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Formation of Mass-gap Black Holes from Neutron Star X-ray Binaries with Super-Eddington Accretion

Electromagnetic and gravitational wave observations indicate that there is dearth of compact objects with mass $\sim 2.5-5~{\rm M_\odot}$. This so-called "mass gap" may be linked to the supernova explosion mechanisms that produce neutron stars (NSs) and black holes (BHs). However, the existence of a few mass-gap compact objects, some of which have been confirmed to be BHs, poses a challenge to the traditional theory of black hole formation. In this work we investigate the possible formation channel of BHs from accretion-induced collapse (AIC) of NSs in X-ray binaries. In particular, we consider the influence of super-Eddington accretion of NSs. Recent observations of ultraluminous X-ray pulsars suggest that their apparent luminosities may reflect the true accretion luminosities of the accreting NSs, even exceeding the Eddington limit by a factor of $\gtrsim 100$. Thus, NSs accreting at a super-Eddington accretion rate may rapidly grow into BHs in intermediate/low-mass X-ray binaries. Based on the super-Eddington accretion disk models, we have investigated the evolution of NSs in intermediate/low-mass X-ray binaries by combining binary population synthesis and detailed stellar evolutionary calculations. We show that super-Eddington accretion plays a critical role in mass growth of NSs, and the final masses of the descendant BHs are heavily dependent on the NS magnetic fields, the metallicity of the donor star, and the bifurcation period of the binaries. AIC of NSs may account for some of the observed mass-gap BHs like GRO J0422+32. We also present the parameter distributions of the potential mass-gap BHs in a Milky Way-like galaxy, and point out that future space-based gravitational wave observations may provide important test of or constraints on the formation of mass-gap BHs from the AIC channel.