Yunhe Hu, Feng Huang, Taotao Fang

We investigate the thermal impact of dark matter (DM) capture and annihilation on neutron stars (NSs) in the Galactic Center (GC). Accounting for both kinetic energy deposition and internal annihilation, we systematically evaluate the influence of various DM density profiles, ranging from cored to cuspy distributions, on the late-time thermal evolution of NSs. For NSs older than $\sim 10^7~\mathrm{yr}$, the surface temperature approaches an equilibrium value $T_\mathrm{s}^{\mathrm{eq}} \sim 10^4$--$10^6~\mathrm{K}$, depending on the stellar location and the ambient DM density. In the presence of a density spike, enhanced heating shifts the emission toward ultraviolet (UV) and soft x-ray bands; however, strong interstellar extinction and large hydrogen column densities significantly suppress the observable flux density. We further provide an estimate of the cumulative infrared surface brightness from the NS population in the GC. The predicted flux density from an individual NS remains below $\sim 0.1\,\mathrm{nJy}$, while the integrated emission yields an average surface brightness $I_ν\lesssim 10^{-9}\,\mathrm{Jy\,arcsec^{-2}}$, corresponding to a signal-to-noise ratio well below current detection thresholds. Our results indicate that thermal signatures from DM-heated NSs in the GC remain below the sensitivity limits of current instruments, although nearby systems with lower extinction may provide more promising targets for detection.