Brown Dwarfs on the H-R diagram

Smythe

Do Brown Dwarfs appear on the lower right hand "tail" of the main sequence of the H-R diagram?

Or are they separate from the main sequence?

The location here:
https://en.wikipedia.org/w/index.php?title=File:HR-diag-instability-strip.svg&page=1
appeared to show them in that location, but I wasn't sure if they are actually separate from the main sequence as the diagram isn't that clear on their location.

Thank you.

WACO

As a cloud of gas contracts, this 'protostar' evolves along what is known as the 'Hayashi' track. The protostar radiates energy due to the gravitational collapse of the cloud via convection - it converts the gravitational potential energy into thermal energy. Protostars of all masses do this, they evolve along their respective Hayashi track until they reach a point where the core temperature is high enough to begin nuclear fusion. This point is the Main Sequence, or more correctly, the Zero Age Main Sequence (ZAMS).

For brown dwarfs, they do not have enough mass (less than ~0.1 Solar mass) to burn Hydrogen in their cores, but they do end up on the ZAMS. So it would be correct to say that they are on the MS.

It is often overlooked, that a star gets to it's proper place on the ZAMS purely from the conversion of gravitational potential energy into thermal energy, which of course depends on the mass. The fusion in the core of the star is a self regulating mechanism, and merely prolongs the timescale over which the star remains stable (hydrostatic equilibrium). In essence, the energy radiated by a star is replaced exactly by the energy generated in the nuclear fusion process.

As for brown dwarfs, they can't replace the energy they radiate and so their evolution after the ZAMS is quite complicated - a whole other thread!

ps200306

The main sequence represents the stable hydrogen burning phase of stars of different temperatures/luminosities. Brown dwarfs don't have such a phase, so in that sense they are not on the main sequence. That is not to say that brown dwarfs do not undergo any core fusion processes. It's just that the fusion rate is not enough to balance the energy radiated from their surface, a situation which only occurs above about 0.08 solar masses.

If we just treat the HR diagram as a graph of temperature against luminosity, and if we extend it enough to the lower right, there will be a point that brown dwarfs may fall on at some point in their evolution. But they don't stay there. The Hayashi track of a brown dwarf takes it from above right of the main sequence (like "proper" stars) but when it reaches the main sequence it doesn't stop -- it falls right through. Compare that to the smallest stars above the brown dwarf limit ... they are the longest lived ones, with main sequence lifetimes in the hundreds of billions of years.

WACO

That's a good point, the brown dwarfs don't linger on the MS!

I'd have to disagree with what you say about fusion processes in brown dwarfs - they are, by definition, not stars but sub-stellar objects. Stars are, by definition, objects that undergo nuclear fusion in their cores. If a brown dwarf suddenly has nuclear fusion occurring, it is no longer a brown dwarf, but a star!

ps200306

I'll have to slightly disagree back.

Fusion rates are highly temperature dependent, so it would be nitpicking of me to say that hydrogen fusion occurs at some non-zero rate in brown dwarfs, which would be true even though the rate is negligible. However, when you look at the reaction rate of the second step of the proton-proton chain, at a temperature of one million degrees it goes a thousand trillion times faster than the first step. That second step is deuterium fusion, and it turns out that it goes at an appreciable rate even at 100k degrees. And the primordial material from which the protostar forms contains 0.01% deuterium.

So it turns out that the star has exhausted its first supply of fuel even before it arrives on the main sequence -- even though we tend to think of that happening with the increasingly exotic reactions that occur after the end of the main sequence lifetime. Deuterium burning delays the onset of hydrogen burning (by keeping the core convective, and the temperature below a million degrees) in the pre-main sequence stage. A brown dwarf is an object in which hydrogen burning never eventually takes over, but it can nevertheless "shine" (very redly, presumably) for tens of millions of years by deuterium fusion.

http://en.wikipedia.org/wiki/Deuterium_burning#In_substellar_objects

WACO

Well, you learn something new every day! I'll have to revise my definition of a star! How would you put it? "A star is an object that produces Helium-4 by nuclear fusion"?

Also, you're saying that Deuterium fusion (an exothermic reaction) raises the temperature gradient high enough for convection? Or, similarly, that the density gradient wrt pressure is not a steep as for an adiabatic change?

And all of this happens before it reaches the MS?

Sorry, I should really ask my professor all of this, maybe I can trick him!

ps200306

Well first of all -- ask your professor ... I'm a lowly student meself!

But yes, I suppose a star is something that produces helium from the lightest isotope of hydrogen for some fraction of its lifetime. As I understand it, the smaller a star is, the further down its convective envelope reaches -- for "real" stars, not just brown dwarfs. Below about a third of a solar mass the convection reaches all the way down to the core, which allows heat to escape more efficiently. I'm hazy on the details after that, because as I understand it, there still has to be some radiative layer within the core in order for it to be blanketed enough for the temperature to rise to the million degrees needed for the commencement of hydrogen burning. This doesn't happen in brown dwarfs.

My favourite statistic about the sun gives a good idea why it needs to be well insulated for the temperature to remain elevated. Apparently the rate of energy production per unit volume in the core is about the same as your average garden compost heap!

EDIT: I read that the lower mass limit for deuterium burning to commence is 0.013 solar masses. So your brown dwarf range is about 13 to 80 Jupiter masses.