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