The nonlinear development of the thermal instability in the atomic interstellar medium and its interaction with random fluctuations

We discuss the nonlinear development of the isobaric mode of thermal instability (TI) in the context of the atomic interstellar medium (ISM), in both isolation and in the presence of either density or velocity fluctuations, in order to assess the ability of TI to establish a well-segregated multiphase structure in the turbulent ISM. The key parameter is the ratio of the cooling time to the dynamical crossing time eta. First, we discuss the degree to which the condensation process of large-scale perturbations generates large velocities and the times required for them to subside. Using high-resolution simulations in one dimension and fits to recently published cooling rates, we find that density perturbations of sizes greater than or similar to15 pc in media with mean density similar to1 cm(-3) develop inflow motions with Mach numbers larger than 0.5 and a shock that propagates outward from the condensation, bringing the surrounding medium out of thermal equilibrium. The time for the dynamical transient state to subside ranges from 4 to 30 Myr for initial density perturbations of 20% and sizes 3 75 pc. By the time the condensations have formed, a substantial fraction of the mass is still traversing the unstable range. Smaller (0.3-3 pc) perturbations may condense less dynamically and reach nearly static configurations in shorter times (e.g., similar to3.5 Myr for perturbations of similar to0.3 pc), but they may be stable if they have a turbulent origin (see below). We thus suggest that, even if TI were the sole cloud-forming agent in the ISM, clouds formed by it should be bounded by accreting gas traversing the unstable range, rather than by sharp transitions to the stable warm phase. Second, we discuss the competition between a spectrum of density perturbations of various sizes. We empirically find that, in order for small-scale perturbations not to significantly alter the global evolution, progressively larger values of eta are necessary as the initial spectrum becomes shallower. Finally, we discuss the development of the instability in the presence of random velocity forcing, which we argue is the most realistic way to emulate density fluctuation production in the actual ISM. Such fluctuations are quasi-adiabatic rather than quasi-isobaric in the large-eta limit and trigger the wave mode of TI, rather than the condensation mode, being stable to first order. Indeed, we find that the condensation process can be suppressed for arbitrarily long times if the forcing causes a moderate firms Mach number (greater than or similar to0.3) and extends to small enough scales or occurs in low enough density environments that the turbulent crossing time becomes smaller than the cooling time at those scales. We suggest that this mechanism, and the long times required to evacuate the unstable phase, may be at the origin of the relatively large amounts of gas mass in the unstable regime found in both observations and simulations of the ISM. The gas with unstable temperatures is expected to be out of thermal equilibrium, suggesting that it can be observationally distinguished by simultaneously measuring two of its thermodynamic variables. We remark that in the (stable) warm diffuse medium, eta is large enough that the response to velocity perturbations of scales up to several parsecs is close to adiabatic, implying that it is relatively weakly compressible and thus consistent with recent observations that suggest a nearly Kolmogorov power spectrum in this medium.