Jeans' gravitational instability and nonextensive kinetic theory

The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the unperturbed self-gravitating collisionless gas is kinetically described by the q-parameterized class of power law velocity distributions. It is found that the critical values of wavelength and mass depend explicitly on the nonextensive q-parameter. The standard Jeans wavelength derived for a Maxwellian distribution is recovered in the limiting case $q=1$. For power-law distributions with cutoff, the instability condition is weakened with the system becoming unstable even for wavelengths of the disturbance smaller than the standard Jeans length $\lambda_{\rm J}$.