July/August 1999 Table of Contents
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.
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.
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
Woes of Core Collapse
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.
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
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?
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.
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.
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.
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.
ones here, little ones over there"
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.
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.
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.
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
to the Rescue
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
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.
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
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
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.
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.
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.
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...
ejected from the system, leaving the binary unaltered;
exchanged with one of the binary members; or
with one of the binary members.
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.
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.
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.
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
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.
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
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 email@example.com.
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
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.
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.