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I sometimes read that only deuterium-deuterium fusion can occur in brown dwarfs... And maybe deuterium-proton fusion? To He-3?

In order to overcome Coulombic repulsion and, occasionally, fuse, protons have to be continuously jammed together under immense pressure and heat...

Does this still happen, albeit less often, in brown dwarfs?

Can even free protons in the icy cold of outer space fuse together, perhaps via the magic of quantum tunneling?

(I understand that even inside true stars like our Sun, colliding protons only form deuterium about one-in-ten-octillion times that they DO collide with each other, since one has to spontaneously turn into a neutron....)

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Does coal burn at room temperature? Most people would say "no". For an oxygen molecule to react with an atom of carbon in the coal, a certain amount of energy is required to break the bonds joining the atoms together. Once these bonds have been broken, then new bonds can form releasing energy (and the energy released is more than the energy required to break the bonds - it is an exothermic reaction)

But at room temperature most of the oxygen molecules are moving too slowly; they don't have enough energy to react, so no reaction occurs. Of course not every molecule of oxygen has the same speed, some have more energy. A very very small proportion might have enough energy to react. Yet even so, you would not say that coal burns at room temperature.

Well much the same is true in a Brown dwarf. The protons need a lot of energy to overcome the electrostatic repulsion of two positively charged protons. There is a distribution of energies among the protons and there must be a very very small proportion of protons that do have sufficient energy but just as you could leave a piece of coal from millions of years, Brown dwarfs will never convert more than an utterly neglible amount of their mass their mass into helium

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Image from Review of the Universe

The reaction rate drops preciptously below about 3 million K. A key reason is that just as with coal, as the temperature rises, and the random reaction rate increases, at a certain point the energy released, which gets transferred to nearby particles, causes the reaction rate to increase further. A positive feedback loop. For coal, or other flammable this when we say it has caught fire. For dwarf stars, this is when we say that the core is supported by fusion and gravitational collapse has been halted: the mark of a true star.

So while there will, inevitably, be very rare fusion events, below about 3million K no self sustaining p-p chain reactions can occur, and the core of the brown dwarf will continue to collapse under gravity.

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  • $\begingroup$ One might ask "how rare?" Is it like a broken egg spontaneously reassembling itself in that it's technically possible but just so stupendously unlikely you'd almost surely never see it happen once in the entire universe run until heat death? $\endgroup$ Apr 1, 2023 at 23:03
  • $\begingroup$ “Does coal burn at room temperature? Most people would say "no".” Yeah, I bet Satan would differ. LOL $\endgroup$ Apr 2, 2023 at 23:42
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Wikipedia discusses this matter. Essentially, the mass limit of brown dwarfs is defined in a way that excludes proton-proton fusion, which requires higher temperature and pressure (thus stronger gravitational compression and more mass) than some other fusion reactions that do occur in brown dwarfs. In addition to deuterium-deuterium, sufficiently massive brown dwarfs can fuse protium (hydrogen-1) with lithium-7, which produces two nuclei of helium-4 ($^7\text{Li} +\text{ }^1\text{H}\to 2\text{ }^4\text{He}$) with release of energy.

None of the fusible constituents is very abundant in typical gas-cloud compositions, so many brown dwarfs seen today have already exhausted their fusion supply and are simply glowing with their residual temperature as they cool off, like white dwarfs.

It might be added that the most massive stars also do not primarily fuse protons directly. With sufficient temperature and pressure various CNO cycles take over, these requiring more activation energy than proton-proton fusion but going faster once this energy is supplied. Unlike the deuterium- and lithium-based fusion reactions occurring in brown dwarfs, the CNO cycles do not deplete any reactants other than protium; the carbon, nitrogen and oxygen isotopes are interconverted cyclically. Thus stars massive enough to undergo significant CNO cycling can sustain it.

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