Accretion from a Shock-Inflated Companion: Spinning Down Neutron Stars to Hour-Long Periods

Recent observations have unveiled a population of pulsars with spin periods of a few minutes to hours that lie beyond the traditional ``death line.'' If they originate from neutron stars (NSs), the existence of such ultra-long period pulsars (ULPs) challenges our current understanding of NS evolution and emission. In this work, we propose a new channel for disk formation based on NSs born in close binaries with main-sequence companion stars. Using a hydrodynamic simulation of supernova-companion interactions, we show that a newborn NS may gravitationally capture gas as it moves through the complex density field shaped by the explosion. For a binary separation of 20~R_ and a companion mass of 4~M_, we find the occurrence fraction for disk formation around unbound NSs to be ~10%. By modeling the disk evolution and its interaction with the NS, we find a bimodal distribution in spin periods: canonical pulsars with P10\,s are the ones who lack disks or whose magnetospheres never interacted with the disk, and ULPs with 10³ P<10⁵\,s are produced when the system undergoes a short-lived ``propeller'' phase during which the NS undergoes rapid spin-down. Such ULPs are formed under strong initial dipolar magnetic field strengths B₀10¹⁴\,G, with a formation rate of 10⁻⁴\,yr⁻¹ in the Milky Way. We also find that a small population of pulsars with moderate magnetic field strengths (10¹³~B₀10¹⁴\,G) and relatively slow initial periods (P₀0.1\,s) evolve to P~10²\,s, filling the gap between the bimodal distribution. Thus, our model provides a unified explanation for pulsars beyond the ``death line.''