Potential-density pairs and vertical tilt of the stellar velocity ellipsoid

TL;DR

This paper introduces new potential-density pairs and investigates how the flattening of galactic potentials influences the tilt of the stellar velocity ellipsoid, providing insights into the shape of the dark matter halo.

Contribution

It presents new potential-density pairs and analyzes the effect of potential flattening on the velocity ellipsoid tilt using numerical and analytical methods.

Findings

At 1 kpc above the Galactic plane, tilt angle varies by 5 degrees depending on halo shape.

Results suggest the Galactic dark halo is not extremely flattened.

The study constrains dark halo flattening based on velocity ellipsoid tilt measurements.

Abstract

We define new potential-density pairs and examine the impact of the potential flattening on the vertical velocity ellipsoid tilt, $\delta$. By means of numerical integrations and analytical calculations, we estimate $\delta$ in a variety of galactic potentials. We show that at 1 kpc above the Galactic plane at the solar radius, $\delta$ can differ by 5 degrees, depending on whether the dark matter halo is flat or spherical. This result excludes the possibility of an extremely flattened Galactic dark halo.