system
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human
Do accreting binary stars have a habitable zone?

This came to me over my coffee this morning. I'm imagining a supernova progenitor: a white dwarf accreting mass from a red giant companion, but it could be a neutron star with a main sequence or giant companion.

I don't know much about exoplanets, so I've got to ask: could a planet exist far enough from the binary to have stable orbit around a binary, but close enough that it receives significant energy to support life? Would the presence of the giant companion star make this impossible? 

Would the asymmetry in radiation from the binary create inhospitable temperature swings on the planet, or could the period of the binary's orbit be high enough that the planet could maintain a suitable heating a cooling cycle?
gpt
Let's see here. First, if you have a binary with a white dwarf/neutron star with a main sequence/giant star companion, the light from the WD/NS is going to be negligible. They are very faint compared to normal stars, and giants especially. So your habitable zone will depend only on the giant. However, the two stars will have relatively equal masses, which means the motion of the giant star could be rather large as it orbits.

If the giant star has a luminosity 10x that of the sun, the habitable zone will be moved out by ~sqrt(10)~3. So the habitable zone would be from maybe 2.7AU to 4.5AU. This is certainly feasible and would be a stable orbit for a planet. The question is just a matter of what is the orbital period of the binary star, and thus how much does the insolation from the giant star change depending on where it is in its own orbit. But the binary orbit could certainly be short enough (<50 days or so should do it) to ensure that the planet would be in the habitable zone its entire orbit.
Edit: Just realized that if this is an actively accreting system, then *of course* the binary orbital period is short, so the habitable zone won't shift too much, and you could definitely have stable habitable zone planets.