In 1962, V. A. Antonov did some remarkable simulations showing that even in Newtonian mechanics, gravitating systems can violate the usual rules of th

The Gravo-Thermal Catastrophe | Azimuth

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2024-09-21 06:00:03

In 1962, V. A. Antonov did some remarkable simulations showing that even in Newtonian mechanics, gravitating systems can violate the usual rules of thermodynamics. Instead of reaching equilibrium they can get hotter and hotter!

Suppose you put a lot of stars in a large sphere, and suppose (unrealistically) that they bounce elastically off the walls of this sphere. In fact suppose they’re point masses, so they never collide, and interact only gravitationally. Also suppose they’re ‘gravitationally bound’. This means their total energy, kinetic and potential, is negative. That means they couldn’t all shoot off to infinity even if the sphere wasn’t there holding them in.

If the sphere is small enough, the stars will seem to come into equilibrium, like a gas of roughly constant density. Antonov showed numerically that this happens if the radius R of the sphere obeys

In this case some stars will collect near the center and form a dense cluster. Eventually this cluster will start to collapse, and get very ‘hot’. That is: stars in the cluster start to move very fast. Some shoot out of the cluster at high speeds… but other stars fall into the cluster, replenishing it.