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Astrophysical Disks

An Overview

As I have written elsewhere in these pages, observers like to joke that theorists approach all problems by assuming an object is a sphere. In the observer's mind, a theorist would dot a farm with round buildings and populate its fields with round cows. But theorists have a much more expansive view of the world than this; while the cows, farm house, and barn might be round (to first approximation), our farm would also have columns and disks—silos and fields. The point is that there are several simple shapes that, to first approximation, give a reasonable description to the structure of most astronomical objects. These shapes arise from several simple physical principles.

The spherical structure that is so common in the universe occurs when the dominant force countering gravity in a system is the random motion of the objects in the system. In a gas, this random motion of the atoms provides pressure that counteracts gravity; in a stellar system, the random motion of the stars counteract their mutual gravitational attraction. The result is a universe filled with spherical objects: planets, stars, globular star cluster, elliptical galaxies, and rich galaxy clusters.

But random motion is not the only process that can counter gravity. In a system with sufficiently-high angular momentum, gravity is counteracted predominately by centrifugal force. These systems are disks, and like spheres, they appear on all scales in astronomy. On the smallest level, disks appear around planets and around compact stars such as neutron stars. They are found around black hole candidates (objects that should be black holes if general relativity is the correct theory of gravity). They are seen as the disks of spiral galaxies. The Kuiper belt is the remnant of the disk that rotated around the Sun, the disk that gave rise to the planets of our Solar System.

The basic structure of a disk is the same in all of these systems. A disk rotates around a central object. Usually the central object provides all of the gravitational force on the disk, but in some cases there are additional sources of gravity, such as the self-gravity of the disk itself. The orbit of the material in the disk is close to circular.

The rotation of a disk is generally differential, so that the rotation velocity and the rotation period change with distance from the center. If all of the gravitational force is provided by the central object, the disk is a Keplerian disk, and the rotation period depends on radius according to the Keplerian laws of orbital motion: P ∝ R3/2, where P is the orbital period and R is the distance from the center of the disk. Keplerian disks are the most common disks that are encountered. The disk of Saturn, the ancient disk that surrounded the Sun, the accretion disks around neutron stars in binary systems are all examples of Keplerian accretion disks. Disks that are not Keplerian are the disks in spiral galaxies, which are embedded in an invisible halo of gravitating material, and the massives self-gravitating disks that are found around some black hole candidates at the cores of galaxies.

While centrifugal force is the dominant force that balances gravity within an accretion disk, the random motion of the particles in the disk provide a second force that balances gravity. The random motion balances the gravitational tidal force perpendicular to the plane of the disk. This balance determines the thickness of the disk. For disks such as the ring around Saturn, the random motion is very small, and the rings are very thin. In gas disks around black-hole candidates, the temperatures are high, and the disks are relatively thick. Which regime a disk is in depends on the efficiency of converting the energy associated with differential rotation into random motion versus the efficiency of converting the energy of random motion into electromagnetic radiation. In other words, the temperature of the disk depends on the efficiency of heating the disk versus the efficiency of cooling the disk. For gas disks, this temperature is the temperature of the gas, but in a disks of objects, such as the disk of ice blocks around Saturn, the temperature is the average kinetic energy of the ice blocks' random motion, and not the temperature of the ice itself. A gas disk loses energy by the direct creation of infrared, optical, ultraviolet, and x-ray light. A disk of objects, such as ice chunks, loses energy through inelastic collisions, which convert the random kinetic energy into thermal energy, which is radiated away.

The energy lost by the disk usually does not extract angular momentum from the disk; instead, the energy loss causes the disk to transports angular momentum outward. Angular momentum from the inner portions of a disk is carried outward to the outer portions, causing the inner edge of the disk to move inward towards the central source, and the outer edge to move outward. The energy loss within a disk therefore causes it to spread out.

The flow of energy from differential rotation into random motion and then into electromagnetic radiation drives the broad range of phenomena seen in disks. For the rings of Saturn, the flow of energy creates its complex ringlet structure. For the plane of a spiral galaxy, the flow of energy drives the spiral waves. For gas disks around neutron stars and black-hole candidates, the flow of energy produces a bright source of x-rays. For gas disks around the massive black-hole candidates at the centers of active galaxies, the flow of energy drives jets of gas moving at nearly the speed of light and extending hundreds of parsecs way from their source. The energy flow through astrophysical jets therefore drives some of the most interesting phenomena in astrophysics.

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