Hunting wide-area optical surveys for high proper motion isolated neutron stars

High-velocity neutron stars (HVNSs) that were kicked out from their birth location can be potentially identified with their large proper motions, and possibly with large parallax, when they come across the solar neighborhood. In this paper, we study the feasibility of hunting isolated HVNSs in wide-area optical surveys by modelling the evolution of NS luminosity taking into account spin-down and thermal radiation. Assuming the upcoming 10-yr Vera C. Rubin Observatory's LSST observation, our model calculations predict that about 10 HVNSs mainly consisting of pulsars with ages of 10(4)-10(5) yr and thermally emitting NSs with 10(5)-10(6) yr are detectable. We find that a few NSs with effective temperature < 5 x 10(5) K, which are likely missed in the current and future X-ray surveys, are also detectable, and the detectability highly depends on NS cooling models. In particular, if considering dark matter heating in NS cores, we find that such cold NSs would account for 70 per cent of the whole detectable sample, and they are typically older than 10(6) yr and tend to have slow transverse velocities, less than or similar to 100 km s(-1), compared to already known pulsars. Thus, the future optical observation will give a unique NS sample, which can provide essential constraints on the NS cooling and heating mechanisms. Moreover, we suggest that providing HVNS samples with optical surveys is helpful for understanding the intrinsic kick-velocity distribution of NSs.