Spectroscopy of TOI-1259B -- an unpolluted white dwarf companion to an inflated warm Saturn

TOI-1259 consists of a transiting exoplanet orbiting a main sequence star, with a bound outer white dwarf companion. Less than a dozen systems with this architecture are known. We conduct follow-up spectroscopy on the white dwarf TOI-1259B using the Large Binocular Telescope (LBT) to better characterise it. We observe only strong hydrogen lines, making TOI-1259B a DA white dwarf. We see no evidence of heavy element pollution, which would have been evidence of planetary material around the white dwarf. Such pollution is seen in ~ 25 - 50% of white dwarfs, but it is unknown if this rate is higher or lower in TOI-1259-like systems that contain a known planet. Our spectroscopy permits an improved white dwarf age measurement of 4.05 (+1.00 -0.42) Gyrs, which matches gyrochronology of the main sequence star. This is the first of an expanded sample of similar binaries that will allow us to calibrate these dating methods and provide a new perspective on planets in binaries.