Description of the physical properties of galaxy clusters using sunyaev-zel’dovich observations in ACES.

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Resumen

En este trabajo se presenta el análisis y los resultados de las observaciones milimétricas hacia en la sub-muestra de cúmulos de galaxias del AzTEC Cluster Environment Survey. Nuestra sub-muestra está compuesta por 19 cúmulos de galaxias masivos (Mtot &2.0×1014M⊙) identíficados previamente

en observaciones en el óptico y rayos-X. En contraste con estudios previos de la cámara AzTEC, los cuales están centrados en la detección y caracterización de la población de galaxias submilim’etricas (SMGs), este trabajo se centra en la recuperación de la señal extendida proveniente del incremento del efecto SZE (SZE).

La detección de emisión extendida débil (_≃ 1mJy beam−1) desde telescopios (sub)-milimétricos

terrestres es bastante desafiante, ya que la atmósfera es parcialemente transparente a estas longuitudes de onda. Además, la emisión proveniente de la atmósfera no es estacionaria e introduce fluctuaciones de gran escala en el brillo del cielo. La aproximación típica para estimar la contribución de la atmós-fera en este tipo de observaciones es remover las variaciones comunes en las señales registradas por los bolómetros. Sin embargo, este proceso tiene la desventaja de remover la emisión proveniente de las fuentes extendidas de origen astronómico. Para solucionar este problema, este trabajo implementa la técnica CMP en el código de reducción de datos de AzTEC. La técnica CMP utiliza el método presentado por Cottingham (Cottingham 1987) para estimar las variaciones en el dominio del tiempo y añade un ajuste polinomial para las fluctuaciones en el dominio espacial.

Con el propósito de verificar el funcionamiento de la técnica CMP, este trabajo desarrollo un con-junto de herramientas para realizar simulaciones con el código de AzTEC. Estas herramientas tienen la capacidad de proyectar en el dominio del tiempo cualquier distribución de brillo superficial de origen astronómico, además de producir realizaciones aleatorias de la emisión atmosférica con las mismas propiedades estadísticas que las presente en las observaciones de ACES. A través de modelar en medio intra-cúmulo (ICM) con un perfil isotérmico (modelo β), las simulaciones muestran que la técnica CMP recupera la emisión del SZE hasta una escala angular de_≃ 3′_{. Esto representa una}

mejora de un factor 2 comparada con le técnica estándar de reducción. Ademas, las simulaciones permiten establece un vínculo entre las propiedades de la distribución de flujo observado con los parámetros que describen el ICM.

El análisis de las observaciones del SZE es susceptible a la contaminación debida a la abundante población de SMGs y radio galaxias. Sin embargo, la profundidad y la resolución angular de las obser-vaciones de AzTEC permite realizar una sustracción de la densisdad de flujo de las galaxias brillantes. En este trabajo, la contaminación de fuentes débiles se modela como una emisión difusa de fondo y es caracterizada utilizando un método similar al reportado en Montaña (2012). Concluimos que la contribución de este fondo es despreciable para los cúmulos mas masivos (Mtot & 6.0×1014M⊙),

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En este trabajo reportamos la detección del incremento del SZE en 9 cúmulos de galaxias obser-vados en ACES. Después de la sustracción de fuentes puntuales brillantes, la distribución angular del flujo observado tiene una morfología similar a la reportada por observaciones de rayos-X y del decremento de SZE disponibles en la literatura. A la vez, este trabajo provee una estimación de la masa total, la masa de gas y la fracción barioníca para los cúmulos detectados.

Las técnicas desarrolladas en esta tesis son de gran importancia para las observaciones de cien-cia temprana de AzTEC en el Gran Telescopio Milimétrico así como para las futuras observaciones galácticas, extragalácticas y de la estructura a gran escala que sea realizarán con la nueva generación de cámaras bolométricas de gran formato como MUSCAT y ToLTEC.

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Abstract

In this work we present the millimeter wavelength observations of the galaxy cluster sub-sample of the AzTEC Cluster Evolution Survey (ACES). This sub-sample is composed by a set of 19 massive galaxy clusters (Mtot & 2.0×1014M⊙) previously identified in optical and X-ray observations. In

contrast with previous AzTEC studies, which were focused on the detection and characterization of the population of star-forming submillimeter galaxies (SMGs), this work aims to recover the extended emission from the increment of the SZE effect (SZE).

The detection of faint (_≃ 1mJy beam−1) extended structures in ground-based (sub)-millimeter

observations is quite challenging, since the atmosphere is partially transparent at these wavelengths. Moreover the atmosphere emission is not stationary and introduces large angular scale fluctuations in the observed sky brightness. A typical approach to estimate the atmosphere emission is to remove the common-mode variations in the bolometer timestreams. This approach has the disadvantage of removing the emission from extended astronomical sources. To overcome this problem, this work im-plements into the AzTEC reduction pipeline the CMP technique, an atmosphere template estimation optimized for extended sources. The CMP technique is based on the Cottingham method (Cottingham 1987) for the time-domain variations and a masked polynomial fit for the angular-domain fluctuations. In order to test the performance of the CMP technique, this work have developed a simulation framework for the AzTEC pipeline. This simulation framework is able to map into the time-domain an arbitrary astronomical surface brightness as well as produce random realizations of the atmosphere emission with the same statistical properties as the observed in the ACES observations. By modeling the intra-cluster medium (ICM) with a isothermalβ-profile, the simulations show that the CMP is able to recover the emission of SZE up to angular scales of_≃3′_{, an improvement of a factor of 2 compared}

to the standard SMG optimized reduction of the AzTEC pipeline. Moreover these simulations allow to provide a link between the observed angular flux distribution in the AzTEC maps and the galaxy cluster ICM model parameters.

The analysis of the observations of the SZE is susceptible to the contamination from the abundant population of SMGs and radio galaxies in the direction of galaxy clusters. However, the depth and angular resolution of the AzTEC observations allow to subtract the contribution of bright point-like source with flux densities larger than 3.5mJy beam−1. This subtraction is carried out by a joint fit

to the galaxy cluster emission and the flux density from the point sources. The contamination from fainter point-like sources is assumed to be a diffuse background and is estimated using a similar proce-dure to the reported in Montaña (2012). We conclude that the contribution of the diffuse background is negligible for the most massive galaxy clusters (Mtot & 6.0×1014M⊙) but it can account up to ≃20%of the observed central flux for galaxy clusters with smaller total mass values.

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tion has a similar morphology as the observed by X-ray and other SZE experiments. We also provide an estimation for the total mass, gas mass and baryon fraction for the detected galaxy clusters.

The techniques developed in this thesis are of paramount importance for the ongoing early science observations of AzTEC on the Large Millimeter Telescope and for the future galactic, extragalactic and large scale surveys to be carried out with the next generation of large bolometer arrays like MUSCAT and TolTEC.

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Agradecimientos

A mi familia, que siempre me ha apoyado sin importar el camino que siga,

brindán-dome del amor y cariño que me ha ayudado a conseguir mis metas. A mi asesor, Dr.

David H. Hughes, por la oportunidad de pertenecer a este proyecto, por las largas

pláticas en las que aprendí tanto, por su confianza y paciencia. A los miembros de

mi jurado de examen, Dra. Anna Lia Longinotti, Dr. Daniel Rosa González, Dr. Iván

Rodríguez Montoya, Dr. Yair Krongold Herrera y Dr. Miguel Chávez Dagostino por

los comentarios que ayudaron a mejorar este trabajo. A mis compa´neros y amigos,

por hacer más especial el tiempo que he pasado en el instituto. Al Instituto

Na-cional de Astrofísica, Óptica y Electrónica por el apoyo brindado en la realización

del Doctorado. Al Consejo Nacional de Ciencia y Tecnología (CONACYT) por la

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Chapter 1 Introduction.

In the late 1970’s, the observations of the galaxy density in the nearby universe demon-strated that the underlying matter distribution was not uniform, but organized in a complex web like structure, known as the Large Scale Structure (LSS). The large 3D galaxy surveys such as the Two Degree Field Galaxy Redshift Survey (2dFGRS, Peacock et al. 2001) and Sloan Digital Sky Survey (SDSS, Raddick 2003; J. et al. 2005) found several degrees of galaxy agglutination: large (_≃ 10₋200h−1_M_pc_{) unrelaxed filament and wall like} struc-tures which converge into the compact regions known as galaxy groups and galaxy clusters where a large density contrast exists with regions containing only a few galaxies known as voids.

The models of structure formation predict that the elements of the LSS have not evolved independently but are the result of the gravitational-driven growth of the small quantum fluctuations in the primordial density field after the inflation epoch. Moreover the ever increasing level of detail available in N-body simulations confirm that this complex pat-tern can arise using as initial conditions an isotropic and homogeneous matter distribu-tion perturbed with a small Gaussian field, consistent with the temperature anisotropies

∆T _∼10−4_{K observed in the Cosmic Microwave Background (CMB). Figure 1.1 shows}

a comparison between the observed distribution of galaxies observed by the SDSS and the distribution of dark matter and ionized gas obtained from the Magneticum N-body simulation (Dolag, Komatsu, and Sunyaev 2015).

Within this Cosmic Web, the galaxy clusters are of particular interest since they are the most massive, gravitationally bound, semi-virialized objects, gathering a total mass of MT ≃ 1013−1015M⊙ within a volume of a few megaparsecs in radius and accounting

for_≃4%of the total mass of the Universe (Weygaert and Bond 2008), hence representing

the largest concentrations of dark matter with an overdensity contrast∆ & 1000 relative

to the average density of the Universe.

Galaxy clusters are complex environments. They host the most massive elliptical galax-ies which dominate the optical luminosity of the cluster, denominated the brightest cluster Galaxies (BCG). Up to 20% of these galaxies have an associated diffuse extended stellar envelope and are therefore classified as type cD. These cD galaxies are only found in the richest galaxy clusters suggesting that their formation is a consequence of the increased

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accretion rate and merging events inside the deep gravitational well of the cluster (Dressler 1984).

An important characteristic of galaxy clusters is that the member galaxies are embedded into a diffuse ionized gas (T _≃106₋₁₀8_{K) known as the Intra-Cluster Medium (ICM).} The ICM temperature is consistent with the shock heating of primordial gas driven by gravitational accretion. The ICM is enriched, and at low redshift (z < 0.45) the average

metallicity is Z _≃ 0.3Z⊙ (Hofmann et al. 2016) where all but the heavy elements are

ionized, providing a free electron population with a densityne ≃ 10−4−10−2cm−3. In

rich galaxy clusters, the gas mass contained in the ICM (Mgas & 1013M⊙) exceeds by an

order of magnitude the mass deposited in all the galaxies (Sarazin 2008).

1300 Mpc

Figure 1.1:(left) The redshift distribution of nearby galaxies as seen by the Sloan Digital Sky Survey (SDSS,

J. et al. 2005). The color is an indication of the galaxy density. This density field is organized into wall and filament like structures where the most dense regions, the galaxy clusters occurs at the intersections of such structures. (right) 2D matter-density field atz = 0from the Magneticum Pathfinder Simulation (Dolag, Komatsu, and Sunyaev 2015) a Cosmological Hydrodynamic Simulation

1.1 Galaxy Clusters as Cosmological Probes

The concordance cosmological mode, or theΛCDM model, postulates a flat Universe

with a low matter-density and dominated by a cosmological constant component (Λ),

which drives its accelerated expansion. This model has been widely adopted since it provides an accurate theoretical framework to describe the origin and evolution of the Universe with the advantage of being able to reproduce the observed properties of several cosmological tracers like the type Ia Supernovae (SNIa), the Baryon Acoustic Oscillations (BAO), the growth of the Large Scale Structure and the CMB.

Despite the success of the ΛCDM model, its description is far from being complete since the physics of the two components that dominate up to _≃ 96% of the total energy density of the universe is not completely understood. The first component, the dark matter,

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1.1. Galaxy Clusters as Cosmological Probes

was proposed as an explanation for the flattening of galaxy rotation curves at large radii (Zwicky 1938). This dark matter particles have avoided direct detection since they inter-act only by gravitational forces. The second component, the cosmological constant, has been explained by means of an energy density associated with the quantum vacuum en-ergy. Nevertheless, its observed energy density value is, in the best case scenario,_≃ 1070 times smaller than the value predicted from quantum theory. This“Fine Tuning Problem”

has motivated the development of theories that allow the evolution of the cosmological constant and this component is now referred as “dark energy”.

The state of the art cosmological studies are focused on identifying the source of the dark matter and dark energy based on their effects over a set of indirectly measurable properties of the Universe known as cosmological parameters. This task is challenging

since the directly observable properties of the astronomical phenomena does not depend on a single cosmological parameter but on a combination of these.

In this context, the individual and statistical properties of galaxy clusters provide a valuable probe that allows one to describe the evolution of the initial perturbations in the matter density field with the Cosmic Time. In the linear regime (i.e. assuming that the amplitude of the perturbations is small and neglecting the effect of gas processes), the statistics of the matter fluctuation field can be represented by a random Gaussian process:

σ2(M) = 1 (2π)3

Z

d3kW2(kR)Pm(k, θΩ) (1.1)

wherePm(k, θΩ)is the Matter Angular Power Spectrum of the primordial density field, andW is a window function that encodes the amount of matter fluctuations averaged over a sphere of radius R, usually described in the literature as a top-hat spatial filtering. The relationship with the underlying Cosmological Model is contained in the θΩ parameter vector. Using the framework of theΛCDM cosmology then:

θΩ ={Ωbh2,Ωch2,ΩΛ} (1.2)

where h = H0/100kms−1Mpc−1 is an arbitrary normalization of the Hubble’s con-stant, which measures the local expansion rate of the Universe, and theΩb,Ωc andΩΛ pa-rameters are the energy densities of the baryon, dark matter and dark energy components respectively. TheΩxnotation represent the normalization of a species energy density with

respect to thecritical densityρcr

Ωx =

ρx

ρcr

(1.3)

= 8πGρx

3H2 (1.4)

The shape of the power spectrumPmis fully determined by the values of the

cosmolog-ical parameters, however its normalization is arbitrary and depends on the spatial filtering

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measured a deviance σ2 _≃ ₁ _{inside spheres of such length (Davis and Peebles 1983).} Consequently the mass power spectrum normalization parameter is denoted asσ8.

1.1.1 Galaxy Cluster Mass Function

The analysis of the correlation functions of rich galaxy clusters (Kaiser 1984; Bardeen et al. 1986) and the ever increased detail of the N-Body simulations (Springel 2005; Boylan-Kolchin et al. 2009; Dolag, Komatsu, and Sunyaev 2015) have demonstrated that the baryonic matter inside galaxy clusters traces the underlying dark matter halo distri-bution. Therefore accurate mass determination of galaxy clusters have the potential to statistically characterize the halo distribution and its evolution with cosmic time.

The expected number of dark matter halos for a specific mass M is given by the ex-pression:

dn

dlnM = ρ M

dlnσm

dlnM

f(σm, z) (1.5)

wheref(σ, z)is the collapse rate of a mass fluctuation of amplitudeσm. The collapse

rate can be estimated from assuming a spherical collapse (Press and Schechter 1974; Bor-gani 2008), this is known as the Press-Schechter formalism:

f(σm, z) =

r

2

π δc

σm

exp(₋1 2 δ2 c σ2 m ) (1.6)

whereδcis the relative contrast of a perturbation related to the average densityρ

δc =

ρ₋ρ(z)

ρ(z) (1.7)

Deviations from the Press-Schechter formalism can be studied in detailed N-body sim-ulations, including effects of non-spherical collapse and gas effects.

Since the dark matter can not be observed directly, the galaxy clusters integrated num-ber counts can be measured in order to recover the massive end of the halo numnum-ber density:

N(M > M′, z) =

Z ∞

M′

dn

dlnM

dV

dz (1.8)

whereN(M > M′_{, z}₎_{is the number of galaxy clusters with a total mass larger than}_M′

in a comoving volumeV. Figure 1.2 shows the sensitivity of the galaxy cluster integrated number counts to the values of cosmological parameters. Its is important to note that the different model predictions are able to reproduce the observed galaxy cluster volume density at lower redshifts. However it is only with measurements at larger redshift that it is possible to notice a deviation from the model predictions.

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1.1. Galaxy Clusters as Cosmological Probes

Figure 1.2: Sensitivity of the galaxy clusters integrated number counts to the underlying Cosmological

Model. The solid lines represent the prediction of Equation 1.8 for the example of two different set of cosmological parameters aΛ-dominated universe (top frame) and a universe without a cosmological constant (bottom frame). The data points are the measurements of the total mass for a sample of 37 galaxy clusters observed withChandra(blue points) at a mean redshift_hzi= 0.55and 49 galaxy clusters observed with

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1.2 The Galaxy Cluster Angular Distribution

Another interesting property of the population of galaxy clusters arises from the statis-tics of their angular distribution since it encodes the clustering properties of the underlying dark matter distribution. These studies rely on measuring the two point correlation func-tion for a particular subset of galaxy clusters separated by a comoving distance r. The spatial covariance of the galaxy cluster counts can be written as (Dalal et al. 2008; Cunha, Huterer, and Doré 2010):

C_ijm = _h(Nmi−Nmi)(Nmj −Nmj)i (1.9)

= NmiNmjξijm (1.10)

wheremrepresents a mass bin,i, jrepresent the redshift bins,Nmiis the mean number

of galaxy clusters in a given mass and redshift bin can be obtained by integrating Equation 1.5 in the comoving volume covered by thei-th bin:

Nmi(M, z) =

Ai 4π

Z zi+1

zi

dzdV

dz

Z Mm+1

Mm

dlnM dn

dlnM (1.11)

whereAiis the solid angle covered by thei-th bin. The quantityξijmrepresents the

real-space spatial correlation between mass-redshift bins (Allen, Evrard, and Mantz 2011):

ξm =

Z _d_k

(2π)3|Wi(k)Wj(k)|f(k∆r)bmibmjPm(k, z) (1.12) wheref is a geometric term that depends on the separation of thei-th andj-th cell and W is the bin averaging window function.

An equivalent approach is to analyze the angular power spectrum of the mass observ-able. This method has several advantages compared to the spatial correlation analysis since it does not require knowledge of the redshift distribution of the sampled population nor a high significance detection of individual clusters. It instead relies on the statistical signifi-cance of the observed cluster population. Therefore is robust against selection effects and substructure in the ICM (Komatsu and Seljak 2002). The power in a given angular scale represented by the multipole number can be obtained by:

C_ℓ₌

Z

dzdV

dz

Z

dlnM dn

dlnM§(M, z, ℓ) (1.13)

where_§is the spherical harmonic transformation of the cluster spatial observable which introduces an additional connection to the cosmological parameters and for some observ-ables it also introduces degeneracies with the comoving volume elementdV.

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1.3. Multiwavelength Observations of Galaxy Clusters

1.3 Multiwavelength Observations of Galaxy Clusters

As described in section 1.1.1 the total mass of halos and their abundance are a proxy to recover the overall properties of the Universe using the cosmological parameters. This has motivated the development of different methods that rely on the different observable properties of galaxy clusters to estimate their mass.

Historically galaxy clusters were discovered by locating the largest overdensities of galaxies in optical wavelengths (Zwicky 1938). Later, George Abell created a catalog of the richest galaxy clusters establishing a criteria to classify these astronomical objects that is nearly independent of the distance to the cluster (Abell 1958).

In the optical and near infrared regimes, the current resolution of ground and space based telescopes can resolve individual galaxies associated with the galaxy cluster. By taking spectra of such galaxies the radial velocity distribution can be constructed. The total mass can be estimated assuming that the cluster is in virial equilibrium:

Mvir =

2_hv_i2_R

vir

G (1.14)

where _hv_i is the mean velocity of the member galaxies. This mass estimate is also known asdynamical mass(Mdyn). As in many astronomical objects the extent of a galaxy

cluster is difficult to establish, therefore the correlation between the cluster’s radius and its mass can not be derived from observations only. To overcome this problem, the mass and radius estimates for a galaxy clusters are related to the density contrast with respect to the universe critical density at the cluster’s redshift:

ρX =

ρ(r=RX)

ρcr(z)

(1.15)

Its common in the literature to use the approximationR200 ≃ Rvir. ConstrainingMdyn

can be time expensive since it requires spectroscopic observations to assess the member-ship and the radial velocity of a large number of galaxies in the cluster field. Therefore some photometric methods and empirical relationships have been developed based on the BCG properties, the cluster richness and the cluster luminosity. As an example Reyes et al. (2008) found the empirical power laws:

MN200 = M_N0

N200 20

αN

LBCG

αNN200βN

!γN

(1.16)

ML200 = M_L0

L200 40

αL _L

BCG

αLLβ200L

!γL

(1.17)

whereMN200andML200are the total mass insideR200estimated from the galaxy richness

N200 and optical luminosityL200 respectively,M_N0 andM_L0 are normalization constants,α,

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Another approach to obtain the total mass contained in a galaxy cluster is to use the am-plification and shape distortion of the background galaxies due to the gravitational lensing effect. Two regimes are available for this kind of analysis: the strong lensing regime where amplification factors are large,µ_≫1, producing multiple images and arc-like fea-tures located very close to the peaks in the mass distribution within the Galaxy Cluster. The weak lensing regime where amplification factors are smaller µ _≃ 1with the advantage

of acting over a larger surface area when compared to the strong lensing. For a spherical mass distribution the projected mass within a radiusrcan be expressed by:

MLens(r) = c

2

4G

DOSDOL

DLS

r∂rφ(r) (1.18)

whereφ(r)is the projected lensing potential,DOS is the distance between the observer

to the background source,DOLis the distance from the observer and the gravitational lens

(i.e. the Galaxy Cluster), DLS is the distance from the lens to the background source and

∂rdenote the partial derivative with respect to the radial coordinate. The lensing potential

can be recovered from themagnification matrix:

Ã−1 = 1−∂rrφ −∂r(

1

r∂θφ) −∂r(1_r∂θφ) 1− 1_r∂rφ− _r1r∂θθφ

!

(1.19)

= 1−κ−γ1 −γ2 −γ2 1−κ+γ1

!

(1.20)

whereκ is the isotropic deformation or convergence, γ = (γ1, γ2)is the shear vector and the amplification is defined byµ=det(Ã−1).

Galaxy Clusters are very bright in X-ray observations, with luminosities up to_≃1045_e_{rgs s}−1_, where the hot ICM appears as an extended source in high resolution (XMM, Chandra) ob-servations (Jones et al. 2008). The main emission mechanism at these wavelengths is the thermal Bremsstrahlung and line emission due to heavy metal nuclei. These observations allows to estimate the total mass of the galaxy cluster by assuming hydrostatic equilibrium (HSE) of the ICM gas pressure with the cluster’s gravitational potential well:

∇ΦG=− 1

ρ∇P (1.21)

where ΦG is the cluster gravitational potential, ρ is the gas density and P is the gas

pressure. Assuming a spherical distribution of an ideal gas then:

GM r2 =−

kB

ρ(r)µmP

d

drρ(r)T(r) (1.22)

whereM is the mass enclosed inside the galaxy cluster at radius r, µ is the average molecular weight,mpis the proton mass,T(r)is the temperature profile,p(r)is the density

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1.3. Multiwavelength Observations of Galaxy Clusters

profile and kB is the Boltzmann constant. Both the temperature and density profiles are

related to the X-Ray emission:

SX ∝

Z

n2_e(r)Λ(T, r, Z)dl (1.23)

whereZ is the ICM metal abundance andΛis the cooling function for a pure

Bremss-trahlung emission process Λ(T, Z) _∝ T−1/2 _{(Böhringer and Hensler 1989; Peterson and} Fabian 2006). To break the degeneracy between the electron density and the temperature, spectroscopic X-Ray observations of the FeXXVI and Fe XXV recombination lines at

6.7keVcan be used.

Equation 1.22 requires the assumption of some radial and angular distribution for both the temperature and electron density but the observed X-ray surface brightest measures the line-of-sight projected quantities. This inverse problem is not easy to solve and usually re-quires one to assume some model to describe both distributions. Early X-ray observations were consistent with the isothermalβ-model, an approximation of the King’s model to a single-temperature self-gravitating sphere (Cavaliere and Fusco-Femiano 1978; Jones and Forman 1984; Sarazin 1986; Mulchaey 2000):

nβ_e(r) =n0 1 +

r2

c

!−₂3β

(1.24)

wherercis the cluster core radius,βis the profile logarithmic slope at scales larger than

the core size andn0 is the electron density at the cluster center. The isothermal model has the advantage of providing a relatively simple expression for the hydrostatic equilibrium (HSE) mass:

M = ₋ r

2_k

BT

Gµ2_m2

Pn β e(r)

d drmPn

β e(r)

= ₋ r

2_k

BT

Gµ2_m

P −3βr

r2

c

1 + r

2

r2

c

!−1

= 3βkBT

GµmP

r3

r2

c +r2

(1.25)

HSE mass estimates are particularly sensitive to the presence of non-thermal effects and merging events. Simulations have shown that HSE estimates can be incorrect up to

a factor of _≃ 20% (Fang, Humphrey, and Buote 2009; Lau 2010; Suto et al. 2013). A

comparison of HSE and lensing estimates show a similar discrepancy level (Zhang et al. 2008; Merten et al. 2015).

Perhaps the most iconic demonstration of the value of multiwavelength observations towards galaxy clusters is the joint analysis of optical and X-ray imaging of the Bullet cluster system. This system is composed of two clusters undergoing a major merger event.

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Figure 1.3: From Clowe et al. (2006). The Galaxy Cluster 1E0657-56 a major merger system where the separation of the member galaxies (Optical Image from Magellan Telescope1 _{) and the ICM observed in}

X-ray (Red Area, Image from Chandra Space Observatory) is observed. The blue area is the location of the lensing magnification region dominated by the cluster dark matter. This component separation has been proposed as a demonstration for the existence of cold dark matter in Galaxy Cluster.

The collision plane is perpendicular to the sky plane which allows to detect a significant offset between the matter density profile and the hot gas emission (Figure 1.3). This offset is considered to be an indirect detection of dark matter (Clowe et al. 2006).

In the past few decades the technology to observe a different section of the electro-magnetic spectrum has been developed, the (sub)-millimeter regime. This has opened the opportunity to probe the dust-obscured star forming regions in the nearby and high-z Uni-verse since, at these wavelengths, many of the observable quantities are weakly dependent on the redshift.

As an example, the Sub-millimeter Galaxies (SMGs) are a set of intensive star forming galaxies that are thought to be the high redshift counterparts of the Ultra-Luminous Infra-red Galaxies (ULIRGs) in the nearby universe (Smail, Ivison, and Blain 1997; Hughes et al. 1998). Due to the properties of its thermal emission and the accelerated expansion of the Universe, the observed flux at λ = 1.1mm is roughly constant within the range

z = 1₋10. This effect is known as thenegative K-correctionfor the (sub)-millimeter regime. This enhanced detectability of SMGs facilitates the study of the evolution of the star formation with cosmic time.

In the radio and (sub)-millimeter regime, observations of the hot ICM gas are also possible. At these wavelengths the inverse Compton scattering of the CMB photons by the ICM free electrons, known as the Sunyaev-Zel’dovich Effect (SZE, Sunyaev and Zel-dovich (1970, 1972)), is a powerful tool to conduct cluster surveys. The SZE has a rather particular spectral signature. It is observed as a negative temperature fluctuation in the CMB surface brightness at wavelengths larger than1.4mm. Furthermore, it is observed as a positive fluctuation at wavelengths smaller than 1.4mmwhilst it is almost negligible at

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1.4. Overview of this Thesis

wavelengths _≃ 1.4mm. This unique spectral signature of the SZE enables the blind de-tection of unknown clusters. Moreover, the amplitude of the effect depends on the galaxy cluster gas pressure and it is almost independent of the cluster redshift. This redshift inde-pendence is one of the advantages of the SZE when compared to X-ray observations, since the later suffer from a strong positive K-correctionSX ∝(1 +z)−4.

1.4 Overview of this Thesis

My thesis work aims to develop the tools necessary to produce an estimate of the physi-cal properties (i.e. total mass, gas mass, dynamiphysi-cal state) for a sample of 19 massive galaxy clusters previously identified in optical and X-ray surveys. This sample was observed by the AzTEC bolometer array at 1.1mm. while installed on the Atacama Submillimeter Telescope Experiment (ASTE) during 2007 and 2008. This configuration provides an an-gular resolution of _≃30′′_{. This spatial resolution is intermediate between the all-sky and}

large area surveys (ACT, SPT, Planck) that are able to blindly detect new cluster systems while exploring the galaxy cluster population statistical properties, and the high resolution targeted observations that provide more information of the properties of individual galaxy clusters.

In chapter 2 a detailed description of the Sunyaev-Zel’dovich effect and its applications are provided, highlighting its unique tracer feature like its spectral signature and the ability to produce constraints on the galaxy cluster peculiar velocity. Also a review of the current state of observational work is provided.

Chapter 3 introduces the galaxy cluster sample analyzed in this work, a subset of the AzTEC Cluster Environment Survey (ACES). This sample covers a non-continuous area of _≃ 1sq. deg. The ACES observations are centered on the galaxy cluster position and

cover _≃ 6′ _{around it enabling the detection of a considerable fraction of the faint SMG}

population in the field. The population of SMGs, albeit a contaminant to the galaxy clus-ter emission, can be used to refine the knowledge on the impact of the cosmic infrared background to cosmological studies. An example of its applications is presented in sec-tion 3.2.2.

In my MSc. thesis I demonstrated that the AzTEC data reduction pipeline severely modified the surface brightness of resolved sources (Sánchez-Argüelles 2009). These modifications are introduced mainly on the atmosphere subtraction algorithm used in the AzTEC pipeline. In chapter 4 the implementation of a custom atmosphere subtraction method based on the Cottingham method is presented. This custom method is tested by a set of simulations of the expected angular flux distribution of the ICM. These simulations are useful to establish the properties of the two dimensional flux distribution recovered by the proposed method.

Chapter 5 presents the estimation of the physical properties of the ACES sample of galaxy clusters, taking special consideration to partially remove the contamination of emis-sion from radio galaxies and sub-millimeter galaxies.

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additions to the AzTEC reduction pipeline in the on-going Early Science observations of AzTEC on LMT. Moreover, the future work will be focused on the development of similar tools for the new generation of bolometer array currently being developed by the LMT instrumentation group.

Unless otherwise stated, this work assumes ΛCDM flat cosmology. The

cosmologi-cal parameters values from the Planck satellite + BAO + SDSS-II/SNLS3 supernovae are adopted (Planck Collaboration et al. 2016a), i.e. a dark matter densityΩm = 0.308±0.012,

the baryon densityΩb = 0.049±0.003, the dark energy densityΩΛ = 0.69±, the Hubble parameterH0 = 67.7±0.46kms−1Mpc−1and a CMB temperatureTCMB= 2.75K.

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Chapter 2 The Sunyaev-Zel’dovich Effect.

In the framework of the Big Bang theory, the universe originated in a hot, dense state which rapidly started to expand. In this scenario, after the primordial nucleosynthesis, the atomic nuclei and the available population of free electrons were tightly coupled to the radiation field via ionization equilibrium. As the expansion continued, the temperature decreased enough (T _≃10000₋3000°K) for the nuclei to recombine with the electrons. The corresponding emitted photons are then allowed to propagate freely through the uni-verse, generating a nearly isotropic radiation field known as the CMB. These physical conditions were originally described by Gamow and collaborators to explain the origin and abundance of atomic species (Alpher, Bethe, and Gamow 1948; Gamow 1948a,b). Later the CMB was accidentally detected by Penzias and Wilson as a uniform, isotropic, unpolarized, invariant radio noise excess (Penzias and Wilson 1965).

The analysis of CMB observations has become one of the fundamental foundations of modern cosmology, particularly since the detection of small deviations (or anisotropies) from a perfect black body spectrum measured by theCOBEsatellite (Mather et al. 1990;

Smoot et al. 1991). These small temperature anisotropies (∆T _≃ 10−4_{K) encode a vast} amount of cosmological information over a broad range of angular scales (Hu, Sugiyama, and Silk 1997).

The anisotropies can be separated into two categories based on the physical processes from which they originate. The primary anisotropies are result of the imprint of the acoustic oscillations introduced by the interplay between the compression due to the grav-itational attraction, caused by the peaks on the matter distribution, against the radiation pressure at the recombination epoch. The angular power spectrum of these anisotropies has been used to constrain the overall curvature of the universe, the matter and baryon energy density as well as the effective number of neutrino families.

In contrast thesecondary anisotropiesarise from the interaction of the CMB photons with the matter distribution in the line-of-sight of the observer. The origin of these ani-sotropies can be either by the gravitational redshift due to the constant growth of the LSS (known as the Integrated Sachs-Wolfe effect (Sachs and Wolfe 1967; Rees and Sciama 1968)) or by electromagnetic scattering with hot energetic plasma present at the reion-ization epoch (z _∼ 11₋13) (Hu and Sugiyama 1995; Trombetti and Burigana 2012) or

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the gravitational heated gas located in the most massive structures like galaxy groups and clusters (known as the Sunyaev-Zel’dovich effect).

The unique value of the CMB observations has motivated the development of several ground and space based experiments specifically designed to provide enough sensitivity and wavelength coverage over a wide range of angular scales. These features are necessary to remove the contribution of any astrophysical foregrounds (i.e. galactic dust and radio emission, dusty star forming galaxies, etc) and accurately measure the anisotropies.

Figure 2.1: All sky map of the temperature anisotropies as observed by the Planck satellite. This map is

the result of combining the information of both the high and low frequency instruments aboard Planck, the 9-year WMAP data between 23 and 94 GHz and all sky 408 MHz maps, the analysis of this multiwavelength information allows to remove the contribution of foregrounds like the galactic dust, free-free and synchrotron emissions.

In this context, an important milestone in the“precision cosmology era”was achieved

by the Wikilson Microwave Anisotropy Probe (WMAP) a space mission able to produce an all-sky map of the CMB anisotropies with an angular resolution of_≃0.2deg(Bennett et

al. 2003). WMAP constrained the angular power spectrum around the peak of the acoustic oscillations and provided a set of tight constraints on the baryon, cold dark matter and dark energy densities with an accuracy of _∼ 1.5% (Bennett et al. 2013; Hinshaw et al.

2013). More recently, these maps have been superseded by the observations of the Planck satellite Planck Collaboration et al. (2011a) by using an improved angular resolution_≃5' (see Figure 2.1), a broader wavelength coverage and enhanced polarization capabilities.

This chapter introduces the physics of the SZE effect focusing on its applications as a nearly redshift independent galaxy cluster tracer and total mass proxy. It also presents a brief result of the results and implications derived from the large area SZE surveys with arcminute angular resolutions and the advantages of arcsecond resolution follow up of

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2.1. Physics of the Sunyaev-Zel’dovich Effect

SZE detected cluster to provide a detailed insight into the cluster properties and derive improved constraints to the cluster mass and structure.

2.1 Physics of the Sunyaev-Zel’dovich Effect

At the ICM temperature most of the atoms are ionized, therefore it contains a large population of energetic free electrons(Ee≃8.6keV) . These electrons have enough energy

to interact with the photons of the CMB. The inverse Comptoninteraction is described by the equation:

ǫ= ǫ

′

1 + ǫ

mec2(1−cosφ12)

(2.1)

whereǫy ǫ′ _{are the energy of the electron before and after the interactions and} _φ

12 is the deflection angle for the CMB photon. Assuming that the photon energy is small and a non-relativistic electron population (ǫ_≪mec2 ≃510keV), the collision is elastic (ǫ→ǫ′)

and the Compton differential cross section can be used to simplify the calculation.

The photon frequency change in the observer’s reference frame is described by the equation:

v′ =v1 +βµ ′

1₋βµ (2.2)

wherev,v′ _{are the photon frequency before and after the interaction,}_µ₌_cos₍_φ₎_{, µ}′ ₌ cos(φ′₎ _with_φ _{being the scattering angle and the electron velocity is parametrized}

rela-tively to the speed of light ve = βc. Following Birkinshaw and Lancaster (2008), the

frequency change is described by the probability distribution:

P(s;β)ds=

Z

p(µ)dµ φ(µ′;µ)

dµ′ ds

ds (2.3)

whereφ(µ′_;_µ₎ _{is the photon scattering probability and}_s ₌ _log₍v′

v)is the photon

fre-quency shift. Assuming that the free electrons have a Maxwell distribution:

p(β)dβ = γ

5_β2_e_Θγ_dβ

ΘK2(Θ−1)

(2.4)

whereΘ = kbTe

mec2

is the normalized temperature andK2 is the second kind Bessel function of second order, then the probability of the Compton interaction is:

P(s) =

Z 1

βlow

pe(s)P(s;β)dβ (2.5)

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βlim =

e|s|₋₁

e|s|_{+ 1} (2.6)

The relatively low density of the ICM allows one to assume that the photon is scattered only once while crossing the galaxy clusters so the change in radiation intensity is:

∆I0(v) =

2h c2

Z ∞

−∞

P(s) v

3 0

ehv0/kTrad−1 −

v3

ehv/kTrad−1 !

ds (2.7)

wherev0 is the photon frequency before the interaction andI0 is the CMB black body intensity:

I0(v) =

2hv3

c2

ehv/kbTCMB₋₁−1 _(2.8)

The scattering probability can be further simplified by describing such scattering as a

diffusion process (Kompaneets 1956). This is known as the Kompaneetsapproximation,

and allows one to replace the scattering probability by the Kompaneets kernel (Sunyaev

1980; Bernstein and Dodelson 1990; Birkinshaw 1999):

PK(s) = 1 √

4πyexp

(s+ 3y)2

4y (2.9)

whereyis the Compton parameter:

y= σTkB

mec2

Z

neTedl (2.10)

with σT is the Thompson’s cross section, kB is the Boltzmann’s constant, me is the

electron mass, ne and Te are the electron number density and temperature respectively.

The Compton parameter is a measure of the gas pressure inside the ICM integrated along the line-of-sight.

2.1.1 The Thermal Sunyaev-Zel’dovich

TheKompaneets approximation allows to describe spectral dependence of the

fluctu-ation of the CMB mean intensity introduced by the hot electrons of the ICM. Using the

Kompaneetskernel on Equation 2.8 we can find the expressions:

∆I0(x) = ycI0CMBf(x) (2.11)

f(x) = x

4_ex

(ex₋₁₎2xcoth(x/2)−4 (2.12) where∆I0 is the change on the brightness relative to the average intensity of the CMB

ICMB

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0 200 400 600 800 1000

Frequency [GHz]

−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 ∆ ISZ E

[M

Jy/

sr]

Non Relativistic Relativistic

Thermal Sunyaev-Zeldovich Spectral Signature

f(x)

yc= 2. 00 × 10−4 Te= 20. 0keV yc= 1. 30 × 10−4 Te= 15. 0keV yc= 0. 75 × 10−4 Te= 10. 0keV yc= 0. 25 × 10−4 Te= 5. 0keV

210 215 220 225 230

Frequency −0.010 −0.0050.000 0.005 0.010 ∆

ItSZE

Relativistic Null Frequency Shift

Figure 2.2:The Thermal Sunyaev-Zel’dovich Fluctuations for a set of galaxy clusters with different central

Compton parameters y0 and electronic temperaturesTe. The unique spectral signature with a decrement

on frequencies ν ≤ 217GHz(1.4mm), a null effect atν = 217GHzand an increment atν ≥ 217GHz

provides an efficient technique to blindly detect Galaxy Clusters. The dashed lines represent the relativistic corrections from (Nozawa et al. 2000); this corrections are strongly dependent on theTe, where larger values

of the electronic temperature shift the null frequency of the SZE to larger frequencies.

x= hv

kBTCMB

(2.13)

This change in brightness is known as the Thermal Sunyaev-Zel’dovich (Sunyaev

and Zeldovich 1970, 1972) and it is the dominant contribution to the secondary CMB anisotropies at scales of a few arcminutes.

Equation 2.12 demonstrates the main advantages of Sunyaev-Zel’dovich observations. First the frequency dependence f(x) is unique compared to other astronomical sources.

The Sunyaev-Zel’dovich shows as a decrement in brightness for wavelengthsλ_≥1.4mm,

a null detection of the effect at 1.4mm and an increment at shorter wavelengths λ _≤

1.4mm. This spectral signature is shown in Figure 2.2.

Second, there is not an explicit dependence in the surface brightness fluctuation with the redshift independent. More over the SZE provides access to the thermodynamic properties of the cluster through the Compton parameter. These thermodynamic properties can be used as a proxy for the total mass, the gas mass and the total energy content of the galaxy clusters (see Section 2.2.1).

In the case of observations at 1.1mm (ν _≃ 270 GHz) the expected central flux of a galaxy cluster with a projected central Compton parameteryc = 1×10−4 can be written

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F1.1mm=y0ICMBf(x1.1mm)ΘFWHM (2.14) whereΘFWHMis the telescope angular resolution. As an example, SZE experiments

ob-serving with angular resolutionsΘFWHM_≃1' the expected flux isF1.1mm ≃7.0mJybeam−1.

Relativistic Corrections to the Thermal Sunyaev-Zel’dovich

For electron temperaturesTe ≥ 10keV, the Kompaneets kernel is not longer accurate

since relativistic effects introduce a significant asymmetry in the photon shift probability. Therefore for the hottest galaxy clusters a relativistic correction is necessary. This correc-tion is calculated by either a series expansion or numerical integracorrec-tion ofP(s)on Equation 2.5. In the literature it is common to use the series expansion approach by introducing a small perturbation to Equation 2.12

∆I(x) = yg(x) (2.15)

∆I(x) = yf(x)(1 +δrel)I0

δrel = n

X

i=1

ΘiYi(x) +R(x, Θ) (2.16)

where x is the normalized frequency and Θ is the normalized temperature, R(x, Θ)

is the residual term of the series expansion. The expression for the Yi(x)functions can

be obtained from Challinor and Lasenby (1998), Itoh, Kohyama, and Nozawa (1998) and Nozawa et al. (2000).

Intra Cluster Medium Model

To establish a relationship between the SZE observable quantity (i.e. the Compton parameter) and the cluster physical properties, it is necessary to assume a model for the distribution of the ICM. The current generation of the SZE studies consider two families of models to describe the pressure profile of the galaxy clusters as a function of the angular distance from the cluster center. The isothermalβ-model, which was introduced in section 1.3, has the advantage that it can be analytically integrated. The line-of-sight integrated SZE Compton parameter for the isothermalβ-model is:

yβ(θ) = kBσT

mec2

Z

l

Tenβe(θ)dl (2.17)

yβ(θ) = y0 1 +

θ2

c

!1−₂3β

(2.18)

where θ = r/Da(z)is the angular distance from the cluster center and Da(z) is the

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dependent on the cluster central density, the electron temperature and the ICM spatial extent (Birkinshaw and Lancaster 2008):

y0 =√π

kBTe

mec2

ne(0)σTθcΓ(3β/2−1/2)

Da(z)Γ(3β/2)

(2.19)

whereΓ(x) = (x₋1)!is the Gamma function. This model can not be used to describe

clusters with a cool core, i.e. galaxy clusters where the cluster core cooling time is less than the Hubble time (tcool < 7.7h

1/2

70 Gyr, Hudson et al. 2010). For cool core galaxy clusters a double isothermal β-model has been used to describe their ICM angular distribution Bonamente et al. 2006; Vikhlinin et al. 2009:

yβ(θ) = y0 



f 1 +

θ2

c1

!1−₂3β

+ (1₋f) 1 + θ

2

θ2

c2

!1−₂3β 



 (2.20)

where0< f <1.

On the other hand, the Navarro-Frenk-White(NFW,Navarro, Frenk, and White (1995)) models have been used to fit the mass spatial distribution of the dark matter halos in cosmo-logical N-body simulations. A particular subtype of these models has been more recently proposed as an “Universal Pressure Profile” for the ICM (Nagai, Kravtsov, and Vikhlinin 2007; Arnaud et al. 2010):

PGNFW(x) = P0

xγ_{(1 +}_xα₎(β−γ)/α (2.21)

x = c500

θ θs

(2.22)

θs = θ500/c500 (2.23)

wherec500 is the concentration factor atr500andα, β, γ are parameters that control the logarithmic slope of the profiles in the regionsθ_≪θs, θ ∼θs, θ ≫θs.

2.1.2 Kinetic Sunyaev-Zel’dovich Effect

An additional fluctuation is generated due to the bulk velocity of the ICM relative to the rest frame defined by the CMB. This generates a bipolar anisotropy for the photon energy in the reference frame of the ICM:

∆I(x) =₋τe

vp

c

x4_ex

(ex₋₁₎2I0 (2.24)

where vp is the projection of the cluster peculiar velocity in the line of sight of the

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τe =

Z

neσTdl (2.25)

The Kinetic Sunyaev-Zel’dovich Effect (kSZE) has the same spectral shape of the CMB black body spectrum with a peak approximately where the tSZE is null (atλ _≃ 1.4mm). As a caveat the kSZE is more difficult to detect since usually its amplitude is one order of magnitude smaller than the tSZE for massive clusters (see Figure 2.3). However it is possible to make a joint estimation of both the tSZE and the kSZE if several multiwave-length measurements are carried out. An alternative for direct detection is to target less massive galaxy clusters or galaxy groups, where the tSZE is not significant. This systems will require a projected peculiar velocity ofvp ≥1000kms−1.

0 200 400 600 800 1000

Frequency [GHz]

−0.04 −0.03 −0.02 −0.01 0.00 0.01 0.02 0.03 0.04 0.05

∆

ISZE

[M

Jy/

sr]

Thermal + Kinetic Sunyaev-Zeldovich Effect

vp= 0. 0km/s vp= − 4000. 0km/s vp= 4000. 0km/s

Figure 2.3: Expected fluctuation for the combined Thermal and Kinetic SZE Effect. The solid lines

repre-sent the expected change in the CMB brightness caused by the combination of the tSZE and the kSZE. The dashed line represent the fluctuation of the kSZE only. The kSZE introduces a small frequency shift on the location of the tSZE null, therefore for low temperature galaxy clusters Te ≤ 5keVthe peculiar velocity

could be measured on this frequency directly.

At the time of this work there is only evidence of a joint detection of the tSZE and kSZE in the Galaxy Cluster MACS J0717.5+3745 (Sayers et al. 2013a), a system undergoing a major merger. By analyzing data at 140 and 268GHz both the tSZE and kSZE are fitted to a model consistent with avp = 3450±900kms−1.

The relative motion of the LSS has been statistically detected using the kSZE in the ACT and Planck maps (Hand et al. 2012; Planck Collaboration et al. 2016c) using the mean pairwise velocity of the distribution of luminous galaxies. The main assumption in these studies is that the distribution of luminous galaxies in optical wavelengths are a tracer of the cluster overdensities.

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2.2. Applications of the Thermal Sunyaev-Zel’dovich Effect

2.2 Applications of the Thermal Sunyaev-Zel’dovich

Ef-fect

As described in section 2.1.1, one of the straightforward applications of the tSZE is the blind detection of massive galaxy clusters at any redshift. This is possible due to its three regime spectral signature which provide a significant contrast when compared to the typical power law spectral energy distributions used to characterize the emission of dusty star forming and radio galaxies respectively. The tSZE can be used to estimate the total mass of the dark matter halo under some simplifying assumptions. As an example if hydrodynamical equilibrium and an isothermal gas distribution are assumed then equation 1.22 reduces to:

M(r) =₋ r

2_k

BTe

ρ(r)µmpG

dρ(r)

dr (2.26)

where the mass density profile is derived from equation 1.24:

ρ(r) = 3µmP

4π3 ne(0) 1 +

r2

c

!−3₂β

= ρ(0) 1 + r

2

r2

c

!−3₂β

(2.27)

and the total mass inside a sphere of radiusris:

M(r) = 3βkBTe

µmPG

r2

r2₊_r2

c

(2.28)

Notice that for the isothermalβ-model the mass is independent from the central electron densityne(0). This clearly demonstrates that the estimated total mass from X-ray and SZE

surveys depend on the model used to describe the electron density and temperature profile.

2.2.1 Scaling Relations

As stated before, galaxy clusters are thought to form in a hierarchical, gravitational driven process. This formation mechanism allows to predict the correlation between the galaxy cluster observable quantities (total luminosity, optical galaxy richness, integrated pressure) and the cluster total mass (Kaiser 1986; Bryan and Norman 1998). These cor-relations are known as the scaling cor-relations. As an example, from Equation 2.19, we can derive the following a power law relationship between the central Compton parameter and the total mass:

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y0 ∝ ne(0)Ter (2.29) ∝ fgasMTTer−2

∝ fgasMTTeE2(z)

whereE(z) =

ΩR(1 +z)4+ ΩM(1 +z)3 + ΩK(1 +z)2+ ΩΛ 1/2

. A desirable prop-erty of a scaling relation is to provide a low intrinsic scatter proxy for the galaxy cluster mass regardless if the cluster is in hydrostatic equilibrium or not. As an example, Bona-mente et al. (2008) studies the following scaling relations for a sample of 38 massive galaxy clusters:

Y D_A2 _∝ fgasT_e5/2E(z) (2.30)

Y D_A2 _∝ fgasM

5/2

T E

2/3₍_z₎ _(2.31)

Y D2

A ∝ fgas−2/3Mgas5/3E2/3(z) (2.32)

whereDAis the angular distance andY is the solid angle integrated Compton

parame-ter:

Y = 2π

Z θ200

0

y(θ)θdθ (2.33)

Simulations have shown that the scaling relations based onY have a smaller intrinsic scatter and are less sensitive to cluster merger events and other ICM physical processes (da Silva et al. 2004; Motl et al. 2005; Wik et al. 2008).

This scaling relations can be calibrated for low redshift systems, where independent measurements of the total mass and the electron temperature can be derived from optical lensing and X-Ray observations (Bonamente et al. 2008; Marrone et al. 2009; Planck Collaboration et al. 2011c). After calibration they can be used to estimate the mass of high-z galaxy clusters detected by the SZE only.

2.2.2 The Hubble Constant

H

0

Both the SZE and X-Ray observations trace the hot ICM, although their dependence on the electron temperature and the electron density are different. The cluster depth in the line-of-sight Lcan be calculated from the ratio between the SZE and X-Ray surface brightness, assuming a uniform electron density and temperature in the ICM on Equations 2.10 and 1.23:

L_∝ ∆ISZE SX

Λ(Te)

ne

(2.34)

Assuming that the ICM distribution is spherical thenL =DA(z)and the Hubble

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2.3. Sunyaev-Zel’dovich in the era of Large Surveys

H0 =

1 1 +zc

1

DA

Z zc 0

cdz

E(z) (2.35)

wherezc is the cluster redshift. It is important to notice the dependence onE(z)which

implies thatH0 derived by this method is not completely independent from the cosmolog-ical model and it is constraint to a set ofΩmandΩΛvalues.

The values of the Hubble constant derived from samples of a few tens of galaxy clusters show that these estimations are dominated by systematic errors associated with the non-spherical distribution of the ICM. Reese et al. (2002) found aH0 = 68+4+13-4-18 kms−1Mpc

−1 (statistic+systematic error) using a sample of 18 clusters between 0.14 _≤ z _≤ 0.78and Bonamente et al. (2006) found a H0 = 76.9+3.9+10.0-3.9-8.0 kms−1Mpc−1 using a sample of 38

galaxy clusters up toz = 0.89.

2.2.3 Baryon Fraction

Structure formation models and numerical simulation show that the ratio of baryons and dark matter on rich, massive galaxy clusters must be proportional to the cosmological value fg ∝ Ωb/Ωm. However non-linear processes like star formation, ICM cooling and

active galactic nuclei feedback can modify this ration. Nevertheless, when the correct as-sumptions for the cosmological model are made the gas fraction is not expected to depend on redshift. Therefore, if averaged over a large sample of massive galaxy clusters over a wide redshift range, it is possible to place constraints on the cosmological parameters.

Assuming an isothermalβ-model the gas mass inside a sphere of radiusrcan be found by integration of the density profile:

Mgas= 4πµmP ne(0)DA3(z)

Z r/DA 0

1 + θ

2

θ2

c

!−3β/2

θ2dθ (2.36)

and the gas fraction can be obtained dividing by equation 2.28. LaRoque et al. (2006) derived the gas fraction for a sample of 38 massive clusters in a redshift range of 0.14 _≤

z _≤0.89using both X-ray and radio SZE decrement observations. They found an average value of fg = 0.11±0.003 for X-ray observations and afg = 0.12±0.005for the SZE

observations. Despite the slightly larger uncertainty in the SZE results they prove to be not sensitive to the cluster structure.

2.3 Sunyaev-Zel’dovich in the era of Large Surveys

Given the importance of galaxy clusters as cosmological tracers, the most recent all-sky and wide area (&200sq.deg.) CMB anisotropies surveys have incorporated into their de-sign the wavelength coverage and sensitivity to detect the de-signal of the SZE. Experiments like ACT (Fowler et al. 2007), SPT (Carlstrom et al. 2011) and Planck (Planck

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significant fraction (_≃ 30%) of newly discovered systems (Hasselfield et al. 2013; Bleem et al. 2015; Planck Collaboration et al. 2015a).

These hundreds of galaxy clusters with no previous optical or X-ray detections demon-strated the capabilities of the tSZE observations to locate clusters over a wider redshift range, with new detections up to z = 1.5. Figure 2.4 show the coverage of these surveys in the mass-redshift space.

Figure 2.4: Mass versus Redshift coverage for galaxy clusters detected in Large Sunyaev-Zel’dovich

sur-veys (Planck Collaboration et al. 2015a). These graphs demonstrate the advantages of SZE sursur-veys for cluster identification. Notice the SZE observations are more sensitive to high redshift systems compared to the X-ray surveys. Also notice the weak dependence on the mass detection threshold with redshift.

The discovery of massive clusters like ACT-CL J0102-4915 (“El Gordo”) M200 =

(2.16_±0.32) _×1015_h−1

70M⊙ at z = 0.87 (Menanteau et al. 2013) and SPT-CL

J2106-5844M200 = (1.27±0.21)×1015h−701M⊙atz = 1.18(Foley et al. 2011) set a challenge

to the models of structure formation under a ΛCDM paradigm, since they are located in

the MT −z plane close to the maximum growth of structure with cosmic time given the

opposite contributions of gravitational force driven by dark matter and dark energy driven cosmic expansion. Figure 2.5 shows the 95% confidence exclusion lines for ACT and SPT surveys.

On the other hand, the analysis of CMB primordial anisotropies power spectrum is has been used by ground and space based telescopes to constraint the cosmological parameters. The secondary anisotropies, those which are generated by the interaction of the CMB photons with the matter distribution, are used to restrict the confidence regions of these parameters.

The Large SZE surveys are able to estimate the power spectrum of the SZE since the virial mass of a rich galaxy cluster is very similar to the mass perturbation enclosed inside a sphere of radiusR = 8h−1_M_pc_{on a flat Universe (White et al. 1993). The amplitude of the} SZE power spectrum is particularly sensitive to the CMB power spectrum normalization parameter (Sehgal et al. 2010; Shaw et al. 2010):

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2.3. Sunyaev-Zel’dovich in the era of Large Surveys

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Redshift 0 1 2 3 4 5 M200 [ 10 15 h − 1 70 M⊙ ] ACT-CL J0102-4915 SPT-CL J2106-5844 SPT-CL J0205-5829

ΛCDM Galaxy Cluster Exclusion Lines

ACT 755 deg2

ACT+SPT 2800 deg2

Full Sky

Figure 2.5:ΛCDM Exclusion Lines for ACT and SPT Surveys extracted from the formulas fitted in

(Mor-tonson, Hu, and Huterer 2011). These lines set a 95% Confidence Limit for the detection of a Galaxy Cluster given the SZE Survey. A single detection of a Galaxy Cluster of massM200at a given redshift above these

lines will overrule theΛCDM as a valid cosmological model. The most massive cluster to date found at

z >1using the SZE, SPT-CL J0205-5829 (Stalder et al. 2013) atz= 1.32is shown as reference.

ASZ ∝

h

0.71

1.8

σ8

0.8

8.3

Ωb 0.044

2.8

(2.37)

whereASZ is the maximum amplitude of the SZE power spectrum and σ8 is the nor-malization parameter defined in Equation 1.1.The joint measurements of the tSZE+kSZE power spectrum done by ACT (Fowler et al. 2010; Das et al. 2011; Calabrese et al. 2013), SPT (Reichardt et al. 2012) and Planck (Planck Collaboration et al. 2015b) yield a σ8 = 0.831±0.013

It is important to notice that the detection of the SZE power spectrum is quite challeng-ing, since it requires a careful characterization of the potential sources of contamination. As an example, the population of radio and dusty star formation galaxies dominates the observed power at ℓ & 2000 (see Figure 2.6). Therefore, to extract the SZE power

spec-trum it is necessary to model the different contributions to the observed power and its correlations and incorporate multiwavelength observations.

In addition the SZE angular power spectrum can be used to constrain the overall prop-erties of the ICM physics, Shaw et al. (2010) finds that an increase of the galaxy feed-back efficiency parameter can shift the position of the peak amplitude of the SZE power spectrum to lower multipole values. In contrast, an increase in the non-thermal pressure component can increase the maximum amplitude of the observed power.

(40)

Figure 2.6:Estimation of the Sunyaev-Zel’dovich Effect Power Spectrum done by ACT (Fowler et al. 2010) using at600< ℓ <8000. The power due to the SZEASZand the Poisson component of point sourcesAp

start to dominate over the primordial anisotropies atℓ >3000, this work finds a upper limit ofσ8SZ <0.8.

To the date the constraints onASZ have improved significantly (see Das et al. (2011) and Reichardt et al.

(2012)

2.3.1 Advantages of intermediate and high resolution millimeter

wave-length Cluster observations

The most important challenge for these surveys is to accurately relate the tSZE ob-servable to the galaxy cluster mass. The optimal angular resolution used to search for SZE signalsθFWHM &1′ also increases the amount of contamination from radio or dusty galaxies and significantly smears out the signals from merging substructures within the cluster.

Simulations have shown that in order to reduce the uncertainties in the estimation of cosmological parameters to a few percent level the combination of SZE power spectrum constraints and accurate mass measurements within a broad redshift distribution are nec-essary (Majumdar and Mohr 2004).

The targeted ground based SZE observations on telescopes like the Caltech Submillime-ter Observatory (CSO) (Sayers et al. 2012; Czakon et al. 2015), the Sunyaev-Zel’dovich Array (Culverhouse et al. 2010; Reese et al. 2012), the Green Bank Telescope (GBT) (Ma-son et al. 2010; Korngut et al. 2011; Young et al. 2015) and the Arcminute Microkelvin

Description of the physical properties of galaxy clusters using sunyaev-zel’dovich observations in ACES.

Contents

Resumen

Abstract

Agradecimientos

A mi familia, que siempre me ha apoyado sin importar el camino que siga,

brindán-dome del amor y cariño que me ha ayudado a conseguir mis metas. A mi asesor, Dr.

David H. Hughes, por la oportunidad de pertenecer a este proyecto, por las largas

pláticas en las que aprendí tanto, por su confianza y paciencia. A los miembros de

mi jurado de examen, Dra. Anna Lia Longinotti, Dr. Daniel Rosa González, Dr. Iván

Rodríguez Montoya, Dr. Yair Krongold Herrera y Dr. Miguel Chávez Dagostino por

los comentarios que ayudaron a mejorar este trabajo. A mis compa´neros y amigos,

por hacer más especial el tiempo que he pasado en el instituto. Al Instituto

Na-cional de Astrofísica, Óptica y Electrónica por el apoyo brindado en la realización

del Doctorado. Al Consejo Nacional de Ciencia y Tecnología (CONACYT) por la

Chapter 1

Introduction.

1.1

Galaxy Clusters as Cosmological Probes

1.1.1

Galaxy Cluster Mass Function

1.2

The Galaxy Cluster Angular Distribution

1.3

Multiwavelength Observations of Galaxy Clusters

1.4

Overview of this Thesis

Chapter 2

The Sunyaev-Zel’dovich Effect.

2.1

Physics of the Sunyaev-Zel’dovich Effect

2.1.1

The Thermal Sunyaev-Zel’dovich

Frequency [GHz]

[M

Jy/

sr]

Thermal Sunyaev-Zeldovich Spectral Signature

Relativistic Null Frequency Shift

2.1.2

Kinetic Sunyaev-Zel’dovich Effect

Frequency [GHz]

[M

Jy/

sr]

Thermal + Kinetic Sunyaev-Zeldovich Effect

2.2

Applications of the Thermal Sunyaev-Zel’dovich

Ef-fect

2.2.1

Scaling Relations

2.2.2

The Hubble Constant

H

2.2.3

Baryon Fraction

2.3

Sunyaev-Zel’dovich in the era of Large Surveys

2.3.1

Advantages of intermediate and high resolution millimeter

wave-length Cluster observations