What happens to the gravitational energy of a cooling brown dwarf galaxy?

[wolram]

Brown dwarf galaxies are, i think the coldest systems in the universe, If they continue to loose heat energy they must loose gravitational energy as well, eventually these galaxies will be ripped apart by the tidal effects of more massive galaxies.
So if this is correct what happened to the gravitational energy that held the system together?

 

[PeterDonis]

Brown dwarf galaxies are, i think the coldest systems in the universe, If they continue to loose heat energy

If they really are "the coldest", then they won't be losing heat energy; they will be gaining it (because something that's colder than anything else in the universe can only get warmer, not colder, as it interacts with other things).

That said, I don't think these objects (do you have a reference for "brown dwarf galaxies"? not sure what they are supposed to be, I know what "brown dwarfs" are as single objects but I'm not aware of whole galaxies composed of them) are colder than the CMBR, which is at 2.7 degrees above absolute zero. So they would, in fact, continue to radiate heat energy, because they aren't really the "coldest" things in the universe.

they must loose gravitational energy as well

The dwarf will "lose energy" in one sense, yes; but not in another sense. Suppose there is a brown dwarf all alone in empty space, far from all other objects. You are somewhere far enough away from it that its gravity doesn't affect your motion, but you can watch it slowly radiate heat energy.

As the radiated energy passes you on its way outward, the mass that you measure for the brown dwarf will decrease, yes; in that sense it does "lose energy". However, as this happens, the brown dwarf becomes *more* tightly bound, gravitationally--i.e., it becomes *harder* to tear it apart (in the sense that it would take more energy to do so). So in that sense, it is not "losing gravitational energy"--its binding energy (the energy it would take to disassemble it) is increasing, not decreasing.

what happened to the gravitational energy that held the system together?

As the above shows, the "gravitational energy" you are referring to is *negative*. The system gets more tightly bound as it loses energy. In order for the system to be torn apart, sufficient energy has to be *added* to it; as the system loses heat energy and becomes more tightly bound, the amount of energy it takes to do this *increases*. So the accounting always balances.

 

[Matterwave]

As an astrophysicist, I must say, I have never heard the term "brown dwarf galaxies"...only brown dwarfs...o.o

 

[Chalnoth]

Brown dwarf galaxies are, i think the coldest systems in the universe, If they continue to loose heat energy they must loose gravitational energy as well, eventually these galaxies will be ripped apart by the tidal effects of more massive galaxies.
So if this is correct what happened to the gravitational energy that held the system together?

As gravitational systems lose heat, they collapse inward.

 

[Chronos]

I am curious, why would you think a brown dwarf loses gravitational potential by cooling? How would that differ from white dwarfs that ultimately cool to become black dwarfs - and in a time frame which is probably shorter than that of a brown dwarf temperature dropping below the CMB. I agree with Matterwave, the notion of a brown dwarf galaxy is not a term with which I am familiar. No offense, but, it appears you are connecting dots that lack definition.