Transiently accreting neutron stars in quiescence (Lx<10^34 erg/s) have been observed to vary in intensity by factors of few, over timescales of days to years. If the quiescent luminosity is powered by a hot NS core, the core cooling timescale is much longer than the recurrence time, and cannot explain the observed, more rapid variability. However, the non-equilibrium reactions which occur in the crust during outbursts deposit energy in iso-density shells, from which the thermal diffusion timescale to the photosphere is days to years. The predicted magnitude of variability is too low to explain the observed variability unless - as is widely believed - the neutrons beyond the neutron-drip density are superfluid. Even then, variability due to this mechanism in models with standard core neutrino cooling processes is less than 50 per cent - still too low to explain the reported variability. However, models with rapid core neutrino cooling can produce variability by a factor as great as 20, on timescales of days to years following an outburst. Thus, the factors of few intensity variability observed from transiently accreting neutron stars can be accounted for by this mechanism only if rapid core cooling processes are active.
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