Eclipsing binaries observed with the WIRE satellite^*

II. β Aurigae and non-linear limb darkening in light curves

¹ Department of Physics, University of Warwick, Coventry, CV4 7AL, UK e-mail: jkt@astro.keele.ac.uk
² School of Physics A28, University of Sydney, 2006 NSW, Australia e-mail: bruntt@physics.usyd.edu.au
³ US Air Force Academy, Department of Physics, CO, USA e-mail: Derek.Buzasi@usafa.af.mil

Received: 29 January 2007
Accepted: 13 March 2007

Abstract

Aims.We present the most precise light curve ever obtained of a detached eclipsing binary star and use it investigate the inclusion of non-linear limb darkening laws in light curve models of eclipsing binaries. This light curve, of the bright eclipsing system β Aurigae, was obtained using the star tracker aboard the wire satellite and contains 30 000 datapoints with a point-to-point scatter of 0.3 mmag.

Methods.We analyse the wire light curve using a version of the ebop code modified to include non-linear limb darkening laws and to directly incorporate observed times of minimum light and spectroscopic light ratios into the photometric solution as individual observations. We also analyse the dataset with the Wilson-Devinney code to ensure that the two models give consistent results.

Results.ebop is able to provide an excellent fit to the high-precision wire data. Whilst the fractional radii of the stars are only defined to a precision of 5% by this light curve, including an accurate published spectroscopic light ratio improves this dramatically to 0.5%. Using non-linear limb darkening improves the quality of the fit significantly compared to the linear law and causes the measured radii to increase by 0.4%. It is possible to derive all of the limb darkening coefficients from the light curve, although they are strongly correlated with each other. The fitted coefficients agree with theoretical predictions to within their fairly large error estimates. We were able to obtain a reasonably good fit to the data using the Wilson-Devinney code, but only using the highest available integration accuracy and by iterating for a long time. Bolometric albedos of 0.6 were found, which are appropriate to convective rather than radiative envelopes.

Conclusions.The radii and masses of the components of β are R_A = 2.762±0.017, R_B = 2.568±0.017, M_A = 2.376±0.027 and M_B = 2.291±0.027, where A and B denote the primary and secondary star, respectively. Theoretical stellar evolutionary models can match these parameters for a solar metal abundance and an age of 450-500 Myr. The Hipparcos trigonometric parallax and an interferometrically-derived orbital parallax give distances to β which are in excellent agreement with each other and with distances derived using surface brightness relations and several sets of empirical and theoretical bolometric corrections.