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.