The evolution of the neutral gas in planetary nebulae: theoretical models

Transcription

1 Astron. Astrophys. 337, (1998) The evolution of the neutral gas in planetary nebulae: theoretical models Antonella Natta 1 and David Hollenbach 2 1 Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I Firenze, Italy 2 MS 245-3, NASA Ames Research Center, Moffett Field, CA , USA ASTRONOMY AND ASTROPHYSICS Received 25 February 1998 / Accepted 18 June 1998 Abstract. This paper theoretically models the emission expected from shells (generalized to include tori or clumps) expanding away from the hot central stars of PNe. We examine the effects of shocks, FUV (6 ev <hν<13.6 ev), and soft X rays (50 ev < hν < 1 KeV) on the predominantly neutral gas and follow the time dependent chemistry for H 2, solving for the chemical and temperature structure and the emergent spectrum of the evolving shell. We consider a large interval of values for the mass of the central star (from 0.6 to M ) and for the shell properties, using its density and filling factor as free parameters. The calculations give the time dependent physical and chemical properties of the shell (temperature, fractional abundances of HII, HI, H 2 and electrons), as well as the intensities of a number of lines of molecular hydrogen (H 2 v=1-0s(1); v=2-1s(1); and v=0-0s(0), S(1), S(2), S(3), and S(4)) Brγ and the metal lines CII 158µm, OI 63µm, SiII 35µm, OI 6300Å, FeII 1.26µm, which can be compared to the observations and used to determine the physical parameters of the ejection process. We focus on the shell evolution after the star has achieved T > 30, 000 K. If the column density in the shell is sufficiently high, a threelayered shell is produced with an inner HII region, a central HI region, and an outer H 2 region. In this case, we can identify three phases in the evolution of the neutral shell. i) The early evolution (T 30, 000 K) is dominated by FUV photons, as the FUV photon luminosity Φ FUV of the central star peaks. The shell has a large column of warm H 2 and is very bright in all lines. The vibrationally excited H 2 lines at 2µm are dominated by thermal emission from collisionally excited levels; the heating is predominantly by grain photoelectric heating and FUV pumping of H 2. ii) At somewhat later times, as Φ FUV and gas density decline, the molecular gas becomes cooler and the line intensity decreases rapidly. This is the only phase in which the emission of the v=1-0 H 2 lines can be dominated by fluorescence, and this fluorescent phase is present only in PNe with low-mass central stars. iii) At even later times, the star heats to T >100,000 K and soft X-rays heat and partially ionize the neutral gas well above the values determined by the FUV stellar radiation. Send offprint requests to: A. Natta The duration (and presence) of these phases depends on the evolution with time of the stellar radiation field (i.e., on the mass of the central star), which is the main parameter that controls the PN evolution. For example, we find that a standard M =0.6M central star produces phase (i) from roughly 1000 to 5000 yrs, phase (ii) from 5000 to 7000 yrs, and phase (iii) from 7000 yrs onward. PNe with high mass central stars reach high effective temperatures very quickly, and spend most of their life in the X-ray dominated phase. A M =0.836 M case reaches phase (iii) in roughly 1000 yrs. The decrease with time of the H 2 line intensity (both in the near and mid-infrared) is less rapid than in PNe with low-mass central stars. Time-dependent H 2 chemistry enhances even further the intensity of these lines. As a result, we find that models with high-mass central stars are the only cases which radiatively produce strong hydrogen molecular line intensities in old (large) PNe. For standard values of the parameters the emission in the vibrationally excited H 2 lines produced in the shock between the expanding shell and the precursor red giant wind is generally small compared to the PDR emission. However, for large red giant wind mass loss rates, Ṁ RG > 10 5 M yr 1, the shock emission can be significant. Therefore, strong H 2 2 µm emission may also arise from shocks in old PNe. Key words: shock waves ISM: lines and bands ISM: molecules ISM: planetary nebulae infrared: ISM: lines and bands 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 0.1 M (Rodriguez et al. 1985; Schneider et al. 1987; Taylor et al.

2 518 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 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 ( M ) of cool molecular gas. Perhaps the largest body of evidence, however, comes from the observation of the H 2 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 H 2 v=2-1s(1)/h 2 v=1-0s(1) ratio is low, 0.1, 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 H 2 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 toruslike, 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 4π 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 H S(1) and 2-1S(1) emission, and the relative strength of the H 2 emission compared with the Brγ emission from the ionized nebula. The H 2 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 H 2 is either pumped and heated by FUV (11 ev< hν < 13.6 ev), or soft X-rays (50 ev < hν < 1 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 H 2 2µm emission. In addition to the vibrationally excited H 2 lines and to Brγ, we compute the intensity of a number of H 2 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 and erg cm 2 s 1 for the CII and OI line, respectively; ISO can detect lines with fluxes of the order of > erg cm 2 s 1. Finally, we compute the OI 6300Å and the FeII 1.26µm emission from the very warm (T > 3000 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 M sh M and a velocity v sh 25 km s 1, and fills a fraction f n of the solid angle seen from the star (see Pottasch 1984). The ionized gas is assumed to have a filling factor f HII f n ; f HII = f n corresponds to the case where only the inside of the neutral shell is ionized. An incomplete shell (f n < 1) 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 v RG 10 km s 1 (Loup et al. 1993). The shell has traveled R cm in t 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 T 30, 000 K, initiating a rapid rise in the luminosity of FUV (6eV<hν <13.6eV) photons, Φ FUV, and of Lyman continuum photons, Φ i. Later, T 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 T > 30, 000 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 threelayered shell is produced with an inner HII region, a central HI region, and an outer H 2 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

3 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 519 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 v sh, then the density in the shell will evolve as n t 2. 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 n t 3 (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 H 2 chemical timescale may be longer than the dynamical timescale and/or the timescales for the evolution of Φ FUV and Φ i. We therefore follow the time dependent chemistry of H 2, solving for the chemical and temperature structure and the emergent spectrum of the evolving shell (Hollenbach & Natta 1995). Bobrowsky & Zipoy (1989) model the H 2 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 The model 2.1. Shell morphology and evolution The central star is assumed to have had a prior red giant epoch of mass loss ṀRG M yr 1 and wind speed v RG 5 30 km s 1 (Loup et al. 1993). In our model where a constant velocity shell overtakes and shocks the red giant wind, these wind parameters only affect the intensities of the lines produced in the shock, and we can therefore separately calculate the FUV/Xray-induced emission from the PDR in the shell and the shock emission. It is the calculation of the thermal, chemical and dynamical evolution of the PDR shell which constitutes the bulk of this paper. We briefly discuss how the shock intensities vary with v RG and ṀRG in Sect. 4.4 and Sect The red giant wind epoch is followed by the onset of a rapid phase of high mass loss rate, or the ejection of a shell of mass M sh M. The shell formation and acceleration to speeds in excess of v RG may be associated with the rise in the effective temperature of the central star and the consequent increase in the radiation pressure on the outflowing gas and dust (see, e.g., Kwok 1993). Kwok et al. (1978) and Kwok (1982) have postulated that a high-velocity (> 1000 km s 1 ), radiationdriven wind is produced once the central star radiates primarily in the UV. The action of this wind on the slow red giant wind drives an overtaking dense shell into the coasting red giant wind. We have assumed that the end of the red giant epoch is marked by the ejection of a shell or by a period of extremely high mass loss, which begins as the effective temperature of the central star rises above T = 5000 K(t =0). The shell moves outward initially at 8 km s 1 (the speed of the red giant wind), but accelerates smoothly to 25 km s 1 as T rises from 20,000 K to 30,000 K (Kwok 1993). Once T >30,000 K, the shell moves outward at constant velocity v sh 25 km s 1 (Pottasch 1984). This occurs at a radius R cr = , , , and cm and time t cr = 2200, 760, 120, and 120 yr for the four cases of central stellar mass M =0.6, 0.64, 0.696, and M we consider. For t>t cr, R is given simply: R = R cr +(t t cr )v sh. (1) As a function of time, as the shell expands, the shell density n decreases. We model two cases which should represent the extrema in the density evolution of the gas. We assume that n = n 0 (R 0 /R) α, (2) with α =2or 3 representing, respectively, the case of a significant driving pressure (radiation or wind) from the central star or the case of a freely expanding, coasting shell. For constant mass shells with thickness dominated by the neutral gas, R is constant for α =2and R/R is constant for α =3. For convenience, we choose the fiducial radius R 0 = cm, as a typical size of a young PNe. Because of the different evolution in T for stars of different mass, and therefore the different times t cr when the shell accelerates to 25 km s 1, the time t 0 corresponding to R 0 varies somewhat with M : t 0 = 3000 yr for M =0.6M, 2450 yr for M =0.64 M, and 2050 yr for both M =0.696 and M. The neutral gas density n 0 at R 0 is related to the mass ejected in the shell, the solid angle of the shell, and the thickness of the shell. The neutral shell subtends solid angle Ω n =4πf n as seen from the central star; a similar equation with f HII applies for the solid angle subtended by the ionized shell. The parameter f n can therefore be utilized to model the ejection of toroidal or clumpy shells (f n < 1) as well as spherical shells (f n =1). We will use n 0 as our major free parameter. However, there is a minimum value n 0 required to fit the ejected mass in the specified volume at R 0. Assuming the shell is entirely neutral and that the density throughout the shell is n 0,itis ( ) n 0 > Msh f n cm 3. (3) 0.3M However, n 0 refers to the H 2 -emitting (T 1000 K) PDR density, and the outer (shielded) parts of the shell may be much cooler and denser. A weaker criterion is that the inner, hot PDR column of cm 2 (Tielens & Hollenbach 1985) must fit inside R 0. This criterion is simply n 0 > cm 3. We assume that the total mass M sh of the shell, including ionized and neutral components, is fixed. At any given time, the

4 520 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae Fig. 1. Sketch of the model geometry. See text for the symbols. total thickness of the shell is R, with an inner ionized portion of thickness R HII (the PN) and the possible existence of an outer neutral region of thickness R n. The density of the ionized region and the PDR portion of the neutral region are fixed at any instant of time: the electron density n e in the inner HII region is related to the assumed constant hydrogen nucleus density n in the FUV-illuminated inner neutral region by the relation n e =0.1 β HII n. (4) The parameter β HII is generally taken to be 0.5, which reflects the expectation that either the temperature in the neutral photodissociation region (PDR) will be 1000 K, or that the microturbulent velocities, which provide the neutral pressure, will be of order 3 km s 1 (Tielens & Hollenbach 1985). The implicit assumption is that pressure equilibrium applies between the HII plasma and the neutral PDR gas, and within the neutral shell. These assumptions are approximate, but necessary to speed the computation. When model results are compared to data, n should be interpreted as the average density of the H 2 emitting gas in the shell. It should be noted again that we have allowed for the ionized gas to expand away from the neutral torus or clumps and effectively fill a larger solid angle than the neutral gas, but we assume the electron density is constant throughout the HII volume that dominates the emission measure. In summary, the shell evolution is defined by the following parameters: M sh, v sh, α, n 0, f n, and f HII. In this paper, we assume M sh 0.3 M, v sh 25 km s 1, α =2 3, f HII = f n, and vary the PDR density n 0 at R 0 = cm (n 0 > cm 3 ) and the filling factor f n (< 1). Fig. 1 shows a schematic diagram of the shell model The evolution of the central star We have used the evolutionary tracks of Schönberner (1983) and Blöcker (1995) to determine the evolution of the FUV photon luminosity Φ FUV (t) and the Lyman continuum photon luminosity Φ i (t), as well as the effective temperature of the central star T (t). In these models, the mass of the progenitor star affects the resultant evolution and we have chosen four tracks, having core masses M =0.6, 0.644, and M, with precursor masses of 3, 3, 4 and 5 M, respectively. These models span the expected range of spectral evolution. Fig. 2 shows the evolution of T,L, Φ i and Φ FUV with time for the four models. The last two quantities have been computed using the model atmospheres of Clegg & Middlemass (1987) for T 180,000 K, and blackbody curves for higher T. The basic evolution of the four stars is similar, with a sharp increase of Φ i and Φ FUV as the stellar photospheric temperature increases, followed by a quick decline because, although T is continuing to rise, the photosphere is shrinking to maintain roughly constant bolometric luminosity. The rapid decline of Φ i and Φ FUV ceases when the star reaches the white dwarf cooling sequence. There is considerable uncertainty in the soft X-ray spectrum emitted from the central star of a planetary nebula (cf., Husfeld et al. 1984, Henry & Shipman 1986, Clegg & Middlemass 1987). As a standard case, we assume that the central star has a soft X-ray spectrum given by a blackbody of temperature T. Although the pattern followed by the four stars is similar, the evolutionary time scales are very different. Less massive stars peak in T, Φ i and Φ FUV at later times, reach lower maximum T (300,000 K for M =0.836 M vs. 150,000 K for M =0.6 M ), and then decline more slowly in all three parameters than more massive stars. The difference in maximum T has a very large effect on the soft X-ray heating of the neutral gas. 3. The ionized region For a given electron density n e =0.1β HII n and number of ionizing photons Φ i a simple ionization equilibrium calculation at T =10 4 K results in a value of the mass of ionized gas given by ( )( ) α M HII = Φ i48 n 1 fhii R 06 M, (5) β HII R 0 where Φ i48 =Φ i /10 48 s 1, n 06 = n 0 /10 6 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 n 06 /f HII to rather large values. Fig. 3 shows the values of M HII as a function of time for n 06 /f HII =10, α=2 (lower panel) and α=3 (upper panel). Fig. 3 and Eq. 5 demonstrate that the condition that the shell remain partially neutral for t < 10 4 yrs is ( ) ( )( ) n0 > Mcr fhii f 106 cm 3, (6) n M sh β HII f n where M cr 0.1M for M =0.6M and 0.02M for the higher stellar mass cases. Fig. 3 shows another important aspect of the PN evolution, namely that the fractional mass of ionized gas, which depends

5 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 521 Fig. 2. The four panels describe the evolution with time of the stellar radiation field for the four core masses we have considered: M =0.6 M (dot-short-dashed curve), M =0.64 M (dot-longdashed curve), M =0.696 M (dashed curve), and M =0.836 M (solid curve). The top left panel plots the effective temperature T, the top right panel the core luminosity L, the bottom-left panel the number of ionizing photons Φ i, the bottom-right panel the number of FUV photons Φ FUV. on the ratio Φ i /n, first increases with time, following the steep increase of Φ i, then decreases as Φ i 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 H 2 in the PDR. We characterize the emission of the ionized region with the radiated Brγ intensity, which, for an ionization-bounded shell, is given by I(Brγ) = R 2 17 Φ i48 erg cm 2 s 1 sr 1, (7) where R 17 = R/10 17 cm. Note that I(Brγ) does not depend on shell parameters such as density and filling factor, but provides a direct measurement of the stellar Lyman continuum radiation field. 4. Physical processes in the neutral region Fig. 3. Mass of ionized gas as a function of time for n 0/f HII = 10 7 cm 3 and four different core masses: M =0.6 M (dot-shortdashed curve, template model), M =0.64 M (dot-long-dashed curve), M =0.696 M (dashed curve), and M =0.836 M (solid curve). The upper panel is for n R 3, the lower panel for n R X-ray ionization and heating The bulk of the Lyman continuum flux incident upon the neutral shell, especially those photons with hν < 54.4 ev (the He + ionization energy), are absorbed (and produce) in the ionized HII region (the planetary nebula) interior to the neutral shell, with density n e and thickness R HII. However, a small fraction of the Lyman continuum photons, those with energies hν > 100 ev, significantly penetrate into the neutral gas to columns N cm 2, and partially ionize and heat the atoms and

6 522 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae molecules there. As T rises to its maximum of K, this fraction rises to values of We follow the attenuation of the soft X-ray flux and the ionization of the neutral gas, using standard cross sections for H, He and H 2 (e.g., Maloney, Hollenbach, & Tielens 1996). At the relevant photon energies ( 100 ev) hydrogen and helium dominate the X-ray opacity and the ionization is dominated by secondary electron collisions. An approximate analytic solution to the X-ray ionization rate ζ (per H) as a function of effective shielding column Ñ (see Maloney et al. for a description of the method of solution) is given: ζ = Ñ F 0 b Ñ e 18 b 0.75 s 1, (8) where Ñ18 = Ñ/1018 cm 2, Ñ = N 0 +N, N is the column in the PDR, N 0 = b cm 2, b = hν He +/kt, and F 0 is a parameter proportional to the incident X-ray photon flux (see below). Eq. 8 is valid for Ñ N 0, so that the ionization rate is dominated by photons with hν significantly above the He + ionization threshold. N 0 is furnished by the X-ray shielding column in the HII region and in the cm 2 transition region between the totally ionized HII region and the partially ionized PDR. F 0 is given by the following expression for the incident photon flux F ν (in photons cm 2 s 1 Hz 1 ) for hν > 54.4 ev or ν>ν He +: ( ) 2 ν F ν = F 0 e hν/kt, (9) ν He + ( r ) 2 ( νhe ) + 2 F 0 =2π, (10) R c where r is the stellar radius and ν He + = Hz is the threshold frequency for He + ionization. Eq. 8 is derived assuming that 0.4 of the primary electron energy goes into secondary ionizations, appropriate for x e < 10 2 (Shull & van Steenberg 1985). In our models the X-rays are mainly important as a heating mechanism for columns cm 2 < N < cm 2 and when the central star temperature rises above 10 5 K. The soft X-ray heating per hydrogen nucleus is given by (see Maloney et al. 1996) h x 2.5 f x hν H ζ, (11) where f x is the fraction of the primary electron s energy which is converted to heat, ν H is the Lyman edge frequency and ζ is the X-ray ionization rate given by Eq. 8. We adopt f x = [1 (1 x e )] from Shull & van Steenberg (1985); f x when X-ray heating is important Chemistry in the photodissociation region (PDR) Initially, the gas in the ejected shell or torus is assumed to be molecular, with all hydrogen H 2 and either all gas phase carbon (C/O< 1) or oxygen (C/O> 1) incorporated into CO. In this paper we assume a carbon-rich environment such that gas phase C/O > 1. The grains are assumed to be identical to interstellar dust, with standard abundances and size distributions. The HII region mass, the chemical abundances in the neutral gas, and the neutral gas temperature all then evolve with the rise and fall of the incident FUV, EUV (Lyman continuum) and X-ray fluxes and the falling gas density as the shell expands outwards. The EUV photons with 13.6 ev< hν < 54.4 ev create an inner HII layer, with evolving mass M HII (Fig. 3) and density n e. The FUV and soft X-rays dominate the chemistry and heating in the PDR. We note that the generalized definition of a PDR includes regions where the gas is entirely molecular H 2, but where the FUV or X-ray photons still dominate the heating or the dissociation of CO, OH or H 2 O (Tielens & Hollenbach 1985) H 2 chemistry The neutral hydrogen is initially entirely molecular, but the onset of the FUV flux sends a wave of dissociation into the neutral shell. We adopt a simple expression for the photodissociation rate from Draine & Bertoldi (1996, their Eq.[37]), ( ) [ dnh = I n H2 dt FUV ( ÑH 2 ) ] (1+ÑH e ) 0.5, (12) (1 + ÑH 2 ) 0.5 where the term in brackets represents the self shielding, ÑH 2 = N H2 / cm 2, N H2 is the H 2 column density, I = G 0 e N/ cm 2 s 1 is the dissociation rate without self shielding (the exponential term is the dust shielding of the FUV), G 0 is the FUV flux in the interval 11 ev< hν<13.6 ev in units of the ISRF ( photons cm 2 s 1 ), and n H2 is the H 2 density. H 2 is also dissociated by collisions with H, H 2 and electrons, by the ionization caused by non-thermal electrons from the soft X-rays (see Sect. 4.1), by reaction with O + (Maloney et al. 1996), and by reaction with C + and O at high (T > 500 K) PDR temperatures which allow activation energy barriers to be overcome. The O + destruction mechanism is only important in the X-ray ionized regions in which H + charge exchanges with O to form relatively high abundances of O +. The H 2 reforms on grain surfaces, and we assume the grains to have interstellar properties so that the formation rate of H 2 is given ( ) dnh2 dt gr = γ gr nn H, (13) with γ gr = cm 3 s 1, n the gas density and n H the atomic hydrogen density (cf., Tielens & Hollenbach 1985). H 2 can also be formed by the reaction of H with H. When X-rays are important, the electron (and therefore H ) abundance

7 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 523 is elevated so that this rate can become comparable to grain formation. This rate can be written ( ) dnh2 = γ dt H n e n H, (14) H where the rate coefficient γ H (in cm 3 s 1 ) is given by (Hollenbach & McKee 1989) ( γ H = T3 0.8 x(h) x(h)+53x(h + )T K ), (15) with T 3 = T/1000 K, x(h) is the fractional abundance of atomic hydrogen, x(h + ) that of protons, K = Φ FUV47 n 1 6 R 2 17 represents the photodissociation term for H, Φ FUV47 =Φ FUV /10 47 s 1, and n 6 = n/10 6 cm 3. In summary, we treat the H 2 chemistry in detail, numerically integrating the time dependent equations as the density and radiation fields evolve and as the ionization front and dissociation front move with respect to the PDR gas. Time dependent calculations are needed, for example, when the timescale for H 2 formation, τ H2 (10 9 /n) yrs (see Eq. 13), exceeds the yr timescale for changes in the FUV flux (see Fig. 2) or the timescale for molecular gas to advect through the PDR as the dissociation front advances Carbon and oxygen chemistry In this initial paper, we have greatly simplified the carbon and oxygen chemistry in order to maintain a relatively simple and efficient computer code. As discussed below, we analytically estimate the columns of C + and O, and estimate the possible contribution of OH and H 2 O to the cooling. We defer a careful treatment of the carbon and oxygen chemistry to a subsequent paper (Latter et al, in preparation), in which the results of this paper will be used as input to a separate chemical code which will provide, for example, CO, CO +, and HCO + line intensities and a careful calculation of OH and H 2 O abundances and the C + /CO boundary layer. The PDR results of Tielens & Hollenbach (1985), Wolfire, Tielens, & Hollenbach (1989), and Hollenbach, Tielens & Takahashi (1991) show that carbon is ionized to hydrogen columns of roughly N cr = ( n/g 0 ) 1 cm 2 and the oxygen is entirely atomic to this same column. Beyond N cr for C/O> 1, the oxygen is in CO, and all carbon not in CO is assumed to be atomic. For the case C/O<1, all the carbon is in CO and all oxygen not in CO remains atomic beyond N cr.in this initial paper, we use this prescription for the abundances of C + and O and calculate the temperature structure and the CII 158µm and OI 63µm, OI 145µm intensities. At columns <N cr, and when the temperature of the neutral gas is > 300 K and significant H 2 is present, neutral-neutral reactions with activation energies E/k , 000 K can proceed at a sufficiently rapid rate to produce large quantities of OH and H 2 O. The OH and H 2 O are destroyed by C + and by FUV photodissociation. O + H 2 > OH + H OH + H 2 > H 2 O + H C + + OH > CO + + H C + + H 2 O > HCO + + H The rate coefficients for these reactions, the reverse reactions, and the FUV photodissociation reactions are given, for example, in Hollenbach & McKee (1989). Although most of the oxygen is atomic, the cooling by OH and H 2 O in some cases may be important. We include this reaction sequence to provide an estimate of OH and H 2 O abundances in the extreme cases where their cooling may dominate in the PDR Ionization balance If the star has not reached its X-ray emitting temperatures, the ionization balance in the PDR zone is simply given by the FUV ionization of C to C +. However, when X-rays are important, H, H 2, and He are ionized by X-rays to form H +,H + 2 and He+. These ions are destroyed by recombination with electrons, reactions with atoms and molecules, and collisions with small grains and PAHs. Maloney et al. (1996) detail this chemistry and give approximate analytic solutions for the electron abundance x e. We use these analytic results, appropriately modified to include the effect of the external FUV field. The resultant electron abundance sets the level of X-ray heating (see Sect. 4.1) and helps to set the formation rate of H 2 via H Thermal balance and radiative transfer Heating mechanisms X-ray heating, which is important at low columns and high stellar temperatures, has been discussed in Sect The neutral gas is also heated by grain photoelectric heating (Bakes & Tielens 1994), FUV photodissociation of H 2 and photoionization of C, and FUV pumping or formation pumping of the H 2 molecule, followed by collisional deexcitation of the excited vibrational levels (cf., Tielens & Hollenbach 1985, Hollenbach & McKee 1989, Burton, Hollenbach & Tielens 1990). These processes are well known and are often applied in the context of equilibrium chemistry. The time dependent H 2 chemistry tends to produce higher H 2 abundances than an equilibrium calculation, and, as a result, enhances the significance of FUV pump heating by H Cooling mechanisms and radiative transfer Significant coolants in the neutral region include vibrational and rotational transitions of H 2, rotational transitions of CO, OH, and H 2 O, fine structure transitions of O, C + and C 0, grain cooling of the gas, and cooling due to adiabatic expansion. We also include collisional excitation of Lyα, OI 6300Å, SII 6730Å, and FeII 1.26µm, FeII 1.64µm, which are significant coolants if the neutral region is driven to T > 10 4 K. The

8 524 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae cooling rates for these processes have been taken from Hollenbach & McKee (1979,1989) and Tielens & Hollenbach (1985). The OI 63µm, CII 158µm, CO, OH, and H 2 O lines are treated with the escape probability formalism described in Hollenbach & McKee (1979), because their line opacities can be large and self-absorption followed by collisional deexcitation may be important. The emergent intensities in the lines are found by integrating the (escape probability-corrected) thermal emissivities through the thickness of the neutral slab, and dividing by 4π. For the case of the vibrational emission from H 2, we add to the thermal component a nonthermal contribution to the 1-0S(1) and 2-1S(1) intensities caused by the FUV pumping and formation pumping of the vibrational states (see Burton et al for details of this procedure). Our model for H 2 does not assume LTE, but calculates the statistical equilibrium of the vibrational levels as they are populated by collisions and FUV pumping and depopulated by spontaneous emission and collisions. We have checked in some cases our model results with those of Draine & Bertoldi (1996) and find good agreement (to within a factor of 2) with their more detailed treatement which included more up to date collisional rates and 299 bound states of the H 2 molecule. We also include the excitation caused by the collisions of H 2 with nonthermal electrons produced by X-rays (Voit 1991) Shock processes The shell, moving at v sh 25 km s 1, overtakes and shocks the red giant wind (v RG 10 km s 1 ) at a relative speed of v s 15 km s 1. Relative speeds of this order probably provide the maximum output of H 2 2µm shock emission. Slower shocks do not heat the gas sufficiently to produce the vibrational emission (which originates 6000 K above ground); faster shocks (v s > 25 km s 1 ) dissociate the H 2 (e.g., Burton, Hollenbach & Tielens 1992). The preshock density n RG (in cm 3 ) is given by the ambient density of the red giant wind at distance R from the central star n RG = R 2 17 Ṁ RG5 f 1 RG v 1 RG6 (16) where ṀRG5 is the rate of mass-loss in units of 10 5 M yr 1, f RG is the filling factor of the red giant wind and v RG6 = v RG /10 6 cm s 1. The intensity I 1 0 and I 2 1 (in erg cm 2 s 1 sr 1 ) of the 1-0S(1) and 2-1S(1) H 2 lines emerging normal to the shock is taken from an analytic fit to the J shock model described in Burton, Hollenbach & Tielens (1992). I 1 0 = v 2 s6 e v 2 s6 nrg4 ( n RG4 ) 1 (17) I 2 1 = v 2 s6 e 2.25v 2 s6 nrg4 ( n RG4 ) 1 (18) where n RG4 is the pre-shock density in units of 10 4 cm 3. These intensities are calculated from shock models by integrating the H 2 line emissivity through the shock. The population in the upper state of the transition is determined from a statistical equilibrium calculation which includes excitation by collisions and depopulation by collisions and spontaneous emission (see Hollenbach & McKee 1989). Eqs. 17 and 18 are good to within a factor of 2 for 0.5 < v s6 < 2 where v s6 = v s /10 6 cm s 1.We treat the shock as a J shock, as opposed to a C shock (Draine 1980), because the magnetic field in the red giant wind is presumably very small. In any event, our km s 1 J shocks produce more H 2 2 µm emission than a km s 1 C shock, which is cooler, so our treatment provides at least an upper limit to the H 2 2 µm shock emission. The luminosity in the lines (in units of L )isgiven L 1 0 = vs6 2 v 1 RG6 e v 2 s6 L 2 1 = vs6 2 v 1 RG6 e 2.25v 2 s6 f n f RG Ṁ RG5 (19) f n f RG Ṁ RG5 (20) for n RG < cm 3 and f RG f n. With these expressions, the ratio L 2 1 /L for v s =10 km s 1 and 0.2 for v s =17 km s 1, a value we have used in most of our calculations. It should be noted that in cases where the shell is driven by a fast (v w 1000 km s 1 ) wind from the central star, there are two shocks: a wind shock on the inside of the shell where the wind overtakes and drives the shell, and the ambient outer shock we have modelled above where the shell overtakes the red giant wind. Because the wind shock is highly dissociative, it is not a strong source of H 2 emission (Hollenbach & McKee 1989). It could, however, be a source of X-rays which penetrate and radiatively heat the neutral shell. 5. Results The numerical code used for the calculations treats the H 2 chemistry as a time-dependent problem and has been described by Hollenbach & Natta (1995). At t =0, the hydrogen in the shell is all molecular. As the temperature of the central star increases, the gas begins to dissociate and, at somewhat later times, to ionize. For our PNe modelling, the 1995 code is modified to include the formation of H 2 by H, the destruction of H 2 by X-ray ionization and by C +, O and O +, and the time-dependent change of density and column density caused by the expansion of the shell and the advance (or recession) of the ionization front caused by the time dependence of the incident ionizing flux and the changing density. We have run a grid of models, varying the shell parameters (e.g., n 0, f n, α) and the central core mass M. In this section, we will discuss the properties and evolution of the shell by referring to a standard case (see Table 1; He, C and O abundances are from Perinotto 1991, other metal abundances are solar), which provides a useful template for the understanding of the physical processes. The template model has a core with mass M =0.6 M, which is typical for PNe in general, but which may be lower than the stellar masses associated with H 2 -emitting PNe. As discussed in Sect. 1, the latter group is observed at low galactic latitudes and are thought to originate

9 Table 1. Parameters of the Template Model A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 525 M = 0.6 M M sh = 0.3 M v sh =25kms 1 for T eff 30,000 K n 0 =10 6 cm 3 α=2 f n=0.1 f HII=0.1 β HII=0.5 He/H=0.13 C/H= O/H= from more massive progenitors than average. The model has a value of n 0 /f n =10 7 cm 3, which ensures that a portion of the shell remains neutral for all relevant times, yet which results in an electron density n e0 = cm 3 at R 0 = cm that does not greatly exceed observational limits. We note that if f HII f n, n e0 refers to the high density HII gas directly adjacent to (and in thermal pressure equilibrium with) the neutral PDR gas, whereas considerable HII may be at lower densities. The main purpose of the template model is to allow us to discuss the various physical processes and their relative importance in different phases of the evolution. As we will see, the same phases occur for higher M, but the duration of some is much shorter. We will first (Sects. 5.1 to 5.5) discuss the structure of the shell as a function of time and the H 2 emission which originates in the irradiated neutral shell. For simplicity, we will define this emission as PDR emission. The H 2 emission produced in the shock between the expanding shell and the precursor red giant wind will be discussed in Sect The shock emission does not depend on the shell structure, as long as there is sufficient column in the shell to shield the preshock gas and maintain the H 2 abundance in the red giant wind. The shock emission depends only on the shell speed and on the preshock density and speed of the red-giant precursor wind (cf. Eqs. 17 and 18). Fig. 4-8 summarize the properties of the PN shell in the template model. Fig. 4 shows the mass of the ionized, atomic and molecular gas and the density of the atomic gas as function of time. The structure of the neutral shell at selected times is shown in Fig. 5, which plots temperature, electron abundance and atomic and molecular hydrogen abundance as functions of the depth in the shell. The slight discontinuities at N cr cm 2 are due to our simplified chemistry, which abruptly introduces CO at that column. Fig. 6 and 7 show for the same times the rates of gas heating and cooling and the dominant processes of formation and destruction of H 2. Fig. 8 plots the intensity of the PDR H 2 1-0S(1) line and the ratio of 2-1S(1)/1-0S(1) as a function of time. Fig. 4. The dependence of the density on time in the template model is shown by the solid curve. The fractional shell mass in ionized (dashed line), atomic (dotted line) and molecular (dot-dashed line) hydrogen are also plotted as a function of time. Note that this shell remains mostly neutral; the HII region contains only a small fraction of the total mass, 1% at most. central star, as G 0 /n, or equivalently (Φ FUV /R 2 )/n, increases (Fig. 4). The hydrogen chemistry is dominated by formation of H 2 on grain surfaces and by destruction of H 2 by FUV photons and by reaction with C + and O. The maximum of G 0 for the template star occurs at about 2200 yr. At this time, the shell is mostly atomic to a column of about cm 2 and there is a large column of warm H 2 (T> 1000 K), heated by the grain photoelectric heating mechanism and FUV pump heating of H 2 (Fig. 5 and 6). The average temperature of the H 2 2 µm-emitting layers is 2000 K and the ratio of the 2-1S(1) to 1-0S(1) line is of the order of The PN is very bright in the H 2 lines, with an intensity in the 1-0S(1) of the order of 10 3 erg cm 2 s 1 sr 1 between 500 and 3000 yr. This thermal FUV-dominated phase lasts until about t 5000 yr. For t > 2200 yrs, G 0, n, and G 0 /n all decrease. The dissociation front moves to lower column density (< cm 3 at t=4000 yr) and the molecular gas is cooler and less dense. The H 2 emission decreases and fluorescent emission becomes relatively more important and dominates the spectrum for t yr. The H 2 ratio 2-1S(1)/1-0S(1) increases and may reach 0.5, characteristic of fluorescent emission. In this fluorescent FUV-dominated phase at t 5000 yr, the template PN has a typical surface brightness in the 1-0S(1) line of erg cm 2 s 1 sr FUV-dominated phases: thermal and fluorescent At t=0 the shell is completely molecular. As time proceeds, the fraction n H /n H2 begins to increase on the shell side facing the 5.2. X-ray dominated phase In the later stages of the evolution (t >5000 yrs in the template model) the star heats to T >100,000 K and soft X-rays

10 526 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae Fig. 5. Temperature (solid line) and fractional abundance of H I (dotted line), H 2 (dot-dashed line) and electrons (long-dashed line) are shown as function of the column density of hydrogen nuclei in the neutral shell at different times for the template model. The star illuminates the shell from the left. At each time, column density zero marks the edge between the ionized and neutral regions of the shell. The effect of soft X-rays on the electron abundances is clearly seen at columns N < cm 2 for t> 4000 yrs. There is considerable H 2 at T 1000 KatN cm 2. heat and ionize the neutral gas well above the values determined by the FUV stellar radiation. This results in an enhanced emission of all those lines that are temperature sensitive, such as the thermal component of the H 2 2 µm lines as well as optical (e.g., OI 6300Å and near-ir metal (e.g., FeII 1.26µm and FeII 1.64µm) lines. The increased importance of the soft X-ray relative to FUV photons affects not only the line emission but the hydrogen chemistry as well. In a relatively cool shell, H 2 forms on grain surfaces and is destroyed by FUV photodissociation. When X- rays are present, the chemistry becomes much more complex. A number of other processes, such as destruction of H 2 by collisions in T > 4000 K gas, by reaction with C +, O and O + and, in some cases, by direct dissociation from the non-thermal electrons produced by the X-rays, as well as formation of H 2 by reaction with H, become important. Cooling by collisionally excited metal optical lines and Lyα dominates at small column densities where T > 5000 K. The importance of the X-ray emission of the central star in the later stages of the PN evolution can be better appreciated by comparing the thermal component of the H 2 intensity to the results of models with the same parameters where the X-ray flux of the central star is artificially set to zero (Fig. 9, top panel). The line intensity is the same in the two models at early times, when the shell physics is dominated by the FUV photons, but diverges at later times (t 5000 yr for M =0.6 M ), following the decrease of Φ FUV. It should be emphasized that the intrinsic soft X-ray luminosity of the central star is quite uncertain; therefore the observation of X-ray heated H 2 emission at late times may probe the soft X-ray spectrum from a given core. Note that in the template model the H 2 emission in the vibrationally excited lines is dominated by fluorescent emission for t yr, and the effects of the X-rays on the total H 2 line intensity is negligible. Fig. 9 shows only the thermal component of the line emission. In terms of the H 2 2 µm emission, it is more important to include X-rays in the PDR description of PNe with high mass cores (see Sect. 5.3) than with low mass cores High mass central stars The shell evolution depends strongly on the mass of the central star, which, in turn, determines the time dependence of the radiation field to which the shell is exposed. A higher mass core results in a faster evolution of the physical properties and emission spectrum of the surrounding shell. The FUV thermal phase and the X-ray thermal phase still exist (the fluorescent phase never dominates the 1-0S(1) emission for high mass cores), but occur on much shorter timescales. Moreover, since higher mass cores reach higher T, soft X-rays are more important and dominate most of the evolution of the shell.

11 A. Natta & D. Hollenbach: The evolution of the neutral gas in planetary nebulae 527 Fig. 6. The dominant heating and cooling rates are shown as function of the column density in the neutral shell at various times for the template model. t=2200 yr: the solid line is the rate of net grain photolectric heating, the dot-long-dashed curve the heating due to FUV pumping of H 2 followed by collisional de-excitation, the long-dashed line the cooling rate for H 2 rotational and vibrational line emission, the dot-short-dashed line (labelled H 2d) the rate of cooling due to dissociation of H 2, the short-dashed line the rate of OH+H 2O cooling, the dotted line the rate of CO cooling. At this time, two other cooling processes (cooling by emission in the OI 6300Å, SII 6700Å and FeII 1.26µm and FeII 1.64µm lines and cooling due to collisions with grains) contribute to the total cooling at small column density. We have omitted them to avoid confusion. t=4000 yr: the heating is due to FUV pumping of H 2 (dot-long-dashed), photoelectric effect (solid) and X-ray heating (dotted), the cooling to emission in the H 2 vibrational and rotational lines (long-dashed), O I 63µm (short-dashed) and optical and near-ir lines (dot-short-dashed). t=7000 yr: the heating is due to X-rays (dotted) and H 2 FUV pumping followed by collisional deexcitation (dotlong-dashed), the cooling to emission of Ly α (solid), O I 63µm (short-dashed), optical and near-ir lines (dot-short-dashed), and H 2 (long dashed). Fig. 10 compares the H 2 predicted emission for models with increasing core mass. The other parameters are as in the template model (Table 1). All the curves begin at the time t cr when T =30,000 K. (this corresponds roughly to the 1-0S(1) peak in the thermal FUV-dominated phase). The curves initially decrease rapidly with time as G 0, n, and G 0 /n decline (see Fig. 2). This sharp decline stops as soon as the stars reach the white dwarf cooling tracks. The different components of the H 2 1-0S(1) line for M =0.836 M are shown in Fig. 11 panel a). We use a logarithmic time scale, to show the early evolution of this model in detail. The X-ray peak at t 440 yr corresponds to the peak in T (see Fig. 2), which is also traced by the peak in the contribution from direct excitation of H 2 by the nonthermal electrons produced by the X-rays. Fig. 9, bottom panel compares the H 2 intensity to the results of a model where the X-ray flux is set to zero at all times. For this extremely high mass core the FUVdominated phase lasts only few hundreds years, and the X-ray radiation heats the gas and maintains the H 2 excitation at later times. Without X-rays the H 2 intensity falls below < 10 5 erg cm 2 s 1 sr 1 after t 1300 yr, while, when the X-rays are included, the intensity of this line is still > 10 5 erg cm 2 s 1 sr 1 at t 3800 yr. The intensity of the 2-1S(1) line is shown in Fig. 11, panel b), and the ratio of the two lines in Fig. 11, panel c). The 2-1S(1) line has a large fluorescent contribution at t > 1000 yr. The relatively high 2-1/1-0 ratio at earlier time is due to the high temperature of the H 2 -emitting gas. The small thermal peak in 1-0S(1) at t = 470 years, with the corresponding dip in the 2-1/1-0 ratio, may not be real but may result from the H 2 dissociation front, the dominant 2 µm emitting region, and the (artificial) C + /CO transition all occurring at the same column at this time. More realistic C + /CO chemistry will likely remove this glitch. We have tested and found it not to be a product of (space or time) numerical grid size, but a product of the combination of time dependent H 2 chemistry with the C + reaction on H 2 at the C + /CO boundary Time-dependent H 2 chemistry The importance of properly taking into account the time dependence of H 2 chemistry can be assessed by looking at the results shown in Fig. 12, where we plot the ratio of the H 2 1-0S(1) intensity to the predictions of equilibrium models with the same parameters. Time-dependent models predict an H 2 intensity higher than equilibrium models in those phases of the