On the effect of pulsar evaporation on the cooling of white dwarfs

Evolution of a large part of low-mass X-ray binaries (LMXBs) leads to the formation of rapidly rotating pulsars with a helium white dwarf (He WD) companion. Observations indicate that some He WDs in binary pulsar systems are ultracool (with the effective temperatures $T_{\rm eff}\lesssim$ 4000\, K). It is hard to cool down a He WD to such low temperatures within the Hubble time, because a thick hydrogen envelope was left behind around the He core after the mass transfer process. A possible mechanism that can accelerate the WD cooling is the evaporative wind mass loss from the He WD driven by the high-energy radiation from the recycled pulsar. In this paper, we evolve a large number of LMXBs and investigate the influence of the pulsar's high-energy radiation on the WD cooling with different input parameters, including the neutron star's spin-down luminosity, the evaporation efficiency and the metallicity of the companion star. By comparing our results with observations we note that, for relatively hot He WDs (with $T_{\rm eff}> 7000$ K), standard WD cooling without evaporation considered is able to reproduce their temperatures, while evaporation is probably required for the He WDs with relatively low temperatures ($T_{\rm eff}$ <5000 K).