Exploring Selection Biases in Fast Radio Burst Dispersion–Galaxy Cross-correlations with Magnetohydrodynamical Simulations

Abstract The dispersion measures (DMs) of fast radio bursts (FRBs) 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 ≤ z ≤ 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 ∼0 . ° 1, corresponding to ∼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.