A few definitions are in order!
Deuterium is hydrogen, plus a neutron. Most hydrogen in the universe, and on Earth, is one proton, one electron, and no neutrons. It’s the simplest atom out there, and hydrogen in this form is the most abundant atom in the universe. Deuterium, with its one proton, one electron, and one neutron, is much less common than its simpler counterpart - it’s only 0.016% of all the hydrogen out there. That’s approximately 160 atoms of deuterium for every million standard hydrogen atoms.
The other fun fact about deuterium is that it’s effectively not produced by any ongoing natural process. Stars don’t create it - in fact, they actively destroy deuterium. So, we think all the deuterium in the universe was created in the Big Bang, and we’ve been slowly eating away at it ever since.
Brown dwarfs, meanwhile, are little balls of gas that didn’t quite make it to being a star. They don’t have enough mass to create the temperatures and pressures in their cores needed to start burning hydrogen the way our sun does. Brown dwarfs are typically so much smaller than the rest of the stars in the universe that instead of being weighed in units of “stellar masses”, which are multiples of or fractions of the mass of our sun, we use “Jupiter masses”. Brown dwarfs tend to come in somewhere between 13 times the mass of Jupiter and about 83 times the mass of Jupiter. The upper limit here is the mass required to ignite hydrogen burning - in different units, this is 0.08 times the mass of the sun. The lower mass limit is a bit fuzzier, and that’s when you tend to run into the issue of “Is this a really large planet or is it a star”, particularly if it’s hanging around another star that is much larger than it is. You can have brown dwarfs that are smaller than 13 Jupiter masses, and planets larger than 13 Jupiter masses - it depends what’s going on inside of the object.
By definition, brown dwarfs can’t burn hydrogen, but it turns out that they can burn deuterium. Deuterium burns at lower temperatures and pressures, so if the brown dwarf is above the 13 Jupiter-mass cutoff, the internal pressure of a brown dwarf can trigger the start of deuterium burning. The temperature at which this happens is about 10^6 Kelvin - one million degrees. Keep in mind that this is the temperature at the very core of the star, not at the surface! By the time you get to the surface of the star, you’re down to somewhere between 2000 degrees Kelvin and 750 degrees Kelvin, depending on the size of your brown dwarf.
Remember that there are still only 160 atoms of deuterium per million atoms of hydrogen - these brown dwarfs are made of this same mixture. This means of course, that there is not a lot of deuterium around in the star to be burned. Most brown dwarfs race through their deuterium in about 100 million years - a flash, in cosmic time. (By comparison, our sun will be stable for about 8 billion years.) Once the star has burned all the deuterium it can reach, it’s burning days are over. The heat it built up through burning deuterium will slowly fade away, and the dwarf will truly be a “failed star”.
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