Kinematics of Ellipticals
|Remember how we characterize velocity of populations
In the disk of our galaxy, v=220 km/s, sigma=30 km/s, so
~ 7. This is called a cold disk.
rotation (v): the net
rotational velocity of a group of stars
dispersion (sigma): the
characteristic random velocity of stars
Elliptical galaxies have much higher velocity dispersions,
100s of km/s. These are kinematically hot
systems. v/sigma ranges (roughly) from 0 to 1.
Would you expect flattened ellipticals to have higher
or lower values of v/sigma? Why?
v/sigma actually correlates with luminosity.
Lower luminosity ellipticals have higher v/sigma -- rotationally
Higher luminosity ellipticals have lower v/sigma -- pressure
The Faber-Jackson law
Remember the Tully-Fisher law
for disk galaxies: L ~ v4.
Can we make a similar law for elliptical galaxies?
The Faber-Jackson law
has a lot of scatter: at a given velocity
dispersion, there is a range of +/- 2 magnitudes in luminosity. Compare
this to the Tully-Fisher relationship, where at a given circular velocity,
there is a range of a few tenths of a magnitude in luminosity.
Clearly, there is something messing with the relationship
-- a second parameter.
The Fundamental Plane
In 1987, two teams of astronomers identified the second parameter
-- the effective radius. Rather than two parameters correlating (in which
case you fit a line), there are three parameters correlating (in which
case you fit a plane).
We have 4 things we can measure:
There are only three independant
variables here (L, re, and <Ie> are
not all independant).
Effective radius (re)
Mean surface brightness (<Ie>)
Velocity dispersion (sigma)
If you plot one versus another, the third introduces scatter,
Surface brightness versus luminosity
Velocity dispersion versus effective radius
But if you plot one versus a combination of the other
two, you can see a very tight correlation:
This correlated plane is now referred to as the
fundamental plane. Since we have four observables, only three
of which are independant, there are different representations of the FP
which are all expressing the same thing. Here is another one:
Or in other words
Why would this be useful?
Doing some simple algebra, you can (and will!) show that
one implication of the fundamental plane is that mass-to-light ratio depends
on galaxy luminosity:
Why would luminous ellipticals have higher mass-to-light