# Measuring the baryon fraction in cluster of galaxies with Kinematic Sunyaev Zeldovich and a Standard Candle

## TL;DR

This paper introduces a novel method combining kinematic Sunyaev-Zeldovich effect and Type Ia supernovae to measure the baryon fraction in galaxy clusters, leveraging future survey data for improved accuracy.

## Contribution

The paper proposes a new approach to determine galaxy cluster baryon fractions using supernova-hosting clusters and the kinematic Sunyaev-Zeldovich effect, enhancing previous methods.

## Key findings

- Estimated 4500 clusters per year with supernovae for the method.
- Identified redshift range $0.4<z<0.6$ as optimal for measurements.
- Highlighting the importance of improved distance modulus accuracy.

## Abstract

We propose a new method to use the kinematic Sunyaev-Zeldovich for measuring the baryon fraction in cluster of galaxies. In this proposal we need a configuration in which a supernova Type Ia resides in a brightest cluster galaxy of intermediate redshift clusters. We show this supernova Type Ia can be used to measure the bulk velocity of a galaxy cluster. We assert that the redshift range of $0.4<z<0.6$ is suitable for this proposal. The main contribution to the deviation of standard candles distance modulus from cosmological background prediction in this redshift range comes from peculiar velocity of the host galaxy and gravitational lensing. In this work we argue that by the knowledge of the bulk flow of the galaxy cluster and the cosmic microwave background photons temperature change due to kinematic Sunyaev-Zeldovich, we can constrain the baryon fraction of galaxy cluster. The probability of this configuration for clusters is obtained. We estimate in a conservative parameter estimation the large synoptic survey telescope can find spectroscopically followed $\sim 4500$ galaxy clusters with a bright cluster galaxy which hosts a type Ia Supernova each year. Finally, we show the improving of the distance modulus measurement is the key improvement in future surveys which will be crucial to detect the baryon fraction of cluster with the proposed method.