Constraints on Undetected Long-period Binaries in the Known Pulsar Population

Although neutron star–black hole binaries have been identified through mergers detected in gravitational waves, a pulsar–black hole binary has yet to be detected. While short-period binaries are detectable due to a clear signal in the pulsar’s timing residuals, effects from a long-period binary could be masked by other timing effects, allowing them to go undetected. In particular, a long-period binary measured over a small subset of its orbital period could manifest via time derivatives of the spin frequency incompatible with isolated pulsar properties. We assess the possibility of pulsars having unknown companions in long-period binaries and put constraints on the range of binary properties that may remain undetected in current data, but that may be detectable with further observations. We find that for 35% of canonical pulsars with published higher-order derivatives, the precision of measurements is not enough to confidently reject binarity (period ≳2 kyr), and that a black hole binary companion could not be ruled out for a sample of pulsars without published constraints if the period is >1 kyr. While we find no convincing cases in the literature, we put more stringent limits on orbital period and longitude of periastron for the few pulsars with published higher-order frequency derivatives ( n ≥ 3). We discuss the detectability of candidates and find that a sample pulsar in a 100 yr orbit could be detectable within 5–10 yr.