First discovery of an ultra-cool white dwarf benchmark in common proper motion with an M dwarf

Ultra-cool white dwarfs are among the oldest stellar remnants in the Universe. Their efficient gravitational settling and low effective temperatures are responsible for the smooth spectra they exhibit. For that reason, it is not possible to derive their radial velocities or to find the chemistry of the progenitors. The best that can be done is to infer such properties from associated sources, which are coeval. The simplest form of such a system is a common proper motion pair where one star is an evolved degenerate and the other a main-sequence star. In this work, we present the discovery of the first of such a system, the M dwarf LHS 6328 and the ultra-cool white dwarf PSO J1801+625, from the Pan-STARRS 1 3$\pi$ survey and the $Gaia$ Data Release 2. Follow-up spectra were collected covering a usable wavelength range of 3750-24500 {\AA}. Their spectra show that the white dwarf has an effective temperature of 3550K and surface gravity of $\log g = 7.45 \pm 0.13$ or $\log g = 7.49 \pm 0.13$ for a CO or He core, respectively, when compared against synthetic spectra of ultra-cool white dwarf atmosphere models. The system has slightly subsolar metallicity with -0.25 < [Fe/H] < 0.0, and a spatial velocity of (U, V, W) = ($-114.26 \pm 0.24$, $222.94 \pm 0.60$, $10.25 \pm 0.34$) km s $^{-1}$ the first radial velocity and metallicity measurements of an ultra-cool white dwarf. This makes it the first and only benchmark of its kind to date.