Apparently ultra-long period radio sources from self-lensed pulsar-black hole binaries

Abstract

Pulsar-black hole (BH) close binary systems, which have not been found yet, are unique laboratories for testing theories of gravity and understanding the formation channels of gravitational-wave sources. We study the self-gravitational lensing effect in a pulsar-BH system on the pulsar's emission. Because this effect occurs once per orbital period for almost edge-on binaries, we find that it could generate apparently ultra-long period (minutes to hours) radio signals when the intrinsic pulsar signal is too weak to detect. Each of such lensed signals, or 'pulse', is composed of a number of amplified intrinsic pulsar pulses. The model is applied to three recently found puzzling long-period radio sources: GLEAM-X J1627, PSR J0901-4046, and GPM J1839-10. To explain their observed signal durations and periods, the masses of their lensing components would be \(\sim10^4 M_{\odot}\), \(\sim4 M_{\odot}\) and \(\sim10^{3-6} M_{\odot}\), respectively. Their binary coalescence times are from a few tens to thousands of years. We estimate that a radio telescope with a sensitivity of 10 mJy could detect approximately 20 systems that emit such signals in our galaxy. For a binary containing a millisecond pulsar and a stellar-mass BH, the Shapiro delay effect would cause at least a 10% variation of the profile width for the sub-pulses in such lensed signals.