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Fig. 7.8 Fitting line profiles. This figure, Fig. 6 in Mukherjee et al. (1996), shows fitted versus observed profiles. Courtesy J. D. Mukherjee

7.3.9 Fitting of Line Profiles

Although it never became available as public software, Mukherjee et al. (1996) combined the theory of stellar line broadening for local profiles with the WD program and used it to estimate rotation rates of Algol binaries by fitting line profiles to observed data. They used the Simplex algorithm and the method of Differential Corrections to adjust the damping constant r, number Nf of absorbers along the line-of-sight, turbulent velocity vtur, absorption versus scattering parameter e, and the rotation parameter F1for the primary star. Figure 7.8 shows the observed and fitted line profiles for some rapidly (U Cep, S Cnc) and slowly (RZ Cas, TV Cas) rotating Algols. For the full analysis we refer the reader to Mukherjee et al. (1996).

7.4 The Future

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This section looks into the future of the WD program. We keep the Future as Seen in 1999 (the year when the first edition was printed), add comments [in square brackets] where significant progress has been made, and then lend a current perspective on future developments.

7.4.1 "The Future" as Envisioned in 1999

The history of the WD program has been one of various special purpose versions that were developed for particular problems, followed by absorption of their capabilities into the general program. For example, it is anticipated that the 1998 version computes light curves, radial velocity curves, spectral line profiles, and images, while versions that compute polarization curves and X-ray pulse arrival times now exist separately and eventually will be absorbed. Generalizations that a user need not worry about are embedded invisibly wherever practical. For example, computational shortcuts for many special case situations speed execution without compromising more intricate cases. The 1998 version (Wilson 1997; private communication) will have the following changes/additions vis-a-vis 1992:

1. The model can have circumstellar scattering regions (see Sect. 3.4.4) that attenuate star light by several scattering mechanisms. A first application is toAX Monocerotis (Elias et al. 1997).

2. Spectral line profiles can be computed, with the various proximity and eclipse effects and blending. Line profiles can be associated with specific regions on a star. This feature permits analysis of chromospheric fluorescence and also lines from star spots.

3. Either time or phase can be the independent variable. We can thereby solve for ephemeris parameters, including time derivatives of the period and argument of periastron, and can combine data from several epochs.

4. Simulated observational error can now be added to light curves so as to facilitate solution tests on synthetic data.

5. Output needed to make pictures of a binary, including spots, is now provided. The data can be used as input to any commercial or private plotting program.

6. The Levenberg-Marquardt procedure can be applied by entering a nonzero value for the damping constant X.

7. The program is now entirely in double precision.

8. Input and output formats have been revised so as to assure entirely adequate numbers of digits, even for rare and extreme cases. Some quantities that previously were in floating format are now in exponent format.

9. Because of the options to compute additional kinds of quantities, a control integer now determines the LC input/output format and triggers certain decisions about what will be computed. The output is thereby easier to read because LC does not try to squeeze everything into the page width.

10. Because of a preference in the literature for standard deviations, as opposed to probable errors, the parameter error estimates are now standard deviations.

Several improvements await incorporation:

• Polarimetry is a ripe field for exploitation in light curve analysis. The data are scarce but the means to incorporate them into analytical methods could encourage further observational progress in this demanding field. It is expected that in a few years the WD light curve program will support the analysis of polarimetry data. [NB.: The development and deployment of ESPaDOnS (for Echelle SpectroPolo-metric Device for the Observation of Stars) on the Canada-France-Hawaii Telescope (CFHT) will be a boon for polarimetric studies of EBs, both hot and cool systems. The instrument is capable of producing spectra from 0.37 to 1.00 ^m at a resolution of 50,000. The study of stellar magnetic properties has experienced vigorous growth over the past two decades, and with an instrument such as this on a major facility at a site with excellent seeing, continued growth of the field seems assured (assuming that practitioners are granted time by telescope allocation committees). A number of investigations of rapidly rotating early- and late-type stars have been studied with this instrument, yielding information about magnetic field structures. It will be interesting to see such investigations carried out on binary stars.]

• Atmospheric eclipses for components with extended atmospheres.

• Improved accuracy, e.g., light curve quadrature and spot geometry.

An accuracy improvement for WD is on the way, but is intricate and not yet debugged. At present the work is a "back burner" project. The accuracy improvement will be major and might be used either to reduce error or to reduce execution time for the same level of precision. On a shorter timescale, we can expect line profile improvements such that several broadening mechanisms (e.g., thermal and turbulent Doppler broadening, damping) will be included or the capability to fit spectral line profile parameters. Also, the circumstellar scattering regions mentioned above will be made to scatter starlight into the line-of-sight, in addition to their present function as attenuatingclouds. Clouds might be treated on the basis of rigidhydrodynamics. The effects of streams in Algol systems on light curves have been modeled outside WD by several workers, cf. Terrell (1994), who developed a hydrodynamic code. This work could be combined withcloud modeling in a more extended module (see Sect. 9.1.1 for a definition of modular structure and modules). Having clouds in the models also requires us to model Thomson scattering and other types of scattering and absorption. Although the program has a simple stellar atmosphere capability (main sequence stars only), the atmosphere provisions of some other programs [e.g., Linnell (1991), Milone et al. (1992b)] are major improvements and very important. Therefore it is anticipated that a relatively general atmosphere routine will be added to the WD program at some point. [NB.: The improvement of the least-squares engine to a damped least-squares one has been a major advance. Eclipses caused by discrete clouds in atellar atmospheres can now be carried out in WD programs. Kurucz atmospheres are now standard in the most recent WD programs and have been directly incorporated into the code instead of relying on auxiliary files of model atmosphere to blackbody fluxes as had to be the case in the WD9 8k93 and W9 8 package programs developed by Milone, Kallrath, and collaborators. There still need to be auxiliary files for the individual metallicities, however. Wilson's own 2007 version of WD incorporates ramp functions to move between regions for which Kurucz models are applicable and those where black bodies must be used. The atmospheric models are available for a wide variety of metallicities and can be applied for a large number of passbands.]

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