Maximum likelihood estimation of local stellar kinematics

TL;DR

This paper introduces a maximum likelihood method for estimating local stellar kinematics using only transverse velocities, effectively handling observational errors and incomplete data, and outperforming previous projection techniques.

Contribution

It formulates and tests a new maximum likelihood approach for kinematic estimation with incomplete stellar data, improving accuracy and reliability.

Findings

Maximum likelihood yields more accurate dispersion estimates with errors.

The method guarantees a positive-definite dispersion matrix.

It outperforms the projection method in simulations and real data.

Abstract

Context. Kinematical data such as the mean velocities and velocity dispersions of stellar samples are useful tools to study galactic structure and evolution. However, observational data are often incomplete (e.g., lacking the radial component of the motion) and may have significant observational errors. For example, the majority of faint stars observed with Gaia will not have their radial velocities measured. Aims. Our aim is to formulate and test a new maximum likelihood approach to estimating the kinematical parameters for a local stellar sample when only the transverse velocities are known (from parallaxes and proper motions). Methods. Numerical simulations using synthetically generated data as well as real data (based on the Geneva-Copenhagen survey) are used to investigate the statistical properties (bias, precision) of the method, and to compare its performance with the much simpler "projection method" described by Dehnen & Binney (1998). Results. The maximum likelihood method gives more correct estimates of the dispersion when observational errors are important, and guarantees a positive-definite dispersion matrix, which is not always obtained with the projection method. Possible extensions and improvements of the method are discussed.