arXiv subjects

Matt Hilton

Publications and source records attributed to Matt Hilton.

At least 109 records · Page 6Linked to original sources

arXiv2013

The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data

We present constraints on cosmological and astrophysical parameters from high-resolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power ell^2 C_ell/2pi of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 +\- 1.4 muK^2 at ell=3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 muK^2. Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be Neff=2.79 +\- 0.56, in agreement with the canonical value of Neff=3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be Sigma m_nu < 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Yp = 0.225 +\- 0.034, and measure no variation in the fine structure constant alpha since recombination, with alpha/alpha0 = 1.004 +/- 0.005. We also find no evidence for any running of the scalar spectral index, dns/dlnk = -0.004 +\- 0.012.

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arXiv2013

The Atacama Cosmology Telescope: the stellar content of galaxy clusters selected using the Sunyaev-Zel'dovich effect

We present a first measurement of the stellar mass component of galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect, using 3.6 um and 4.5 um photometry from the Spitzer Space Telescope. Our sample consists of 14 clusters detected by the Atacama Cosmology Telescope (ACT), which span the redshift range 0.27 < z < 1.07 (median z = 0.50), and have dynamical mass measurements, accurate to about 30 per cent, with median M500 = 6.9 x 10^{14} MSun. We measure the 3.6 um and 4.5 um galaxy luminosity functions, finding the characteristic magnitude (m*) and faint-end slope (alpha) to be similar to those for IR-selected cluster samples. We perform the first measurements of the scaling of SZ-observables (Y500 and y0) with both brightest cluster galaxy (BCG) stellar mass and total cluster stellar mass (M500star). We find a significant correlation between BCG stellar mass and Y500 (E(z)^{-2/3} DA^2 Y500 ~ M*^{1.2 +/- 0.6}), although we are not able to obtain a strong constraint on the slope of the relation due to the small sample size. Additionally, we obtain E(z)^{-2/3} DA^2 Y500 ~ M500star^{1.0 +/- 0.6} for the scaling with total stellar mass. The mass fraction in stars spans the range 0.006-0.034, with the second ranked cluster in terms of dynamical mass (ACT-CL J0237-4939) having an unusually low total stellar mass and the lowest stellar mass fraction. For the five clusters with gas mass measurements available in the literature, we see no evidence for a shortfall of baryons relative to the cosmic mean value.

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arXiv2013

The Atacama Cosmology Telescope: Sunyaev-Zel'dovich Selected Galaxy Clusters at 148 GHz from Three Seasons of Data

[Abridged] We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zel'dovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey of 504 square degrees on the celestial equator. A subsample of 48 clusters within the 270 square degree region overlapping SDSS Stripe 82 is estimated to be 90% complete for M_500c > 4.5e14 Msun and 0.15 < z < 0.8. While matched filters are used to detect the clusters, the sample is studied further through a "Profile Based Amplitude Analysis" using a single filter at a fixed θ_500 = 5.9' angular scale. This new approach takes advantage of the "Universal Pressure Profile" (UPP) to fix the relationship between the cluster characteristic size (R_500) and the integrated Compton parameter (Y_500). The UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters is used to obtain cosmological constraints. We first confirm that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements based on galaxy velocity dispersions. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding σ_8 = 0.829 \pm 0.024 and Ω_m = 0.292 \pm 0.025. The results include marginalization over a 15% bias in dynamical mass relative to the true halo mass. In an extension to LCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7+BAO+Hubble constant measurements to constrain Σm_ν< 0.29 eV (95% C. L.).

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arXiv2013

The Atacama Cosmology Telescope: Dynamical Masses and Scaling Relations for a Sample of Massive Sunyaev-Zel'dovich Effect Selected Galaxy Clusters

We present the first dynamical mass estimates and scaling relations for a sample of Sunyaev-Zel'dovich effect (SZE) selected galaxy clusters. The sample consists of 16 massive clusters detected with the Atacama Cosmology Telescope (ACT) over a 455 sq. deg. area of the southern sky. Deep multi-object spectroscopic observations were taken to secure intermediate-resolution (R~700-800) spectra and redshifts for ~60 member galaxies on average per cluster. The dynamical masses M_200c of the clusters have been calculated using simulation-based scaling relations between velocity dispersion and mass. The sample has a median redshift z=0.50 and a median mass M_200c~12e14 Msun/h70 with a lower limit M_200c~6e14 Msun/h70, consistent with the expectations for the ACT southern sky survey. These masses are compared to the ACT SZE properties of the sample, specifically, the match-filtered central SZE amplitude y, the central Compton parameter y0, and the integrated Compton signal Y_200c, which we use to derive SZE-Mass scaling relations. All SZE estimators correlate with dynamical mass with low intrinsic scatter (<~20%), in agreement with numerical simulations. We explore the effects of various systematic effects on these scaling relations, including the correlation between observables and the influence of dynamically disturbed clusters. Using the 3-dimensional information available, we divide the sample into relaxed and disturbed clusters and find that ~50% of the clusters are disturbed. There are hints that disturbed systems might bias the scaling relations but given the current sample sizes these differences are not significant; further studies including more clusters are required to assess the impact of these clusters on the scaling relations.

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arXiv2013

The Atacama Cosmology Telescope: Relation Between Galaxy Cluster Optical Richness and Sunyaev-Zel'dovich Effect

We present the measured Sunyaev-Zel'dovich (SZ) flux from 474 optically-selected MaxBCG clusters that fall within the Atacama Cosmology Telescope (ACT) Equatorial survey region. The ACT Equatorial region used in this analysis covers 510 square degrees and overlaps Stripe 82 of the Sloan Digital Sky Survey. We also present the measured SZ flux stacked on 52 X-ray-selected MCXC clusters that fall within the ACT Equatorial region and an ACT Southern survey region covering 455 square degrees. We find that the measured SZ flux from the X-ray-selected clusters is consistent with expectations. However, we find that the measured SZ flux from the optically-selected clusters is both significantly lower than expectations and lower than the recovered SZ flux measured by the Planck satellite. Since we find a lower recovered SZ signal than Planck, we investigate the possibility that there is a significant offset between the optically-selected brightest cluster galaxies (BCGs) and the SZ centers, to which ACT is more sensitive due to its finer resolution. Such offsets can arise due to either an intrinsic physical separation between the BCG and the center of the gas concentration or from misidentification of the cluster BCG. We find that the entire discrepancy for both ACT and Planck can be explained by assuming that the BCGs are offset from the SZ maxima with a uniform random distribution between 0 and 1.5 Mpc. Such large offsets between gas peaks and BCGs for optically-selected cluster samples seem unlikely given that we find the physical separation between BCGs and X-ray peaks for an X-ray-selected subsample of MaxBCG clusters to have a much narrower distribution that peaks within 0.2 Mpc. It is possible that other effects are lowering the ACT and Planck signals by the same amount, with offsets between BCGs and SZ peaks explaining the remaining difference between measurements. (Abridged)

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arXiv2013

The Atacama Cosmology Telescope: Temperature and Gravitational Lensing Power Spectrum Measurements from Three Seasons of Data

We present the temperature power spectra of the cosmic microwave background (CMB) derived from the three seasons of data from the Atacama Cosmology Telescope (ACT) at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. We detect and correct for contamination due to the Galactic cirrus in our equatorial maps. We present the results of a number of tests for possible systematic error and conclude that any effects are not significant compared to the statistical errors we quote. Where they overlap, we cross-correlate the ACT and the South Pole Telescope (SPT) maps and show they are consistent. The measurements of higher-order peaks in the CMB power spectrum provide an additional test of the Lambda CDM cosmological model, and help constrain extensions beyond the standard model. The small angular scale power spectrum also provides constraining power on the Sunyaev-Zel'dovich effects and extragalactic foregrounds. We also present a measurement of the CMB gravitational lensing convergence power spectrum at 4.6-sigma detection significance.

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arXiv2013

The Atacama Cosmology Telescope: Physical Properties of Sunyaev-Zel'dovich Effect Clusters on the Celestial Equator

We present the optical and X-ray properties of 68 galaxy clusters selected via the Sunyaev-Zel'dovich Effect at 148 GHz by the Atacama Cosmology Telescope (ACT). Our sample, from an area of 504 square degrees centered on the celestial equator, is divided into two regions. The main region uses 270 square degrees of the ACT survey that overlaps with the co-added ugriz imaging from the Sloan Digital Sky Survey (SDSS) over Stripe 82 plus additional near-infrared pointed observations with the Apache Point Observatory 3.5-meter telescope. We confirm a total of 49 clusters to z~1.3, of which 22 (all at z>0.55) are new discoveries. For the second region the regular-depth SDSS imaging allows us to confirm 19 more clusters up to z~0.7, of which 10 systems are new. We present the optical richness, photometric redshifts, and separation between the SZ position and the brightest cluster galaxy (BCG). We find no significant offset between the cluster SZ centroid and BCG location and a weak correlation between optical richness and SZ-derived mass. We also present X-ray fluxes and luminosities from the ROSAT All Sky Survey which confirm that this is a massive sample. One of the newly discovered clusters, ACT-CL J0044.4+0113 at z=1.1 (photometric), has an integrated XMM-Newton X-ray temperature of kT_x=7.9+/-1.0 keV and combined mass of M_200a=8.2(-2.5,+3.3)x10^14 M_sun/h70 placing it among the most massive and X-ray-hot clusters known at redshifts beyond z=1. We also highlight the optically-rich cluster ACT-CL J2327.4-0204 (RCS2 2327) at z=0.705 (spectroscopic) as the most significant detection of the whole equatorial sample with a Chandra-derived mass of M_200a=1.9(-0.4,+0.6)x10^15 M_sun/h70, comparable to some of the most massive known clusters like "El Gordo" and the Bullet Cluster.

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arXiv2012

The Atacama Cosmology Telescope: A Measurement of the Thermal Sunyaev-Zel'dovich Effect Using the Skewness of the CMB Temperature Distribution

We present a detection of the unnormalized skewness induced by the thermal Sunyaev-Zel'dovich (tSZ) effect in filtered Atacama Cosmology Telescope (ACT) 148 GHz cosmic microwave background temperature maps. Contamination due to infrared and radio sources is minimized by template subtraction of resolved sources and by constructing a mask using outlying values in the 218 GHz (tSZ-null) ACT maps. We measure = -31 +- 6 μK^3 (measurement error only) or +- 14 μK^3 (including cosmic variance error) in the filtered ACT data, a 5-sigma detection. We show that the skewness is a sensitive probe of sigma_8, and use analytic calculations and tSZ simulations to obtain cosmological constraints from this measurement. From this signal alone we infer a value of sigma_8= 0.79 +0.03 -0.03 (68 % C.L.) +0.06 -0.06 (95 % C.L.). Our results demonstrate that measurements of non-Gaussianity can be a useful method for characterizing the tSZ effect and extracting the underlying cosmological information.

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arXiv2012

Evolution in cluster cores since z~1

A large fraction of the stellar mass in galaxy clusters is thought to be contained in the diffuse low surface brightness intracluster light (ICL). Being bound to the gravitational potential of the cluster rather than any individual galaxy, the ICL contains much information about the evolution of its host cluster and the interactions between the galaxies within. However due its low surface brightness it is notoriously difficult to study. We present the first detection and measurement of the flux contained in the ICL at z~1. We find that the fraction of the total cluster light contained in the ICL may have increased by factors of 2-4 since z~1, in contrast to recent findings for the lack of mass and scale size evolution found for brightest cluster galaxies. Our results suggest that late time buildup in cluster cores may occur more through stripping than merging and we discuss the implications of our results for hierarchical simulations.

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arXiv2012

Subaru weak-lensing measurement of a z = 0.81 cluster discovered by the Atacama Cosmology Telescope Survey

We present a Subaru weak lensing measurement of ACT-CL J0022.2-0036, one of the most luminous, high-redshift (z=0.81) Sunyaev-Zel'dovich (SZ) clusters discovered in the 268 deg^2 equatorial region survey of the Atacama Cosmology Telescope. For the weak lensing analysis using i'-band images, we use a model-fitting (Gauss-Laguerre shapelet) method to measure shapes of galaxy images, where we fit galaxy images in different exposures simultaneously to obtain best-fit ellipticities taking into account the different PSFs in each exposure. We also take into account the astrometric distortion effect on galaxy images by performing the model fitting in the world coordinate system. To select background galaxies behind the cluster at z=0.81, we use photometric redshift (photo-z) estimates for every galaxy derived from the co-added images of multi-passband Br'i'z'Y, with PSF matching/homogenization. After a photo-z cut for background galaxy selection, we detect the tangential weak lensing distortion signal with a total signal-to-noise ratio of about 3.7. By fitting a Navarro-Frenk-White model to the measured shear profile, we find the cluster mass to be M_200\barρ_m = [7.5^+3.2_-2.8(stat.)^+1.3_-0.6(sys.)] x 10^14 M_\odot/h. The weak lensing-derived mass is consistent with previous mass estimates based on the SZ observation, with assumptions of hydrostatic equilibrium and virial theorem, as well as with scaling relations between SZ signal and mass derived from weak lensing, X-ray, and velocity dispersion, within the measurement errors. We also show that the existence of ACT-CL J0022.2-0036 at z=0.81 is consistent with the cluster abundance prediction of the Λ-dominated cold dark matter structure formation model. We thus demonstrate the capability of Subaru-type ground-based images for studying weak lensing of high-redshift clusters.

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arXiv2012

The Atacama Cosmology Telescope: Data Characterization and Map Making

We present a description of the data reduction and mapmaking pipeline used for the 2008 observing season of the Atacama Cosmology Telescope (ACT). The data presented here at 148 GHz represent 12% of the 90 TB collected by ACT from 2007 to 2010. In 2008 we observed for 136 days, producing a total of 1423 hours of data (11 TB for the 148 GHz band only), with a daily average of 10.5 hours of observation. From these, 1085 hours were devoted to a 850 deg^2 stripe (11.2 hours by 9.1 deg) centered on a declination of -52.7 deg, while 175 hours were devoted to a 280 deg^2 stripe (4.5 hours by 4.8 deg) centered at the celestial equator. We discuss sources of statistical and systematic noise, calibration, telescope pointing, and data selection. Out of 1260 survey hours and 1024 detectors per array, 816 hours and 593 effective detectors remain after data selection for this frequency band, yielding a 38% survey efficiency. The total sensitivity in 2008, determined from the noise level between 5 Hz and 20 Hz in the time-ordered data stream (TOD), is 32 micro-Kelvin sqrt{s} in CMB units. Atmospheric brightness fluctuations constitute the main contaminant in the data and dominate the detector noise covariance at low frequencies in the TOD. The maps were made by solving the least-squares problem using the Preconditioned Conjugate Gradient method, incorporating the details of the detector and noise correlations. Cross-correlation with WMAP sky maps, as well as analysis from simulations, reveal that our maps are unbiased at multipoles ell > 300. This paper accompanies the public release of the 148 GHz southern stripe maps from 2008. The techniques described here will be applied to future maps and data releases.

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arXiv2012

Evidence of Galaxy Cluster Motions with the Kinematic Sunyaev-Zel'dovich Effect

Using high-resolution microwave sky maps made by the Atacama Cosmology Telescope, we for the first time present strong evidence for motions of galaxy clusters and groups via microwave background temperature distortions due to the kinematic Sunyaev-Zel'dovich effect. Galaxy clusters are identified by their constituent luminous galaxies observed by the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. We measure the mean pairwise momentum of clusters, with a probability of the signal being due to random errors of 0.002, and the signal is consistent with the growth of cosmic structure in the standard model of cosmology.

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arXiv2012

The XMM Cluster Survey: The Stellar Mass Assembly of Fossil Galaxies

This paper presents both the result of a search for fossil systems (FSs) within the XMM Cluster Survey and the Sloan Digital Sky Survey and the results of a study of the stellar mass assembly and stellar populations of their fossil galaxies. In total, 17 groups and clusters are identified at z < 0.25 with large magnitude gaps between the first and fourth brightest galaxies. All the information necessary to classify these systems as fossils is provided. For both groups and clusters, the total and fractional luminosity of the brightest galaxy is positively correlated with the magnitude gap. The brightest galaxies in FSs (called fossil galaxies) have stellar populations and star formation histories which are similar to normal brightest cluster galaxies (BCGs). However, at fixed group/cluster mass, the stellar masses of the fossil galaxies are larger compared to normal BCGs, a fact that holds true over a wide range of group/cluster masses. Moreover, the fossil galaxies are found to contain a significant fraction of the total optical luminosity of the group/cluster within 0.5R200, as much as 85%, compared to the non-fossils, which can have as little as 10%. Our results suggest that FSs formed early and in the highest density regions of the universe and that fossil galaxies represent the end products of galaxy mergers in groups and clusters. The online FS catalog can be found at http://www.astro.ljmu.ac.uk/~xcs/Harrison2012/XCSFSCat.html.

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arXiv2012

The XMM Cluster Survey: Evidence for energy injection at high redshift from evolution of the X-ray luminosity-temperature relation

We measure the evolution of the X-ray luminosity-temperature (L_X-T) relation since z~1.5 using a sample of 211 serendipitously detected galaxy clusters with spectroscopic redshifts drawn from the XMM Cluster Survey first data release (XCS-DR1). This is the first study spanning this redshift range using a single, large, homogeneous cluster sample. Using an orthogonal regression technique, we find no evidence for evolution in the slope or intrinsic scatter of the relation since z~1.5, finding both to be consistent with previous measurements at z~0.1. However, the normalisation is seen to evolve negatively with respect to the self-similar expectation: we find E(z)^{-1} L_X = 10^{44.67 +/- 0.09} (T/5)^{3.04 +/- 0.16} (1+z)^{-1.5 +/- 0.5}, which is within 2 sigma of the zero evolution case. We see milder, but still negative, evolution with respect to self-similar when using a bisector regression technique. We compare our results to numerical simulations, where we fit simulated cluster samples using the same methods used on the XCS data. Our data favour models in which the majority of the excess entropy required to explain the slope of the L_X-T relation is injected at high redshift. Simulations in which AGN feedback is implemented using prescriptions from current semi-analytic galaxy formation models predict positive evolution of the normalisation, and differ from our data at more than 5 sigma. This suggests that more efficient feedback at high redshift may be needed in these models.

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arXiv2012

Measurement of the intracluster light at z ~ 1

A significant fraction of the total photospheric light in nearby galaxy clusters is thought to be contained within the diffuse intracluster light (ICL), which extends 100s of kpc from cluster cores. The study of the ICL can reveal details of the evolutionary histories and processes occurring within galaxy clusters, however since it has a very low surface brightness it is often difficult to detect. We present here the first measurements of the ICL as a fraction of total cluster light at z \sim 1 using deep J-band (1.2 μm) imaging from HAWK-I on the VLT. We investigate the ICL in 6 X-ray selected galaxy clusters at 0.8< z <1.2 and find that the ICL below isophotes μ(J) = 22 mag/arcsec2 constitutes 1-4% of the total cluster light within a radius R500. This is broadly consistent with simulations of the ICL at a similar redshift and when compared to nearby observations suggests that the fraction of the total cluster light that is in the ICL has increased by a factor 2 - 4 since z\sim1. We also find the fraction of the total cluster light contained within the Brightest Cluster Galaxy (BCG) to be 2.0-6.3% at these redshifts, which in 5 out of 6 cases is larger than the fraction of the ICL component, in contrast to results from nearby clusters. This suggests that the evolution in cluster cores involves substantial stripping activity at late times, in addition to the early build up of the BCG stellar mass through merging. The presence of significant amounts of stellar light at large radii from these BCGs may help towards solving the recent disagreement between the semi-analytic model predictions of BCG mass growth (e.g. De Lucia & Blaziot, 2007) and the observed large masses and scale sizes reported for BCGs at high redshift.

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arXiv2012

The XMM Cluster Survey: The interplay between the brightest cluster galaxy and the intra-cluster medium via AGN feedback

Using a sample of 123 X-ray clusters and groups drawn from the XMM-Cluster Survey first data release, we investigate the interplay between the brightest cluster galaxy (BCG), its black hole, and the intra-cluster/group medium (ICM). It appears that for groups and clusters with a BCG likely to host significant AGN feedback, gas cooling dominates in those with Tx > 2 keV while AGN feedback dominates below. This may be understood through the sub-unity exponent found in the scaling relation we derive between the BCG mass and cluster mass over the halo mass range 10^13 < M500 < 10^15Msol and the lack of correlation between radio luminosity and cluster mass, such that BCG AGN in groups can have relatively more energetic influence on the ICM. The Lx - Tx relation for systems with the most massive BCGs, or those with BCGs co-located with the peak of the ICM emission, is steeper than that for those with the least massive and most offset, which instead follows self-similarity. This is evidence that a combination of central gas cooling and powerful, well fuelled AGN causes the departure of the ICM from pure gravitational heating, with the steepened relation crossing self-similarity at Tx = 2 keV. Importantly, regardless of their black hole mass, BCGs are more likely to host radio-loud AGN if they are in a massive cluster (Tx > 2 keV) and again co-located with an effective fuel supply of dense, cooling gas. This demonstrates that the most massive black holes appear to know more about their host cluster than they do about their host galaxy. The results lead us to propose a physically motivated, empirical definition of 'cluster' and 'group', delineated at 2 keV.

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arXiv2012

The XMM Cluster Survey: Predicted overlap with the Planck Cluster Catalogue

We present a list of 15 clusters of galaxies, serendipitously detected by the XMM Cluster Survey (XCS), that have a high probability of detection by the Planck satellite. Three of them already appear in the Planck Early Sunyaev-Zel'dovich (ESZ) catalogue. The estimation of the Planck detection probability assumes the flat Lambda cold dark matter (LambdaCDM) cosmology most compatible with 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) data. It takes into account the XCS selection function and Planck sensitivity, as well as the covariance of the cluster X-ray luminosity, temperature, and integrated comptonization parameter, as a function of cluster mass and redshift, determined by the Millennium Gas Simulations. We also characterize the properties of the galaxy clusters in the final data release of the XCS that we expect Planck will have detected by the end of its extended mission. Finally, we briefly discuss possible joint applications of the XCS and Planck data.

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arXiv2012

The Atacama Cosmology Telescope: Detection of Sunyaev-Zel'dovich Decrement in Groups and Clusters Associated with Luminous Red Galaxies

We present a detection of the Sunyaev-Zel'dovich (SZ) decrement associated with the Luminous Red Galaxy (LRG) sample of the Sloan Digital Sky Survey. The SZ data come from 148 GHz maps of the equatorial region made by the Atacama Cosmology Telescope (ACT). The LRG sample is divided by luminosity into four bins, and estimates for the central Sunyaev-Zel'dovich temperature decrement are calculated through a stacking process. We detect and account for a bias of the SZ signal due to weak radio sources. We use numerical simulations to relate the observed decrement to Y200 and clustering properties to relate the galaxy luminosity bins to mass. We also use a relation between brightest cluster galaxy luminosity and cluster mass based on stacked gravitational lensing measurements to estimate the characteristic halo masses. The masses are found to be around 1e14 M_sun.

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