text: 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 Schwarzschild black hole, the innermost stable circular orbit (ISCO) occurs at three times the event horizon, at .
  For a Keplerian disk, .