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

TL;DR

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

Contribution

It introduces a novel calibration technique combining photometry and atmospheric models to derive RR Lyrae star parameters, extending the quasi-static atmosphere approximation to dynamic conditions.

Findings

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

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

Provided estimates of luminosity and temperature consistent with theoretical expectations.

Abstract

A photometric calibration of Kurucz static model atmospheres is used to obtain parameters of RR Lyrae stars: variation of stellar angular radius $\vartheta$, effective temperature $T_{\rm e}$, and gravity $g_{\rm e}$ as a function of phase, interstellar reddening $E(B-V)$ toward 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, $L_{\rm eq}=45.9\pm 9.3L_\odot$, $T_{\rm eq}=6813\pm 20$ K.