Hubble constant constraint using 117 FRBs with a more accurate probability density function for ${\rm DM}_{\rm diff}$

TL;DR

This work refines FRB-based cosmology by deriving an exact, fully analytic FRB dispersion-measure likelihood that treats the extragalactic DM as a convolution of a host-galaxy term and a diffuse component. It introduces a more accurate treatment of the diffuse-DM PDF through a true standard deviation ${\sigma_{\Delta}}$ and its relationship to ${\sigma_{\rm diff}}$, defining parameters ${S}$ and ${F}$ and exposing the redshift domain where the traditional ${\sigma_{\rm diff}}\sim F/\sqrt{z}$ approximation holds. Applying a sample of ${N_{FRB}=44}$ high-redshift FRBs (filtered from an initial ${N_{FRB}=117}$) with a maximum-likelihood approach yields constraints ${S=0.133^{+0.034}_{-0.045}}$ and ${H_0\Omega_b f_{\rm diff}=2.813^{+0.250}_{-0.258}}$ km s$^{-1}$ Mpc$^{-1}$, translating to ${H_0=66.9^{+6.8}_{-5.5}}$ km s$^{-1}$ Mpc$^{-1}$ when combined with Planck18 and ${f_{\rm diff}=0.84}$; the equivalent ${F}$ value is ${0.357^{+0.043}_{-0.067}}$. The analysis demonstrates that the traditional ${F}$-based linearization overestimates or misrepresents constraints outside a restricted redshift range, highlighting the need for the accurate $igl(\sigma_{\rm diff}(\sigma_{\Delta})\bigr)$ treatment for current and future localized FRB samples. Overall, the work provides a robust, physics-motivated framework to exploit FRB DMs for cosmology as the sample of localized FRBs grows.

Abstract

Fast radio bursts (FRBs) are among the most mysterious astronomical transients. Due to their short durations and cosmological distances, their dispersion measure (DM) - redshift ($z$) relation is useful for constraining cosmological parameters and detecting the baryons in the Universe. The increasing number of localized FRBs in recent years has provided more precise constraints on these parameters. However, the larger dataset reveals limitations in the widely used probability density function ($p_{\rm diff}$) for ${\rm DM}_{\rm diff}$, which refers to the diffuse electron term of FRB DM. In this project, we collect 117 of the latest, localized FRBs, discuss the effect of a more accurate $σ_{\rm diff}$, which is a parameter in $p_{\rm diff}$ and once thoughts as ``effective standard deviation'', and more clearly rewrite their likelihood to better constrain the parameters above. We find that the widely used approximation $σ_{\rm diff} \sim F/\sqrt{z}$ only works under contrived assumptions and shows the greatest deviation from the true standard deviation in low redshift. In general, one should use an accurate method to derive this parameter from $p_{\rm diff}$. Our method yields better constraints on $H_0Ω_b f_{\rm diff} = 2.813_{-0.258}^{+0.250}\;{\rm km/s/Mpc}$ or $H_0 = 66.889_{-5.459}^{+6.754} \;{\rm km/s/Mpc}$ when combining the FRB data with CMB measurements and taking $f_{\rm diff} = 0.84$. This fully analytical correction helps us better constrain cosmological parameters with the increasing number of localized FRBs available today.

Figures (6)

• Figure 1: ${\rm DM}_{\rm ext}-z$ relation for 117 localized FRBs, where ${\rm DM}_{\rm ext}={\rm DM}-{\rm DM}_{\rm MW}$ is the extragalactic DM. The dashed red line is the best fitting linear function for all data, while the back line shows the theoretical line from Eq. \ref{['eq:DM_diff']} adding $100\,\rm pc\,cm^{-3}$ for ${\rm DM}_{\rm host}$. We also show 90$\%$ confidence interval in shaded region calculated from our parameters searching results. The black data points are those FRBs $z\ge 0.25$ that $p_{\rm diff}(\Delta)$ worked within this range.
• Figure 2: $\sigma_\Delta-\sigma_{\rm diff}$ relation in $\log_{10}$ space. The dashed black line is the best linear fitting line for the nearly linear part for $\sigma_{\rm diff}(\sigma_{\Delta})$.
• Figure 3: Cosmological dependence of $F$ when choosing different value of $\sqrt{\overline{\sigma^2}_{\rm halo}}$.
• Figure 4: MCMC contour plot with our $\sigma_{\rm diff}$ correction
• Figure 5: Macquart's $\sigma_{\rm diff}=F/\sqrt{z}$ with FRBs $z\ge 0.25$