The accretion disk is a gas disk found around numerous types of object, ranging from newborn stars to massive black hole candidates at the centers of galaxies. As implied by their name, these disks transport gas to the object at their centers; depending on the system, the gas is pulled into the accretion disk from the interstellar medium or from another star. Accretion disks exist because gas falling onto a gravitating object inevitably has some angular momentum that forces it into orbit around the object. Once in the disk, gas slowly spirals to the disk's center, becoming hotter as its gravitational potential energy is converted into thermal energy. This energy is radiated away as infrared, visible, ultraviolet, and x-ray light. Accretion disks around white dwarfs, neutron stars, and black hole candidates that are in binary systems can radiate massive amounts of energy at the ultraviolet and x-ray frequencies; some of these binary systems are among the brightest x-ray sources in the sky.
The rotation of a disk is differential, with the inner portions completing an orbit faster than the outer portions. The basic idea behind the accretion disk is that viscosity in the gas disk converts the free energy of differential rotation into thermal energy, which is then radiated away. As the potential energy is released, the gas slowly spirals inward, completing many revolutions around the central object before significantly changing its distance from the central source. The amount of gravitational potential energy release by the gas in the disk increases as the gas draws closer to the central object. This means that most of the energy released by an accretion disk comes from the disk's inner edge. In its spiral to the inner edge of the disk, the gas liberates half of its gravitational potential energy as radiation; the remaining half is the kinetic energy of a circular orbit around the central source. This remaining energy can be released if the gas falls onto the central object, and that object is a star; if the object is a black hole, then the energy will be lost into the black hole.
This conversion of potential energy into radiation conserves angular momentum, so as the gas spirals inward, angular momentum must be transported outward. The fate of the angular momentum depends on the details of the disk physics. One outcome is that magnetic fields generated within the disk dump the angular momentum into a wind blowing away from the disk. A second outcome is that the angular momentum is dumped into the outer edges of the accretion disk, forcing the outer portions of the disk to expand in radius.
While some basic characteristics can be derived for Keplerian accretion disks from Newtonain mechanics, a complete understanding of disks requires study with sophisticated computer codes. The physics of creating and transporting light through a disk is similar to that encountered in stars, so this part of the problem is well understood. The big problem encountered by theorists is understanding the source of the viscosity in the accretion disk. It is the viscosity that converts the energy associated with the differential rotation of the disk into thermal energy, and it is the viscosity that transports the angular momentum to the outer portions of the accretion disk. For many decades, theorists had no firm explanation for the viscosity in accretion disks. Current studies suggest that turbulence and the generation of magnetic fields produces the required viscosity; the nature of accretion disk viscosity is an ongoing topic of research.