A TURBULENT MODEL FOR THE INTERSTELLAR-MEDIUM .1. THRESHOLD STAR-FORMATION AND SELF-GRAVITY

We present numerical simulations of self-gravitating turbulent compres sible flows in two dimensions with model terms for local stellar heati ng, diffuse background heating, radiative cooling (assuming an optical ly thin medium), and large-scale shear. Star formation (SF) is modeled by assuming that a local heating center is turned on every time the l ocal density exceeds a threshold value. The heating then remains on fo r a time typical of the lifetimes of OB stars. Supernovae, magnetic fi elds, and rotation effects (Coriolis and centrifugal forces) are not c onsidered. We discuss both the structure and the evolution of the mode l using parameters appropriate to the interstellar medium (ISM) at the scale of 1 kpc in the plane of the Galactic disk, although many of th e results should be applicable to other scales with marginally importa nt self-gravity. Also discussed are dynamical aspects of the turbulenc e in these flows. The model exhibits a self-sustaining cycle in which no single process is fully responsible for SF; turbulence generates de nsity fluctuations which, due to cooling and gravity, reach the thresh old value for SF, which in turn generates more turbulence through expa nding ''H II'' regions. Both spontaneous and self-propagating SF event s occur in the models. The main source of energy for turbulence mainte nance is stellar heating, with an efficiency similar to 0.06%. Simulat ions with reduced gravitational strength cannot sustain the cycle, and thus they engage in decaying regimes with vanishing SF. Large-scale, long-period (1-2 x 10(8) yr) oscillations in the gravitational energy and the star formation rate are observed in the models, which are cons istent with the periods expected for gravito-acoustic waves at the lar gest scales. The peaks of the oscillations constitute SF ''bursts'' wh ich are terminated when SF activity disperses the density field, for t otal burst durations similar to 7 x 10(7) yr. Thermal timescales are a t least an order of magnitude shorter than dynamical timescales. Also, the cooling and diffuse heating functions used give no thermal instab ility at the temperatures reached by the model. Thus, the system is al most always in thermal equilibrium (except in the neighborhood of hot stars), and the temperature and pressure are effectively ''slaved'' to the density by the relations T proportional to rho(-1/n) and P propor tional to rho(gamma eff), where gamma(eff) = 1 - 1/n and n is the temp erature exponent in the cooling function. The effective polytropic exp onent gamma(eff) lies in the range 0.33-0.66. An exception to this beh avior are expanding ''H II'' regions and their immediate surroundings. The main cloud and cloud-complex formation mechanism in the model is turbulent ram pressure. Clouds form at the interfaces of colliding flo w streams, confirming speculations of earlier workers. Thermal pressur e plays a role in the formation of expanding shells and small subconde nsations within them. The flow thus segregates into a diffuse, low-vor ticity, warm phase at rho similar to 0.2 cm(-3) and T similar to 10(4) K, and a dense, high-vorticity, cool phase at rho similar to 3 cm(-3) and T similar to 1500 K. A sample of clouds in the simulations exhibi ts a significant dispersion in the ratio of gravitational to (kinetic + thermal) energies, the longest lived clouds being those closest to v irial equilibrium. Although incomplete due to the absence of self-grav itating clouds associated with details of the thermal modeling, the si mulations do suggest the conjecture that the ISM may not have a tenden cy to form virialized clouds, but that their observed overabundance ma y be a direct consequence of their longer lifetimes.