# Planck/SDSS Cluster Mass and Gas Scaling Relations for a Volume-Complete redMaPPer Sample

## TL;DR

This study uses Planck and SDSS data to analyze SZ gas pressure profiles and derive cluster mass and gas scaling relations for a large, volume-complete sample of optically selected clusters, revealing new insights into cluster properties.

## Contribution

It provides the first detailed SZ-based pressure profiles and mass-richness relations for a large, volume-complete sample of optically selected clusters, extending previous work to lower masses.

## Key findings

- SZ pressure profiles are well detected over a wide mass range.
- SZ-based masses are ~24% lower than weak lensing masses, indicating hydrostatic bias.
- Derived Y_500-M_500 relation has a slope of 1.72 +/- 0.07, consistent with previous SZ studies.

## Abstract

Using Planck satellite data, we construct SZ gas pressure profiles for a large, volume-complete sample of optically selected clusters. We have defined a sample of over 8,000 redMaPPer clusters from the Sloan Digital Sky Survey (SDSS), within the volume-complete redshift region 0.100 < z < 0.325, for which we construct Sunyaev-Zel'dovich (SZ) effect maps by stacking Planck data over the full range of richness. Dividing the sample into richness bins we simultaneously solve for the mean cluster mass in each bin together with the corresponding radial pressure profile parameters, employing an MCMC analysis. These profiles are well detected over a much wider range of cluster mass and radius than previous work, showing a clear trend towards larger break radius with increasing cluster mass. Our SZ-based masses fall ~24% below the mass-richness relations from weak lensing, in a similar fashion as the "hydrostatic bias" related with X-ray derived masses. We correct for this bias to derive an optimal mass-richness relation finding a slope 1.22 +/- 0.04 and a pivot mass log(M_500/M_0)= 14.432 +/- 0.041, evaluated at a richness lambda=60. Finally, we derive a tight Y_500-M_500 relation over a wide range of cluster mass, with a power law slope equal to 1.72 +/- 0.07, that agrees well with the independent slope obtained by the Planck team with an SZ-selected cluster sample, but extends to lower masses with higher precision.