Constraining the Hubble constant with scattering in host galaxies of fast radio bursts

Measuring the Hubble constant (H$_0$) is one of the most important missions in astronomy. Nevertheless, recent studies exhibit differences between the employed methods. Fast radio bursts (FRBs) are coherent radio transients with large dispersion measures (DM) with a duration of milliseconds. DM$_{\rm IGM}$, DM in the intergalactic medium (IGM), could open a new avenue for probing H$_0$. However, it has been challenging to separate DM contributions from different components (i.e., the IGM and the host galaxy plasma), and this hampers the accurate measurements of DM$_{\rm IGM}$ and hence H$_0$. We adopted a method to overcome this problem by using the temporal scattering of the FRB pulses due to the propagation effect through the host galaxy plasma (scattering time). The scattering-inferred DM in a host galaxy improves the estimate of DM$_{\rm IGM}$, which in turn leads to a better constraint on H$_0$. In previous studies, a certain value or distribution has conventionally been assumed of the dispersion measure in host galaxies (DM$_{\rm h}$). We compared this method with ours by generating 100 mock FRBs, and we found that our method reduces the systematic (statistical) error of H$_0$ by 9.1% (1%) compared to the previous method. We applied our method to 30 localized FRB sources with both scattering and spectroscopic redshift measurements to constrain H$_0$. Our result is H$_0$=74$_{-7.2}^{+7.5}$ km s$^{-1}$ Mpc$^{-1}$, where the central value prefers the value obtained from local measurements over the cosmic microwave background. We also measured DM$_{\rm h}$ with a median value of $103^{+68}_{-48}$ pc cm$^{-3}$. The reduction in systematic error is comparable to the Hubble tension ($\sim10$%). Combined with the fact that more localized FRBs will become available, our result indicates that our method can be used to address the Hubble tension using future FRB samples.