In astrophysics

Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

, particularly the study of accretion disks, the epicyclic frequency is the frequency at which a radially displaced fluid parcel will oscillate. It can be referred to as a "Rayleigh

John Strutt, 3rd Baron Rayleigh

John William Strutt, 3rd Baron Rayleigh, OM was an English physicist who, with William Ramsay, discovered the element argon, an achievement for which he earned the Nobel Prize for Physics in 1904...

discriminant". When considering an astrophysical disc with differential rotation , the epicyclic frequency is given by

, where R is the radial co-ordinate.

This quantity can be used to examine the 'boundaries' of an accretion disc - when becomes negative then small perturbations to the (assumed circular) orbit of a fluid parcel will become unstable, and the disc will develop an 'edge' at that point. For example, around a Schwarzchild black hole, the Innermost Stable Circular Orbit (ISCO) occurs at 3x the event horizon - at .

For a Keplerian disk, .