Constraining pulsar birth properties with supernova X-ray observations

Using a model of the very young pulsar wind nebula's dynamical and spectral evolution, with pulsar wind and accelerated particle parameters assumed similar to those inferred from modeling young pulsar wind nebulae (PWNe) in our Galaxy, we show that X-ray observations of supernovae, a few years to decades after the explosion, constitute a favored window to obtain meaningful constraints on the initial spin-down luminosity of the newly-formed pulsar. We examine the expected emerging PWN spectral component, taking into account the X-ray opacity of the expanding supernova ejecta, and find that it is typically best detectable in < 10 keV X-rays some years after the explosion. We use this framework to assess available X-ray observations and flux upper limits on supernovae, building on the work of Perna et al. (2008). We note that a resulting limit on spin-down luminosity corresponds univocally to a limit on the maximum magnetospheric acceleration potential, irrespective of the specific combination of magnetic field and rotation period that achieves it. We use available X-ray observations of supernovae to place constraints on the birth spin-down luminosity and period distribution of classical pulsars. We also examine the case of magnetars, born with much higher magnetic fields, and show that their much shorter initial spin-down time implies that any plausible signature of young magnetar wind nebulae can only be observed in harder X-ray or gamma-rays.