2024ApJ...972...60X

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 ultralong 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. We estimate that a radio telescope with a sensitivity of 10 mJy could detect a few systems that emit such signals in our Galaxy. 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 are estimated as ∼10⁴M_⊙, ∼4 M_⊙, and 10^3–6M_⊙, respectively, with their binary coalescence times ranging from a few tens to thousands of years. However, the implied merger rates (as high as ∼10^3–4 Myr^–1 per galaxy) and the large period decay rates (>10^–8 s s^–1) tend to disfavor this self-lensing scenario for these three sources. Despite this, our work still provides observational characteristics for self-lensed pulsar-BH binaries, which could help the detection of related sources in the future. Finally, for a binary containing a millisecond pulsar and a stellar-mass BH, the Shapiro delay effect would cause a ≥10% variation of the profile width for the subpulses in such lensed signals.