Kurucz Atmospheres in WD

Van Hamme & Wilson (2003) implemented the following Kurucz atmosphere approximation in the WD program. It requires only a few additional a priori computed files and increases the computational time only slightly. As the scheme models temperature dependence of passband intensities6 through Legendre polynomial approximation functions, the only remaining interpolation is in log g. The Legendre approximations reproduce normal emergent stellar atmosphere passband intensities in absolute units with errors typically smaller than astrophysical uncertainties in the original atmospheres and are used to compute the integrated response for the 25 passbands listed in the WD program documentation.7 Among these

6 Note that the Legendre approximation is not used for a specific wavelength but directly over the whole integrated passband response. This is more accurate than a posteriori integration over all wavelengths of the passband.

7 Monograph ebdoc2007 available at ftp://ftp.astro.ufl.edu/pub/wilson/lcdc2007

are Johnson standard UBVR]I], RCIC, and Stromgren uvby, the nominal extended Johnson infrared passbands JHKLMN, and the HIPPARCOS hip and TYCHO BT and VT passbands.

Their computations are based on the normal emergent intensities provided on CD-ROMs 16 and 17 described in Kurucz (1993) for microturbulent velocity 2 km/s. Intensities are given at 1,221 wavelengths from 9 to 160,000 nm and 11 log g's from 0.0 to 5.0 (cgs).

For each atmosphere model Van Hamme & Wilson integrated intensities over each passband, weighted by response function, and similarly integrated blackbody intensities. Irrespective of abundance or surface gravity, Legendre polynomials represent passband intensities accurately as functions of Teff over four subintervals, with passband-dependent beginning and end points. Accordingly, four Teff subin-tervals were bounded by lower (7]) and upper (Th) effective temperatures with Teff scaled according to (pT = (Teff - Tl)/(Th - Tl). The coefficients (pT result from least-squares Legendre fits of degree m with m < 9 based on the number of points in a subinterval, which leads to a maximum of 10 Legendre coefficients. Use of a subinterval end point as the starting point of the next subinterval greatly reduces discontinuities at subinterval boundaries.

In many close binaries, especially those with tidally distorted components, at least one of the stars has part of its surface outside the range of available atmosphere models. Van Hamme & Wilson (2003) give one example; late-type W UMa over-contact binaries with low gravity connecting necks are provide other examples. It would be perverse to abandon atmosphere models for the entire star because of such range limitations, yet a simple blackbody patch would impose an artificial discontinuity that could introduce very bad numerical effects in light curve computation. To avoid radiative discontinuities in very high and very low temperature regions, Van Hamme & Wilson developed polynomial ramping functions in Teff and log g that smoothly transition from atmosphere to blackbody regions. If a (Teff, log g) pair is outside the range of atmosphere applicability, the program smoothly connects atmosphere model intensities to blackbody band intensities over built-in ranges in log g and Teff whose limits can easily be changed. This strategy allows atmosphere computations of spotted stars with surface parts hotter or cooler than existing atmosphere models.

7.3 Applications and Extensions

Abeunt studia in mores (You are what you learn)

This section describes specific astrophysically interesting applications and resulting experiences with the most recent versions of the Wilson-Devinney program, or special extensions (pulse arrival times, line profile analysis, LC93KS, and WD95) of the Wilson-Devinney program. The intention is to provide hints about what can be achieved and how various extensions can be used to derive astrophysical results. The binaries discussed also demonstrate how interesting binary star astrophysics can be. HD 77581/GP Velorum is an X-ray pulsar which makes it a very rich data source. Some binaries in the ancient globular cluster NGC 5466 and some others in M71

provide useful information both on binaries and clusters, although they are very faint stars. The binary H235 in the open cluster NGC 752 is an interesting example of the evolution of binary stars in clusters. The 24.6-day period EB AI Phoenicis is one of the best-studied field EB systems. Finally, the chapter provides some results on the analysis of fast and slowly rotating Algols based on line profile fitting.

7.3.1 The Eclipsing X-Ray Binary HD 77581/Vela X-1

This binary contains an X-ray pulsar. The pulse arrival times are an additional observable used in asimultaneous analysis described in Sect. 4.1.1.6 and are modeled as outlined in Sect. 3.8. For more background on pulse arrival time modeling, we refer the reader to Wilson & Terrell (1998) on the methodology of incorporating pulse arrival times in light curve modeling.

The ellipsoidal variableHD 77581/GP Velorum is the optical counterpart of the pulsed, eclipsing X-ray source Vela X-1. A B0.5 supergiant and a neutron star move in an eccentric orbit of about e = 0.1 and a period of 8.96 days. Spectral line broadening indicates that the optical star rotates subsynchronously with 0.5 < F2 < 0.75 (Zuiderwijk 1995). The analyses by Wilson & Wilson & Terrell (1994, 1998), performed with the original WD program, demonstrate the fruitfulness of asimultaneous least-squares analysis of all available data. The analysis included the data shown in Fig. 7.1:

1. B and V light curves observed by Van Genderen (1981);

2. optical (He I) radial velocity curves by Van Paradijs et al. (1977), Petro & Hiltner (1974), Van Kerkwijk et al. (1995), and Stickland et al. (1997);

3. pulse arrival times measured by Rappaport et al. (1980) and other sources given in Wilson & Terrell (1998); and

4. estimations of the X-ray eclipse duration8 by Watson & Griffiths (1977).

The light curves were used only in preliminary experiments, not in the final solution. The known X-ray eclipse duration was included in the analysis as an additional constraint with the formalism implemented in subroutine DURA (see Appendix E.11). In thesimultaneous fitting of many types of data, appropriateweighting is very important (see Sect. 4.1.1.6). Wilson & Terrell (1994, 1998) commented on which observations contribute most to specific output parameters:

X-ray eclipse ^ relative size of the B star, pulse arrival times ^ orbital eccentricity, radial velocities and pulse arrival times ^ absolute dimensions.

Neither the X-ray nor optical variations can yield the inclination. They indicate only that the orbit is close enough to edge-on to produce broad eclipses. The important point is that all relationships are used simultaneously to ensure a self-consistent solution.

8 The 1994 analysis used the eclipse duration data by Avni (1976), Ogelman et al. (1977), and also by Van der Klis and Bonnet-Bidaud (1984).

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