Dark matter capture in celestial objects: improved treatment of multiple scattering and updated constraints from white dwarfs

We revisit dark matter (DM) capture in celestial objects, including the impact of multiple scattering, and obtain updated constraints on the DM-proton cross section using observations of white dwarfs. Considering a general form for the energy loss distribution in each scattering, we derive an exact formula for the capture probability through multiple scatterings. We estimate the maximum number of scatterings that can take place, in contrast to the number required to bring a dark matter particle to rest. We employ these results to compute a dark luminosity L-DM, arising solely from the thermalized annihilation products of the captured dark matter. Demanding that L-DM not exceed the luminosity of the white dwarfs in the M4 globular cluster, we set a bound on the DM-proton cross section: sigma(p) less than or similar to 10(-44) cm(2), almost independent of the dark matter mass between 100 GeV and 1 PeV and mildly weakening beyond. This is a stronger constraint than those obtained by direct detection experiments in both large mass (M greater than or similar to 5 TeV) and small mass (M less than or similar to 10 GeV) regimes. For dark matter lighter than 350 MeV, which is beyond the sensitivity of present direct detection experiments, this is the strongest available constraint.