The Well Studied System AI Phoenicis

This 24.6-day period binary is one of the best-studied field EB. Its discovery on sky patrol plates taken at a Remeis-Sternwarte Bamberg Southern Station was announced by Strohmeier (1972). Subsequently, Reipurth (1978) obtained uvby data and Imbert (1979) obtained the first radial velocities and analyzed the system. Hrivnak & Milone (1984) obtained the first UBVRI light curves and performed the first light curve analyses with the WD program using the blackbody option. This was one of the earlier uses of the program to study an eccentric orbit binary. They found the components to be a mid-F dwarf of mass (1.12 ± 0.03) M0 and (1.77 ± 0.03) R0 and a late G subgiant of (1.16 ± 0.03) M& and (2.85 ± 0.03) R&, respectively. Vandenberg & Hrivnak (1985) investigated the evolutionary state of the system. From the color indices, they deduced the bounds of the metallicity (Z = 0.0169 to 0.04) and used these to establish bounds for the helium content and the age: For Y = 0.33, t = (4.3 ± 0.3) Gyr, whereas for Y = 0.43, t = (2.9 ± 0.2) Gyr. Subsequently, Andersen et al. (1988) made use of additional uvby photometry, new radial velocities, and highresolution (R « 50,000) spectra obtained at good S/N (~200) to reanalyze all existing data with the NDE model, although they do not specify the program they used (presumably therefore a version of EBOP). Andersen et al. (1988) do not show the computed light curves but the radial velocity predictions are seen to be in excellent agreement with the data, and they reported good fittings of the separate passband solutions to the light curve data. They found somewhat larger uncertainties for the elements at least partially because they rejected two points on the rising portion of the light curve that had been accepted by Hrivnak & Milone (1984) and improved precision for the uvby light curves. Andersen et al. (1988) concluded from an analysis of their high- resolution spectra that [Fe/H] = -0.14±0.10, and Z = 0.012 ±0.003; from this they derived Y = 0.27 ± 0.02 and t = (4.1 ±0.4) Gyr.

Thus, even before the modeling with improved atmospheres options, the elements of AI Phe were among the best determined of all evolved systems. Milone et al. (1992b) reanalyzed all previously published data and IUE ultraviolet observations obtained in the primary minimum. The latter had been obtained in order to investigate the limb darkening in the hotter component, which, on the basis of earlier work by Imbert (1979) was thought to be a solar analogue with a spectral type of G2V, and suitable for direct comparison with the solar center-to-limb variation studied by Kjeldseth-Moe & Milone (1978). Milone et al. (1992b) made use of the Kurucz (1979) atmospheres option in the University of Calgary version of the WD program, WD83K83, and obtained a multiwavelength solution consistent with individual passband elements. This modeling used the empirical corrections of Wade & Rucinski (1985) to fit the ultraviolet light curves better than any previous modeling. They found the mass and radius for the hotter and cooler star, respectively, to be (1.190 ± 0.006) M& and (1.762 ± 0.007) R&; and (1.231 ± 0.005) M& and (2.931 ± 0.007) R0. With the temperature of the hotter component taken as 6310 K (±150 K, assumed), that of the secondary was determined to be (5151±150) K. Subsequently, modeling with WD93K93 was carried out to test the effects of multiple reflections and slight changes in metallicity with flux files that made use of the atmosphere models by Kurucz (1993). This modeling has produced little improvement at the present writing, but this was expected given the small range of metallicity of the models attempted so far ([Fe/H] = -0.02, 0, +0.02). In the later 1990s AlPhe has been analyzed with WD95, as a test for this new package. Finally, in Sect. 8.4 we briefly indicate how the distribution of residuals in the AI Phe modeling process have been analyzed.

It is useful to summarize why this system has been of such interest. The main reason is that the components have evolved from the main sequence, and at different rates. Their intrinsic properties thus provide the means to test evolution models. A precise determination of the elements is possible in this case because the system is double-lined, and the eclipses are total (i = 88?45±0?01) despite the long period of the system, so that the shape of the minima can be observed in detail. The improved modeling has provided more precise values of the radiative and at least as precise values of the nonradiative properties as previous studies, but with improved confidence. Additional reasons for modeling this system are the significant differences between the component's colors and magnitude, due to the relatively cool temperature of the secondary component. The modeling of the flux of the cool secondary is a challenge for stellar atmosphere theory. The far-ultraviolet limb darkening of the hotter star can be studied more easily because of the lack of contribution from the cooler component. Finally, effects seen in other systems involving a late-type subgiant are absent, namely the RS CVn-type behavior, which can complicate the determination of fundamental stellar properties.

Current modeling involves the exploration of the effects of multiple reflection, of nonlinear limb darkening, and of chemical composition. The models tested have thus far not included stars as deficient as -0.1 and -0.2 but this is planned for the near future.

The full sweep of the importance of systems such as AI Phe and binaries in clusters is beyond the scope of this book, but we refer to Andersen (1991) for an extensive discussion of the former, and the contributions detailed in Milone & Mermilliod (1996) for the latter.

7.3.8 HP Draconis

The 1076-day period, eccentric orbit double-lined eclipsing binary HP Draconis was among the systems used to test the capability of the GAIA mission to yield fundamental stellar data; cf. Milone et al. (2005). The system was discovered as variable in the HIPPARCOS mission albeit with an incorrect period (6d 67). The test involved using HIPPARCOS and TYCHO photometric data, which were of somewhat lower precision than GAIA was expected to provide, and radial velocities measured from echelle spectra obtained at Asiago Observatory. The mean standard errors for the HIPPARCOS and TYCHO light curves were 0.012 and 0.11 magn., respectively; the spectral resolution is 20,000 and the mse of the RV

curve is 3 km/s. The latter is higher than expected for the GAIA spectroscopy but the latter were to include more observations in compensation. The main problem with the photometry was the paucity of data in the minima: only three data points in the primary minimum and seven in the secondary minimum of the hip light curve. The TYCHO data were even worse: the minima could not be identified. They were, however, useful for determining colors and thus temperatures; T1 was taken as 6,000 K. The modeling code was the package WD2 0 02, in which the simplex program and self-iterating damped least-squares routines were used. The converged solution was able to yield very good results for some parameters and excellent if preliminary results, for others. Among the preliminary results were a significant drn/dt term.

Independently, Kurpinska-Winiarska et al. (2000) with photometry from Cracow Observatory determined the system to be eccentric. The Cracow photometry consisted of B and V light curves with complete coverage of the minima and this group obtained additional radial velocities from the ELODIE spectrograph on a telescope at the Haute Provence Observatory.

In 2008-2009 all available data except the TYCHO set were analyzed with the Wilson-Devinney program, 2007 version. Nineteen parameters were simultaneously adjusted, 13 of which are curve independent: a, e, y, T2, i, 2, q, t0, P, dP/dt, drn/dt, L 1(B,V,hip), l3(B,V,hip). Initial values were taken from the solutions obtained by Milone et al. (2005) and Kurpinska-Winiarska et al. (2000). This program is not self-iterating and the method of non-correlating subsets was used to improve fittings from run to run. Solar composition was assumed for the stellar atmospheres corrections, which are completely internal in this version. Several thousand runs were carried out in several series. The lowest SSRs were obtained with a set of elements that included a significant third light component ineach of the B,

HP Draconis B light curve (PM)

HP Draconis B light curve (PM)

Phase

Fig. 7.6 The fitting of the B primary minimum of the HP Draconis light curve. The data are from Cracow Observatory. Courtesy, M. Kurpinska-Winiarska and E. Oblak

Phase

Fig. 7.6 The fitting of the B primary minimum of the HP Draconis light curve. The data are from Cracow Observatory. Courtesy, M. Kurpinska-Winiarska and E. Oblak

HP Draconis B light curve (SM)

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