The Empirical Mass-Luminosity Relation for Low Mass Stars

TL;DR

This paper develops an improved empirical mass-luminosity relation for low mass stars, accounting for observational errors and the mass-metallicity-luminosity relation, resulting in more accurate models across multiple spectral bands.

Contribution

It introduces a novel weighting scheme for fitting observational data with errors in multiple dimensions and refines the mass-luminosity and mass-metallicity-luminosity relations for low mass stars.

Findings

Identified a plateau in the mass-luminosity relation from 0.28 to 0.50 solar mass.

Derived three-piecewise continuous relations in multiple spectral bands.

Enhanced the mass-metallicity-luminosity relation using new empirical data.

Abstract

This work is devoted to improving empirical mass-luminosity relations and mass-metallicity-luminosity relation for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the mass-luminosity relation. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28 to 0.50 solar mass. Three-piecewise continuous improved mass-luminosity relations in K, J, H and V bands, respectively, are obtained. The visual mass-metallicity-luminosity relation is also improved based on our K band mass-luminosity relation and the available observational metallicity data.