We discuss the nonlinear development of the isobaric mode of thermal instability ( TI ) in the context of the atomic interstellar medium ( ISM ) , both in isolation and in the presence of either density or velocity fluctuations , in order to assess the ability of TI to establish a well-segregated multi-phase 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 1D and fits to recently published cooling rates , we find that density perturbations of sizes \gtrsim 15 pc in media with mean density \sim 1 cm ^ { -3 } develop inflow motions with Mach numbers larger than 0.5 and a shock that propagates outwards 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 to 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. , \sim 3.5 Myr for perturbations of \sim 0.3 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 alter significantly 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 rms Mach number ( \gtrsim 0.3 ) 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 .