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We revisit dark matter (DM) capture in celestial objects, including theimpact of multiple scattering, and obtain updated constraints on the DM-protoncross section using observations of white dwarfs. Considering a general formfor the energy loss distribution in each scattering, we derive an exact formulafor the capture probability through multiple scatterings. We estimate themaximum 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 tocompute a "dark" luminosity $L_{\rm DM}$, arising solely from the thermalizedannihilation products of the captured dark matter. Demanding that $L_{\rm DM}$not exceed the luminosity of the white dwarfs in the M4 globular cluster, weset a bound on the DM-proton cross section: $\sigma_{p} \lesssim 10^{-44} {\rmcm}^2$, almost independent of the dark matter mass between 100 GeV and 1 PeVand mildly weakening beyond. This is a stronger constraint than those obtainedby direct detection experiments in both large mass $\left(M \gtrsim 5 \,\,\rmTeV\right)$ and small mass $\left(M \lesssim 10\,\, \rm GeV\right)$ regimes.For dark matter lighter than 350 MeV, which is beyond the sensitivity ofpresent direct detection experiments, this is the strongest availableconstraint.

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