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Eclipsing Binaries Observed with the WIRE Satellite II A&A 467, 1215–1226 (2007) Astronomy DOI: 10.1051/0004-6361:20077184 & c ESO 2007 Astrophysics Eclipsing binaries observed with the WIRE satellite II. β Aurigae and non-linear limb darkening in light curves J. Southworth1, H. Bruntt2, and D. L. Buzasi3 Department of Physics, University of Warwick, Coventry, CV4 7AL, UK e-mail: [email protected] School of Physics A28, University of Sydney, 2006 NSW, Australia e-mail: [email protected] US Air Force Academy, Department of Physics, CO, USA e-mail: [email protected] 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 Aur are RA = 2.762 ± 0.017 R, RB = 2.568 ± 0.017 R, MA = 2.376 ± 0.027 M and MB = 2.291 ± 0.027 M, 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 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. Key words. stars: fundamental parameters – stars: binaries: eclipsing – stars: binaries: spectroscopic – stars: distances – stars: evolution – stars: individual: β Aurigae 1. Introduction Field Infra-red Explorer (wire) satellite. wire was launched in March 1999 but the coolant for the main camera was lost only The study of detached eclipsing binaries (dEBs) is our primary a few days after launch. Since then the star tracker on wire has source of accurate physical properties of normal stars (Andersen been used to monitor the variability of bright stars of all spec- 1991). By modelling their light curves and deriving radial veloc- tral types, as described in the review by Bruntt (2007). The main ities of the two components from their spectra, it is possible to aims of the current work are to accurately measure the physical measure the masses and radii of the two components to accura- properties of the systems and to investigate whether the currently cies of better than 1% (e.g., Southworth et al. 2005c; Lacy et al. available eclipsing binary light curve models can provide a good ff 2005). The e ective temperatures and luminosities of the stars fit to observational data with measurement uncertainties substan- ff can be found by a variety of di erent methods, including pho- tially below 1 mmag. We expect the answer to the second ques- tometric calibration, spectral analysis and measuring trigono- tion to be “yes”, but this matter is becoming increasingly impor- metric parallaxes. These data can be used to measure accurate tant in light of current and forthcoming space missions, such as distances to stellar systems (Ribas et al. 2005; Southworth et al. Kepler (Basri et al. 2005) and CoRoT (Michel et al. 2006), which 2005a) and to critically investigate the accuracy of the predic- aim to obtain extremely high-quality light curves of a large num- tions resulting from theoretical stellar models (e.g., Ribas 2006). berofstars. We are undertaking a project to obtain accurate and ex- tensive light curves of selected bright dEBs using the Wide Our first paper in this series presented the serendipitous discovery that the bright star ψ Centauri is a long-period dEB Full Table 2 is only available in electronic form at the CDS via (Bruntt et al. 2006, hereafter Paper I). The wire light curve anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via of this object shows deep total eclipses arising from a system http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/467/1215 containing two stars of quite different sizes. dEBs containing Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20077184 1216 J. Southworth et al.: WIRE satellite photometry of β Aurigae two dissimilar stars are particularly useful because the co- Table 1. Identifications and astrophysical data for β Aur. evolutionary nature of the two components can put strong con- straints on the predictions of theoretical models (Southworth β Aur References et al. 2004b). However, one of the most interesting aspects of Bright Star Catalogue HR 2088 1 this work is that we were able to measure the relative radii of Henry Draper Catalogue HD 40183 2 the two stars (radii expressed as a fraction of the orbital size) Hipparcos Catalogue HIP 28360 3 h m s to a precision of better than 0.2%, where the uncertainties were α2000 05 59 31.7229 3 + ◦ estimated from extensive Monte Carlo simulations but did not δ2000 44 56 50.758 3 include error contributions from some sources such as the use Spectral type A1m IV + A1m IV 4, 5 ff Trigonometric parallax 39.72 ± 0.78 mas 3 of di erent algebraic laws to describe the limb darkening of the ± stars. Distance 25.18 0.49 pc 3 Tycho B magnitude (BT ) 1.989 ± 0.005 6 Tycho V magnitude (VT ) 1.904 ± 0.005 6 1.1. β Aurigae References: (1) Hoffleit & Jaschek (1991); (2) Cannon & Pickering wire (1918); (3) Perryman et al. (1997); (4) NJ94; (5) Lyubimkov et al. In this work we present a light curve for the dEB β Aurigae (1996); (6) Høg et al. (1997). (Menkalinan), which is composed of two A1 IV stars orbiting each other with a period of 3.96 days (Table 1). This light curve contains 30 015 datapoints with a point to point scatter of less containing two stars of almost the same size, particularly if they than 0.3 mmag. We chose β Aurasatargetforthewire satel- exhibit shallow eclipses, the ratio of the stellar radii is poorly de- lite due to its brightness, which not only made our observations termined by the light curves (Popper 1984), so NJ94 constrained more precise but also makes it a very difficult object to study their light curve solution with an accurate spectroscopic light ra- with modern telescopes. In addition, it has an accurate trigono- tio. The resulting properties of the stars have since been used for metric parallax from the Hipparcos satellite which means the studies of the helium–metal enrichment law (Ribas et al. 2000) effective temperatures and surface brightnesses of the stars can and the fundamental effective temperature scale (Smalley et al. be measured directly and used to calibrate these quantities for 2002). other objects. β Aur was one of the first stars discovered to be a spectro- 2. Observations and data reduction scopic binary system, by Maury (1890), and an orbit was calcu- lated by Rambaut (1891) from the published observations. It was β Aur was observed with the wire star tracker from subsequently discovered by Stebbins (1911) to undergo shallow 2006 March 30 to April 20. During each 93.2 min orbit of Earth eclipses, and so was also one of the first known eclipsing bina- wire switched between two targets in order to minimise the in- ries. A detailed discussion of early work, and an investigation fluence of scattered light from the daytime side of Earth. In the into whether the speed of light is dependent on wavelength, was data reduction we discarded the datapoints at the very begin- given by Baker (1910). ning and the end of each orbit, resulting in a duty cycle of 25%. The brightness of β Aur and the shallowness of its eclipses Observations were obtained during every orbit for 21 days. The has made it difficult to observe photometrically, and only wire passband is approximately V+R (Bruntt et al. 2007). It the study by Johansen (1971) has provided accurate results. may in future be possible to obtain a more precise description of Johansen obtained light curves of β Aur in seven passbands, the response function by considering the the total set of observa- four of which closely resemble the Strömgren uvby system, and tions obtained using the wire star tracker.
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