The 3D Galactocentric velocities of Kepler stars: marginalizing over missing RVs

TL;DR

This paper infers 3D velocities of Kepler stars by marginalizing over missing radial velocities, combining Gaia and spectroscopic survey data, to enable advanced galactic studies despite incomplete velocity data.

Contribution

It introduces a method to estimate full 3D stellar velocities by marginalizing over missing radial velocities, tailored for the Kepler field using combined Gaia and spectroscopic data.

Findings

Provided 3D velocities for 148,590 Kepler stars.

Median velocity uncertainties are approximately 4 km/s for vx and vz, and 18 km/s for vy.

Method enables kinematic studies even with incomplete velocity data.

Abstract

Precise Gaia measurements of positions, parallaxes, and proper motions provide an opportunity to calculate 3D positions and 2D velocities (i.e. 5D phase-space) of Milky Way stars. Where available, spectroscopic radial velocity (RV) measurements provide full 6D phase-space information, however there are now and will remain many stars without RV measurements. Without an RV it is not possible to directly calculate 3D stellar velocities, however one can infer 3D stellar velocities by marginalizing over the missing RV dimension. In this paper, we infer the 3D velocities of stars in the Kepler field in Cartesian Galactocentric coordinates (vx, vy, vz). We directly calculate velocities for around a quarter of all Kepler targets, using RV measurements available from the Gaia, LAMOST and APOGEE spectroscopic surveys. Using the velocity distributions of these stars as our prior, we infer velocities for the remaining three-quarters of the sample by marginalizing over the RV dimension. The median uncertainties on our inferred vx, vy, and vz velocities are around 4, 18, and 4 km/s, respectively. We provide 3D velocities for a total of 148,590 stars in the Kepler field. These 3D velocities could enable kinematic age-dating, Milky Way stellar population studies, and other scientific studies using the benchmark sample of well-studied Kepler stars. Although the methodology used here is broadly applicable to targets across the sky, our prior is specifically constructed from and for the Kepler field. Care should be taken to use a suitable prior when extending this method to other parts of the Galaxy.