Origin of the black hole spin in lower-mass-gap black hole-neutron star binaries

During the fourth observing run, the LIGO-Virgo-KAGRA Collaboration reported the detection of a coalescing compact binary (GW230529(-)181500) with component masses estimated at 2.5 - 4.5 M-circle dot and 1.2 - 2.0 M-circle dot with 90% credibility. Given the current constraints on the maximum neutron star (NS) mass, this event is most likely a lower-mass-gap (LMG) black hole-neutron star (BHNS) binary. The spin magnitude of the BH, especially when aligned with the orbital angular momentum, is critical in determining whether the NS is tidally disrupted. An LMG BHNS merger with a rapidly spinning BH is an ideal candidate for producing electromagnetic counterparts. However, no such signals have been detected. In this study, we employ a detailed binary evolution model that incorporates new dynamical tide implementations to explore the origin of BH spin in an LMG BHNS binary. If the NS forms first, the BH progenitor (He-rich star) must begin in orbit shorter than 0.35 days to spin up efficiently, potentially achieving a spin magnitude of chi(BH) > 0.3. Alternatively, if a nonspinning BH (e.g., M-BH = 3.6 M-circle dot) forms first, it can accrete up to approximate to 0.2 M-circle dot via case BA mass transfer (MT), reaching a spin magnitude of chi(BH) approximate to 0.18 under Eddington-limited accretion. With a higher Eddington accretion limit (i.e., 10.0 M-Edd), the BH can attain a significantly higher spin magnitude of chi(BH) approximate to 0.65 by accreting approximately 1.0 M-circle dot during case BA MT phase.