1. Gravitational Lensing
ASTC22. Lectures L21
Gravitational Lensing
SMP on Lensing
(continued L20:)
Are these two empirical laws similar? The same?
Isothermal spheres
Isothermal distribution functions
Isothermal singular sphere
Isothermal non-singular sphere
Conclusions for the magnitude of dynamical friction in
dark halos: the reason for efficient mergers
Rotation and flattening of elliptical galaxies: only a weak
connection

2. Tully-Fisher relationship, a correlation between the luminosity
and rotation for disk
galaxies
Log Vc
-2.5 log L

3. Faber-Jackson relationship:
Luminosity ~ sigma^4
applies to ellipticals
Tully-Fisher relationship
Luminosity ~ (Vc)^3.85
applies to disk galaxies
but the two are almost identical:
both the disks and the ellipticals
are immersed in the same type
of dark halos which determines
the maximum Vc via potential
well depth.

6. (sorry, that’s
my teenage
daughter)

7. Good for modeling
flat-Vc galaxies
in dark halos

10. ...so this is one major reason why
mergers of galactic systems are
so rapid (a few to a few dozen periods)

11. One more empirical correlation: between rotation and flattening of ellipticals,
which can be understood based on stellar dynamics
Fastest rotation
according to theory
But remember: theory gives the upper envelope only. Most ellipticals are
NOT supported or flattened by rotation. They simply are not relaxed; flattening
comes from initial conditions, including geometry of encounter.