

The dominant conduction mechanism in the germanium thermometer is the variable range hopping between localised sites and the résistance of the device varies with both applied voltage and température. The relation between the résistance and the température of the bolometer is set from the variety of the doped semiconductors:

71 ! \n eEL R(T, E) = R*e{ T } KbT (3.2)
where Tg is a characteristic parameter of the material, R* is a parameter depending on the material and the geometry of the element, L is related to the average hopping distance and E is the electric field across the device.

In absence of electrical non-linearities and other effects such as electronphonon decoupling, the thermistor résistance dépends only on température: R(T) = R,e^" (

At first order the thermal model of a bolometer can be described in the following the way (see Fig 3 .2): the incoming optical power is absorbed by the mesh and thermalizes the whole bolometer sensitive element including the thermometer. C(T) is the total heat capacity of the bolometer and G (T)

is the thermal conductance to a heat sink at reference température (100mA in case of HFI). The absorbed optical power will détermine a change in the température of germanium thermometer; if the detector is mounted in an appropriate circuit and polarized with a bias current, we can measure a variation of voltage at the end of the bolometer. The total power dissipated in the bolometer is W = P + Q where Q is the absorbed radiant power and P(t) = V(t)I(t) is the electrical power.

In static conditions the balance équation for a bolometer is:

Ga(Tb-T0) = P + Q (3.4) In Eq 3.5 the thermal capacity C is equal to:

C = 1T + A(^f (3.6)
where 6 is the Debye température (phonon contribution), 7 is the Sommerfeld constant of the considered material (electronic contribution) and A is a scaling constant.

Eq3.5 represent a first-order thermal model of a bolometer. Its dynamical response is that of a first-order low-pass filter with a time constant equal to C/Ge. Its transfer function will be:

TFbolo(f) = 1 1 + 2j7t/t (3.7)
and a cut-off frequency equal to fc = 1/(27rr).

For a range of frequencies between lmHz and 1Hz we expect a fiat re sponse. An accurate knowledge of this range of frequency is very important for in-flight calibrations on the CMB dipole (see chapter 5).

Unfortunately, as showed by PFM ground calibrations, a first order ther mal model is not sufficient to reach the level of accuracy fixed for scientific goals. Measurements showed an evidence of a low frequency excess response (see section 4.6.2). More complex models (empirical and physical) are being developed in order to fit properly experimental data taken during PFM Calibrations and CSL tests, (see section 4.6.3).

Electrical model of readout circuit

To make a bolometer work it is necessary to connect it to a readout circuit. Let us assume that AC bias frequency Fmod is much higher than the bolome ter cut-off frequency (Fmo(i » t^). Then we can consider only the average electrical power and a steady state response and neglect short term varia tion. We can dérivé a modified Zwerdling's formula for the responsivity by following the method used in the previous section for a DC biased bolometer:

(XVAcRbh

Géc

where AC the dynamic thermal conductance is equal to:

To) --1)

Here the LpAc factor is: The parameter describing the noise is the Noise Equivalent Power (NEP).

It is defined as the power producing a signal equal to the noise in a postdetection bandwidth of 1Hz.

NEP(f) = < A^((/)) >05 [START_REF] Gamow | Expanding Universe and the Origin of Eléments[END_REF][START_REF] Padmanabhan | Structure formation in the universe[END_REF][START_REF] Guth | Inflazionary Universe: a possible solution to the horizon and flatness problems[END_REF][START_REF] Penzias | A Measurement of Excess Antenna Température at 4080 Mc/s[END_REF][START_REF] Eisenstein | Cosmic Complementarity: Joint Parameter Estimation from Cosmic Microwave Background Experiments and Redshift Surveys[END_REF][START_REF] Lamagna | S Z constraints on the dependence of the CMB température on redshift[END_REF][START_REF] Smoot | Cobe observation and results[END_REF][START_REF] Mather | Calibrator Design for the COBE Far-Infrared Absolute Spectrophotometer (FIRAS)[END_REF][START_REF] Bond | Measuring cosmological parameters with cosmic microwave background experiments[END_REF][START_REF] Chluba | Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments[END_REF][START_REF] Piat | Cos mic background dipole measurements with the Planck-High Frequency Instrument[END_REF][START_REF] Hu | A CMB Polarization Primer[END_REF][START_REF] Hildebrand | The Shapes and Alignment Properties of Interstellar Dust Grains[END_REF][START_REF] Delabrouille | Diffuse source séparation in CMB observations[END_REF][START_REF] Mather | Spectra and Sky Maps from the COBE Far Infrared Spectraphotometer (FIRAS)[END_REF][START_REF] Fixsen | The Spectral Results of the Far-Infrared Absolute Spectrophotometer Instrument on COBE[END_REF][START_REF] Bennett | The Microwave Anisotropy Probe (MAP) Mission[END_REF][START_REF] De Bernardis | Détection of anisotropy in the Cosmic Microwave Background at horizon and sub-horizon scales with the BOOMERanG experiment[END_REF][START_REF] Hanany | MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on Angular Scales of 10-5deg[END_REF][START_REF] Benoît | The cos mic microwave background anisotropy power spectrum measured by Archeops[END_REF] where A S2 is the power spectral density of the signal fluctuation and is the responsivity of the detector. NEP is measured in [Watt/y/Hz].

In this model we take into account ail the principal sources of noise in bolometric détection:

Johnson noise: Johnson noise is the electronic noise generated by the ther mal agitation of électrons inside a bolometer at equilibrium. It has a white noise spectrum. The NEP for DC biased bolometers is [START_REF] Mather | Bolometer noise: nonequilibrium theory[END_REF]:

NEPJohnson = <j4kBTbRbIi^+ ^(3. 23
)
Where R& is the bolometer résistance and Zb is its dynamic impédance.

Let us notice with Mather [START_REF] Mather | Bolometer noise: nonequilibrium theory[END_REF] that Johnson noise does not dépend on load impédance. Let us assume here that it does not dépend on stray capacitance in the case of AC biased bolometers. Hereafter, we shall use Eq 3.23 indifferently with a DC model or an AC Model.

Phonon noise: The parameters of the bolometer are strongly dépendent on the température, so small variations in température inside the bolometer produce a voltage variation at the ends of the detector with a white noise spectrum.

It results [START_REF] Mather | Bolometer noise: nonequilibrium theory[END_REF]:

NEPPhonons = (3.24)
This resuit is independent from the REU.

Photon noise: The Photon noise cornes from the fluctuations of the inci dent radiation due to the Bose-Einstein distribution of the photon émission.

The NEP is [START_REF] Lamarre | Photon noise in photometric instruments at far-infrared and submillimeter wavelengths[END_REF]:

NEPphotons = 2 [ hvQudv + (1 + P2) [ A{v)Q2udv (3.25) J Anu J Au
Where Q" is the absorbed optical power per unit of fréquence, A(i/) is the cohérence spacial factor (equal to number of the modes-1 = 1 if diffraction limited) and P is the polarisation degree (0 non-polarised 1 polarised).

Preamplifier noise: it results from the impossibility to amplify a signal without adding noise, which results itself directly from the Heisemberg indé termination principle. It dépends also on the available components and on the design of the amplifier. We assume that the power spectrum of signal fluctuation is constant for ail the bolometers and equal to:

V< AS2 >pre = 6.

3.2.8

Computing the Response with a Square Bias With the same bias circuit (Fig3.4) it is possible to dérivé the performaces of a REU in which a square wave voltage applied to the bolometer as in HFI. Let us assume that if the REU is balanced, a perfect square wave bias is passing through the bolometer even in presence of a stray capacitance.

In HFI this is achieved by using a triangular wave plus a square wave (see section 2.3 in chapter 2).

A square wave can be decomposed as:

Vb(uj) = acos(cüt) + -cos(3(jüt) + -cos{3ujt) + = On the contrary we cannot dérivé the electrical power following the same logic: if we keep the same set up of the REU, after a little step in température the bias passing through the bolometer is not a square wave anymore so the Eq3.37 is not applicable. We hâve to correct each term of the sum as follow:

Impact on HFI

The conséquences of these results on HFI are:

• The bias current corresponding to the minimum of NEP (best bias) with the square AC modulation is of the order of two times larger than the one calculated in a DC model; so the optimisation of this parameter has to be done taking into account the AC square model.

• A stray capacitance as measured in HFI (~150pF) gives a loss of NEP in the worst case (100GHz bolometer) of 10%. In the best case the loss of NEP is equal to 4% (857GHz bolometer).

• If we consider as nominal a modulation frequency of 90Hz, the losses of NEP are between 0.8 and 2% from 100GHz to 857GHz bolometers with re spect to the minimum frequency of 86Hz.

• The scheduled mission is expected to last 30 months. Let the scientifîc goals be completely fulfilled if during this period the plate température of

Comparison between the two modulation tech niques

In Fig3.17 and Fig3. [START_REF] Fixsen | The Spectral Results of the Far-Infrared Absolute Spectrophotometer Instrument on COBE[END_REF] The total NEP and the responsivity of the sample bolometers with a sine AC model and a square AC model are over plotted for the three sample bolometers. Ail the curves are plotted considering an HFI-like set of parameters (Fmod=90Hz, Cp=150pF, T0=100mK).

In ail the cases the performances of a sine AC model are better than the square model. This is more obvious in the Responsivity (better by about 10%) than in the total NEP (better by about 4%). So we can conclude that at NEP level a bolometer connected to a sine AC biased REU would be more sensitive for a static signal.

Let us remark that the advantage in NEP is modest. Let us also notice that an AC sine bias would induce important variations of the température of the fastest Planck bolometers, bringing them in a non-linear régime. Therefore the simple model would not be accurate for an AC sine Planck case.

On the other hand, the square bias deposits a nearly constant power in the bolometers, that deviate from their mean température only by small amounts. This make the simple model an adéquate modelling tool to predict the static response of HFI. Tref is equal to lOOmKelvin ( [START_REF] Sudiwala | Evaluation of prototype 100 mK bolometric detector for Planck Surveyor[END_REF]).

The SEB model engine intégrâtes these two équations versus time by a 4th order Runge-Kuta method. After the model of the response of the bolometers, SEB model provides a simulation of the whole electronic chain to produce as output a signal in scientific units (ADU). This is done using calibration measurements performed at CESR.

The parameters that can be varied in the current SEB model are: My contributions to the SEB hâve been in particular to make is usable for predicting the time response. Currently the SEB model prédictions are not yet accurate enough to be used to describe the instrument performances for The regulated températures are the 2 K plate (LHe bath at low pressure -MKS regulator), the 4 K HFI interface (LHe bath + heater) and the 20 K HFI interface (Hélium Gas + heater). In addition, an auxiliary of gas He circuit will be provided for the pre-cooling of HFI.

The optical System on the 2 K plate was designed using optical simulation Integrating sphere An Integrating sphere is an optical component consisting of a cavity with its interior with a high diffuse reflectivity. The shape of the cavity is spherical. Its relevant property is a uniform scattering or diffusing of light. Light rays incident on any point on the inner surface are, by multiple scattering reflections, distributed equally to ail other such points and effects of the original direction of such light are minimized. An integrating sphere may be thought of as a diffuser which préserves the total power but destroys spatial information. In the calibration facility the integrating sphere is used to cou ple optical sources with the HFI instrument. It is thermally coupled to the cold plate. On the top of the sphere two Mickey ears appears in order to contain the CS2 source (see below) and the reference bolometer volumes.

Sources

In the calibration facility it is possible to use several optical source:

-CSl (Cold Source 1): it is attached to the integrating sphere in order to simulate the background produced by Planck telescope. It consists of an annular blackbody (with a throughput of 1000rara2sr) changing from about 50 K and the température of the cavity (source turned-off).

-CS2 (Cold Source 2): it is a chopped blackbody feeding the integrating sphere. Operation température is between 2 K and 20 K.

-External Sources: they are coupled to the integrating sphere by the FTS line. It consists of a Fourier Transform Spectrometer and chopped sources.

The Fourier Transform Spectrometer used to measure the spectral response of the instrument is obtained from a commercial model (Sciencetech) with a spectral range from 2 to 100 cm~l a resolution as good as 0,015 cm~l (60 cm optical travel) and a minimum scanning speed slower than 0.02 cmsec~l.

This FTS will be equiped with a wide band beam splitter (polariser type interferometer), and an internai bolometer détection System on a dedicated output port (for tests and System monitoring).

These sources are monitored by an absolute bolometer and a reference bolome ter: except for the cavity in thermal equilibrium with ail the source inside, the calibration facility does not include any absolute source. Therefore, it rnust be calibrated itself with an absolute detector : we will use a bolome ter with well known beam characteristics and response, called the absolute bolometer. The absolute bolometer will be operated at 300 mK to be able to measure signais in the dynamic range of HFI. The readout electronics is identical to one channel of the HFI readout. In order to control the reproducibility of the sources, a bolometer System will monitor the flux inside the integrating sphere during caractérisation and use of the calibration facility. This is the reference bolometer.

Mirror

The mirror conjugates the sphere output and the FPU focal plane with a magnification of about 1.2. The mirror diameter is 320 mm, spherical with a radius of 180 mm. The mirror is made of aluminium with a sinooth sur face in order to insure a reflectivity greater than 0.98 in the HFI wavelength range. The mirror must be strongly coupled to the cold plate to keep it at 2 K.

Polariser

A polarizer is a device that converts an unpolarized beam (coming from integrating sphere) into a beam with a single polarization state. In Calibra tion facility a 140 mm diameter polariser from MICRONIC company with a grid step of 40^ra has been used. The polariser is placed in a converging beam in front of the horns thanks to a support that can take three positions:

one with a rotative polariser in the beam, one with the crosstalk sources in the beam, and one with nothing in the beam.

Optimization of the REU Parameters

The strategy of ground calibrations as it has been estabilished, is to fix the REU parameters (exept Fmo(i and température of bolometer) and to measure the relation volt versus optical power for a set of fixed parameters close to those we will hâve in flight, so we can deduce the model with a polynominal fit with the experimental data and the responsivity with its dérivative. With this approach it is necessary to find a way to fix the REU parameters.

We discuss in this section the optimisation of the bias current, Sphase parameter and the calibration of the F2 parameter.

The Bias Current

The bias current tuning test is a key point in optimisation of the HFI per formance. Both the static and dynamic response strongly dépend on the bias current. The level of noise is also affected by changing it. We need to optimise this parameter taking into account ail these effects and in a range of realistic flight backgrounds.

The starting point is the use of SEB and SOS simulators (see section related) to perform static simulations of the HFI instrument with an appropriate background.

The method used to détermine the optimal bias current was [START_REF] Catalano | Optimal Bias Current for HFI GRound Calibrations[END_REF]:

• Estimation of the range of possible backgrounds and calculation of the signal to noise ratio (SN) for a source of lmK. This calculation has been made using SEB model and SOS model.

• Détermination of an empirical law between time constant and bias cur rent using JPL data. • Extension of the results in the domain of optical modulation frequencies.

• Calculation of the best bias current (using a toy model of noise).

• Extension of the calculation at different températures of the bolome ters.

Characterization of backgrounds

Let us defîne 3 cases by playing with ail the parameters that détermine the background by using the SOS simulator.

^Telescope [A"] Telescope Emis. [%]

LOW Background

Time Constant

The physical model of the bolometers (chapter 3) shows that the bias current affects strongly their time constant. In this case, an empirical solution has been preferred rather than a theoretical model using the knowledge of the

Optical Modulation Frequency

To measure properly the best bias current we hâve to respect as well as possible the flight condition during the mission so it is necessary to take into account the optical modulation frequency (angular speed of satellite around his spin axis) in order to understand the range of interest in frequency for each channel of HFI.

We know that the FWHM changes versus HFI channels. So the maximum frequency of interest is given by the relation: The frequency of optical modulation is related to the momentum l of the spherical harmonies: The optical modulation frequency changes (worse) the signal to noise ratio. If we consider a fiat noise (early in the project), we hâve:

/
Ail the optical modulation frequencies are possible up to the limit set by the beam size and the angular speed of the satelite.

The best Bias Current Calculation

In the figure 4.4 the signal to noise ratio for the different backgrounds is presented. To compute the best bias current let us consider the intersection between backgrounds and into this set the bias current is calculated where the sum of the SN for the different backgrounds is maximum. For the 100GHz channel we consider a range of 0-20 Hz, which corresponds to the range of effective l accessible with the 9.2 arcmin beam.

Température

The nominal value of the température during the work conditions will be 100mA. We hâve shown the variation of the NEP versus plate température on chapter 3 (see Fig. 3.14). We hâve also iterated the process for different températures for two reason:

• The cryogénie System may not work perfectly during the mission so we hâve to be able to predict the response of the instrument at different tem pératures.

• A température slightly different from 100mA, even though it reduces the sensitivity on a single measure, could increase a lot the lifetime of the cryogénie System. It can increase the sensitivity of the mission. This will be known better after calibration and finalised once flight background are known.

Measuring Optimal Bias Current

During PFM calibration campaign we performed a test sequence "best bias" looking for a validation of the predicted value. This test had a twofold goal: (the value is normalised by the preliminary set derived from simulations). As expected, maximum response happens generally for normalized applied bias slightly less than one because the effect of time constant is not taken into account in the measurements. The green curve is calculated considering the effect of time constant of bolometers taking into account the measurement from JPL with the same procedure than simulations. A few measurements

were not successful due to incorrect settings of the Vbal and Tbias. The optimal bias was recommended by analogy with bolometers of the same kind.

Full data réduction of noise and response measurements (cite by FX

Optimising the SphaSe Parameter

The Sphase parameter has been defined in Cap2. We performed a test in order to optimise Sphase to get the maximum response [START_REF] Catalano | Optimi sation of Ibias and Sphase[END_REF].

The response to the carbon fibre CSM source modulated at 2.5Hz has been measured under background conditions that approximate the guessed in-flight conditions (CS1=30K and T platform=2.0K). The modulation frequency was 86.09 Hz (Fdiv=136 and Ns=40). Sphase has been varied from 1 to 15 by steps of 2. An Optimization of the REU was performed after every phase change, which was the only way we found to obtain acceptable oper ation with grouped TC (Fig 4

.6). A channel Autobalance or Optimisation

is an automated procedure that adjusts the transition compensation of the bias voltage so that the bias current is as near an possible of a square wave (see 2.3).

The results were fitted with a 4th order polynomial and the optimal Sphase value was derived. Some channels give responses obviously wrong, which was expected because they were known not to converge when "optimized". For these channels we forced results to a regular value. The pré dictions of the SEB model prove to be accurate, and can be a basis to set (if^--32768)(-"") -

V N s ample ' v O REU ' 1 -El
where:

Nsampie is the total number of sampled points in an half period.

Greu represents the programmable gain of REU, Gcaiib is the one used during REU calibration in CESR.

Vbai is the square compensation voltage.

Fi is another calibration parameter. It represents the amplitude of the volt age applied to the bolometer for a given (and single) Rias command, and a given impédance of the bolometer.

F2 parameter represents the ratio between delivered signal from REU [ADU]

and digit parameter in case of only use of a compensation square in the electronic chain (Fig4.7).

F2 = -2!fi?^[ADU/Digit]

Vbal At PAU level a pass-band filter (5-600Hz) is présent so F2 could be affected by a changing of modulation frequency (Fmo<i). At this moment in the IMO instrument function (Eq(4.5)) F2 parameter is a constant for each bolometer.

The sequence consists in checking the raw signal instrument response versus modulation frequency for ail the bolometric belt-channels of HFI [START_REF] Catalano | Fmod Sequence[END_REF].

During the sequence there is no current on the bolometer {Iuas -0 and Tbias -0 hfta/= 100). We perform the sequence setting Fmoci from 86.09Hz Same strategy of analysis used by CESR [START_REF] Montier | RU Calibration PFM[END_REF] is performed in order to calculate F2.

The data from 87,68Hz are not reliable because of command problems during the sequence. After data analysis we can remark that in general if we set Fmod at 100Hz the F2 corrections calculated can be up to 3% (Fig( 4.9)).

These results show that we hâve to correct the F2 parameter in the instru ment équation with a vector of values depending on the Fmo(i we use.

In tab 4.2 we présent the results of the linear fit coefficients.

Belt-Channel

Best Bias (Meas)

[nA] (at 100 mK) The calibration facility was used to measure the various terms of the photo metric équation of HFI.

Principles of the EFF calibration sequence

If we consider a nominal top-hat spectral band of 33% with respect the cen tral frequency, the optical power absorbed by the bolometers is given by: The basic measurement sequence is common for ail the photometric sequencies:

• Variation of the température of the source.

• After stabilization in température of the source, we perform an autobal ance in order to calculate the optical power on the bolometer with a classical bolometer model (biased in a DC mode).

WoPt = -0 (7f+l + -Rbll 1ref\P + V

where:

Gb is the thermal conductance between the bolometer and the heat sink, TioomK is the real température of the lOOmK stage, Trej is the reference température (lOOmK in our case), /3 is an experimental parameter, A is the bias current on the bolometer and Tb Rb are the température and resistence derived from the IMO.

• Using data from two different stabilized températures we calculate AWOJ)t

• When the températures of the other background sources are constant, AWopt only dépends on the température variation of the studied source.

• We calculate the optical parameter comparing AW^t to the différence of two black bodies at the same températures.

a w%r EFF ^JAl/n^ABB, Where Qeff represents the generic optical parameter.

There was a température drift of the 2K platform during the 1.6K and 4K

sequence so we hâve to correct the general procedure taking into account these déviations.

In Fig 4 .11 a detailed plot of the impédance timeline of the whole EFF sequence is presented for a 100GHz bolometer:

• EFF1 : measure the emissivity of the CSl source.

• EFF2-Füter Wheel: measure of the low frequency response using the response to Heavyside steps produced by opening and closing the cryogénie filter wheel (see section 4.6.1).

• EFF2-4 K: Measure of the coupling factor of the 4K cryogénie stage.

• EFF2-1.6K: Measure of the coupling factor of the 1.6K cryogénie stage.

• EFF3-1 : Measure of the total efïiciency of HFI.

• EFF3-2 : Measure of the Steady State response function of HFI (see section 4.5)

Background Conditions

During the calibration run the température of the 100mK stage was very stable (~2fiK/h). We report in Fig( 4.12) the history of the cryogénie stage

The REU Autobalance procedure is quantised and it introduces some noise (for example no change of parameters where one is expected)(Fig4.13).

This could introduce some systematics in the sequences where the signal to noise ratio is small. CSl is a black body embeded in the cavity. Its brightness is diluted in the intégration sphere. We can consider therefore CSl as a grey body with a characteristic emissivity.

In Fig (4.14) we présent the signal for one bolometer for each family of detectors. We performed a température change of CSl from 30K to 2K (tem pérature in which CSl is switched off and thermalized with the platform).

Let us remark that during this sequence the température drifts from the background sources were negligible with respect to the signal to noise ratio, so for this analysis we use the general procedure to analyse the data.

In Fig (4.15) and table we présent the results for the CSl efficiency detected by ail the 52 bolometers of HFI. For 4 bolometers the autobalance procedure did not work. It means that these bolometers worked in saturation condi tions so the results for these 4 bolometers are not significant.

To calculate the best température to set CSl source in order to simulate the background from the telescope, we perform a y2 test to minimize the differ-

4.4.5

Thermal émission of the 4K and 1.6K stage

The thermal émission of the 4K and 1.6K stages of the FPU is a constitutive part of the background power absorbed by the bolometers. They also constitute a potential source of additional low frequency noise, if the température of these stages is not stable enough.

A drift in température of the platform induced a difficulty in interpreting the thermal émission sequence during the calibration run.

To compensate the drift we consider the sequence corresponding to the absolute calibration (see 4.4.6) and in particular the relation between the signal of the bolometers and the température of the platform during this sequence.

Let us consider they hâve a linear relation. We performed this analysis for ail bolometers and in both sequences, the results are summarized in Fig (4.19).

In the 1.6K sequence the results show that high frequency channels are not sensitive (a tiny emmission from 1.6K stage at high frequency).

Total Efficiency

We used the whole Saturne cavity as a blackbody (ail sources are OFF for température uniformity) to measure the absolute response of the instrument.

The range of température was from 2K to 3.7K. The most important différences between calibration run and Cardiff measurements appear for the high frequency channels (Fig 4.17). One possible explanation is a different spectral index between used sources.

In the table 4.3 the total efficiency is presented In this case the photometric équation is: This équation is the one implemented in the IMO and in the SOS model.

TL /"OO r W°pt = -, , d-[AqPAReff / x(.v)-BBu{TSource,v)dv+coupAK / A2-BBu(TAK,v)dv+ r -j-1 J o J Av +coupi'6K A2 • BB"(Ti'QK, v)dv] J Av (4.8) B-C Opt ID CSleff [%] C,4A'[%] Ci.6/c

Conversion Factor Wrj -Wstage

It is useful to quantify the optical power produced by cryogénie stages with respect an optical RJ source using results from EFF sequences [START_REF] Catalano | Convertion Factor between the Cryogénie Stages and a RJ Source[END_REF].

The optical power absorbed by the bolometers, for the different cryogénie stages and for the RJ source, is represented here by a simplified model (the emissivity and transmission are constant in each spectral band):

WVob = WRJ = 1 l + P L 1 l + P 1 l + P • coup4k / A2 • BBu{TAKi v)dv J A1S4K • coupAK / A2 • BBv(Ti£K, v)dv JAvi .6K r OO n\l PAReff / x(y)BBu{TRJ, v)dv Jo J
where:

PAReff is the Normalisée! factor coming from the absolute calibration sé The basic calculation corresponding to a variation of lmK for both RJ and cryogénie stage, is:

Factor = AWrj stage
The results are presented in table 4.4. Looking at results of EFF sequence we find that the coupling coefficients between two PSB of the same pair are different. The same effect occurs on total efficiencies. This seems strange since the pair of PSB has exactly the same optical chain in front of it. In fact optical transmission dépends on both the optical chain and the quantic coupling of a photon with the bolometer itself.

This cross section is a function of manufacturing material of the bolometer and of its position in the cavity at the end of the horn. JPL measurement on bolomers showed that the différences between two PSB of the same pair could be in same case of the order of 15%.

On the other hand if the illustrated différences dépends only on this cross section we could hâve:

-PSBa /~-PSBb 'Tôt / rTot coupB^Ba /coupBBBb

In Fig 4 .23 the results of this calculation are presented. We can conclude that the degree of polarised systematic of the optical change is not relevant. The red point corresponds to a ratio between a pair of PSB in which the autobalance procedure did not work The steady state (or static) response function is the relation between the incoming power (in watts) and the instrument output data in digital units (ADU), once ail transients hâve died away.

It is expected to be non-linear because both the conductance between the bolometer and the heat sink and the bolometer impédance hâve a non-linear dependence with température (see model of bolometer in section 3.2.1).

We shall show that the non-linearities of the response curve is negligible for the signal from the CMB anisotropies, while this is not the case for strong source. Order of magnitude are given in table 4.5.

Let us define the instrument responsivity (ADU/Watt) as the dérivative of the response function with respect to detected optical power:

S(G, R , I) dDATA dîvôpt (4.10)
In nominal condition, the background on HFI bolometers is much higher than the dipole signal which is not the case for bright sources like planets (Table 3.2.1). An experimental characterisation of static function is therefore very important to recover properly the optical power of the incoming signal. Since in case of HFI the experimental response is taken in digital units (ADU), we are interested to recover the static function binding ADU to optical power directly. Jupiter, Satum and Mars. Optical power is calculated using optical parameters derived from calibration. The background is calculated when the ail the source in integrating sphere are thermalized with the cavity at 3K.

Measurements of the Response Function

The measurement of the response function consists in measuring the responsivity, that is the local dérivative of the response function under a large range of background conditions. Practically, the responsivity is measured by illuminating ail bolometers by the CSM carbon fibre source modulated at a frequency of about 1 Hertz. The average background power is explored by slowly changing the température of the CS1 source [START_REF] Catalano | HFI Calibration Report -EFF Sequence[END_REF].

The amplitude of the modulated signal is:

Meas = S • Wf^e (4. 11
)
where S is the responsivity of the instrument and Wfibre the optical power of CSM.

An indefinite intégration gives the integrated measure MT. Let us extrapolate the measurement up to saturation limit.

We fit the experimental results with a two degree polynomial curve: Where the lin and the q subscript refer to a linear and second order fit respectively.

Wopt = Wo + PlinADU + ( 4
For high frequency channels we can define in the same way a non-linearity parameter referred to planets.

Time Response

As I showed in section 3.2.1, bolometers hâve not an instantaneous response.

The effect on the response is a filtering of the high frequencies coming from the optical signais adding with respect the filtering effect due to the beam.

In the HFI, the filtering due to the effect of bolometer lias to be added to the intégration of the modulated signal over a half-period and the presence of a stray capacitance. This makes a complex time response.

We hâve shown that the response of ail channels is very linear for ail the sky excepted for the brightest planets. Therefore the time response is well described in the Fourier domain by a pseudo transfer function, defined as the ratio of the Fourier function of the output in ADU to that of the optical input in Watt.

The measurement of the time response is an essential results for HFI scientihc goals. For example the propagation of the flight calibration from the dipole to the higher order moments of the spherical harmonies dépends strongly on the accuracy of the measurement (expected to be better than 0.2%). In addiction the time response is one of the most difhcult quantities to measure in flight so a good characterisation on the ground was a key point during PFM ground calibrations. The Semi-empirical model intends to fit experimental data with a transfer function of this form:

TF{f) = LP(f) Hrej(f) Hres(f) (

Where LP(f) is a first order low-pass filter due to the bolometer thermal time constant.

Hrej{f) is a rejection filter (centred at modulation frequency) with a free parameter fc related to the width of the filter itself. Such a rejection filtering centred on modulation frequency Fmo(i is expected due to the design of the filters in read out electronics.The filter has this form:

Hrej = -, (4-19)
/i 12 V (f-fmod)2
Hres(f) is a low-pass second order filter with a résonance centred on Fmod'-

Hres 1 + 1 (f-fmod)2 (l + Q)fmod (4.20)
Where Q represent a pseudo-quality parameter to fit with experimental data.

For a given set of environmental and REU parameters, the model has only Finally the FilterWheel data show that the signal takes more than one second to cover the last 2% and converge to its the asymptotic value (Fig

4.32).

The LFER is important because it change the response to the CMB dipole (a signal at 16mHz), which is the reference signal for in-flight calibration of the CMB channels.

During CSL calibration in Liege a sequence of time response measurements has been performed. The modulated source is a carbon fibre source inserted in a small central aperture in the cold load in front of the FPU. These mea surements plus the use of semi-empirical models will give us a good knowl edge of the transfer function in the whole frequency range of interest and in the functional checkout will be done in order to verify that the basic functions are available for the scientific operations.

The main goals of CPV phase are listed here:

• To check that performances of Planck payload are adéquate to perform the nominal mission.

• To obtain the in-orbit characterization of the instruments (LFI and HFI) in terms of ail the tuning parameters.

• To characterise the instruments in the in-orbit conditions.

• To check the performance of spacecraft and payload subsystems which cannot be checked out during the commissioning phase.

Formally the calibration and performance vérification (CPV) phase starts when the payload is at the nominal operational températures. Due to the complex cryogénie cooling System and the related operations, commissioning activities and calibration and test activities can be, and in several cases are, required to take place already in the cool-down period.

The timeline of the HFI tasks during CPV phase are listed in the next:

• Tuning: This stage involves the tuning and checkout of HFI subsystems and includes détermination of the HFI thermal coupling parameters. • Sensitivity: noise and compatibility tests are performed

• Final Tunings. The HFI will perform the final parameter adjustments assurning that the instrument sub-systems are sufficiently relaxed.

• HFI Optical Calibrations: This stage includes the activities which require the instruments to be operational for routine survey. The in flight optical calibration consists of ail the activities not well ground-calibrated and ail the optical health test.

In the next I will detail the activities related to CPV phase in which I am involved.

Checking for coupling parameters and Non-Linearities

In this test we measure the coupling parameters of cryogénies stages 4K and The test consists in measuring the optical coupling parameters for the 4K cryogénie stage with a check in parallel of the static function and its nonlinearities. We want to perform a step in température of the stage of about 60mk (heating the 4K PID) and then corne back to the original setup. After stabilisation in température we integrate the signal for about 2 hours in order to reach a good signal to noise ratio for the dipole. We repeat the sequence twice in order to reach a better signal to noise ratio and in order to hâve some redundancy in measures. The test duration is of the order of 10-12

hours.

The intégration of the signal of about 2 hours means an over-integration for the coupling parameters recovering but is strictly sufficient for recovering data from non-linearities. The non-linearity test in fact, in accordance with PFM non-linearities calibration, consists in controlling the change in ampli tude of a modulated source with a changing background. During CPV phase the candidate modulated source is dipole for CMB channels and Galaxy for high frequency channels. In this case the critical parameter is the signal to noise ratio for the dipole. From eq4.22 we obtain for a 100GHz channel, a signal to noise ratio of about 5000 for a 2 hours integrated dipole.

During the PFM ground calibrations we hâve estimated the non-linearities coefficients for low frequency bolometers in the case of dipole signal (see ta ble 4.6). For a 100GHz PSB bolometer this coefficient is about 0.4%. This means that with 2 hours integrated dipole we can recover the non-linearities of 100GHz bolometers with a signal to noise ratio of about 20 which is a good trade-off.

1.6K stage

We perform a step in température of about 30mk (heating the 1.6K PID)

and then corne back to the original setup. we integrate signal after stabilisa tion of the cryogénie stage for 10m and repeat the sequence several times for redundancy. The test duration is estimated to be of the order of 8 hours. Planets are point-like sources with a very good approximation when compared to FWHM of the HFI channels; furthermore, because their mm-wave brightness température is rather well known, observable planets are perfectly suitable for mapping the beam shape [START_REF] De Bernardis | Détection of anisotropy in the Cosmic Microwave Background at horizon and sub-horizon scales with the BOOMERanG experiment[END_REF].

The différences of physical characteristics between giants planets and terrestrial planets (and asteroids), affect the variation of their brightness tempér ature versus frequency. While it is a good approximation to consider the température of Mars versus the frequency as a constant (in the HFI range) thanks to total or just about total absence of atmosphère, for Giants plan ets the situation is diametrically opposite; because of the absorption lines of the gas of which these planets are constituted, their brightness température measured in different bands, can strongly vary with frequency (up to 30%).

In the following section I will présent the Signal to Noise Ratio for planets in ail the HFI channels. In the section 5.6 a study on effect of under-sampling beams will be also presented.

Freq.

[GHz]

Simulated Beams

We are using beams computed with GRASP 9 at the central frequency with an idéal Planck telescope, i.e. a perfect implémentation of the Planck design [START_REF] Noviello | HFI Beams Patterns Archive[END_REF].

The horn field is generated using the scattering matrix (mode matching) approach. A corrugated horn is viewed as a succession of cylindrical waveguide segments with varying radii. Each junction has its own scattering matrix and the overall scattering matrix for the complété horn is calculated by cascading the matrices describing consecutive segments. This final matrix contains the reflection and transmission coefficients for the total System.

SNR on Planets

Planck will spin at ~lrpra and every detector observes a Circle each turn.

This is nearly a great circle, since the central point of the detector array corresponds to a line of sight making an angle of 85 degrees with respect to the spin axis. We can defined also a Ring as the signal from circles of one bolometer 60 minutes of intégration.

The Signal to Noise Ratio (SNR) related to planets on the HFI [START_REF] Catalano | Beams Calibration Requirements for Planck HFI[END_REF] channels per ring and per circle, is obtained using the following équations:

When a planet is at the main pointing position of the detector, the optical background coming from the planet on bolometer is equal to: frequency fsample (right). This is often described as an aliasing of the initial spectrum about Fsample/2. The "aliased" part of the spectrum is added to the initial spectrum with a phase that dépends on exact sampling times (right).

The reconstruction of the far side lobes with the planets is not possible because for the ail planets the SNR is less than 1 in this région of beams.

Therefore, the reconstruction of the far side lobes has to perform with measurements using other sources (for instance with galactic centre) together with models.

Effect of Under-Sampling Beams

A de-pointing step of 2' is now considered in the Planck scanning strategy.

The expected benefits are that maps reconstructed with a single detector should provide an acceptable sampling of the sky for ail channels dedicated to CMB measurements. In this section I présent in the Fourier domain the aliasing of the signal due to under-sampling.

This work is intended to estimate the errors made when measuring sources with HFI with respect to the séparation between scans [71].

We compute the Fourier transform of the beams and evaluate the maximum error by integrating the module of the part that is aliased by under-sampling.

The aliased spectrum cannot be removed from the initial spectrum be cause its phase steeply dépends on the exact position of the sampling, which can be considered as random for random sources on the sky (Fig 5 .2). The produced by under-sampling. We hâve computed the module of the Fourier transform (Fig. 5.3, middle) of the beam (Fig. 5.3, left). Let us note here the effect of using a truncated beam that produces a low level cross-shaped feature in the Fourier domain. We hâve checked that this artefact has no impact on the results.

The intégral along the cross scan direction of the aliased spectrum has been computed and renormalized by the intégral of the whole spectrum. This quantity is the possible relative sampling error. The error increases as soon as the Nyquist criterion is not met. Applying the same procedure to the square of the module provides us with the error produced by under-sampling on the second order statistics of the maps (Fig. 5.4, right), which is not essential here. This method has the advantage of requiring no assumption on the beam reconstruction process. It supposes that the module of the Fourier transform is a good estimator of the sampling error. Another prerequisite is that the source has a white spectrum, whether it is a point source or random source with white spectrum. If the source has a different spectrum (i.e. the interstellar medium) it has to be accounted for by weighting the FT by the source spectrum.

This process has been applied to six receivers of Planck-HFI, one per frequency. Fig. 5.3 represents the beams, their Fourier transforms and the possible errors produced by aliasing. The 857GHz beam is the average of beams computed at three frequencies in the bandwidth of this channels, which somewhat compensâtes for the steep variation of the beam shape with frequency. Other beams hâve been computed at the centre frequency only.

Ail are the best available versions at the date of the édition of this thesis.

Conséquences on Point Sources

The 2' sampling interval is good enough for the 100GHz and 143GHz channels. The aliasing error is less than 0.5% for the 217GHz and 353GHz beams, which may be considered as acceptable for photometric calibration of any kind of source and for map reconstruction from individual bolometers. This would not the case with 2.5' intervals, that would make sampling errors larger than 1% RMS. The two multi-mode beams (545GHz and 857GHz) are strongly under-sampled at 2' and even 1.25' sampling intervals, which induces random errors up to 20%, and is probably not acceptable for most of the scientific applications. Fully solving this issue would imply using a scanning step of 0.8' or less. On the other hand the proper movement of mars (1.24 arcmin in one hour) will improve these results so that a greater scanning step can be used for high frequency channels too. Other methods, based on the accurate beam knowledge and/or on the use of the detailed features of the real scanning strategy can restore an acceptable accuracy to the measurement of point sources.

Conséquences on Interstellar Medium

Measuring the interstellar medium is important both as a scientific object in itself and for component séparation. Would it hâve a fiat spectrum, the aliasing error made would hâve exceeded the acceptable error budget for component séparation, even with the 1,25' sampling at 857GHz. We hâve taken an angular PSD with a power law of k-5/3 down to k = 1 per degree, and fiat at lower angular frequencies. The estimated aliasing is less than 1% for 2' sampling steps and 0.2% to 0.3% for 1,25'.. This looks acceptable for ISM removal. Due to the rather simplistic estimate of this first approach both from the point of view of the method and of the représentation of the AGN balances the gas cooling (see for instance [START_REF] Cattaneo | AGN self-regulation in cooling flow clus ters[END_REF][START_REF] Conroy | Thermal Balance in the Intracluster Medium: Is AGN Feedback Necessary[END_REF], and [START_REF] Mcnamara | Heating Hot Atmosphères with Active Galactic Nuclei[END_REF]). Also, from high redshift, the rate of supernovae drives the strength of the galactic winds and thus the amount of material that ends ejected within the IGM and the ICM ( [START_REF] Loewenstein | On Iron Enrichment, Star Formation, and Type la Supernovae in Galaxy Clusters[END_REF]). These ejecta are then mixed in the environment by the action of the surrounding gravitational potential and the dynamics of cluster galaxies within.

Since long, X-ray observations hâve shown the abundant presence of heavy éléments within the ICM (see for instance review works [START_REF] Sarazin | X-ray émission from clusters of galaxies[END_REF][START_REF] Arnaud | X-ray observations of clusters of galaxies[END_REF]). Physical processes like ram-pressure stripping, AGN interaction with the ICM, galaxygalaxy interaction or mergers are scrutinized within analytical models and numerical simulations in order to explain the presence of metals (see for in stance works by [START_REF] Domainko | En richment of the ICM of galaxy clusters due to ram-pressure stripping[END_REF][START_REF] Domainko | En richment of the ICM of galaxy clusters due to ram-pressure stripping[END_REF][START_REF] Moll | Simula tions of métal enrichment in galaxy clusters by AGN outflows[END_REF]). Moreover, it is obvious that the process of tearing of material from galaxies leads not only to the enrichment of the ICM/IGM in métal, but in gas, stars and dust as well. Recent work on nu merical simulations [START_REF] Murante | The Diffuse Light in Simulations of Galaxy Clusters[END_REF][START_REF] Murante | The importance of mergers for the origin of intracluster stars in cosmological simulations of galaxy clusters[END_REF][START_REF] Conroy | Thermal Balance in the Intracluster Medium: Is AGN Feedback Necessary[END_REF] hâve stressed the rôle of hierarchical buiding of structures in enriching the ICM with stars in a consistent way with the observed amount of ICM globular clusters, and ICM light. Indeed, the overall light coming from stars in between cluster galaxies represent an important fraction of the total cluster light: for instance it has been measured [START_REF] Krick | Diffuse Optical Light in Galaxy Clus ters. II. Corrélations with Cluster Properties[END_REF] 6 to 22% from a sample of 10 clusters. The effect of a diffuse dust component within the IGM/ICM, and its effect is less known. A few observational studies with the ISO and the Spitzer satellites hâve tried without frank success to detect the signature of such a component [START_REF] Stickel | Farinfrared émission of intracluster dust in the Coma galaxy cluster[END_REF][START_REF] Stickel | Far-infrared émission from intracluster dust in Abell clusters[END_REF][START_REF] Bai | Infrared Luminosity Function of the Coma Cluster[END_REF][START_REF] Bai | IR Observations of MS 1054-03: Star Formation and Its Evolution in Rich Galaxy Clusters[END_REF]. More successfully, [START_REF] Montier | Dust émission from clusters of galaxies: statistical détection[END_REF] hâve obtained a statistical détection, via a stacking analysis, of the overall infrared émission coming from clusters of galaxies. However, they

were not able to disentangle the IR signal from dusty cluster galaxies from a possible ICM dust component. On the other hand, from a theoretical point of view a few works hâve looked at the effect of dust on the ICM [START_REF] Popescu | On the FIR émission from intracluster dust[END_REF] or in conjunction with the enrichment of the ICM in metals [START_REF] Aguirre | Métal Enrichment of the Intergalactic Medium in Cos mological Simulations[END_REF]. However, the ef fect of dust on a ICM/IGM-type thermalized plasma has been formalized by Montier and Giard [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF]. These authors hâve computed the cooling function of dust taking into account the energetic budget for dust. They hâve shown the ability of dust to be a non negligible cooling/heating vector depending on the physical properties of the environment.

Dust thus cornes, within the ICM/IGM, as an added source of nongravitational physics that can potentially influence the formation and the évolution of large scale structure in a significant way. Indeed, since redshift of z ~2 -5 during which the star formation activity reached its maximum in the cosmic history, large amounts of dust has been produced and thus ejected out of the galaxies due to violent galactic winds into the IGM [START_REF] Springel | The history of star formation in a A cold dark matter universe[END_REF].

As this material is then accreted by the forming halos, one can wonder about the impact produced by dust on the overall properties of clusters of galaxies once assembled and thermalized. In a hierarchical Uni verse, the population of clusters is self-similar, thus is expected to présent well defined structural and scaling properties. However, to date, it is common knowledge that the observed properties deviate form the prédiction by a purely gravitational model (see [START_REF] Voit | Tracing cosmic évolution with clusters of galaxies[END_REF][START_REF] Arnaud | X-ray observations of clusters of galaxies[END_REF] for review works). It is thus important to address the issue of the impact of dust on the statistical properties of structures such as clusters of galaxies, the same way it is done for AGNs, supernovae, stripping or mergers.

In order to tackle this question, we hâve put into place the first N-body numerical simulations of hierarchical structure formation implementing the cooling effect of dust according to the dust nature and abundance. In this chapter, we présent the first results of this work focusing at the scale of galaxy clusters, and more specifically on their scaling properties. The paper is organized as follows: we start by presenting the physical dust model and how it is implemented in the numerical simulation code. In Sec. 6.2, we describe the numerical simulations and the various runs (i.e. model) that hâve been tested. From these simulations our analysis concerns the galaxy cluster scale, and focus on the impact of the presence of dust on the scaling relation of clusters. In Sec. 6.3, we présent our results on the M -T, the S -T, the Y -T and the L\ -T relations. The derived results are presented in Sec. 6.4 and discussed in Sec.6.5.

The dust model

In our numerical simulations the implémentation of the physical effect of dust grains is based on the computation by Montier and Giard [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF] of the dust heating/cooling function. We decided to limit our implémentation to the dust cooling effect only. Indeed the goal of this paper is to study the effect of dust at the galaxy cluster scales. The heating by dust grains is mainly effective at low températures (i.e Te < 105 K) and is a localised effect strongly dépendent of the UV radiation field. Our numerical simulations (see Sec. 6.2 and 6.5.2) do not directly implement this level of physics.

Dust grains in a thermal plasma with 106 < T < 109 K are destroyed by thermal sputtering, which efficiency was quantified by [START_REF] Weingartner | Photoelectric Emis sion from Dust Grains Exposed to Extrême Ultraviolet and X-Ray Radiation[END_REF]. The sputtering time dépends on the column density and on the grain size. For grain sizes ranging form 0.001/rm to 0.5/rm, and an optically thin plasma (n ~10"3 atom/cm2), the dust lifetime spawns from 106 yr for small grains up to 109 yr for big grains. This lifetimes are therefore large enough for the cooling by dust in the IGM/ICM to be considered. Evidently, it is also strongly linked to the injection rate of dust, thus to the physical mechanism that can bring and spread dust in the IGM/ICM.

Our implémentation of the dust cooling power is based on the model by [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF]. We recall bellow the main aspects of this model and describe the practical implémentation within the 7V-body simulations.

The dust cooling function

Dust grains within a thermal gas such as the ICM or the IGM can either be a heating or a cooling vector depending on the physical state of the surrounding gas and on the radiative environment. Heating can occur via the photo-electric effect if the stellar radiation field (stars and/or QSOs) is strong enough ( [START_REF] Weingartner | Photoelectric Emis sion from Dust Grains Exposed to Extrême Ultraviolet and X-Ray Radiation[END_REF] and references therein). Indeed, the binding energies of électrons in dust grains are small, thus allowing électrons to be more easily photodetached than in the case of a free atom or a molécule. On the other hand, the cooling by dust occurs through re-radiation in the IR of the collisional energy deposited on grains by impinging free électrons of the ICM/IGM l.

Montier and Giard [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF] hâve computed the balance of the heating and cooling by dust with respect to the dust abundance: cooling by dust domi nâtes at high températures in the hot IGM of virialized structures (i.e clusters of galaxies), and heating by dust dominâtes in low température plasma under high radiation fluxes such as in the proximity of quasars. The details, of course, dépend on the local physical parameters such as the grain size and the gas density.

Assuming local thermal equilibrium for the dust, the overall balance between heating and cooling in dust grains can be written as follows:

A9(a, Td) = H9coü(a, Te, ne), (

with Hcoii being the collisional heating function of the grain and A the cooling function due to thermal radiation of dust. a is the grain size, Te and ne are respectively the electronic température and density of the medium and Td is the dust grain température.

The heating of the dust grain was taken from [START_REF] Dwek | Cooling and évolution of adiabatic blast waves in a dusty medium[END_REF] and can be expressed in a general way as:

H%ou(a> Te, ne) oc ne aa T? (6.2) where the values of a and (3 are dépendent of the value of the ratio a2^3/Te.

The relevant dust parameters affecting the cooling function are the grain size and the metallicity. Indeed, the smaller the grains and the higher the treme values roughly bracket the current theoretical and observational constraints on dust abundance in the ICM/IGM (i.e 10.~5 and 10~3 in terms of dust-to-gas mass ratio) [START_REF] Popescu | On the FIR émission from intracluster dust[END_REF][START_REF] Giard | The Infrared Luminosity of Galaxy Clusters[END_REF]. For low values of fd the impact of dust cooling is significantly reduced. For example, in the case of model D5, the contribution of dust to the total cooling rate is negligible at Z/Zq = 0.33 for ail températures. Therefore we do not expect to obtain significant différences between simulations with these two models.

6.2 Numerical Simulations

Simulation description

Simulations were carried out with the public code package Hydra, [START_REF] Couchman | Hydra: an Adaptive-Mesh Implémentation of P 3M-SPH[END_REF], an adaptive particle-particle/particle-mesh (AP3M), [START_REF] Couchman | Mesh-refined P3M -A fast adaptive N-body algorithm[END_REF] gravity solver with a formulation of smoothed particle hydrodynamics (SPH), see [START_REF] Thacker | Implementing Feedback in Simulations of Galaxy Formation: A Survey of Methods[END_REF], that con serves both entropy and energy. In simulations with cooling gas particles are allowed to cool using the method described in [START_REF] Thomas | Simulating the formation of a cluster of galaxies[END_REF] and the cooling rates presented in previous section. At a given time step, gas particles with overdensities (relative to the critical density) larger than 104, and températures below 1.2 x 104K are converted into collisionless baryonic matter and no longer participate in the gas dynamical processes. The gas metallicity is assumed to be a global quantity that evolves with time as Z = 0.3(t/to)^©, where ZQ is the solar metallicity and t/t0 is the âge of the uni verse in units of the current time.

Ail simulations were generated from the same initial conditions snapshot, at 2: = 49. The initial density field was constructed, using N = 4,096, 000 particles of baryonic and dark matter, perturbed from a regular grid of fixed comoving size L = 100/i-1Mpc. We assumed a A-CDM cosmology with parameters, fl -0.3, fl\ = 0.7, flb = 0.0486, erg = 0.9, h = 0.7. The am plitude of the matter power spectrum was normalized using <j8 = 0.9. The matter power spectrum transfer function was computed using the BBKS for mula [102], with a shape parameter T given by the formula in [103]. With this choice of parameters, the dark matter and baryon particle masses are

Catalogue construction

Cluster catalogues are generated from simulations using a modified version of the Sussex extraction software developed by Thomas and collaborators [START_REF] Springel | Genus statistics of the Virgo N-body simulations and the 1.2-Jy redshift survey[END_REF]. Briefly, the cluster identification process starts with the création of a minimal-spanning tree of dark matter particles which is then split into -1/3 clumps using a maximum linking length equal to 0.5 Ab ' times the mean inter-particle séparation. Here Ab the contrast predicted by the spherical collapse model of a virialized sphere [START_REF] Eke | The Evolution of X-Ray Clusters in a Low-Density Universe[END_REF]. A sphere is then grown around the densest dark matter particle in each clump until the enclosed mass vérifiés 47t Ma(< Ra) = -(6.5)

where A is a fixed overdensity contrast, pcv\t(z) = (8Hq/8ttG)E2(z) is the critical density and E(z) = H(z)/H0 = ^/(fl(l + z)3 + QA. Cluster properties are then computed in a sphere of radius i?200, ie with A = 200, for ail objects found with more than 500 particles of gas and dark matter. This means that our original catalogues are complété in mass down to 1.18x 1013/i-1Msun.

For the study presented in this paper we hâve trimmed our original catalogues to exclude galaxy groups with masses below Myim = 5x 10 uh~lMsun. In this way the less massive object considered in the analysis is resolved with a min imum of 2100 particles of both gas and dark mater. Our catalogues at z=0 hâve at least 60 clusters with masses above M\im. This number drops to about 20 clusters at z=l.

Cluster properties investigated here are the mass, M, mass-weighted tem pérature, Tmw and entropy, S (defined as S = kBT/n~2/3), integrated Compton parameter, Y (i.e roughly the SZ signal times the square of the angular diameter distance to the cluster), and core excised (50 h~1kpc) X-ray bolometric luminosity, Lx-These were computed in the catalogues according to their usual définitions, see [START_REF] Da Silva | Hydrodynamical simulations of the Sunyaev-Zel'dovich effect: cluster scaling relations and X-ray properties[END_REF]: where summations with the index i are over hot (T* > 105K) gas particles and the summation with the index k is over ail (baryon and dark matter) particles within i?2oo-Hot gas is assumed fully ionised. The quantities ra*, Ti, rii and pi are the mass, température, number density and mass density of gas particles, respectively. Aboi is the bolometric cooling fonction in [START_REF] Sutherland | Cooling functions for low-density astrophysical plasmas[END_REF] and Z is the gas metallicity. Other quantities are the Boltzmann constant, /cb, the Thomson cross-section, <tt, the électron mass at rest, rae, the speed of light c, the Hydrogen mass fraction, X = 0.76, the gas mean molecular weight, /i, and the Hydrogen atom mass, mu-

Scaling Relations

In this paper we investigate the scalings of mass-weighted température, Tmw, entropy, S, integrated Compton parameter, Y and core excised X-ray bolo metric luminosity, Lx, with mass, M. Taking into account Eq. (6.5) these cluster scaling relations can be expressed as: Tmw = A™ (M/M0)a™ (1 + zf™ E(zf/3, (6.11)

5 = ASm (M/M0)"yt (1 + , (6.12)
Y = Ayt (M/M0)"yu (1 + z)/3ym 5, (

Lx = Alm (M/M0)aLM (1 + z)^M E{z)v3 , 6.13)
where M0 = 1014h-1MQ and the powers of the E(z) give the predicted évo lution, extrapolated from the self-similar model, [START_REF] Kaiser | Evolution and clustering of rich clusters[END_REF], of the scalings in each case. The quantities, A, a, and /?, are the scalings normalisation at z = 0; the power on the independent variable; and the departures from the expected self similar évolution with redshift.

These scalings can be expressed in a condensate form,

V f(z) = 2/0(2) (x/x0)a , (6.15)
where y and x are cluster properties (e.g. Tmw, M), 2/0(2) = A{l + zf , (6.16) and f(z) is sonie fixed power of the cosmological factor E(z). To détermine A, a, and f3 for each scaling we use the method described in [START_REF] Da Silva | Hydrodynamical simulations of the Sunyaev-Zel'dovich effect: cluster scaling relations and X-ray properties[END_REF][START_REF] Aghanim | Cluster scaling relations from cosmological hydrodynamic simulations in dark energy dominated universe[END_REF]. To summarize, the method involves fitting the simulated cluster populations at each redshift with Eqs. (6.15) and (6.16) written in logarithmic form. First we fit the cluster distributions with a straight-line in logarithmic scale at ail redshifts. If the logarithmic slope a remains approximately constant (i.e.

shows no systematic variations) within the redshift range of interest, we then set û: as the best fit value at 2 = 0. Next, we repeat the fitting procedure with a fixed to a(z = 0) to détermine the scaling normalisation factors y0(z). This avoids unwanted corrélations between a and yo(z). The r.m.s. dispersion of the fit is also computed at each redshift according to the formula, ^log y1

N ^5^(log(y'i/y'W, i (6.17) where y' = yf (see Eq. (6.15)) and y\ are individual data points. Finally, we perform a linear fit of the normalisation factors with redshift in logarithmic scale, see Eq. (6.16), to détermine the parameters A and /?.

We note that above 2 = 1.5 the number of clusters in our catalogues decreases typically below 10, hence, we do not fit the scaling relations above this redshift value.

6.4 Results

Scaling relations at z = 0

In this section we présent cluster scaling relations obtained from simulations at redshift zéro. We investigate the four scalings presented in Section 6.3 for ail models under investigation. Generally, the inclusion of dust tends to increase température and entropy because the additional cooling increases the formation of collisionless (star forming) material leaving the remaining particles in the gas phase with higher mean températures and entropies. The decrease of Y and X-ray luminosities reflects the effect of lowering the hot gas fraction and density due to dust cooling. These effects dominate over the effect of increasing the température.

In fact a doser inspection of Fig. 6.3 indicates that différences for the same cluster in different models (note that ail simulations hâve the same initial conditions so a cluster-to-cluster comparison can be made), reflect the différences of intensity between cooling functions presented in Figure 6.1. For example, the différences between models D4 and C are clearly small as one would expect from the small différences between cooling functions displayed in the bottom panel of Figure 6.1. Another interesting example is that an increase of one order of magnitude in fd from D4 to D2 seems to cause a stronger impact in the properties of the most massive clusters than the différences arising from changing the dust grain sizes from D2 to Dl. Again this reflects the différences between cooling functions, which in the latter case are smaller at higher températures (see bottom panel of Figure 6.1).

A way of quantifying the effect of dust, is to look at the best fit slope, a, and normalisation, log A, parameters of these scalings which are presented in Table 6.2 for ail cooling models considered. We find that fitting parameters are quite similar for models C, D5, and D4 whereas models with high dust abundances provide the strongest variations of the fitting parameters, particularly for the normalisations. In several cases, différences are larger than the (statistical) best-fit errors, particularly for the Dl and D2 models. We also investigated scalings at redshift zéro for the A (adiabatic) model and found they were consistent with self-similar prédictions. As expected, the results obtained for the adiabatic and cooling models are in very good agreement with the findings of [START_REF] Da Silva | Hydrodynamical simulations of the Sunyaev-Zel'dovich effect: cluster scaling relations and X-ray properties[END_REF][START_REF] Aghanim | Cluster scaling relations from cosmological hydrodynamic simulations in dark energy dominated universe[END_REF] which use similar simulation parameters and cosmology.

Evolution of the scaling relations

We now turn to the discussion of the évolution of the cluster scaling laws in our simulations. Here we apply the fit to a power law procedure described in Section 6.3 to dérivé the logarithmic slope, /?, of our fitting functions, Eqs. (6.11)-(6.14). As mentioned earlier, this quantity measures évolution departures relative to the self-similar expectations for each scaling.

In Figs. 6.4, 6.5, 6.6, and 6.7 we plot the redshift dependence of the power log(1 + z) We end this section by noting that we find positive évolution (relative to the expected self-similar évolution, i.e. for a given x in Eq (6.15) the property yf is higher at higher redshifts) for the Y -M and Lx -M (models DI and D2 only) relations whereas the Tmw -M, and S -M relations show négative évolutions relative to the self-similar model. This is in line with the findings from simulations with radiative cooling of similar size and cosmology, (see [START_REF] Da Silva | Hydrodynamical simulations of the Sunyaev-Zel'dovich effect: cluster scaling relations and X-ray properties[END_REF][START_REF] Aghanim | Cluster scaling relations from cosmological hydrodynamic simulations in dark energy dominated universe[END_REF]).

6.5 discussion

Efficiency of the dust cooling

In agreement with the cooling functions of [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF], the dust cooling is most effective in the cluster température régime. The relative importance of the dust cooling with respect to the gas radiative cooling is strongly dépendent on the dust abundances and the intrinsic physical properties of the dust. This is clearly shown in our scaling relations results:

• the Tmw -M relation is almost unchanged when adding dust cooling to the radiative gas cooling (see Fig. 6.4). Our results show that the (mass weighted) temperature-mass relation within R200, is essentially driven by the gravitational heating of the gas (due to its infall 011 the cluster potential well), and that the physics of baryons (at least for the physics implemented in the simulations presented in this paper) play very little rôle in the outer parts of halos which dominate the estimation of the mass-weighted température and integrated mass. Since gas cooling tends to disturb the dark matter distribution at the centre of clusters in high resolution simulations [START_REF] Gnedin | Response of Dark Matter Halos to Condensation of Baryons: Cosmological Sim ulations and Improved Adiabatic Contraction Model[END_REF], the cooling by dust may amplify this effect, and thus modify scaling relations like the Tmw -M. In the case of observationally derived quantifies, scaling laws will be drawn from overall quantifies that will proceed from mixed-projected information over a wide range of radii. If a gradient exist in the dust effect towards the cluster centre, an "overall" température might bear the signature of well with observational constraints (mainly provided by X-ray observations of the Fe-K line) which indicate high metalicity values, Z ~0.3Z0, up to redshifts above 1.0 [START_REF] Cora | On the dynamical origin of the ICM metallicity évolution[END_REF][START_REF] Borgani | The Chemical Enrichment of the ICM from Hydrodynamical Simulations[END_REF]. This shows that, as for the stellar component which is already in place in galaxies when clusters form, the métal enrichment of the ICM/IGM has occured through the feedback of galaxy formation and évolution, and therefore it de facto strongly enriched the IGM/ICM bellow z = 1. It also might give hints that the high metallicity of clusters could be correlated to the dust enrichment of the IGM/ICM. Indeed, the amount of gaseous iron in galaxies such as the Milky Way is ~O.O1Z0. An early enrichment of dust in the IGM and/or the ICM, which once sputtered will provide metals, could explain part of the iron abundances found in the ICM at low redshifts. This hypothesis seems to be Consolidated by the few works that hâve investigated dust as a source for metals in the material stripped from galaxies via dynamical removal within already formed clusters [START_REF] Aguirre | Métal Enrichment of the Intergalactic Medium in Cos mological Simulations[END_REF] or via an early IGM enrichment at high redshift during the peak of star for mation around 2 = 3 [START_REF] Bianchi | Intergalactic medium métal enrichment through dust sputtering[END_REF]. The latter work stressed that only big grains (a > 0.1/im) can be transported on a few lOOkpc physical scale, however leading to a very inhomogenous spatial enrichment in metals once the dust grains are sputtered. For ail these reasons, by underestimating the metal licity at high redshifts, we might hâve underestimated the amount of dust injected in the ICM at high redshift, and thus the efhciency of dust cooling when integrated from early epoch down to redshift zéro.

Conclusion

As conclusion we can summarize our results as:

• The cooling due to dust is effective at the cluster régime and has a significant effect on the "baryon driven" statistical properties of cluster such as Lx -M, Y -M,5 -M scaling relations. As an added nongravitational cooling process dust changes the normalisation of these laws by a factor up to 27% for the Lx -M relation, and up to 10% for the Y -M and S -M relations. On the contrary, dust has almost no effect on a "dark matter driven" scaling relation such as the Tmw -M relation.

• The inclusion of cooling by dust does not change significantly the slopes of the cluster scaling laws investigated in this paper. They compare with the results obtained in the radiative cooling simulation model.

• Through the implémentation of our different dust models, we hâve demonstrated that the dust cooling effect at the scale of clusters dé pends strongly on the dust abundance in the ICM, but also on a similar proportion on the size distribution of dust grains. Therefore the dust efficiency is strongly dépendent on the nature of the stripped and ejected galactic material, as well as the history of these injection and destruc tion processes along the cluster history. Indeed the early enrichment of dust might provide an already modified thermodynamical setup for the "to-be-accreted" gas at lower redshifts.

The setup of our simulations and the limitation of our dust implémen tation can be considered at a "zéro order" test with which we demonstrated the active effect of dust on structure formation and especially at the cluster scale. In order to go one step further, a perspective of this work will be needed to couple the radiative cooling function of dust with a physical and dynamical implémentation of the création and destruction processes of dust in the IGM/ICM.

Figure 1 . 1 :

 11 Figure 1.1: Events in the history of the Universe as it evolved frorn the Big Bang (http://www.jwst. nasa.gov/firstlight. html).

  Photon pressure resists compression of the fluid due to gravitational infall and sets up acoustic oscillations. During this epoch the température falls low enough to permit électrons and protons to recombine. The photon Compton cross-section with électrons decreases rapidly. At redshift 2 ~1100, recom bination produces neutral hydrogen and the photons last scatter. Régions of compression and raréfaction at this epoch represent hot and cold spots respectively. Photons also suffer gravitational redshifts from climbing out of the potentials on the last scattering surface. The résultant fluctuations appear to the observer today as anisotropies 011 the sky (Last Scattering Sur face LSS). This epoch corresponds to a température of 3000K which means,

Multipole Moments • /Figure 1 . 3 :

 13 Figure 1.3: Power spectra as a function of I for s cale-invariant models, with various values given to the cosmological constant = 0;0.4), Hubble con stant (h = 0.5 and 0.65,) [11/.

Figure 1 . 4 :

 14 Figure 1.4: Dipole maps from FIRAS

3 )

 3 measurements we find Vlg -627 ± 22 toward l = 276 ± 3 and b = 30 ± 3 degrees. The most probable cause for this motion is gravitational instability. An open question is over which distance do density fluctuations contribute to the gravitational field that defines the Local Group motion. This seems to be around 100-200Mpc, as suggested by optical and X-ray studies.The measurement of the Dipole Anisotropy is a key point for CMB obser vations: this signal could be used as the best photometric calibrator for extended sources in the microwave domain([START_REF] Chluba | Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments[END_REF]). In fact, if it is possible to measure very accurately the CMB Dipole in the whole sky (for instance, over a period of a year), we can use that part of the anisotropy associated with the orbital motion of the Earth around the Sun which is the best known component of the Dipole signal. At the same time we can improve the dé termination of the peculiar motion of the solar System using the Plankian nature of the CMB ([13]). 1.1.2 The Polarisation of CMB That the CMB anisotropies are polarised is a conséquence of the gravita tional instability paradigm. Under this paradigm, the small fluctuations of the early Universe grow into the large scale structure we can see today. If the 8This is the only term taken into account to produce a fluctuation of the order of 3.3mK

Figure 1 . 5 :

 15 Figure 1.5: Thompson Scattering : ifthe incoming radiation has a quadrupole component the outgoing radiation has a linear polarisation [14/•

Figure 1 . 6 :

 16 Figure 1.6: Power spectra for scalar perturbations only (Température TT, E-modes EE and corrélation spectra TE): the polarisation power spectrum is about 90% smaller then the température power spectrum at high l [lf).

Figure 1 . 7 :in GHz 100 Figure 1 . 8 :

 1710018 Figure 1.7: Power spectra for the case of pseudo-scalar perturbations only lui

1 .

 1 Depending from the observed région on the sky, Synchrotron émission can be polarised from 10% to 75%. The r.m.s. fluctuation of Syn chrotron émission corresponds to a change in température of about 50[iK. Synchrotron émission and its polarisation is the dominant source of foregrounds at frequencies lower than 100GHz (see Fig 1.10).

Figure 1 .

 1 Figure 1.10: r.m.s. fluctuation spectra (thermodynamic température units) of foreground components at 1 degree resolution (Davies et al 2006).

Figure 1 . 11 :

 111 Figure 1.11: Accurately measuring the C(l) curve should be achieved in the first decade of the 21st century, as shown by the 3-years WMA P results (Spergel et al 2007) (lower left), the ACBAR measurements (Reichardt et al 2008) from the South Pôle (upper left) and a simulation of the Planck data (lower right), with a launch expected end 2008.

Figure 1 . 16 :Figure 1 . 17 :

 116117 Figure 1.16: The LFI radiometer array assembly (left) with details of the ail units (right): the HFI is inserted into the focal plane unit of LFI.

Figure 1 . 18 :

 118 Figure 1.18: Straylight incoming in focal plane unit: on the left a geometrical study from the hom to the sky. This study shows the possibility for straylights to corne into the horns from 4 different directions. In the centre and on the right simulations and measurements of signal from straylight respectively. In these plots the level of saturation corresponds to -45dB in gain.

Figure 1 . 19 :

 119 Figure 1.19: Focal Plane Units (FP U) of the HFI instrument. The position of the Homs is optimazed taking into account the distortion of FPU due to the design of the Telescope. The size of the HFI FPU corresponds to 4 degrees in the sky

Figure 2 . 1 :Figure 2 . 2

 2122 Figure 2.1: A general view of Planck HFI instrument.

Figure 2 . 2 :

 22 Figure 2.2: Diagram of HFI Hom Position and PSB orientation on the RDP (Reference Detector Plane).

Figure 2 . 3 :Figure 2 . 4 :

 2324 Figure 2.3: On the top: optic of one channel of the FPU. On the bottom: example of lf3 HFI back-to-back hom with a top view of the front hom in the back-to-back hom.

The

  Spectral and geometrical properties of the horns hâve been measured individually. A typical measurement of beam with the comparison with the model is presented on Fig2.4.

Figure 2 . 5 :Figure 2 . 6 :

 2526 Figure 2.5: Characterisation of the stack of mesh filters in fK and 1.6K stage

Figure 2 . 7 :

 27 Figure 2.7: Domain of interest of bolometers for astrophysical observations.

Figure 2 . 8 :

 28 Figure 2.8: Image of a typical HFI spiderweb and a PSB (polarised sensitive bolometer)

  The capacitance is polarized by a triangular wave voltage which produces a square wave current into the capacitor. A second square bias voltage which produces transient currents is added in order to correct for the capacitive of the cables (stray capacitance). A third square voltage (Vbai) in opposition of phase is added to Vboiometer to balance the signal, that is to keep its amplitude well inside the range accepted by the amplification and démodulation electronics. The amplitude of these three voltages are controlled by three 12 bit DACs (Digital to Analogical Converter) with a reference voltage of 2.5 Volts. The amplitude of square balance and transient voltage and the slope of triangular bias voltage are (Montier private communications): represent the telecomand expressed in digit controlled by a software, Vrej is the reference voltage, tmod is the time period, ,4095 is the range in digit of the DAC and:

Figure 2 . 9 :

 29 Figure 2.9: Scheme of the HFI AC bias (sum of two signais) with a capacitive load and a stray capacitance in parallel with the detector

  6) and filtered by a band pass filter (5-600 HZ). Finally the signal is converted into digital signal, called Raw-Signal S by a 16 bit ADC. This signal is expressed in ADU, from 1 to 65535, and centered around 32768. The scientific signal (DSN) is given as the sum of the raw-signal S on each half-periods: DSN+ = ]TS{i) + DSN~=Y,SÜ) with DSN+ the scientific signal on the first half-period and DSN~on the second half-period. The computation of DSN dépens on 2 parameters: Nsampie = number of points per half-period (Nsampie= 36, 40 and 45).

Figure 2 Figure 2 . 11 :

 2211 Figure 2.10: HFI Thermal Path Summary

Figure 2 . 12 :

 212 Figure 2.12: The dilution cooler

The 3 H

 3 e 4He mixture delivers its full cooling power to the incoming fluids along a heat exchanger wound-up in a spiral along the conical support. The base of this support is cooled at 1.4K by Joule-Thomson expansion of the mixture. The duration of life of this open loop System limits the duration of the whole mission. The nominal spécifications indicate at minimun a life of 14 months (2 surveys) for the dilution System.2.5.2 4K Cooler A 4K stage is required for cooling the dilution refrigerator and the focal plane unit. Fig 2.14 shows a schematic plot of the major components of the 4K System. This System has been developed at the Rutherford Appleton Laboratory ([45]) and constructed by Astrium. This cooler uses a mechanical compressor to realize a Joule-Thompson cycle of 4 He gas which is able to cool the cryostat down to a température of 4K. The Hélium gas is pre-cooled at 18K by the LVHX1 stage of the Sorption cooler.

•Figure 2 . 14 :

 214 Figure 2.14: Schematic view of the fK cooler System.

Figure 2 . 15 :

 215 Figure 2.15: Logic of formation of the signal in HFI.

  permits to predict the telecommand to set the working point of PID. It also permits to predict fluctuations of température of different cryogénie stages and their propagation to eliminate parasitical effects (like for instance the effect of the température of the sorption cooler on the LFI and HFI detectors). Simulation of the Optical Signal (SOS): It is the model wich permits to calculate the integrated optical power incident on the bolometer. This model has been developed at LERMA using models and results from PFM calibra tions. I report details in the next section. Response of the instrument: Different models hâve been developed in order to simulate the response of the instrument. An analytical model has been developed at LERMA in order to check rapidly different static behaviours of the HFI. The time response of the bolometer to a varying optical power is simulated by two similar models: the SEB IDL Models (developed by CESR and LERMA) and the SimHFI labview model (developed by Rashmi Sudiwala from University of Cardiff): Both models solve the differential thermal and electronics équations of bolometers and include a functional description of the whole readout System (see section 3.2.11).

Equation 3 .Figure 3 . 1 :

 331 Figure 3.1: Outputs of SOS model: a Jupiter scan is calculated for typical deterctors of Planck HFI (100GHz, lf3GHz, 217GHz, 353GHz, 54 5GHz, 857GHz) with a nominal background

Figure 3 . 2 :

 32 Figure 3.2: Schematic diagrams of a bolometric detector

Figure 3 . 4 :

 34 Figure 3.3: DC bias circuit

Figure 3 . 5 :

 35 Figure 3.5: Responsivity versus bias ouvrent for DC (blue curve) and AC sine (red courve) bias currents. For A C model we consider a sine polarisation with a stray capacitance ofCp = 150pF and plot the responsivity versus the r.m.s. value of the bias ouvrent . The bias corresponding to the maximum of the Responsivity are different and equal to = 0.12nA and l£fft = 0.22nA

Figure 3 . 6 :Figure 3 . 7 :Figure 3 . 8 : 32 )Figure 3 . 9 :Figure 3 . 10 :Figure 3 . 11 :Figure 3 . 12 :

 3637383239310311312 Figure 3.6: NEP of the 4 considered sources of noise for a PSBIOOGHz bolometer with a sine AC electronic modulation: NEP Johnson (dashed black curve), Pre-amplificator NEP (dashed brown curve), Photon NEP (blue dashdot curve) and Phonon NEP (red dash-dot-dot curve)

37 )

 37 2n + 1 )ut)The r.m.s. Vf, is equal to:If the température of the bolometer is given and the optical power is constant we can calculate the r.m.s.Vf, as we did for the sine bias case (Eq3.28 and Eq3.27). So we hâve:The r.m.s. Voltage is equal to: n U = a-Ev/2(2n + 1) (3.39) 71=0 And the r.m.s. bias current passing through the bolometer is: s dérivé the Responsivity. As for the sine AC case, so we can calculate the Rb\, Wtot\, the TF 1 starting by a small step in température due to an incoming optical signal.

Figure 3 . 13 :Figure 3 . 14 :Figure 3 . 15 :Figure 3 . 16 :

 313314315316 Figure 3.13: Total NEP for three different HFI bolometers at 100GHz (dashed line), 353GHz (dash-dot line) and 857GHz (dash-dot-dot line) for an AC square modulation

  the bolometers is set at lOOmK. With a linear approximation we find that for a 100GHz bolometer, a change of the plate température of lmK gives a change in NEP of 0.8 %. This means a change of about 6 days in the duration of the mission is needed to reach the same sensitivity than the one we had at lOOmK. A longer observational time has the advantage of improving the redundancy of the data. Both criteria (the final S/N and the redundancy) seem to favour the Fmin2 option (defined as the Hélium lowest flow option of the dilution).

Figure 3 . 17 :Figure 3 . 18 :

 317318 Figure 3.17: Responsivity of the three sample bolometers in case of an AC sine model (blue curves) and a square AC model (red curves)

Figure 3 . 19 :

 319 Figure 3.19: Principle of the readout electronics. It consists of a signal generator and a measurement section delivering digital data.

92 dataFigure 3 . 20 : 4 Ground-

 923204 Figure 3.20: Comparison of the measured raw signais with SEB prédictions for Belt 0 Channel 3 [56].

Figure 4 . 1 :

 41 Figure 4.1: On the left: view of the Saturne cryostat in the IAS clean room. On the right: schematic view of the optical setup

(figure 4 . 1

 41 on the right) taking into account the constraints of the cryostat. It consists on a 2K plate which the HFI FPU and several optical components are mounted.

Backgrounds

Figure 4 . 2 :

 42 Figure 4.2: Range of backgrounds: incident power on the HFI bolometers for max, high, central, low and min backgorunds.

Table 4 . 1 :

 41 Variation of telescope parameters to compute three different back grounds After the electrical and optical tests performed at JPL and Cardiff, many parameters hâve been tested at first order (total optical efficiency, spectral transmission etc.). The telescope is the most uncertain and variable object in the optical chain, because its emissivity is unknown. It dépends mainly on dust deposited during launch. It will also change during flight (micrometeorites and aging of coating). In addition its température can change with of the distance to sun and solar activity. For these reasons let us neglect the uncertainties on backgrounds coming from 4K and 1.6K cryogénie stages, and define three backgrounds (low, cen tral, high) by changing the parameters (température and emissivity) of the telecope. In this way it is reasonably sure that ail possible backgrounds are covered in flight (Tab 4.1).

Figure 4 . 3 :

 43 Figure 4.3: Bolometer PSBIOOGHz 36J12. Time Constant empirical model (continuons line) and experimental points from JPL versus bias current.

(4. 3 )Figure 4 . 4 :

 344 Figure 4.4: On the left the Signal to noise ratio (for a source of lmK RJ at a bolometer température of lOOmK) versus bias current is plotted for the bolometer PSB 100GHz (position in the focal plane 3A): we présent the in tersection between the three different background and we take account of the dépendance of the optical modulation frequencies. The best bias current for this bolometer is 0.22 nA. On the right the percentual loss of energy versus the optical modulation frequency is plotted.

Figure 4 . 5 :

 45 Figure 4.5: Measured and recommended bias ouvrent (normalized by the preliminary setting) for the 52 bolometers of HFI

Figure 4 . 6 :

 46 Figure 4.6: Response to the CSM fibre source versus Sphase. Some channels give neaningless results due to incorrect Tbias and Vbal settings.

Figure 4 . 7 :Figure 4 . 8 :Figure 4 . 9 :

 474849 Figure 4.7: Définition of F2 parameter: it represents the amplitude of the square signal calculated at the end of each half period

to 100 .

 100 21Hz according to four different steps fig(4.8) (86.09Hz, 87, 68Hz, 90, 19Hz, 100.21Hz). I fit results with a slope as: /) -fli + «2 • / (4.6)

Figure 4 . 10 :

 410 Figure 4.10: EFF sequence during 30th of june for one bolometer each frequency

Figure 4 . 11 :

 411 Figure 4.11: Detailed plot for 100GHz bolometer bc=00 of EFF sequence

Figure 4 . 12 :Figure 4 . 13 :Figure 4 . 14 :

 412413414 Figure 4.12: Time évolution of température of thelOOmK stage from the thermometer bc-90 during the first day of the EFF sequence

Figure 4 . 15 :

 415 Figure 4.15: Results fronn EFF1: emissivity of CSl source measured by ail 52 HFI bolometers. During this sequence the autobalance procedure for four detectors did not work.

Figure 4 . 16 :

 416 Figure 4.16: EFF2-1.6K sequence (one bolometer of each kind) and Detailed plot for 100GHz bc=00

Figure 4 . 17 :

 417 Figure 4.17: EFF2-fK sequence (one bolometer of each kind) and Detailed plot for 100GHz bc=00

Figure 4 . 18 :Figure 4 . 19 :

 418419 Figure 4.18: Trend between signal and température of 2K platform. With this relection we calculate the (3 parameter

Figure 4 . 20 :

 420 Figure 4.20: EFF3-1 efficiency sequence (one bolometer of each kind) and Detailed plot for 100GHz bc-OO

Figure 4 . 21 :

 421 Figure 4.21: Results from EFF3-1 sequence: total optical efficiency calculed with a nominal top-hat band.A comparison with Cardiff Results (black points) is performed.

4. 4 . 7 HFI

 47 Photometric Equation implemented in the IMO The total optical efficiency as derived in section 4.4.6, represents the physical Total efficiency of the instrument if we use top-hat nominal bands. The spec tral bands lias been derived with interferometric measurements during PFM calibration[START_REF] Savini | HFI Spectral Calibration report of the IAS measurements[END_REF] as a product of the real shape of the spectral bands and the beam throughput of the instrument. Ail the beams hâve been normalised to one at their maximum point. In this case, according to the general procedure presented in the section 4.4.2, we hâve: beam throughput at central frequency of channel x{v) is the spectral transmission of the optical chain (normalised to 1 on the pick).PAReff parameter does not represent the physical total efficiency of the instrument but it is a normalisation parameter that takes in account the integrated power in the spectral bands. In Fig 4.22 results of this analysis are presented.

  the normalized spectral transimission BBu{T,v) is the blackbody radiation function BBy{Tfu^]y) is the RJ blackbody function (BBRJ = ^ÿ-kTRj) AÏÏ, is the beam throughput TRj is the température of the RJ source coupx is the product between emissivity and transmission of the considered cryogénie stage.

Figure 4 . 23 :

 423 Figure 4.23: Study of the degree of polarised systematics in the optical chain.

125 4 . 5 Steady

 45 State Response and Non-Linearities

UFigure 4 . 24 :

 424 Figure 4.24: EFF3-2 sequence (one bolometer for each freq) and detailed plot for 100 GHz bc=00. The change of background is produced by CS1 source while the modulated signal is produced by the CSM carbon fiber source

  of the instrument derived with this procedure is presented in Fig(4.25).

Figure 4 . 25 : 2 Wtot

 4252 Figure 4.25: Réponse function of the instrument for one bolometer of each kind. In the range of background examined the saturation occurs only in the 857GHz channels.

Figure 4 . 26 :

 426 Figure 4.26: Déviation from a linear response. The linearity ofthe bolometers in this range of background (except for 851GHz bolometers is that saturate less than 1%

Figure 4 . 27 :

 427 Figure 4.27: Extrapolation of the response up to saturation. The range covered by Satum is overplotted.

4. 6 . 1

 61 Measurements of the Transfer Function Three different sequences has been performed to measure the time response of HFI during PFM ground calibration: TauELS (LERMA in charge) intends to measure the time response from

Figure 4 . 28 :

 428 Figure 4.28: Results of the analysis data from TauELS: the vertical dashed line is represents the modulation frequency of the measurement. Data with an mechanical frequency of the chopper faster than Fmo(i are aliased belowFmod On the left results with aliasing. On the right results with a de-aliasing procedure trasposing the aliased results at frequencies above Fm0(f[START_REF] Coulais | HFI PFM Ground Tau ELS Measurements[END_REF]

Figure 4 . 29 :

 429 Figure 4.29: Experimental data for a 353GHz bolometer. It cannot be properly fitted by a first order low pass filter expected from classical models.

3

  free parameters: time constant of the low-pass filter and the parameter coming from the rejection and résonant filters fc and Q. Results of the fit are presented in Fig 4.30.

Figure 4 . 30 :

 430 Figure 4.30: The measures (points) and the semi-empirical model (red curves) for six different channels.

Figure 4 . 31 : 5 Figure 4 . 32 :

 4315432 Figure 4.31: On the left: response of bolometers 353-fb and 143-lb to the carbon fibre nearly square wave source (Black curves). The red curves represent the tentative to fit data with a first order model in the time domaine. On the right: Amplitude of the transfer function from Tau-ELS for the bolometer 353 -4b. The semi-empirical model does not fit with data because of an evidence of a low frequency excess response.

Figure 4 . 33 :

 433 Figure 4.33: OverView of the main periods before routine phase. The timeline is given in operational days (ODs) since launch. Both Commissioning and CPV activities take place during the active cooldown period. CPV proper starts around OD50.

1 .

 1 6K. With the same data taken from this test we will be able to cover a small range of the static response curve of the HFI instrument. It allows us to reconstruct the whole static response function by merging data with the PFM ground calibrations. This is a good health test for HFI (2-level), indeed except for an évident problem in the instrument, expected results has to be a confirmation of PFM calibration. The test will be done with a strategy as close as possible to PFM tests. The dipole will be the reference source during the sequences. Let's give a simplistic estimation of the signal to noise ratio not taking into account ail the foregrounds in its estimation.The dipole signal produces a sinusoidal fluctuation of the CMB of the order of 7 mK peak-peak. With a RMS estimation we can find a fluctuation of 3.5mK peak-peak.The NE AT (Noise Equivalent Température Fluctuation) for a 100GHz HFI channel results from PFM calibration: NEAT ~60fiK • s05 (4.21)The signal to noise ratio for an intégration of 1 hour results:

  accurate beam knowledge is essential for science objectives of Planck because it détermines the knowledge of the transfer function of the experiment in the domain of angular frequencies. The use of the planets for this goal is the most accurate way to measure the main beam.

Figure 5 . 1 :

 51 Figure 5.1: SNR for a circle in case of Mars for a typical sélection of HFI

3 :

 3 y) = nmodesX20PAREFFc) an / x{y)BBi(v, Tb)dv (5.1) ' tBeam •'O where nlmode correspond to the number of the modes of the horn for the i-th channel; chiv is the optical efficiency of the instrument and PAREFF (see table 4.3) is the normalisation factor associated to x(y) for each chan nel measured from Calibration campaign. The factor is the Dilution Beam Factor of the planet in the beam of HFI. The SNR per circle for one sample is: the total noise équivalent power of the channel (from Table2.4) and Fmod is the modulation frequency of the REU, i.e. the effec tive band pass of the post-detection signal. For these simulations the Fmod has been set at 100Hz Now, the SNR per ring results from intégration in one hour of the SNR per ring as: SNRr = SNRC • VEÔ (5.3) In the following are presented the nominal characteristic of the instrument and the évaluation of the SNR per circle and per ring for each planet visible from the satellite (except for Pluto), for each frequency. SNR per Ring and per Circle at the central point of the beam (in which the optical efficiency is assumed to be 0.3) for ail the HFI channels.

5. 3 . 1

 31 Discussion on SNR ResultsFull beam reconstruction requires the observation of both a bright planet (Mars, Jupiter, Satura) and of a fainter one (Uranus, Neptune) to check for non-linear model of the bolometers.

Figure 5 . 2 :

 52 Figure 5.2: Sampling in the time domain produces in the frequency domain the co-addition of the initial spectrum shifted by multiples of the sampling

Figure 5 . 3 :Figure 5 . 4 :

 5354 Figure 5.3: Six HFI beams (one per frequency), their Fourier transform (mod ule) and the aliased amplitude vs. the sampling interval (see next figure for details).

Figure 5 . 5 :

 55 Figure 5.5: Relative amplitude of aliased signal. The 2' and 1,25' sampling internais represent the nominal pointing step and the staggering interval between homs at a same frequency.

Figure 5 . 6 :

 56 Figure 5.6: Aliased amplitudes for a source with a spectrum inspired from that of the interstellar medium.

Tab. 6 .

 6 1 lists code names and simulation details of ail runs used in this work. In case of models DI to D5, simulation cooling rates are given by the added effect of cooling due to dust and radiative gas cooling. Total cooling functions are displayed (non-coloured lines) in the bottom panel of Fig 6.1 for each of these models at ZjZ0 = 0.33. As the Figure indicates, the effect of dust cooling is stronger for models with higher dust-to-metal mass abundance parameters, /<*, and for smaller grain sizes (model Dl).

Figure 6 . 2 :

 62 Figure 6.2: Density maps (on top) of the same cluster in the cooling (on the left) and cooling+dust (on the right) simulations. Emission weighted température maps (in the bottom) of the same cluster in the cooling (on the left) and cooling+dust (on the right) simulations.

Figure 6 .

 6 Figure 6.3 shows the Tmw -M (top left panel), 5mw-M, (top right panel), Y -M (bottom left panel), and Lx -M (bottom right panel) scalings, with ail quantities computed within AE2oo-In each case, the main plot shows the cluster distributions for the C (triangles), D4 (diamonds), D2 (filled circles) and DI (crosses) simulations, whereas the embedded plot présents the power law best fit lines (solid, triple dot-dashed, dashed and dot-dashed for C, D4, D2 and DI models, respectively) obtained in each case, colour coded in the sanie way as the cluster distributions. Here we hâve chosen to display dust models that allow us to assess the effect of dust parameters individually. For example, the dust models in runs D4 and D2 only differ by the dust-to-metal mass ratio parameter, whereas models D2 and DI hâve different grain sizes but the same /^. The shaded gray areas in the embedded plots give the r.m.s. dispersion of the fit for cooling (C) model. The dispersions obtained for the other models hâve similar amplitudes to the C case. The scalings of entropy and X-ray luminosity with mass show larger dispersions because they are more sensitive to the gas physical properties (density and température) in the inner parts of clusters than the mass-weighted température and Y versus mass relations which are tightly correlated with mass. An inspection of Fig. 6.3 allows us to conclude that the cluster scalings laws studied here are sensitive to the underlaying dust model, and in particular to models where the dust cooling is stronger (model DI and D2).

Figure 6 . 3 :

 63 Figure 6.3: Cluster scalings at redshift zéro for the Tmw -M (top left panel), S -M, (top right panel), Y -M (bottom left panel), and Lx -M (bottom right panel). Displayed quantities are computed within i?200? the radius where the mean cluster density is 200 times larger than the critical density. Blue colour and triangles stand for the cooling (C) run, cyan and diamonds are for the D4 run, yellow and filled circles are for clusters in the D2 run, and red and crosses are for the DI run. The lines in the embedded plots are the best-fit lines to the cluster distributions and the shaded areas are the fit r.m.s. dispersions for the C model, for each scaling.

Figure 6 . 4 :

 64 Figure 6.4: Evolution of the slope (top panel), normalisation (middle panel), and normalisation best fit lines (bottom panel) of the Tmw -M cluster scaling relation for the C (triangles, solid line), D4 (diamonds, triple-dotdashed line), D3 (squares, short-dashed line), D2 (circles, dashed line) and DI (crosses, dot-dashed line) simulation models. Colour bands are best fit errors to the cluster distributions at each redshift. The shaded area in the bottom panel is the rms dispersion of the normalisation fit for the cooling model.

Figure 6 . 5 :

 65 Figure 6.5: Evolution of the slope (top panel), normalisation (middle panel), and normalisation best fit Unes (bottom panel) of the S -M cluster scaling relation for the C, D4, D3, D2, DI simulation models. Symbols, lines and colours are the same as in Fig 6.4.

Figure 6 . 6 :

 66 Figure 6.6: Evolution of the slope (top panel), normalisation (middle panel), and normalisation best fit Unes (bottom panel) of the Y -M cluster scaling relation for the C, D4, D3, D2, DI simulation models. Symbols, lines and colours are the same as in Fig 6.4.

Figure 6 . 7 :

 67 Figure 6.7: Evolution of the slope (top panel), normalisation (middle panel), and normalisation best fit Unes (bottom panel) of the Lx -M cluster scaling relation for the C, D4, D3, D2, DI simulation models. Symbols, lines and colours are the same as in Fig 6.4.

  stolen a bit of his nose. I thank Jean-Michel for his skills in exhorting and inciting me when facing scientihc challenges. Fm really glad to hâve met Jean-Michel in my life.I would like to thank my colleague Alain Coulais who kept an eye on the progress of my work and always was available when I needed his advises.Thank you to Etienne Pointecouteau, Ludovic Montier and Antonio da Silva who helped me to study the dust effect in the ICM and in general for their liking. I would like also to thank the other members of HFI core team who helped me to build a researcher profile.Thank you Laurent, Eric and Annick of LERMA for teaching me this "strange" language which is French tongue and to be always available when needed. I am glad to be part of the 8th floor gang.Energy and vitality during the past years was provided externally thanks to my friends in the cité universitaire where maybe I hâve found love (....who knows?). Thank you ail Guys! Facing problems with optimism inspired me to better understand my origins and the world. Thank you dad. You could not even realize how much I hâve learned from you. Mamma, you held me in your lap and then you kept my feet on the ground. I hâve always been crazy of you!

  will detail the Planck optical System in the chapter 2 on section 2.1.

	Sorption Cooler
	JPL I The sorption cooler provides the cooling of LFI instrument with the control-
	l*>K ling of the interface HFI-LFI flange température and the cooling of the HFI /
	Instrument
	Interfaces 18K stage on which the Hélium of the 4K cooler is pre-cooled.
	The working principle of this absorption compressor is based on the prop-/ erties of hydride LaAT4.78SVio.22-This hydride can absorb a large quantity
	.11 hxpanskm of Hydrogen molécules when it has a low pressure and température thanks
	Valve to the high ratio between surface and volume of the solid. The compressor
	injects hot gas with constant pressure in the Joule-Thompson circuit. This
	Hydrogen gas is pre-cooled by three V-grooves of the satellite. Then the gas
	expands thanks to a Joule-Thompson expansion10 in a valve mounted on the
	top of the two warm excenge pipes LVHX1 and LVHX2. Finally the fluid
	Hydrogen at a température of 18K and 20K respectively circulâtes into two
	exchangers before coming back to a cold tank of compressor to restart the
	whole cycle (see Fig 1.20).
	To make the Sorption Cooler working the satellite has to produce a elec-
	trical power of 300W with a period of 940sec (Nominal values derived from
	PFM Calibration campaign). The Température of LVHX1 is critical for the
	whole HFI cryogénie chain. So it is necessary to check the fluctuation of
	this plate. During the test in CSL a r.m.s. fluctuation of 420mK has been
	measured. This is acceptable for HFI. The duration of life is fixed by the
	wear and tear of the Hydride chamber. With the nominal spécification of
	Sorption cooler (power and period) the duration of life of the whole cryogénie
	chain is not limited by the sorption cooler.
	The Service Module houses consists of warm electronics , the ancillary equip-
	ment of the spacecraft (Télécommunications units, solar panels and batteries,
	attitude control, propellant tanks etc...). It is an octagonal box built around
	a conical tube which supports the satellite loads. The propellant tanks and
	the tanks containing cryogénie fluids for HFI coolers are located inside the
	tube. Most other units are located outside the tube, mounted on side panels
	of the octagonal box, allowing them to radiate to space. Figure 1.20: Design of Sorption Cooler by JPL

Table 2 .

 2 .4 measurements of the NEP are presented for typical channels of HFI. The table shows that the nominal requirements for sensitivity

	are reached.
	Bolo	Ibias	NEPtot	N EPphot	N EPph(m	N EPjohn	NEPfet	N EPcomp
		[nA]	[attoW att / VH z]
	PSB100	0.262	14.4	10.6	4.9	6.6	2.9	4.3
	PSB143	0.293	17.5	13.7	5.0	7.5	3.1	5.3
	SWB143	0.343	19.5	13.6	5.7	10.3	4.5	5.9
	PSB217	0.283	18.4	14.6	5.1	7.6	3.3	5.6
	SWB217	0.374	26.3	21.3	7.2	10.3	3.5	7.9
	PSB353	0.277	25.3	21.9	5.3	8.0	2.8	7.6
	SWB353	0.337	28.7	25.3	4.5	8.7	3.7	8.7
	SWB545	0.666	47.9	38.4	14.3	18.6	7.2	14.4
	SWB857	0.690	78.4	69.8	14.6	20.5	7.8	23.6

1: Principal contributions of the NEP (photon, phonon, johnson, Jfet and compression) of typical HFI bolometers for nominal bias current. Total NEP is also presented. ((fO], (fl])

Table 4 . 2

 42

			Best Bias (Sim)	Best «S'p/iase	ai	«2
			[nA] (at 100 mK)	[digit]	[ADU/dig]	[ADU/(dig /)]
	0	0,271	0.25	10	271.060	0.402457
	0	0,306	0.24	10	269.113	0.414250
	0	0,297	0.27	9	270.562	0.404969
	0	0,288	0.28	9	268.908	0.415777
	0	0,397	0.43	8	268.976	0.416219
	0	0,346	0.40	7	271.662	0.399113
	1	0,356	0.31	10	271.125	0.401986
	1	0,329	0.33	8	269.763	0.408334
	1	0,292	0.31	9	267.794	0.422606
	1	0,342	0.48	7	268.864	0.413432
	1	0,649	0.78	8	267.830	0.424019
	1	-	-	-	269.089	0.408524
	2	0,270	0.27	9	270.808	0.405827
	2	0,297	0.28	9	270.448	0.404649
	2	0,417	0.50	9	271.863	0.383817
	2	0,306	0.30	9	271.884	0.400512
	2	0,298	0.33	8	270.602	0.405490
	2	0,761	0.76	8	270.219	0.406297
	3	0,287	0.27	9	269.574	0.411966
	3	0,298	0.28	9	271.018	0.401803
	3	0,292	0.28	9	268.932	0.416161
	3	0,295	0.34	8	270.314	0.409169
	3	0,664	0.89	7	269.559	0.412629
	3	0,682	0.65	9	270.305	0.406522
	4	0,279	0.22	9	270.137	0.404928
	4	0,251	0.25	9	270.691	0.403013
	4	0,370	0.34	8	271.111	0.398881
	4	0,295	0.25	9	270.969	0.399043
	4	0,282	0.29	8	271.596	0.401397
	4	0,394	0.37	9	269.477	0.415201
	5	0,314	0.37	9	267.270	0.441982
	5	0,297	0.36	6	268.557	0.425540
	5	0,407	0.35	9	269.447	0.415496
	5	0,297	0.31	8	270.379	0.405400
	5	0,284	0.32	8	269.552	0.409669
	5	0,645	0.69	8	270.311	0.403043
	6	0,363	0.32	10	268.989	0.415372
	6	0,283	0.24	10	269.996	0.411739
	6	0,280	0.17	10	267.032	0.443202
	6	0,348	0.35	9	269.786	0.414935
	6		0.32	8	269.148	0.418552
	6	0,730	0.75	8	270.805	0.404634
	7	0,356	0.30	10	267.084	0.443582
	7	0,291	0.33	8	266.100	0.445994
	7	0,289	0.29	9	268.442	0.424953
	7	0,659	0.80	8	273.415	0.375547
	7	0,647	0.56	6	268.071	0.428543
	7	-	-	-	266.321	0.445826
	8	0,266	0.21	9	265.933	0.449745
	8	0,276	0.22	10	270.222	0.405870
	8	0,283	0.27	9	269.989	0.407632
	8	0,279	0.29	9	269.067	0.415956
	8	0,381	0.45	8	269.875	0.409462
	8	0,389	0.46	8	268.725	0.418329

: Summari zing table: Best bias measured and simulated Best Sphase and linear fit coefficients for F2 calculation are presented.

Table 4 .

 4 3: Summarizing table: Bolo Identification and optical parameters are presented. The parameter PAReff is calculated with real spectral bands.

	[%J	TTot[%]	P AReff[%\

Optical Efficiency

Figure 4.22: Normalisation parameter calculed with the real spectral band. A comparison with Cardiff results is performed (Black points)

Table 4 .

 4 5: Typical incoming optical power on bolometers: background, dipole,

	BOLO	BACK	DIP	JUP	SAT	MARS
		\pWatt]	[attoWatt]	\pWatt]	\pWatt]	\pWatt]
	100-3a	0.33	360	0.17	0.03	0.01
	143-3a	0.37	599	0.67	0.10	0.04
	217-6a	0.43	350	1.58	0.25	0.09
	353-5a	0.50	108	2.55	0.40	0.16
	545-2	4.54	97.6	9.67	1.69	0.83
	857-2	12.98	4.45	27.6	4.18	2.22

Table 4 . 6

 46

	NEhfc =	PLANETSiin(ADU) -PLANETSq(ADU) P LAN ETSun{ADU)	(4.17)

: Non-Linearity summarizing table

  It is possible compute the position of the planets with respect the Planck lines of sight (see table5.2 ). The first problem is to establish how rnany times every planet is visible by the satellite; it is a fimdamental infor mation to know the suitability of a planet with respect the others. In the table 5.1 of brightness température of the plantes and the results of simula tions are presented.

			100	143	217	353	545	857
		MARS	206	206	206	206	206	206
		JUPITER	173	176	179	178	133	145
		SATURN	141	144	146	141	118	114
		URANUS	120	120	120	120	120	120
		NEPTUNE	117	117	117	117	117	117
	Table 5.1: Brightness Température of Planets and Ceres. [65], [66], [67],
	M
	5.1	Planets Suitability
	We assume that the Planck mission will start to observe the sky on the 1-
	1-2009.

Table 6 .

 6 to arrive to redshift zéro. For each run we stored a total of 78 snapshots in the redshift range 0 < z < 23.4. Individual snapshots were dump at redshift intervals that correspond to the light travel time through the simulation box, ie simulation outputs stack in redshift.

	1: Simulation parameters: fd, dust-to-métal mass ratios (see Eq. 6.4),
	grain sizes, and number of timesteps taken by simulation runs to evolve from
	z=49 to z=0. Cosmological and simulation parameters were set the same in
	ail simulation, as follows: D -0.3, Da = 0.7, Qb = 0.0486, a8 = 0.9, h = 0.7,
	boxsize L = 100/i-1Mpc, and number of baryonic and dark mater particles,
	N = 4,096,000.
	2.1 x 1010 h~1MQ and 2.6 x 109 h~lM0 respectively. The gravitational soften-
	ing in physical coordinates was 25 h~lkpc below z = 1 and above this redshift
	scaled as 50(1 + z)~l h~lkpc.

We generate a total of 7 simulation runs, listed in Table

6

.1. The first two runs, which will be referred hereafter as 'adiabatic' (or model 'A') and 'cooling' (or model 'C') simulations, do not include dust. Simulations 3 to 7 differ only on the dust model parameters assumed in each case, and will be referred to as 'dust' runs, and are labeled as 'Dl' to 'D5' models (see Sec. 6.1.3 for details on the dust models définition). This will allow us to investigate the effects of the dust model parameters on our results. The last column in the table gives the total number of timesteps required by each simulation

Table 6 .

 6 2: Best fir values of the parameters a, logv4 and (3 as well as their respective la errors. These values are valid within the redshift range 0 <

			Model C	Model D5	Model D4	Model D3	Model D2	Model DI
	tnw	M
	« TM	0.61 ± 0.02	0.61 ±0.02	0.61 ±0.02	0.62 ± 0.02	0.63 ± 0.02	0.63 ±0.02
	log ATM	0.195 ±0.002	0.195 ±0.003	0.196 ±0.002	0.197 ±0.003	0.201 ± 0.002	0.204 ± 0.002
	AEtm		-0.14 ±0.01	-0.14 ±0.01	-0.14 ±0.01	-0.15 ±0.01	-0.16 ±0.01	-0.16 ±0.01
	S -M
	«SM		0.55 ± 0.03	0.54 ± 0.03	0.54 ± 0.03	0.56 ± 0.03	0.55 ± 0.02	0.54 ± 0.02
	log Asm	2.443 ± 0.002	2.444 ± 0.002	2.445 ± 0.002	2.451 ± 0.002	2.468 ± 0.002	2.488 ±0.02
	AEsm		-0.33 ± 0.01	-0.34 ±0.01	-0.34 ±0.01	-0.36 ±0.01	-0.40 ±0.01	-0.42 ±0.01
	Y -M
	«YM	1.74 ±0.03	1.72 ±0.03	1.73 ±0.03	1.72 ±0.02	1.74 ±0.02	1.76 ±0.02
	log AYm	-5.909 ± 0.002	-5.907 ± 0.002	-5.910 ±0.002	-5.914 ±0.002	-5.933 ± 0.002	-5.957 ± 0.002
	Pym		0.12 ±0.01	0.11 ±0.01	0.13 ±0.02	0.13 ±0.01	0.17 ±0.01	0.21 ±0.01
	Lx -m
	«LM		1.69 ±0.07	1.68 ±0.07	1.65 ±0.07	1.61 ±0.08	1.67 ±0.05	1.67 ±0.05
	log Alm	3.330 ± 0.006	3.334 ± 0.006	3.333 ± 0.005	3.323 ± 0.005	3.265 ± 0.005	3.207 ± 0.004
	Plm		0.01 ±0.03	-0.02 ± 0.03	-0.02 ±0.03	0.02 ± 0.03	0.18 ±0.03	0.23 ± 0.03

^< 1.

comportement des bolomètres, la réponse statique et dynamique des chaines de mesure. Ils sont ajustés grâce à des séquences d'étalonnage particulières. Ce mémoire présente le satellite Planck et l'instrument HFI. Il décrit les sé quences de calibration auxquelles j'ai personnellement participé. Il détaille des méthodes des mesures originales qui ont été développées pour Planck comme la mesure expérimentale des défauts de linéarité des détecteurs. Je présenterai aussi une avancée dans la théorie des bolomètres, qui permet de prédire la réponse et le bruit d'un bolomètre polarisé en courant alternatif. Parallèlement à ce travail très instrumental, j'ai développé un travail pure ment astrophysique sur les amas de galaxies. Il concerne la physique des com posantes dans le milieu intra-amas. Les observations en optique et proche infrarouge ont montré la présence, en plus du gaz baryonique et de la matière noire, d'une composante stellaire intra-amas. Cette population stellaire est fort probablement associée à une composante diffuse de poussière, qui doit être un vecteur de refroidissement et/ou de chauffage, mais qui reste à quan tifier. En collaboration entre Antonio da Silva, Centro de Astrofisica da Universidade do Porto et Etienne Pointecouteau, Ludovic Montier, Martin Giard du CESR de Toulouse, nous avons exploité un modèle numérique de formation des structures, incluant le refroidissement radiatif et de la pous sière dans le milieu intra-amas. Mon travail a consisté à analyser le résultat de ces simulations numériques en comparant les propriétés statistiques (rela tions Lx-M, Y-M et S-M) de la population d'amas simulés dans les cas d'un modèle gravitation+refroidissement radiatif et gravitation-|-refroidissement radiatif+poussière. On a montré que le refroidissement radiatif a un effet significatif et que sa prise en compte permet d'améliorer l'accord entre les modèles et les observations.

In the galactic medium the cooling occurs through re-radiation of the power absorbed in the UV and visible range.

Acknowledgements 4

Acknowledgements

The first person I would like to thank is my tutor Jean-Michel Lamarre. His knowledge and instinct on research hâve deeply affected me. I hope I hâve

Chapter 2

The HFI Instrument Wopt ---n'[TTot [ ^2-BB"{Tsat, v)dv+-Trottes\ [ \2-BBly(Tcsuv)di'-\- BB(Tx,v) is the blackbody radiation function of the considered extended source n\2 is the beam throughput. For the multi-moded channels the A2 is multiplied to the équivalent numbers of modes. We use 3.4 for 545GHz, 8.3 for 857GHz and 1 for the others.

Tx is the température of the considered spread source (Saturne, CS1, 4K and 1.6K stage)

Au represents the nominal top-hat spectral band.

P is Polarisation factor. We consider HFI bolometers as idéal bolometers with P = 1 if PSB and P = 0 if SWB.

TT0t is the total efficiency of the optical System including the bolometer efficiency.

ex is the emissivity of the considered source.

T4fc and rl.GK are the applicable effective transmission for the cryogénie stages.

Note that r4k is not the transmission of the 4K stage but the transmis sion of the colder stages. It is the same for T\ w Ail the efficiencies and transmissions are considered as constant in the band of frequencies of each channel.

Based on the CQM (Cryo-Qualification Model) data analysis, it has been found that the straylight in the calibration facilities is very low ( [START_REF] Pajot | Calibration Team[END_REF]): so in the EFF data analysis we do not consider this contribution. Because and C4K cannot be measured separately, from now we define this product as the Coupling parameter. The same for t\^k * £\.gk product.

COUp4x -r4K • C4K

COUpiüK = T\£K ' Cl.6K

The Goal of EFF sequence is to measure the tt0u coup4K, coupi^x, tesi parameters.

Chapter 6

The impact of dust on the scaling

Introduction

From the first stages of star and galaxy formation, non-gravitational pro cesses drive together with gravitation the formation and the évolution of structures. The complex physics they involve rule the baryonic component within clusters of galaxies, and in a more general context within the intergalactic medium (see the review [START_REF] Voit | Tracing cosmic évolution with clusters of galaxies[END_REF] ). The study of these processes is the key to our understanding of the formation and the évolution of large-scale structure of the Universe. Indeed, understanding how their heating and cool ing abilities affect the thermodynamics of the IGM at large scales and high redshifts, and thus that of the intra-cluster medium (hereafter ICM) once the gas get accreted onto massive halos is a major question still to be answered.

The continuous accretion and the merger events through which a halo assembled lead to a constant interaction of the IGM gas with the evolving galactic component. Within denser environments, like clusters, feedback provided by metallicity, the higher is the cooling power of the dust. Thus the total cooling function due to a population of dust grains can be expressed as a function of these two parameters as:

Ha,Td) = / j j AHa,Td)d-^ndVdadZ (6.3) where d7V(a, Z, V) / dV dadZ is the differential number of dust grains per size, metallicity and volume element.

Cooling by dust happens to increase with the square root of the gas density, whereas the heating by dust is proportional to the density. As stressed by Montier and Giard [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF] the cooling by dust is more efficient within the température range of 106 < T < 108 K (i.e 0.1 < kT < 10 keV), which is typically the IGM and ICM thermal conditions.

The dust abundance

The abundance of dust is a key ingrédient to properly weight in our implé mentation. Observations indicate that dust represents only a tiny fraction of the baryonic matter: Mdust/Mgas ~0-01 in our Milky Way, and this is possibly lower by a factor 100 to 1000 in the ICM: Mdust/Mgas = 10-5 -10~4 [START_REF] Popescu | On the FIR émission from intracluster dust[END_REF][START_REF] Aguirre | Métal Enrichment of the Intergalactic Medium in Cos mological Simulations[END_REF]. We defined the abundance of dust as the ratio of the dust mass with respect to the gas mass:

Mdust Mgas fd ry ^d 0 Zjq (6.4) where Z is the metallicity in units of solar metallicity, Zdo = 0.0075 is the solar dust abundance, i.e the dust-to-gas mass ratio in the solar vincinity, and fd is the abundance of dust in the ICM in units of solar dust abundance.

Dust enrichment occurs via the feedback of galaxy formation and évolu tion in the ICM through interaction, stripping, mergers, galactic winds and AGNs outburst. At ail redshifts, it is linked to the star formation rate (SFR) which drives the production of dust in cluster galaxies. However, in our hydrodynamic simulations (see Sect. 6.2) the SFR is not physically modeled, but it is inferred by the cooling State of the gas particles within the simula tions: gas particles below a given threshold of température and above a given threshold of density are considered as colisionless matter, forming stars and galaxies (see Sec. 6.2). In order to tackle this problem, we choose to directly link the dust abundance to the métal abundance using Eq. (6.4). Therefore, the dust distribution in our simulations mimics the métal distribution. at different values of metallicity. The blue and black lines are the radiative cooling rates from [START_REF] Sutherland | Cooling functions for low-density astrophysical plasmas[END_REF] and the total (i.e radiative plus dust cooling) rate, respectively.

Together with an adiabatic run (i.e model A) and a "standard" radiative run (model C -see Sect. 6.2 for further details), we ran a total of five runs implementing various population of grains (i.e named Dl to D5) characterized by their sized and dust-to-metal mass ratio:

• We tested three types of sizes: two fixed grain sizes with a = 1CT3 //m and a = 0.5 //m), respectively labeled small and big. The third assumes for the IGM dust grains a distribution in sizes as defined by Mathis [96] for the galactic dust: N (a) oc a~35 within the size interval of [0.001,0.5] /im. It is hereafter referred as the 'MRN' distribution.

• We investigate three values of /^: 0.001, 0.01 and 0.1. The two ex-the structural effect of dust. There is also no significant effect between the different dust models and the radiative case on the évolution of the slope and normalisation of the Tmw -M relation.

• The increase of normalisations for the S -M and Tmw -M relations with added dust cooling is also in line with expectations because cooling converts cold, dense, gas into collisionless star forming material, which raises the mean température and entropy of the remaining gas.

• Our simulations allow us to quantify the relative impact of the dust parameters on the investigated cluster scalings (see Figs. 6.4 to 6.7

and Table 6.2). From one model to another one can identify two clear effects due to dust: (i) it shows the expected effect of the dust abundance, which from models D4 to D2 raise by a factor of 10, producing a change of normalisations relative to the purely radiative case (model C), from almost zéro percent contribution to about 14%, 5% and 6% contributions for the Lx -M, Y -M and S -M relations, respectively.

(ii) Even more striking is the effect of the intrinsic dust grain physical properties. The variation of normalisations relative to the C model, change from a zéro percent level for model D4 to about 25% (Lx -M) and 10% (Y -M, and S -M) for the model DI (ie the relative change from models D2 to DI is about 13% and 5%, respectively). Ail these percentages were calculated using normalisations at redshift zéro and M0 = 1014/i-1Mo. Therefore the size of the grains cornes to be an equally important parameter varying the efficiency of the dust cooling.

The smaller the grain, the stronger the cooling.

• From Figs. 6.4, 6.5, 6.6, and 6.7 one finds that différences between normalisations become progressively important with decreasing red-shift. This confirms expectations because metallicity was modelled in simulations as a linearly increasing function of time. Although our implémentation of metallicity should only be regarded as a first order approximation to the modelling of more complex physical processes (acting on scales below the resolution scale of the présent set simula tions), it would be interesting to investigate whether a similar effect remains (ie the effects of dust become progressively important at low redshift) when such processes are taken into account throughout the formation history of galaxy clusters (see discussion below).

Limitation of the dust implémentation

In order to implement the presence of dust in the numerical simulations, we chose a "zéro order approach": we directly correlated the presence of dust with the presence of metals under the assumption that there is no ségrégation in the nature of the material withdrawn from galaxies and injected in the IGM/ICM (metals, gas, stars or dust). However, this assumption suffers from limitations linked to the dust lifetime. Indeed, dust grains strongly suffer of sputtering and within their lifetime they are depleted from metals which, contrary to dust grains, are not destroyed i.e. remain in the ICM/IGM.

Therefore our whole analysis is to be considered within the framework of this assumption, and is to be understood as a basic implémentation of the effects of dust with the objective of assessing whether dust has a significant impact on large scale structure formation, and consequently to quantify these effects at first order.

Moreover, our implémentation is also ad hoc. Indeed, beside the cooling function of dust, our implémentation is not a physical implémentation. We did not deal stricto senso with the physics of the dust création and dust de struction processes. However, making use of the cooling function by Montier and Giard [START_REF] Montier | The importance of dust in cooling and heating the InterGalactic Medium[END_REF], we hâve performed a fully self-consistent implémentation of the effect of dust as a cooling vector of the ICM/IGM. Indeed, on the basis of the cooling function, the implémentation encapsulâtes the major physical processes to which dust is subjected and acts as a non-gravitational process at the scale of the ICM and the IGM.

As already mentioned, we directly correlated the abundance of dust with metallicity, thus to the metallicity évolution, which chosen évolution law is quite drastic: Z = 0.3(t/to)ZQ. Indeed, if the metallicity at z = 0 is normalized to the value of 0.3ZQ, it is lowered to ~0.2 at z = 0.5 and ~0.1 at z = 1. However, other numerical works based on simulations including phys ical implémentation of métal enrichment processes but without dust agréé