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Astron. Astrophys. 337, 517-538 (1998)

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3. The ionized region

For a given electron density [FORMULA] and number of ionizing photons [FORMULA] a simple ionization equilibrium calculation at [FORMULA] K results in a value of the mass of ionized gas given by

[EQUATION]

where [FORMULA] s-1, [FORMULA] cm-3.

Since in this paper we are interested in the neutral shells of planetary nebulae, we require that the shell remains in part neutral over a significant fraction of its lifetime. This constrains the ratio [FORMULA] to rather large values.

Fig. 3 shows the values of [FORMULA] as a function of time for [FORMULA]=10, [FORMULA]=2 (lower panel) and [FORMULA]=3 (upper panel). Fig. 3 and Eq. 5 demonstrate that the condition that the shell remain partially neutral for [FORMULA] yrs is

[EQUATION]

where [FORMULA] for [FORMULA] and [FORMULA] for the higher stellar mass cases.

[FIGURE] Fig. 3. Mass of ionized gas as a function of time for [FORMULA] cm-3 and four different core masses: [FORMULA]=0.6 [FORMULA] (dot-short-dashed curve, template model), [FORMULA]=0.64 [FORMULA] (dot-long-dashed curve), [FORMULA]=0.696 [FORMULA] (dashed curve), and [FORMULA]=0.836 [FORMULA] (solid curve). The upper panel is for [FORMULA], the lower panel for [FORMULA].

Fig. 3 shows another important aspect of the PN evolution, namely that the fractional mass of ionized gas, which depends on the ratio [FORMULA], first increases with time, following the steep increase of [FORMULA], then decreases as [FORMULA] decreases, and finally increases again at even later times due to density decline. The advance of the ionization front has important consequences on the properties (position and temperature) of the dissociation front, as rapid advection of molecular material into the PDR takes place. The recession adds atomic gas to the PDR surface and results in non-equilibrium formation of H2 in the PDR.

We characterize the emission of the ionized region with the radiated Br[FORMULA] intensity, which, for an ionization-bounded shell, is given by

[EQUATION]

where [FORMULA] cm. Note that I(Br[FORMULA]) does not depend on shell parameters such as density and filling factor, but provides a direct measurement of the stellar Lyman continuum radiation field.

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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
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