Probing massive neutrinos with the Minkowski functionals of the galaxy distribution

The characteristic signatures of massive neutrinos on large-scale structure (LSS), if fully captured, can be used to put a stringent constraint on their mass sum, $M_{\nu}$. Previous work utilizing N-body simulations has shown the Minkowski functionals (MFs) of LSS can reveal the imprints of massive neutrinos on LSS, provide important complementary information to two-point statistics and significantly improve constraints on $M_{\nu}$. In this work, we take a step forward and apply the statistics to the biased tracers of LSS, i.e. the galaxies, and in redshift space. We perform a Fisher matrix analysis and quantify the constraining power of the MFs by using the Molino mock galaxy catalogs, which are constructed based on the halo occupation distribution (HOD) framework with parameters for the SDSS $M_r < -21.5$ and -22 galaxy samples. We find the MFs give tighter constraints on all of the cosmological parameters that we consider than the power spectrum. The constraints on $\Omega_{\mathrm{m}}, \Omega_{\mathrm{b}}, h, n_s, \sigma_8$, and $M_\nu$ from the MFs are better by a factor of 1.9, 2.9, 3.7, 4.2, 2.5, and 5.7, respectively, after marginalizing over the HOD parameters. Specifically, for $M_{\nu}$, we obtain a 1$\sigma$ constraint of 0.059 eV with the MFs alone for a volume of only $\left(1 h^{-1} \mathrm{Gpc}\right)^3$.