Unveiling the distribution and redshift dependence of host galaxy dispersion measures using localized fast radio bursts

Fast Radio Bursts (FRBs) are enigmatic radio pulses whose origins are poorly understood. The dispersion measure of host galaxy (${\rm DM_{host}}$) provides critical insights into the local environment of FRB sources. In this study, we analyze a sample of 117 well-localized FRBs to investigate the statistical properties of ${\rm DM_{host}}$ and its potential correlations with host galaxy parameters, including redshift, stellar mass, star formation rate (SFR), and galaxy age. Our results reveal that ${\rm DM_{host}}$ is consistent with a log-normal distribution, with the mean $\mu_{\rm host}=5.03\pm 0.02$ and standard deviation $\sigma_{\rm host} = 0.96\pm 0.03$, which corresponds to a median value ${\rm Med}({\rm DM_{host}})=\exp(\mu_{\rm host})=153\pm 3~{\rm pc~cm^{-3}}$. We find a moderate positive correlation between ${\rm DM_{host}}$ and redshift, but no statistically significant correlations are found between ${\rm DM_{host}}$ and stellar mass, SFR, or galaxy age. Our findings highlight the importance of ${\rm DM_{host}}$ as a diagnostic tool for unraveling FRB origins, and underscore the need for future FRB surveys with deep multiwavelength host galaxy follow-up.