Like the Milky Way, external spiral galaxies are supported against collapse by their rotation. By using the Doppler shifts in spectral lines to measure galaxies' line-of-sight velocity as a function of position, we can measure their rotation curves (speed of material following circular orbits around the centre of the galaxy as a function of radius). We can derive this quantity from: 21cm emission from atomic hydrogen Optical emission lines from hotter gas Optical absorption lines from the stellar component

Although the enclosed mass, M(r), continues to grow apparently without limit, the enclosed luminosity, L(r), tends to a finite limit as we reach the edge of the luminous material in the galaxy. There must therefore be significant amounts of dark matter which continue to contribute to M(r) out to very large radii. Out to the furthest point measured, typical galaxies have a luminosity of L ~ 10^10 solar luminosities, and a typical enclosed mass of M ~ 10^11 solar masses. The "mass-to-light ratio" M/L is hence ~ 10 solar units. ~ 90% of the material in the galaxy is dark!

Spiral Arms:

Spiral arms come in different "flavors": ~10% grand-design (two well-defined spiral arms) ~60% multiple-arm ~30% flocculent spirals (no well-defined arms at all) Spiral arms seem to be trailing arms, but this is very hard to determine. In some rare cases, spiral arms may lead.

Elliptical Kinematics:

velocity of stellar populations are characterized by: rotation (v): the net rotational velocity of a group of stars velocity dispersion (sigma): the characteristic random velocity of stars In the disk of our galaxy, v=220 km/s, sigma=30 km/s, so v/sigma ~ 7. This is called a cold disk. 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 supported Higher luminosity ellipticals have lower v/sigma -- pressure supported

Fundamental Plane:

Four observables for ellipticals luminosity effective radius mean surface brightness (luminosity density) velocity dispersion Faber-Jackson law shows there is a correlation between velocity dispersion and luminosity (as well as radius and surface brightness) lots of scatter implies another parameter

of the four observables, only three independent variables plotting linear combination of parameters reveals very tight, linear correlation = fundamental plane. in other words, and this implies