Modeling the H$\alpha$ Emission Surrounding Spica using the Lyman Continuum from a Gravity-darkened Central Star

The large, faint H$\alpha$ emission surrounding the early B-star binary Spica has been used to constrain the total hydrogen recombination rate of the nebula and indirectly probe the Lyman continuum luminosity of the primary star. Early analysis suggested that a stellar atmosphere model, consistent with Spica A's spectral type, has a Lyman continuum luminosity about two times lower than required to account for the measured H$\alpha$ surface brightness within the nebula. To more consistently model both the stellar and nebular emission, we have used a model atmosphere for Spica A which includes the effects of gravity darkening as input to photoionization models to produce synthetic H$\alpha$ surface brightness distributions for comparison to data from the Southern $H\alpha$ Sky Survey Atlas (SHASSA). This paper presents a method for the computation of projected surface brightness profiles from 1D volume emissivity models and constrains both stellar and nebular parameters. A mean effective temperature for Spica A of $\simeq$ 24,800 K is sufficient to match both the observed absolute spectrophotometry, from the far-UV to the near-IR, and radial H$\alpha$ surface brightness distributions. Model hydrogen densities increase with the distance from the star, more steeply and linearly towards the southeast. The northwest matter-bounded portion of the nebula is predicted to leak $\sim$17% of Lyman continuum photons. Model H II region column densities are consistent with archival observations along the line of sight.