Dark matter capture and annihilation in stars: Impact on the red giant
  branch tip
  Context: While stars have often been used as laboratories to study dark
matter (DM), red giant branch (RGB) stars and all the rich phenomenology they
encompass have frequently been overlooked by such endeavors. Aims: We study the
capture, evaporation, and annihilation of weakly interacting massive particle
(WIMP) DM in low-mass RGB stars ($M=0.8-1.4~\mathrm{M_{\odot}}$). Methods: We
used a modified stellar evolution code to study the effects of DM
self-annihilation on the structure and evolution of low-mass RGB stars.
Results: We find that the number of DM particles that accumulate inside
low-mass RGB stars is not only constant during this phase of evolution, but
also mostly independent of the stellar mass and to some extent stellar
metallicity. Moreover, we find that the energy injected into the stellar core
due to DM annihilation can promote the conditions necessary for helium burning
and thus trigger an early end of the RGB phase. The premature end of the RGB,
which is most pronounced for DM particles with $m_\chi \simeq
100~\mathrm{GeV}$, is thus achieved at a lower helium core mass, which results
in a lower luminosity at the tip of the red giant branch (TRGB). Although in
the current WIMP paradigm, these effects are only relevant if the number of DM
particles inside the star is extremely large, we find that for light WIMPs
($m_\chi \simeq 4~\mathrm{GeV}$), relevant deviations from the standard TRGB
luminosity ($\sim 8\%$) can be achieved with conditions that can be realistic
in the inner parsec of the Milky Way.
