Correcting velocity dispersions of dwarf spheroidal galaxies for binary orbital motion

TL;DR

This paper presents a method to accurately correct dwarf spheroidal galaxy velocity dispersions for binary star orbital motion using two-epoch observations and a threshold fraction approach, improving the precision of intrinsic dispersion measurements.

Contribution

It introduces a new correction technique based on threshold fractions and Bayesian analysis to account for binary orbital effects in velocity dispersion measurements.

Findings

Binary orbital motion inflates velocity dispersions by less than 20%.

Two-epoch observations with 1-2 years are optimal for correction.

The threshold fraction correlates with binary-induced velocity dispersion.

Abstract

We show that measured velocity dispersions of dwarf spheroidal galaxies from about 4 to 10 km/s are unlikely to be inflated by more than 20% due to the orbital motion of binary stars, and demonstrate that the intrinsic velocity dispersions can be determined to within a few percent accuracy using two-epoch observations with 1-2 years as the optimal time interval. The crucial observable is the threshold fraction--the fraction of stars that show velocity changes larger than a given threshold between measurements. The threshold fraction is tightly correlated with the dispersion introduced by binaries, independent of the underlying binary fraction and distribution of orbital parameters. We outline a simple procedure to correct the velocity dispersion to within a few percent accuracy by using the threshold fraction and provide fitting functions for this method. We also develop a methodology for constraining properties of binary populations from both single- and two-epoch velocity measurements by including the binary velocity distribution in a Bayesian analysis.