# Galaxies: Colors, Star Formation, Stellar Population, and Mass-to-Light Ratios

Along the Hubble sequence we find a trend of color with galaxy type. E and S0 galaxies have red colors, and the colors get progressively bluer for later galaxy types:

When we look at 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 can use stellar population synthesis modeling to study how the spectra and colors of a population of stars evolve with time, under different input star formation histories. For example, an evolving population of stars formed in a single burst of star formation looks like this:

One very simple parameterization of star formation history would be an exponentially declining star formation rate, with differing e-folding timescales: SFR(t) ~ e-(t/tau) where tau is left as a free parameter. (These are, not surprisingly, called "tau models"). Imagine galaxies with four different star formation histories (different taus) and watch how evolve differently in color:

So red galaxies have stars which, on average, are generally older, while bluer galaxies have younger stars.

(Thanks to Ken Duncan for his population synthesis software that helped make these plots!)

## Stellar Mass-to-Light Ratios

If we understand the properties of the stellar populations we are observing, we can use their total luminosity to infer the amount of mass in stars by invoking the stellar mass-to-light ratio, written (M/L)*.

This quantity has units of Msun/Lsun, so the Sun has a (M/L)* = 1 Msun / 1 Lsun = 1 Msun/Lsun.

An A-type main sequence star might have a luminosity of 12 Lsun and a mass of 2 Msun, so it would have a (M/L)* = 2 Msun / 12 Lsun = 0.17 Msun/Lsun.

A faint K-type main sequence star would have L = 0.3 Lsun and mass = 0.75, so (M/L)* = 0.75 Msun / 0.3 Lsun = 2.5 Msun/Lsun.

To get the (M/L)* for a population of stars, you sum up all their light to get the total luminosity, sum up all their mass to get the total mass, and then divide mass by light. Since we almost never see the individual stars in a galaxy (most galaxies are too far away to see individual stars), we usually have to infer the stellar population by modeling the integrated colors or spectrum of the galaxy. But then we can take the observed luminosity and the inferred (M/L)* to estimate the total mass in stars in a galaxy -- its "stellar mass" (which is very different from its total mass, which would include gas and dark matter as well).