Mass Calibration and Cosmological Analysis of the SPT-SZ Galaxy Cluster Sample Using Velocity Dispersion ${\sigma }_v$ and X-ray $Y_{\text{X}}$ Measurements

Abstract

We present a velocity dispersion-based mass calibration of the South Pole Telescope Sunyaev-Zel'dovich effect survey (SPT-SZ) galaxy cluster sample. Using a homogeneously selected sample of 100 cluster candidates from 720 deg2 of the survey along with 63 velocity dispersion (${\sigma }_v$) and 16 X-ray Yx measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. The calibrations using ${\sigma }_v$ and Yx are consistent at the $0.6\sigma$ level, with the ${\sigma }_v$ calibration preferring ~16% higher masses. We use the full cluster dataset to measure ${\sigma }_8({\Omega }_m/0.27{)}^{0.3}=0.809\pm 0.036$. The SPT cluster abundance is lower than preferred by either the WMAP9 or Planck+WMAP9 polarization (WP) data, but assuming the sum of the neutrino masses is $\sum m_{\nu }=0.06$ eV, we find the datasets to be consistent at the 1.0$\sigma$ level for WMAP9 and 1.5$\sigma$ for Planck+WP. Allowing for larger $\sum m_{\nu }$ further reconciles the results. When we combine the cluster and Planck+WP datasets with BAO and SNIa, the preferred cluster masses are $1.9\sigma$ higher than the Yx calibration and $0.8\sigma$ higher than the ${\sigma }_v$ calibration. Given the scale of these shifts (~44% and ~23% in mass, respectively), we execute a goodness of fit test; it reveals no tension, indicating that the best-fit model provides an adequate description of the data. Using the multi-probe dataset, we measure ${\Omega }_m=0.299\pm 0.009$ and ${\sigma }_8=0.829\pm 0.011$. Within a $\nu$CDM model we find $\sum m_{\nu }=0.148\pm 0.081$ eV. We present a consistency test of the cosmic growth rate. Allowing both the growth index $\gamma$ and the dark energy equation of state parameter $w$ to vary, we find $\gamma =0.73\pm 0.28$ and $w=-1.007\pm 0.065$, demonstrating that the expansion and the growth histories are consistent with a LCDM model ($\gamma =0.55;w=-1$).

Accepted by ApJ (v2 is accepted version); 17 pages, 6 figures

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