Flavor blocking of dark matter thermalization in neutron stars

Neutron stars (NSs) provide exceptional laboratories for probing dark matter (DM) interactions beyond the reach of terrestrial experiments. We investigate a scenario in which DM couples to electrons and muons through a lepton-flavor-violating (LFV) coupling. In the strong gravitational field of NSs, infalling DM attains semi-relativistic velocities that activate inelastic transitions $\chi e \leftrightarrow \chi \mu$, leading to efficient energy deposition through scattering and annihilation. We show that this latter heating mechanism remains efficient even for $p$-wave suppressed annihilations. This is due to \textsl{flavor blocking} of DM thermalization with the NS, as LFV interactions become forbidden for low kinetic energies of $\chi$. The resulting DM-induced heating can sustain NS surface temperatures of $T_s \gtrsim 2 \times 10^3~\mathrm{K}$, providing an observable signature for future infrared searches. This establishes NS heating as a powerful probe of flavor-violating DM portals, capable of probing thermal targets beyond the reach of direct, indirect, and accelerator-based searches, as we illustrate for the axion-like particle (ALP) mediator.