How to determine temperatures for a binary system?

Question

How to make a guess for temperatures of an eclipsing binary from light curves measured in UBVR filters of the Johnson system? I assume that differences of indexes U, B, V will be necessary, right? Thank you

Answer 1

Yes, you're exactly on the right track. There are several methods people use to estimate the temperature from the color indices, but most of them estimate the temperature from the average index (i.e. over the entire light curve). My master's thesis and PhD dissertation focus on eclipsing binaries, and in my experience, it's better to focus on the color index at specific phases to get a more accurate temperature estimate. I'd link my first (and so far only) published paper, but I'm not sure if that's appropriate on StackExchange or not. Instead, I'll outline my method here. Note that this requires a light curve that covers all phases fairly well and at least two bands of nearly simultaneous observation (i.e. a series of consecutive images like B, V, B, V, B, V, ...). It also requires that the data is transformed into apparent magnitudes in a standard filter system (like Johnson-Cousins UBVRI).

1. Pick one band (say V) in which you'll use the observed data directly.
2. In the other band you're using (B in our case), you can't directly use the observed data because it was taken at a slightly different time than the V data. Instead, use linear interpolation between the observed B data to estimate the B magnitude at the time of each V observation.
3. Calculate the B - V color index by subtracting the observed V magnitude from the interpolated B magnitude.
4. Convert the B - V indices to be a function of phase rather than time so that you can combine data from multiple nights.
5. This is where I disagree with the "traditional" method of determining the temperature. If you find the average B - V index over the whole light curve, you get a color index that is a flux-weighted average of both stars, which isn't very useful. However, realize that, in most cases, the combined flux of the system during the shallower eclipse is mostly (or entirely, in the case of a total eclipse) from the hotter star. Therefore, finding the color index right around the shallower eclipse (phase 0.5 for circular orbits) gives a much more accurate value for the primary's color than the "traditional" method.
6. Once you have the color index, you use a source from the literature to convert this to a temperature estimate. I personally use Flower (1996).
7. If you have data in other bands, you can repeat this process to find those color indices and get another estimate for temperature.

Hope this helps!