Thermal Sunyaev-Zeldovich Effect Research Articles

Anomalies in the low CMB multipoles and extended foregrounds

We discuss how an extended foreground of the cosmic microwave background (CMB) can account for the anomalies in the low multipoles of the CMB anisotropies. The distortion needed to account for the anomalies is consistent with a cold spot with the spatial geometry of the local supercluster (LSC) and a temperature quadrupole of order $\ensuremath{\Delta}{T}_{2}^{2}\ensuremath{\approx}50\text{ }\text{ }\ensuremath{\mu}{K}^{2}$. If this hypothetic foreground is subtracted from the CMB data, the amplitude of the quadrupole ($\ensuremath{\ell}=2$) is substantially increased, and the statistically improbable alignment of the quadrupole with the octopole ($\ensuremath{\ell}=3$) is substantially weakened, increasing dramatically the likelihood of the cleaned maps. By placing the foreground on random locations and then computing the likelihood of the cleaned maps we can estimate the most likely place for this foreground. Although the 1-year WMAP data clearly points the location of this hypothetical foreground to the LSC or its specular image (i.e., the vicinity of the poles of the cosmic dipole axis), the three-year data seems to point to these locations as well as the north ecliptic pole. We show that this is consistent with the symmetries of the cosmic quadrupole. We also discuss a possible mechanism that could have generated this foreground: the thermal Sunyaev-Zeldovich effect caused by hot electrons in the LSC. We argue that the temperature and density of the hot gas which are necessary to generate such an effect, though in the upper end of the expected range of values, are marginally consistent with present observations of the X-ray background of spectral distortions of the CMB.

The non-Gaussian cold spot in Wilkinson Microwave Anisotropy Probe: significance, morphology and foreground contribution

The non-Gaussian cold spot in the 1-yr Wilkinson Microwave Anisotropy Probe (WMAP) data, described by Vielva et al. and Cruz et al., is analysed in detail in the present paper. First of all, we perform a more rigorous calculation of the significance of the non-zero kurtosis detected in WMAP maps by Vielva et al. in wavelet space, mainly generated by the Spot. We confirm the robustness of that detection, since the probability of obtaining this deviation by chance is 0.69 per cent. Afterwards, the morphology of the Spot is studied by applying Spherical Mexican Hat Wavelets with different ellipticities. The shape of the Spot is found to be almost circular. Finally, we discuss if the observed non-Gaussianity in wavelet space can arise from bad subtracted foreground residues in the WMAP maps. We show that the flat frequency dependence of the Spot cannot be explained by a thermal Sunyaev–Zeldovich effect. Based on our present knowledge of Galactic foreground emissions, we conclude that the significance of our detection is not affected by Galactic residues in the region of the Spot. Considering different Galactic foreground estimates, the probability of finding such a big cold spot in Gaussian simulations is always below 1 per cent.

Challenges for Precision Cosmology with X‐Ray and Sunyaev‐Zeldovich Effect Gas Mass Measurements of Galaxy Clusters

We critically analyze the measurement of galaxy cluster gas masses, which is central to cosmological studies that rely on the galaxy cluster gas mass fraction. Using synthetic observations of numerically simulated clusters viewed through their X-ray emission and thermal Sunyaev-Zeldovich effect (SZE), we reduce the observations to obtain measurements of the cluster gas mass. We quantify the possible sources of uncertainty and systematic bias associated with the common simplifying assumptions used in reducing real cluster observations, including isothermality and hydrostatic equilibrium. We find that intrinsic variations in clusters limit the precision of observational gas mass estimation to ~10% to 1 σ confidence, excluding instrumental effects. Gas mass estimates show surprisingly little trending in the scatter as a function of cluster redshift. For the full cluster sample, methods that use SZE profiles out to roughly the virial radius are the simplest, most accurate, and unbiased way to estimate cluster mass. X-ray methods are systematically more precise mass estimators than are SZE methods if merger and cool-core systems are removed, but slightly overestimate (5%-10%) the cluster gas mass on average. We find that cool-core clusters in our samples are particularly poor candidates for observational mass estimation, even when excluding emission from the core region. The effects of cooling in the cluster gas alter the radial profile of the X-ray and SZE surface brightness even outside the cool-core region. Finally, we find that methods using a universal temperature profile estimate cluster masses to higher precision than those assuming isothermality.

Brillouin scattering and the CMB

Brillouin scattering of photons off the density fluctuations in a fluid is potentially important for cosmology. We derive the Brillouin spectral distortion of blackbody radiation, and discuss the possible implications for the cosmic microwave background. The thermal Sunyaev-Zeldovich effect is slightly modified by Brillouin distortion, but only at very long wavelengths.

Prospects for ACT: Simulations, power spectrum, and non-Gaussian analysis

A new generation of instruments will reveal the microwave sky at high resolution. We focus on one of these, the Atacama Cosmology Telescope, which probes scales 1000<l<10,000, where both primary and secondary anisotropies are important. Including gravitational lensing, thermal and kinetic Sunyaev–Zeldovich (SZ) effects, and extragalactic point sources, we simulate the telescope’s observations of the CMB in three channels, then extract the power spectra of these components in a multifrequency analysis. We present results for various cases, differing in assumed knowledge of the contaminating point sources. We find that both radio and infrared point sources are important, but can be effectively eliminated from the power spectrum given three (or more) channels and a good understanding of their frequency dependence. However, improper treatment of the scatter in the point source frequency dependence relation may introduce a large systematic bias. Even if all thermal SZ and point source effects are eliminated, the kinetic SZ effect remains and corrupts measurements of the primordial slope and amplitude on small scales. We discuss the non-Gaussianity of the one-point probability distribution function as a way to constrain the kinetic SZ effect, and we develop a method for distinguishing this effect from the CMB in a window where they overlap. This method provides an independent constraint on the variance of the CMB in that window and is complementary to the power spectrum analysis.

The Integrated Sunyaev-Zeldovich Effect as a Superior Method for Measuring the Mass of Clusters of Galaxies

We investigate empirical scaling relations between the thermal Sunyaev-Zeldovich effect (SZE) and cluster mass in simulated clusters of galaxies. The simulated clusters have been compiled from four different samples that differ only in their assumed baryonic physics. We show that the strength of the thermal SZE integrated over a significant fraction of the virialized region of the clusters is relatively insensitive to the detailed heating and cooling processes in the cores of clusters, by demonstrating that the derived scaling relations are nearly identical among the four cluster samples considered. For our synthetic images, the central Comptonization parameter shows significant boosting during transient merging events, but the integrated SZE appears to be relatively insensitive to these events. Most importantly, the integrated SZE closely tracks the underlying cluster mass. Observations through the thermal SZE allow a strikingly accurate mass estimation from relatively simple measurements that do not require either parametric modeling or geometric deprojection and thus avoid assumptions regarding the physics of the intracluster medium or the symmetry of the cluster. This result offers significant promise for precision cosmology using clusters of galaxies.

The temperature of the intergalactic medium and the Comptonyparameter

The thermal Sunyaev-Zeldovich (SZ) effect directly probes the thermal energy of the Universe. Its precision modelling and future high-accuracy measurements will provide a powerful way to constrain the thermal history of the Universe. In this paper, we focus on the precision modelling of the gas density weighted temperature T g and the mean SZ Compton y parameter. We run high-resolution adiabatic hydrodynamic simulations adopting the WMAP cosmology to study the temperature and density distribution of the intergalactic medium (IGM). To quantify possible simulation limitations, we run n = -1, - 2 self-similar simulations. Our analytical model on Tg is based on energy conservation and matter clustering and has no free parameter. Combining both simulations and analytical models thus provides the precision modelling of Tg and y. We find that the simulated temperature probability distribution function and T g shows good convergence. For the WMAP cosmology, our highest-resolution simulation (1024 3 cells, 100 Mpc h -1 box size) reliably simulates T g with better than 10 per cent accuracy for z > 0.5. Toward z = 0, the simulation mass-resolution effect becomes stronger and causes the simulated T g to be slightly underestimated (at z = 0, ∼20 per cent underestimated). Since y is mainly contributed by the IGM at z? 0.5, this simulation effect on y is no larger than ∼10 per cent. Furthermore, our analytical model is capable of correcting this artefact. It passes all tests of self-similar simulations and WMAP simulations and is able to predict Tg and y to several per cent accuracy. For a low matter density ACDM cosmology, the present Tg is 0.32 (σ 8 /0.84) 3.05-0.15Ω m(Ω m /0.268) 1.28-0.2σ 8 keV, which accounts for 10 -8 of the critical cosmological density and 0.024 per cent of the cosmic microwave background (CMB) energy. The mean y parameter is 2.6× 10 -6 (s 8 /0.84) 4.1-2Ω m(Ω m /0.268) 1.28-0.2σ 8. The current upper limit of y < 1.5 x 10 -5 measured by FIRAS has already ruled out combinations of high σ 8 ? 1.1 and high Ω m ? 0.5.

Measurement of the gravitational potential evolution from the cross-correlation betweenWMAPand the APM Galaxy Survey

Models with late time cosmic acceleration, such as the Lambda-dominated CDM model, predict a freeze out for the growth of linear gravitational potential at moderate redshift z<1, what can be observed as temperature anisotropies in the CMB: the so called integrated Sachs-Wolfe (ISW) effect. We present a direct measurement of the ISW effect based on the angular cross-correlation function, w_{TG}, of CMB temperature anisotropies and dark-matter fluctuations traced by galaxies. We cross-correlate the first-year WMAP data in combination with the APM Galaxy survey. On the largest scales, theta = 4-10 deg, we detect a non-vanishing cross-correlation at 98.8 % significance level, with a 1-sigma error of w_{TG} = 0.35 +/- 0.14 microK, which favors large values of Omega_Lambda \simeq 0.8 for flat FRW models. On smaller scales, theta < 1deg, the correlations disappear. This is contrary to what would be expected from the ISW effect, but the absence of correlations may be simply explained if the ISW signal was being cancelled by anti-correlations arising from the thermal Sunyaev-Zeldovich (SZ) effect.

Cross-correlation of the cosmic microwave background with the 2MASS galaxy survey: Signatures of dark energy, hot gas, and point sources

We cross-correlate the cosmic microwave background temperature anisotropies observed by the Wilkinson Microwave Anisotropy Probe (WMAP) with the projected distribution of extended sources in the Two Micron All Sky Survey (2MASS). By modeling the theoretical expectation for this signal, we extract the signatures of dark energy [integrated Sachs-Wolfe effect (ISW)], hot gas [thermal Sunyaev-Zeldovich (SZ) effect], and microwave point sources in the cross-correlation. Our strongest signal is the thermal SZ, at the $3.1--3.7\ensuremath{\sigma}$ level, which is consistent with the theoretical prediction based on observations of x-ray clusters. We also see the ISW signal at the $2.5\ensuremath{\sigma}$ level, which is consistent with the expected value for the concordance $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology, and is an independent signature of the presence of dark energy in the Universe. Finally, we see the signature of microwave point sources at the $2.7\ensuremath{\sigma}$ level.

Magnetic Sunyaev-Zel'dovich Effect in Galaxy Clusters

This Letter explores the influences of intracluster magnetic fields (1 μG) submerged in the hot electron gas on the classic Sunyaev-Zel'dovich effect (SZE) and on the thermal bremsstrahlung in X-ray emissions. As the Larmor frequency is much higher than all collision frequencies, the presence of a magnetic field may lead to an anisotropic velocity distribution of hot electrons. For the two-temperature relativistic Maxwell-Boltzmann distribution, we compute modifications to the classical thermal SZE. Intracluster magnetic fields tend to enhance the SZE with steeper radial variations, which bear important consequences for cluster-based estimates of cosmological parameters. By applying the magnetic SZE theory to spectral observations of SZE and Chandra X-ray emissions from the galaxy cluster A2163, a ~30-40 μG central core magnetic field B0 is predicted. For the SZE and Chandra X-ray spectral observations of the Coma Cluster, our theoretical analysis is also consistent with an observationally inferred B0 10 μG. As the magnetic SZE is redshift (z) independent, this mechanism might offer a potentially important and unique way of probing intracluster magnetic fields in the expanding universe.

Relativistic corrections to the Sunyaev-Zeldovich effect for extremely hot clusters of galaxies

We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The numerical table is provided for the ranges 0.002 ≤ θ e ≤ 0.100 and 0 ≤ X < 20, where θ e ≡ k B T e /m e c 2 , X ≡ hω/k B T 0 , T e is the electron temperature, ω is the angular frequency of the photon and T 0 is the temperature of the cosmic microwave background radiation. We also present an accurate analytic fitting formula that reproduces the numerical results with high precision.

The Effects of Relativistic Corrections on Cosmological Parameter Estimations from Sunyaev‐Zeldovich Effect Cluster Surveys

Sunyaev-Zeldovich effect (SZE) cluster surveys are anticipated to yield tight constraints on cosmological parameters, such as the equation of state of dark energy. In this paper, we study the effect of relativistic corrections of the thermal SZE on the cluster number counts expected from a cosmological model and thus, assuming that other cosmological parameters are known to high accuracies, on the determination of the w-parameter and σ8 from an SZE cluster survey, where w = p/ρ (with p the pressure and ρ the density of dark energy) and σ8 is the rms of the extrapolated linear density fluctuation smoothed over 8 Mpc h-1. For the purpose of illustrating the effects of relativistic corrections, our analyses mainly focus on ν = 353 GHz and Slim = 30 mJy, where ν and Slim are the observing frequency and the flux limit of a survey, respectively. These observing parameters are relevant to the Planck survey. It is found that from two measurable quantities, the total number of SZE clusters and the number of clusters with redshift z ≥ 0.5, σ8 and w can be determined to a level of ±1% and ±8%, respectively, with 1 σ uncertainties from a survey of 10,000 deg2. Relativistic effects are important in determining the central values of σ8 and w. If we choose the two quantities calculated relativistically from the flat cosmological model with σ8 = 0.8284 and w = -0.75 as input, the derived σ8 and w would be 0.819 and -0.81, respectively, if relativistic effects are wrongly neglected. The location of the resulting σ8 and w in the σ8-w plane is outside the 3 σ region around the real central σ8 and w.

The Sunyaev‐Zeldovich Effect Signature of Excess Entropy in Distant, Massive Clusters

Studies of cluster X-ray scaling relations have led to suggestions that nongravitational processes, e.g., radiative cooling and/or "preheating," have significantly modified the entropy of the intracluster medium (ICM). For the first time, we test this hypothesis through a comparison of predicted thermal Sunyaev-Zeldovich (SZ) effect scaling relations with available data from the literature. One of the relations that we explore, in principle, depends solely on SZ effect observations, thus offering an X-ray-independent probe of the ICM. A detailed comparison of the theoretical relations with the largest compilation of high-z SZ effect data to date indicates that the presence of an entropy floor is favored by the data. Furthermore, the inferred level of that floor, K0 ≳ 300 keV cm2, is comparable to that found in studies of X-ray scaling relations of nearby massive clusters. Thus, we find no evidence for significant evolution of the entropy floor out to z ~ 0.7. We further demonstrate that the high-quality data to be obtained from the upcoming Sunyaev-Zeldovich Array (SZA) and the (soon to be) upgraded Owens Valley Radio Observatory (OVRO) array will open powerful new windows into the properties of the ICM. Specifically, the new measurements will allow for accurate measurements of the ICM entropy for even the most distant galaxy clusters.

Cluster Sunyaev‐Zeldovich Effect Scaling Relations

X-ray observations of an in nearby groups and clusters of galaxies offer evidence that important nongravitational processes, such as radiative cooling and/or preheating, have strongly influenced the evolution of the intracluster medium (ICM). We examine how the presence of an entropy floor modifies the thermal Sunyaev-Zeldovich (SZ) effect. A detailed analysis of scaling relations between X-ray and SZ effect observables and also between the two primary SZ effect observables is presented. We find that relationships between the central Compton parameter and the temperature or mass of a cluster are extremely sensitive to the presence of an entropy floor. The same is true for correlations between the integrated Compton parameter and the X-ray luminosity or the central Compton parameter. In fact, if the entropy floor is as high as inferred in recent analyses of X-ray data, a comparison of these correlations with both current and future SZ effect observations should show a clear signature of this excess entropy. Moreover, because the SZ effect is redshift independent, the relations can potentially be used to track the evolution of the cluster gas and possibly discriminate between the possible sources of the excess entropy. To facilitate comparisons with observations, we provide analytic fits to these scaling relations.

A convolution integral representation of the thermal Sunyaev Zel dovich effect

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution integrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this description of the SZE related to light scattering in optically thin plasmas are discussed.

The Gravitational Potential Reconstruction from Peculiar Velocity and Weak Lensing Measurements

We present an analytic method for rapidly forecasting the accuracy of the gravitational potential reconstruction from measurements of radial peculiar velocities of every galaxy cluster with M > Mth in solid angle θ2 and over a redshift range zmin < z < zmax. These radial velocities can be determined from measurements of the kinetic and thermal Sunyaev-Zeldovich effects. For a shallow survey with 0.2 < z < 0.4, one mode of the potential (on length scales 60 Mpc) can be reconstructed for every approximately eight cluster velocity determinations. Deeper surveys require measurements of more clusters per a signal-to-noise ratio greater than 1. Accuracy is limited by the undersampling noise because of the nonobservation of a large fraction of mass that is not in galaxy clusters. Determining the potential will allow us to study in detail the relationship between galaxies and their surrounding large-scale density fields over a wide range of redshifts and to test the gravitational instability paradigm on very large scales. Observation of weak lensing by large-scale structure is complementary since lensing is sensitive to the tangential modes that do not affect the velocity.

Modification of cluster radio halo appearance by the thermal Sunyaev-Zeldovich effect

We discuss the consequences of the spectral and morphological modification of galaxy cluster radio halos due to the Sunyaev-Zeldovich (SZ) effect for the interpretation of existing and upcoming high frequency radio observations. Likely these modifications have affected the interpretation of the existing Coma cluster radio data. The radio halo emission visible at low ( 10 GHz) frequencies completely over-compensated by the thermal SZ decrement. Thus, the total radio emission of a galaxy cluster goes through zero (in comparison to the constant cosmic microwave background (CMB) emission) at a frequency of several GHz. Since the radio halo brightness has a narrow radial profile compared to the SZ decrement, a central emission region is surrounded by a decrement within the intermediate frequency range of several GHz. The size of this emission regions shrinks with increasing frequency until the decrement dominates everywhere in the cluster.

Radio Point Sources and the Thermal Sunyaev‐Zeldovich Power Spectrum

Radio point sources are strongly correlated with clusters of galaxies, so a significant fraction of the thermal Sunyaev-Zeldovich (SZ) effect signal could be affected by point-source contamination. Based on empirical estimates of the radio galaxy population, it is shown that the rms temperature fluctuations of the thermal SZ effect could be underestimated by as much as 30% at an observing frequency of 30 GHz at l ≳ 1000. The effect is larger at higher multipoles. If the recent report of excess power at small angular scales is to be explained by the thermal SZ effect, then radio point sources at an observing frequency of 30 GHz must be a surprisingly weak contaminant of the SZ effect for low-mass clusters.

Kinetic Sunyaev‐Zeldovich Effect from Halo Rotation

We discuss the kinetic Sunyaev-Zeldovich (SZ) contribution to cosmic microwave background (CMB) temperature fluctuations due to the coherent rotational velocity component of electrons within halos. This effect produces a distinct dipole-like temperature distribution across the cluster and provides a promising way to measure the angular momentum distribution of gas inside clusters. Information obtained from such a measurement may provide new insights to the origin and evolution of angular momentum in hierarchical structure formation theory. For typical well-relaxed clusters of mass a few times 1014 M☉, the peak fluctuation is of the order of a few μK, depending on the rotational velocity and the inclination angle of the rotational axis. For clusters that had undergone a recent merger, the contribution to temperature fluctuations could be even larger. This dipole signature is similar to the one produced by lensed CMB toward galaxy clusters, although the lensing contribution spans a larger angular extent than the one due to rotational scattering, since the former depends on the gradient of the cluster potential. Since the lensing contributions toward clusters are aligned with the large-scale CMB gradient, when higher resolution observations toward clusters are combined with a wide-field CMB map, these two effects can be separated. An additional, but less important, source of confusion is the dipolar pattern produced by the moving-lens effect involving, again, the gradient of the cluster potential and the transverse velocity. The angular power spectrum of temperature anisotropies produced by the halo rotation is expected to be smaller than those due to the thermal SZ and peculiar-velocity kinetic SZ effects.

Radiative processes in the intracluster plasma

We present useful analytic fitting formulae for the study of the radiative processes which take place in the hot intracluster plasma (the plasma which exists in the clusters of galaxies). The first is for the frequency-integrated emissivity of the relativistic thermal bremsstrahlung. The Gaunt factor for the relativistic thermal bremsstrahlung as a function of the ionic charge Z j , the electron temperature T e , and the photon frequency ω has been recently calculated by us and its analytic fitting formula has been presented. In this paper we will integrate this Gaunt factor over the photon frequency ω and express the results by accurate analytic fitting formulae. These results will be useful when one wishes to evaluate the total amount of energy emitted by the hot intracluster plasma as well as other hot plasmas that exist in supernova remnants. The present results for the frequency-integrated emissivity of the thermal bremsstrahlung generally have accuracy of the order of 0.1%, thus making the present results the most accurate to date that calculate the thermal bremsstrahlung due to electron-ion scattering. The present accurate results will be especially useful for the analysis of the precision data taken by the Chandra X-Ray Observatory and XMM-Newton . The second analytic fitting formula that we will present in this paper is for the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The thermal Sunyaev-Zeldovich effect for clusters of galaxies has been recently calculated with high precision by the present authors as well as by other groups. We have, in particular, presented an analytic fitting formula for this effect. In this paper we will present an analytic fitting formula which has still higher accuracy. The present fitting formula will be particularly suited for the forthcoming measurements of the kinematical Sunyaev-Zeldovich effect such as the BOLOCAM project that will be carried out in the crossover frequency region where the thermal Sunyaev-Zeldovich signal changes from negative to positive sign.