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R. Armstrong

Publications and source records attributed to R. Armstrong.

At least 37 records · Page 2Linked to original sources

Cosmology constraints from shear peak statistics in Dark Energy Survey Science Verification data

Shear peak statistics has gained a lot of attention recently as a practical alternative to the two point statistics for constraining cosmological parameters. We perform a shear peak statistics analysis of the Dark Energy Survey (DES) Science Verification (SV) data, using weak gravitational lensing measurements from a 139 deg$^2$ field. We measure the abundance of peaks identified in aperture mass maps, as a function of their signal-to-noise ratio, in the signal-to-noise range $0<\mathcal S / \mathcal N<4$. To predict the peak counts as a function of cosmological parameters we use a suite of $N$-body simulations spanning 158 models with varying $Ω_{\rm m}$ and $σ_8$, fixing $w = -1$, $Ω_{\rm b} = 0.04$, $h = 0.7$ and $n_s=1$, to which we have applied the DES SV mask and redshift distribution. In our fiducial analysis we measure $σ_{8}(Ω_{\rm m}/0.3)^{0.6}=0.77 \pm 0.07$, after marginalising over the shear multiplicative bias and the error on the mean redshift of the galaxy sample. We introduce models of intrinsic alignments, blending, and source contamination by cluster members. These models indicate that peaks with $\mathcal S / \mathcal N>4$ would require significant corrections, which is why we do not include them in our analysis. We compare our results to the cosmological constraints from the two point analysis on the SV field and find them to be in good agreement in both the central value and its uncertainty. We discuss prospects for future peak statistics analysis with upcoming DES data.

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A Dark Energy Camera Search for an Optical Counterpart to the First Advanced LIGO Gravitational Wave Event GW150914

We report initial results of a deep search for an optical counterpart to the gravitational wave event GW150914, the first trigger from the Advanced LIGO gravitational wave detectors. We used the Dark Energy Camera (DECam) to image a 102 deg$^2$ area, corresponding to 38% of the initial trigger high-probability sky region and to 11% of the revised high-probability region. We observed in i and z bands at 4-5, 7, and 24 days after the trigger. The median $5σ$ point-source limiting magnitudes of our search images are i=22.5 and z=21.8 mag. We processed the images through a difference-imaging pipeline using templates from pre-existing Dark Energy Survey data and publicly available DECam data. Due to missing template observations and other losses, our effective search area subtends 40 deg$^{2}$, corresponding to 12% total probability in the initial map and 3% of the final map. In this area, we search for objects that decline significantly between days 4-5 and day 7, and are undetectable by day 24, finding none to typical magnitude limits of i= 21.5,21.1,20.1 for object colors (i-z)=1,0,-1, respectively. Our search demonstrates the feasibility of a dedicated search program with DECam and bodes well for future research in this emerging field.

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CMB lensing tomography with the DES Science Verification galaxies

We measure the cross-correlation between the galaxy density in the Dark Energy Survey (DES) Science Verification data and the lensing of the cosmic microwave background (CMB) as reconstructed with the Planck satellite and the South Pole Telescope (SPT). When using the DES main galaxy sample over the full redshift range $0.2 < z < 1.2$, a cross-correlation signal is detected at $6 σ$ and $4σ$ with SPT and Planck respectively. We then divide the DES galaxies into five photometric redshift bins, finding significant ($>$$2 σ$) detections in all bins. Comparing to the fiducial Planck cosmology, we find the redshift evolution of the signal matches expectations, although the amplitude is consistently lower than predicted across redshift bins. We test for possible systematics that could affect our result and find no evidence for significant contamination. Finally, we demonstrate how these measurements can be used to constrain the growth of structure across cosmic time. We find the data are fit by a model in which the amplitude of structure in the $z<1.2$ universe is $0.73 \pm 0.16$ times as large as predicted in the LCDM Planck cosmology, a $1.7σ$ deviation.

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Weak lensing by galaxy troughs in DES Science Verification data

We measure the weak lensing shear around galaxy troughs, i.e. the radial alignment of background galaxies relative to underdensities in projections of the foreground galaxy field over a wide range of redshift in Science Verification data from the Dark Energy Survey. Our detection of the shear signal is highly significant (10 to 15$σ$ for the smallest angular scales) for troughs with the redshift range z in [0.2,0.5] of the projected galaxy field and angular diameters of 10 arcmin...1°. These measurements probe the connection between the galaxy, matter density, and convergence fields. By assuming galaxies are biased tracers of the matter density with Poissonian noise, we find agreement of our measurements with predictions in a fiducial Lambda cold dark matter model. The prediction for the lensing signal on large trough scales is virtually independent of the details of the underlying model for the connection of galaxies and matter. Our comparison of the shear around troughs with that around cylinders with large galaxy counts is consistent with a symmetry between galaxy and matter over- and underdensities. In addition, we measure the two-point angular correlation of troughs with galaxies which, in contrast to the lensing signal, is sensitive to galaxy bias on all scales. The lensing signal of troughs and their clustering with galaxies is therefore a promising probe of the statistical properties of matter underdensities and their connection to the galaxy field.

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Redshift distributions of galaxies in the DES Science Verification shear catalogue and implications for weak lensing

We present photometric redshift estimates for galaxies used in the weak lensing analysis of the Dark Energy Survey Science Verification (DES SV) data. Four model- or machine learning-based photometric redshift methods -- ANNZ2, BPZ calibrated against BCC-Ufig simulations, SkyNet, and TPZ -- are analysed. For training, calibration, and testing of these methods, we construct a catalogue of spectroscopically confirmed galaxies matched against DES SV data. The performance of the methods is evaluated against the matched spectroscopic catalogue, focusing on metrics relevant for weak lensing analyses, with additional validation against COSMOS photo-zs. From the galaxies in the DES SV shear catalogue, which have mean redshift $0.72\pm0.01$ over the range $0.3<z<1.3$, we construct three tomographic bins with means of $z=\{0.45, 0.67, 1.00\}$. These bins each have systematic uncertainties $δz \lesssim 0.05$ in the mean of the fiducial SkyNet photo-z $n(z)$. We propagate the errors in the redshift distributions through to their impact on cosmological parameters estimated with cosmic shear, and find that they cause shifts in the value of $σ_8$ of approx. 3%. This shift is within the one sigma statistical errors on $σ_8$ for the DES SV shear catalog. We further study the potential impact of systematic differences on the critical surface density, $Σ_{\mathrm{crit}}$, finding levels of bias safely less than the statistical power of DES SV data. We recommend a final Gaussian prior for the photo-z bias in the mean of $n(z)$ of width $0.05$ for each of the three tomographic bins, and show that this is a sufficient bias model for the corresponding cosmology analysis.

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Wide-Field Lensing Mass Maps from DES Science Verification Data: Methodology and Detailed Analysis

Weak gravitational lensing allows one to reconstruct the spatial distribution of the projected mass density across the sky. These "mass maps" provide a powerful tool for studying cosmology as they probe both luminous and dark matter. In this paper, we present a weak lensing mass map reconstructed from shear measurements in a 139 sq. deg area from the Dark Energy Survey (DES) Science Verification (SV) data. We compare the distribution of mass with that of the foreground distribution of galaxies and clusters. The overdensities in the reconstructed map correlate well with the distribution of optically detected clusters. We demonstrate that candidate superclusters and voids along the line of sight can be identified, exploiting the tight scatter of the cluster photometric redshifts. We cross-correlate the mass map with a foreground magnitude-limited galaxy sample from the same data. Our measurement gives results consistent with mock catalogs from N-body simulations that include the primary sources of statistical uncertainties in the galaxy, lensing, and photo-z catalogs. The statistical significance of the cross-correlation is at the 6.8-sigma level with 20 arcminute smoothing. A major goal of this study is to investigate systematic effects arising from a variety of sources, including PSF and photo-z uncertainties. We make maps derived from twenty variables that may characterize systematics and find the principal components. We find that the contribution of systematics to the lensing mass maps is generally within measurement uncertainties. In this work, we analyze less than 3% of the final area that will be mapped by the DES; the tools and analysis techniques developed in this paper can be applied to forthcoming larger datasets from the survey.

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Constraints on the Richness-Mass Relation and the Optical-SZE Positional Offset Distribution for SZE-Selected Clusters

We cross-match galaxy cluster candidates selected via their Sunyaev-Zel'dovich effect (SZE) signatures in 129.1 deg$^2$ of the South Pole Telescope 2500d SPT-SZ survey with optically identified clusters selected from the Dark Energy Survey (DES) science verification data. We identify 25 clusters between $0.1\lesssim z\lesssim 0.8$ in the union of the SPT-SZ and redMaPPer (RM) samples. RM is an optical cluster finding algorithm that also returns a richness estimate for each cluster. We model the richness $λ$-mass relation with the following function $\langle\lnλ|M_{500}\rangle\propto B_λ\ln M_{500}+C_λ\ln E(z)$ and use SPT-SZ cluster masses and RM richnesses $λ$ to constrain the parameters. We find $B_λ= 1.14^{+0.21}_{-0.18}$ and $C_λ=0.73^{+0.77}_{-0.75}$. The associated scatter in mass at fixed richness is $σ_{\ln M|λ} = 0.18^{+0.08}_{-0.05}$ at a characteristic richness $λ=70$. We demonstrate that our model provides an adequate description of the matched sample, showing that the fraction of SPT-SZ selected clusters with RM counterparts is consistent with expectations and that the fraction of RM selected clusters with SPT-SZ counterparts is in mild tension with expectation. We model the optical-SZE cluster positional offset distribution with the sum of two Gaussians, showing that it is consistent with a dominant, centrally peaked population and a sub-dominant population characterized by larger offsets. We also cross-match the RM catalog with SPT-SZ candidates below the official catalog threshold significance $ξ=4.5$, using the RM catalog to provide optical confirmation and redshifts for additional low-$ξ$ SPT-SZ candidates.In this way, we identify 15 additional clusters with $ξ\in [4,4.5]$ over the redshift regime explored by RM in the overlapping region between DES science verification data and the SPT-SZ survey.

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Eight New Milky Way Companions Discovered in First-Year Dark Energy Survey Data

We report the discovery of eight new Milky Way companions in ~1,800 deg^2 of optical imaging data collected during the first year of the Dark Energy Survey (DES). Each system is identified as a statistically significant over-density of individual stars consistent with the expected isochrone and luminosity function of an old and metal-poor stellar population. The objects span a wide range of absolute magnitudes (M_V from -2.2 mag to -7.4 mag), physical sizes (10 pc to 170 pc), and heliocentric distances (30 kpc to 330 kpc). Based on the low surface brightnesses, large physical sizes, and/or large Galactocentric distances of these objects, several are likely to be new ultra-faint satellite galaxies of the Milky Way and/or Magellanic Clouds. We introduce a likelihood-based algorithm to search for and characterize stellar over-densities, as well as identify stars with high satellite membership probabilities. We also present completeness estimates for detecting ultra-faint galaxies of varying luminosities, sizes, and heliocentric distances in the first-year DES data.

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Mass and galaxy distributions of four massive galaxy clusters from Dark Energy Survey Science Verification data

We measure the weak-lensing masses and galaxy distributions of four massive galaxy clusters observed during the Science Verification phase of the Dark Energy Survey. This pathfinder study is meant to 1) validate the DECam imager for the task of measuring weak-lensing shapes, and 2) utilize DECam's large field of view to map out the clusters and their environments over 90 arcmin. We conduct a series of rigorous tests on astrometry, photometry, image quality, PSF modeling, and shear measurement accuracy to single out flaws in the data and also to identify the optimal data processing steps and parameters. We find Science Verification data from DECam to be suitable for the lensing analysis described in this paper. The PSF is generally well-behaved, but the modeling is rendered difficult by a flux-dependent PSF width and ellipticity. We employ photometric redshifts to distinguish between foreground and background galaxies, and a red-sequence cluster finder to provide cluster richness estimates and cluster-galaxy distributions. By fitting NFW profiles to the clusters in this study, we determine weak-lensing masses that are in agreement with previous work. For Abell 3261, we provide the first estimates of redshift, weak-lensing mass, and richness. In addition, the cluster-galaxy distributions indicate the presence of filamentary structures attached to 1E 0657-56 and RXC J2248.7-4431, stretching out as far as 1 degree (approximately 20 Mpc), showcasing the potential of DECam and DES for detailed studies of degree-scale features on the sky.

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Optical Spectroscopy and Velocity Dispersions of Galaxy Clusters from the SPT-SZ Survey

We present optical spectroscopy of galaxies in clusters detected through the Sunyaev-Zel'dovich (SZ) effect with the South Pole Telescope (SPT). We report our own measurements of $61$ spectroscopic cluster redshifts, and $48$ velocity dispersions each calculated with more than $15$ member galaxies. This catalog also includes $19$ dispersions of SPT-observed clusters previously reported in the literature. The majority of the clusters in this paper are SPT-discovered; of these, most have been previously reported in other SPT cluster catalogs, and five are reported here as SPT discoveries for the first time. By performing a resampling analysis of galaxy velocities, we find that unbiased velocity dispersions can be obtained from a relatively small number of member galaxies ($\lesssim 30$), but with increased systematic scatter. We use this analysis to determine statistical confidence intervals that include the effect of membership selection. We fit scaling relations between the observed cluster velocity dispersions and mass estimates from SZ and X-ray observables. In both cases, the results are consistent with the scaling relation between velocity dispersion and mass expected from dark-matter simulations. We measure a $\sim$30% log-normal scatter in dispersion at fixed mass, and a $\sim$10% offset in the normalization of the dispersion-mass relation when compared to the expectation from simulations, which is within the expected level of systematic uncertainty.

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Redshifts, Sample Purity, and BCG Positions for the Galaxy Cluster Catalog from the first 720 Square Degrees of the South Pole Telescope Survey

We present the results of the ground- and space-based optical and near-infrared (NIR) follow-up of 224 galaxy cluster candidates detected with the Sunyaev-Zel'dovich (SZ) effect in the 720 deg^2 of the South Pole Telescope (SPT) survey completed in the 2008 and 2009 observing seasons. We use the optical/NIR data to establish whether each candidate is associated with an overdensity of galaxies and to estimate the cluster redshift. Most photometric redshifts are derived through a combination of three different cluster redshift estimators using red-sequence galaxies, resulting in an accuracy of Δz/(1+z)=0.017, determined through comparison with a subsample of 57 clusters for which we have spectroscopic redshifts. We successfully measure redshifts for 158 systems and present redshift lower limits for the remaining candidates. The redshift distribution of the confirmed clusters extends to z=1.35 with a median of z_{med}=0.57. Approximately 18% of the sample with measured redshifts lies at z>0.8. We estimate a lower limit to the purity of this SPT SZ-selected sample by assuming that all unconfirmed clusters are noise fluctuations in the SPT data. We show that the cumulative purity at detection significance ξ>5 (ξ>4.5) is >= 95 (>= 70%). We present the red brightest cluster galaxy (rBCG) positions for the sample and examine the offsets between the SPT candidate position and the rBCG. The radial distribution of offsets is similar to that seen in X-ray-selected cluster samples, providing no evidence that SZ-selected cluster samples include a different fraction of recent mergers than X-ray-selected cluster samples.

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A Measurement of the Correlation of Galaxy Surveys with CMB Lensing Convergence Maps from the South Pole Telescope

We compare cosmic microwave background lensing convergence maps derived from South Pole Telescope (SPT) data with galaxy survey data from the Blanco Cosmology Survey, the Wide-field Infrared Survey Explorer, and a new large Spitzer/IRAC field designed to overlap with the SPT survey. Using optical and infrared catalogs covering between 17 and 68 square degrees of sky, we detect correlation between the SPT convergence maps and each of the galaxy density maps at >4 sigma, with zero cross-correlation robustly ruled out in all cases. The amplitude and shape of the cross-power spectra are in good agreement with theoretical expectations and the measured galaxy bias is consistent with previous work. The detections reported here utilize a small fraction of the full 2500 square degree SPT survey data and serve as both a proof of principle of the technique and an illustration of the potential of this emerging cosmological probe.

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SPT-CL J0205-5829: A z = 1.32 Evolved Massive Galaxy Cluster in the South Pole Telescope Sunyaev-Zel'dovich Effect Survey

The galaxy cluster SPT-CL J0205-5829 currently has the highest spectroscopically-confirmed redshift, z=1.322, in the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey. XMM-Newton observations measure a core-excluded temperature of Tx=8.7keV producing a mass estimate that is consistent with the Sunyaev-Zel'dovich derived mass. The combined SZ and X-ray mass estimate of M500=(4.9+/-0.8)e14 h_{70}^{-1} Msun makes it the most massive known SZ-selected galaxy cluster at z>1.2 and the second most massive at z>1. Using optical and infrared observations, we find that the brightest galaxies in SPT-CL J0205-5829 are already well evolved by the time the universe was <5 Gyr old, with stellar population ages >3 Gyr, and low rates of star formation (<0.5Msun/yr). We find that, despite the high redshift and mass, the existence of SPT-CL J0205-5829 is not surprising given a flat LambdaCDM cosmology with Gaussian initial perturbations. The a priori chance of finding a cluster of similar rarity (or rarer) in a survey the size of the 2500 deg^2 SPT-SZ survey is 69%.

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Weak-Lensing Mass Measurements of Five Galaxy Clusters in the South Pole Telescope Survey Using Magellan/Megacam

We use weak gravitational lensing to measure the masses of five galaxy clusters selected from the South Pole Telescope (SPT) survey, with the primary goal of comparing these with the SPT Sunyaev--Zel'dovich (SZ) and X-ray based mass estimates. The clusters span redshifts 0.28 < z < 0.43 and have masses M_500 > 2 x 10^14 h^-1 M_sun, and three of the five clusters were discovered by the SPT survey. We observed the clusters in the g'r'i' passbands with the Megacam imager on the Magellan Clay 6.5m telescope. We measure a mean ratio of weak lensing (WL) aperture masses to inferred aperture masses from the SZ data, both within an aperture of R_500,SZ derived from the SZ mass, of 1.04 +/- 0.18. We measure a mean ratio of spherical WL masses evaluated at R_500,SZ to spherical SZ masses of 1.07 +/- 0.18, and a mean ratio of spherical WL masses evaluated at R_500,WL to spherical SZ masses of 1.10 +/- 0.24. We explore potential sources of systematic error in the mass comparisons and conclude that all are subdominant to the statistical uncertainty, with dominant terms being cluster concentration uncertainty and N-body simulation calibration bias. Expanding the sample of SPT clusters with WL observations has the potential to significantly improve the SPT cluster mass calibration and the resulting cosmological constraints from the SPT cluster survey. These are the first WL detections using Megacam on the Magellan Clay telescope.

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The Blanco Cosmology Survey: Data Acquisition, Processing, Calibration, Quality Diagnostics and Data Release

The Blanco Cosmology Survey (BCS) is a 60 night imaging survey of $\sim$80 deg$^2$ of the southern sky located in two fields: ($α$,$δ$)= (5 hr, $-55^{\circ}$) and (23 hr, $-55^{\circ}$). The survey was carried out between 2005 and 2008 in $griz$ bands with the Mosaic2 imager on the Blanco 4m telescope. The primary aim of the BCS survey is to provide the data required to optically confirm and measure photometric redshifts for Sunyaev-Zel'dovich effect selected galaxy clusters from the South Pole Telescope and the Atacama Cosmology Telescope. We process and calibrate the BCS data, carrying out PSF corrected model fitting photometry for all detected objects. The median 10$σ$ galaxy (point source) depths over the survey in $griz$ are approximately 23.3 (23.9), 23.4 (24.0), 23.0 (23.6) and 21.3 (22.1), respectively. The astrometric accuracy relative to the USNO-B survey is $\sim45$ milli-arcsec. We calibrate our absolute photometry using the stellar locus in $grizJ$ bands, and thus our absolute photometric scale derives from 2MASS which has $\sim2$% accuracy. The scatter of stars about the stellar locus indicates a systematics floor in the relative stellar photometric scatter in $griz$ that is $\sim$1.9%, $\sim$2.2%, $\sim$2.7% and$\sim$2.7%, respectively. A simple cut in the AstrOmatic star-galaxy classifier {\tt spread\_model} produces a star sample with good spatial uniformity. We use the resulting photometric catalogs to calibrate photometric redshifts for the survey and demonstrate scatter $δz/(1+z)=0.054$ with an outlier fraction $η<5$% to $z\sim1$. We highlight some selected science results to date and provide a full description of the released data products.

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Galaxy clusters discovered via the Sunyaev-Zel'dovich effect in the first 720 square degrees of the South Pole Telescope survey

We present a catalog of 224 galaxy cluster candidates, selected through their Sunyaev-Zel'dovich (SZ) effect signature in the first 720 deg2 of the South Pole Telescope (SPT) survey. This area was mapped with the SPT in the 2008 and 2009 austral winters to a depth of 18 uK-arcmin at 150 GHz; 550 deg2 of it was also mapped to 44 uK-arcmin at 95 GHz. Based on optical imaging of all candidates and near-infrared imaging of the majority of candidates, we have found optical and/or infrared counterparts for 158 clusters. Of these, 135 were first identified as clusters in SPT data, including 117 new discoveries reported in this work. This catalog triples the number of confirmed galaxy clusters discovered through the SZ effect. We report photometrically derived (and in some cases spectroscopic) redshifts for confirmed clusters and redshift lower limits for the remaining candidates. The catalog extends to high redshift with a median redshift of z = 0.55 and maximum redshift of z = 1.37. Based on simulations, we expect the catalog to be nearly 100% complete above M500 ~ 5e14 Msun h_{70}^-1 at z > 0.6. There are 121 candidates detected at signal-to-noise greater than five, at which the catalog purity is measured to be 95%. From this high-purity subsample, we exclude the z < 0.3 clusters and use the remaining 100 candidates to improve cosmological constraints following the method presented by Benson et al., 2011. Adding the cluster data to CMB+BAO+H0 data leads to a preference for non-zero neutrino masses while only slightly reducing the upper limit on the sum of neutrino masses to sum mnu < 0.38 eV (95% CL). For a spatially flat wCDM cosmological model, the addition of this catalog to the CMB+BAO+H0+SNe results yields sigma8=0.807+-0.027 and w = -1.010+-0.058, improving the constraints on these parameters by a factor of 1.4 and 1.3, respectively. [abbrev]

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Optical followup of galaxy clusters detected by the South Pole Telescope

The South Pole Telescope (SPT) is a 10 meter telescope operating at mm wavelengths. It has recently completed a three-band survey covering 2500 sq. degrees. One of the survey's main goals is to detect galaxy clusters using Sunyaev-Zeldovich effect and use these clusters for a variety of cosmological and astrophysical studies such as the dark energy equation of state, the primordial non-gaussianity and the evolution of galaxy populations. Since 2005, we have been engaged in a comprehensive optical and near-infrared followup program (at wavelengths between 0.4 and 5 μm) to image high-significance SPT clusters, to measure their photometric redshifts, and to estimate the contamination rate of the candidate lists. These clusters are then used for various cosmological and astrophysical studies.

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Cosmological Constraints from Sunyaev-Zel'dovich-Selected Clusters with X-ray Observations in the First 178 Square Degrees of the South Pole Telescope Survey

We use measurements from the South Pole Telescope (SPT) Sunyaev Zel'dovich (SZ) cluster survey in combination with X-ray measurements to constrain cosmological parameters. We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology. The method is generalizable to multiple cluster observables, and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints. We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg2 of the 2500 deg2 SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM. Assuming a spatially flat LCDM cosmological model, we find the SPT cluster sample constrain sigma_8 (Omega_m/0.25)^0.30 = 0.785 +- 0.037. In combination with measurements of the CMB power spectrum from the SPT and the seven-year WMAP data, the SPT cluster sample constrain sigma_8 = 0.795 +- 0.016 and Omega_m = 0.255 +- 0.016, a factor of 1.5 improvement on each parameter over the CMB data alone. We consider several extensions beyond the LCDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses (sum mnu), the effective number of relativistic species (Neff), and a primordial non-Gaussianity (fNL). We find that adding the SPT cluster data significantly improves the constraints on w and sum mnu beyond those found when using measurements of the CMB, supernovae, baryon acoustic oscillations, and the Hubble constant. Considering each extension independently, we best constrain w=-0.973 +- 0.063 and the sum of neutrino masses sum mnu < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 improvement, respectively, over the constraints without clusters. [abbrev.]

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