5. THEORIES OF THE ISM

5.1. The Two-Phase Model

Field, Goldsmith & Habing (1969) developed the first quasi-static theory of a multi-phase ISM. The FGH model contained two stable phases, the `cold' neutral phase at a temperature of ~ 100K and a `warm' phase at ~ 10⁴ K where about 10% of the gas is ionized. The model uses cosmic ray heating to balance the cooling of these two phases. The cooling is dominated by fine-structure excitations from C⁺ in the cool gas, and collisional excitations (Ly) in the warm gas. The model predicts an ISM where the majority of the volume is occupied by the warm (~ 10⁴ K) intercloud medium while the majority of the mass is contained within the dense cold clouds.

However, the FGH model indicated that the ISM should be stratified perpendicular to the Galactic disk, which was known to violate the observed properties of the ISM. They therefore appealed to the collective explosive effects of HII regions and supernovae, which impart sufficient turbulent motions to destroy any gravitationally induced stratification. The FGH model allows the cold clouds to have a large range of sizes. The smallest clouds are destroyed by thermal conduction within the warm layer, while the largest are gravitationally unstable and prone to collapse. Otherwise, there is no limit on the size or shape of the expected neutral structures.

FGH also raised the possible existence of another stable phase at a temperature of ~ 10⁶ K, dominated by bremsstrahlung cooling. However, prior to observations of the soft x-ray background or high-ionization UV spectra, there was no need to invoke the actual existence of this medium.

In the FGH model, supernovae (and HII regions) were required to destroy the gravitationally-induced vertical stratification of the ISM. This inspired theoretical models of the expansion and thermal evolution of supernova remnants, and it was then that the full importance of supernovae came to be realized. Supernovae generate blast waves with speeds of 10,000 km s^-1 which shock the ambient material, producing gas at ~ 10⁶ K which then slowly cools through bremsstrahlung emission and line emission from highly ionized ions. The remnant structure is a hot bubble surrounded by a thin, relatively dense shell of cool ~ 10³ K gas. This situation proves to be quite stable; the hot bubble cannot expand through the shell expanding ahead of it. After a million years, the radius of the hot bubble is roughly 80 pc. At this point, the interior pressure of the bubble reaches the ambient pressure of the ISM. This static situation remains until the hot bubble cools and contracts after four million years or so.

Cox & Smith (1974) were the first to recognize the importance of this evolutionary sequence for the dynamical and thermal balance of the ISM. If an expanding supernova remnant happens to intersect the static hot cavity of another remnant, the expanding remnant `breaks out' through the old, hot remnant. Due to the low density within the static bubble, the expanding shock wave propagates preferentially into it, reheating the matter inside. Depending upon the rate of Galactic SNR, the ISM could therefore evolve towards an interconnected tunnel network filled predominantly by hot gas.

To estimate the importance of such a tunnel network, a porosity parameter was introduced such that

(1)

where r is the average SN rate per unit volume, is the lifetime of an isolated bubble, and V_sn is the final volume of the average SN-generated bubble. For q << 1, q is the proportion of the total interstellar volume that would be filled with hot bubbles. For a SN frequency of 1 per 80 yr, they found q ~ 0.1. This implies that 10% of interstellar space should be filled by unconnected, hot, SN-generated bubbles. Therefore, the probability of any new SN occurring within a preexisting cavity was 0.1, but the probability that any new SNR would expand into and reheat another older remnant was 0.55. The consequences of the overlap on the phase structure of the ISM were radical.

This chain of reasoning rests heavily upon supernovae occurring randomly throughout the Galactic volume and the expansion of the hot bubble not being inhibited by magnetic pressure, for example. The simple conclusion prompted many to believe in the `porosity imperative', that is the need for a hot 10⁶K phase to occupy the majority of the interstellar volume. The cold and warm (~ 10⁴ K) phases were relegated to the walls between the pervasive bubbles. Large filamentary structures in the ISM seem to support this, except that the overall pervasiveness and smoothness of the ISM is in conflict with this picture.