Formation of PSR J1012+5307 with an Extremely Low-mass White Dwarf: Testing Magnetic Braking Models

PSR J1012+5307 is a millisecond pulsar with an extremely low-mass white dwarf (WD) companion in an orbit of 14.5 hr. Magnetic braking (MB) plays an important role in influencing the orbital evolution of binary systems with a low-mass (≲1–2 M _⊙ ) donor star. At present, there exist several different MB descriptions. In this paper, we investigate the formation of PSR J1012+5307 as a probe to test plausible MB models. Employing a detailed stellar evolution model with the MESA code, we find that the convection- and rotation-boosted MB and “Intermediate” MB models can reproduce the WD mass, WD radius, WD surface gravity, neutron star mass, and orbital period observed in PSR J1012+5307. However, our simulated WD has a higher effective temperature than the observations. Three other MB mechanisms, including the standard MB model, are too weak to account for the observed orbital period in the Hubble time. A long cooling timescale caused by H-shell flashes of the WD may alleviate the discrepancy between the simulated effective temperature and the observed value.