Semi-analytical formulas for the Hertzsprung-Russell Diagram

TL;DR

This paper introduces semi-analytical formulas for the Hertzsprung-Russell diagram that enable the estimation of stellar physical parameters and improve distance and classification measurements, especially for white dwarfs.

Contribution

It develops a new semi-analytical framework for the Hertzsprung-Russell diagram that deduces stellar parameters and enhances calibration accuracy without extensive data.

Findings

Applied to local star samples and clusters, improving distance estimates.

Achieved smaller χ² in white dwarf calibration compared to standard methods.

Clarified theoretical basis through Taylor expansion of Planck distribution.

Abstract

The absolute visual magnitude as function of the observed colour (B-V), also named Hertzsprung-Russell diagram can be described through five equations; that in presence of calibrated stars means eight constants. The developed framework allows to deduce the remaining physical parameters that are mass, radius and luminosity. This new technique is applied to the first 10 pc, the first 50 pc, the Hyades and to the determination of the distance of a cluster. The case of the white dwarfs is analysed assuming the absence of calibrated data: our equation produces a smaller $\chi^2$ in respect to the standard colour-magnitude calibration when applied to the Villanova Catalog of Spectroscopically Identified White Dwarfs. The theoretical basis of the formulae for the colours and the bolometric correction of the stars are clarified through a Taylor expansion in the temperature of the Planck distribution.