Info

with phase of first contact, 01. A theoretical expression for A2m is

where a is the fractional loss of light, « indicates the separation of the components so that «0 = cos i, namely, the value of « at closest approach (at 0 = 0), and 51j2 mark separations at first and second contact, respectively. The analysis also requires the determination of the coefficients cj of the light curve representation

Although his approach and the notation used above is based mostly on uniform, circular disks, some corrections are applied for limb- and gravity-darkened, tidally distorted nonspherical stars with light curve perturbations (Kopal, 1989, 1990). The analysis of the moments yields the elements of the system. For perturbed light curves, the prescriptive procedure is as follows:

1. determine the necessary number of moments of the light curves (at least 4);

2. evaluate the necessary number of constants cj=1n (at least 4) from the light curve maxima and take their weighted sum;

3. evaluate the (normalized) moments;

4. evaluate the r1j2, i, and L 1j2 from the moments;

5. compute the light curves from the elements and evaluate the perturbations, P2m;

6. use the perturbations to obtain improved moments; and

7. iterate Steps 3-6 to the final set of elements.

Kopal (1979, p. 193) asserts that no "time-domain" analyses , by which he characterizes all the other methods described here, can make use of empirical data to convert observed light curves into a form from which the elements can be derived directly; keeping in mind that the whole idea of least-squares procedures is to extract parameters indirectly, it is not clear why the direct determination of parameters should be an advantage. Interpreting the assertion to mean that a closed analytic solution cannot be found for such cases, the question remains whether this method can do so either. Its claimed superiority has yet to be demonstrated.

The Fourier analysis frequency domain method is a rather formal mathematical approach suffering from the following disadvantages:

1. the components are assumed to be spheres, or at best, corrected spheres (Kopal 1989, 1990);

2. it is doubtful that a few Fourier coefficients can reveal fully the information in a light curve, generally. The Fourier analysis method uses an integral moment11 of the observations, thus masking the contribution of each point to the value of A2m, particularly for small sin2m 0 as m increases. That means that perturbation terms for proximity effects are evaluated essentially from the uneclipsed portion of the light curve;

3. it is necessary to specify the luminosity scaling;

4. the value of the angle 01 of external tangency must be specified; and

5. it is not easy to introduce additional physical effects into the model in this analysis.

11 This process smoothes the observations. Strictly speaking, information is thrown away in the process.

Budding (1993, p. 211) notes similarly that although the method is straightforward, in practical situations complications arise, especially because the proximity effect representation must be very precise, but the cj quantities "are not well suited to accurate numerical derivation." He also notes that the procedure loses the advantage of simplicity for partial eclipses.

Light curve analysis based on the solution of an inverse problem with an underlying physical model as its core is not limited by these disadvantages. Physical models are open to the implementation of improved physics.

6.5.3 Mochnacki's General Synthesis Code, GENSYN

The GENSYN code was developed by Mochnacki and Doughty in the early 1970s, of Mochnacki & Doughty (1972a, b), and further improved around 1983. Mochnacki's work began by using Lucy's (1968) code, which he found to be reliable but slow due to its use of a "ray-tracing" algorithm. The GENSYN code was intended to do both light curve and line profile synthesis. It used a cylindrical coordinate scheme making the radius vector a single-valued function for all configurations: contact and noncontact. This might be an advantage, although not a crucial one, because there is no problem finding the correct surface in spherical coordinates either. The program was designed to be compact, fast, and numerically stable but, unlike the Wilson-Devinney LC program, did not incorporate an accurate correction scheme for horizon visibility. GENSYN was applied originally to totally eclipsing A-type contact systems (such as AW Ursae Majoris and V566 Ophiuchi). According to Mochnacki, it was the first Roche geometry-based light curve code to incorporate full mutual irradiation by mapping each surface element to all those illuminating it.

6.5.4 Collier-Mochnacki-Hendry GDDSYN Spotted General Synthesis Code

Andrew Collier and Stefan Mochnacki combined their programs SPOTTY and GENSYN in 1987 to analyze spotted eclipsing systems. An improved geodesic grid system with triangular elements was introduced by Paul Hendry as part of his MSc thesis at the University of Toronto under Mochnacki's direction. Mochnacki states that the resulting code, GDDSYN, is both faster and more accurate than WD93. All grid elements have comparable surface areas and there is little aliasing due to projected symmetries (Hendry & Mochnacki, 1992). In addition, Hendry wrote a program to determine the most likely spot distribution which makes use of a maximum entropy algorithm, and combined it with GDDSYN and SPOTTY to determine spot distributions in contact systems (Hendry et al. 1992). Finally, Hendry more recently wrote a program to fit both orbital elements and spot distributions to photometric and spectroscopic data. Mochnacki notes that this code was used to analyze several years of DDO observations as part of Hendry's PhD thesis.

6.5.5 Other Spot Analysis Methods

A long-standing tradition at the Osservatorio Astrofisico di Catania, on the island of Sicily, has been the study of the effects of star spots on light curves. Their work has focused on the RS CVn (e.g., Rodono et al. 1995) and to the similar systems AR Lac, II Peg, and SZ Psc. This work was then extended to the somewhat more complicated system RTLac, discussed earlier. The spot modeling technique is described in several papers; see Lanza et al. (1998, 2002) and references contained therein. Their goal has been to observe the spot distribution as a function of longitude on the star's surface and to study spot migrations over longer intervals of time and modulation over shorter intervals. Information of this sort can lead to an understanding of magnetic structures and their relationship to the rotational and orbital dynamics of the system. Eclipsing systems provide the necessary spatial resolution to explore the brightness distribution on the surface of the eclipsed component, which is divided into several hundred pixels, each of which is allowed to vary within constrained limits. Fittings were obtained with the use of a priori assumptions supplied by a maximum entropy criterion, and, in an independent check on the results, a Tikhonov regularization criterion. According to the authors, the use of such criteria leads to stable and unique solutions of the distribution over the surfaces of the stars. A lengthy series of observations extending over decades provided the database, and the maximum brightness of the system observed during that time served as a kind of unspotted calibration for the pixels. In the case of AR Lac, data were available for 20 annual light curves in the interval 1968-1992. The system is subject to variations exceeding 0.05 magnitudes in a single day, possibly due to flares on timescales of tens of minutes. The reference level was established for the system as observed in 1987 when V = 6m 030 ± 0 m005 at orbital phase 07395. The EB model for the system, at least for the earlier studies, involved tri-axial ellipsoids for the stellar shapes but also Kopal's (1959) geometric treatment of ellipsoids, reflection, and gravity darkening (Lanza et al. 1998). The resulting longitude distributions are obtained for each component and show general agreement for particular years for each of the two restrictive criteria.

6.6 Selected Bibliography

This section is intended to guide the reader to recommended books or articles on light curve models and programs.

• The review article by Wilson (1994) gives an excellent overview on light curve models. It provides a historical view and discusses the underlying astrophysics.

• An early overview on modern Light Curve Modeling of Eclipsing Binaries is provided by Milone (1993). In this collection, several authors briefly describe or comment on the latest versions of some of the better-known light curve models and programs.

• The Determination of the Elements of Eclipsing Binaries by Russell & Merrill (1952) is probably the best and most complete description of material related to the Russell-Merrill model.

• In his review Close Binary Star Observables: Modeling Innovations 2003-06, Wilson (2007) summarizes the developments of the WD program during 2003 and 2006.

• The journal publication Eclipsing Binary Solutions in Physical Units and Direct Distance Estimation by Wilson (2008) is a pleasant-to-read article on the assumption and implications of direct distance estimation.

References

Andersen, J. & Gr0nbech, B.: 1975, The Close O-type Eclipsing Binary TU Muscae, A&A 45, 107-115

Antokhina, Eh. A. & Cherepashchuk, A. M.: 1987, SS 433: Parameters of the Eclipsing System with a Thick Precessing Accretion Disk, Sov. Astron. 31, 295-307 Antokhina, Eh. A., Pavlenko, E. P., Cherepashchuk, A. M., & Shugarov, S. Y.: 1993, The Best Candidate for a Black Hole - X-Ray Nova V404 Cygni: the Light Curve and Parameters, Astron. Rep. 37, 407-411

Antokhina, Eh. A., Seyfina, E. V., & Cherepashchuk, A. M.: 1992, Analysis of X-Ray Eclipses in

SS 433, Sov. Astron. 36, 143-146 Bevington, P. R.: 1969, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York

Binnendijk, L.: 1960, Properties of Double Stars, University of Pennsylvannia Press, Philadelphia, PA

Binnendijk, L.: 1974, The Intrinsic Light Variations in Very Close Eclipsing Binary Systems, Vistas 16, 61-83

Binnendijk, L.: 1977, Synthetic Light Curves for Binaries, Vistas 21, 359-391 Budding, E.: 1993, An Introduction to Astronomical Photometry, Cambridge University Press, Cambridge, UK

Budding, E. & Zeilik, M.: 1987, An Analysis of the Light Curves of Short-Period RS CVn stars:

Starspots and Fundamental Properties, ApJ 319, 827-835 Buser, R.: 1978, A Systematic Investigation of Multicolor Photometric Systems, A&A 62, 411-424 Carbon, D. F. & Gingerich, O.: 1969, A Grid of Model Stellar Atmospheres from 4000 to 50,000 K, in O. Gingerich (ed.), Theory and Observation of Normal Stellar Atmospheres, Proc. of the Third Harvard-Smithonian Conference on Stellar Atmospheres, pp. 377-400, MIT University Press, Cambridge, MA Chandrasekhar, S.: 1950, Radiative Transfer, Oxford University Press, Oxford, UK Cherepashchuk, A. M.: 1966, Determination of the Elements of Eclipsing Systems Containing a

Component with an Extended Atmosphere, Sov. Astron. 10 (3), 227-252 Cherepashchuk, A. M.: 1971, Eclipses of Spherical Stars (Arbitrary Limb Darkening Law), in V. P. Tsesevich (ed.), Eclipsing Variable Stars, pp. 225-269, Nauka, Moscow, (English translation, 1973, New York)

Cherepashchuk, A. M.: 1973, The Direct Method of Light Curve Solution of the Eclipsing Binary System with an Extended Atmosphere. Calculation and Application of Weights. Computer Programmes, Peremennye Zvezdy (Variable Stars) 19, 227-252 Cherepashchuk, A. M.: 1975, Photometric Elements of the Eclipsing Binary V444 Cygni, and the

Nature of the Wolf-Rayet Component, Sov. Astron. 19(1), 47-57 Cherepashchuk, A. M.: 2005, Atmospheric Eclipses in Wr+o Binaries: From Kopal and Shapley to Present Days, Ap. Sp. Sci. 296, 55-65

Cherepashchuk, A. M., Goncharsky, A. V., & Jagola, A. G.: 1973, The Algorithm and Computer Programme for Light Curve Solution of an Eclipsing Binary System Containing the Component with an Extended Atmosphere, Peremennye Zvezdy (Variable Stars) 18, 535-569 Cherepashchuk, A. M., Goncharsky, A. V., & Jagola, A. G.: 1975, A Class of Monotonie Functions as a Solution of Eclipsing Binary Light Curves, Sov. Astron. 18(4), 460-463 Cherepashchuk, A. M., Goncharsky, A. V., & Yagola, A. G.: 1967, An Interpretation of Eclipsing

Systems as an Inverse Problem of Photometry, Sov. Astron. 11(6), 990-999 Cherepashchuk, A. M. & Khaliullin, K. F.: 1976, Nature of the Wolf-Rayet Component of the

Binary System V444 Cygni, Sov. Astron. 19(6), 727-733 Crampton, D. & Hutchings, J. B.: 1981, The SS 433 Binary System, ApJ251, 604-610 Crawford, J.: 1992, A Photometric and Spectroscopic Analysis of the Chromospherically Active

Binary RT Lacertae, Dissertation, San Diego State University, Department of Astronomy Davidge, T. J. & Milone, E. F.: 1984, A Study of the O'Connell Effect in the Light Curves of

Eclipsing Binaries, ApJSuppl. 55, 571-584 Devor, J.: 2005, Solutions for 10,000 Eclipsing Binaries in the Bulge Fields of OGLE II Using

DEBiL, ApJ 628,411-425 Devor, J. & Charbonneau, D.: 2006a, MECI: A Method for Eclipsing Component Identification, ApJ 653,647-656

D'Odorico, S., Oosterloo, T., Zwitter, T., & Calvani, M.: 1991, Evidence that the Compact Object in SS 433 is a Neutron Star and not a Black Hole, Nature 353, 329-331 Eaton, J. A. & Hall, D. S.: 1979, Starspots as the Cause of the Intrinsic Light Variations in RS

Canum Venaticorum Type Stars, ApJ227, 907-922 Eggleton, P. P. & Kiseleva-Eggleton, L.: 2002, The Evolution of Cool Algols, ApJ 575, 461-473 Etzel, P. B.: 1981, A Simple Synthesis Method for Solving the Elements of Well-Detached Eclipsing Systems, in E. B. Carling & Z. Kopal (eds.), Photometric and Spectroscopic Binary Systems, pp. 111-120, D. Reidel, Dordrecht, Holland Etzel, P. B.: 1993, Current Status of the EBOP Code, in E. F. Milone (ed.), Light Curve Modeling of Eclipsing Binary Stars, pp. 113-124, Springer, New York Fabrica, S. N. & Bychkova, L. V.: 1990, The Mass Function of SS 433, A&A Letters 240, L5-L7 Goncharsky, A. V., Cherepashchuk, A. M., & Yagola, A. G.: 1978, Numerical Methods for Solving

Inverse Problems of Astrophysics, Nauka, Moscow (in Russian) Goncharsky, A. V., Cherepashchuk, A. M., & Yagola, A. G.: 1985, Ill-Posed Problems of Astrophysics, Nauka, Moscow (in Russian) Goncharsky, A. V., Romanov, S. Y., & Cherepashchuk, A. M.: 1991, Finite-Number Parametric

Inverse Problems ofAstrophysics, Moscow University Press, Moscow, Russia (in Russian) Hadrava, P.: 1997, FOTEL 3 - User's Guide, Technical report, Astronomical Institute of the

Academy of Sciences of the Czech Republic, 25165 Ondrejov, Czech Republic Hadrava, P.: 2004, FOTEL 4 - User's guide, Publications of the Astronomical Institute of the

Czechoslovak Academy of Sciences 92, 1-14 Hendry, P. D. & Mochnacki, S. W.: 1992, The gddsyn Light Curve Synthesis Method, ApJ 388, 603-613

Hendry, P. D., Mochnacki, S. W., & Cameron, A. C.: 1992, Photometric Imaging of VW Cephei, ApJ 399,246-264

Hill, G.: 1979, Description of an Eclipsing Binary Light Curve Computer Code with Application to Y Sex and the wuma Code of Rucinski, Publ. Dom. Astrophys. Obs. 15, 297-325 Hill, G., Fisher, W. A., & Holmgren, D.: 1990, Studies of Late-Type Binaries. IV. The Physical

Parameters of ER Vulpeculae, A&A 238, 145-159 Hill, G. & Rucinski, S. M.: 1993, light2: Alight-curve modeling program, in E. F. Milone (ed.),

Light Curve Modeling ofEclipsing Binary Stars, pp. 135-150, Springer, New York Holmgren, D. E.: 1988, The Absolute Dimensions of Ten Eclipsing Binary Stars with Components of Early Spectral Type, PhD Dissertation, University of Victoria, Department of Physics and Astronomy, University of Victoria Huenemoerder, D. P.: 1985, Hydrogen Alpha Observations of RS Canum Venaticorum Stars. IV. Gas Streams in RT Lacertae, AJ 90, 499-503

Huenemoerder, D. P.: 1988, Optical and Ultraviolet Activity in RT Lacertae in 1985 and 1986, PASP 100, 600-603

Huenemoerder, D. P. & Barden, S. C.: 1986a, Optical and UV Spectroscopy of the Peculiar RS CVn System, RT Lacertae, in M. Zeilik & D. M. Gibson (eds.), Cool Stars, Stellar Systems, and the Sun. Proc. 4th Cambridge Workshop, Santa Fe, pp. 199-201, Springer, New York Huenemoerder, D. P. & Barden, S. C.: 1986b, Optical and UV Spectroscopy of the Peculiar RS

CVn System RT Lacertae, AJ 91, 583-589 Hutchings, J. B.: 1968, Expanding Atmospheres in OB Supergiants. I., MNRAS 141, 219-249 Irwin, J.: 1962, Tables Facilitating the Least-Squares Solution of an Eclipsing Binary Light-Curve, ApJ 106,380-426

Jurkevich, I.: 1970, Machine Solutions of Light Curves of Eclipsing Binary Systems, in A. Beer (ed.), The Henry Norris Russell Memorial Volume, Vol. 12 of Vistas, pp. 63-116, Pergamon Press, Oxford, UK Kopal, Z.: 1959, Close Binary Systems, Chapman & Hall, London Kopal, Z.: 1979, Language of the Stars, D. Reidel, Dordrecht, Holland Kopal, Z.: 1989, The Roche Problem, Kluwer Academic Publishers, Dordrecht, Holland Kopal, Z.: 1990, Mathematical Theory of Stellar Eclipses, Kluwer Academic Publishers, Dordrecht, Holland

Kurucz, R. L.: 1979, Model Atmospheres for G, F, A, B, and O Stars, ApJSuppl. 40, 1-340 Kurucz, R. L.: 1993, New Atmospheres for Modelling Binaries and Disks, in E. F. Milone (ed.),

Light Curve Modeling of Eclipsing Binary Stars, pp. 93-102, Springer, New York Lanza, A. F., Catalano, S., Cutispoto, G., Pagano, I., & Rodono, M.: 1998, Long-term Starspot

Evolution, Activity Cycle and Orbital Period Variation of AR Lacertae, A&A 332, 541-560 Lanza, A. F., Catalano, S., Rodono, M., Ibanoglu, C., Evren, S., Tag, G., Cakirli, O., & Devlen, A.: 2002, Long-term Starspot Evolution, Activity Cycle and Orbital Period Variation of RT Lacertae, A&A 386, 583-605 Linnell, A. P.: 1984, A Light Synthesis Program for Binary Stars, ApJ Suppl. 54, 17-31 Linnell, A. P.: 1989, A Light Synthesis Program for Binary Stars. III. Differential Corrections, ApJ 342,449-462

Linnell, A. P.: 1991, A Light Synthesis Study of W Ursae Majoris, ApJ 374, 307-318

Linnell, A. P.: 1993, Light Synthesis Modeling of Close Binary Stars, in E. F. Milone (ed.), Light

Curve Modeling of Eclipsing Binary Stars, pp. 103-111, Springer, New York Linnell, A. P., Etzel, P. B., Hubeny, I., & Olson, E. C.: 1998, A Photometric and Spectrophotometry of MR Cygni, ApJ 494, 773-782 Linnell, A. P. & Hubeny, I.: 1994, A Spectrum Synthesis Program for Binary Stars, ApJ 434, 738-746

Lucy, L. B.: 1968, The Light Curves of W Ursae Majoris, ApJ 153, 877-884

Marquardt, D. W.: 1963, An Algorithm for Least-Squares Estimation of Nonlinear Parameters,

SIAMJ. Appl. Math. 11, 431-441 McNally, D. (ed.): 1991, Reports on Astronomy Symposium on the Theory of Computing,

No. XXIA in Close Binary Stars, The Netherlands, IAU Milone, E. F.: 1976, Infrared Photometry of RT Lacertae, ApJ Suppl. 31, 93-109 Milone, E. F.: 1977, Preliminary Solution for RT Lacertae, AJ 82, 998-1007 Milone, E. F. (ed.): 1993, Light Curve Modeling of Eclipsing Binary Stars, Springer, New York Milone, E. F.: 2002, A Reprise of the Properties of the Exotic Eclipsing Binary RT Lacertae, in C. A. Tout & W. van Hamme (eds.), Exotic Stars as Challenges to Evolution, Vol. 279 of Astronomical Society of the Pacific Conference Series, pp. 65-71 Mochnacki, S. W. & Doughty, N. A.: 1972a, A Model for the Totally Eclipsing W Ursae Majoris

System AW UMa, MNRAS 156, 51-65 Mochnacki, S. W. & Doughty, N. A.: 1972b, Models for Five W Ursae Majoris Systems, MNRAS 156, 243-252

Nagy, T. E.: 1975, The Binary System V566 Oph Revisited, Bull. Amer. Astr. Soc. 7, 533 Nelson, B. & Davis, W. D.: 1972, Eclipsing-Binary Solutions by Sequential Optimization of the Parameters, ApJ 174, 617-628

Plavec, M. J.: 1980, IUE Observations of Long Period Eclipsing Binaries: A Study of Accretion onto Non-Degenerate Stars, in M. J. Plavec, D. M. Popper, & R. K. Ulrich (eds.), Close Binary Stars: Observations and Interpretation, pp. 251-261, D. Reidel, Dordrecht, Holland Popper, D. M.: 1991, Orbits of Close Binaries with CA II H and Kin Emission. IV-Three Systems with Mass Ratios far from Unity, AJ 101, 220-229 Popper, D. M.: 1992, The Cool ALGOLS, in Y. Kondo, R. Sistero, & R. S. Polidan (eds.), Evolutionary Processes in Interacting Binary Stars, Vol. 151 of IAU Symposium, pp. 395-398 Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T.: 1992, Numerical Recipes -

The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 2nd edition Proctor, D. D. & Linnell, A. P.: 1972, Computer Solution of Eclipsing-Binary Light Curves by the

Method of Differential Corrections, ApJ Suppl. 24, 449-477 Rodono, M., Lanza, A. F., & Catalano, S.: 1995, Starspot Evolution, Activity Cycle and Orbital

Period Variation of the Prototype Active Binary RS Canum Venaticorum., A&A 301, 75-88 Russell, H. N.: 1912a, On the Determination of the Orbital Elements of Eclipsing Variable Stars.

I, ApJ 35,315-340

Russell, H. N.: 1912b, On the Determination of the Orbital Elements of Eclipsing Variable Stars.

Russell, H. N. & Merrill, J. E.: 1952, The Determination of the Elements of Eclipsing Binary Stars,

Princeton. Obs. Contr. 26, 1-96 Russell, H. N. & Shapley, H.: 1912a, On Darkening at the Limb in Eclipsing Variables. I, ApJ36, 239-254

Russell, H. N. & Shapley, H.: 1912b, On Darkening at the Limb in Eclipsing Variables. II, ApJ36, 385-408

Southworth, J.: 2008, Homogeneous Studies of Transiting Extrasolar Planets -1. Light-curve Analyses, MNRAS 386, 1644-1666 Southworth, J., Bruntt, H., & Buzasi, D. L.: 2007a, Eclipsing Binaries Observed with the WIRE Satellite. II. ß Aurigae and Non-linear Limb Darkening in Light Curves, A&A 467, 1215-1226 Southworth, J., Maxted, P. F. L., & Smalley, B.: 2004a, Eclipsing binaries in Open Clusters - I.

V615 Per and V618 Per in h Persei, MNRAS 349, 547-559 Southworth, J., Maxted, P. F. L., & Smalley, B.: 2004b, Eclipsing Binaries in Open Clusters - II.

V453 Cyg in NGC 6871, MNRAS 351, 1277-1289 Southworth, J., Smalley, B., Maxted, P. F. L., & Etzel, P. B.: 2004c, Accurate Fundamental Parameters of Eclipsing Binary Stars, in J. Zverko, J. Ziznovsky, S. J. Adelman, & W. W. Weiss (eds.), IAU Symposium, pp. 548-561 Southworth, J., Wheatley, P. J., & Sams, G.: 2007b, A Method for the Direct Determination of the

Surface Gravities of Transiting Extrasolar Planets, MNRAS 379, L11-L15 Tamuz, O., Mazeh, T., & North, P.: 2006, Automated analysis of eclipsing binary light curves - I.

EBAS - a new Eclipsing Binary Automated Solver with EBOP, MNRAS 367, 1521-1530 Tikhonov, A. N.: 1963a, Regularization of Incorrectly Posed Problems, Dokl. Akad. Nauk USSR 153,49-52

Tikhonov, A. N.: 1963b, Solution of Incorrectly Formulated Problems and the Regularization

Method, Dokl. Akad. Nauk USSR 151, 501-504 Tikhonov, A. N. & Arsenin, V. Y. (eds.): 1979, Methods for Solving Ill-Posed Problems, Nauka, Moscow

Tsesevich, V. P. (ed.): 1973, Eclipsing Variable Stars, A Halsted Press Book, Wiley, New York Van Hamme, W.: 1993, New Limb-Darkening Coefficients for Modeling Binary Star Light Curves, AJ 106,2096-2117

Van Hamme, W. & Wilson, R. E.: 2003, Stellar Atmospheres in Eclipsing Binary Models, in U. Munari (ed.), GAIA Spectroscopy: Science and Technology, Vol. 298 of Astronomical Society of the Pacific Conference Series, pp. 323-328, San Francisco Van Hamme, W. & Wilson, R. E.: 2007, Third-Body Parameters from Whole Light and Velocity Curves, ApJ 661, 1129-1151

Wade, R. A. & Rucinski, S. M.: 1985, Linear and Quadratic Limb-darkening Coefficients for a

Large Grid of LTE Model Atmospheres, A&A Suppl. 60, 471-484 Wehrse, R.: 1987, Theory of Circumstellar Envelopes, in I. Appenzeller & C. Jordan (eds.), Cir-cumstellar Matter, IAU Symposium 122, pp. 255-266, Kluwer Academic Publishers, Dordrecht, Holland

Wilson, R. E.: 1979, Eccentric Orbit Generalization and Simultaneous Solution of Binary Star

Light and Velocity Curves, ApJ234, 1054-1066 Wilson, R. E.: 1989, The Relation of Algols and W Serpentis Stars, Space Sci. Rev. 50, 191-203 Wilson, R. E.: 1990, Accuracy and Efficiency in the Binary Star Reflection Effect, ApJ 356, 613-622

Wilson, R. E.: 1993, Computation Methods and Organization for Close Binary Observables, in J. C. Leung & I.-S. Nha (eds.), New Frontiers in Binary Star Research, Vol. 38 of ASP Conference Series, pp. 91-126, Astronomical Society of the Pacific, San Francisco, CA Wilson, R. E.: 1994, Binary-Star Light-Curve Models, PASP 106, 921-941 Wilson, R. E.: 1998, Computing Binary Star Observables (Reference Manual to the WilsonDevinney Programm, Department of Astronomy, University of Florida, Gainesville, FL, 1998 edition

Wilson, R. E.: 2007, Close Binary Star Observables: Modeling Innovations 2003-06, in W. I. Hartkopf, E. F. Guinan, & P. Harmanec (eds.), Binary Stars as Critical Tools and Tests in Contemporary Astrophysics, No. 240 in Proceedings IAU Symposium, pp. 188-197, Kluwer Academic Publishers, Dordrecht, Holland Wilson, R. E.: 2008, Eclipsing Binary Solutions in Physical Units and Direct Distance Estimation, ApJ 672,575-589

Wilson, R. E. & Devinney, E. J.: 1971, Realization of Accurate Close-Binary Light Curves: Application to MR Cygni, ApJ 166, 605-619 Wilson, R. E. & Devinney, E. J.: 1973, Fundamental Data for Contact Binaries: RZ Comae

Berenices, RZ Tauri, and AW Ursae Majoris, ApJ 182, 539-547 Wolf, B.: 1987, Some Observations Relevant to the Theory of Expending Envelopes, in I. Appenzeller & C. Jordan (eds.), Circumstellar Matter, IAU Symposium 122, pp. 409-425, Kluwer Academic Publishers, Dordrecht, Holland Wood, D. B.: 1971, An Analytic Model of Eclipsing Binary Star Systems, AJ 76, 701-710 Wood, D. B.: 1972, A Computer Program for Modeling Non-Spherical Eclipsing Binary Star Systems, Technical Report X-110-72-473, GSFC, Greenbelt, MD Yamasaki, A.: 1981, Light Curve Analysis of Contact Binaries: Characteristic Quantities of the

Light Curve, Ap. Sp. Sci. 77, 75-109 Yamasaki, A.: 1982, A Spot Model for VW Cephei, Ap. Sp. Sci. 85, 43-48

Telescopes Mastery

Telescopes Mastery

Through this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!

Get My Free Ebook


Post a comment