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

TL;DR

This work addresses the arbitrariness of bolometric-correction zero-points by empirically anchoring the BC$_V$ scale to the IAU 2015 definitions. Using 128 high-resolution spectra from multiple instruments, it derives the BC$_V$ zero-point $C_{ m 2}$ from spectroscopic luminosity fractions $L_{ m V}/L$ and fixes the visual zero-points $C_{ m V}$ and $c_{ m V}$, dependent on the chosen visual filter profile $S_\\lambda(V)$. It introduces and fits spectroscopic BC$_V$–$T_{ m eff}$ relations for two $S_\\lambda(V)$ profiles (Bessell 1990 and Landolt 1992) and compares them with a photometric BC$_V$–$T_{ m eff}$ relation, finding the spectroscopic forms substantially more precise. The study shows that, with accurate parallax and modest interstellar extinction, the indirect method can predict stellar luminosities to about 1–5% precision, substantially reducing uncertainties tied to nonstandard BCs and enabling robust luminosity and extinction determinations from high-quality spectra. The framework sets the stage for extending empirical BC calibrations to additional bands and metallicities, with broad implications for stellar parameter determinations and distance-scale work.

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 $S_λ(V)$ transparency profiles of Bessell and Landolt. Computed $BC_{\rm V}$ are found accurate within several milimagnitudes and the effect of different $S_λ(V)$ 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 $S_λ(V)$ profile revealed $C_{\rm 2} = 2.3653\pm0.0067$ mag if $S_λ(V)$ profile of Bessell is used, and $C_{\rm 2} = 2.3826\pm0.0076$ mag if $S_λ(V)$ 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 $S_λ(V)$ of Bessell. The zero-point constants corresponding to $S_λ(V)$ 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.

Figures (11)

• Figure 1: Top panel: SED models of two stars (HD 32630 and HD 208266) with different interstellar extinctions. Bottom panel:$\chi^2$ map of models given in the top panel.
• Figure 4: Normalized solar spectrum and V filter profile (a), de-normalized flux and V filter spectra (b), and the convoluted spectrum of the Sun (c). Dividing the area under the convoluted spectrum by $\sigma T_{\rm eff}^4 (\odot)$ gives solar $L_{\rm V}/L$ = 10.49 or 10.19 percent for Bessell1990 and the Landolt1992 profile functions, respectively.
• Figure 6: Distribution of the sample stars on H-R diagram. ZAMS and TAMS, according to PARSEC evolution models Bressan2012 are indicated. Symbols: $\triangle$, HERMES; $\filledtriangleup$, PEPSI; $\bullet$, FIES; $\circ$, FEROS; $\filledsquare$, ESPaDOnS; $\filledsquare$, NARVAL; $\filledtriangledown$, FTS.
• Figure 7: Uncertainty histograms of $T_{\rm eff}$ (top), $R$ (middle), and $L$ (bottom).
• Figure 8: Bolometric correction ($BC_{\rm V}$) for the visual magnitudes (bottom) as the difference between the absolute bolometric (top) and the visual (middle) magnitudes. Evolved stars are shown by the filled symbols.