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Stars glow with (almost) a black body spectrum. The fourth-power dependency on temperature means that there are large differences in surface brightness between hotter and cooler stars.

The coolest stars are about 2000K while the hottest exceed 10000K, which represents a 625-fold difference in surface brightness.

Consider a 2000K red dwarf star in orbit around a 10000K blue giant at a distance of 10 blue-giant radii away. This is far enough that tidal effects are mild for both stars (tidal heating can be avoided if they are tidally locked).

The substellar point of the red dwarf will absorb about 6 times more energy than it radiates. Would this radiation heat the dwarf star and cause it to expand? If so could the core decompress and adiabatically cool, stopping fusion?

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  • $\begingroup$ Insolation in regards to stars other than the Sun is called "instellation". Not to be nitpicky or anything, I just learned of that term recently and thought I'd share it. $\endgroup$
    – BMF
    Jan 17, 2023 at 0:23

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The coolest star would be an elderly L2 dwarf with a mass of $0.08M_\odot$ a radius about that of Jupiter and an intrinsic luminosity of $0.001L_\odot$.

A 10,000 K blue giant might have a radius of $100 R_\odot$ and a luminosity of $10^5 L_\odot$.

If you separate them by $1000 R_\odot$, then the low mass star will receive about $2\times 10^{-4} L_\odot$ of radiation from the hot star, some of which will be absorbed.

Since this is a significant fraction of its own luminosity, it is likely to change its internal structure. The overall effect would be expand the star in a homologous way leading, by the virial theorem, to a lower interior temperature and possibly, temporarily, extinguishing fusion.

Important Edit: Why temporarily? Well, because the hot star is short-lived, and will probably end in the form of a supernova. Once the source of insolation has gone, the low mass star will contract again on its thermal timescale of a few hundred million years and recommence fusion. Note that, in this scenario, the separation of 5 au is probably sufficient to avoid engulfment by the massive primary. It might however gain some mass by accreting from the slower wind present in the red supergiant phase - raising the possibility that something that was just a brown dwarf could become a star after this (see Can a brown dwarf accrete enough mass from red giant to become a star?).

However, there is an important caveat to all this. The hypothetical scenario presented is almost impossible to arrange. The lifetime of the high mass star is probably 50 million years or less, whilst the timescale for the low-mass star the reach the main sequence is a few hundred million years.

So, although the insolation and expansion would take place, it couldn't happen to an elderly L2 dwarf undergoing fusion unless it had somehow been captured into that system. This is incredibly unlikely, so in practice, you would need the hot star to have been born in a binary with a more massive ($>0.5 M_\odot$) low-mass object in order for it to be undergoing hydrogen burning whilst the hot star was still there. But then, the insolation received would be a tiny fraction of its luminosity and would be nowhere near enough to halt fusion in its core.

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  • $\begingroup$ I have always wondered what would happen to stars if one put then in the thermal batoh (like CMB) with temperature much larger than 3K. Intiutively, I would also expect they will expand and possibly dissolve. $\endgroup$
    – Leos Ondra
    Jan 15, 2023 at 12:23
  • $\begingroup$ As a caveat to this otherwise correct answer: There is no "brown-red" dwarf middle ground in the long run and thus a red dwarf could be theoretically converted into a brown dwarf by starlight! But "long" means billions of years. The blue star will supergiant in a few million years and swallow it whole. $\endgroup$ Feb 13, 2023 at 5:40

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