SOLVING THE EXCITATION AND CHEMICAL ABUNDANCES IN SHOCKS: THE CASE OF HH 1^*

In total, we detect more than 500 lines, the spectrum being particularly rich in [Fe ii] and H₂ lines. In deeper detail, we detect fine structure ionic lines from atoms with Z $\leqslant$ 28 and with excitation energy up to ∼40,000 cm⁻¹, H i recombination lines of the Balmer, Paschen, and Brackett series, several He i recombination lines (plus one He ii line), and H₂ ro-vibrational lines with ${v}_{\mathrm{up}}\;\leqslant$ 9 (excitation energy up to ∼50,000 cm⁻¹). For comparison, Solf et al. (1988) found around 100 lines in their 3700–10830 Å spectrum: the sensitivity reached with X-shooter therefore led the number of emission line detections to increase by about a factor of five (although within a larger wavelength range). More importantly, we detect lines from low-abundance elements, like P, Cl, Ti, and Co, together with high-v_up H₂ lines, which fall mainly in the optical range. The complete list of the detected lines is reported in the Appendix (Tables 5–7), where we give, together with the spectral identification, the energy of the upper and lower level, and the measured flux with the associated uncertainty. Apart from H i lines, the large majority of the other lines are not resolved in velocity, and therefore the full-width at half-maximum (FWHM) of the line profile is typically the instrumental one (i.e., ∼0.5, 0.7, 1.5 Å in the UVB, VIS and NIR arm, respectively). The flux was derived by means of a Gaussian fit to the line profile, while the associated uncertainty was estimated by multiplying the spectral noise (rms) at line base times the FWHM. At the adopted spectral resolution, some lines are blended with each other and were not used in the subsequent analysis. Finally, we note that a few, bright lines present a second, fainter and redder component, whose flux was eventually added to that of the principal component to get the total line flux. Since detailed study of the shock kinematics and geometry is far from our scientific scope, the analysis of these individual (possibly resolved) line components is not considered further in this paper.

The method adopted to derive the local extinction (A_V) is described in Paper I. We just recall here that we estimate A_V using pairs of lines coming from the same upper level, whose difference between the observed and theoretical flux ratios is a function only of the local reddening (see, e.g., Gredel 1994). We considered flux ratios between H i lines of Balmer and Paschen series and Paschen and Brackett series, along with flux ratios of visible and infrared H₂ and atomic fine structure lines. Taking into account all the uncertainties and a total-to-selective extinction (R_V) between 3 and 5, we get 0.0 mag $\leqslant$ $\;{{\rm{A}}}_{V}\;\leqslant$ 0.8 mag. We adopted A_V = 0.4 mag to correct the observed fluxes by applying the reddening law of Cardelli et al. (1989). Also, the flux uncertainty due to the A_V estimate (0.4 mag) was statistically added to the ΔFlux of Tables 5–7 and taken into account in the line ratios used to derive the gas physical conditions.

The physical conditions of each ionic species were derived by comparing the line ratios of their brightest lines with the predictions of an excitation model, which adopts the Non-local Thermal Equilibrium (NLTE) approximation for line excitation. The equations of the statistical equilibrium are solved by considering the electronic collisional excitation/de-excitation and the radiative spontaneous decay as processes level populations. Possible influences on line emissivity due to photo-excitation and stimulated emission are discarded at this step of the analysis, but they are considered a posteriori by examining line ratios particularly sensitive to such processes (Section 4.1.1). The free parameters of the excitation model are the electron temperature ${T}_{{\rm{e}}}$ and the electron density n_e, which are derived from the measured flux ratios once corrected for the estimated A_V. In order to reveal possible temperature and density gradients inside the shock we estimated T_e and n_e for each species separately. In particular, the excitation model was developed for all the ionic species for which collisional and radiative rates are available in the literature (all ions but Na i and Co ii). Air frequencies and radiative rates are taken from "The atomic line list"³ and from the "NIST" database⁴ , with the exception of the radiative rates of Cr ii which were taken from Quinet (1997). In Table 1 we summarize the details of each model. In particular, in the second column we report the average IP_ave = (IP${}_{i-1}$ + IP_i)/2 between the ionization potentials of the ionic stages i-1 and i, to have an idea of the energy range corresponding to the ionization stage i of the considered species. We also give the number of levels considered in the model (column 3), the literature reference for collisional rates with electrons (column 4), and the temperature range in which these rates have been computed, which, roughly speaking, covers higher temperatures for species with higher IP_ave (column 5). In agreement with this occurrence, we have constructed a grid of model solutions in the range: 3000 K $\;\leqslant \;{T}_{{\rm{e}}}\;\leqslant \;$ 20,000 K ($\delta {T}_{{\rm{e}}}\;$= 1000 K), 5000 K $\;\leqslant \;{T}_{{\rm{e}}}\;\leqslant \;$ 30,000 K ($\delta {T}_{{\rm{e}}}\;$= 1000 K), and 10,000 K $\;\leqslant \;{T}_{{\rm{e}}}\;\leqslant \;$ 80,000 K ($\delta {T}_{{\rm{e}}}\;$= 5000 K) for ions having IP_ave less than 20 eV, between 20 and 30 eV, and higher than 30 eV, respectively. All the grids cover the range 10³ cm${}^{-3}\leqslant {n}_{{\rm{e}}}\;\leqslant$ 10⁷ cm⁻³ (in steps of log₁₀($\delta {n}_{{\rm{e}}}/{\mathrm{cm}}^{-3}$) = 0.1). We make available these grids, containing the emissivities of selected lines, at the website: http://www.oa-roma.inaf.it/irgroup/line_grids/Atomic_line_grids/Home.html.

Table 1.  Parameters of the Excitation Model

Ion	IP${}_{\mathrm{ave}}$ a	N${}_{\mathrm{lev}}$ b	Coll.rates	Rangec	${T}_{{\rm{e}}}$	${n}_{{\rm{e}}}$
	(eV)			(104 K)	(104 K)	(104 cm−3)
Mg i	3.822	8	[1]	0.1–1	0.4–1.0d	0.1–1.5
C i	5.628	5	[2]	0.05–2	0.5–1.6e	0.1–6.0
O i	6.807	5	[3]	0.5–3	1.0–1.2e	0.1–10
N i	7.265	5	[4]	0.05–2	0.6–1.3	0.15–0.2
Ca ii	8.989	5	[5]	0.3–3.8	1.4–1.8	≤100
Ti ii	10.195	30	[6]	0.4–2	⋯	⋯
Fe ii	12.025	159	[7]	0.1–2	1.0–1.2	0.3–0.5
Ni ii	12.891	17	[8]	0.2–3	0.9–1.4	0.2–1.0
P ii	15.102	5	[9]	0.1–4	⋯	⋯
S ii	16.878	5	[10]	0.5–10	1.0–1.4	∼0.2
Cl ii	18.405	5	[11]	1	⋯	⋯
N ii	22.061	5	[12]	0.5–10	1.0–1.2e	0.5–2.0
Fe iii	23.411	34	[13]	0.5–2	0.9–3.5	20–100
Cr ii	23.70	13	[14]	0.2–10	1.5–2d	0.1–10
O ii	24.631	5	[15]	0.5–2	≥2.0	0.1–0.2
S iii	29.200	5	[16]	0.1–10	2.0–3.0	0.1–10
Ar iii	37.580	5	[16]	0.1–10	2.5–5.0	≤100
O iii	45.002	5	[17]	0.1–10	2.7–4.7e	0.1–10
Ar iv	50.345	5	[18]	0.2–5	7.5–8.5f	10–60
Ne iii	52.285	5	[19]	0.1–10	≥6.0f	⋯

Notes.

^aIP_ave is the average between the ionization potentials of the ionic stages i-1 and i. ^bNumber of levels considered in the excitation model. ^cRange of validity of the collisional rates. ^eMinimum ${T}_{{\rm{e}}}$ corresponds to maximum ${n}_{{\rm{e}}}$ and vice versa. ^dMinimum ${T}_{{\rm{e}}}$ corresponds to minimum ${n}_{{\rm{e}}}$ and vice versa. ^fTemperature derived assuming ${{\rm{X}}}^{i}\;\leqslant \;$ ${{\rm{X}}}_{\odot }^{i}.$

References. (1) Osorio et al. (2015), (2) Hollenbach & McKee (1989), (3) Bhatia & Kastner (1995), (4) Pequignot & Aldrovandi (1976), (5) Meléndez et al. (2007), (6) Bautista et al. (2006), (7) Bautista & Pradhan (1998); (8) Bautista (2004), (9) Tayal (2004), (10) Tayal & Zatsarinny (2010), (11) Mendoza (1983), (12) Stafford et al. (1994), (13) Zhang (1996), (14) Wasson et al. (2010), (15) Pradhan (1976), (16) Galavis et al. (1995), (17) Lennon & Burke (1994), (18) Zeippen et al. (1987), (19) Butler & Zeippen (1994).

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We were able to derive an estimate of ${T}_{{\rm{e}}}$ and n_e from line ratios of most of the observed species, with the exceptions of Cl ii, P ii and Ti ii. Indeed, Cl ii and P ii lines come from the same upper level and therefore their ratio is independent from the gas physical conditions, while lines of Ti ii have too low of a signal-to-noise ratio to provide meaningful determinations. However, models for these species were constructed to compute the intrinsic line emissivities once we assumed the physical parameters, since these predictions are needed to derive the chemical abundances (see Section 4.4).

To derive the fractional ionization x_e = n_e/n_H (where n_H = ${n}_{{{\rm{H}}}^{0}}\;$+$\;{n}_{{{\rm{H}}}^{+}}$) and the relative abundances Xⁱ/X${}^{i+1}$ of the atomic species in different ionization stages, we developed an ionization code that takes into account the following processes: collisional ionization, radiative and dielectronic recombination, and direct and inverse charge-exchange with hydrogen. Ionization, radiative, and dielectronic recombination rates are taken from Landini & Monsignori Fossi (1990) with the exception of the iron data (Arnaud & Raymond 1992). Charge-exchange data are from Kingdon & Ferland (1996) apart from carbon data (Stancil et al. 1998). Dielectronic recombination coefficients at low temperatures have been considered in O, N, and C models (Nussbaumer & Storey 1983). Notably, while the ionization and recombination processes are a function of only the electron temperature, direct and inverse charge-exchange also depend on the fractional ionization ${x}_{{\rm{e}}}.$ Out of the species detected in different ionization stages, charge-exchange rates are relevant for the processes N⁰ + ${{\rm{H}}}^{+}\;\rightleftarrows$ ${{\rm{N}}}^{+1}$ + H⁰, Fe${}^{+1}$ + ${{\rm{H}}}^{+}\;\rightleftarrows$ Fe${}^{+2}$ + H⁰, O⁰ + ${{\rm{H}}}^{+}\;\rightleftarrows$ ${{\rm{O}}}^{+1}$ + H⁰, and ${{\rm{O}}}^{+1}$ + ${{\rm{H}}}^{+}\;\rightleftarrows$ ${{\rm{O}}}^{+2}$ + H⁰.

Since different ionic stages are found in different regimes of temperature and density (Section 4.1), we have fitted ${x}_{{\rm{e}}}$ (0 $\leqslant \;{x}_{{\rm{e}}}\;\leqslant$ 1 in steps $\delta {x}_{{\rm{e}}}$ = 0.05) in the range of ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ in which adjacent ionization stages are expected to co-exist in significant percentages. The fit results and their implications are discussed in Section 4.2.

Most of the observed lines come from the first five fine structure levels of the ground state. For these species 5-level models have been considered, and ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ have been derived from diagnostic diagrams involving the brightest lines. Examples are given in Figure 6. For complex atomic systems, e.g., Fe ii, Fe iii, and Ni ii, we have constructed more complicated models, and derived the physical parameters following the best-fitting method proposed by Hartigan & Morse (2007), which consists in iteratively changing the line used for the normalization to minimize the ${\chi }^{2}$ value of the fit. The best fits are shown in Figure 7.

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Temperature and density fitted by the excitation model in each ion are reported in Table 1 (columns 6 and 7). For the large majority of the ions, the derived ${T}_{{\rm{e}}}$ falls inside the range of validity of the model (column 5). A remarkable exception is O ii, whose temperature was derived by extrapolating the collisional rates from their maximum value. With reference to Figure 6 we note that while for some ions we are able to precisely derive both ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ (e.g., N i, O ii, S ii), for others we can significantly constrain only one of the two parameters (e.g., C i, O iii). However, for the highly ionized species, the information derived from the line ratios can be integrated with other constraints. This is, for example, the case of Ar iv shown in the bottom-left panel of Figure 6. Indeed, while the ratio 4740 Å/4711 Å is a good indicator of the density, it is almost independent from the local temperature. However, the latter can be evaluated by adding as a constraint the Argon abundance X(Ar) derived from the [Ar iii] lines (X(Ar) = 1.1 ${10}^{-5}\;\div$ 1.7 10⁻⁵ X(H), see Section 4.4). Taking this range, we get that the observed fluxes of the Ar iv lines are fitted by the excitation model only if ${T}_{{\rm{e}}}$(Ar iv) is in the range 75,000 K $\div$ 85,000 K. For example, if ${T}_{{\rm{e}}}$(Ar iv) were ≲60,000 K, X(Ar) should exceed the solar value by an order of magnitude. Similarly, we find that to reproduce the observed lines of Ne iii at temperatures lower than ∼50,000 K, X(Ne) should exceed the solar abundance by about a factor of five. More reasonably, imposing that X(Ne) ≲ X(Ne)${}_{\odot },$ we put a lower limit of 60,000 K to the Ne iii temperature.

From Table 1 it can be noted that higher ${T}_{{\rm{e}}}$ are found for ions with higher IP_ave. This is better shown in Figure 8, where we plot IP_ave versus ${T}_{{\rm{e}}}$, finding a significant correlation (regression coefficient R = 0.95) between the two quantities. The linear best fit through the data points is Log(${T}_{{\rm{e}}}$) = 0.02 IP_ave + 3.8. Hints of a correlation were already found by Solf et al. (1988), their Figure 2), although with a temperature plateau at ∼35,000 K above 30 eV where no more data points were available. With the new X-shooter observations we extend the correlation up to ∼80,000 K, i.e., at temperatures expected in the recombination region immediately behind a fully dissociative shock front (J-ump shocks, Hollenbach & McKee 1989).

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The electron density is well constrained by a few line ratios. Roughly speaking, we can identify two density regimes: a more tenuous gas component with ${n}_{{\rm{e}}}$ between 1.0 10³ cm⁻³ and 5.0 10³ cm⁻³, probed by [N i], [Fe ii], [S ii], and [O ii] line ratios, and a denser gas component, with ${n}_{{\rm{e}}}\;\gtrsim$ 1.0 10⁵ cm⁻³, probed by [Fe iii], [Ar iv] and possibly [S iii], [Ar iii] and [O iii] line ratios. Therefore, the densest component seems to be associated with the highest temperatures. With reference to Figure 2, this scenario is consistent with the presence of two partially mixed ionized gas components, one spatially narrower with ${T}_{{\rm{e}}}$ ≳ 30,000 K and ${n}_{{\rm{e}}}$ ≳ 1.0 10⁵ cm⁻³ located close to the shock front (roughly peaking at 2''–3'' from the bow-shock edge), and a second, rear, and broader component with lower temperature and electron density. We also identify a rather neutral component (namely that emitting the bulk of the O i and C i emission, see Section 4.2), which encompasses the entire slit length at a roughly constant level of emission, as shown for example by the [C i]9850 spatial profile of Figure 2. For this component ${n}_{{\rm{e}}}$ is not representative of the total gas density, being less than 10% of the neutral hydrogen density ${n}_{{\rm{H}}}$ (we estimate ${x}_{{\rm{e}}}$(O i) ∼ 0). Since the lower limit to ${n}_{{\rm{e}}}$ is 10³ cm⁻³ for both O i and C i (Table 1), we derive ${n}_{{\rm{H}}}\;\gt$ 10⁴ cm⁻³ for this neutral region.

4.1.1. Role of Fluorescence

The results of the ionization model are presented in Figure 9, where we plot the flux ratios of lines from adjacent ionization stages as a function of ${x}_{{\rm{e}}}$ for the three atoms (N, O, Fe) that are sensitive to charge-exchange processes. The top-left panel shows the [N i]5198 Å /[N ii]6585 Å ratio versus ${x}_{{\rm{e}}}$ assuming the ranges of ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ derived from the N ii excitation model. We fit 0.55 $\leqslant \;{x}_{{\rm{e}}}\;\leqslant$ 0.85. However, since part of the N i emission comes from a region with ${T}_{{\rm{e}}}\;\lt$ 10⁴ K (see Table 1), only a fraction of the observed [N i]5198 Å line can be attributed to the same gas emitting the [N ii]6585 Å line. In this sense, the observed ratio has to be regarded as an upper limit, with a consequent shift of ${x}_{{\rm{e}}}$ toward higher values. In the two bottom panels of Figure 9 we show the results of the ${\mathrm{Fe}}^{+1}$–${\mathrm{Fe}}^{+2}$ equilibrium code, which has been solved by assuming the density range derived from [Fe iii] lines (note that the dependence between fractional ionization and electron density is very shallow). Also, since the temperature is practically not constrained by the [Fe iii] lines, we fixed ${T}_{{\rm{e}}}$ at 10,000 K. Several flux ratios have been examined, obtaining 0.50 $\leqslant \;{x}_{{\rm{e}}}\;\leqslant$ 0.70. For the same reasons as those explained for the N⁰–N${}^{+1}$ equilibrium, if Fe iii mostly came from a gas component with a temperature higher than 10⁴ K, all the [Fe iii] line fluxes should be considered as upper limits and ${x}_{{\rm{e}}}$ would slightly decrease. Finally, as far as oxygen is concerned, we note that the temperature fitted by [O i] and [O ii] lines are substantially different (see Table 1). The ionization code indicates that at ${T}_{{\rm{e}}}\;\sim$ 10⁴ K (fitted from O i lines) the percentage O⁰:O${}^{+1}$ is 99:1, therefore, it is likely that the bulk of the [O i] emission comes from a substantially neutral region. Conversely, the lower limit of 2.0 10⁴ K derived for the region where oxygen is singly ionized is compatible with the range of ${T}_{{\rm{e}}}$ derived from [O iii] line ratios. The ionization equilibrium between ${{\rm{O}}}^{+1}$ and ${{\rm{O}}}^{+2}$ was therefore solved for the physical conditions got from the [O iii] lines. As shown in Figure 9, top-right panels, the gas component emitting O iii lines is practically fully ionized.

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In Figure 8 the red points represent ${x}_{{\rm{e}}}$ versus IP_i, while in Table 3 we summarize the results of the ionization equilibrium model. The first column lists the element for which the code was solved, while the second column contains the ionization stages taken into consideration. In the third column we report the values of ${x}_{{\rm{e}}}$ derived from the above analysis. For the atomic species for which we could not directly derive ${x}_{{\rm{e}}},$ we assume the value estimated from the element (among nitrogen, oxygen, and iron) with IP_ave similar to that of the element under consideration.

Table 3.  Parameters of the Ionization Model

Element	Ionization Stage	${x}_{{\rm{e}}}$	${T}_{{\rm{e}}}$	Fractional Abundancea
Helium	He0/He${}^{+1}$	1.0b	2.0 104	He0:∼100
		1.0b	3.0 104	He0:He${}^{+1}$ = 75:25
		1.0b	4.0 104	He0:He${}^{+1}$ = 23:77
		1.0b	5.0 104	He0:He${}^{+1}$ = 7:93
Carbon	C0/C${}^{+1}$	∼0b	1.0 104	C0:${{\rm{C}}}^{+1}$ = 95:5
Nitrogen	N0/N+1	0.50–0.85	1.1 104	N0:N+1 = (53–47):(40–60)
Oxygen	O0/O+1/O+2	∼0b	1.1 104	O0:O+1 = 99:1
		1.0	3.0 104	O+1:O+2 = 99:1
		1.0	4.5 104	O+1:O+2 = 92:8
Magnesium	Mg0/Mg${}^{+1}$	∼0b	7.0 103	Mg0:Mg${}^{+1}$ = 46:54
Sulphur	S0/S+1/S+2	0.50-0.70b	1.2 104	S0:S+1 = 41:59
		0.50-0.70b	3.0 104	S0:S+1:S+2 = (13–6):(72–80):(14–16)
Argon	Ar+2/A+3	1.0b	3.0 104	Ar+2 = 100
		1.0b	8.0 104	Ar+2:A+3 = 79:21
Calcium	Na0/Na+1/Na+2	0.50–0.85b	1.4 104	Na0:Na${}^{+}$ = 10:90
Iron	Fe0/Fe+1/Fe+2/Fe+3	0.50–0.70	1.1 104	Fe0:Fe+1:Fe+2 = (6–5):(84–75):(9–19)
		0.50-0.70	2.2 104	Fe+1:Fe+2 = (70–50):(30–50)
		0.50-0.70	3.5 104	Fe+1:Fe+2 = (56–35):(44–65)
Nichel	Ni0/Ni${}^{+1}$	0.50-0.85b	2.5 104	Ni0:Ni${}^{+1}$ = (86–52):(14–48)

Notes.

^aWe report only fractional abundances ≥1%. When a range is given, this refers to two values of ${x}_{{\rm{e}}}$ of the third column. ^bAssumed value (see text).

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The ionization equilibrium code allows one also to derive the relative abundance of adjacent ionization stages, as a function of ${x}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}.$ We give these quantities in the last column of Table 3, computed at the temperatures given in the fourth column (that roughly coincide with the average ${T}_{{\rm{e}}}$ derived from the excitation model) and for the ${x}_{{\rm{e}}}$ values of the third column. When a range of ${x}_{{\rm{e}}}$ is given, Xⁱ/X${}^{i+1}$ is computed accordingly. In particular, we note that the equilibrium ionization of He indicates that a relevant percentage of He${}^{+1}$ is found only if the gas temperature exceeds ∼30,000 K (in agreement with the relation of Figure 5, being IP_ave(He) = 39.5 eV). This result, as well as the relative abundances, will be used in the following to derive the atomic abundances (Section 4.4).

As anticipated in Section 2.1, the spectrum of HH 1 is extremely rich in H₂ line emission, observed both in the VIS and NIR segments. In total, around 200 ro-vibrational lines with 1 $\leqslant$ $\;{v}_{\mathrm{up}}\;\leqslant$ 9 are detected. In total, around 200 ro-vibrational lines with 1 $\leqslant$ $\;{v}_{\mathrm{up}}\;\leqslant$ 9 are detected. Line identifications and fluxes are reported in Table 7. The H₂ emission was analyzed in the framework of a Boltzmann diagram, i.e., a plot of ${\rm{ln}}({N}_{(v,J)}/{g}_{J}{g}_{s})$ against ${E}_{(v,J)}/k,$ where ${N}_{(v,J)}$ (cm⁻²) is the column density of level (v,J), ${E}_{(v,J)}/$k (K) its excitation energy and g_Jg_s = (2J + 1)(2I + 1) its statistical weight. In the assumption of optically thin emission, ortho-to-para (o/p) ratio of 3, and thermalization at a single temperature, the points in the diagram fall onto a straight line, while for a range of kinetic temperatures the Boltzmann diagram forms a curve. Moreover, data points coming from the same upper level are expected to superpose in the diagram once de-reddened. The Boltzmann diagram of the H₂ lines detected with a S/N $\geqslant$ 5 is represented in Figure 10, top panel. To minimize the uncertainties we have also discarded lines close in wavelength to the atmospheric holes or affected by artifacts (e.g., sky residuals or bad pixels, mainly present in the NIR part of the spectrum). The best fit was obtained by simultaneously optimizing both the A_V value and the gas temperature. We get A_V = 0.5 mag, which has been applied to all lines. The temperature is found as the reciprocal of the slope of the straight line through the data points. If all the lines are considered (solid line) we get an average temperature over the whole H₂ region of ∼5500 K. However, columns of low-excited lines (typically lines with v_up = 1 and ${E}_{(v,J)}\;\leqslant$ 15,000 K) are severely underestimated by this fit. Rather, the overall emission is better reproduced considering two temperature components, at ∼2500 K and ∼6300 K (dashed lines). We note that the first temperature component is in quite good agreement with the determination of 2750 K obtained by Gredel (1996) on the base of the NIR spectrum only.

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The analysis of the H₂ emission suggests some considerations. First, the fact that the data points are fitted under LTE conditions, indicates that the gas density must be higher than the critical densities of the levels from which the lines originate (to have an indication, ${n}_{{\rm{crit}}}\;\gtrsim$ 10⁴ cm⁻³ at T = 3000 K for most of the levels). Therefore, as derived for the neutral gas component, also the molecular emission should arise from a region with density exceeding 10⁴ cm⁻³.

Second, we note that the fitted temperatures the H₂ gas is expected to have reached equilibrium between the ortho and para form, corresponding to o/p = 3. We have verified this circumstance, since in the opposite case the data points on the Boltzmann diagram would anymore align onto a straight line, but rather would follow a well defined zig-zag distribution (e.g., Nisini et al. 2010).

Third, both the high temperature fitted and the detection of lines with high excitation energy (up to ${E}_{(v,J)}/k\;\sim$ 50,000 K) may indicate that the H₂ emission is at least partially influenced by ultraviolet pumping. Indeed, the strong ultraviolet continuous emission detected in the range 1400 Å $\leqslant \;\lambda$ 1600 Å by Böhm et al. (1993) was likely attributed to a fluorescent H₂ continuum. We compared our data with the model by Sternberg & Dalgarno (1989), who have predicted the fluxes of bright H₂ lines for increasing electron density and for a local radiation field that is a factor of 100 higher than the interstellar field (χ parameter). We plot in Figure 10, in the second to bottom panel, the ratios of the observed lines over their theoretical values for 10³ cm${}^{-3}\;\leqslant n\;\leqslant$ 10⁶ cm⁻³, being $n={n}_{{{\rm{H}}}_{2}}$ + ${n}_{{\rm{H}}}.$ A marginal agreement with the theoretical predictions is found only for high-density values, at which, however, collisional excitation is expected to have a major role. Therefore, we can conclude that fluorescence is fairly negligible in H₂ line excitation (at least as far as the observed wavelength range is concerned), thus confirming what was also found for the atomic emission in Section 4.1.1.

Finally, if we consider the gas as purely collisionally excited, we can derive some hints on the nature of the shock from the rotational diagram, giving the fact that the level populations are sensitive to the shock parameters (pre-shock density, shock velocity and age, and strength of the magnetic field). In particular, the presence of a magnetic field acts to dampen and broaden the shock wave; therefore, an increased magnetic field strength enhances the departure from LTE (e.g., Flower et al. 2003). Conversely, a J-type shock is associated to a narrow shock wave, more easily thermalized and with higher column densities of the levels with larger vibrational numbers. In a very qualitative way, this second scenario appears to be more suitable in representing the observed H₂ emission.

Chemical abundances of the atomic species have been obtained by comparing fluxes of bright lines with the flux of the Hβ line. Indeed, the atomic abundance is a direct function of the observed flux ratio according to the relationship:

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{X}}}{{\rm{H}}}=\displaystyle \frac{{F}_{\mathrm{line}}}{{F}_{{\rm{H}}\beta }}\times {\left[\displaystyle \frac{{\epsilon }_{\mathrm{line}}({T}_{{\rm{e}}},{n}_{{\rm{e}}})}{{\epsilon }_{{\rm{H}}\beta }(({T}_{{\rm{e}}},{n}_{{\rm{e}}})}\displaystyle \frac{{{\rm{X}}}^{i}}{{\rm{X}}}\displaystyle \frac{{\rm{H}}}{{{\rm{H}}}^{+}}\right]}^{-1},\end{eqnarray} \tag{ 1 }$$

where X/H is the abundance of the X atomic species relative to hydrogen, ${F}_{\mathrm{line}}/{F}_{{\rm{H}}\beta }$ is the observed (de-reddened) flux ratio between a line of the Xⁱ ion and Hβ, ${\epsilon }_{\mathrm{line}}({T}_{{\rm{e}}},{n}_{{\rm{e}}})$ and ${\epsilon }_{{\rm{H}}\beta }({T}_{{\rm{e}}},{n}_{{\rm{e}}})$ are the line and Hβ emissivities computed at the physical conditions derived in Table 1, ${X}^{i}/X$ is the percentage of the atom X in the Xⁱ ionization stage, and ${\rm{H}}/{{\rm{H}}}^{+}$ is the reciprocal of ${x}_{{\rm{e}}}.$

We selected the brightest lines observed in each species and applied the above formula to derive $X/H.$ While ${\epsilon }_{\mathrm{line}}({T}_{{\rm{e}}},{n}_{{\rm{e}}})$ is an output of our excitation model, ${\epsilon }_{{\rm{H}}\beta }({T}_{{\rm{e}}},{n}_{{\rm{e}}})$ is tabulated by Storey & Hummer (1995) under case B approximation, whose validity has been demonstrated in Paper I. As shown in the same paper, the bulk of hydrogen line emission comes from gas at temperatures not exceeding ∼20,000–25,000 K, so that the above formula cannot be applied to the highest ionized atoms (i.e., ${{\rm{S}}}^{+2},$ Ar${}^{+2},\;$ ${{\rm{O}}}^{+2}$), which are excited at much higher temperatures. To compute the abundance of these species we have therefore taken as a reference the He ii 4–3 line, which is expected to be excited at ${T}_{{\rm{e}}}\;\geqslant$ 30,000–40,000 K (see Table 3). and whose emissivity as a function of ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ is taken from Storey & Hummer (1995). Abundance with respect to hydrogen is then derived by assuming X(He)/X(H) = 0.0995, measured by Esteban et al. (2004) in the Orion nebula. Similarly, since magnesium and carbon emit mainly in neutral and low-temperature zones inside the shock, we compute X(Mg) and X(C) taking as a reference the [O i]6300Å line, assuming the oxygen abundance derived from [O iii] lines and considering that also the [O i] lines come from a region where ${x}_{{\rm{e}}}\;\sim$ 0, as shown in Section 4.2.

The derived chemical abundances are given in Table 4, column 2. We give for each species a range of values, which are obtained by computing the line emissivities for the extreme physical conditions of Table 1. The abundances of phosphorus and chlorine, for which we were unable to directly derive ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}},$ were estimated by assuming the conditions of ions with similar IP_ave, i.e., Fe${}^{+1}$ and ${{\rm{S}}}^{+1},$ respectively.

Table 4.  Chemical Abundances^a

Element	HH 1	Sunb	Sun-HH 1	Orion Nebulac	Orion Nebula-HH 1
C	7.52 $\div$ 7.95	8.39 (0.05)	0.39 $\div$ 0.92	8.40 $\div$ 8.44	0.45 $\div$ 0.92
N	7.57 $\div$ 7.70	7.78 (0.06)	0.02 $\div$ 0.27	7.65 $\div$ 7.73	−0.04 $\div$ 0.16
O	8.60 $\div$ 8.71	8.66 (0.05)	−0.10 $\div$ 0.11	8.51 $\div$ 8.65	−0.20 $\div$ 0.04
Mg	6.11 $\div$ 6.77	7.53 (0.09)	0.67 $\div$ 1.51	⋯	⋯
P	5.00 $\div$ 5.15	5.36 (0.04)	0.17 $\div$ 0.40	⋯	⋯
S	6.78 $\div$ 7.02	7.14 (0.05)	0.07 $\div$ 0.41	7.06 $\div$ 7.22	0.04 $\div$ 0.44
Cl	4.97 $\div$ 5.39	5.50 (0.30)	−0.19 $\div$ 0.83	5.33 $\div$ 5.46	−0.05 $\div$ 0.49
Ar	6.06 $\div$ 6.23	6.18 (0.08)	−0.13 $\div$ 0.20	6.50 $\div$ 6.62	0.27 $\div$ 0.56
Ca	5.12 $\div$ 5.81	6.31 (0.04)	0.46 $\div$ 1.23	⋯	⋯
Ti	4.41 $\div$ 4.67	4.90 (0.06)	0.17 $\div$ 0.55	⋯	⋯
Cr	5.49 $\div$ 5.65	5.64 (0.10)	−0.11 $\div$ 0.25	⋯	⋯
Fe	6.91 $\div$ 7.24	7.45 (0.05)	0.16 $\div$ 0.59	5.86 $\div$ 6.23	−0.68 $\div$ −1.38
Ni	5.60 $\div$ 6.07	6.23 (0.04)	0.12 $\div$ 0.67	⋯	⋯

Notes.

^aIn units of 12 + log(X/H). ^bFrom Asplund (2005). ^cFrom Esteban et al. (2004).

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In columns 3–4 we compare the abundances derived in HH 1 with the solar values. First, we note that most of our determinations are below the solar abundances. This is indeed an unsurprising result, since abundances below the solar ones are found in different environments of our Galaxy (like diffuse clouds, H ii regions, surroundings of B-type stars, see Wilson & Rood 1994 and Savage & Sembach 1996), and, in particular, in the atmospheres of young stars in the Gould's Belt (Biazzo et al. 2012; Spina et al. 2014).

Non-refractory species are, on average, ∼0.15 dex under-abundant, while species commonly bound on dust grains present an average deviation of ∼0.5 dex, magnesium and calcium being the most depleted species. Such a result proves the presence of dust inside the shock. Several studies have been done to evaluate the degree of depletion of the refractory species. In particular, sparse iron depletion factors have been estimated in shock regions, going from around 80% (Mouri & Taniguchi 2000; Podio et al. 2006), to intermediate values between 40% and 70% (Nisini et al. 2002; Giannini et al. 2008, 2013) up to negligible percentages (Böhm & Matt 2001; Pesenti et al. 2003). In this respect, the depletion factor of ∼40% found in HH 1 represents an intermediate case.

An interesting comparison of the found abundances is in principle with the determinations obtained inside the Orion nebula, since the possible differences would directly reflect the effect of the shock passage through the surrounding medium. However, the differences we find with the determinations by Esteban et al. (2004; columns 5–6), mainly for C, Ar and O, are likely more due to a different computational approach than to intrinsic abundance fluctuations. For example, X(C) was computed by Esteban et al. by means of recombination lines, which, as shown by the same authors, always give larger estimates than the forbidden lines. Also, the high, over-solar, X(Ar) measured in that paper, likely arises to the low temperature, not exceeding ∼10,000 K, estimated for the emitting gas. The only species for which the abundance difference between HH 1 and the Orion nebula is really significant is represented by X(Fe). In the Esteban et al. work, X(Fe) is computed under different hypotheses on iron fractional ionization, but in any case X(Fe) is a factor ∼$5\;\div$ 25 lower than in HH 1. Such a major difference likely indicates that iron is highly depleted inside the nebula while partially released in gas-phase inside the shock.

More in detail, our result can be compared with specific studies done on HH 1 in previous works. Beck-Winchatz et al. (1994, 1996) have computed the iron depletion degree in HH 1 by comparing [Fe ii] with [O i] and [S ii] line fluxes, finding abundance ratios similar to the solar ones. As in the case of the Orion nebula, the partial discrepancy with the present result could be due to the approximation on the physical conditions (one single temperature and density) and fractional ionization assumed in those works.

Finally, it is interesting to compare the abundances in the HH 1 bow-shock with those determined in the jet for the refractory species by Nisini et al. (2005) and Garcia Lopez et al. (2008). Hints of a selective depletion were evidenced in those papers by comparing the ratios of different species in knots located at increasing distances from the jet driving source. For example, assuming for all the species the solar abundance, the iron depletion degree decreases from 80% to ∼30% from the internal to the external knots, while the ratio [Fe ii]16435/[Ti ii]21599 increases from 150 to 280, implying a gas-phase X(Fe)/X(Ti) ratio from 3.3 to 1.8 times lower than the solar value (corresponding to [Fe ii]16435/[Ti ii]21599 $\simeq$ 500). Notably, in the bow-shock the iron depletion factor is roughly the same as the external knots, but the above line ratio is ≃500. In a very simple view, these observational evidences can only be explained with an "overabundance" of the gas-phase titanium with respect to iron inside the jet, while in the bow-shock the two species are depleted in similar percentages.