Weighing neutrinos with cosmic neutral hydrogen

We investigate the signatures left by massive neutrinos on the spatial distribution of neutral hydrogen (HI) in the post-reionization era by running hydrodynamic simulations that include massive neutrinos as additional collisionless particles. We find that halos in massive/massless neutrino cosmologies host a similar amount of neutral hydrogen, although for a fixed halo mass, on average, the HI mass increases with the sum of the neutrino masses. Our results show that HI is more strongly clustered in cosmologies with massive neutrinos, while its abundance, $\Omega_{\rm HI}(z)$, is lower. These effects arise mainly from the impact of massive neutrinos on cosmology: they suppress both the amplitude of the matter power spectrum on small scales and the abundance of dark matter halos. Modelling the HI distribution with hydrodynamic simulations at $z > 3$, and a simple analytic model at $z<3$, we use the Fisher matrix formalism to conservatively forecast the constraints that Phase 1 of the Square Kilometre Array (SKA) will place on the sum of neutrino masses, $M_\nu\equiv \Sigma m_{\nu}$. We find that with 10,000 hours of interferometric observations at $3 \lesssim z \lesssim 6$ from a deep and narrow survey with SKA1-LOW, the sum of the neutrino masses can be measured with an error $\sigma(M_\nu)\lesssim0.3$ eV (95% CL). Similar constraints can be obtained with a wide and deep SKA1-MID survey at $z \lesssim 3$, using the single-dish mode. By combining data from MID, LOW, and Planck, plus priors on cosmological parameters from a Stage IV spectroscopic galaxy survey, the sum of the neutrino masses can be determined with an error $\sigma(M_\nu)\simeq0.06$ eV (95% CL).