Statistical modelling of the cosmological dispersion measure

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