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Astron. Astrophys. 321, 907-920 (1997)

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5. The excitation of molecular hydrogen

In addition to information on the morphology and kinematics of AFGL 2688 and NGC 7027, the present data provide new constraints on the H2 excitation, the physical conditions in the inner envelopes, and their evolution through the onset of PN formation. The following discussion addresses each of these aspects in turn.

The excitation of molecular hydrogen has been the subject of several theoretical investigations which are reviewed by Sternberg (1990) and Burton (1992). In proto-PNe and PNe molecular hydrogen can be excited in shock-heated gas (e.g., Draine et al. 1983; Burton et al. 1992) or excited by ultraviolet photons in photon-dominated regions (e.g., Sternberg & Dalgarno 1989; Burton et al. 1990). The infrared spectrum of the excited molecular hydrogen depends on the excitation mechanism and the physical conditions of the gas (but also on uncertain parameters such as the molecular hydrogen formation rate and the optical properties of the grains) and, in principle, the relative and absolute intensities of the ro-vibrational lines of H2 can discriminate between shock-excited and UV-excited H2. In shock-excited gas, the H2 spectrum is thermal and the relative intensities mainly depend on the density and the shock velocity (e.g., Shull & Hollenbach 1978). However, the line intensities also depend on the structure of the shock front and model predictions in the case of continuous (C-type) or jump (J-type) shocks differ by several orders of magnitude for the same density range (Burton et al. 1992). When the UV-excitation dominates, the molecular hydrogen emission spectrum varies with the density and the strength of the UV radiation field. For low radiation fields, radiative fluorescent emission is produced in low density gas, and collisional fluorescent emission is produced in denser gas (see Black & van Dishoeck 1987; Sternberg & Dalgarno 1989). In dense regions which are heated by intense UV radiation fields, collisions lead to thermal H2 emission for the low lying vibrational levels, similar to that seen in shocks (Sternberg & Dalgarno 1989; Burton et al. 1990).

Figures 6 and 7 display representative spectra (between 4480 and [FORMULA]) towards selected positions in AFGL 2688 and NGC 7027, respectively. Note that the profiles of the strongest lines show the characteristic sinc power function shape, indicating that the lines are not fully resolved, which should be possible with further observations using the same instrumentation. The intensities of the H2 transitions in AFGL 2688, which are identified in the lower left panel of Fig. 6, are listed in Table 1 for the four clumps (at the peak positions) and the [FORMULA] filament linking clumps N and E. Besides the molecular hydrogen lines, the spectra of NGC 7027 show the He I, He II, and Br [FORMULA] lines (identified in Fig. 7). Table 2 lists the H2 line intensities derived in NGC 7027 for the east and west peaks of the torus region, and for the northern, southern and north-east peaks of the outer structure.

[FIGURE] Fig. 6. K'-band spectra towards the four H2 clumps and the region connecting the northern and the eastern clump in AFGL 2688. The molecular hydrogen lines are identified in the spectra of the eastern clump
[FIGURE] Fig. 7. K'-band spectra towards selected positions in NGC 7027. The atomic lines are identified in the spectrum of the eastern torus and the H2 transitions in the spectrum of the north-eastern loop


Table 1. H2 Line Intensities at selected positions in AFGL 2688


Table 2. H2 Line Intensities at selected positions in NGC 7027

The range of the intensities of the 1-0 S(1) H2 lines observed in AFGL 2688 and NGC 7027 and listed in Tables 1 and 2 are compared in Fig. 8 with model calculations for shock-excited H2 and for excitation in dense PDRs (references to the models are given in the figure caption).

[FIGURE] Fig. 8. Model predictions of the 1-0 S(1) H2 intensity for shock-excited gas (upper panel) and UV-excited gas in dense photon-dominated regions (lower panel). a The predictions for the shock-excited H2 1-0 S(1) intensity is given as a function of shock velocity and pre-shock gas density for different shock front structures. The curves labeled C1 and C2 show the predictions for C-type shocks based on the models by Draine et al. (1983) with densities and transverse magnetic field strength of (104 cm-3, 50 [FORMULA] G) and (106 cm-3, 500 [FORMULA] G), respectively. The curves labeled J1 and J2 display the intensities predicted in the case of J-shocks by the model of Burton et al. (1992) - with the same paramaters as above. The curve J3 presents the intensities expected for a J-shock with a pre-shock density of 106 cm-3 in the absence of H2 O cooling and molecular reformation (based on the model by Brand et al. 1988 as given in Burton et al. 1992). b The H2 1-0 S(1) intensities predicted by PDR models are displayed as a function of density and radiation field strength in units of the interstellar radiation field (Habing, 1968). The predictions for [FORMULA]  10, 100 are from Sternberg & Dalgarno (1989) and those for [FORMULA] =103 -105 from Burton et al. (1990, 1992). The intensity range of the H2 1-0 S(1) line measured at the positions in NGC 7027 and AFGL 2688 (listed in Tables 1 and 2) is shown by shaded areas

For NGC 7027, the far-UV radiation at [FORMULA] from the star is estimated to be [FORMULA] (in units of the interstellar radiation field as given by Habing 1968) for a distance of 700 pc (Hajian et al. 1993) and a central star luminosity and temperature of [FORMULA] and T = 200,000 K, respectively (Robberto et al. 1993). The strong radiation field in NGC 7027 together with the typical observed H2 1-0 S(1) line intensities along the loops, i.e., the inner surface of the molecular envelope ([FORMULA]) are in agreement with the model predictions for UV-excited H2 in dense ([FORMULA]) PDRs. Such high densities are also required from analysis of millimeter and submillimeter transitions of molecules such as HCO [FORMULA], CN, or HCN (Cox et al. in preparation). Shock excitation is unlikely since the observed intensities would require shock-velocities in excess of [FORMULA] (Fig. 8a) and there is no indication in NGC 7027 of shocked molecular gas at these velocities.

However, the predicted intensities for [FORMULA] are lower than the 1-0 S(1) H2 intensities observed in NGC 7027. In order to reproduce the intensities of [FORMULA] radiation fields of at least [FORMULA] are needed, clearly inconsistent with the physical parameters of NGC 7027. Limb brightening could account for most of the discrepancy especially since the layer of hot gas emitting in H2 is very thin (with an optical depth of 0.1 to 0.3 mag) - see also Graham et al. (1993). But the many uncertainties inherent in the models (including the grain properties or the molecular formation rate) could also contribute to the present differences between the observed and the predicted values. In addition, there may be significant differences between the predictions of plane parallel static models and the complicated expanding surface seen in NGC 7027. Time dependent effects in PDRs have recently been discussed by Goldschmidt & Sternberg (1995), Hollenbach & Natta (1995) and Bertoldi & Draine (1995) and it appears that the emission from H2 can be significantly enhanced over the static case. Very large enhancements of the H2 emission (of several orders of magnitude) can occur at early times for low gas densities and high values of [FORMULA], but for the parameters relevant to NGC 7027 noted above the effects are expected to be relatively small (e.g, Fig. 7 of Hollenbach & Natta). In any event, in view of all these considerations we conclude that the H2 emission lines in NGC 7027 are compatible with excitation in dense UV excited gas.

Compared to NGC 7027, the central star of AFGL 2688 is extremely cool (T [FORMULA]  = 6500 K) and the UV field extremely weak. For an adopted distance of 1 kpc and a luminosity of [FORMULA] (Crampton et al. 1975), the far-UV radiation field is estimated to be only 10 times the interstellar radiation field at [FORMULA] which is the projected distance of the H2 clumps to the central stellar source. The intense 1-0 S(1) H2 lines observed in AFGL 2688 (Table 1) together with the weak UV radiation field cannot be accounted for by the PDR models summarized in Fig. 8b, or by time dependent enhancements. Dense, shock-heated gas appears thus as the only reasonable explanation of the H2 intensities observed in AFGL 2688 (Fig. 8a). For shock velocities of 10-30 km s-1, both J-type and C-type shock models predict the right intensities if the densities are high enough ([FORMULA]). The J-type model developed by Brand et al. (1988) - where H2 O cooling and molecule reformation have been ignored - predict the highest intensities (see curve J3 in Fig. 8a) and seems the most appropriate to explain the observed intensities. The model intensities of the H2 line are drastically reduced if H2 O cooling is included in the models (models J1 and J2) and for densities of [FORMULA] only a narrow velocity range around 13  [FORMULA] (model J2) may be able to reproduce the observed 1-0 S(1) intensities in the four clumps. The C-type shocks could also account for the observed intensities if the shock velocity is 20-30  [FORMULA] for densities of [FORMULA] or higher (models C1 and C2). High-velocity gas has been reported in AFGL 2688 at 20-40  [FORMULA] towards the clumps (Smith et al. 1990, this paper), together with gas at velocities of at least [FORMULA] (Young et al. 1992). High density gas (106  cm-3) in AFGL 2688 is indicated by the detection of strong CS(7-6) by Jaminet et al. (1992) and the detections of three far-infrared rotational transitions of CO by Justtanont et al. (1995). Among the possible shock models which can explain the H2 emission in AFGL 2688, the additional constraint introduced by the carbon-rich nature of this proto-PN favors the Brand et al. model (with no H2 O cooling) making the H2 1-0 S(1) line one of the main cooling lines in this source. The alternative explanation proposed by Jura and Kroto (1990) that the H2 emission arises in hot gas created by rapid supersonic streaming of the grains might reproduce the emission in the polar lobes but appears difficult to explain the equally strong H2 emission detected in the eastern and western clumps.

From the H2 line intensities observed in AFGL 2688 and NGC 7027 (Tables 1 and 2) vibrational and rotational excitation temperatures can be estimated. The rotational excitation temperature ([FORMULA]) was calculated from the [FORMULA] and [FORMULA] transitions, and the vibrational excitation temperature ([FORMULA]), for the v=2 level, from the [FORMULA] and [FORMULA] transitions. The results are given in Tables 1 and 2 for AFGL 2688 and NGC 7027, respectively. For both sources, T [FORMULA] is high relative to T [FORMULA]. In AFGL 2688, the difference amounts to 600 K for the northern and eastern blobs and to more than 1000 K for the southern and western blobs. The present temperature estimates are in good agreement with those made by Hora & Latter (1994). Using the same pairs of lines as above, we derive from the H2 line ratios listed in Table 3 in Hora & Latter (1994) T [FORMULA] and 1430 K for the eastern and northern blobs and T [FORMULA] for the eastern blob, in good agreement with the temperatures given in Table 1. From the more complete data set obtained by Hora & Latter, the northern and eastern blobs in AFGL 2688 do not appear to show significant deviations from a collisionally-excited spectrum. The estimated excitation temperature of 1600 K is close to the value of T [FORMULA]. The western and southern clumps have lower rotational temperatures (950 K) than the northern and eastern clumps (1600 K), which indicates that the red-shifted clumps in AFGL 2688 are less excited than their blue-shifted counterparts. In AFGL 2688, we derive for the northern blob a peak column density in the v=1, J=3 level of 8.2 1015  cm-2 after correcting for extinction (Table 1). Adopting T [FORMULA] =1650 K, we estimate a total column density N(H2) [FORMULA]  cm-2 (using a partition function of 40/T - see Isaacman 1984) in agreement with the estimate made by Hora & Latter.

For NGC 7027, the derived values for T [FORMULA] vary from 520 to 1350 K. This is in agreement with the rotational temperature of 870 K estimated from the [FORMULA] ratio of 4.1 measured in a 7 arcsec beam over the entire surface of the nebula by Smith et al. (1981). It is also in agreement with the values tabulated in Tanaka et al. (1989) who measured values of 5.2 and 3.1 in a 20 arcsec beam for the [FORMULA] and [FORMULA] ratios, respectively, yielding T [FORMULA] and T [FORMULA]. We note that using the [FORMULA] and [FORMULA] ratios, Tanaka et al. derived 1100 K and 1860 K for T [FORMULA] and T [FORMULA], respectively. In NGC 7027, T [FORMULA] is thus significantly smaller than [FORMULA] (Table 2, Smith et al. and Tanaka et al.). These deviations from a collisionally-excited spectrum are characteristic of UV-excited H2. The peak column densities in the v=1, J=3 level (after correction for extinction) are given in Table 2 for the main regions of NGC 7027. Adopting an excitation temperature of 1000 K, we estimate in NGC 7027 total column densities N(H2) [FORMULA]  cm-2, comparable to the values found in AFGL 2688.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998