TOI-1259Ab: A Warm Jupiter Orbiting a K-dwarf White-Dwarf Binary is on a Well-aligned Orbit

The evolution of one member of a stellar binary into a white dwarf has been proposed as a mechanism that triggers the formation of close-in gas giant planets. The star's asymmetric mass loss during the AGB stage gives it a "kick" that can initiate Eccentric Lidov-Kozai oscillations, potentially causing a planet around the secondary star to migrate inwards and perturbing the eccentricity and inclination of its orbit. Here we present a measurement of the stellar obliquity of TOI-1259Ab, a gas giant in a close-in orbit around a K star with a white dwarf companion about 1650 au away. By using the NEID spectrograph to detect the Rossiter-McLaughlin effect during the planetary transit, we find the sky-projected obliquity to be $\lambda = 6^{+21}_{-22}\,^\circ$. When combined with estimates of the stellar rotation period, radius, and projected rotation velocity, we find the true 3D obliquity to be $\psi = 24^{+14}_{-12}\,^\circ$ ($\psi < 48^\circ$ at 95% confidence), revealing that the orbit of TOI-1259Ab is well aligned with the star's equatorial plane. Because the planet's orbit is too wide for tidal realignment to be expected, TOI-1259Ab might have formed quiescently in this well-aligned configuration. Alternatively, as we show with dynamical simulations, Eccentric Lidov-Kozai oscillations triggered by the evolution of the binary companion are expected to lead to a low obliquity with a probability of about $\sim$14%.