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 $L_{\rm DM}$, 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.
