Probing WHIM around Galaxy Clusters with Fast Radio Bursts and the Sunyaev-Zel'dovich effect

We propose a new method to probe the Warm Hot Intergalactic Medium (WHIM) beyond the virial radius (R_200) of a cluster of galaxies, where X-ray observations are not easily achievable. In this method, we use dispersion measures (DMs) of Fast Radio Bursts (FRBs) that appear behind the cluster and the Sunyaev-Zel'dovich (SZ) effect towards the cluster. The DMs reflect the density of the intracluster medium (ICM) including the WHIM. If we observe a sufficient number of FRBs in the direction of the cluster, we can derive the density profile from the DMs. Similarly, we can derive the pressure profile from the SZ effect. By combining the density and the pressure profiles, the temperature profile can be obtained. Based on mock observations of nearby clusters, we find that the density of the WHIM can be determined even at > 2 R_200 from the cluster center when FRB observations with the Square Kilometre Array (SKA) become available. The temperature can be derived out to r~ 1.5 R_200, and the radius is limited by the current sensitivity of SZ observations.