Statistical measurements of dispersion measure fluctuations of FRBs

Extragalactic Fast Radio Bursts (FRBs) have large dispersion measures (DMs) and are unique probes of intergalactic electron density fluctuations. By using the recently released First CHIME/FRB Catalog, we reexamined the structure function (SF) of DM fluctuations. It shows a large DM fluctuation similar to that previously reported in Xu & Zhang (2020), but no clear correlation hinting towards large scale turbulence is reproduced with this larger sample. To suppress the distortion effect from FRB distances and their host DMs, we focus on a subset of CHIME catalog with DM $<500$ pc cm$^{-3}$. A trend of non-constant SF and non-zero correlation function (CF) at angular separations $\theta$ less than $10^\circ$ is seen, but with large statistical uncertainties. The difference found between SF and that derived from CF at $\theta \lesssim 10^\circ$ can be ascribed to the large statistical uncertainties or the density inhomogeneities on scales on the order of $100$ Mpc. The possible correlation of electron density fluctuations and inhomogeneities of density distribution should be tested when several thousands of FRBs are available.