I’m researching eclipsing variable stars and have read that the relative sizes of the stars can be determined from the light curve, but I couldn’t find the methodology on how to do this. I’d also like to know if it’s possible to distinguish between detached and contact binaries using a light curve. Could anyone provide guidance?
Miro,
See the attached short paper and the attached separate light curve to get you started. The paper contains typical light curves of detached EBs and a short description of how light curves can be interpreted to determine the relative sizes of the components of an EB.
In a detached system, the start and end of each eclipse can be identified visually in the light curve. In a contact system, the light curve is continuously changing, so that it is impossible to see the beginning or end of an eclipse.
VSS Newsletter 2016 3 Jul Richards.pdf (2.3 MB)
Roy
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Thanks for the reply Roy. Although I’m still confused on how to get the relative sizes of the two stars. The paper mentions that you need to measure how long it takes the star to go from the start of the eclipse to its minima but I’m unsure on what to do after that.
Miro
From the light curve alone, the diameters of the two stars can be calculated only relative to the radii of the orbits.
For Fig. 2 in the paper, the formulae are:
2pi(t4 - t1)/P = D2/a2
2pi(t2 --t1)/P = D1/(a1 + a2)
Where:
D1 and D2 are the stellar diameters
a1 and a2 are the radii of the orbits
The above assumes the orbits are circular and that the line of sight to the system is along the plane of the orbits (i.e., the orbits are seen “edge on” from Earth). When real systems are studied, these assumptions may not be correct.
Roy
The above formulae are not really useful. To go further, you need software for complex analysis of the properties of eclipsing binary systems.
One such is Binary Maker 3 available from https://daniel.eastern.edu/faculty_personal/dbradstr/
It is not freeware. The cost is I think US$100.
Using it is not trivial.
Edit: If the input is from light curves alone, it does not provide accurate, calculated parameters, but estimates based on an iterative process as you enter and refine assumed (or known) parameters of each system.
One very useful feature of the programme is that it has a library of light and radial velocity curves of many eclipsing systems. Browsing those gives you a good feel for the relationship between types of EBs and their light curves.
Roy
Perhaps the following two webpages might provide some background on the process by which we can determine the properties of eclipsing binary stars. They assume that radial velocity measurements have been made for each star, and make a number of simplifying assumptions … but there is a worked example.
http://spiff.rit.edu/classes/phys373/lectures/eclipsing_example/eclipsing_example.html
http://spiff.rit.edu/classes/phys373/lectures/eclipse_lab/eclipse_lab.html
Good luck!