Thermal instability and the formation of clumpy gas clouds

The radiative cooling of optically thin gaseous regions and the formation of a two-phase medium and of cold gas clouds with a clumpy substructure is investigated. We demonstrate how clumpiness can emerge as a result of thermal instability. In optically thin clouds, the growth rate of small density perturbations is independent of their length scale as long as the perturbations can adjust to an isobaric state. However, the growth of a perturbation is limited by its transition from isobaric to isochoric cooling when the cooling timescale is reduced below the sound crossing timescale across its length scale. The temperature at which this transition occurs decreases with the length scale of the perturbation. Consequently, small-scale perturbations have the potential to reach higher amplitudes than large-scale perturbations. When the amplitude becomes nonlinear, advection overtakes the pressure gradient in promoting the compression, resulting in an accelerated growth of the disturbance. The critical temperature for transition depends on the initial amplitude. The fluctuations that can first reach nonlinearity before their isobaric to isochoric transition will determine the characteristic size and mass of the cold dense clumps that would emerge from the cooling of an initially nearly homogeneous region of gas. Thermal conduction is, in general, very efficient in erasing isobaric, small-scale fluctuations, thus suppressing a cooling instability. A weak, tangled magnetic field, however, can reduce the conductive heat flux enough for low-amplitude fluctuations to grow isobarically and become nonlinear if their length scales are of order 10(-2) pc. If the amplitude of the initial perturbations is a decreasing function of the wavelength, the size of the emerging clumps will decrease with increasing magnetic field strength. Finally, we demonstrate how a two-phase medium, with cold clumps being pressure confined in a diffuse hot residual background component, would be sustained if there is adequate heating to compensate the energy loss.