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 HMapper observations of the H ii regionsurroundingtheO9.5VstarOph.Our modelsinvestigate theporosityoftheinterstellarmediumaroundOph andtheeffectsofthree-dimensionaldensitiesontheHsurfacebrightnessandvariationinthe(Nii)k6583/Hline ratio. TheOph 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. Bysimulating the observations, we estimate the porosity of the medium in the vicinity ofOph 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 surroundingOph, 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 widespreadwarmionizedmedium.Thiscomplicatestheinterpretationofthepredictedrapidriseofsomeemission- line ratios near the edge of uniformdensity Hiiregions 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-Hii interfaces. Subject headingg H ii regions — ISM: structure — radiative transfer — stars: individual (� Ophiuchi)