HIGHLY EXCITED H₂ IN HERBIG–HARO 7: FORMATION PUMPING IN SHOCKED MOLECULAR GAS?

Shock waves in molecular clouds are often created by the collisions of supersonic outflowing gas from pre-main sequence stars with ambient molecular gas from the clouds out of which the stars formed. The shock structure and physics are commonly studied using the emission lines of molecular hydrogen (H₂), which is dissociated when collisions of H₂ and atoms or molecules occur at speeds exceeding 20–24 km s⁻¹ (Hollenbach & Shull 1977; Kwan 1977; London et al. 1977). In many cases the relative velocities of the outflow and cloud far exceed this limit (e.g., Nadeau & Geballe 1979), yet in many shocked clouds, strong H₂ lines with broad velocity profiles are seen.

The commonly accepted solution to this puzzle has been to invoke continuous shocks (C-shocks), in which the ambient cloud is heated and gradually accelerated, first by collisions with ions in a magnetic precursor, and then by previously swept up molecular gas (Draine 1980; Chernoff et al. 1982; Draine & Roberge 1982). The slower acceleration can result in a low peak temperature (typically 2000 K) of the shock-heated gas and the rough maintenance of that temperature over a long column of shocked gas (Smith et al. 1991), reducing the amount of dissociation. Shocks speeds can be as high as ∼45 km s⁻¹ before complete dissociation of the molecular gas occurs (Draine et al. 1983). The expected relative line intensities in such low temperature C-shocks are in contrast to jump shocks (J-shocks), in which, for velocities exceeding several km s⁻¹, the molecular gas is suddenly heated to much higher temperatures and then quickly cools, resulting in a wide range of temperatures in the post-shock gas. Excitation of H₂ by ultraviolet radiation produced in the shock is another means by which the H₂ can be excited into emission in its ro-vibrational lines (Black & van Dishoeck 1987; Sternberg & Dalgarno 1989; Burton et al. 1990). UV excitation produces a spectral signature distinct from that of collisionally heated H₂. An additional possibility is dissociation of the H₂ at the shock front, followed by reformation of H₂ on dust grains behind the shock front, with radiative cascading of H₂ ejected from the grains down the vibrational ladder, eventually resulting in vibrational local thermodynamic equilibrium (LTE), as well as collisional thermalization of rotational levels (Flower et al. 2003).

Early attempts to distinguish between various shock types and cooling zones, which utilized measured relative intensities of H₂ lines mostly in the Orion Molecular Cloud (Beckwith et al. 1978) and comparisons of velocity profiles at Peak 1 (Moorhouse et al. 1990), all found that that by themselves C-shock models were incompatible with the observations (Brand et al. 1988, 1989; Burton et al. 1989b). Probably the most significant of these tests (Brand et al. 1988) was the measurement of 19 ro-vibrational and pure rotational lines between 2 and 4 μm at Peak 1, whose upper energy levels ranged up to ∼25,000 K. The extinction-corrected relative intensities appeared to be more consistent with post-shock cooling starting at very high temperatures, i.e., in the absence of a shock-softener.

All of the tests mentioned above were made with angular resolutions of several arcseconds, so it is possible that each observation took in a large number of C-shocks producing widely different peak temperatures, which might have blurred a potentially observable distinction between C-shocks and other possible explanations. More recent observations (e.g., Fernandes & Brand 1995) used smaller apertures, but covered only small regions of the shocked gas. In addition, the lower instrumental sensitivities at those earlier times, although allowing the detection of a number of weak lines from energy levels much higher than expected in C-shocked gas, may have prevented a more complete understanding of the line emission. Now, more than two decades later, larger telescopes and improvements in instrumentation have made it possible to observe H₂ lines at an order of magnitude higher angular resolution and with much higher sensitivity, and thus to begin to examine shocked interstellar molecular gas in greater detail.

The collimated outflow (jet) from the protostar SVS13 has produced a collection of Herbig–Haro objects, HH7–HH11, with a classic bow shock, HH7, at its eastern end, as shown in Figure 1. The bow shock is bright in line emission from molecular hydrogen (Garden et al. 1990). As in the shock in the Orion Molecular Cloud, H₂ lines from upper energy levels as high as ∼25,000 K have been detected in HH7 (Fernandes & Brand 1995). At a distance of only 250 pc (Enoch et al. 2006), HH7 is at about half the distance of the Orion Molecular Cloud and its morphology projected onto the sky is much simpler. Estimates of the inclination of HH7 to the line of sight vary considerably, but suggest an angle of ∼40° (Bachiller & Cernicharo 1990; Carr 1993; Fernandes & Brand 1995; Khanzadyan et al. 2003; Smith et al. 2003). The proximity of HH7, the relative simplicity of the geometry of the shock, and the brightness of the line emission suggested to us that HH7 would be a favorable object for investigating the detailed physics in a molecular shock.

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Integral field spectra of a small section of the HH7 bow shock (shown in Figure 1), adjacent to the cap of the bow shock, were acquired at the Frederick C. Gillett Gemini North Telescope on Maunakea, Hawaii using the facility Near-Infrared Field Spectrometer (NIFS; McGregor et al. 2003) on UT 2007 October 16 and December 22, for program GN-2007B-Q-47. The field of view of NIFS is 30 × 30 with individual spaxel sizes of 004 × 010. The grating in NIFS, which provides a spectral resolving power of 5000, corresponding to a velocity resolution of 60 km s⁻¹, and a velocity sampling of 30 km s⁻¹, was positioned to cover the wavelength range 2.01–2.45 μm. Adaptive optics was not employed, as no nearby star of sufficient optical brightness is available for natural guide star adaptive optics and no suitable tip-tilt star is available near HH7 to allow laser guide star adaptive optics. The observations were made in photometric skies with seeing of 035 or better (FWHM) in the K-band. The precipitable water vapor above Maunakea was ∼3 mm on the first night and ∼2 mm on the second.

The observations of HH7 consist of 10 exposures of 552 seconds each on 2007 October 16 and 16 exposures of 660 seconds each on 2007 December 22, with half of the exposures on target and half on adjacent sky. The target position was acquired each night by offsetting from a nearby star. A telluric standard (HIP 10559; A0V) was observed immediately prior to HH7 on each night.

Baseline reductions of the NIFS data cubes were performed using Gemini software within the NIFS IRAF package. The calibration data included K-band flats, spectra of argon and xenon arc lamps, darks, and flats observed through a Ronchi mask. The science and telluric standard data were both dark-subtracted and divided by the flat field. The wavelength solutions to the arc spectra were applied and the data shifted to a heliocentric wavelength scale. Some bad pixels were replaced by interpolated values. The spectra of HH7 were divided by the spectrum of the reference star to remove the effects of atmospheric absorption and instrumental transmission and to provide flux calibration.

In the K-band the bow shock is visible only in H₂ emission, which has no point-like distinguishing characteristics. Consequently, blind offsetting from a nearby visible point source was used to position the field of view of NIFS. This resulted in a small positional difference between the two nights. During each night positional offsets were minimal. After inspection by eye the images from one night were shifted to align the two data sets and then all images were combined. The alignment is believed to be accurate to better than a spaxel. This cube was then trimmed to remove outer regions of low signal-to-noise ratios, mostly regions where the data cubes from the two nights did not overlap. The final data cube has 005 × 005 elements covering a 36 × 29 region (R.A. × decl.) and spans the wavelength interval 2.011–2.446 μm. The spectra in the cube have been multiplied by a blackbody function having the temperature of the A0V reference star (9480 K) to produce final ratioed spectra in dimensions of F_λ. Approximate flux calibration was obtained by scaling the NIFS spectra at the peak of the H₂ line emission to the observations by Smith et al. (2003).

Figure 2 is a map of the 1–0 S(1) line intensity (integrated over its full velocity profile) in the observed region, and Figure 3 contains separate intensity maps of the two velocity components that make up the bulk of the line emission. The morphology of the total line emission closely matches that of Figure 1 (Khanzadyan et al. 2003), with the leading edge of the bow on the eastern edge of the field of view and the brightest emission approximately 0.8 arcsec to the west of that edge. Further to the west a second and considerably fainter ridge of line emission is present across the region. At the location of the tip of the bow (top left of Figure 2) the intensity is somewhat lower than along the side of the bow, also consistent with the image of Khanzadyan et al. (2003).

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Figures 4 and 5 show sets of spectra of 030 × 030 regions at fixed declinations, crossing the bow shock in right ascension (with decreasing R.A. from top to bottom in these figures). As discussed below, all of the observed emission lines are from H₂. Velocity profiles of the 1–0 S(1) line in each region are shown on the right sides of the figures. The locations of these spectra are marked in Figure 2. The spectra reveal that the peak intensities of all of the stronger lines vary roughly in lockstep as the individual line intensities change by over an order of magnitude across the region. The 1–0 S(1) line profiles show that the line emission occurs largely in two velocity intervals. Intensity maps of these two components are shown in Figure 3. The brightest emission, in the eastern part of the data cube, peaks near −15 km s⁻¹ (all velocities are in LSR, the Local Standard of Rest). The line profiles there are roughly symmetric as viewed at the instrumental resolution. Behind the front (to the west) this velocity component weakens rapidly to one-tenth of its peak intensity, the line broadens, and the line centroid shifts to more negative velocities, as a second component centered near −100 km s⁻¹ appears. Due to the intrinsic velocity widths of these components and the modest resolution of NIFS the two components are only partially resolved. The blueshifted second velocity component appears in the total intensity map in Figure 2 as the aforementioned ridge to the west of the brightest region, whereas in Figure 3 it is clearly seen as a separate morphological feature. The location of this second component is consistent with the findings of Davis et al. (2000), who observed HH7 at higher spectral resolution but lower angular resolution. Both the location and the high negative velocity suggests that this component is associated with the reverse shock in the jet, created as the outflow from SVS13 begins to impact the bow shock.

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Close inspection of the profiles of the strongest lines reveal very weak wings extending ±300 km s⁻¹ from line centers. However, spectra of strong arc lamp lines show similar wings, so the wings are instrumental artifacts.

Thirty-eight emission lines due to H₂ are detected in the data cube. Most of the lines can be seen in the spectra contained in Figures 4 and 5, but in order to provide higher signal-to-noise ratios on the very weak lines for more detailed analysis, a spectrum of the 06 × 09 region centered at R.A. and decl. offsets of −10 and 05, respectively, was extracted and is shown in a more expanded form in Figure 6. The lines and their relevant parameters are listed in Table 1. The dynamic range, between the strongest (1–0 S(1)) and weakest detected lines, is approximately 1500. It is this high dynamic range together with the high sensitivity of NIFS that makes possible the new analysis presented in this paper.

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Table 1.  Observed H₂ Emission Lines^a

Line	Rest λ	Upper Level	A	Observed	Dereddened	Notes
ID	Vac. (μm)b	Energy (K)b	10−7 s−1c	Intensityd	Rel. Intensitye
1–0 S(2)	2.0338	7585	3.98	80.8	43.0	⋯i
4–3 S(17)	2.0475	42,022	13.4	0.39	0.20	⋯k
5–3 O(9)	2.0571	30,064	1.56	0.13	0.07	⋯k
3–2 S(22)	2.0616	47,012	⋯	0.13	0.07	⋯k
3–2 S(5)	2.0656	20,857	4.50	3.2	1.7	⋯k
2–1 S(3)	2.0735	13,890	5.77	23.4	12.0	⋯i, k
4–3 S(18)	2.0781	43,614	16.7	0.17	0.09	⋯j
4–3 S(7)	2.1004	27,707	2.98	0.34	0.17	⋯
4–3 S(19)	2.1163	45,204	19.9	0.35	0.17	⋯
3–2 S(23)	2.1181	48,690	22.2	0.25	0.12	⋯i
1–0 S(1)	2.1218	6952	3.47	203.3	100.0	⋯
3–2 S(4)	2.1280	19,912	5.22	1.5	0.73	⋯
4–3 S(6)	2.1460	26,615	3.54	0.16	0.08	⋯
5–4 S(13)	2.1528	39,539	5.08	0.20	0.10	⋯
2–1 S(2)	2.1542	13,151	5.60	8.7	4.2	⋯
4–3 S(20)	2.1630	46,783	22.8	0.08	0.04	⋯f, j
5–4 S(14)	2.1634	40,948	7.53	0.08	0.04	⋯f, j
2–1 S(27)	2.1790	52,643	⋯	0.13	0.06	⋯
5–4 S(15)	2.1818	42,379	10.4	0.23	0.11	⋯
4–3 S(5)	2.2010	25,624	3.22	1.1	0.51	⋯g
3–2 S(3)	2.2014	19,087	5.63	3.1	1.43	⋯g
7–5 O(7)	2.2047	36,590	4.87	0.13	0.06	⋯
8-6 O(5)	2.2107	39,221	8.81	0.08	0.04	⋯
4–3 S(21)	2.2196	48,345	25.3	0.23	0.10	⋯
1–0 S(0)	2.2233	6472	2.53	40.5	18.4	⋯
5–4 S(17)	2.2433	45,275	16.1	0.27	0.12	⋯
2–1 S(1)	2.2477	12,551	4.98	16.2	7.2	⋯
3–2 S(25)	2.2663	51,939	30.7	0.14	0.06	⋯h
4–3 S(4)	2.2668	24,734	4.02	0.36	0.16	⋯h
3–2 S(2)	2.2870	18,387	5.63	1.6	0.69	⋯
4–3 S(3)	2.3445	23,955	4.58	1.1	0.46	⋯j
2–1 S(0)	2.3556	12,095	3.68	3.6	1.49	⋯k
3–2 S(1)	2.3864	17,819	5.14	2.6	1.06	⋯j
6–5 S(15)	2.4030	45,526	12.1	0.17	0.07	⋯j
1–0 Q(1)	2.4066	6149	4.29	127.5	51.1	⋯k
1–0 Q(2)	2.4134	6472	3.03	40.5	16.2	⋯k
1–0 Q(3)	2.4237	6952	2.78	176.3	70.0	⋯k
1–0 Q(4)	2.4375	7585	2.65	51.5	20.3	⋯

Notes.

^aIn 06 × 09 (R.A. × decl.) region shown in Figure 2. ^bDabrowski (1984), Wolniewicz et al. (1998). ^cTurner et al. (1977). ^dArb. units; 1σ ≈ 0.04 for weak lines. ^eFor A_K = 1.09 mag; scaled to 1–0 S(1) = 100; 1 unit is 1.0 × 10⁻⁴ erg cm⁻² sr⁻¹. ^fBlend, assume equal contributions. ^gBlend, see Section 4.2. ^hBlend, deconvolved. ⁱSignificant contamination by OH sky emission line. ^jLine peak within one res. element of 0.5 < τ < 1 telluric absorption line. ^kLine peak within one res. element of τ > 1 telluric absorption line.

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The upper state energy levels of the observed lines range from 6471 K for the 1–0 S(0) line to 52,643 K for the 2–1 S(27) line. For comparison the dissociation energy of H₂ from its ground state (Herzberg 1970; Balakrishnan et al. 1992), has an equivalent temperature of 51,967 K, apparently exceeded by that of the observed v = 2 J = 29 level. No spontaneous transition rate has been published for the 2–1 S(27) line.

The detection of roughly a dozen infrared lines from ro-vibrational states that are 40,000–50,000 K above the ground state is surprising. Previously in regions of shocked molecular hydrogen, the highest excitation energies detected were ∼25,000 K. Most of the highest excitation lines are quite weak, but both the excellent matches of their observed wavelengths to their predicted wavelengths and their morphologies, which are similar to those of the stronger lines in the brightest regions, argue conclusively for our identifications. In the spectra in Figure 4 and Figure 5 they are only detected in the region of strongest line emission. Some other very weak features are evident in Figure 6, but because these do not exhibit the same morphology, having a patchy spatial distribution at best, we interpret them to be due to noise fluctuations or contamination by cosmic rays.

All but three of the H₂ lines in Figure 6 are fundamental (Δv = 1) band transitions. The other three are first overtone transitions. Three of the emission features, at 2.163, 2.201, and 2.267 μm, are blends of pairs of lines. In the case of the strongest blended feature, the 4–3 S(5) line at 2.2010 μm and the 3–2 S(3) line at 2.2014 μm, both deconvolution and modeling (see Section 4.2) show that the higher excitation line contributes approximately 25% of the signal.

While many of the H₂ lines are clear of interference from moderate strength or strong telluric absorption lines, some are affected, as indicated in Table 1. For medium strength telluric lines we estimate that calibrated line strengths are affected, at most, at the few percent level by uncertainty in the correction; in the second instance the effect could be much larger, and our analysis has avoided such lines. In addition, residual OH sky lines, present in the data cube due to the sky emission varying during the observations, may seriously contaminate a few of the H₂ lines, as indicated in the table; these lines also are avoided in our analysis. Uncertainty in the extinction correction (discussed in Section 4.1) also contributes to uncertainty in the values in column 6 of Table 1, but its effect on the scientific thrust of this paper is negligible.

In this section we restrict our analysis to the areas of brightest line emission and to regions where the contribution from the blueshifted velocity component (see Figure 3) to the total line intensity is insignificant, so that the emission is likely to originate in one contiguous region rather than two or more widely separated regions. This restricted area is a ∼15 wide swath extending from the leading edge of the bow shock, near its tip, to the southwest, and is the mapped region in Figure 7 and some subsequent figures.

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Much of our of our analysis and discussion is based on the relative intensities of H₂ lines and on maps of several line intensity ratios: 1–0 Q(3)/1–0 S(1), 2–1 S(1)/1–0 S(1), 3–2 S(3)/2–1 S(1), 3–2 S(1)/2–1 S(1), and 4–3 S(3)/3–2 S(1), covering a wide range of upper energy levels. Prior to determining intensity ratios we binned the original NIFS reduced data cube, whose elements are 005 × 005, into a coarser cubes whose elements cover 015 × 015 and 030 × 030 regions. The latter undersamples the seeing but gives sufficiently high signal-to-noise ratios to produce meaningful line intensity ratios involving the weakest of the above lines. Line strengths were determined by numerical integration across each line profile, as there is no continuum.

4.1. Extinction Correction

Extinction by dust attenuates the H₂ lines in the K-band spectra by wavelength dependent amounts. Understanding the physical processes occurring in the molecular shock depends on reliable values of the relative intensities of lines from different energy levels, and could be skewed if extinction, including its variation across the line-emitting region, is not taken into account. Uncertainty in the exact form of the extinction law results in some residual uncertainty in the line ratios after the correction. In our choice of line ratios to analyze we have reduced this residual by selecting pairs of lines that are close in wavelength. We apply the extinction correction as follows.

We use the 1–0 S(1) and Q(3) emission lines of H₂, which have the same upper energy level and are widely separated in wavelength, to determine and correct for extinction. (A second pair of lines, 1–0 S(2) and 1–0 Q(4), have a somewhat larger wavelength separation, but the former line is coincident with strong night sky OH emission and was judged unsatisfactory.) From the spontaneous decay rates of these lines (Turner et al. 1977; Wolniewicz et al. 1998), the intrinsic Q(3)/S(1) line intensity ratio is 0.70. The observed ratio ranges from 0.85 to 1.10, as can be seen in Figure 7. We assume the extinction has the wavelength dependence λ^−1.7 (Indebetouw et al. 2005) and calculate its value in the K-band at 2.20 μm using equations from O'Connell et al. (2005),

$$\begin{eqnarray}&&{A}_{K}=\displaystyle \frac{{\rm{\Delta }}}{{\left(\tfrac{2.2}{{\lambda }_{2}}\right)}^{1.7}-{\left(\tfrac{2.2}{{\lambda }_{1}}\right)}^{1.7}},\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{\rm{\Delta }}=2.512\mathrm{log}\left[\displaystyle \frac{{F}_{Q3}}{0.70{F}_{S1}}\right],\end{eqnarray} \tag{ 2 }$$

with the F as the observed line fluxes. Then the correction factor for a line at wavelength λ is

$$\begin{eqnarray}&&{f}_{\mathrm{corr}}={2.512}^{\left({A}_{K}{\left(\displaystyle \frac{2.2}{\lambda }\right)}^{1.7}\right)}.\end{eqnarray} \tag{ 3 }$$

We have scaled each line flux by the correction factor determined from the extinction measured at its location, using the above expression. In Table 1 both the observed and extinction-corrected relative line strengths are presented; in the latter the strength of the 1–0 S(1) line is set to 100. The extinction in the K-band is found to vary from to 1.0 to 2.3 mag, corresponding to a range in visual extinction of 12–28 mag. In general the lowest extinctions are located near the leading edge of the shock. This suggests that the leading edge of the shock, including its foreground flank as viewed from Earth, is closer to breaking through the ambient cloud than the other regions of the shock observed here, and implies that the ambient cloud into which the outflow is penetrating is highly non-uniform.

4.2. 3–2 S(3) Blending Correction

Of the H₂ lines that we employ for analysis of the excitation conditions in the shock, one, the 3–2 S(3) line at 2.201 μm, is blended with the 4–3 S(5) line; their wavelength difference corresponds to a velocity separation of only 55 km s⁻¹. We have used the 4–3 S(3) and 3–2 S(1) lines, which have almost the same energy difference as the blended lines, to estimate the relative contributions of 3–2 S(3) and 4–3 S(5) to the bended emission. For these two line pairs, using the upper level energies and spontaneous decay rates of the transitions and the level degeneracies g_J = 21, 33, 45 for the upper rotational levels, J = 3, 5, 7, respectively, the ratios of the line strengths are

$$\begin{eqnarray}&&{R}_{\tfrac{4-3S(5)}{3-2S(3)}}=0.78{e}^{-6537/T}\end{eqnarray} \tag{ 4 }$$

and

$$\begin{eqnarray}&&{R}_{\tfrac{4-3S(3)}{3-2S(1)}}=1.425{e}^{-6137/T},\end{eqnarray} \tag{ 5 }$$

so that

$$\begin{eqnarray}&&{R}_{\tfrac{4-3S(5)}{3-2S(3)}}=0.55{e}^{-400/T}{R}_{\tfrac{4-3S(3)}{3-2S(1)}}\approx 0.50\;{R}_{\tfrac{4-3S(3)}{3-2S(1)}}\end{eqnarray} \tag{ 6 }$$

for values of T of several thousand Kelvin or more. The observed value of ${R}_{4-3S(3)/3-2S(1)}$ is typically 0.5, implying that 3–2 S(3) typically contributes 75% of the flux of the blend at 2.201 μm. This is consistent with the relative intensities of these two lines in Table 1.

From the de-reddened relative intensities, I_i, listed in Table 1, level column densities, N_i, can be derived from

$$\begin{eqnarray}&&{I}_{i}={N}_{i}{A}_{i}h{\nu }_{i}/4\pi ,\end{eqnarray} \tag{ 7 }$$

where A_i is the radiative decay rate from the ro-vibrational level i (from Wolniewicz et al. 1998), and ν_i is the frequency of the transition (from Turner et al. 1977).

A standard plot of level column density versus energy is shown in Figure 8. Clearly, a single temperature Boltzmann distribution cannot account for all of the the observed line intensities, as the slope of the plot is significantly different at low and high energies. Instead, a two-component Boltzmann distribution with temperatures T_warm and T_hot has been fit to the column densities, as follows:

$$\begin{eqnarray}&&{N}_{i}={N}_{i,\mathrm{warm}}+{N}_{i,\mathrm{hot}},\end{eqnarray} \tag{ 8 }$$

with

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{i,\mathrm{hot}}}{{N}_{\mathrm{hot}}}=\displaystyle \frac{{g}_{i}{e}^{-{T}_{i}/{T}_{\mathrm{hot}}}}{Z({T}_{\mathrm{hot}})},\end{eqnarray} \tag{ 9 }$$

where N_hot is the total column of hot gas, g_i, the level degeneracy, is $3\times (2J+1)$ for ortho (odd J) states and 2J+1 for para (even J) states, and T_i is the energy level (in K). The formula for N_warm is similar. Z(T) is the partition function, given by

$$\begin{eqnarray}&&Z(T)=\displaystyle \frac{2T}{{T}_{\mathrm{rot}}}(1-{e}^{-{T}_{\mathrm{vib}}/T}),\end{eqnarray} \tag{ 10 }$$

with rotational and vibrational constants T_rot = 88 K and T_vib = 6000 K (see Burton et al. 1989a).

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A Levenberg–Marquard minimum-χ² fit to Equation (8) has been made using the lmfit routine in IDL.⁶ Excellent agreement with the observations is obtained, as shown in Figure 8.⁷ We find that T_warm = 1803 ± 12 K and T_hot = 5200 ± 12 K. To avoid being overly constrained by artificially high signal-to-noise ratios on the strong lines, since the dynamic range of the H₂ line strengths is so large, we set the maximum signal-to-noise ratio for any individual line to be 50 in the fitting analysis. Of the line-emitting gas, 98.5% is at 1800 K and 1.5% is at 5200 K. For individual lines the fraction of the emission arising from the hot and warm components depends on the upper level energy. For instance, for the fiducial 1–0 S(1) line, 92% of the line emission comes from the warm component and 8% from the hot component. For the (unobserved) lower rotational levels of the ground vibrational state, nearly all of the H₂ is warm; for example, 99.0% of the H₂ in the v = 0, J = 3 state is in the warm gas. In contrast, for H₂ in levels of energy ∼40,000 K and higher less than 0.01% is in the warm gas. The H₂ at energy levels near 13,650 K, which corresponds roughly to v = 2, J = 5 (the upper level of the 2–1 S(3) line at 2.0735 μm), is composed roughly equally of hot and warm gas.

5.1. Comparisons with Previous Results

5.2. Missing and Unidentified Lines

The excitation temperature, T₂₁, of a pair of H₂ lines, is determined from their extinction-corrected intensities, I, upper level energies, E, spontaneous decay rates, A, and the degeneracies of the rotational levels, g, by

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{2}}{{I}_{1}}=\displaystyle \frac{{A}_{2}{g}_{2}{\lambda }_{1}{e}^{\tfrac{-{E}_{2}}{{T}_{21}}}}{{A}_{1}{g}_{1}{\lambda }_{2}{e}^{\tfrac{-{E}_{1}}{{T}_{21}}}}\quad .\end{eqnarray} \tag{ 11 }$$

Maps of the excitation temperature for selected H₂ line pairs (2–1 S(1)/1–0 S(1), 3–2 S(1)/2–1 S(1), 3–2 S(3)/2–1 S(1), and 4–3 S(3)/3–2 S(1)), based on values in 03 × 03 regions, are shown in Figure 9, and histograms of each line ratio are displayed in Figure 10. Scatterplots of pairs of line ratios are shown in Figure 11. In the latter figure the opacity of a data point scales with the strength of the 1–0 S(1) line, and thus roughly with the strengths of all of the lines. Although each ratio apparently has a range of ±25%–50% the values for the stronger lines cluster within much smaller ranges, centered on approximately 0.10 for 2–1 S(1)/1–0 S(1), 0.16 for 3–2 S(1)/2–1 S(1), 0.20 for 3–2 S(3)/2–1 S(1), and about 0.45 for 4–3 S(3)/3–2 S(1). Because the strengths of all of these lines scale roughly with the strength of the 1–0 S(1) line, and the signal-to-noise ratios on the 3–2 and 4–3 lines are not very high, we believe that much of the scatter is due to noise (random fluctuations and/or cosmic rays that produced slightly spurious data points not obvious enough to be removed or corrected). Our derived 2–1 S(1)/1–0 S(1) flux ratios in the bright portion of the shocked gas are somewhat lower than that found by Smith et al. (2003).

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The above values of the line ratios correspond to excitation temperatures of 2150 K, 2920 K, 2960 K, and 5300 K, respectively. The trend, that ratios involving transitions from higher energy levels are associated with higher excitation temperatures, is similar to that seen previously in HH7 and elsewhere, as discussed in Section 5.1. However, Figure 8 makes it clear in that in HH7 the excited H₂ producing the K-band lines is not distributed over a wide range of temperatures but instead is predominantly at only two temperatures, ∼2000 and ∼5000 K, and thus that the different excitation temperatures reflect the different contributions to the line emission from the two components.

7.1. Introduction

7.2. Possible Origins of the 5000 K H₂

These results, particularly those relating to the existence of the hot H₂, pose many questions requiring additional observations and calculations. Foremost among them are determining the uniqueness of ∼5000 K gas and understanding its origin. First, does the temperature of this hot gas and its abundance relative to the warm gas vary with location in the HH7 shock? As pointed out, the weak lines are difficult to observe far from the brightest portions of the shock. However, we have only observed a part of the brightest region. In particular, it could be revealing to observe the K-band H₂ spectrum in the cap of the bow shock, where one would expect that there is more dissociation. If the hot H₂ is newly reformed it might constitute a higher fraction of the line-emitting gas there. Second, are the temperature of the hot gas, and indeed its existence, unique to HH7? We expect that the answer to the second part of this question is no, as lines from energy levels as high as 25,000 K have been seen elsewhere in collisionally excited H₂, as discussed earlier, and reveal a similar dependence of excitation temperature on upper energy level as found in HH7. We have very recently obtained deep K-band spectra of shocked H₂ in the OMC-1 outflow extending from near its Peak 1 through one of the bright H₂ "bullets" (Allen & Burton 1993; Tedds et al. 1999), which should shed light on both parts of this question. Third, could spectra at higher velocity resolution than presented here of lines from a wide range of upper level energies provide clues to the relationship of the hot component to the warm component?

On the theoretical side, if the hot H₂ is recently reformed on grains it is important to determine its formation rate and its initial energy level distribution as it leaves the grains, and to understand the competition between energy loss via line emission and via collisions. If the internal energy is redistributed from a higher temperature distribution or from an initial non-LTE initial distribution the resulting (observed) temperature is likely to be sensitive to the physical conditions in the shocked gas, and in particular its density. Finally there is even the question of how a single hot temperature would result from any redistribution. The high quality of the two-temperature fit suggests that, if the hot H₂ in HH7 is reformed H₂, it must cool quickly from ∼5000 to ∼2000 K so that intermediate temperatures are not detected in a population diagram. If that is not the case then the hot H₂ would seem to have to be located in a separate environment that is physically detached from the bulk of the post-shock gas.

This research is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). We thank the staff of Gemini Observatory for its support of this research and Richard McDermid for assistance with the data reduction. We also thank Peter Brand for helpful discussions regarding this research, as well as for all that he has taught us and that we have learned together with him over several decades.