Absolute parameters for AI Phoenicis using WASP photometry

Abstract

AI Phe is a double-lined, detached binary, in which a K-type sub-giant star totally eclipses its main-sequence companion every 24.6 days. This configuration makes AI Phe ideal for testing stellar evolutionary models. Difficulties in obtaining a complete lightcurve mean the precision of existing radii measurements could be improved. Our aim is to improve the precision of the radius measurements for the stars in AI Phe using high-precision photometry from WASP, and use these improved radius measurements together with estimates of the masses, temperatures and composition of the stars to place constraints on the mixing length, helium abundance and age of the system. A best-fit ebop model is used to obtain lightcurve parameters, with their standard errors calculated using a prayer-bead algorithm. These were combined with previously published spectroscopic orbit results, to obtain masses and radii. A Bayesian method is used to estimate the age of the system for model grids with different mixing lengths and helium abundances. The radii are found to be $R_1=1.835\pm0.014$ R$_{\odot}$, $R_2=2.912\pm0.014$ R$_{\odot}$ and the masses $M_1=1.1973\pm0.0037$ M$_{\odot}$, $M_2=1.2473\pm0.0039$ M$_{\odot}$. From the best-fit stellar models we infer a mixing length of 1.78, a helium abundance of $Y_{AI}=0.26^{+0.02}_{-0.01}$ and an age of $4.39\pm0.32$ Gyr. Times of primary minimum show the period of AI Phe is not constant. Currently, there are insufficient data to determine the cause of this variation. Improved precision in the masses and radii have improved the age estimate, and allowed the mixing length and helium abundance to be constrained. The eccentricity is now the largest source of uncertainty in calculating the masses. More binaries with parameters measured to a similar level of precision would allow us to test for relationships between helium abundance and mixing length.