Cosmological Constraints from Galaxy Clusters in the 2500 square-degree SPT-SZ Survey

TL;DR

This study analyzes SZ-selected galaxy clusters from the 2500 deg$^2$ SPT-SZ survey, calibrating mass proxies with Chandra $Y_X$ measurements and a weak-lensing prior to infer cosmological parameters from cluster abundances across redshift. A novel, linear-scaling multi-proxy likelihood connects observed SZ-significance and X-ray proxies to halo masses via calibrated scaling relations, enabling efficient cosmological inferences when combined with external datasets (Planck CMB, BAO, SNe, and $H_0$ priors). In ΛCDM with a fixed total neutrino mass, the authors find $\sigma_8 = 0.784 \pm 0.039$ and $\Omega_m = 0.289 \pm 0.042$, with tighter joint constraints when including weak-lensing mass-scale priors; they also explore extensions including $\Sigma m_\nu$, $N_{\mathrm{eff}}$, and a free equation-of-state parameter $w$, finding mild evidence for extra relativistic species and improving dark-energy constraints when clusters are combined with geometrical probes. Overall, the results are consistent with Planck and WtG constraints, and they demonstrate the power of SZ-selected clusters for cosmology, with future improvements anticipated from enhanced WL mass calibration and CMB-cluster lensing measurements.

Abstract

(abridged) We present cosmological constraints obtained from galaxy clusters identified by their Sunyaev-Zel'dovich effect signature in the 2500 square degree South Pole Telescope Sunyaev Zel'dovich survey. We consider the 377 cluster candidates identified at z>0.25 with a detection significance greater than five, corresponding to the 95% purity threshold for the survey. We compute constraints on cosmological models using the measured cluster abundance as a function of mass and redshift. We include additional constraints from multi-wavelength observations, including Chandra X-ray data for 82 clusters and a weak lensing-based prior on the normalization of the mass-observable scaling relations. Assuming a LCDM cosmology, where the species-summed neutrino mass has the minimum allowed value (mnu = 0.06 eV) from neutrino oscillation experiments, we combine the cluster data with a prior on H0 and find sigma_8 = 0.797+-0.031 and Omega_m = 0.289+-0.042, with the parameter combination sigma_8(Omega_m/0.27)^0.3 = 0.784+-0.039. These results are in good agreement with constraints from the CMB from SPT, WMAP, and Planck, as well as with constraints from other cluster datasets. Adding mnu as a free parameter, we find mnu = 0.14+-0.08 eV when combining the SPT cluster data with Planck CMB data and BAO data, consistent with the minimum allowed value. Finally, we consider a cosmology where mnu and N_eff are fixed to the LCDM values, but the dark energy equation of state parameter w is free. Using the SPT cluster data in combination with an H0 prior, we measure w = -1.28+-0.31, a constraint consistent with the LCDM cosmological model and derived from the combination of growth of structure and geometry. When combined with primarily geometrical constraints from Planck CMB, H0, BAO and SNe, adding the SPT cluster data improves the w constraint from the geometrical data alone by 14%, to w = -1.023+-0.042.

Figures (10)

• Figure 1: A plot comparing cluster weak lensing and $Y_\mathrm{X}$-based mass estimates. Plotted along the $y$-axis are weak lensing-based mass estimates from WtG (red) and $Y_\mathrm{X}$-based mass estimates using the scaling from V09 (black). On the $x$-axis are weak lensing-based mass estimates from H15. For the H15/V09 comparison (black points), we have re-estimated the H15 masses using the X-ray implied $r_{500}$. The solid grey line shows a one-to-one relation, and the dashed black and red lines give the normalization implied for the bootstrap mean fit to the ratio of the masses (for details see text).
• Figure 2: Comparison of cluster constraints on $\sigma_8$ and $\Omega_m$ from this work with those from previous SPT publications. The B13 analysis (outermost, gray contours) used 18 clusters, 14 of which have Chandra observations. The number of clusters increased to 100 in R13 (red contours), whereas this work uses 377 cluster candidates, 82 of which have high-quality Chandra observations. If we adopt the same observable-mass priors as B13 and R13, we obtain the innermost, purple contours. However, the main results in this paper assume a new weak lensing-based prior on the X-ray scaling relation normalization, which changes the central value by 10% and increases the 1$\sigma$ uncertainty slightly from 9% to 11%. The $\sigma_8$-$\Omega_m$ constraints using this prior and the current cluster data are shown by the light-blue contours.
• Figure 3: Number density of clusters as a function of redshift (left panel) and of the SPT-SZ mass proxy $\xi$ (right panel). The data points show the measured abundance with $\sqrt{N}$ error bars. The grey bands show the $68\%$ and $95\%$ allowed model ranges after marginalizing over all cosmological and scaling relation parameters in the $\Lambda$CDM model with the SPT$_{\hbox{\scriptsize CL}}$+$H_0$+BBN dataset. In the right hand panel, the $\xi$ axis is shown on a logarithmic scale and the abundance axis has been multiplied by three powers of $\xi$ in order to visualize the abundance over a range of $\xi$ values despite the extreme steepness of the measured mass function.
• Figure 4: Comparison of cluster constraints on $\sigma_8$ and $\Omega_m$ to constraints from primary CMB anisotropies, assuming a $\Lambda$CDM cosmology. The cluster constraints, when combined with either the $H_0$ or BAO$+\theta_s$ prior, are in agreement with the CMB datasets.
• Figure 5: Contour triangle plot showing the degeneracies between scaling relation parameters and cosmological parameters. Parameters $\Omega_b h^2$, $H_0$, $n_s$, $\sigma_{\ln \mathrm{Yx}}$, and $\rho_{\zeta,\mathrm{Yx}}$ are marginalized over and not shown since they are primarily constrained by priors, or by the Planck data. The cluster likelihood is nearly flat over the explored range of these parameters.