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.
