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The progenitor of binary millisecond radio pulsar PSR J1713+0747 (Research Note)

PSR J1713+0747 is a binary system comprising millisecond radio pulsar with a spin period of 4.57 ms, and a low-mass white dwarf (WD) companion orbiting the pulsar with a period of 67.8 days. Using the general relativistic Shapiro delay, the masses of the WD and pulsar components were previously found to be $0.28\pm 0.03 M_{\odot}$ and $1.3\pm 0.2 M_{\odot}$ (68% confidence), respectively. Standard binary evolution theory suggests that PSR J1713+0747 evolved from a low-mass X-ray binary (LMXB). Here, we test this hypothesis. We used a binary evolution code and a WD evolution code to calculate evolutionary sequences of LMXBs that could result in binary millisecond radio pulsars such as PSR J1713+0747. During the mass exchange, the mass transfer is nonconservative. Because of the thermal and viscous instabilities developing in the accretion disk, the neutron star accretes only a small part of the incoming material. We find that the progenitor of PSR J1713+0747 can be modelled as an LMXB including a donor star with mass $1.3-1.6 M_{\odot}$ and an initial orbital period ranging from 2.40 to 4.15 days. If the cooling timescale of the WD is 8 Gyr, its present effective temperature is between 3870 and 4120 K, slightly higher than the observed value. We estimate a surface gravity of ${\rm Log} (g) \approx 7.38 - 7.40$.