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Astron. Astrophys. 331, 347-360 (1998)

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1. Introduction

The theory of the evolution of H II regions has been developed with a variety of analytical and numerical studies (see review by Yorke 1986, and the standard reference books by Osterbrock 1989and Spitzer 1978). Although a considerable degree of physical complexity has been attained in steady-state solutions of the ionization structure (Harrington et al. 1982; Ferland 1990), most hydrodynamic models have been quite approximate in their treatment of the radiative transfer and the solution of the energy and ionization equations (Mathews 1965; Tenorio-Tagle 1976; Manfroid 1976; Bodenheimer, Tenorio-Tagle & Yorke 1979). However, these numerical models together with the analytical studies based on autosimilar solutions, have composed a complete picture of the dynamical evolution of H II regions in the "standard case", i.e. under the assumption of a constant-density medium and a constant ionizing photon flux. Thus, when a massive ionizing star enters the main sequence, its UV photons create a supersonic weak-R type ionization front (IF, see Spitzer 1978for a classification of IFs) that moves through the gas, leaving it hot and ionized but dynamically unperturbed. When the ionized region has reached its Strömgren radius ([FORMULA]), the dimension of the volume within which the number of recombinations equals the UV stellar photon output (Strömgren 1939), the large pressure gradient across the IF causes the expansion of the H II region. The expansion is supersonic with respect to the ambient neutral material and creates a shock wave that accelerates and piles up the neutral gas into a dense shell.

Departures from the classical evolution during the phases of formation and expansion, as outlined above, have been studied by changing the initial distribution of density or by simulating the UV flux turn-off when the star leaves the main sequence. Studies of evolved H II regions after the star flux begins to decline (Beltrametti, Tenorio-Tagle & Yorke 1982, hereafter BTY, and Tenorio-Tagle et al. 1982, hereafter TBBY) have shown how the decrease in the ionizing flux causes the IF to recede supersonically towards the star. Once the recession speed of the IF becomes comparable to [FORMULA] the ionized gas can react to the pressure gradient across the IF and a second expansion of the ionized region begins. This picture undergoes a further variation with the inhibition of the reionization phase for low values of the initial density (see TTBY). The relaxation of the assumption of constant ambient density leads to the well-known "champagne" phase when an IF overruns a density gradient and the large pressure gradient found within the ionized gas leads to the disruption of the densest medium (Tenorio-Tagle 1979). Numerical and analytical studies of this phase have shown that it can produce highly supersonic flows. Franco, Tenorio-Tagle & Bodenheimer (1990) also showed that for a cloud with a power-law density distribution ([FORMULA]) the evolution can follow the classical scheme of IF + shock ([FORMULA]) or the champagne phase ([FORMULA]). In a more recent paper Rodríguez-Gaspar, Tenorio-Tagle & Franco (1995) calculated the optical appearance of these regions in [FORMULA] 5007 and H [FORMULA] showing that during the champagne phase the formation of these lines may arise from different sectors of the flow. Yorke, Tenorio-Tagle & Bodenheimer (1983, 1984) also calculated the optical and radio maps of 2-D models of the champagne phase (Bodenheimer et al. 1979 and Tenorio-Tagle 1979). All these line-transfer calculations based on the numerical output of hydrocodes that considered only the ionization of hydrogen clearly had to make strong assumptions on the ionization structure of H II regions.

Here we present an efficient method for solving the equations of hydrodynamics coupled with a detailed description of the temperature and ionization structure of a nebula. The method is meant to be general enough to allow for any source of ionization as well as possible intrinsic time variations in their spectra. Moreover, the necessary tools to calculate quantities directly comparable with the observations have been installed.

In Sect. 2 we present the general equations and approximations made to handle both the hydrodynamic and line-transfer equations. Sect. 3 presents the tests performed on the code and a comparison with the results from CLOUDY; a widely used steady-state photoionization code. Sect. 4 is a review of the classical evolution of an H II region in a low constant density medium focusing on the calculated observables (such as surface brightness, line profiles, as well as their spatial distribution, and diagnostic diagrams). Finally, Sect. 5 summarizes our main conclusions and future work. The treatment of the diffuse field and the calculation of the line transfer are given as appendices.

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© European Southern Observatory (ESO) 1998

Online publication: February 4, 1998
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