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

TL;DR

This study assesses how observational selection biases affect FRB dispersion measure–galaxy cross-correlations used to map extragalactic free electrons. It employs a ray-tracing pipeline through the IllustrisTNG simulation to generate realistic FRB and foreground galaxy catalogs and uses an optimal quadratic estimator to extract the angular cross-power spectrum $C_\ell^{Dg}$, connecting it to the 3D $P_{eg}$ via the Limber relation. The authors find the cross-correlation is largely robust to host properties, optical follow-up biases, and CHIME-like propagation effects, but DM-dependent selection that preferentially removes high-$\mathrm{DM}$ FRBs can bias the amplitude by over a factor of two on relevant scales, underscoring the need to model or mitigate such biases in future surveys. They also provide a transparent estimator framework and a detailed ray-tracing pipeline, enabling bias-aware analyses for upcoming large FRB samples that aim to probe the large-scale structure with FRB DMs. These results inform survey design (e.g., preserving high-DM FRBs, higher frequency observations) and highlight the importance of incorporating realistic selection functions when interpreting FRB-based baryon probes.

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 $0.3\leq z\leq 0.4$ . 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.

Figures (10)

• Figure 1: The $48$ square sky regions (shaded gray) used in this study (out to $z_{\max} = 0.4$) for independent realizations of the DM and galaxy field. The regions are chosen from the "good" regions of the sky (white) that avoid spurious geometrical effects from the simulation's periodic boundary conditions.
• Figure 2: Comparison of $P_{eg}(z_g)$ computed directly from the electron density and galaxy overdensities at redshift $z_g=0.2$ (black) to the electron galaxy power spectrum calculated from $C_\ell^{Dg}$ using Equation \ref{['eqn:CDG_PEG']} (red). The top panel shows the ratio of the two power spectra, with the error bars calculated from the variance of different realizations of $C_\ell^{Dg}$. This demonstrates the validity of the theory that relates the observable dispersion angular power spectrum to the underlying three dimensional power spectrum of free electrons.
• Figure 3: Comparison of theoretical expectation of the error on $C_\ell^{DG}$ as predicted by Equation \ref{['eq:theory_variance']} in the case of a Gaussian field to the true standard deviation of our measured $C_\ell^{DG}$ over many realizations for FRB cross correlated with galaxies. Here, we have FRB drawn uniformly distributed over the sky (one FRB/pixel) to avoid the additional effect the window function has on the variance. The true variance of the data is increasingly larger than the Gaussian expectation at smaller scales.
• Figure 4: Comparison of cross correlation measurement when FRB are drawn uniformly over all pixels (red) to when FRB are drawn based on SFR (Equation \ref{['eq:sfrweight']}). That FRB stocastically---rather than uniformly---sample the DM field induces no bias on the power spectrum.
• Figure 5: Top: Apparent magnitude distribution for fiducial sample of FRB in the redshift range ($0.3 < z_g \leq 0.4$). Bottom: Host galaxy incompleteness does not significantly affect the cross-correlation, even for an aggressive $m_g$ cut.