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A semi analytic model: Combining stellar wind and ionizing radiation

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  • Figure 1: Sketch illustrating the structure of a stellar wind boosted HII region. Regions 1 and 2 make up the typical stellar wind bubble. In this equilibrium model the shell of the stellar wind bubble is missing, because it has mixed with the photo ionized medium. The density in the stellar wind bubble is many orders of magnitude smaller than in region 3 (the photo ionized region). Therefore, we can assume that all ionizing photons get absorbed in region 3. Region 2 and 3 are in pressure equilibrium. Rw/RIF is dependent on the density and the type of source. More massive stars have disproportionately stronger winds and larger wind bubbles. Region 4, the shocked ISM, is a dense shell around the stellar wind boosted HII region.
  • Figure 2: The plot shows the radii of the HII regions RIF (solid lines), the shocked wind regions Rw (dashed lines), and the free wind region Rfw (dotted lines). Shown are the analytic solution from Hosokawa & Inutsuka (2006) in grey, and the solution to our semi analytic model of the stellar wind boosted HII region in purple (with αp=10). Orange and yellow show the sizes of the bubbles derived from hydrodynamics (HD) simulations with and without stellar wind respectively. The HD simulation shows a transition from the early phase to the phase, where pressure equilibrium establishes (here at around t=200kyr). The time it takes to reach the pressure balance decreases with increasing resolution of the HD simulation.

Sebastian Vider

Stars are born in clusters from the gas of giant molecular clouds. The dense interstellar gas collapses due to gravity and forms new stars, but only a fraction of the total mass from the parent cloud ends up in stars. Feedback from massive stars is thought to be the primary mechanism stopping further accretion and collapse of the molecular material. Massive stars interact with their gaseous environment via various feedback mechanisms including super novae, jets, radiation and stellar winds. While jets are important in the early formation stage of these stars, and super novae are the grand finale of their lives, stellar winds and ionizing radiation are the primary feedback mechanisms throughout their main sequence lives.

Existing analytic models try to understand how ionizing radiation (see Spitzer, Hosokawa & Inutsuka 2006, Raga et al. 2011) or stellar winds (see Weaver et al. 1977, Lancaster et al. 2021) interact with the environment, but treat both mechanisms separately.

Our model takes the "efficiently cooled" (EC) wind bubble approach from Lancaster et al. (2020a,b) and combines it with the momentum equation from Hosokawa & Inutsuka (2006). Fig. 1 shows a sketch of the combined stellar wind and ionizing radiation feedback, where four regions make up the HII region. The free wind region, the shocked wind region and the photo ionized region are in pressure equilibrium with each other. The wind bubble fills a significant fraction of the volume, its size determined by pressure equilibrium, and therefore, boosts the pressure and the expansion of the HII region. In our semi analytic approach we numerically integrate a system of differential equations, which provides us with the mass, radius and expansion velocity of the stellar wind boosted HII region. The free parameter of the EC model αp contains information about how much thermal energy is contained within the stellar wind bubble. We determine αp by fitting the model to hydrodynamics (HD) simulations of stellar wind boosted HII regions and find that αp ≈ 10.

Fig. 2 shows the predicted expansion of the free wind, shocked wind and comlete HII region alongside values obtained from HD simulations. The semi analytic model correctly predicts the due to the wind boosted expansion of the HII region and the sizes of the shocked wind and free wind regions. The model improves our understanding of the interaction between stellar wind and ionizing radiation and due to the efficiency of the algorithm (in comparison with HD simulations) opens the door for a large parameter study, where we can vary the central source (different stars or star clusters) and surrounding density profile.