Faint light of old neutron stars from dark matter capture and
  detectability at the James Webb Space Telescope
  Neutron stars (NS) of age $>10^9$ yrs exhaust thermal and rotational energies
and cool down to temperatures below $\mathcal{O}(100)$ K. Accretion of particle
dark matter (DM) by such NS can heat them up through kinetic and annihilation
processes. This increases the NS surface temperature to a maximum of $\sim
2600$ K in the best case scenario. The maximum accretion rate depends on the DM
ambient density and velocity dispersion, and on the NS equation of state and
their velocity distributions. Upon scanning over these variables, we find that
the effective surface temperature varies at most by $\sim 40\%$. Black body
spectrum of such warm NS peak at near infrared wavelengths with magnitudes in
the range potentially detectable by the James Webb Space Telescope (JWST).
Using the JWST exposure time calculator, we demonstrate that NS with surface
temperatures $\gtrsim 2400$ K, located at a distance of 10 pc can be detected
through the F150W2 (F322W2) filters of the NIRCAM instrument at SNR $\gtrsim
10$ (5) within 24 hours of exposure time.
