The masses of the millisecond pulsar J1012+5307 and its white-dwarf companion

We report on spectroscopy of the white-dwarf companion of the millisecond radio pulsar PSR J1012+5307. We find strong Balmer absorption lines, as would be expected for a cool DA white dwarf. The profiles are much narrower than usual, however, and lines are seen up to H12, indicating that the companion has a low gravity and hence a low mass. This is consistent with the expectation---based on evolutionary considerations and on the mass function---that it is a low-mass white dwarf with a helium core. By comparing the spectra to model atmospheres, we derive an effective temperature $T_{\rm{}eff}=8550\pm25\,$K and a surface gravity $\log{}g=6.75\pm0.07$ (cgs units). Using the Hamada-Salpeter mass-radius relation for helium white dwarfs, with an approximate correction for finite-temperature effects, we infer a mass $\mwd=0.16\pm0.02\,\msun$. This is the lowest mass among all spectroscopically identified white dwarfs. We determine radial velocities from our spectra, and find a radial-velocity amplitude of $280\pm15\,\kms$. With the pulsar's radial-velocity amplitude, the mass ratio $\mpsr/\mwd=13.3\pm0.7$. From all constraints, we find that with 95\% confidence $1.5<\mpsr/\msun<3.2$.