PG 1258+593 and its common proper motion magnetic white dwarf counterpart

We confirm SDSS J130033.48+590407.0 as a common proper motion companion to the well-studied hydrogen-atmosphere (DA) white dwarf PG1258+593 (GD322). The system lies at a distance of 68 ± 3 pc, where the angular separation of 16.1 ± 0.1 arcsec corresponds to a minimum binary separation of 1091±7 au. SDSS J1300+5904 is a cool (T_eff =6300±300 K) magnetic white dwarf (B ≈ 6 mG). PG1258+593 is a DA white dwarf with T eff = 14790 ± 77K and log g = 7.87 ± 0.02. Using the white dwarf mass-radius relation implies the masses of SDSS J1300+5904 and PG 1258+593 are 0.54 ± 0.06 and 0.54 ± 0.01M_⊗, respectively, and therefore a cooling age difference of 1.67 ± 0.05 Gyr. Adopting main-sequence lifetimes from stellar models, we derive an upper limit of 2.2M_⊗ for the mass of the progenitor of PG 1258+593. A plausible range of initial masses is 1.4-1.8 M_⊗ for PG1258+593 and 2-3M_⊗ for SDSS J1300+5904. Our analysis shows that white dwarf common proper motion binaries can potentially constrain the white dwarf initial mass-final mass relation and the formation mechanism for magnetic white dwarfs. The magnetic field of SDSS J1300+5904 is consistent with an Ap progenitor star. A common envelope origin of the system cannot be excluded, but requires a triple system as progenitor.