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Mon. Not. R. Astron. Soc. 339, 524í536 (2003)

Anatomy of the HerbigíHaro object HH7 bow shock
Michael D. Smith,
1 2

1

Tigran Khanzadyan

1

and Christopher J. Davis2

Armagh Observatory, Armagh, Northern Ireland, BT61 9DG ïï Joint Astronomy Centre, 660 N. A'ohoku Place, University Park, Hilo, Hawaii 96720, USA

Accepted 2002 October 18. Received 2002 October 3; in original form 2002 August 21

ABSTRACT

We perform a detailed shock diagnosis of the HerbigíHaro object HH7, a well-defined bow shock from a protostellar outflow. We first present molecular hydrogen images in the 2í1 S(1) and 1í0 S(1) K -band emission lines. We then introduce revised models for magnetohydrodynamic bow shocks that incorporate a limited C and O chemistry and account for the shock thickness. We employ these models to interpret the new images as well as ISO data, the line profile, H2 positionívelocity diagram, optical images and the proper motion. This yields a C-shock model that satisfies the constraints, confirming that ambipolar diffusion is the linchpin in the shock physics. The best model is a slow-moving paraboloidal bow of speed 55 km s-1 , with a pre-shock density of 8 ½ 103 cm-3 and an H2 /H number ratio of just 0.25. The bow moves at an angle of 30 to the line of sight and at a position angle of 95 in the plane of the sky rather than along the outflow axis of 123 . The bow model also predicts the observed low line emission from H2 O, without the need for gas-phase depletion. Predictions for imaging and spectroscopy at far-infrared wavelengths, employing the 63-²m [O I] line, are presented. Key words: ISM: HerbigíHaro objects í ISM: individual: HH7 í ISM: jets and outflows í ISM: lines and bands í ISM: structure.

1 INTR ODUCTION Bow-shaped structures are observed in the environments of young stars, sometimes as isolated entities and sometimes as segments of coherent collimated structures (e.g. Schwartz 1978; Ogura 1995; Hartigan et al. 1996; Reipurth & Bally 2001). The symmetry axis of their concave structure, their high brightness and their proper motion usually suggest that they form when a flow is deflected around the head of a supersonic jet or dense clump which has propagated directly away from a young star (Mundt, Brugel & Buehrke 1987; Eisloffel, Mundt & Bohm 1994). Emission-line properties imply è è that the gas is excited by shock waves (Bohm 1978; Schwartz 1983). è Therefore, these bow shocks are either the locations of impact between protostellar outflows and their star-forming environments or internal shocks within collimated outflows. In the first case, a bow shock is significant as a medium to transfer momentum and energy into the cloud, which may help support or disrupt it. In the second case, the shock properties conceal information about the outflow physics and history. In either case, detailed modelling can improve our understanding of molecular dynamics and magnetohydro-dynamics (MHD) in star-forming regions. The HerbigíHaro object HH7 is an extensively investigated bow shock, separated from the probable driving protostar by other

E-mail: mds@star.arm.ac.uk (MDS); tig@star.arm.ac.uk (TK); c.davis @jach.hawaii.edu (CJD)

HerbigíHaro objects, denoted HH8í11, covering a projected extent of 2.4 ½ 1017 (D/220 pc) cm (Bohm, Mannery & Brugel 1980; Solf è &Bohm 1987). Here we shall assume a distance of D = 220 pc (see è Khanzadyan et al. 2002). In the optical emission-line images, HH7 does not actually possess a classical bow shape (Hartigan, Curiel & Raymond 89). As with Stapelfeldt et al. (1991), we interpret this as due to the superposition of two components: the forward-facing bow apex and a high-speed reverse shock in an advancing jet. HH7 belongs to a class of low-excitation HH objects (Bohm et al. 1980), è suggesting shock speeds under 100 km s-1 (Bohm & Solf 1990). è We present in this work a new near-infrared image produced from H2 when vibrationally excited to the second level. This 2í1 S(1) line emission is typically generated from gas with temperatures in the range 1000í5000 K or from gas fluorescently excited by ultraviolet (UV) or X-ray photons. Here, the bow shock wings dominate the jet shock, and these high-resolution United Kingdom Infrared Telescope (UKIRT) images place excellent constraints on the possible interpretations. Besides the 2í1 S(1) line, we reanalyse the 1í0 S(1) image presented by Khanzadyan et al. (2002) and the 1í0 S(1) positionívelocity diagram of Davis, Smith & Eisloffel (2000b). è Many previous near-infrared imaging and spectroscopy studies have made salient contributions [see Zealey, Williams & Sandell (1984), Zinnecker et al. (1989), Stapelfeldt et al. (1991), Gredel (1996) and others discussed below], mainly by analysing the emission from warm H2 . Further constraints are derived from diagnostics of even cooler gas, detected with the ISO: CO rotational lines and oxygen fine-structure lines were measured, albeit in rather large
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apertures which also encompass nearby HH objects (Molinari et al. 2000). Proper and radial motions in the optical and near-infrared yield additional model constraints for HH7. Noriega-Crespo & Garnavich (2001) have recently summarized the optical proper motion data, which yield a proper motion of 0.024 ‘ 0.014 arcsec yr-1 , with the position angle 108 ‘ 10 , rather than the direction away from the driving source of 123 . The tangential speed is thus below 25 ‘ 15 km s-1 (D/220 pc). Corrected near-infrared proper motions in the H2 1í0 S(1) line yield <47 km s-1 (D/220 pc) (Khanzadyan et al. 2002). Radial velocities are higher, partly because of the reverse shock in the jet, which can be distinguished spatially. The reverse shock generates H2 emission with radial speeds in a narrow range of about -80 to -100 km s-1 (Hartigan et al. 1989; Davis et al. 2000a). This same velocity range was found for `component 3' of the atomic lines H and [S II] by Solf & Bohm (1987). In contrast, è the local standard of rest (LSR) peak radial velocity for the bow shock emission is about -4 km s-1 (Zinnecker et al. 1989; Carr 1993; Davis et al. 2000a) for the H2 emission and about -51 ‘ 20 km s-1 for the optical atomic lines (Solf & Bohm 1987). The above è optical data yield an inclination angle to the line of sight in the range 8 í52 for D = 220 pc, only mildly constrained. Bow shock models are forged on the chosen combination of geometry, chemistry and physics (Raga, Bohm & Solf 1986; è Hartigan, Raymond & Hartmann 1987; Smith & Brand 1990b). Optical line emission from bows has been intensively modelled (e.g. Raga & Bohm 1986; Morse et al. 1993; Indebetouw & Noriegaè Crespo 1995). Model parameters are then varied to determine if a plausible region of parameter space exists. For the molecular emission, the main choice is between slow non-dissociative J-shock and C-shock physics (Hollenbach 1997). Without sufficient observational data, many recent investigations have still proved inconclusive (e.g. Yu et al. 2000; Larsson, Liseau & Men'shchikov 2002). For HH7, however, we now have an exceptionally wide set of observational constraints to attempt to model simultaneously. We have therefore refurbished the models to complement the data quality. Specifically, we have revised the cooling functions and chemistry of the CBOW (Smith & Brand 1990b) and JBOW (Smith 1994) models. Previously, we took a bow to be sufficiently large that the cooling length and shock thickness are negligible in comparison to the bow size. While this may be a good approximation at high densities, for the suspected low density of HH7 (104 cm-3 , Molinari et al. 2000) this may be false. Hence, we now include the distance travelled from the shock front in simulating the images. Four problems we would like to address for HH7 are as follows. (i) Carr (1993) raised the point that the bow shock models of Smith (1991a) predicted a hole in the H2 emission because the axis, where molecules are destroyed, should lie projected on to the bow. However, he did not observe the predicted hole (or the corresponding double-peaked distribution on a positionívelocity diagram). (ii) Fernandes & Brand (1995) concluded that a fluorescent contribution to the H2 emission lines is produced by UV radiation from the apex of a bow moving with a speed of 140 km s-1 . This contradicts the speeds derived from both proper motions and radial velocities. (iii) Everett (1997) found no evidence for a significant fluorescent component but, along with Fernandes & Brand (1995), found that line ratios such as the 2í1/1í0 S(1) ratio display no significant spatial variation. This would favour J-shock models, as discussed
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above. Yet the bow structure appears to be too compressed to be J-type. (iv) Molinari et al. (2000) remark on the lack of H2 O emission from HH7 and suggest that the water remains in the form of ice on the mantles of grains. This is supported by the presence of an H2 O crystalline feature. The prominent [O I] 63-²m emission line may then be due to oxygen release and excitation at the bow apex. If this oxygen was also present in the wings, however, it should be transformed into H2 O given a moderate shock heating to a few hundred kelvins. 2 OBSER VA TIONS AND D A T A REDUCTION 2.1 UFTI observations Observations of HH7 were carried out on the night of 2000 December 10, with the Fast Track Imager (UFTI) camera installed at the 3.8-m UKIRT, on the summit of Mauna Kea, Hawaii. The UFTI camera is supplied with a 1024 ½ 1024 pixel HgCdTe array and with internal optics that provide a pixel scale of 0.091 arcsec. This provides a total field of view of 1.55 ½ 1.55 arcmin2 . Images were obtained in the v = 1í0 S(1) transition of the H2 line using a 1 per cent narrow-band filter centred at = 2.122 ²m with full width at half-maximum (FWHM) of 0.02 ²m as well as in the [Fe II] line filter centred at = 1.644 ²m with FWHM of 0.016 ²m. Data reduction proceeded through standard routines which are presented in Khanzadyan et al. (2002); standard stars were observed to provide the flux calibration. 2.2 IRCAM 3 observations HH7 was also observed on 2000 December 11, using a newly reconfigured IRCAM 3 camera installed on UKIRT. IRCAM 3 has a 256 ½ 256 InSb array with a scale of 0.081 arcsec pixel-1 which provides a total field of view 20.8 ½ 20.8 arcsec2 . Images were obtained in the v = 2í1 S(1) transition of H2 using a 1 per cent narrow-band filter centred at = 2.25 ²m with FWHM of 0.04 ²m. Data reduction again proceeded through the above cited methods. There were no stars in the limited field of view of the IRCAM frames for frame registration. However, tip-tilt offset guiding was employed throughout the long integrations in 2í1 S(1) emission. During this time the pointing error between adjacent frames was better than 0.1 arcsec [and probably better than 0.5 arcsec between the first and last frame taken in 2í1 S(1) emission]. Consequently, registration based on telescope positions was employed to produce the final mosaic, which, when compared to the 1í0 S(1) image taken over a much shorter time-span, shows no evidence of smearing or frame misalignment (compare the images in Fig. 2). Note that each image was calibrated independently using standard stars observed for that purpose. 3 OBSER VA TION AL RESUL TS Fig. 1 displays the HH7 bow shock in detail. Sub-knot structures are labelled as a1 to a6. Table 1 presents the photometric results for the subknots. The circular aperture in arcseconds (second column), H2 1í0 S(1) line flux (third column), H2 2í1 S(1) line flux (fourth column) and [Fe II] line flux in units of 10-19 Wm-2 (fifth column) are listed. Note that the 1í0/2í1 S(1) flux ratio is typically in the range [9, 11]. Circular apertures were chosen to provide a simple and non-subjective measure for knots which will eventually change shape and strength.

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Figure 1. The HH7 bow in the H2 1í0 S(1) line with knot and subknot designations. Offsets are measured from the peak value. Table 1. Photometric resultsa for HH7A bow. Object H2 peak Ridge a1 a2 a3 a4 a5 a6
a

confirmation of the most plausible model below. The slit was located along the source axis, connecting HH7 with SVS 13.
[Fe II] (1.644 ²m) no det. no det. no det. 14 no det. no det. no det. no det.

Circ. apert. (arcsec) 2 2 2 2 2 2 2 2

1í0 S(1) (2.122 ²m) 259 231 136 132 71 104 97 86

2í1 S(1) (2.248 ²m) 26 24 13 9 no det. 11 8 7

4 THE MODELS AND MODELLING METHOD In the J-shock model, the medium first encounters a steep wave (the jump) which provides impulsive heating and acceleration. For shock speeds in excess of 25 km s-1 , a narrow zone in which the molecules are dissociated in energetic collisions then follows (e.g. Smith 1994). This is followed by rapid cooling in a radiative zone which produces the molecular emission. In the C-shock model, thrust from the magnetic pressure is gradually transferred to the molecules in a thick continuous region (Draine, Roberge & Dalgarno 1983). The transfer is mediated by the ions. With a low fraction of ions, the ions and magnetic field can diffuse through the neutral gas over a considerable distance, gradually transferring momentum via ambipolar diffusion. The much lower heating rate implies much more infrared emission from molecules up to shock speeds that can exceed 50 km s-1 (Smith & Brand 1990a; Smith, Brand & Moorhouse 1991b). Previous modelling suggests that J-type shocks are the exception mainly because they predict high-excitation H2 spectra, which are rarely observed (e.g. HH91A, Smith 1994; and HH43, Giannini et al. 2002). The H2 emission from J-type bows has also been shown to have a more extended spatial distribution than usually encountered (Davis & Smith 1996; Davis, Eisloffel & Smith 1996). è The schematic picture of a bow shock (Fig. 5) displays an apex around which molecules are rapidly destroyed. Notice that the shock speed is determined locally as the component of the bow speed transverse to the surface element, i.e. v s = v = v bow sin . Hence, sufficiently into the bow wings, molecules are not dissociated but
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Flux is given in 10-19 W m-2 units. Background noise level is 0.6 ½ 10-19 W m-2 for H2 1í0 S(1), 1 ½ 10-19 W m-2 for H2 2í1 S(1), and 0.4 ½ 10-19 W m-2 for [Fe II] observations.

The left panels of Fig. 2 present the two H2 images, rotated through 90 for ease of comparison with the models. This demonstrates the overall similarity of the flux distribution. The four right panels compare the linear flux distributions for the two H2 lines along two perpendicular slits through the 1í0 S(1) peak. This quantifies the depth of the emission `hole' and demonstrates the similarity of the flux distributions in both lines. The [Fe II] image is displayed in Fig. 3. Note that this flux is distributed very differently from the H2 fluxes, with no leading ridge and a peak lying well back from both the H2 peak as well as the H2 hole. A weak signal is apparent from within the hole. We include here a reprocessed UKIRT/CGS4 1í0 S(1) positioní velocity diagram, from data taken by Davis et al. (2000a). This diagram, Fig. 4, will be compared to a simulated diagram as a further

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Figure 2. Left panels: HH7 in emission from two vibrational levels of H2 S(1). An image rotation of 90 was performed to display as in the model figures. Offsets are measured from the HH7 peak; no continuum subtraction has been performed (unnecessary for HH7). The lower panel is in the v = 2í1 transition taken with IRCAM 3 and magnified for aligning with the UFTI image. The upper panel is in v = 1í0, taken with UFTI. Grey-scale bars indicate calibrated flux levelin10-19 Wm-2 arcsec-2 . Middle panels: Declination flux cross-cuts in the H2 v = 1í0 S(1) (upper) and H2 v = 2í1 S(1) (lower) line fluxes, measured along slits of width 0.54 arcsec. The offsets are measured in arcseconds from the peak value. The flux level is in 10-19 W m-2 arcsec-2 . Right panels: The same cross-cuts for the right ascension slits, labelled as `slit 2'.
18 16 14 12 arcseconds 10 8 6 4

Jet

Bow

- 4.3 km/s

- 83.7 km/s
2

3.2 km/s
0 -100 -80 -60 -40 velocity (km/s) -20 0 20

Figure 4. A positionívelocity diagram for the H2 1í0 S(1) emission from HH7 from a slit directed along the source axis, as defined by the HH7 and the exciting source SVS 13. The original data, observed with UKIRT/CGS4 and described by Davis et al. (2000a), have been reanalysed here.

Figure 3. HH7 in the [Fe II] line (grey-scale) overlaid with H2 v = 1í0 S(1) line (contours). Offsets are measured from the peak value in the H2 line which shows the difference between the peak locations.

vibrationally excited, while in the far flanks we may expect emission from low-lying rotational lines of H2 and CO, as well as oxygen fine-structure emission (partly depending upon the preshock conditions). We have thus established a CBOW model
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(Smith & Brand 1990b; Smith, Brand & Moorhouse 1991a; Smith 1991a) which has been employed to explain various data sets (e.g. Smith 1991b; Davis & Smith 1996; Eisloffel et al. 1996; è Froebrich, Smith & Eisloffel 2002). C-type bow shocks are parè ticularly difficult to model due to the sensitivity to the magnetic field strength and direction. For simplicity, we (1) parametrize the geometry of the bow surface, (2) treat each element of the bow surface as a distinct planar shock wave, (3) take a homogeneous pre-shock medium with a uniform magnetic field

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M. D. Smith, T. Khanzadyan and C. J. Davis
the total intensities and then determine the ion fraction and magnetic field. In our models, a uniform pre-bow field and ion fraction are the standard conditions, and ion conservation is applied (note that molecular ions may neutralize within a C shock whereas metal ions are long-lived). The carbon and oxygen abundances, (C) and (O), are subsequently varied in order to match any observed fluxes from O, C, OH, H2 O and CO. An initial H2 abundance, (H2 ), is also chosen, and contributes to determining the intensities and H2 excitation. An abundance of helium (He) = 0.1 and standard dust properties are included variables (which, however, we shall hold constant here). The shock may still be C-type even in locations where the field is parallel to the shock normal (Smith 1992). The effective transverse magnetic field is modelled as in Smith (1993) to account for this MHD switch-type property. The field direction thus contributes to the determination of v diss (Smith 1993) as well as to the spatial distribution of intensities. It can also be responsible for observed asymmetries despite a symmetric geometry. We model the bow shock as a large number of planar shocks, integrating over the polar and azimuthal angles and , after choosing the angles , and . We thus assume that the individual shocks, while resolved, are thin with respect to the local curvature. The component of fluid speed parallel to the shock surface is conserved, while the transverse components (neutrals and ions separately) decelerate as the fluid is compressed. Steady-state equations are applied. Planar C shocks are, however, unstable under a wide range of conditions when the transverse Alfven number (as determined by the transverse speed and the ef‡ fective transverse magnetic field) exceeds about 5 (Wardle 1990). The instability results when ions are pushed down magnetic field lines. This probably leads to a thicker, cooler shock than predicted here, along with isolated hot structures (Mac Low & Smith 1997; Stone 1997). On the other hand, ion neutralization would inhibit the instability. Runaway ionization through impacts can be initiated by fast ioníneutral streaming (Draine et al. 1983). We restrict the relative streaming speed to <42 km s-1 to account for this (Smith & Brand 1990a). The cooling function is composed of 14 separate parts (one of which heats the gas), as follows: 1 is gas-grain (dust) cooling; 2 is collisional cooling associated with vibrational and rotational modes in molecular hydrogen; 3 is collisional cooling of atoms; 4 is cooling through rotational modes of water induced by collisions with both atomic and molecular hydrogen; 5 is cooling through vibrational modes of water induced by collisions with molecular hydrogen; 6 is for vibrational modes of water induced by collisions with atomic hydrogen; 7 is cooling from the dissociation of molecular hydrogen; 8 is heating resulting from the re-formation of molecular hydrogen; 9 is cooling through rotational modes of carbon monoxide induced by collisions with both atomic and molecular hydrogen; 10 is cooling through vibrational modes of carbon monoxide induced by collisions with molecular hydrogen; 11 is cooling through vibrational modes of carbon monoxide induced by collisions with atomic hydrogen; 12 is [O I] fine-structure cooling; 13 is OH cooling; and 14 is [C I] fine-structure cooling, assuming local thermodynamic equilibrium (LTE).
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Figure 5. Top: The locations where radiative coolants make their maximum contribution are spread across a bow shock, as indicated here. Bottom: Several geometrical parameters are required to model C-type shocks with dissociative J-type caps: the bow shape, the orientation of the magnetic field, B, and the direction to the line of sight, , must be specified.

and (4) limit the time-dependent chemistry to that involving H, H2 , C and O. Several critical parameters influence the appearance of a bow shock in distinct manners, as described below. The bow shock geometry is chosen to be a surface of revolution of the form z 1 = d s R d
s

(1)

in cylindrical coordinates, where, for a paraboloid, d is also known as the semilatus rectum. The scalelength d and shape s are partly determined by matching the observed and model bow structures. The bow velocity v bow determines the location of the H2 emission (Smith 1991a): for bow speeds exceeding the dissociation speed, v diss , molecules are destroyed in the apex region before producing much radiation and the emission is dominated by the wings (Fig. 5). The orientation of the bow motion to the line of sight, , also influences the structure. Angles close to the line of sight are inclined to produce bright elliptical 1í0 S(1) structures (when v bow exceeds v diss ) since a warm annulus immediately behind the bow cap may then dominate (Fig. 5). The hydrogen nucleon density, n = n ( H) + 2n (H2 ), and the bow speed determine the total power, and hence strongly influence individual line intensities. The density is also critical to the shock cooling length, which combines with d to determine the relative thickness of the curved bow ridge. The ion fraction, , and magnetic field strength, B, also contribute to determining the shock thickness and the value of v diss (Smith & Brand 1990a; Smith 1993). Hence, we first estimate the density from

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All of these except 14 are transplanted from appendix A of Smith & Rosen (2002). A limited non-equilibrium chemistry is included, involving O, OH, C, CO and H2 O with rates as collected together in appendix B of Smith & Rosen (2002). 5 P ARAMETER FITTING 5.1 Spatial distribution We begin by taking a C-type bow shock and varying the velocity, orientation and bow shape. We find that a paraboloid (s = 2) at 30 to the line of sight with a speed 55 km s-1 reproduces the main features of the spatial distributions of the H2 1í0 and 2í1 S(1) emission lines. First, Fig. 6 demonstrates that an angle of = 15 produces a very

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circular hole in the H2 image. The corresponding intensity profiles, also shown in Fig. 6, possess deep minima, clearly inconsistent with the observed profiles of Fig. 2. On the other hand, an orientation of = 45 generates only a small dip with the emission dominated by the limb-brightened wings. An angle of = 30 , however, reproduces the observed characteristics of Fig. 2 extremely well. The best set of physical parameters, based on the following modelling, is termed our standard `Model A'. We derive a bow speed = 55 km s-1 , hydrogen density n = 8 ½ 103 cm-3 ,H2 fraction (H2 ) = 0.1, magnetic field B = 0.97 ½ 10-4 G (Alfven speed = 2kms-1 ), ‡ ion fraction = 5 ½ 10-6 , (O) = 5 ½ 10-4 , (C) = 4.1 ½ 10-4 , initially most of the C and O tied up in CO: (CO) = 4 ½ 10-4 . Fig. 7 shows that bow speeds of 30 and 80 km s-1 are inconsistent with the observations: 30 km s-1 generates a compact blunt arc

Figure 6. Three viewing angles of the same C-type bow shock (Model A). The bow has been rotated by 5 from the vertical direction, which we find reproduces the difference in level of the two maxima in the intensity profile of the horizontal slit (slit 1). Note that the maximum flux level is normalized to unity for display purposes.
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Figure 7. The bow speed determines the relative strength of the wings and the compactness in the H2 lines for the CBOW model. Note that the bow image has been calculated within a 60 ½ 80 grid, which can then be rotated through any angle and placed on the displayed 100 ½ 100 display grid. A rotation angle of 5 results in an asymmetry in the horizontal slit.

followed by a weak diffuse tail, whereas 80 km s-1 yields a strong tail with weak emission from the leading edge. Fig. 8 demonstrates that a shape close to a paraboloid is predicted. A too conical shape with no prominent hole results for the case s = 1.5 whereas a blunt shape with a deep hole in the emission results for the hyperboloid s = 2.5. The 2í1 S(1) image for the favoured model is displayed in Fig. 9. The similarity to the 1í0 S(1) image has led to the C-bow model being dismissed since it should arise from closer to the apex where hotter gas is present (Everett 1997). One can see, however, from Fig. 9 that the coincidence can be largely accounted for by projection. In particular, the intensity profiles across both slits match the observed intensity profiles. In the above manner, we have derived a `standard' bow configuration. To complete the modelling, we then determine the density and ion fraction. First, note that, given the shape and orientation, we find the size d = 4.2 ½ 1015 cm. A low density is required to explain the fluxes and derived cooling rates listed in Table 2. Moreover, the relatively low H2 fluxes indicate a low H2 fraction. The model value derived here is that 20 per cent of the H nucleons are in molecular form. We can query if this is consistent with the expected conditions in a molecular cloud or outflow. The formation time of H2 on grain surfaces is of the order of 1016 /(n cm-3 ) s in cool gas. Hence, the hydrogen atoms would associate on a time of order 40 000 yr for the predicted bow density. This is short in comparison to typical molecular cloud or clump ages, which can range from 106 to 108 yr. This suggests that the molecules have been partly destroyed in the outflow before HH7 arrives.

If HH7 has maintained the bow speed of 55 km s-1 , it is just 3000 yr since it departed from the source SVS 13. Therefore, molecule formation at the predicted density could certainly yield of the order of 10 per cent molecules in the flow time-scale. Molecule formation, however, can proceed much faster in a clumpy turbulent medium. Overall, the quite low H2 fraction is consistent with HH7 propagating through pre-shocked material. We find that the high CO fluxes require a high abundance of preshock CO. Nevertheless, plausible O and C abundances are found here. The strong [O I] emission is produced in the wings of the bow (as shown in Fig. 13), while H2 and CO cooling dominate near the front. In the bow wings, temperatures of a few hundred kelvins are not sufficient to transform the oxygen into water, while the quite low density increases the relative contribution of CO and H2 to the radiative line emission. Therefore, emission from H2 O does not dominate the cooling anywhere along the bow surface, explaining the few detected lines (Molinari et al. 2000). Note, however, that there is considerable uncertainty in how much of the large-aperture ISO fluxes should be attributed to HH7 itself. The extinction, which mainly reduces the observed shortwavelength H2 lines, is also uncertain. In Table 2, we apply the extinction as evaluated by Gredel (1996). The magnetic field orientation can influence the images when the field is strong, i.e. when the Alfven speed is high. Runs with ‡ transverse, rather than parallel, fields have been executed in the present low Alfven speed case, and no significant change found. ‡ A model with a resolved cooling length fits the observations. For comparison, a bow with unresolved shock thickness was simulated by increasing d by 10 to 4.2 ½ 1016 cm. The thickness of the
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Figure 8. The shape parameter s strongly influences the spatial distribution of the H2 emission in the CBOW model (Model A). In comparison to the middle panels of Fig. 6, the shape s = 1.5 yields a far too aerodynamic shape, and s = 2.5 presents a blunt nose.

Figure 9. The 2í1 S(1) image and intensity profiles for the standard HH7 CBOW model. These profiles can be compared to the observed profiles of Fig. 2.

leading arc (Fig. 10) was then found to be reduced to that generated by pure geometric considerations. This confirms, as concluded by Chrysostomou et al. (2000), that the C-shock structure is resolved in HH7. Increasing the ion fraction not only reduces the cooling length but moves the emission region away from the apex (since the dissociation speed decreases). A lower magnetic field has a similar effect. 5.2 Velocity distribution Further constraints stem from the resolved velocity information for the H2 1í0 S(1) emission. Positionívelocity diagrams derived from slits through the apex and hole show three components (Carr 1993;
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Davis et al. 2000a). As shown in Fig. 4, one component lies at about -84 km s-1 . It is spatially coincident with the [Fe II] and optical peak, distinct from the rest of the emission on the positionívelocity diagram. This is interpreted as the reverse shock in the jet, which appears to take the form of a Mach disc (see Fig. 3). The other two major peaks are coincident with the leading edge and the blueshifted edge which surround the bow apex. The leading edge is centred at a low radial speed (about -5 km s-1 ) relative to the local cloud (at 8 km s-1 ), while the weak blueshifted component is at about -12 km s-1 (see Fig. 4). The simulated positionívelocity diagram reproduces the two high peaks in their observed positions. The two peaks shown in Fig. 11 lie at about -4kms-1 and abo