Properties of Spiral Galaxies 

Luminosity Profiles

 

As with the Milky Way, the surface brightness (flux per unit area) of spiral disks is described by an exponential law:


Or, if we convert this to magnitudes per square arcsecond:

Note that while the observed brightnesses and sizes of galaxies drop at larger distances, surface brightness does not change.


So we can measure the surface brightness of spiral galaxies and learn immediately the luminosity density -- the density of stars -- inside the galaxy without knowing the distance. Very useful!

To an observer, surface brightness in magnitudes per square arcsecond can be computed simply by mu = m + 2.5log(Area), where m is the magnitude, and area is measured in square arcseconds. Because of the fact that surface brightness measures an intrinsic property of the galaxy, the surface brightness can be converted into the physical density of stellar light in the galaxies, in units of solar luminosities per square kiloparsec. You'll do this in HW#3.....

Galaxies show a wide range in central surface brightnesses; there is no preferred central surface brightness. On the left is M101, a high surface brightness galaxy; on the right is Malin 1, a low surface brightness galaxy.
 

M101
Malin 1

 

Kinematics of Spirals

 
Spiral galaxies typically show flat rotation curves. Dark Matter!
 

The luminosity of a spiral galaxy correlates with its rotation velocity: the Tully-Fisher Relationship

or
or, in magnitudes

 
 
 
First, remember what determines the circular velocity:


so that


we don't know the mass of a galaxy, but we know its luminosity, so let's make up a quantity called the mass-to-light ratio:


now remember that surface brightness is luminosity over area:


or, solving for R:


OK. Now, mass is mass:


so equate our two mass expressions:


substitute in for R:


and solve for L:

Whew! So Tully-Fisher works if surface brightness time mass-to-light-ratio squared is constant. In other words, the stars and the dark matter are somehow linked.

Why would that be true?
We don't understand it, but it seems to work!
But this tells us something fundamental about how galaxies formed. Any model for galaxy formation must explain the Tully-Fisher relationship.

OK, so let's look at the Tully-Fisher relationship for nearby galaxies using different wavelengths:
 
B (Blue) Tully Fisher
R (Red) Tully Fisher
H (Infrared) Tully Fisher
  • slope: -8.0
  • alpha: 3.2
  • scatter: 0.25 mag
  • slope: -8.8
  • slope: 3.5
  • scatter: 0.25 mag
  • slope: -11.0
  • alpha: 4.4
  • scatter: 0.19 mag

Question: Why would the relationship change depending on what wavelength you look at?