Info

-0.4---'—1—■—'——'---—1—'—'—•—1—'—1—'—1—■—'—

phase

-0.4---'—1—■—'——'---—1—'—'—•—1—'—1—'—1—■—'—

phase

Fig. 7.4 Radial velocities of the over-contact system H235. This plot, part of Fig. 5 in Milone et al. (1995), shows the observed and calculated radial velocity curves (three-spot case) of H235 in the open cluster NGC 752

7.3.4 The Field Binary V728 Herculis

Not every application is automatically successful. The system V728 Herculis was modeled with both WD93K93 and LC93KS, but for a long time the latter consistently yielded physically unrealistic temperatures for the secondary which was found to be the hotter component. These earlier runs were carried out under the assumption that both envelopes were radiative - a reasonable assumption because the spectral type is F3-5, and the minima are of similar depth. However, subsequent modeling indicated that deeper valleys existed in parameter space if convec-tive atmospheres were assumed. When gravity brightening and albedo coefficients appropriate for this case were adopted, the Simplex and the WD programs converged to quite similar results. These later trials were concluded with WD93K93 in a two-iteration reflection effect treatment, with nonlinear limb darkening. Both radiative and convective solutions were obtained with binned and unbinned data sets. The results for the convective modeling solution indicate that binning sometimes is significant to the final solution: For the radiative modeling solution, it did not matter (both data sets converged to the same solution). For the convective runs, the results were 1a or more different for some parameters. The observations and analytical results are discussed in Nelson et al. (1995). The final mass ratio was determined to be q = 0.1786 ± 0.0023 and the contact parameter, f = 0.71 ± 0.11. Work by (1995) and Rasio & Shapiro (1994, 1995) suggests that over-contact systems with deep convective envelopes and small mass ratios (q < 0.45) may be unstable and enter into the final merger stage. One of the interesting results of the Nelson et al. (1995) study, however, is that there was no evidence of significant period change that might be expected to accompany such a situation, although more recent times of minimum obtained by Nelson et al. suggest at least a different period if not a variable one is needed to satisfy them. However, forV728 Her, one index of instability, the radius of gyration as defined by Rasio (1995), is found to be in the stable region of Rasio's Fig. 1: k2 = 0.16. The instability of this over-contact system is, therefore, not demonstrated observationally - at least not yet.

7.3.5 The Eclipsing Binaries in M71

There are five known EBs in the globular clusterM7i (Yan & Mateo 1994, Mateo & Yan 1996). The systems are around eighteenth magnitude in V, with V - I & 1 but the Yan & Mateo CCD light curves are relatively smooth. These have been modeled with WD93K93 by J. McVean for an MSc thesis at the University of Calgary. The results are summarized in McVean et al. (1997). He assumed9 initial masses of 1.7 M0, roughly twice the turn-off mass for the cluster, from the models of Bergbusch & Vandenberg (1992). Three of the binaries (V1, V2, and V5) are over-contact

9 The radial velocity curves by Mateo & Yan (1996) were not yet included in this analysis.

Fig. 7.5 Cluster magnitude diagram of M71 with isochrones. It also contains the positions of the binaries and their individual components (open symbols)', from Fig. 2 in McVean et al. (1997)

systems; the other two appear to be detached systems according to the best fit models, but the photometric secondary star of V4 has a contact parameter of -0.11, indicating that it nearly fills its Roche lobe. Due to O'Connell effects in the light curves of V1 and V3, a spot group was required on one of the components of both systems. All five systems have derived distances, within errors, in agreement with those (3.6 ± 0.5 kpc) determined by Cudworth (1985) but V3, has an unusual location on the color-magnitude diagram of the cluster (see Fig. 7.5), and for this reason Yan & Mateo (1994) doubted its membership. The interesting results of the analysis were first that a slight preference was found for the [Fe/H]= -0.3 Kurucz atmosphere fluxes and second that the uncertainties, especially for the mass ratios, were unusually low for systems of this kind, where radial velocities are not available. As in most investigations involving the WD93K93 program, the probable errors for the full set of the final run were used and cited, but in some cases, the formal probable error was of order ~ 2%. This is a purely internal error, of course, and refers only to the uncertainty in the deepest minimum in each of the modeling runs, since uncertainties in the DC output file refer only to the values near the minimum. The true errors in such parameters are certainly higher, but the accuracy of the result nevertheless is very high, mainly on the basis of the extensive Simplex as well as perturbed WD modeling.

7.3.6 The Eclipsing Binaries in 47 Tuc

A HST search for "hot Jupiters" around the stars of the globular cluster NGC 104, otherwise known as 47 Tuc, has been described by Gilliland et al. (2000). A byproduct of the 8-day continual imaging of a portion of the core region of the cluster produced a large number of variables, only some of which were previously known. Subsequent ground-based imaging of wider regions of the cluster produced even more variable star discoveries and more light curves on those that were obtained by Gilliand's experiment, but here we describe only a few results from the HST experiment alone.

Although the data for each light curve are numerous (~1290) in each of passbands transformed to the V and Ic band, respectively), the information is not always as complete as one would desire. Two passbands are the minimal information needed to argue about temperatures of the components from the standpoint of light curve data alone. The faintness of these stars and the crowdedness of the field effectively eliminates the possibility of obtaining radial velocity dispersion spectra for these objects. The only way one can proceed to obtain fundamental data from EB light curves in this cluster is to rely on the very careful studies that have been carried out of the cluster itself. Fortunately, Bergbusch & VandenBerg (2001) have been able to obtain consistent models for the cluster isochrones (curves of constant age on the magnitude-color diagram). With these, Milone et al. (2004) were able to devise and use a method to bootstrap this information and the results of modeling the two passband curves to obtain a consistent set of results for both component stars in a handful of the systems of the cluster. Initial parameter guesses were made from a set of light curve properties (eclipse depths, widths, contact phases) provided by simulated light curves for systems with 47 Tuc metallicity and with the brightness and color of the VandenBerg (2000) isochrone [see also Bergbusch & VandenBerg (2001) and VandenBerg et al. (2002)]. This work is described briefly by Milone et al. (2004). The method to use only the two light curves and the most reliable isochrone for the cluster has been described in Chapter 5. Since the initial modeling work, R. Gilliland (private correspondence to EFM) suggested that the 47 Tuc photometry should be redone. This has been carried out by R. Guhathakurta (2009, private communication) for constant stars; R. Stagg and Milone are examining the impact of revised photometry on the properties of the eclipsing binary star components.

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