Radio pulsars found in binary systems with short orbital periods are usually fast spinning as a consequence of recycling via mass transfer from their companion stars; this process is also thought to decrease the magnetic field of the neutron star being recycled. Here, we report on timing observations of the recently discovered binary PSR J1755$-$2550 and find that this pulsar is an exception: with a characteristic age of 2.1 Myr, it is relatively young; furthermore, with a spin period of 315 ms and a surface magnetic field strength at its poles of 0.88$\times$10$^{12}$ G the pulsar shows no sign of having been recycled. Based on its timing and orbital characteristics, the pulsar either has a massive white dwarf (WD) or a neutron star (NS) companion. To distinguish between these two cases, we searched radio observations for a potential recycled pulsar companion and analysed archival optical data for a potential WD companion. Neither work returned conclusive detections. We apply population synthesis modelling and find that both solutions are roughly equally probable. Our population synthesis also predicts a minimum mass of 0.90 M$_{\odot}$ for the companion star to PSR J1755$-$2550 and we simulate the systemic runaway velocities for the resulting WDNS systems which may merge and possibly produce Ca-rich supernovae. Whether PSR J1755$-$2550 hosts a WD or a NS companion star, it is certainly a member of a rare subpopulation of binary radio pulsars.
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