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Eclipsing binaries observed with the WIRE satellite. II. beta Aurigae and non-linear limb darkening in light curves

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 eclipsing binary light curve models. This light curve, of the bright system beta Aurigae, was obtained using the star tracker aboard the WIRE satellite and contains 30000 datapoints with a scatter of 0.3 mmag. We analyse it using a version of the EBOP code modified to include non-linear limb darkening and to directly incorporate observed times of minimum light and spectroscopic light ratios into the solution as individual observations. We also analyse the dataset with the WD code to ensure that the two models give consistent results. EBOP provides an excellent fit to the WIRE data. Whilst the fractional radii are only defined to a precision of 5%, 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 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, and they agree with theoretical predictions. The radii and masses of the components of beta Aur are R_A = 2.762 +/- 0.017 Rsun, R_B = 2.568 +/- 0.017 Rsun, M_A = 2.376 +/- 0.027 Msun and M_B = 2.291 +/- 0.027 Msun. Theoretical stellar 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 beta Aur 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 (abridged).