Fundamental parameters of RR Lyrae stars from multicolour photometry and Kurucz atmospheric models. I. Theory and practical implementation

TL;DR

This paper develops a method using multicolour photometry and atmospheric models to determine fundamental parameters of RR Lyrae stars, including temperature, gravity, metallicity, and distance, with practical application to SU Dra.

Contribution

It introduces a generalized quasi-static atmosphere approximation and a practical calibration method for deriving stellar parameters from multicolour photometry.

Findings

Derived stellar parameters for SU Dra, including metallicity, reddening, distance, mass, and luminosity.

Validated the method's effectiveness through application to observational data.

Provided a new approach to analyze RR Lyrae stars using atmospheric models and photometry.

Abstract

A photometric calibration of Kurucz static model atmospheres is used to obtain the following parameters of RR Lyrae stars: variation of stellar angular radius $\vartheta$, effective temperature $T_{\rm e}$, gravity $g_{\rm e}$ as a function of phase, interstellar reddening $E(B-V)$ towards the star and atmospheric metallicity $M$. Photometric and hydrodynamic conditions are given to find the phases of pulsation when the quasi-static atmosphere approximation (QSAA) can be applied. The QSAA is generalized to a non-uniformly moving spherical atmosphere, and the distance $d$, mass ${\cal M}$ and atmospheric motion are derived from the laws of mass and momentum conservation. To demonstrate the efficiency of the method, the $UBV(RI)_C$ photometry of SU Dra was used to derive the following parameters: $[M]=-1.60\pm .10$~dex, $E(B-V)=0.015\pm .010$, $d=663\pm 67$~pc, ${\cal M}=(0.68\pm .03){\cal M}_\odot$, equilibrium luminosity $L_{\rm eq}=45.9\pm 9.3L_\odot$ and $T_{\rm eq}=6813\pm 20$~K.