University Lowbrow Astronomers

Gravity, Part 4: Globular Clusters & Galaxies.

by Dave Snyder
Printed in Reflections: October, 2006.

Before the telescope was invented, astronomers were limited to objects visible with the naked eye. Objects like stars, planets, comets and nebulae.

Nebulae (or the singular nebula) referred to fuzzy spots in the night sky—no one knew what they were.

One of these nebulae was Praesepe (also called the Beehive). In the early 1600’s Galileo looked at this object with a telescope. He saw it was a group or “star cluster” of 40 stars. Galileo was convinced that all nebulae would eventually turn out to be star clusters. He was only partially correct: as telescopes improved more nebulae were discovered; many nebulae were examined and eventually resolved into star clusters, but other nebulae never resolved into clusters.

Galileo did not anticipate everything. There are dozens of stars in the constellation Centaurus, none of which seemed unusual. At least not until the year 1677, when Edmond Halley looked at the star named Omega Centauri with a telescope—the image was too fuzzy to be a star. He concluded it was a nebula. The stars in the constellation Tucana also seemed ordinary. In the year 1751, Abbe Nicholas Louis de Lacaille looked at one of these stars (47 Tucanae)—it was too fuzzy to be a star as well.

A number of other astronomers, including Pierre Méchain, Barnabus Oriani and Charles Messier, found new nebulae and/or were able to resolve nebulae into clusters. However most clusters would remain undiscovered until the 1780s. That’s when William Herschel, his sister Caroline, son John and other family members started a systematic survey. They identified many star clusters (including some previously believed to be nebulae including Omega Centauri, 47 Tucanae and M13).

Globular Clusters

William Herschel divided star clusters into two subcategories, open clusters and globular clusters. Globular clusters have between 50,000 and a million stars; open clusters have less than 50,000 stars. (I won’t say anything more about open clusters).

We now know of approximately 150 globular clusters in our galaxy and have found globular clusters in other galaxies (including G1 in the andromeda galaxy).

The globular cluster generates a gravitational field. If a million stars reside inside of a gravitational field, those stars must move. These motions cannot be predicted by the simple methods I explained in part 2, but astronomers have found an alternative, models that provide a rough guide to the motions.

A typical model goes something like this: all stars in the cluster move in Kepler orbits around the center of mass. The Kepler orbits undergo precession because of the influence of the other stars (there is precession in our solar system, but is more pronounced in a globular cluster). This picture shows what the precession of a single star might look like:

Stars have energy. Some stars in the cluster have low energy; typically found close to the center, they move quickly. Others have high energy; typically found away from the center, they move slowly. (This might seem counter-intuitive, but that’s the way it works). If a star has enough energy, it will escape from the cluster and move with an independent orbit through the galaxy.

If we plot the number of stars versus the energy with a histogram, we find a Maxwell-Boltzman distribution (Maxwell-Boltzman distributions are commonly found in large collections of interacting objects). That’s a curve that looks like this:

So far this has been a qualitative description (a description without numbers). Suppose we want to know the average stellar velocity, the size of an average stellar orbit or the mass of the cluster. If so, we need something more. An astronomer can measure the radius of the cluster and the average stellar velocity and use something called the Virial equation to calculate the mass of the entire cluster (to be precise, the average radius and the average velocity dispersion are used). Once the mass is known, other calculations are possible (for example, it is possible to estimate the number of stars given the total mass).

While this model is a good start, it leaves unresolved issues. There isn’t space to explain them all, but I can briefly explain two.

First we would expect that stars within the cluster would from time to time interact gravitationally—in the simplest case two stars interact, one star loses energy and another gains energy. This happens often; orbits orbits change each time there is an interaction and there is typically an interaction every few orbits. Astronomers call these interactions “collisions” even though the stars never come into physical contact with each other. (Note, the term “physical collision” is used when the stars come into physical contact). The interactions are difficult to predict with any precision, the simple model offers no help.

There is another issue: If a star has a high enough energy (there always be a few high energy stars), it can escape from the cluster. A few of the stars remaining will have high energy, and some of them will escape. Repeat this over and over, eventually we would expect all the stars will escape. This is called “evaporation.” How long does this process take? This has proven to be a difficult problem. Astronomers have suspected that binary stars within the cluster hold significant amounts of energy and could affect the evaporation rate. Also stellar interactions also could affect the evaporation rate. Again the simple model can’t give us a precise answer.

To deal with these and other issues astronomers developed new models, but the details are beyond the scope of this article.

I’ll return to globular clusters in a moment.


Astronomers had not finished with nebulae. In 1845 William Parsons noticed that M51 (believed to be a nebula) had a spiral structure. Soon other nebulae were shown to have spiral structures. They became known as spiral nebulae.

But the true nature of spiral nebulae wasn’t determined until 1924. That year, Edwin Hubble found special stars called Cepheids in NGC 6822, M33 and M31. This work proved that spiral nebulae were massive collections of stars, similar to the collection of stars we live in (the Milky Way). These collections became known as galaxies (the term spiral nebula was soon dropped in favor of a new term “spiral galaxy”). Soon Hubble and other astronomers discovered additional galaxies. Not all galaxies are spiral; we now recognize four basic types of galaxies: spiral, lenticular, elliptical and irregular. (NGC 6822 is an irregular galaxy; M33 and M31 are spiral galaxies).

Stars in a galaxy move around the center of mass in Kepler orbits (not unlike the stars in a globular cluster). This is somewhat similar to a globular cluster; however stellar interactions are much less common and stellar motions in spiral galaxies have some interesting complications.

To analyze a galaxy, astronomers use an equation called the Jeans equation. Some sections of the galaxy have lots of stars (lots of mass per volume or high density); other sections have few stars (little mass per volume or low density). The Jeans equation allows you to calculate the expected velocity of stars in a region based on the density in that region (stars move fastest when the density is highest). And you can go the other direction: calculate the density based on the velocity of the stars.

Galaxies can be found in groups called galaxy clusters. The Jeans equation works for galaxies in a galaxy cluster just like it works for stars in a galaxy.

Fritz Zwicky was the first person to use this approach. In the 1930’s he created a catalog of galaxy clusters. He used the Jeans equation to compute the expected velocities of galaxies and compared the results to velocities computed from Doppler shift measurements. Despite what anyone may have thought, the actual velocities were higher than the expected velocities, a strange result that required an explanation.

Zwicky proposed a solution: Some substance, which was named “dark matter,” caused the density to be higher than was thought and in turn caused galaxies in a galaxy cluster to move faster than expected. When individual galaxies were examined the same problem showed up; dark matter was again suggested as a solution.

Computer Models

There were limits to what these methods could accomplish. Recently a new approach has shown promise.

With collections of stars (like globular clusters and galaxies), it is theoretically possible to calculate the effect of Newton’s laws on each object. Until a decade or so ago, this was impractical for objects as complex as globular clusters and galaxies (that’s why the previously mentioned approaches were used). Clever methods and fast computers developed starting in the mid-1990s made it possible to perform computer simulations on these objects. In the process we have been able to answer some questions about globular clusters and galaxies.

Do stars in a globular cluster ever physically collide? Astronomers used to believe physical collisions between stars were extremely rare and there probably has never been such a collision in our galaxy. However recent computer simulations suggest physical collisions happen more often than originally suspected. These collisions are most likely in crowded parts of the galaxy, such as globular clusters.

In the 1950’s astronomers had discovered some unusual stars, called blue stragglers, which no one could explain. Recently an explanation emerged: blue stragglers could have formed as result of a physical collision between two stars. The computer simulations suggest that in a typical globular cluster, 1 out of 100 stars will experience a physical collision over the lifetime of the cluster.

How long do globular clusters last? Observations suggest that some globular clusters are 12 billion years old, and computer simulations suggest an average lifetime of 10 billion years or so (this suggests some clusters have already evaporated, and others will last another 10 billion years or even longer).

Why do galaxies have the shape they do? There have been theories almost as long we’ve known about galaxies. Computer simulations have allowed astronomers to test these theories.


I was forced to gloss over many details, if you want to read more about the topics covered in this article, you might try:

------. 1996. Fundamental Astronomy, Third Revised and Enlarged Edition. Karttunen, H., Kröger P., Oja, H., Poutanen, M., Donner, K. J. editors. Springer: Berlin [the virial equations].

------. Examined August 2006. Web site: “75th Anniversary Astronomical Debate Home Page: Featuring historical background, lecture and ticket information.”[In April 1920, Harlow Shapley and Heber D. Curtis debated “The Scale of the Universe” in the main auditorium of Smithsonian’s Natural History Museum in Washington, DC].

------. Examined August 2006. Web site: “The Messier Catalog.” [History and other information about the brightest galaxies and globular clusters; mainly devoted to Messier objects, but includes some non-Messier objects as well].

Binney, James and Tremaine, Scott. 1987. Galactic Dynamics. Princeton University Press: Princeton, New Jersey [Jeans equations and virial equations].

Heggie, Douglas and Hut, Piet. 2003. The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics. Cambridge University Press: Cambridge, U. K [computers, globular clusters and galaxies].

Hurley, Jarrod R. and Shara, Michael M. 2002. “The Promiscuous Nature of Stars in Clusters.” The Astrophysical Journal, 570:184-189, (May 1).

Jones, Glyn, editor. 1980. Webb Society Deep-Sky Observer’s Handbook, Volume 3: Open and Globular Clusters. Hillside, New Jersey: Enslow Publishers, Inc.

------, editor. 1981. Webb Society Deep-Sky Observer’s Handbook, Volume 4: Galaxies. Hillside, New Jersey: Enslow Publishers, Inc.

Kaufmann, William J. and Freedman, Roger A. 1999. Universe, Fifth Edition. New York: W. H. Freeman and Company.

King, Ivan. 1985. “Globular Clusters.” Scientific American, (June).

O’Meara, Stephen James. 1998. Deep-Sky Companions: The Messier Objects. Cambridge, United Kingdom: The Press Syndicate of the University of Cambridge and Sky Publishing Corporation.

Sargent, W. L. W.; Kowal, C. T.; Hartwick, F. D. A.; van den Bergh, S. “Search for globular clusters in M31. I—The disk and the minor axis.” Astronomical Journal, Vol. 82, Dec. 1977, p. 947-953. [The discovery of G1, a globular cluster found in the Andromeda Galaxy].

Shara, Michael. 2004. “When Stars Collide.” in Scientific American Special Edition—The Secret Lives of Stars, Vol. 14, No. 4 (November 4).

Spitzer, Lymon, Jr. 1987. Dynamical Evolution of Globular Clusters. Princeton University Press: Princeton New Jersey.

Zepf, Stephen E. and Ashman, Keith M. 2003. “The Unexpected Youth of Globular Clusters.” Scientific American (October).


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