3.4. Interstellar Porosity
A conventional parameterization for global mechanical feedback in galaxies is the interstellar porosity, or volume filling factor of superbubbles. Having derived analytic expressions for the superbubble size distribution, it is straightforward to derive expressions for the porosity (Oey & Clarke 1997). This can be written in terms of the star formation rate (SFR), galactic scale height h, and galactic star-forming radius Rg (Oey et al. 2001):
for Milky Way ISM parameters and Salpeter (1955) IMF. The porosity also can be written in terms of galactic parameters, i.e., ISM mass and velocity dispersion (Clarke & Oey 2002). Assuming a feedback origin for the HIM, the interstellar porosity quantifies the relative phase balance between the HIM and cooler ISM phases. Q greater than a critical value of unity therefore indicates an outflow condition for the hot gas, as might be encountered in a starburst situation (Figure 7).
Figure 7. Low and high interstellar porosities are shown schematically in the upper and lower panels, respectively. The lower panel shows how Q = 1 defines a threshold porosity and star-formation rate for galactic outflows and escape of ionizing radiation.
For the Local Group star-forming galaxies, Oey et al. (2001) find Q << 1 in almost all cases, suggesting that the HIM generally does not dominate the ISM volume. The LMC, however, does show Q ~ 1. The Milky Way situation is ambiguous, with different estimates of the SFR yielding Q in the range 0.2 to 1. The truly glaring exception is the starburst galaxy IC 10, for which Q 20, clearly fulfilling the outflow or superwind criterion. Clarke & Oey (2002) also posit the critical Q = 1 condition as a threshold for radiative feedback to the IGM. Once mechanical outflow is established, the merging and blowout of superbubbles also opens free pathways for ionizing photons to escape from the parent galaxy. They apply this simple model to a variety of phenomena, ranging from giant molecular clouds to Lyman break galaxies.