Why doesn't a globular cluster collapse?

Why doesn’t a globular star cluster collapse into a single body due to the mutual gravitational effects of the individual stars?

Originally posted @ Medium!

Globular clusters are strange objects. They’re incredibly old collections of a huge number of stars — somewhere around a few hundred thousand on average, and they orbit around the very edges of galaxies, dotted spherically around. Our own Milky Way has a few hundred that we’ve found — Andromeda, the nearest other large galaxy we can check, has at least 60 some. (We’re likely to miss some around Andromeda, since they’re not the brightest things, and are quite small.) Even some of the Milky Way’s tiny nearby satellite galaxies have their own collection of globular clusters.

When I say that these clusters are incredibly old, we’re talking about as old as you can get. Some of the stars in a globular cluster are so old that they can help us to constrain the age of the universe. (If your globular cluster is nearly 13 billion years old, you can’t have a Universe younger than that.) We’re still not quite sure what conditions are needed for a globular cluster to form, or how they manage to survive for so long.


One thing you can take from their age is that they’re relatively stable. Which, as you have guessed, means that they can’t be in the process of collapsing down onto themselves, or we wouldn’t see so many of them looking so similar. So how do they manage to stay the same size over time?

At a very basic level, you might expect that if you suspended 100,000 stars in space, and let time roll forward, gravity would simply pull everything together. Some stars might get twirled around for a time, but gravity would ultimately crush everything into a mess at the very center of what used to be a globular cluster. And that’s exactly what would happen, if gravity were the only thing at play.


But the stars are moving. And when you have motion, you can defeat gravity for a time. Each star is in orbit around the center of the globular cluster, and the motion of the star in a sideways fashion, combined with the pull of gravity, creates an oval-shaped orbit, and the star can circle the center of the globular cluster reasonably happily for quite some time. Because the star has enough energy to keep moving forward, the tug of gravity won’t be able to haul the star to the center of the cluster.

This is a bit of a simplified picture, because every single other star of the 100,000+ in the cluster is doing the exact same thing, and the orbits of the stars are effectively random, which is why the cluster looks so spherical. If the orbits of the stars were less perfectly scrambled, you would see the cluster look a little more elongated, like a disk (like a spiral galaxy does, from the side), instead of looking pretty much round. Elliptical galaxies, for instance, also have done a pretty effective job of scrambling the orbits of the stars within them, so they look pretty round as well — but contain many millions more stars than a globular cluster. If the stars of an object are in this sort of randomized configuration (instead of rotating nice and orderly in a disk) we call it pressure supported (as opposed to rotation supported). In this context, it’s not that there’s actually any physical push outwards that makes them pressure supported, but the random motions of the stars as they each orbit their center of gravity acts as a resisting force to gravity. It’s not pressure, but it’s not ordered rotation, and it still resists gravity, so: pressure. (Astronomers are bad at naming things.)


Just because these systems are reasonably old and reasonably stable doesn’t mean they don’t change over time, and one thing that does occur with time is that the stars within the cluster will get close enough to each other to interact gravitationally. Not all the stars in the cluster are the same size, so the way they interact will depend on their mass. If the two stars are (for simplicity) roughly equal in mass, but one happens to be moving a bit faster, then the faster star will donate some of its energy to the slower star, giving them both a similar speed when they leave each other’s company, under most circumstances. (There’s no requirement for them to be going the same direction.) If, however, the stars are very different in mass, and they split their total energy, the less massive star will wind up going much faster. Kinetic energy is equal to the mass times the velocity squared — a large mass means a much smaller velocity for the same amount of energy, and vice versa.

This means that over time, the massive stars will tend to slow down, and the light stars will tend to speed up. If a star is slowing down, then gravity gets to take over, and does indeed pull that star down, closer to the core of the cluster. You wind up with some globular clusters collecting all their high mass stars in their very centers, with the lightest stars zooming around the outskirts, going much faster. This pattern of energy allows the cluster to sort itself from heaviest to lightest. (The technical term for this end result is called ‘mass segregation’.)


The other thing that can cause change in a globular cluster is if its orbit takes it too close to the massive galaxy it sits near. Each globular cluster is, as a whole, orbiting a fairly massive galaxy, particularly in comparison to the cluster. This orbit takes a very long time to complete, and it seems that many globular clusters can successfully orbit the galaxy without getting too near — but if the cluster does get too near, then the cluster will experience an intense tidal force because of the gravitational pull of the galaxy. This tidal force can shear off the outer layers of the cluster (if it’s a mass-segregated cluster, this means it looses the smallest stars). These outer layers get pulled away into a long stream of stars, barely detectable in the night sky even with a powerful telescope, and leaving an even denser nucleus of stars behind; at least four such globulars exist in the interior of our own Milky Way.

Although globular clusters don’t collapse, it’s conceivable that the most massive stars — which give rise to black holes — will segregate the fastest, giving rise to an intermediate mass black hole at the centers of globulars. On the other hand, it’s conceivable that black holes are ejected too frequently, as massive stars tend to give rise to far less massive black holes. While stellar-mass black holes have been observed inside a few globular clusters, there’s no consensus as to whether they can contain larger ones at their centers or not; that’s still an open question!

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