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

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 $T_{\mathrm{e}}$, gravity $g_{\mathrm{e}}$ 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 $\mathcal{M}$ 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, $\mathcal{M}=(0.68\pm .03){\mathcal{M}}_{\odot }$, equilibrium luminosity $L_{\mathrm{eq}}=45.9\pm 9.3L_{\odot }$ and $T_{\mathrm{eq}}=6813\pm 20$~K.

8 pages, 3 figures

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