Exploring selection biases in FRB dispersion-galaxy cross-correlations with magnetohydrodynamical simulations

Abstract

The dispersion measure (DM) of fast radio bursts (FRBs) in conjunction with their redshifts can be used as powerful probes of the distribution of extragalactic plasma. With a large enough sample, the free-electron--galaxy power spectrum $P_{eg}$ can be measured by cross-correlating FRB DMs with galaxy positions. However, a precise measurement of $P_{eg}$ requires a careful investigation of selection effects: the probability of both observing the FRB DM and obtaining a host galaxy redshift depends on their properties. We ray trace through the magnetohydrodynamic simulation IllustrisTNG to investigate the impact of expected observational selection effects on FRB dispersion--galaxy angular cross-correlations with a sample of 3000 FRBs at $0.3\le z\le 0.4$ . Our results show that cross-correlations with such an FRB sample are robust to properties of the FRB host galaxy: this includes DM contributions from the FRB host and optical follow-up selection effects. We also find that such cross-correlations are robust to DM-dependent and scattering selection effects specific to the CHIME/FRB survey. However, a DM-dependent selection effect that cuts off the 10\% most dispersed FRBs at a fixed redshift shell can bias the amplitude of the cross-correlation signal by over 50\% at angular scales of $\sim 0.1^{\circ }$, corresponding to $\sim$ Mpc physical scales. Our findings highlight the importance of both measuring and accounting for selection effects present in existing FRB surveys, as well as mitigating DM-dependent selection effects in the design of upcoming FRB surveys aiming to probe large-scale structure with FRBs.

16 pages, 10 figures, comments are welcome