Statistical inference of the distance to ASKAP FRBs

The distances to fast radio bursts (FRBs) are crucial for understanding their underlying engine, and for their use as cosmological probes. In this paper, we provide three statistical estimates of the distance to ASKAP FRBs. First, we show that the number of events of similar luminosity in ASKAP does not scale as distance cubed, as one would expect, when directly using the observed dispersion measure (DM) to infer distance. Second, by comparing the average DMs of FRBs observed with different instruments, we estimated the average redshift of ASKAP FRBs to be $z\sim 0.01$ using CHIME and ASKAP, and $z\lesssim0.07$ using Parkes and ASKAP. Both values are much smaller than the upper limit $z\sim0.3$ estimated directly from the DM. Third, we cross-correlate the locations of the ASKAP FRBs with existing large-area redshift surveys, and see a 3$\sigma$ correlation with the 2MASS Redshift Survey and a 5$\sigma$ correlation with the HI Parkes All Sky Survey at $z\sim0.007$. This corresponds well with the redshift of the most likely host galaxy of ASKAP FRB 171020, which is at $z=0.00867$. These arguments combined suggest an extremely nearby origin of ASKAP FRBs and a local environment with accumulated electrons that contribute a DM of several hundred pc/cm$^3$, which should be accounted for in theoretical models.