An apparent positive relation between spin and orbital angular momentum in X-ray binaries

The origin of current angular momentum (AM) of the black hole (BH) in X-ray binary (XRB) is still unclear, which is related with the birth and/or the growth of the BH. Here we collect the spin parameters $a_{*}$ measured in BH XRBs and find an apparent bimodal distribution centered at $\sim$ 0.17 and 0.83. We find a positive relation between the spin parameter and the orbital period/orbital separation through combining distinct XRB categories, including neutron star (NS) low-mass X-ray binaries (LMXBs), Roche-lobe overflow (RLOF) BH XRBs and wind-fed BH XRBs. It seems that the AM of the compact star and the binary orbit correlates by combining the different XRB systems. These positive relations imply that accretion process is a common mechanism for spinning up the compact star in these diverse XRB systems. We infer that the low and high spin BH XRBs may experience different evolution and accretion history, which corresponds to the bimodal distribution of the BH spin parameters. The low spin BHs ($a_{*}<0.3$) are similar to the NS LMXBs, the compact star of which is spun-up by the low-level accretion, and the high spin BHs ($a_{*}>0.5$) had experienced a short hypercritical accretion ($\gg \dot{M}_\mathrm{Edd}$) period, during which, the BH spin dramatically increased.