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

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

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.

(sorry, that’s my teenage daughter)

Good for modeling flat-Vc galaxies in dark halos

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

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.