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The influence of fallback discs on the spectral and timing properties of neutron stars

Fallback discs around neutron stars (NSs) are believed to be an expected outcome of supernova explosions. Here we investigate the consequences of such a common outcome for the timing and spectral properties of the associated NS population, using Monte Carlo population synthesis models. We find that the long-term torque exerted by the fallback disc can substantially influence the late-time period distribution, but with quantitative differences which depend on whether the initial spin distribution is dominated by slow or fast pulsars. For the latter, a single-peaked initial spin distribution becomes bimodal at later times. Timing ages tend to underestimate the real age of older pulsars, and overestimate the age of younger ones. Braking indices cluster in the range 1.5 <~ n <~ 3 for slow-born pulsars, and -0.5 <~ n <~ 5 for fast-born pulsars, with the younger objects found predominantly below n <~ 3. Large values of n, while not common, are possible, and associated with torque transitions in the NS+disc system. The 0.1-10 keV thermal luminosity of the NS+disc system is found to be generally dominated by the disc emission at early times, t <~ 10^3 yr, but this declines faster than the thermal surface emission of the NS. Depending on the initial parameters, there can be occasional periods in which some NSs switch from the propeller to the accretion phase, increasing their luminosity up to the Eddington limit for ~ 10^3-10^4 years.