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I am constructing my own cluster of solar systems for a story I'm working on and had the idea of adding a black dwarf somewhere to indicate the timeline of this story.

My question is. Does a black dwarf have sufficient mass and gravity to form a P class binary star system with a class G star?

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2 Answers 2

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As you probably know, black dwarfs are just white dwarfs cooled by lots and lots of time, billions to trillions of years, depending on the model. There is not much about them that fundamentally sets them apart from white dwarfs, they'll have the same ~1 solar mass of gravitational influence (or perhaps as light as SDSS J091709.55+463821.8 at 0.17 solar masses).
In order to set the system up properly, you'll want the binary pair to orbit at a distance where distortions in their mutual stellar atmospheres and mass-transfer/accretion are unlikely. Some form of the Chandrasekhar Limit still applies to black dwarfs, so significant accretion can cause the system to experience a nova in short order. It is likely possible to put both stars within the orbit of Mercury (such is nearly the case with the Capella star system), as long as no significant portion of the G-type star's atmosphere crosses into the Roche lobe of the black dwarf star. With our Sun, that's likely doable, but things would go south quickly once the G-type star evolves into a larger, hotter star, and its envelope crosses into the other Roche lobe.

Planets will orbit the barycenter of the binary system, and the P-type habitability zone will be pretty much normal considering the black dwarf does not put out radiation.

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    $\begingroup$ The time needed for a white dwarf to become a black dwarf would exceed the lifespan of any G-type star, so this binary system must be one made of orbital capture of one of the stars by the other, with potential cataclismic results for any planetary system that existed previously. $\endgroup$
    – Rekesoft
    Commented Aug 10, 2022 at 8:34
  • $\begingroup$ @Rekesoft That's for the author to work out. In the cosmic era where black dwarfs are kicking around, the star-forming nebula of the G-type is going to have a very high metallicity, making planet formation abundant. The black dwarf will have to be captured after the accretion disk is settled. If otherwise, depending on the black dwarf and accretion mass, there either may not be any inner planets, only outers, or the whole thing goes up in flames. After the capture, maybe some mechanism causes outer planets to gradually migrate inward. $\endgroup$
    – BMF
    Commented Aug 10, 2022 at 18:02
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Black dwarf stars will have the same mass range of white dwarf stars. This mass can range from an estimated 0.15-1.4 solar masses (https://astronomy.swin.edu.au/cosmos/W/white+dwarf) A P-type orbit applies to the planets around the stars in a binary system. P-type orbit is around the barycenter of both stars, while an S-type orbit is around one of the two stars. The black dwarf star could orbit the G-type star much like the moon orbits Earth, or as an equal-sized body. You would just want to avoid the black dwarf moving close enough to steal stellar material from the G-type star. Nothing precludes it from allowing planets to form P-type orbits.

One question I would ask is how a G-type star was able to form capture the black dwarf without the black dwarf gaining some new hydrogen and reigniting. G-type stars have an average lifespan of 10 billion years. A black dwarf flying through a stellar nursery would pull hydrogen down to its surface and potentially gain enough fuel to heat up. I could see it being more likely that the companion star would not be a G-type, but something like a K-type star or even a red dwarf, which has an extremely long lifespan.

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