Masses of Galaxies

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The masses of galaxies are found from the orbital motion of their stars. Stars in a more massive galaxy will orbit faster than those in a lower mass galaxy because the greater gravity force of the massive galaxy will cause larger accelerations of its stars. By measuring the star speeds, you find out how much gravity there is in the galaxy. Since gravity depends on mass and distance, knowing the size of the star orbits enables you to derive the galaxy's mass.

For spiral galaxies the rotation curve is used to measure their masses like is done to find the mass of the Milky Way. The rotation curve shows how orbital speeds in a galaxy depend on their distance from the galaxy's center. The mass inside a given distance from the center = (orbital speed)2 × (distance from the center)/G. The orbital speed is found from the doppler shifts of the 21-cm line radiation from the atomic hydrogen gas. The angular distance of the piece of the disk from the center is measured, but to use the enclosed mass formula, the piece of the disk's actual linear distance from the center must be found.

Remember way back in the planetary science chapter that the linear distance can be found from the angular distance if you know the distance to the object? The linear distance from the galaxy center = [(2pi× (distance to the galaxy) × (angular distance in degrees)] / 360°. This is why you must first know the distance to a galaxy if you want to measure its mass.

For elliptical galaxies the width of the absorption lines from all of the stars blended together is used to measure the mass of elliptical galaxies. The width of the absorption lines depends on the spread of the distribution of the velocities---the velocity disperion. The elliptical galaxy's mass = k × (velocity dispersion)2 × (the distance the stars are from the galaxy center)/G, where k is a factor that depends on the shape of the galaxy and the angle the galaxy is from Earth.

The stars and gas in almost all galaxies move much quicker than expected from the luminosity of the galaxies. In spiral galaxies, the rotation curve remains at about the same value at great distances from the center (it is said to be ``flat''). This means that the enclosed mass continues to increase even though the amount of visible, luminous matter falls off at large distances from the center. In elliptical galaxies, the gravity of the visible matter is not strong enough to accelerate the stars as much as they are. Something else must be adding to the gravity of the galaxies without shining.

That something else is called dark matter. It is material that does not produce detectable amounts of light but it does have a noticeable gravitational effect. Astronomers are not sure what the dark matter is made of. Possibilities range from large things like planets, brown dwarfs, white dwarfs, black holes to huge numbers of small things like neutrinos or other exotic particles that have not been seen in our laboratories yet. For reasons to be explained in the next section and in the cosmology chapter, astronomers have figured out that the dark matter is a combination of all those things but the exotic particles must make up the vast majority of the dark matter. In fact, of the total matter in the universe, the overall mass of the exotic particles is five times the overall mass of the "ordinary matter" we are more familiar with (matter made of protons, neutrons, electrons, neutrinos, etc.). The nature of dark matter is one of the central problems in astronomy today. Although its nature is unknown, dark matter appears to be such an integral part of galaxies that the presence of dark matter is used to distinguish a small galaxy from a large globular cluster, both of which may have the same number of stars.

The possible discovery in 2018 that the small ultra diffuse galaxy (one with a very small number of stars per volume) 65 million light years from us called NGC 1052-DF2 has little to no dark matter was quite surprising. Perhaps it is "the exception that proves the rule" but the search is on for other small galaxies without dark matter. However, it is also possible that the lack of dark matter conclusion for NGC 1052-DF2 is incorrect because the motions of only ten globular clusters in the small galaxy were used to measure its mass. More objects are needed to make a more certain measurement of the galaxy's mass, so it is possible that the mass measurement was too low and that there is actually a significant amount of dark matter. Another independent method of measuring the galaxy's mass supports the view that this galaxy has little to no dark matter. Furthermore, using seven globular clusters in another galaxy, NGC 1052-DF4, the research team who made the NGC 1052-DF2 discovery found that NGC 1052-DF4 also appears to have no dark matter. The discovery of two galaxies without dark matter shows that dark matter can be found separately from ordinary matter and that argues against the view that dark matter is actually just a misunderstanding of how gravity works for ordinary matter on large scales. Another possibility is that the distances to the two small galaxies have not been measured correctly. If the two galaxies are actually closer to us, then their derived mass to luminosity ratio will be larger and dark matter will need to be present. More observations are needed!

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last updated: May 29, 2019

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel