Extracting host galaxy dispersion measure and constraining cosmological parameters using fast radio burst data

The excessive dispersion measures (DMs) and high Galactic latitudes of fast radio bursts (FRBs) hint toward a cosmological origin of these mysterious transients. Methods of using measured DM and redshift $z$ to study cosmology have been proposed, but one needs to assume a certain amount of DM contribution from the host galaxy (DM$_{\rm HG}$) in order to apply those methods. We introduce a slope parameter $β(z) \equiv d \ln \left< {\rm DM}_{\rm E} \right> / d \ln z$ (where DM$_{\rm E}$ is the observed DM subtracting the Galactic contribution), which can be directly measured when a sample of FRBs have $z$ measured. We show that $\left< {\rm DM_{HG}}\right>$ can be roughly inferred from $β$ and the mean values, $\overline{\rm \left<DM_{\rm E}\right>}$ and $\bar z$, of the sample. Through Monte Carlo simulations, we show that the mean value of local host galaxy DM, $\left<\rm{DM_{HG,loc}}\right>$, along with other cosmological parameters (mass density $Ω_m$ in the $Λ$CDM model, and the IGM portion of the baryon energy density $Ω_b f_{\rm IGM}$) can be independently measured through MCMC fitting to the data.

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