The Jeans instability in an unmagnetized, collisionless self-gravitating plasma characterized by a kappa or Lorentzian velocity distribution is investigated in the framework of kinetic and fluid approaches. We have examined the role of suprathermality on the instability threshold wave number and growth rates. The kinetic analysis, based on the linearized Boltzmann-Vlasov and Poisson equations, yields a $\kappa$-dependent dispersion relation and a modified critical Jeans wave number, which reduces to the classical results in the Maxwellian limit ($\kappa \to \infty$) showing their applicability in high-energy tails. Kinetic theory predicts enhanced growth rates and a wider unstable wave number range due to resonant wave-particle interactions in the suprathermal limit (lower $\kappa$ values). In contrast, the fluid description, which incorporates a $\kappa$-dependent equation of state, introduces a modified sound speed and predicts a stabilizing influence of suprathermal populations. Comparison of the two approaches shows that the enhanced growth rate of the kinetic Jeans instability due to suprathermality signifies the importance of kinetic effects in nonequilibrium astrophysical plasmas under specific conditions. The results are discussed in order to understand the role of suprathermality in the gravitational collapse of the warm-hot circumgalactic medium of the Milky Way.

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• Plasma instabilities