Cross-correlating galaxies and cosmic dispersion measures: Constraints on the gas-to-halo mass relation from 2MASS galaxies and 133 localized fast radio bursts

We conduct a cross-correlation analysis between large-scale structures traced by the Two Micron All Sky Survey (2MASS) galaxy catalog and the cosmic dispersion measures of 133 localized fast radio bursts (FRBs). The cross-correlation signal is measured as a function of the comoving separation $R$ between 2MASS galaxies and background FRB sightlines, making full use of the available redshift information for both datasets. Our measurements are consistent with a null detection over the range $0.01 < R\, [h^{-1}\mathrm{Mpc}] < 1$. Using a halo-based model in which free-electron density profiles are drawn from the hydrodynamical simulation IllustrisTNG-300 (TNG300), we show that the null signal at $R \sim 0.01\, h^{-1}\mathrm{Mpc}$ is inconsistent with the TNG300 prediction. This discrepancy indicates that the hot-gas mass fraction in halos with masses of $10^{12-13}\, M_\odot$ hosting 2MASS galaxies must be lower than that predicted by TNG300. A simple phenomenological modification of the TNG300 model suggests that the hot-gas mass fraction in halos of $10^{12-13}\, M_\odot$ should be below $\sim 10\%$ of the global baryon fraction in the nearby universe, implying the need for stronger feedback in this mass range. Our constraints are consistent with those inferred from X-ray emission and Sunyaev-Zel'dovich measurements in galaxies, while providing a direct estimate of the hot-gas mass fraction that does not rely on electron-temperature measurements. These results demonstrate that galaxy-FRB cross correlations offer a powerful probe of feedback processes in galaxy formation.