Diffuse H in a Fractal Interstellar Medium

Photon Mean Free Paths

The clouds in a fractal interstellar medium are highly clumped, not uniformly dispersed as in the ''standard cloud'' model. This clumping increases the mean free path for photons between the fractal cloud complexes, making the diffusion of photons easier than previously thought.

The change in photon mean free path can be understood from the fractal model in E97a, which gives the average number of subpieces on a line of sight through a fractal cloud complex. This number is for maximum density contrast C and fractal dimension D. If the average number of clouds per kiloparsec is 8, for example, and if each cloud complex contributes 2.5 absorption lines, then the average number of fractal cloud complexes per kpc is 8/2.5=3. The inter-complex mean free path is the inverse of this, or 0.3 kpc. This is so long that most photons that leak out of a midplane HII region can travel nearly to the next HII region or reach the halo. This produces extensive diffuse H that is directly associated with each HII region (see next section). It also allows the halo to be ionized by photons coming from the midplane.

This implication of a long intercloud mean free path is sensible considering the distribution of extinction in the solar neighborhood. Lucke (1978) showed that the gas in the solar neighborhood is clumped into a few large diffuse cloud complexes, spaced by several hundred pc. These clouds produce the local interstellar absorption lines, such as those used by Blaauw (1952) to derive the average of 8 clouds/kpc. Thus, these 8 clouds per kpc are highly clumped in Lucke's map. Also, the mean separation between fractal cloud complexes derived from the model is about the same as the spacing between the Lucke clouds and between the OB associations/GMCs in the solar neighborhood, including Orion, Perseus, Sco-Cen, Cepheus, etc.. Essentially all of the local gas is known to be clumped into a few giant cloud complexes, which are generally composed of both atomic and molecular gas. Since we see the fractal structure of these local clouds directly, in CO and IRAS maps, there is direct evidence for the highly clumped and fractal structure that is emphasized in the new model.

The intercloud medium is presumably the low density part of the interstellar fractal. Another way of seeing why there must be a low density part to the ISM in a turbulent model is by considering the density of thermally stable gas in the local radiation field. This density is in the range of 10 to 100 cm for the cool phase, and much less, such as 0.1 cm, in the warm neutral phase, given the total interstellar pressure. The gas cannot remain stable at the average local density of cm. When turbulence moves gas around, it produces a variety of structures and everywhere locally the gas temperature settles on a value that puts it in thermal equilibrium. The thermal properties of the gas are of secondary importance to this structure because the total pressure is strongly dominated by turbulence and magnetic fields. Thus the temperature is a slave to the dynamics (Vazquez-Semadeni et al. 1995; Elmegreen 1997b). The thermal properties determine the maximum density. This maximum is just the total pressure divided by kT. The point is that turbulence remains supersonic, and therefore highly compressive, because the stable thermal temperature for most of the gas has a sound speed that is much less than the average interstellar turbulent speed. As a result, most of the gas mass in the midplane has the density of a diffuse cloud or larger, and most of the gas occupies a volume filling factor equal to the average density divided by this diffuse cloud density, which is only a few percent. There is no way to spread out the gas to have a uniform density equal to the average density when the cool thermal phase is both highly subsonic and denser than the average. Any random motion inevitably partitions the gas into clouds and an intercloud medium. What is new about the fractal interpretation is the recognition that such turbulence partitioning can lead to fractal structure with well determined and universal properties.

A numerical simulation of compressible hydromagnetic turbulence with enough spatial resolution to see correlated motions and fractal structure in a region that is far removed from the boundaries and sources of excitation is in Elmegreen (1997b). This simulation is only one-dimensional, so many important aspects of real turbulence are not present.

© Copyright Astronomical Society of Australia 1997