Total energy of two merging elliptical galaxies

[jl29488]

If I have two galaxies... i.e Ellipticals.. with same mass, size and velocity dispersion approaching each other and merging to form a bigger galaxy, what would be the total energy of the system?

I'm assuming they would be approaching each other from 'infinity', so E=0 initially. I'm guessing its something to do with the virial theorem?

I'm really stuck! :(

 

[phinds]

Define "energy of a galaxy"

 

[jl29488]

K.E=-1/2P.E (virial thoerem)

Thats providing the galaxy is in a stable, which I'm assuming...

 

[phinds]

K.E=-1/2P.E (virial thoerem)

Thats providing the galaxy is in a stable, which I'm assuming...

Define KE or PE, either one if you think you can, for a galaxy

 

[jl29488]

K.E = 1/2Mv^2 (v=velocity dispersion)

 

[phinds]

K.E = 1/2Mv^2 (v=velocity dispersion)

and what is the "velocity" of a galaxy? Hint: it has an infinite number of different velocities. Do you begin to see what the problem is?

 

[jl29488]

You can use average velocity i guess?

 

[phinds]

Hm ... I see now that there is more to this than I was aware and I might be misleading you. I think I should shut up and leave this for someone who is more familiar w/ the concept of galactic energy.

 

[rootone]

In broadest terms, the total energy of the merged system would be equal to the sum of the energy in the two separate systems.
(I am assuming that the common reference point you use to measure the 'energy' for all objects, is the center of the newly merged galaxy, since that seems most practical)
Internally within the galaxies, some individual objects would likely gain kinetic energy and in other cases lose it.
Energy might change it's form here and there but overall no energy is gained or lost.

(Well some bits of the galaxies might get slung out during the merging, so I guess some energy might be lost in that sense.)