The Coevolution of Stellar Wind-blown Bubbles and Photoionized Gas. I. Physical Principles and a Semianalytic Model

We propose a new framework for the simultaneous feedback of stellar winds and photoionizing radiation from massive stars, distinguishing the locations where forces are applied, and consequences for internal spatiotemporal evolution of the whole feedback bubble (FB). We quantify the relative dynamical importance of wind-blown bubbles (WBBs) versus the photoionized region (PIR) by the ratio of the radius at which the WBB is in pressure equilibrium with the PIR, R_eq, to the Strömgren radius, R_St. ζ ≡ R_eq/R_St quantifies the dynamical dominance of WBBs (ζ > 1) or the PIR (ζ < 1). We calculate ζ and find that, for momentum-driven winds, 0.1 ≲ ζ ≲ 1 for the star-forming regions in (i) typical Milky Way-like giant molecular clouds, (ii) the most massive of individual OB stars, and (iii) dense, low-metallicity environments, relevant in the early Universe. In this regime, both WBBs and the PIR are dynamically important to the expansion of the FB. We develop a semianalytic coevolution model (CEM) that takes into account the spatial distribution of forces and the back reactions of both the WBB and PIR. In the ζ < 1 regime where the CEM is most relevant, the model differs in the total FB momentum by up to 25% compared to naive predictions. In the weak-wind limit of ζ ≪ 1, applicable to individual OB stars or low-mass clusters, the CEM has factors ≳2 differences in WBB properties. In a companion paper, we compare these models to 3D, turbulent hydrodynamical simulations.