In astrophysics, 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 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, .
- p161, Astrophysical Flows, Pringle and King 2007
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