Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model
Abstract
:1. Introduction
The Wilson–Devinney Model and Key Binary Analysis Ideas
- Automatic simultaneous parameter estimation by adjustment of a physical model to observations with a least-squares fitting criterion: This procedure incorporates measurement error statistics into solutions with proper weighting and produces parameter uncertainties. This has advanced the field significantly as it became the de facto standard of the analysis of EB observations;
- The generic character of the physical model allows subsequent extension. This explains why the Wilson–Devinney model has been around for 50 years and still is marching forward into new territories, for example, adding a realistic model of a disk in a binary system;
- Eccentric orbit generalization for an equipotential model (Wilson [3]) (i.e., unification of potential theory covering both asynchronous and synchronous rotation as well as eccentric and circular orbits in any combination). Now, with the generalization as an accepted standard it seems natural to do so, but in 1979 this was a major step and breakthrough that made the model suitable for analyzing many kinds of binary systems;
- Simultaneous analysis of RV and multiband photometric observations (Wilson [3]). Here the same comment applies: This approach appears so natural, but it was a conceptual breakthrough;
- Constrained solutions, including all morphological types based on Roche geometry, that is, the surfaces of both stars are modeled as equipotential surfaces: Detached, semi-detached, over-contact types (see Wilson [3] for the basic idea) and the fourth morphological type (double contact, DBC) (Wilson [6]—paragraph 5, Wilson [7]). Embedding Roche geometry appropriately into the model and program, leads to an important example of improved astrophysical understanding through EB light curve analysis: The successful modeling of W UMa stars as over-contact systems. These very abundant binaries are excellent laboratories for convection in stars. Their fast orbital motion makes them attractive candidates for gravitational wave astronomy;
- Efficient reflection effect, including multiple reflection (Wilson [4]). In terms of accuracy, many situations require multiple reflection to be done correctly, especially where the effective temperatures of the two stars are nearly equal;
2. History, Present and Future
2.1. The Transition from Rectification Techniques to Physical Models
2.2. The WDM Becoming the Most Often Adopted EB Tool: 1980–Present
- System parameters (systemic velocity, third light, distance, extinction);
- Orbital parameters, period change, and apsidal motion;
- Stellar parameters (volume-equivalent radii, masses, surface-averaged effective temperatures);
- Stellar atmospheres parameters and physics (passbands and atmospheres, limb darkening, gravity brightening—sometimes, especially in the older literature, called gravity darkening).
2.3. Recent Progress: 2008–2020
2.4. Future Model Features
3. A Closer Look at the Physical Contributions of the WDM to Astrophysics
3.1. Simultaneous RV and Multiband Light Curve Solutions
3.2. Eccentric Orbit Generalization for an Equipotential Model
3.3. Constrained Morphological Solutions
3.4. Solutions in Standard Physical Units
3.5. Efficient Reflection Effect, Including Multiple Reflection
3.6. Disk Theory and Disk Modeling
3.7. Kinematic Third Body Parameters from Light and RV Curves
3.8. Unification of Ephemeris Analysis
3.9. Other Contributions
4. Software and Programs
- WDwint by Nelson [51] (see also Nelson [52] for graphics output produced by WDwint or http://binaries.boulder.swri.edu/binaries/ (accessed on 18 Janaury 2022).
- Binary Maker 3.0 by Bradstreet and Steelman [54]; see http://daniel.eastern.edu/faculty_personal/dbradstr/ (accessed on 18 Janaury 2022).
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. An Elementary Introduction and Orientation for Non-Binary Researchers
a | semi-major axis of the relative orbit, in units of solar radii |
semi-major axis of the absolute orbit of component j, in units of solar radii | |
d | distance of the binary |
e | the orbital eccentricity = separation of foci / |
F | rotation parameter |
rotation parameter for binary star component j | |
gravity brightening coefficient of component j | |
i | orbital inclination; angle between orbital plane and plane-of-sky (angular degree) |
third light, sum of all contributions from any systems parts beyond the binary pair | |
(usually assumed to be constant) | |
bolometric luminosity (radiant power in Watts, over steradians, units could be | |
W/micron or in units of solar luminosity) | |
monochromatic luminosity (in a specified passband) of component j over | |
steradians | |
mass of component j (in units of solar masses) | |
P | binary orbital period |
q | binary system mass ratio: |
photometric mass ratio | |
spectroscopic mass ratio | |
relative radius of component j | |
mean radius of component j; usually the “equal volume | |
radius" in units of solar radii | |
mean effective temperature of component j | |
limb darkening coefficient of component j | |
damping factor in VLR algorithm | |
radial velocity of the center-of-mass of a binary system | |
argument of periastron | |
Roche potential of component j |
1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
or | √ | √ | √ | √ | |
, , | √ | √ | |||
a, , , , , d | √ | ||||
e, , P | √ | √ | √ | √ | √ |
√ | √ | √ | |||
√ | √ | ||||
i, , , , , , , | √ | √ | √ | ||
√ | (?) | (?) | √ | √ |
1 | However depending on context, the statements are also valid for non-eclipsing binaries. |
2 | For reader convenience, this appendix is, by courtesy and under the license 5181321004554 of Springer Nature, a close excerpt of pages 173 and 174 of the book Eclipsing Binary Stars: Modeling and Analysis by Kallrath and Milone [5]. |
3 | In detached systems, correlations of with , , and other parameters make it almost impossible to derive meaningful photometric mass ratios. In lobe-filling or over-contact binaries either of or is eliminated from the adjustable parameter list. |
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2020 | 2021 | |
---|---|---|
WD71 | 97 | 101 |
W79 | 47 | 41 |
W90 | 42 | 43 |
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Kallrath, J. Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model. Galaxies 2022, 10, 17. https://doi.org/10.3390/galaxies10010017
Kallrath J. Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model. Galaxies. 2022; 10(1):17. https://doi.org/10.3390/galaxies10010017
Chicago/Turabian StyleKallrath, Josef. 2022. "Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model" Galaxies 10, no. 1: 17. https://doi.org/10.3390/galaxies10010017
APA StyleKallrath, J. (2022). Fifty Years of Eclipsing Binary Analysis with the Wilson–Devinney Model. Galaxies, 10(1), 17. https://doi.org/10.3390/galaxies10010017