The local stellar velocity field via vector spherical harmonics

TL;DR

This paper uses vector spherical harmonics to analyze stellar velocities from Hipparcos data, revealing known parameters and unexpected harmonic terms that challenge classical models of Galactic motion.

Contribution

It introduces a novel application of vector spherical harmonics to stellar velocity data, uncovering new harmonic components and their implications for Galactic dynamics.

Findings

Determined the solar velocity relative to local stars.

Estimated Oort's parameters using harmonic decomposition.

Identified a significant magnetic harmonic indicating unexpected stellar rotation.

Abstract

We analyze the local field of stellar tangential velocities for a sample of $42 339$ non-binary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships we determine the solar velocity with respect to the local stars of $(V_X,V_Y,V_Z)=(10.5, 18.5, 7.3)\pm 0.1$ \kms. The Oort's parameters determined by a straightforward least-squares adjustment in vector spherical harmonics, are $A=14.0\pm 1.4$, $B=-13.1\pm 1.2$, $K=1.1\pm 1.8$, and $C=-2.9\pm 1.4$ \kmspc. We find a few statistically significant higher degree harmonic terms, which do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at $\sim -20$ \kmspc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic representing a rigid rotation of the stellar field about the axis $-Y$ pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient $6.2 \pm 0.9$ \kmspc, and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.