Statistical modelling of the cosmological dispersion measure

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 ( 1Mpc) 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, 𝜉 (𝜃) ≈ 2400(𝜃/deg) −1 pc 2 cm −6 , which we anticipate will be confirmed by future observations when thousands of FRBs are available.

Fast Radio Burst Dispersion Measure Distribution as a Probe of Helium Reionization

“…Using cosmological simulations to model baryonic distribution, [36] obtained results well fit by σ IGM ≈ 210 √ z. Further recent simulations bear this out [24,45,[49][50][51][52], and as in [25,27] we adopt…”

Constraining the Cosmic Baryon Distribution with Fast Radio Burst Foreground Mapping

“…However, we note that both Walters et al (2019) and Ravi (2019) appear to have underestimated the scatter arising from the diffuse cosmic web by adopting σ igm ≈ 10 pc cm −3 . This is a factor of ∼ 3 − 10× smaller than the corresponding quantity seen in hydrodynamical simulations (e.g., Jaroszynski 2019;Takahashi et al 2020), which make the forecasts in Walters et al (2019) and Ravi (2019) too optimistic; this despite the fact that they already call for large numbers of localized FRBs, a number unlikely to be achieved in the very near future. In other words, even with large samples of localized FRBs, large-scale variance caused by the density fluctuations in the FRB foreground causes significant uncertainty in the cosmic baryon census that can be achieved using FRB lines-of-sight.…”

“…However, the scatter in DM igm , which we refer to as σ igm , will vary as a function of R sm -with large R sm the variance in DM igm between different sightlines will get washed out. As a comparison, we use the results of Jaroszynski ( 2019), hereafter J19, who studied the statistics of the DM igm distribution in the Illustris cosmological hydrodynamical simulations (see also Takahashi et al 2020;Zhu & Feng 2020;Batten et al 2021). We calculated DM igm (z) at several redshifts using our model (Equation 4), for a few different values of R sm .…”

What it Takes to Measure Reionization with Fast Radio Bursts

“…However this enhancement is negligible at the high redshift of interest and the correction factor approaches unity (e.g. Jaroszynski [16] finds 0.964 at 𝑧 = 4 from the Illustris [99] simulation and Takahashi et al [100] report 0.998 at 𝑧 = 5 using IllustrisTNG [101]).…”