# Contact Binaries

1. Dec 18, 2013

### ckirmser

Hello, group!

I'm wondering how to calculate the HZ for a contact binary system.

Obviously, you can't use just one of the elements, so I wondered how their temperatures would add together. I figure it's not straight addition and I figure it's not just the hotter of the two.

Is there a formula to calculate the combined temperatures?

Thanx!

2. Dec 18, 2013

### Staff: Mentor

The sum is not the blackbody spectrum of a single object with a different temperature. How is "temperature" defined in this case?

3. Dec 19, 2013

### ckirmser

Well, I have premade software that would calculate the HZ, and I assumed it was based upon the temperature of the star - the surface temp, I figured.

But, after your response, I looked up the procedure and see that it is based on magnitude and luminosity.

However, even so, I presume that you can't just sum the magnitudes or luminosities of the components of a contact binary to get the effective values for the system. So, I guess the question becomes, how to sum up the magnitudes and luminosities of a multi-component system to get the effective values for the entire system?

4. Dec 19, 2013

### snorkack

Say, looking for habitable zone of Algol.
Contact binaries have orbital periods of up to a few hours. In case of Algol, 69 hours.
The eclipse takes up up to 10 hours of it.
This is shorter than night (12 hours).
So, the general climate will be depending on the average temperature over the whole cycle.
Algol A is estimated to have the luminosity of about 200 times solar. Algol B has about 3,4 times solar.
So most of time the luminosity is about 203 times solar.
During the eclipses, it drops to about 30 % of maximum, meaning about 60 times solar, or decrease of 140 times solar.
Since the eclipse takes up about 1/7 of the cycle, you wind up with average of 183 times solar.

Actually, most of the 10 hours is a partial eclipse. Also Algol A is deformed, so its area and luminosity change even between eclipses. Basically, take care to integrate the light curve to the precision you feel you need, and find the average luminosity.
For example, if you settle at about 196 times solar luminosity, the habitable zone should be about 14 AU away.