Empirical Bolometric Correction and Zero-Point Constants of Visual Magnitudes from High-Resolution Spectra

TL;DR

This paper presents a new empirical method to accurately determine bolometric corrections and zero-point constants for visual magnitudes using high-resolution spectra, improving stellar luminosity estimates.

Contribution

It introduces a novel empirical approach to derive bolometric corrections and zero-point constants from high-resolution spectra, with precise calibration against established magnitude systems.

Findings

Achieved bolometric correction accuracy within a few millimagnitudes.

Determined zero-point constants with high precision for different spectral profiles.

Analyzed the accuracy limits for stellar luminosity predictions.

Abstract

A method of obtaining bolometric corrections ($BC_{\rm V}$) from observed high-resolution, high-$S/N$ spectra is described. The method is applied to spectra of 128 stars collected from the literature with well-determined effective temperatures ($T_{\rm eff}$) with $S_\lambda(V)$ transparency profiles of Bessell and Landolt. Computed $BC_{\rm V}$ are found accurate within several milimagnitudes and the effect of different $S_\lambda(V)$ is found to be no more than 0.015 mag. Measured visual to bolometric ratio ($L_{\rm V}/L$) from the sample spectra and classically determined $BC_{\rm V}$ from bolometric ($M_{\rm Bol}$) and visual ($M_{\rm V}$) absolute magnitudes helped us to determine the zero-point constant ($C_{\rm 2}$) of the $BC_{\rm V}$ scale. Determined $C_{\rm 2}$ for each star for each $S_\lambda(V)$ profile revealed $C_{\rm 2} = 2.3653\pm0.0067$ mag if $S_\lambda(V)$ profile of Bessell is used, and $C_{\rm 2} = 2.3826\pm0.0076$ mag if $S_\lambda(V)$ profile of Landolt is used. Expanding $C_{\rm Bol} = 71.197425 ...$ mag and $c_{\rm Bol} = -18.997351 ...$ mag announced by IAU2015GARB2, and using definition of $C_{\rm 2} = C_{\rm Bol}-C_{\rm V} = c_{\rm Bol}-c_{\rm V}$, where capital $C$ is for the absolute and small $c$ is for the apparent, subscripts indicating bolometric and visual, the zero-point constants: $C_{\rm V} = 68.8321\pm0.0067$ mag and $c_{\rm V} = -21.3627\pm0.0067$ mag, if $L_{\rm V}$ and are in SI units, were determined corresponding to $S_\lambda(V)$ of Bessell. The zero-point constants corresponding to $S_\lambda(V)$ of Landolt are smaller, but the difference is not more than 0.02 mag. Typical and limiting accuracies for predicting a stellar luminosity from an apparent magnitude and a distance are analyzed.