We identify SDSS J130033.48+590407.0 as a common proper motion companion to the well-studied DA white dwarf PG 1258+593 ( GD322 ) .
The system lies at a distance of 68 \pm 3 pc , where the angular separation of 16.1 \pm 0.1 \arcsec corresponds to a minimum binary separation of 1091 \pm 7 AU .
SDSS J1300+5904 is a cool ( \mbox { $T _ { \mathrm { eff } } $ } = 6300 \pm 300 K ) magnetic white dwarf ( B \simeq 6 MG ) .
PG 1258+593 is a hydrogen-rich ( DA ) white dwarf with \mbox { $T _ { \mathrm { eff } } $ } = 14790 \pm 77 K and \log g = 7.87 \pm 0.02 .
Using the white dwarf mass–radius relation implies the masses of SDSS J1300+5904 and PG 1258+593 are 0.54 \pm 0.06 \mathrm { M } _ { \odot } and 0.54 \pm 0.01 \mathrm { M } _ { \odot } , respectively , and therefore a cooling age difference of 1.67 \pm 0.05 Gyr .
Adopting main-sequence life times from stellar models , we derive an upper limit of 2.2 \mathrm { M } _ { \odot } for the mass of the progenitor of PG 1258+593 .
A plausible range of initial masses is 1.4–1.8 \mathrm { M } _ { \odot } for PG 1258+593 and 2–3 \mathrm { M } _ { \odot } for SDSS J1300+5904 .
Our analysis shows that white dwarf common proper motion binaries can potentially constrain the white dwarf initial-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 can not be excluded , but requires a triple system as progenitor .