PSR J0210+5845; An ultra wide binary pulsar with a B6V main-sequence star companion

We report on radio timing observations of PSR J0210+5845 which reveal large deviations from typical pulsar spin-down behaviour. We interpret these deviations as being due to binary motion around the $V=13.5$ star 2MASS J02105640$+$5845176, which is coincident in celestial position and distance with the pulsar. Archival observations and new optical spectroscopy identify this star as a B6V star with a temperature of $T_\mathrm{eff}\approx 14\,000$K and a mass of $M_\mathrm{c}= 3.5$ to $3.8$M$_\odot$, making it the lowest mass main-sequence star known orbiting a non-recycled pulsar. We found that the timing observations constrain the binary orbit to be wide and moderately eccentric, with an orbital period of $P_\mathrm{b}=47^{+40}_{-14}$yr and eccentricity $e=0.46^{+0.10}_{-0.07}$. We predict that the next periastron passage will occur between 2030 and 2034. Due to the low companion mass, we find that the probability for a system with the properties of PSR J0210+5845 and its binary companion to survive the supernova is low. We show that a low velocity and fortuitously directed natal kick is required for the binary to remain bound during the supernova explosion, and argue that an electron-capture supernova is a plausible formation scenario for the pulsar.