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Mercury, July/August 1999 Table of Contents

In the cramped volume of a globular cluster, astrophysical experiments are underway - cluster dynamics, interactions among stars, pulsar recycling - and astronomers are discovering what we thought might be true is indeed satisfyingly correct.

Brian W. Murphy
Butler University

Imagine yourself on a world where the sky is always ablaze with the sight of a thousand stars as bright as the full Moon. Such would be the view in the crowded confines at the heart of a globular star cluster.

Our own galaxy, the Milky Way, houses about 150 globular clusters, which reside in the halo and are concentrated toward the Galaxy's center. These stellar systems are roughly spherical, average one hundred lightyears in diameter, and contain from ten thousand to ten million stars. Their stars are less abundant than the Sun in elements heavier than hydrogen and helium, indicating that they are among the oldest stars in our galaxy. The crowded conditions in these clusters make them ideal laboratories for testing theories about the dynamical evolution of star clusters. These same cramped conditions also make globular clusters factories that crank out an array of exotic stellar objects.

The Woes of Core Collapse

Stars within each cluster move in a variety of orbits, ranging from a circular orbit to a radial orbit that plunges from a cluster's halo into its core and back out again. Over time these orbits will slowly change as stars gravitationally interact with each other, gradually transferring energy from the core of the globular cluster to its halo. This energy transfer forces stars in the core of the cluster to migrate further toward the center, causing the core to contract while the halo of the cluster expands. And in turn, this contraction accelerates the transfer of energy, causing the center of the cluster to collapse and become up to ten billion times more densely populated with stars than our solar neighborhood in the Milky Way Galaxy. This process, known as "core collapse," occurs rapidly. At deepest collapse, the stars in the cluster's core are on average only as far apart as the Sun and Pluto, and many interesting things can happen as a result.

Observations indicate that roughly 20% of all globular clusters in our galaxy have undergone core collapse. The tell-tale signature of this collapse is when a cluster's surface brightness - a measure of the number of magnitudes of brightness per square arcsecond - rises continually from the cluster's outskirts all the way to its very center. In "normal," uncollapsed clusters, the surface brightness increases until about 3 to 5 lightyears from the center and then remains constant. In other words, the higher density of stars in collapsed-core globular clusters means they will have much brighter centers than normal clusters.

The globular cluster M15, located in the constellation Pegasus. This cluster is the prototypical core-collapsed cluster: The core is so dense stars can have very close interactions with one another. To date, M15 has been found to have one low-mass x-ray binary and seven millisecond pulsars. Image courtesy of the National Geographic Society, Caltech, AURA/STScI, and NASA.

Massive Black Holes?

It was once thought that core collapse could lead to the formation of a massive black hole. The general hypothesis was that the density of stars in the core could become so great that stars would begin to coalesce and form a massive superstar, which would then collapse into a black hole several thousand times the mass of the Sun. Such a black hole would occasionally accrete mass from stars passing too close to it: As the accreting mass spiraled inward toward the black hole, it would be compressed and heated to extreme temperatures of over a million Kelvins. And we know that matter so compressed and heated will radiate primarily x-rays.

Evidence for this hypothesis was first provided by x-ray satellites in the 1970s. The observations showed bright x-ray sources at the centers of several globular clusters. Later, more accurate observations showed that these x-ray sources were too far from the centers of the clusters to be supermassive objects. They are now known to be low-mass x-ray binaries: In a close binary system in which one star is a neutron star, the companion star can transfer mass to the neutron star when the companion begins to evolve off of the main sequence. During the mass-transfer stage it is highly likely that the system will appear as an x-ray source. The mass falling onto the neutron star hits the degenerate remnant's surface at nearly 1/3 the speed of light, causing it to give off copius amounts of x-rays. This phase may last anywhere from ten million to a billion years. Evidently the successive coalescing of stars in a collapsed core takes place slowly enough that the build-up of a massive object cannot occur. Twelve globular clusters in our galaxy are known to have at least one a low-mass x-ray binary.

With galactic nuclei, the high-mass cousins of globular clusters, the outcome is quite different. Here stars merge together at a much faster rate due to higher velocities and densities of stars, and, thus, a massive object can form and become a black hole. Once formed, this "seed black hole" will continue to grow as it swallows stars and other matter that stray too close to it.

These supermassive black holes are thought to be the engines and the accreting matter the fuel that drive the large luminosities of quasars and active galactic nuclei. After several billion years, the fueling of these engines slows and they become quiescent supermassive black holes in the galaxies' hearts. Further, we now believe supermassive black holes occupy the centers of many galaxies, including the Milky Way. The mass of these black holes ranges from a few million solar masses in our own galaxy to a few billion solar masses for the giant elliptical galaxy M87. Isn't it interesting that to fully understand the dynamics and evolution of these bright beacons of the Universe, we must study the much nearer, smaller globular clusters.

"Big ones here, little ones over there"

One interesting aspect of the dynamical evolution of globular clusters is that the most massive stars will segregate to the center of cluster well before core collapse occurs. Globular clusters are extremely old - 12 to 16 billion years old - so the most massive "stars" left in clusters today are likely to be compact objects such as neutron stars of about 1.4 solar masses (at or just above the Chandrasekhar mass limit for white dwarfs) and somewhat lower-mass white dwarfs. Main-sequence stars more massive than 80 percent of the Sun's mass will have already died. Even though a cluster may have only 1 to 2 percent of its mass in neutron stars, most of them will rapidly segregate to the inner regions of the cluster.

During core collapse this segregation is extreme, with neutron stars and white dwarfs outnumbering main-sequence and red giant stars by a ratio of 100 to 1 in the core. For every star we can see in the core of a globular cluster, you can count on there being 100 white dwarfs or neutron stars that we can't see. This concentration of compact objects in such a small space leads to some curious phenomena.

Although we can't see the neutron stars and white dwarfs, the velocity of visible stars near the cluster center tells us they are there. Luminous red giants, for instance, comprise only a small fraction of the total mass of a cluster, but they are quite useful in helping us decipher a cluster's dynamics: The higher the velocities of the luminous stars, the greater the mass in the cluster core. We can estimate the total mass of the cluster from the stellar velocities (or, more correctly, from the cluster's velocity dispersion), and we can then estimate the numbers of neutron stars and white dwarfs that must be present.

While the cores of globular clusters may be hotbeds of activity, at the outer edges of the clusters' halos, the Milky Way's tidal forces are busily stripping away hapless low-mass stars. As more and more stars fall victim to the Milky Way, the globular cluster itself may be completely destroyed. Also, as clusters move on their orbits through the Galaxy, they'll occasionally pass through the disk of the Milky Way. These disk passages cause what are called tidal shocks and can enhance the loss of stars from the cluster. Given the number of mechanisms that strip stars from clusters, it's probable that the current globular cluster population is only a small fraction of what it once was.

Cartoon courtesy of and ©1999 by B. Nath

Binaries to the Rescue

Before the density of stars in the core of a globular cluster can reach infinity, core collapse will be reversed, primarily by the formation of binary stars in the core. Binary stars can be formed in two ways, each of which requires the dense stellar environment found in collapsed-core clusters.

Tidal-capture binaries
In one scenario, two stars pass within three stellar radii of each other. Tides raised on each star cause both stars to slow down and be captured in orbit around each other. This process of binary formation is known as tidal capture.

Three-body binaries
In the other scenario, three single stars pass very near one another. The outcome is that two stars become a binary and the third star is saddled with the excess energy. Because this process uses three stars, the binary formed is called a three-body binary. Typically the two stars of a three-body binary are loosely bound, and most will eventually be disrupted by the close passage of another star. Calculations show that one in ten thousand of these binaries will survive, however, and then drive the post-collapse evolution of the cluster.

Once formed, binary stars can reverse core collapse by transferring energy to passing single stars: When a single star passes close to a binary, the binary's orbit will shrink, causing a loss of gravitational potential energy. The single star benefits from this loss and gains kinetic energy. This three-body interaction causes both the binary and the single star to speed away from their mutual center of mass, and this increase in orbital speed within the cluster causes stars to move out of the core, lowering its density and reversing core collapse.

The central density of a globular cluster versus time. Note the rapid rise in the central density with the onset of core collapse. Once started, the process of collapse accelerates rapidly, causing the density of stars in the core to become up to ten billion times that of our solar neighborhood. During collapse binary stars form that reverse the collapse and cause the core to undergo a series of oscillations. Plot courtesy of author.

A collapsed-core globular cluster has surface brightness that rises all the way to the center of the cluster. This plot shows how the surface density of red giants and neutron stars increases into the cluster center. Because of mass segregation the number of neutron stars at the center of a collapsed-core cluster far exceeds that of the giants and main sequence stars. Because of this mass segregation, most low-mass x-ray binaries and millisecond pulsars tend to be found near a cluster's center. Plot courtesy of author.

What if binary stars were present when the cluster first formed? In our neighborhood of the Milky Way, the majority of stars are binary systems, so we should expect to find primordial binary stars in globular clusters. Observations indicate that 10 to 20 percent of stars in globular clusters are binaries. If binary stars are already present, enough energy can be extracted from them to temporarily stave off core collapse. Such a cluster is likely to be in a quasi-equilibrium phase, in which it is using its binary stars but not undergoing full-blown core collapse. Even in this case the density of stars in the cluster core will be much higher than in an uncollapsed cluster. Eventually any primordial binaries in the cluster core will be used up and the core will fall into deep collapse. Then the scenarios we discussed earlier, in which new binaries form and reverse core collapse, come into play.

Interactions Among Stars

The crowded conditions in globular clusters' cores make it much more likely that stars will physically interact with each other in a variety of ways. It is possible that two stars may collide and form a star with a mass equal to the sum of the masses of its parents. Because these stars are generally more massive than typical stars in the cluster, they will be hotter and bluer, and therefore appear to be younger. These objects have been dubbed blue stragglers - they seem to be lagging behind the evolutionary sequence of other main-sequence stars. Hundreds of blue stragglers have been observed near the center of several globular clusters using the Hubble Space Telescope, confirming that stars do collide in clusters. Their distribution within clusters tends to be more centrally concentrated than that of the red giants; this indicates that the blue stragglers not only formed near the cluster center, but also that their higher masses cause them to segregate to the center.

I mentioned earlier how single stars may pass close to a binary star and be shot out with a higher velocity. Often, however, the stellar interloper may be temporarily captured by the binary, creating a triple star. Models of such interactions indicate that the three stars usually undergo a series of contorted orbits resembling a bowl of spaghetti. In these types of interactions a few things can happen. The single star can...

• be ejected from the system, leaving the binary unaltered;
• be exchanged with one of the binary members; or
• collide with one of the binary members.

If a collision occurs, a blue straggler is the likely product. If an exchange occurs, a neutron star may be brought into the binary system and another type of object can be created.

Gargantuan Recycling

When a massive star ends its life in a supernova explosion a pulsar is born. Pulsars are rapidly rotating neutron stars that beam their radiation much like a lighthouse; after a typical lifetime of 50 thousand years, they slow down due to magnetic braking and eventually stop being pulsars. Neutron stars are the corpses of massive stars, and given the ages of globular clusters, those in globular clusters must be at least 10 billion years old. Because pulsars are so relatively short-lived, astronomers didn't expect to find any in globular clusters. In the late 1980s, however, radio astronomers were very surprised to discover pulsars in a number of globular clusters. Though the majority are single objects, a number of these globular cluster pulsars were found to be members of binary star systems, a fact that hinted at their origins.

Imagine again the spectacle of a low-mass x-ray binary - a main-sequence star locked in an intimate embrace with a slowly rotating neutron star. As its main-sequence companion transfers mass onto it, the neutron star also receives the material's angular momentum. This transfer of angular momentum will spin up the neutron star, turning it into a pulsar. And additional angular momentum only makes it spin faster. When the pulsar's rotation period is much less than a second, it earns the title "millisecond pulsar" - in fact, at this point the neutron star is spinning about as fast as it can without breaking up. Dozens of these recycled pulsars have been discovered in the last decade. They provide evidence that the cores of globular clusters do indeed contain binary stars and that stars do indeed interact with one another.

Because pulsars and, therefore, neutron stars, are much more massive than typical globular cluster stars, we would expect them to reside mainly in cluster cores. This is exactly what observations show. In the collapsed-core globular cluster M15, the low-mass x-ray binary AC211 is found very near the cluster center, as are seven millisecond pulsars. Curiously, an eighth pulsar lies quite far from the center. This can be explained as a binary system that was ejected from the core when it had a violent three-body encounter with another star. Because the distance between the two binary companions decreases with each such encounter, the three-body interaction gets more and more energetic with each encounter. Conservation of momentum dictates that both the single star and the binary will be kicked out of the core into the cluster halo due to the gain in kinetic energy. Eventually the binary will sink back into the core, but the next interaction will likely be so energetic that the binary will be ejected from the cluster.

Stellar dynamics within a globular cluster can be quite complex, especially if a cluster has an appreciable population of binary stars. Because of mass segregation, primordial binaries quickly settle in the core, dominating its stellar makeup. In addition to three-body interactions, it's possible to have four-body (i.e., in binary-binary interactions), five-body, or even six-body interactions.

Though globular star clusters are billions of years old, they remain active into their old age. Given all the possible interactions and the even more complex products that are produced, computer modeling of both the cluster evolution and the stellar interactions within the cluster is a must to properly understand globular clusters. Better cluster models, combined with observations from the Hubble Space Telescope, have given us our best views yet of the evolution and inner life of these ancient outposts at the frontier of the Galaxy.

BRIAN W. MURPHY is an associate professor of physics and astronomy at Butler University in Indianapolis, Indiana. When he's not located in front of his computer, he can usually be found out on the road preparing for his next bicycle race. His email address is murphy@butler.edu.

 In the last decade several advances on the theoretical and observational fronts have greatly improved our knowledge of globular clusters. First and foremost was the launch and deployment of the Hubble Space Telescope in 1990. The HST improved our view of the centers of globular cluster cores enormously, as the crowding of stars and the overpowering brightness of red giants there limit ground-based views of fainter stars. Without the blurring effects of the Earth's atmosphere the HST is able to get clear views of cluster cores. Further, it is even possible to see faint white dwarfs in nearby globular clusters with the HST, an important observation for understanding stellar evolution.

Another advantage of being above the atmosphere is that clusters can be studied in a variety of wavelengths that would otherwise be blocked. Ultraviolet light is useful because the red giants appear fainter, and blue straggler stars can more easily be seen because of their color, while x-rays are useful for finding low-mass x-ray binaries and cataclysmic variables.

A ground-based view (top) and Hubble Space Telescope view (bottom) of the globular cluster 47 Tucanae. The effects of atmospheric blurring in the image from the ground are obvious. The lack of blurring in the HST images allows astronomers to examine fainter populations of stars (e.g., blue stragglers) in the cluster. Images courtesy of R. Saffer (Villanova University) and D. Zurek (STScI), and NASA.

Observations are clearly important to our studies of globular clusters, yet detailed modeling of stellar interactions and the dynamical evolution of clusters is critical to our proper understanding. Astronomers can't physically go to a lab and throw a single star at a binary star, nor can we throw two stars at each other and see if a blue straggler results. All experiments must be done on computers using the laws of motion and gravity. With the advances in computer speed and more efficient computer algorithms, it is now possible to recreate the collisions of stars, interactions of binary stars, mass transfer in binaries, and core collapse itself, all in one model. Of course these models are quite complex and take years to develop and refine. But now we are finally seeing the fruits of our efforts.