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Accretion disk "coin funnel"

You've probably rolled a penny into a coin funnel like this one, and watched it spiral down into the center like a spaceship falling into a black hole, or the Earth falling into the Sun. The applet above resembles one of those coin funnels---click a few times to drop a couple of coins in.

Wait a minute! The Earth isn't falling into the Sun! In reality, actually, spaceships wouldn't spiral towards black holes. That's not how gravity works; the force of gravity puts everything onto stable elliptical orbits, not inward spirals. The Earth orbits the Sun in an nearly-circular, nearly-perfect ellipse; a spaceship would orbit a black hole in a similar ellipse. If you throw a baseball, it will begin following an elliptical path---a very short one, though, because usually the ground will get in the way. In principle, a coin funnel would also allow coins to roll around forever on circular or elliptical orbits. Unfortunately, in those fountains, there's a little bit of friction that makes the coin slow down and spiral inwards. Since the Earth's orbit around the Sun is frictionless, it really does follow one of the perfect non-spirally ellipses that you'll never get in a coin funnel. The applet above shows frictionless orbits; notice that your coins go in circles rather than spirals.

Sometimes you'll hear astronomers talk about matter "spiraling in" to a black hole---a black hole tearing a star to pieces and sucking up the debris. What's going on here? These astronomers are talking about an accretion disk. When there are a lot of particles in orbit at the same time, the particles can rub against one another---that provides a form of friction. Just like in a coin funnel, friction in an accretion disk bumps particles off of their stable circular or elliptical orbits---and that makes it possible for them to migrate inwards. (It also makes it possible for them to migrate outwards!) This inward migration allows matter to fall into the black hole, and (just like a baseball's elliptical journey eventually hits the Earth's surface) such a particle may eventually reach the ISCO, or Innermost Stable Circular Orbit---thereafter, gravity's force is so strong that the elliptical equations no longer hold, and the particle finally spirals inwards.

In the applet above, particles follow perfect circular orbits---but they're allowed to crash into one another. When two particles "bump" (a blue flash will help you spot the event) they'll move apart---one will move closer to the center and one will move farther. Drop two coins in at nearly-identical radii and see if you can make them collide. This is basically what happens when gas clouds rub against one another, and that's what allows gas clouds to be "sucked up" by black holes. The star pours gas onto ordinary circular and elliptical orbits far from the black hole, particle-particle collisions help to move some of it inwards. Try dropping 20-30 particles in a narrow radius band and watch them migrate due to collisions. (About halfway between the center and the edge is a good place to try this. Can you get any to migrate right to the center? Great! You've just demonstrated accretion.

Built with Processing. Implementation notes: This applet would be a computational nightmare if it included realistic elliptical orbits and realistic collisions. The orbits are always circular, and the collisions are simple radial bumps of random magnitude. A quick heuristic rescues us from doing N^2 distance-comparisons per step for N particles, but the cost of this is that sometimes the applet will (incorrectly) ignore a real collision here and there, especially when there are many particles with very similar radii. The orbital periods are Keplerian.

(c) 2008 Benjamin Monreal. bmonreal () mit () edu is happy to hear your comments and provide source code.

Go back to his home page.