Estimating the Porosity of the Interstellar Medium from Three Dimensional Photoionization Modeling of H II Regions

We apply our three-dimensional photoionization code to model Wisconsin H alpha Mapper observations of the H II region surrounding the O9.5 V star zeta Oph. Our models investigate the porosity of the interstellar medium around zeta Oph and the effects of three-dimensional densities on the H alpha surface brightness and variation in the [ N II] lambda 6583/ H alpha line ratio. The zeta Oph H II region has a well-characterized ionizing source, so it is an excellent starting point for three-dimensional models of diffuse ionized gas. We investigate various hierarchically clumped density structures, varying the overall smoothness within the clumping algorithm. By simulating the observations, we estimate the porosity of the medium in the vicinity of zeta Oph and find that within the context of our hierarchically clumped models, around 50%-80% of the volume is occupied by clumps surrounded by a low-density smooth medium. We also conclude that in order for O stars to ionize the diffuse warm ionized medium, the O star environment must be more porous than that surrounding zeta Oph, with clumps occupying less than one-half of the interstellar volume. Our clumpy models have irregular boundaries, similar to observed H II regions. However, in observed H II regions, it is difficult to identify the precise location of the boundary because of the foreground and/or background emission from the widespread warm ionized medium. This complicates the interpretation of the predicted rapid rise of some emission-line ratios near the edge of uniform density H II regions and, combined with the three-dimensional clumpy nature of the interstellar medium, may explain the apparent lack of distinctive emission-line ratios near H I-H II interfaces.