Evidence of Gapless Superfluidity in MXB 1659-29 With and Without Late Time Cooling

The interpretation of the thermal relaxation of some transiently accreting neutron stars in quasipersistent soft X-ray transients, especially MXB 1659-29, has been found to be challenging within the traditional deep crustal heating paradigm. Due to the pinning of quantized vortices, the neutron superfluid is not expected to remain at rest in the crust, as was generally assumed. We have recently shown that for sufficiently large relative superflows, the neutron superfluid could become gapless. This dynamical phase could naturally explain the late-time cooling of MXB 1659-29. However, the interpretation of the last observation of MXB 1659-29 in 2013 before its second accretion phase in 2015 remains debated, with some spectral fits being consistent with no further temperature decline. Here, we revisit the cooling of this neutron star considering the different fits. New simulations of the crust cooling are performed, accounting for neutron diffusion and allowing for gapless superfluidity. In all cases, gapless superfluidity is found to provide the best fit to observations.