Calculating HZ for Contact Binary Systems

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Discussion Overview

The discussion centers on calculating the habitable zone (HZ) for contact binary systems, specifically addressing how to determine the effective temperature and luminosity of such systems. Participants explore the complexities involved in combining the properties of multiple stellar components.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how to calculate the habitable zone for a contact binary system, suggesting that the temperatures of the stars cannot simply be added together.
  • Another participant highlights the need for clarity on how "temperature" is defined in the context of multiple stars.
  • A participant mentions using software to calculate the HZ based on surface temperature, but later acknowledges that the calculation is based on magnitude and luminosity.
  • There is a discussion about the challenges of summing the magnitudes and luminosities of the components in a contact binary system to derive effective values for the entire system.
  • A participant provides specific details about the contact binary Algol, including its luminosity and the impact of eclipses on average luminosity, suggesting that the habitable zone should be calculated based on integrated light curves.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the proper methods for calculating effective temperature and luminosity in contact binary systems. There is no consensus on a definitive approach to summing the properties of multiple components, indicating ongoing debate and exploration of the topic.

Contextual Notes

The discussion reveals limitations in the definitions and methods used for calculating the habitable zone in multi-component systems, particularly regarding the integration of light curves and the assumptions made about temperature and luminosity.

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

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