University of Calgary. Calgary, Alberta, Canada.

The advances in the modeling of eclipsing binary light curves (generically including polarimetric, spectrophotometric, and radial velocity curves, spectral line profiles, spectral indices, and other observables) were last reviewed comprehensively in 1991 at IAU sessions in Argentina. The field has continued to develop, and since light curve models and codes are depended on to produce reliable radii and masses, among other fundamental stellar properties, it is appropriate to review what is new in both models and the programs to implement them.

The new model improvements include more realistic spot simulations, radiative transfer treatment of eclipses by translucent atmospheric clouds, improved radiation interactions between the components, non-linear limb-darkening, and non-solar metallicities. Codes are now available with improved integration and convergence techniques, and are modularized to permit added operations. The session is designed to illustrate these advances and the benefits for binary star research.

This special session is made possible by grants to EFM from NSERC of Canada, the University of Calgary's Research Grants Committee, Research Services, Faculty of Science, and the Department of Physics /& Astronomy, all of which are appreciated.

- Slide 1: Al Phoenicis: Spectra of the Residuals, from above.
- Slide 2: Al Phoenicis: Spectra of the Residuals, from the side.

**Abstract:** Light curve model work has increasingly been extending into general observables. It now includes (or soon will) polarimetry, line profiles, pulse arrival times, and interferometric observations in addition to brightness and radial velocity. The inclusion criterion for the above-listed observation types is not that every one require a physical binary star model, but only that any combinations that are fitted simultaneously involve a physical model. Thus ordinary pulse arrival time analysis involves only the geometry of orbiting point sources, but can involve physical models when combined with light curves and radial velocities. Solution of combined light and velocity observations, although not yet common, is becoming more frequent. Models now have circumstellar disks, stellar atmospheres, and attenuation by circumstellar gas and dust in addition to basic external physical attributes such as tides, reflection, orbital eccentricity, and non-synchronous rotation. Some aspects of the pulse arrival time, line profile, and circumstellar attenuation problems will be discussed here. The pulse discussion centers on an algorithm through which differential corrections solutions can be carried out, including designation of the independent variable and formation of partial derivatives of arrival time with respect to model parameters. The profile discussion focusses on generalization of a binning procedure so as to include various broadening mechanisms and on computational strategies to improve accuracy. The attenuation discussion concerns efficient computation of attenuation in matter of arbitrary optical thickness with effective inclusion of several scattering and absorption mechanisms, arbitrary spatial distribution, and proper wavelength dependence.

**Paper:**PostScript, 148kb.

**Abstract:** We summarize and report recent improvements to a version of the Wilson-Devinney program. This program is widely used for the analysis of eclipsing binary data and is open to extensions and improvements. *WD95* is such an extension and contains our version of the Wilson-Devinney code. It supports the use of the Kurucz atmosphere models; it provides options to use multiple epoch data and multi-wavelength synoptic passbands. The WD95 program contains an improved I/O interface, simplex algorithms for initial searches and tests, and versions of Wilson-Devinney DC and LC programs and options to switch to automatic differential corrections or to a damped least-squares solver using normal equations that are modified as per Levenberg-Marquardt. The damped least-squares solver is tested with simulated data and used to demonstrate the features and performance of the code. The algorithm proves to be less dependent on the quality of guessed initial parameters and thus may be efficiently used to reduce the time
involved in light curve analysis.

This work has been supported by GKSS (Germany; to JK and EFM), NSERC (Canada), and URGC grants (University of Calgary) (to EFM).

- Slide 1: Overview
- Slide 2: Damping Strategies
- Slide 3: Damped Differential Potentials
- Slide 4: Termination Criteria
- Slide 5: Wilson Devinney 1995
- Slide 6: Testing and Experience
- Slide 7: Summary

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**Abstract:** We illustrate radial velocity proximity effects computed with weights based on spectral line strength as well as on continuum flux level. Because absorption line equivalent widths depend on effective temperature, surface gravity, and aspect angle, line strength varies across the surface of tidally distorted stars and ideally should be taken into account when calculating stellar disk-integrated radial velocities. We discuss the implementation of flux-based as well as equivalent width-based weights with a high mass X-ray binary and two W UMa type binaries as examples.

**Paper:**PostScript, 138kb.

**Abstract:**A method is presented to include radiation pressure effects in the modeling of close binaries. Radiative interaction is particularly important for hot OB-type binary stars in close configurations. The potential field has to be calculated by a numerical approach, since no analytical representation is possible, if the Roche potential is accordingly modified. Radiative forces exerted by luminous, hot stars may cause geometric distortions of stellar surfaces and influence the binary configuration and evolution. The principal effects are demonstrated by model calculations.

There are several important implications for the binary structure: the geometry of the stellar surfaces is modified; the Lagrangean points are shifted, and the shape and extent of the Roche lobes are changed; the tendency to take up inner contact is counteracted by radiative forces, while outer contact components (with surfaces incorporating L 2 or L 3 ) may result above some critical radiation pressure strength; obvious consequences exist for the evolution of systems with very hot and luminous components like Wolf-Rayet or X-ray binaries.

The modified Roche potential is used as an improved binary model for the computation of eclipse light curves, based on the Wilson-Devinney technique. The inverse problem is solved by application of the non-linear simplex parameter optimization algorithm. The feasibility of the new method is demonstrated by photometric solutions of a few OB systems. The implementation of radiation pressure effects yields improved light curve representations compared with conventational methods, even in the case of relatively weak radiative forces.

**Paper:**PostScript, 4.1Mb; UNIX Compressed, 1.2Mb;DOS Compressed, 1.2Mb.

**Abstract:** A new software package provides a self-consistent, physically realistic procedure for calculating both synthetic spectra and synthetic light curves of eclipsing binary stars. A system synthetic spectrum calculated for each orbital phase of spectral observation, together with a solution of eclipse light curves, determines a system model, including effective temperatures of both components. Use of the synthetic spectra in a synthetic photometry mode produces consistent system parameters in analysis of UBV photometry. An application to MR Cygni illustrates application of the procedure.

Addition of an accretion disk presents additional complexity. The program uses a visibility key attached to each grid point on the star photospheres, the accretion disk visible face, and the accretion disk rim to determine the contribution of the associated surface element to the system spectrum. Separate output spectra are available for each stellar component, the accretion disk face, and the accretion disk rim. The calculated output includes a composite system spectrum. The program provides an option to model a single bright spot on the rim, with an assignable longitude, azimuthal width, and effective temperature. Application of the program to the cataclysmic variable PG 0859+415 illustrates program performance.

**Paper:**PostScript, 292kb.

**Abstract:** We briefly review previous work on Doppler and photometric imaging of starspot distributions on close binary stars, particularly contact binaries. Difficulties involving standard spherical and cylindrical surface element distributions for imaging are discussed. The method of geodesic distribution binary synthesis (GDDSYN) is faster and more accurate for such work.

The Maximum Entropy regularisation method has been extended to include simultaneous photometry and spectroscopy. A further extension allows auxiliary parameters such as mass ratio and fill-out to be determined, as well as the radial velocity amplitude. The spectrum of third light contamination is also obtained, using theoretical spectrum synthesis for the binary as input. Accurate distances act as a powerful constraint on the fitting process.

The procedure has been applied by PDH to the system VW Cephei. The development of spots over a two year period has been studied. The fraction of the surface covered by spots appears to be be very large.

Future developments will be discussed. This type of approach is essential to obtain good models for cool, heavily-spotted binary systems.

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