Calculating HZ for Contact Binary Systems

[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!

 

[mfb]

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

 

[ckirmser]

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

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?

 

[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.

 

[pmacias]

Hello there!

Calculating the habitable zone (HZ) for a contact binary system can be a bit complicated, but there are a few key factors to consider. The HZ is the region around a star where liquid water could exist on a planet's surface, making it potentially habitable for life as we know it. It is dependent on the star's temperature and luminosity, as well as the distance between the star and the planet.

In the case of a contact binary system, where two stars are in close proximity and may even be touching, the HZ can be affected by the combined temperature of the two stars. However, it is not a simple addition of their individual temperatures. The exact calculation will depend on the specific properties of the stars, such as their masses and radii.

One approach is to use a computer simulation or model to calculate the HZ for a contact binary system. These models take into account the properties of both stars and can provide a more accurate estimation of the HZ. Alternatively, you can use a formula such as the one developed by Selsis et al. (2007) which takes into account the combined luminosity and temperature of the two stars.

In any case, it is important to note that the HZ is not a definitive boundary and can vary depending on factors such as the composition of the planet's atmosphere. It is also worth considering that a contact binary system may not be the most ideal environment for life to develop, as the close proximity of the stars could result in extreme changes in temperature and radiation levels.

I hope this helps to answer your question. Happy calculating!