Mass Calibration and Cosmological Analysis of the SPT-SZ Galaxy Cluster Sample Using Velocity Dispersion $\ddot{I}{ƒ}_v$ 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 ($\ddot{I}{ƒ}_v$) and 16 X-ray Yx measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. The calibrations using $\ddot{I}{ƒ}_v$ and Yx are consistent at the $0.6\ddot{I}ƒ$ level, with the $\ddot{I}{ƒ}_v$ calibration preferring ~16% higher masses. We use the full cluster dataset to measure $\ddot{I}{ƒ}_8(\hat{I}{\text{c◯}}_m/0.27{)}^{0.3}=0.809\pm 0.036$. 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 $\sum m_{\hat{I}}½=0.06$ eV, we find the datasets to be consistent at the 1.0$\ddot{I}ƒ$ level for WMAP9 and 1.5$\ddot{I}ƒ$ for Planck+WP. Allowing for larger $\sum m_{\hat{I}}½$ further reconciles the results. When we combine the cluster and Planck+WP datasets with BAO and SNIa, the preferred cluster masses are $1.9\ddot{I}ƒ$ higher than the Yx calibration and $0.8\ddot{I}ƒ$ higher than the $\ddot{I}{ƒ}_v$ 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 $\hat{I}{\text{c◯}}_m=0.299\pm 0.009$ and $\ddot{I}{ƒ}_8=0.829\pm 0.011$. Within a $\hat{I}½$CDM model we find $\sum m_{\hat{I}}½=0.148\pm 0.081$ eV. We present a consistency test of the cosmic growth rate. Allowing both the growth index ${\hat{I}}^3$ and the dark energy equation of state parameter $w$ to vary, we find ${\hat{I}}^3=0.73\pm 0.28$ and $w=-1.007\pm 0.065$, demonstrating that the expansion and the growth histories are consistent with a LCDM model (${\hat{I}}^3=0.55;w=-1$).

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