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# 15.21 Mass to Light Ratios

The colors of galaxies provide useful information on the types of stars that dominate the light output. Stars that are young, blue, and rich in heavy elements are found in spiral disks. Stars that are old, red, and dominated by only hydrogen and helium are found in elliptical, the bulges of spirals, and the globular clusters that orbit the halos of many galaxies. All of this information can be seen in two nearby examples: the giant elliptical M 87 and the spiral M 83. M 87 shows a uniform halo population of old, red stars. On the periphery of this giant galaxy you can see a swarm of faint globular clusters. The nucleus of M 83 has the pale yellowish-orange color of giants. But the spiral arms are made out of bluish clusters of young stars, along with red-glowing regions of hot gas scattered like rubies in a jeweled brooch.

Hertzsprung-Russell diagram showing color and size of stars. Click here for original source URL

Messier 83, the Southern Pinwheel Galaxy. Click here for original source URL.

Each of the three types of galaxy identified by Hubble has a particular combination of stellar populations and a characteristic color. Irregular galaxies have predominantly young disk stars (even though they may not have a well-organized disk or spiral arms) and are correspondingly blue and gas-rich. Spiral galaxies contain both old and young populations, and they follow a sequence from type Sc to type Sa of increasing amounts of light in the older bulge population. Elliptical galaxies contain mostly old halo stars and are correspondingly red and gas-poor. Therefore, the colors of a galaxy offer some insight into its age and history.

One of the most difficult properties of a galaxy to measure is the mass. The same problem is encountered with stars. It is difficult to estimate the mass of a single star in space unless we have a lot of information about the evolutionary state of the star. With binary stars, we can apply the law of gravity to the orbits and learn about the masses. Similarly, when two galaxies are in a binary orbit, we can measure their masses. But what about the mass of a single, isolated galaxy? It turns out that knowledge of stellar populations leads to a useful estimate.

One useful way to characterize a galaxy is in terms of the ratio of its mass (in units of the mass of the Sun), to its luminosity (in units of the luminosity of the Sun). This quantity is called the mass-to-light ratio. Clearly, if a galaxy consisted entirely of stars like the Sun, it would have a mass-to-light ratio of 1. However, a galaxy is a composite of many millions of stars of differing ages and masses. The global mass-to-light ratio of a galaxy depends on the relative numbers of stars of different types. It turns out that the visible light from galaxies of all types has a mass-to-light ratio in the range 1 to 30. Irregular galaxies, which have the largest percentage of young stars, are at the bottom of that range. Spiral galaxies, with a relatively large percentage of young stars, are in the middle of the range. Elliptical galaxies, with a majority of old stars, tend to be at the top of the range.

Why do galaxies of all types have mass-to-light ratios larger than 1? You can see why if you review the material on H-R diagrams. A young main sequence stars that is more massive than the Sun is enormously more luminous than the Sun. In a calculation of stellar lifetimes, a star of mass 100 solar masses has M/L = 100/106 = 10-4. By contrast, a main sequence star less massive than the Sun has a feeble luminosity. For example, a star of mass 0.1 solar masses has M/L = 0.1/10-3 = 100. Since we also know that high-mass, main-sequence stars are relatively rare, we anticipate an overall mass-to-light ratio above 1. Giants and super giants are massive, but they are highly luminous, so they have low mass-to-light ratios like young main-sequence stars. White dwarfs have mass similar to the Sun but are low-luminosity stars, so they have large mass-to-light ratios.

The calculation of a mass-to-light ratio for an entire galaxy is complex, but the general result is easy to state. The mass to light ratio is dictated by lower main sequence stars and white dwarfs. As a stellar population ages and stars evolve off the main sequence, the mass-to-light ratio will evolve to higher values. Therefore, the sequence of increasing mean age going from irregular to spiral to elliptical galaxies is also a sequence of increasing mass-to-light ratios.

The calculation of a mass-to-light ratio refers only to the visible stellar populations in galaxies. All mass estimates must be reconsidered in light of one of the most profound discoveries in astronomy: the detection of large amounts of dark matter. Models of stellar populations yield an important way to infer the presence of dark matter. Old stellar populations have larger mass-to-light ratios, as massive stars leave the main sequence and many white dwarfs are created. No stellar population is older than about 13 billion years, the age of the oldest globular clusters. So the oldest galaxies define the maximum value of mass-to-light ratio of any group of stars. A mass-to-light ratio much above 30 is evidence for dark matter that cannot be in the form of any normal stellar population.