<p>Brown dwarfs, by definition, do not have a phase where their centres are kept hot by ongoing hydrogen (protium - a nucleus of just a single proton) fusion. The threshold is about <span class="math-container">$0.075M_\odot$</span>. Above that, the core temperature becomes hot enough that the rate of energy release through hydrogen fusion (the pp-chain) matches energy losses at the surface and halts the contraction of the star. Below this threshold, the contracting brown dwarf's degenerate core never heats up sufficiently to generate enough energy from pp-fusion to match energy losses at the surface. The result is continuing (but slowing) contraction and cooling towards a completely degenerate state (a &quot;hydrogen white dwarf&quot; if you like).</p>
<p>Brown dwarfs, again by definition, <em>are</em> able to initiate deuterium fusion.  Deuterons (a proton plus a neutron) can fuse directly with protons at <span class="math-container">$\sim 10^6$</span> K; cooler than the temperatures required for the pp-chain (about <span class="math-container">$5\times 10^6$</span> K). Deuterium burning <em>does</em> lead to a stabilisation of the brown dwarf and should produce something akin to a &quot;deuterium main sequence&quot; (though this has not been observed). The problem is that deuterium is quite rare - only about <span class="math-container">$10^{-4}$</span> as a fraction by number compared with protons. That means that once initiated, a fully convective and mixed brown dwarf soon burns through all its deuterium (see below).</p>
<p>The cooling of brown dwarfs, compared with low-mass stars, including the plateau(s) in luminosity caused by (1) pp-fusion in stars (blue lines) and (2) deuterium fusion in brown dwarfs (green lines), is readily appreciated in this famous plot from <a href="https://arxiv.org/abs/astro-ph/9705201" rel="nofollow noreferrer">Burrows et al. (1997)</a>. You can see that the D-burning plateau lasts between 3-30 million years depending on the mass of the brown dwarf (and an even shorter D-burning plateau in the lowest mass stars). The plot also answers your question about how quickly brown dwarfs cool. Since their radii are almost fixed (at about 1 Jupiter radius) for most of the cooling phase, the reduction in luminosity is directly related to the reduction in surface temperature as <span class="math-container">$T \propto L^{0.25}$</span>.</p>
<p><a href="https://i.sstatic.net/OoRsc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OoRsc.png" alt="Cooling plot for brown dwarfs and stars" /></a></p>

CC BY-SA 4.0
2024-09-22T17:37:04.133Z
And you can also see the D-burning plateau in the stars as well, up there in the top-left corner.
Vikki
CC BY-SA 4.0
2024-09-22T13:05:44.527Z
2024-09-23T22:56:56.907Z
2024-09-23T22:56:56.907Z
ProfRob
<p>I was recently looking into brown dwarf systems, and I read that all brown dwarfs eventually cool due to their low mass/absence of fusion material, though how long does that take? Red dwarfs have a main sequence phase of billions if not trillions of years, so why don't brown dwarfs show a similar stability in their life cycle?</p>

CC BY-SA 4.0
2024-09-21T23:41:35.130Z
I'm not sure what you're asking in point #1, but deuterium & lithium fusion are much faster than plain p-p chain hydrogen fusion. The p-p chain involves converting some protons to neutrons, which involves the weak force, which operates much slower than the strong nuclear force. I have further info at https://astronomy.stackexchange.com/a/43908/16685
PM 2Ring
CC BY-SA 4.0
2024-09-22T00:03:48.523Z
@PM2Ring i see where there may be confusion, I was trying to ask how long does deuterium/lithium fusion take in brown dwarfs and why they aren't as stable as the slightly more massive red dwarfs, though you already answered one of those, thanks!
ArchiveOfStars
CC BY-SA 4.0
2024-09-22T06:32:59.433Z
Generally we have here a policy of one question per... question. Could you please limit your question to one? This looks to me like three related, but quite different questions.
planetmaker
CC BY-SA 4.0
2024-09-22T08:44:02.647Z
Li and D are  not mentioned in your Q at all. They form about a billionth and a ten thousandth of the mass respectively, and their fusion is energetically negligible or not hugely important respectively.
ProfRob
CC BY-SA 4.0
2024-09-22T11:59:12.207Z
@ProfRob By definition, a brown dwarf is massive enough for D fusion, but too small for P-P fusion. But I suppose it's not obvious that the energy produced by fusion in a brown dwarf is small relative to that produced by gravity / the [Kelvin–Helmholtz mechanism](https://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_mechanism).
PM 2Ring
CC BY-SA 4.0
2024-09-22T17:33:50.380Z
I have edited to focus on just the 1st question. If you wish to ask the others, please do so separately.
Rory Alsop
<habitable-zone><brown-dwarf><main-sequence>
"Main sequence" period and habitability of brown dwarf systems
ArchiveOfStars
# "Main sequence" period and habitability of brown dwarf systems

(Asked by: username_0 on 2024-09-21)

I was recently looking into brown dwarf systems, and I read that all brown dwarfs eventually cool due to their low mass/absence of fusion material, though how long does that take? Red dwarfs have a main sequence phase of billions if not trillions of years, so why don't brown dwarfs show a similar stability in their life cycle?

**Tags:** habitable-zone, brown-dwarf, main-sequence
> **Comments:**
> **username_1**: I'm not sure what you're asking in point #1, but deuterium & lithium fusion are much faster than plain p-p chain hydrogen fusion. The p-p chain involves converting some protons to neutrons, which involves the weak force, which operates much slower than the strong nuclear force. I have further info at https://astronomy.stackexchange.com/a/43908/16685  
> **username_0**: @PM2Ring i see where there may be confusion, I was trying to ask how long does deuterium/lithium fusion take in brown dwarfs and why they aren't as stable as the slightly more massive red dwarfs, though you already answered one of those, thanks!  
> **username_2**: Generally we have here a policy of one question per... question. Could you please limit your question to one? This looks to me like three related, but quite different questions.  
> **username_3**: Li and D are  not mentioned in your Q at all. They form about a billionth and a ten thousandth of the mass respectively, and their fusion is energetically negligible or not hugely important respectively.  
> **username_1**: @ProfRob By definition, a brown dwarf is massive enough for D fusion, but too small for P-P fusion. But I suppose it's not obvious that the energy produced by fusion in a brown dwarf is small relative to that produced by gravity / the [Kelvin–Helmholtz mechanism](https://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_mechanism).  
> **username_4**: I have edited to focus on just the 1st question. If you wish to ask the others, please do so separately.  

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## 1 answers

### Answer by username_3 on 2024-09-22. Score: 9

Brown dwarfs, by definition, do not have a phase where their centres are kept hot by ongoing hydrogen (protium - a nucleus of just a single proton) fusion. The threshold is about $0.075M\_\odot$. Above that, the core temperature becomes hot enough that the rate of energy release through hydrogen fusion (the pp-chain) matches energy losses at the surface and halts the contraction of the star. Below this threshold, the contracting brown dwarf's degenerate core never heats up sufficiently to generate enough energy from pp-fusion to match energy losses at the surface. The result is continuing (but slowing) contraction and cooling towards a completely degenerate state (a "hydrogen white dwarf" if you like).

Brown dwarfs, again by definition, *are* able to initiate deuterium fusion. Deuterons (a proton plus a neutron) can fuse directly with protons at $\sim 10^6$ K; cooler than the temperatures required for the pp-chain (about $5\times 10^6$ K). Deuterium burning *does* lead to a stabilisation of the brown dwarf and should produce something akin to a "deuterium main sequence" (though this has not been observed). The problem is that deuterium is quite rare - only about $10^{-4}$ as a fraction by number compared with protons. That means that once initiated, a fully convective and mixed brown dwarf soon burns through all its deuterium (see below).

The cooling of brown dwarfs, compared with low-mass stars, including the plateau(s) in luminosity caused by (1) pp-fusion in stars (blue lines) and (2) deuterium fusion in brown dwarfs (green lines), is readily appreciated in this famous plot from [Burrows et al. (1997)](https://arxiv.org/abs/astro-ph/9705201). You can see that the D-burning plateau lasts between 3-30 million years depending on the mass of the brown dwarf (and an even shorter D-burning plateau in the lowest mass stars). The plot also answers your question about how quickly brown dwarfs cool. Since their radii are almost fixed (at about 1 Jupiter radius) for most of the cooling phase, the reduction in luminosity is directly related to the reduction in surface temperature as $T \propto L^{0.25}$.

[![Cooling plot for brown dwarfs and stars](https://i.sstatic.net/OoRsc.png)](https://i.sstatic.net/OoRsc.png)

> **Comments:**
> **username_5**: And you can also see the D-burning plateau in the stars as well, up there in the top-left corner.  

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