# 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.

• Flux ~ r-2
• Size ~ r-1
• Surface Brightness = flux/area = r-2/(r-1)2 = constant

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

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

• Is there a physical basis for the Tully-Fisher relationship?
• What are these two quantities (L and Vcirc) tracing?

 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?

## Stellar Populations in Spiral Galaxies

How can we study what kinds of stars are in galaxies? We can only resolve individual stars in the very closest of galaxies (Andromeda and a few others). We generally study stellar populations of galaxies using integrated colors or spectra.

We find that disks of spiral galaxies are generally bluer in their outer regions -- this is called a color gradient. What does this tell us about the stellar populations in galaxies?

We also find the bulges of spirals are redder than the disks. What does this tell us?

We can measure the global star formation rate in disk galaxies by using:

• luminosity of HII regions
• far infrared luminosity
and we find that for normal spirals, the star formation rate is a few Msun/year. We can also study the amount of interstellar gas spirals have; it's usually about a few billion Msun. So how long can disk galaxies keep making stars?

The colors and gas contents of spirals show trends along the Hubble sequence: Sa galaxies are redder, and have a relatively low gas:star ratio. Sc galaxies are bluer, and have a high gas:star ratio.

Typically this is explained by different star formation histories: