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

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1. Introduction

Recent observations clearly demonstrate that a significant component of the ejected mass in many planetary nebulae (PNe) is neutral (see, for example, reviews by Rodriguez 1989; Dinerstein 1991, 1995, et al. 1995; Huggins 1992, 1993; Tielens 1993). The atomic gas has been observed by a variety of means. Melnick et al. (1981), Ellis & Werner (1985) and Dinerstein et al. (1991) have observed the fine structure lines of CII 158µm and OI 63µm which originate in the dissociated atomic component of the ejecta. The atomic component is also observed in HI 21cm in few compact PNe with derived H I masses of [FORMULA] [FORMULA] (Rodriguez et al. 1985; Schneider et al. 1987; Taylor et al. 1990). Dinerstein et al. (1995) survey 21 PNe in the Na I D lines which also trace the atomic gas.

With the advent of millimeter arrays and large millimeter dishes with high sensitivity and with ISO, CO (Mufson et al. 1975; Bachiller et al. 1989a,b, 1993, 1997; Huggins & Healy 1989; Healy & Huggins 1990; O'Dell, R.R., & Handron, K.D. 1996; Sahai et al. 1990, 1991; Bieging et al. 1991; Cox et al. 1991; Forveille & Huggins 1991; Jaminet et al. 1991; Huggins et al. 1992, 1996; Yamamura et al. 1994, 1995; Zweigle et al. 1997), HCO+ and CO+ (Deguchi et al. 1990, 1992; Cox et al. 1992; Bachiller et al. 1993; Latter et al 1995), OH masers (Zijlstra et al. 1989) and a number of other molecules (eg., Cox et al. 1992; Bachiller et al. 1993, 1997; Liu et al. 1997; Cernicharo et al. 1997) have also been detected. Their line fluxes suggest the presence of a substantial quantity ([FORMULA] [FORMULA]) of cool molecular gas.

Perhaps the largest body of evidence, however, comes from the observation of the H2 2µm vibrational transitions (Treffers et al. 1976; Beckwith et al. 1978; Storey 1984; Dinerstein et al. 1988; Greenhouse et al. 1988; Webster et al. 1988; Zuckerman & Gatley 1988; Zuckerman et al. 1990; Graham et al. 1993; Hora & Latter 1994, 1996; Kelly & Latter 1995; Latter et al. 1995; Shupe et al. 1995; Cox et al. 1995, 1997; Kastner et al. 1996; Luhman & Rieke 1996). Generally, the H2 v=2-1S(1)/H2 v=1-0S(1) ratio is low, [FORMULA], suggestive of thermal excitation at gas temperatures of roughly 2000 K; however, there are a few reported cases of higher ratios suggestive of FUV-induced fluorescent emission (e.g., Dinerstein 1991). Huggins (1992, 1993) reports that H2 2µm was detected in 33 of 60 surveyed PNe, and that more than 70 PNe have now been detected in molecular lines or H I.

The neutral material appears to be often associated with either young, compact objects or with asymmetric (often torus-like, with "bow tie" optical morphology) ejections. The neutral components are preferentially found at low galactic latitudes around relatively high-mass central stars which presumably had relatively higher mass progenitors with higher mass ejections (Webster et al. 1988, Zuckerman & Gatley 1988, Huggins 1992, Kastner et al. 1996). However, there are interesting exceptions such as the Dumbbell and Helix Nebulae which are relatively old PNe with substantial molecular emission (Zuckerman & Gatley 1988, Huggins 1992). There is growing evidence that the molecules are found in clumps, the Helix being a prime example (Huggins et al. 1992).

Such observations motivate this paper, which theoretically models the emission expected from neutral shells expanding away from the hot central stars of PNe. We use "shells" in a general sense since the models do not require that they fill 4[FORMULA] steradians around the star; therefore, tori and clumps are included as examples of partial shells. These neutral structures do not necessarily lie outside the ionized HII nebulae seen in optical emission lines; the aspherical distribution or the effects of clumpiness may allow neutral material to be embedded in dense regions or clumps inside the nebula (see also Howe et al. 1994, for a theoretical discussion of chemistry in these clumps or globules). The main goal of the theoretical models is to provide an explanation for the origin of the observed H2 1-0 S(1) and 2-1S(1) emission, and the relative strength of the H2 emission compared with the Br[FORMULA] emission from the ionized nebula. The H2 lines may originate in the shock between the shell and the precursor red giant wind or in the photodissociation region (PDR) on the inside of the neutral shell where the H2 is either pumped and heated by FUV (11 eV[FORMULA] eV), or soft X-rays (50 eV [FORMULA] KeV). We include the effects of shocks, FUV, and soft X-rays on the predominantly neutral gas, in order to determine which of these three processes causes the H2 2µm emission.

In addition to the vibrationally excited H2 lines and to Br[FORMULA], we compute the intensity of a number of H2 lines from v=0 (the J=6-4 line at 8.0µm, the J=5-3 at 9.7µm, the J=4-2 at 12µm, the J=3-1 at 17µm and the J=2-0 at 28µm), and three metal lines in the mid and far-infrared, namely CII 158µm, OI 63µm and SiII 35µm. At the moment, there are only a few measurements of PNe in these lines, since they are not accessible from the ground (Dinerstein et al. 1991). We expect, however, that a large number of observations will be available very soon, as the lines are easily detected by the spectrometers on board of the infrared satellite ISO. First LWS results for NGC 7027 (Liu et al. 1996) give fluxes of about 3.5[FORMULA] and 4.3[FORMULA] erg cm-2 s-1 for the CII and OI line, respectively; ISO can detect lines with fluxes of the order of [FORMULA] erg cm-2 s-1. Finally, we compute the OI 6300Å and the FeII 1.26µm emission from the very warm ([FORMULA] K) portion of the atomic regions.

Our model of the evolution of the ejected shell is quite simple and general. The neutral shell is ejected with a mass [FORMULA] [FORMULA] and a velocity [FORMULA] km s-1, and fills a fraction [FORMULA] of the solid angle seen from the star (see Pottasch 1984). The ionized gas is assumed to have a filling factor [FORMULA]; [FORMULA] corresponds to the case where only the inside of the neutral shell is ionized. An incomplete shell ([FORMULA]) could be, for example, an axisymmetric expanding torus or it could be outflowing clumps with an arbitrary distribution around the star. The shell overtakes and shocks the red giant wind from the previous epoch of mass loss; the red giant wind speed is [FORMULA] km s-1 (Loup et al. 1993). The shell has traveled [FORMULA] cm in [FORMULA] years. After a time interval which depends on the mass of the core (we shall hereafter use "core" and "central star of the PNe" interchangeably) and on that of the precursor star, the central star has warmed to [FORMULA] K, initiating a rapid rise in the luminosity of FUV (6eV[FORMULA]h[FORMULA]13.6eV) photons, [FORMULA], and of Lyman continuum photons, [FORMULA]. Later, [FORMULA] may exceed 100,000 K, causing soft X-rays to become important in the chemistry and heating of the neutral gas. This paper focusses on the shell evolution after the star has achieved [FORMULA] K; therefore it is not appropriate for the earlier "protoplanetary" stage of shell evolution.

If the column density in the shell is sufficiently high to absorb the incident ionizing and dissociating photons, a three-layered shell is produced with an inner HII region, a central HI region, and an outer H2 region. For thin shells the timescales for sound waves to traverse the shell are shorter than the dynamical timescale or the radiation field timescale; therefore pressure equilibrium is maintained in the shell. If, as in the "interacting wind" model of Kwok et al. (1978) and Kwok (1982), pressure from a fast stellar wind or from radiation is significant, maintaining the shell velocity at a constant [FORMULA], then the density in the shell will evolve as [FORMULA]. On the other hand, if stellar forces are negligible, the shell will coast until it has swept up its own initial mass, and the density in the shell will evolve as [FORMULA] (free expansion) before the deceleration.

In order for neutral gas to survive the strong Lyman continuum fluxes, dense shells are required, and, in general, the high densities permit the assumption of chemical and thermal balance. However, intermediate density cases exist where the shell is not completely ionized, and the H2 chemical timescale may be longer than the dynamical timescale and/or the timescales for the evolution of [FORMULA] and [FORMULA]. We therefore follow the time dependent chemistry of H2, solving for the chemical and temperature structure and the emergent spectrum of the evolving shell (Hollenbach & Natta 1995). Bobrowsky & Zipoy (1989) model the H2 emission from neutral shells around PNe; our models differ by treating the chemistry, radiative transfer, and time-dependent evolution of the stellar radiation field in more detail and because we include the effects of the soft X-rays emitted by the central star.

This paper is organized as follows. Sect. 2 details the assumptions concerning the shell morphology and evolution and the time dependence of the spectrum from the central star. In Sect. 3 we describe briefly our treatment of the ionized region. In Sect. 4 we discuss the physical processes in the neutral region: chemistry, heating and cooling, radiative transfer, and shock processes. The results are presented in Sect. 5, and discussed in Sect. 6. Summary and conclusions follow in Sect. 7.

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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
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