Statistical theory of thermal instability

A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function characterizes the statistical properties of the multiphase medium of arbitrary spaced three-dimensional structure of arbitrary temperature perturbations. We construct our theory under the isobarical condition (P=const over space), which is satisfied in the short wavelength limit. The developed theory is illustrated in the case of thermal instability of a slowly expanding interstellar cloud. Numerical solutions of equations of the statistical theory are constucted 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 initial spectrum of perturbations is discussed. The proposed theory and numerical models can be relevant to the formation of the two-phases medium in the ~1pc region around quasars. Then small warm (T~10000K) clouds are formed as the result of thermal instability in an expanded gas fragment, which is a product of either a star-star or star-accretion disk collision.