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

Abstract: 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 $L_{\rm DM}$, arising solely from the thermalized annihilation products of the captured dark matter. Demanding that $L_{\rm DM}$ not exceed the luminosity of the white dwarfs in the M4 globular cluster, we set a bound on the DM-proton cross section: $\sigma_{p} \lesssim 10^{-44} {\rm cm}^2$, 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 $\left(M \gtrsim 5 \,\,\rm TeV\right)$ and small mass $\left(M \lesssim 10\,\, \rm GeV\right)$ regimes. For dark matter lighter than 350 MeV, which is beyond the sensitivity of present direct detection experiments, this is the strongest available constraint.