# The Tilt of the Local Velocity Ellipsoid as Seen by Gaia

## TL;DR

This study maps the tilt of the stellar velocity ellipsoid within 5 kpc of the Sun using Gaia data, revealing a near-spherical alignment that varies with position and stellar population.

## Contribution

It provides a detailed empirical measurement of the velocity ellipsoid tilt across the solar neighborhood, highlighting its dependence on location and stellar type.

## Key findings

- Velocity ellipsoid tilt follows a near-arctangent relation with height and radius.
- Tilt is close to spherical alignment, pointing towards the Galactic center.
- Different tilt behaviors are observed for thin disc and halo stars.

## Abstract

The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7,224,631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Sch\"onrich et al. (2019). We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where ($R,z$) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalising constant would be unity) and pointing towards the Galactic centre. Flattening of the tilt of the velocity ellipsoids is enhanced close to the plane and Galactic centre, whilst at high elevations far from the Galactic center the population is consistent with exact spherical alignment. Using the LAMOST catalogue cross-matched with Gaia DR2, we construct thin disc and halo samples of reasonable purity based on metallicity. We find that the tilt of thin disc stars straddles $\alpha = (0.909-1.038)\arctan (|z|/R)$, and of halo stars straddles $\alpha = (0.927-1.063)\arctan (|z|/R)$. We caution against the use of reciprocal parallax for distances in studies of the tilt, as this can lead to serious artefacts.