Measuring the Variance of the Macquart Relation in z-DM Modeling

The Macquart relation describes the correlation between the dispersion measure (DM) of fast radio bursts (FRBs) and the redshift $z$ of their host galaxies. The scatter of the Macquart relation is sensitive to the distribution of baryons in the intergalactic medium (IGM) including those ejected from galactic halos through feedback processes. The width of the distribution in DMs from the cosmic web (${\rm DM}_{\rm cosmic}$) is parameterized by a fluctuation parameter $F$, which is related to the cosmic DM variance by $\sigma_{\rm DM}= F z^{-0.5}$. In this work, we present a new measurement of $F$ using 78 FRBs of which 21 have been localized to host galaxies. Our analysis simultaneously fits for the Hubble constant $H_0$ and the DM distribution due to the FRB host galaxy. We find that the fluctuation parameter is degenerate with these parameters, most notably $H_0$, and use a uniform prior on $H_0$ to measure $\log_{10} F > -0.89$ at the $3\sigma$ confidence interval and a new constraint on the Hubble constant $H_0 = 85.3_{-8.1}^{+9.4} \, {\rm km \, s^{-1} \, Mpc^{-1}}$. Using a synthetic sample of 100 localized FRBs, the constraint on the fluctuation parameter is improved by a factor of $\sim 2$. Comparing our $F$ measurement to simulated predictions from cosmological simulation (IllustrisTNG), we find agreement between $0.4 < z < 2$. However, at $z < 0.4$, the simulations underpredict $F$ which we attribute to the rapidly changing extragalactic DM excess distribution at low redshift.