Statistical modelling of the cosmological dispersion measure

TL;DR

This paper models the statistical properties of the cosmological dispersion measure for fast radio bursts using advanced hydrodynamic simulations, providing analytical tools and predictions for future observational confirmation.

Contribution

It introduces a comprehensive analytical framework for DM statistics based on simulations, including fitting functions for free-electron distribution and bias, and constructs mock sky maps for validation.

Findings

Free-electron power spectrum matches dark matter at large scales

Analytical fitting functions accurately reproduce simulation results

Predicted angular correlation function of DM follows a power law

Abstract

We have investigated the basic statistics of the cosmological dispersion measure (DM) -- such as its mean, variance, probability distribution, angular power spectrum and correlation function -- using the state-of-the-art hydrodynamic simulations, IllustrisTNG300, for the fast radio burst (FRB) cosmology. To model the DM statistics, we first measured the free-electron abundance and the power spectrum of its spatial fluctuations. The free-electron power spectrum turns out to be consistent with the dark matter power spectrum at large scales, but it is strongly damped at small scales ($\lesssim 1$Mpc) owing to the stellar and active galactic nucleus feedback. The free-electron power spectrum is well modelled using a scale-dependent bias factor (the ratio of its fluctuation amplitude to that of the dark matter). We provide analytical fitting functions for the free-electron abundance and its bias factor. We next constructed mock sky maps of the DM by performing standard ray-tracing simulations with the TNG300 data. The DM statistics are calculated analytically from the fitting functions of the free-electron distribution, which agree well with the simulation results measured from the mock maps. We have also obtained the probability distribution of source redshift for a given DM, which helps in identifying the host galaxies of FRBs from the measured DMs. The angular two-point correlation function of the DM is described by a simple power law, $\xi(\theta) \approx 2400 (\theta/{\rm deg})^{-1} \, {\rm pc}^2 \, {\rm cm}^{-6}$, which we anticipate will be confirmed by future observations when thousands of FRBs are available.