Statistical theory of thermal instability

A new statistical approach is presented to study the thermal instability of an optically thin unmagnetized plasma. In the framework of this approach the time evolution of the mass distribution function over temperature ϕ(T) is calculated. Function ϕ(T) characterizes the statistical properties of the multiphase medium of arbitrarily spaced three-dimensional structure of arbitrary (small or large) temperature perturbations. We construct our theory under the isobarical condition (P = constant over space), which is satisfied in the short-wavelength limit of the perturbations. The developed theory is illustrated for the case of the thermal instability of a slowly expanding interstellar cloud (smooth scenario). Numerical solutions of equations of the statistical theory are constructed and compared with hydrodynamical solutions. The results of both approaches are identical in the short-wavelength range when the isobarity condition is satisfied. Also the limits of applicability of the statistical theory are estimated. The possible evolution of the initial spectrum of perturbations is discussed. The proposed theory and numerical models can be relevant to the formation of the two-phase medium in the ∼ 1 pc region around quasars. Then small warm (T ≃ 104 K) clouds are formed as the result of thermal instability in an expanded gas fragment, which is a product of either star—star or star—accretion disc collision.