Foreground Groups and Host-Galaxy Geometry in the Dispersion-Measure Scatter of Fast Radio Bursts

Localized fast radio bursts (FRBs) show substantial scatter in dispersion measure (DM) about the mean cosmic DM–redshift relation, also known as the Macquart relation. Both foreground structure and host galaxies contribute to this scatter. In this work, we examine foreground tracers and host galaxy properties using a parent catalog of 136 localized FRBs with measured DMs and spectroscopic host redshifts. Among 77 FRBs within the Gfinder footprint, DM excess relative to a fixed Macquart mean increases with foreground group count excess, with a Spearman coefficient of 0.459. Adding the foreground term to a mean host baseline reduces the leave-one-out root mean square error (RMSE) and mean absolute error (MAE) in extragalactic DM by $13.0\mathrm{\%}$ and $7.5\mathrm{\%}$, respectively. For 20 of these FRBs with optical host axis ratio measurements, adding a foreground term calibrated on the other 57 FRBs to the host shape model reduces the observer-frame leave-one-out RMSE from $76.3$ to $64.0\mathrm{p}\mathrm{c}\mathrm{c}{\mathrm{m}}^{-3}$ and MAE from $54.2$ to $50.2\mathrm{p}\mathrm{c}\mathrm{c}{\mathrm{m}}^{-3}$. And the in-sample residual standard deviation in the host rest frame decreases by $20.2\mathrm{\%}$. Idealized galaxy models based on the Milky Way electron density distribution produce DM changes with inclination comparable to the fitted amplitude under the adopted assumptions.