  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.
