  The well-known Jeans criterion describes the onset of instabilities in an
infinite, homogeneous, self-gravitating medium supported by pressure. Most
realistic astrophysical systems, however, are not isolated - instead they are
under the influence of an external field such as the tidal field due to a
neighbour. Here we do a linear perturbation analysis for a system in an
external field, and obtain a generalized dispersion relation that depends on
the wavenumber, the sound speed, and also the magnitude of the tidal field. A
typical, disruptive tidal field is shown to make the system more stable against
perturbations, and results in a higher effective Jeans wavelength. The minimum
mass that can become unstable is then higher (super-Jeans) than the usual Jeans
mass. Conversely, in a compressive tidal field, perturbations can grow even
when the mass is lower (sub-Jeans). This approach involving the inclusion of
tidal field opens up a new way of looking at instabilities in gravitating
systems. The treatment is general and the simple analytical form of the
modified Jeans criterion obtained makes it easily accessible.
