Dark matter capture by the Sun: revisiting velocity distribution uncertainties

Among the different strategies aiming to detect WIMP dark matter (DM), a neutrino signal coming from the Sun would be a smoking gun. This possibility relies on the DM capture by the Sun driven by the local DM distribution assumptions: the local mass density and the velocity distribution. In this context, we revisit those astrophysical hypotheses (also relevant for direct detection). We focus especially on the DM velocity distribution considering different possibilities beyond the popular Maxwellian distribution. Namely, some alternatives can be considered through analytical approaches and by looking into cosmological simulations of spiral galaxies. Most of the fitting formulas used to constrain the local velocity distribution function fail to describe the peak and the high velocity tail of the velocity distribution observed in simulations, the latter being improved when adding the local escape velocity of DM into the benchmark fitting models. In addition we test the predictions by the Eddington inversion method and also illustrate the importance of the galactic dynamical history. We estimate the resulting uncertainties on the DM capture rate by the Sun and conclude that different velocity distributions will affect the capture rate of DM by the Sun up to a $15-20\%$. On top of that, the calculation of the intrinsic variance of the capture rate leads to poorly controlled uncertainties especially for high WIMP masses ($>$30 GeV) raising concerns about the capture scenario.