Southern Eclipsing Binaries Project

Modelling the Binary System

An astrophysical model of a binary system consists of values assigned to a range of parameters that describe the system. Some such as the orbital period P are easily obtained (see Light Elements). Others are the masses M of the two stars (or at least the mass ratio q), the temperatures T of each, the inclination i of the pole of the plane of the orbit to line of sight (edge-on orbit = 90°), and luminosity L of the stars (or at least their ratio). A most important parameter is that which describes how close each star is to filling its critical Roche surface (see About EBs). Depending on how it is defined, you will see this stated as an Omega Potential Ω or Fillout Factor f. Then there’s the shapes of the stars, often gravitationally distorted, given by the radii r (as fractions of the orbital radius) in each of the three dimensions defined by the line joining the centres of mass of the two stars and the orbital plane. Those parameters are plainly different from system to system, but others are constant for wide classes of stars. Gravity brightening α measures how surface temperature and hence luminosity varies across a gravitationally distorted star. It’s one value for all stars with radiative photospheres, and another for convective stars - which is why you need to know, from spectral class or otherwise, the stars’ temperatures. Another lis limb darkening x, which can be looked up in tables if you know the temperature of the star, approximate surface gravity g (from another table) and the wavelength of your filter. There are some other parameters too, such as modelling light or dark starspots, and allowing for a “third light”, contamination of your light curve by a faint, unnoticed star in your photometry aperture. How to you find all these out? Aside from P and looking up α and tables for g and x, the answer lies in your light curve. The most widely used program for this is the Wilson-Devinney code (see Wilson 1994 in Downloads). Two popular implementations of this, both freeware, are Bob Nelson’s WDwint and the sophisticated PHOEBE. A different program, widely used by amateurs in particular is David Bradstreet’s BinaryMaker 3, which has excellent graphical output of your modelling. Below is a clip of its user interface from its website. The plots are dynamic. To use these programs, you enter your guesses or knowledge for the above parameters and the program constructs a stellar model accordingly. The light curve it generates is then compared to yours - both visually as in the red (observer) and blue (model) curves in the lower left panel here, and with a figure for the residuals (unsigned differences) between the two. You then tweak some parameters to see if the fit improves. This can go on! The Wilson 1994 article has excellent advice for executing this process, as does the outstanding manual for BM3. This process is not deterministic - many different models can fit your curve equally well. It takes some astrophysical knowledge to know which to reject, and some skill to converge on a good result. In the end you may always be wrong.

Reporting your model

If you’ve got this far you should write a paper on the system. Referees are usually kind enough to help with errors and omissions - they want to see good research published too.

Forging ahead

Apply the experience gained with your first binary system analysis to your next target system. And there certainly are other levels of analysis and modelling you can take on, such as modelling discs and streams, analysing pulsations in one of the component stars, and working with professional teams doing deeper astrophysical work.
Page author: TJR Last edit: 2016-03-19