Physical conditions in Barnard's Loop, components of the Orion-Eridanus bubble, and implications for the warm ionized medium component of the interstellar medium

We have supplemented existing spectra of Barnard's Loop with high accuracy spectrophotometry of one new position. Cloudy photoionization models were calculated for a variety of ionization parameters and stellar temperatures and compared with the observations. After testing the procedure with recent observations of M43, we establish that Barnard's Loop is photoionized by four candidate ionizing stars, but agreement between the models and observations is only possible if Barnard's Loop is enhanced in heavy elements by about a factor of 1.4. Barnard's Loop is very similar in properties to the brightest components of the Orion-Eridanus Bubble and the warm ionized medium (WIM). We are able to establish models that bound the range populated in low-ionization color-color diagrams (I([S II])/I(Hα) versus I([N II])/I(Hα)) using only a limited range of ionization parameters and stellar temperatures. Previously established variations in the relative abundance of heavy elements render uncertain the most common method of determining electron temperatures for components of the Orion-Eridanus Bubble and the WIM based only on the I([N II])/I(Hα) ratio, although we confirm that the lowest surface brightness components of the WIM are on average of higher electron temperature. The electron temperatures for a few high surface brightness WIM components determined by direct methods are comparable to those of classical bright H II regions. In contrast, the low surface brightness H II regions studied by the Wisconsin Hα Mapper are of lower temperatures than the classical bright H II regions.