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Brown dwarfs/failed stars can actually become stars, if they exceed a mass limit of about 80 Jupiter masses. This is when the internal pressure and temperature at the core become high enough to literally ram protium atoms into each other to release energy.

But does this transition occur all of a sudden, i.e. it turns instantly into a star after exceeding the mass limit?

Or does this transition take gradually, i.e. after exceeding this limit, the brown dwarf slowly and gradually turns into a star?

The question here is:

What is it like to see a brown dwarf turn into a star?

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    $\begingroup$ You need to specify a mass accretion scenario. I think the result depends on how much and how quickly the mass is accreted. Low mass protostars can initially be "brown dwarfs" that are not undergoing fusion, but they accrete more mass and will eventually end up as main sequence stars. But I guess this is not what you mean? $\endgroup$
    – ProfRob
    Commented Nov 29, 2022 at 16:24
  • $\begingroup$ No, what I mean is, after reaching the mass limit (regardless of accretion), does it instantly turn into a star, or does it gradually turn into a star, after it passes the mass limit? $\endgroup$
    – Alastor
    Commented Nov 29, 2022 at 16:37
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    $\begingroup$ But it can't be regardless of the accretion. How the object behaves depends on the accretion rate and how the mass is accreted. A "star" of 0.1 solar mass has an earlier life as a 0.1 solar mass ball of gas with no fusion going on in it. So you could have a scenario where the mass is accreted very slowly onto an old brown dwarf, or you could have a sudden dump of mass onto a young brown dwarf or something in between. You then have to specify whether accretion is "cold" or "hot" - in the sense of how much of the accreted kinetic energy can be radiated. $\endgroup$
    – ProfRob
    Commented Nov 29, 2022 at 18:32

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Exactly what this would look like would depend a great deal on how (fast) the mass is accreted and whether there is a significant amount of energy accreted along with the mass.

There are two timescales at play here - the thermal timescale of the brown dwarf and the accretion timescale. If the latter is shorter than the former then the brown dwarf cannot adjust to additional mass and either inflates and becomes more luminous if the accretion is "hot" (if it accretes lots of energy too), or is compressed and becomes less luminous if the accretion is "cold" (most of the accreted energy is efficiently radiated). It will then gradually adjust its structure and luminosity on the thermal timescale of the new object. How the brown dwarf behaves is nothing to do with nuclear fusion here.

For slow accretion that nudges the brown dwarf over the limit then to see the effects of nuclear fusion you still have to wait for a thermal timescale - which is the timescale for the brown dwarf structure to adjust for a difference in energy input. The thermal timescale for an object at the substellar mass boundary is generally quite long, but depends on how old it is. That is because it is basically the gravitational potential energy divided by the luminosity. The former gets bigger as the brown dwarf gets older because it contracts (at a slowing rate). The latter gets smaller as the brown dwarf cools. A minimum timescale would be if the mass is accreted onto a young brown dwarf that is still strongly contracting. It will then approach the zero age main sequence on the thermal timescale of a relatively luminous $0.075M_\odot$ (star/brown dwarf) which is of order 500 million-1 billion years. What you would see is the brown dwarf/star get gradually less luminous over that time until it levelled off at its main sequence luminosity.

If you added the mass to an older, colder brown dwarf, then the timescale for adjustment would be considerably longer. The brown dwarf/star would gradually become more luminous over many billions of years until it reached the zero age main sequence luminosity appropriate for its new mass.

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