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 functionusing the stateoftheart hydrodynamic simulations, IllustrisTNG300, for the fast radio burst (FRB) cosmology. To model the DM statistics, we first measured the freeelectron abundance and the power spectrum of its spatial fluctuations. The freeelectron 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 freeelectron power spectrum is well modelled using a scaledependent bias factor (the ratio of its fluctuation amplitude to that of the dark matter). We provide analytical fitting functions for the freeelectron abundance and its bias factor. We next constructed mock sky maps of the DM by performing standard raytracing simulations with the TNG300 data. The DM statistics are calculated analytically from the fitting functions of the freeelectron 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 twopoint 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.01560
 Bibcode:
 2020arXiv201001560T
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 16 figures, submitted to MNRAS