THE THREE-DIMENSIONAL DYNAMIC STRUCTURE OF THE INNER ORION NEBULA^*

The Huygens region has been the subject of numerous imaging studies. Arguably the most useful ground-based study is that of Pogge et al. (1992), which utilized a Fabry–Perot system to isolate emission from the Hα, Hβ, [O iii] 5007 Å, [N ii] 6583 Å and 6548 Å, [S ii] 6716 Å and 6731 Å, and [He i] 6678 Å lines. O'Dell & Wong (1996) presented a mosaic of the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2) images at the superior resolution of the HST. The particular advantage of the HST images is that the WFPC2 images allow clear discrimination of not only the isolated [O iii] 5007 Å line, but also both the Hα 6563 Å line and the nearby [N ii] 6583 Å line in addition to the filters being narrow enough that they provide a good isolation of the emission lines against the strong scattered light continuum that primarily arises from dust grains in the dense region immediately behind the MIF (O'Dell & Doi 1999). A later HST survey (Henney et al. 2007) with the Advanced Camera for Surveys (ACS) covered a wider field of view with pixels one half the angular size of those in the WFPC2, but the filters used do not allow a clear delineation of the important emission lines (O'Dell 2004). The Huygens region has been mapped with the VLA at about 17 resolution (O'Dell & Yusef-Zadeh 2000) at the extinction free 20.5 cm continuum. By comparing the surface brightness calibrated (O'Dell & Doi 1999) images and the radio images, it was possible to derive a map of the optical extinction across the Huygens region and to generate extinction-corrected versions of the HST WFPC2 emission-line images (O'Dell & Yusef-Zadeh 2000). In this study, we employ the several forms of the WFPC2 images, all processed in part using the IRAF package.⁶ We see in Figure 1 that the Orion-S region to the southwest of the Trapezium resembles the bright bar region in being enhanced in low-ionization [N ii] emission and being much brighter than adjacent areas. These characteristics are consistent with the brightest part of the central Huygens region being both closer to θ¹ Ori C and also being an inclined face of ionized gas. This picture is consistent with the results of the 3D modeling of Wen & O'Dell (1995).

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Although the optical extinction of the Veil has been recognized for some time, it has been established only recently (O'Dell et al. 1992; O'Dell 2002) that most of this extinction arises from the near side of the ionized zone and not within it. The detailed analysis of Abel et al. (2005, 2006) established that the physical conditions in the two 21 cm H i absorption velocity components of the Veil are rather different, the energy density in their component A being dominated by the magnetic field measured from the Zeeman effect. The elements C, S, Mg, and Si are ionized in the Veil by the far-ultraviolet (FUV; 5–13.6 eV) radiation that penetrates it, even though the Veil is optically thick to extreme-ultraviolet (EUV) radiation. There must be a secondary hydrogen ionization front associated with the Veil and on the far side (away from the observer and closer to θ¹ Ori C) of the Veil. Abel et al. (2006) identify emission lines probably arising from the Veil's ionization front.

The radial velocities of the various emission and absorption line components along the line of sight through the Trapezium are summarized in Table 1.

Table 1. Heliocentric Velocities of the Major Orion Nebula Components

Designation	Components	V☉(km s−1)	Source
VOMC	Molecules	25.8 ± 1.7	O'Dell et al. (2008)
VMIF	[O i], [S ii]	25.5 ± 1	O'Dell (2001b)
VMIL	[O ii], [O iii], [N ii], [Cl iii], H+, He+	18.0 ± 1.4	O'Dell (2001b)
VTrap	θ1 Ori A, θ1 Ori B, θ1 Ori D	24 ± 3	Abt et al. (1991)
VCluster	Lower mass stars	25.8 ± 1.0	Fürész et al. (2008)
$V_{\theta ^{1}\rm Ori C}$	θ1 Ori C	13	Stahl et al. (2008)
VArc	Big Arc	9.2 ± 1	This study
$V_{\rm Veil-H^{+}}$	S++, P++, [N ii], He i, [O ii]	3 ± 2	Abel et al. (2006)
VHI − A	H i	23.4 ± 0.01	Abel et al. (2006)
VHI − B	H i	19.3 ± 0.03	Abel et al. (2006)
$V_{\rm H_{2}CO}$	H2CO absorption	28.6 ± 1.6	Mangum et al. (1993)

Note. Local standard of rest velocities can be obtained by subtracting 18.1 km s⁻¹ from V_☉ values.

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An early study (Johnston et al. 1983) at 16'' resolution detected H₂CO in absorption against the radio continuum with the location identified as Orion-S, a region with multiple known molecular emission lines (O'Dell et al. 2008) and well-defined bipolar molecular outflows in CO (Zapata et al. 2005) and SiO (Zapata et al. 2006). A higher resolution (51 × 76) study (Mangum et al. 1993) confirmed the presence of this absorption feature and the results are shown in Figure 1 and Table 1. In Figure 1 we see that the H₂CO absorption is distinct from the bipolar outflows, the strongest IR and radio sources, and the sources of the high-velocity optical outflows (O'Dell & Henney 2008). Mangum et al. (1993) point out that the presence of H₂CO in absorption means that the cloud containing it must lie in front of the ionized gas, a position also taken in more general form by Johnston et al. (1983) and Wilson et al. (2001). Since H₂CO can only exist in a cold dense gas that is optically thick to FUV (and therefore also EUV) radiation, there will be a corresponding high extinction at visual wavelengths. Therefore, we have looked for optical extinction associated with this feature with the results described in the next section.

The optical appearance of the Huygens region is strongly affected by extinction occurring within the Veil. The clearest example is the Dark Bay feature to the east-northeast of the Trapezium. This extinction generally decreases away from the Dark Bay as the line of sight is moved to the southwest. The extinction has been derived in several fashions. In slit spectroscopy, the common approach has been to compare the flux ratios of the strongest Balmer series lines with the ratios expected from theoretical predictions calculated for the local conditions (primarily the electron temperature). A good example of this is the study of Baldwin et al. (1991), who obtained sample spectra along a well-defined east–west path beginning about 30'' west of θ¹ Ori C and derived the extinction by comparing Paschen lines with Hγ. The highest spatial resolution study is that of O'Dell et al. (2003), where calibrated HST WFPC2 Hα and Hβ images from a single WFPC2 pointing to the southwest of the Trapezium were compared with theory. Pixel-by-pixel extinction corrections were obtained as part of a study of electron-temperature fluctuations. The widest field-of-view high-resolution determination of the extinction was that of O'Dell & Yusef-Zadeh (2000) who compared the Hα surface brightness of a mosaic of Gaussian blurred HST WFPC2 images with VLA 20 cm images obtained at 17 resolution. In all these studies similar extinction curves were used (Costero & Peimbert 1970; Cardelli et al. 1989). The derived extinction is commonly expressed as c_Hβ, the logarithm of the extinction at 4861 Å, the wavelength of Hβ. In this work, we will refer to the c_Hβ value derived from the comparison of the radio continuum and Hα as c^vla_hβand to the value derived from comparison of WFPC2 Balmer Hα and Hβ images as c^hα_hβ, while the difference of the two will be $c^{\scriptscriptstyle \mathrm{DIF}}_{\scriptscriptstyle \mathrm{H\beta }}= c^{\scriptscriptstyle \mathrm{VLA}}_{\scriptscriptstyle \mathrm{H\beta }}-c^{\scriptscriptstyle \mathrm{H\alpha }}_{\scriptscriptstyle \mathrm{H\beta }}$.

Although a comparison of the results for c^vla_hβ and c^hα_hβ for nine well-sampled smaller regions showed that there was a good agreement of the results of the two methods for finding c_Hβ (ratio of 0.93 ± 0.19; O'Dell & Yusef-Zadeh 2000), there is reason to expect that the two methods should not agree exactly.

The first reason would be the effect of scattering of the optical lines by dust in the dense photon-dominated region (PDR) that lies immediately beyond the MIF. This scattering is what produces a broad redshifted component in the high-resolution spectra of the intrinsically narrower heavy ion emission lines and it must also be present in the Balmer lines. This is why the continuum of the Orion Nebula is much stronger than expected from simply atomic processes (Baldwin et al. 1991), in effect, the Orion Nebula is also a bright reflection nebula. One would expect the effect of this process to cause an underestimate of c^vla_hβ and would affect c^hα_Hβ less since one is dealing with only the difference in the amount of scattering of the Hα and Hβ lines, rather than the absolute amount at Hα, as done in deriving c^vla_hβ. Taking the fraction of the light scattered in the forbidden lines, this position-dependent effect should only be a few hundredths in the logarithm (dex).

The second reason to expect c^dif_hβ to be nonzero is that when using only the optical emission (the Balmer line ratio method) one is dealing entirely with radiation that has not suffered a large amount of extinction, whereas the radio continuum to Hα method can be thrown off by the fact that some of the total radio continuum is produced by volumes behind regions that are very optically thick to Hα. In this case, one would be using a radio signal from all along the line of sight but Hα emission from only in front of the obscuring material and c^vla_hβ would be too large, i.e. c^dif_hβ would be positive.

The third reason for a difference would be variations in the ratio of total-to-selective extinction. Derivation of c^hα_hβ depends upon the reddening curve adopted, which is primarily determined by the ratio of total-to-selective extinction, while c^vla_hβ is less dependent on this ratio.

Since the presence of H₂CO in absorption indicates that near Orion-S there is a region where radio continuum emission occurs in part behind the totally obscuring cloud, we looked for significant variations in c^dif_hβ in the region southwest of the Trapezium where this could be done. The results are also shown in Figure 1, where we have superimposed the contours of large values of c^dif_hβ. One sees that there are two regions where c^dif_hβ is large, the northerly one nearly coinciding with the H₂CO absorption and the other coinciding with the distinct obscuring feature to its south designated as the stellar wind (SW) cloud (O'Dell & Yusef-Zadeh 2000). This means that in both these regions optical emission lines are recording only part of the ionized gas along the lines of sight. Another way of wording this is that in these regions the model of the MIF based on a single dominant emitting layer cannot be accurate. Since the Wen & O'Dell (1995) study used the reddening-corrected Hα line for reference, in these regions the model will be a depiction of the closer (to the observer) emitting region. This means that the "bump" in the Orion-S region is there, but it is not simply the result of a nearer part of the MIF, but it is an isolated optically thick feature directly ionized on its surface by θ¹ Ori C and behind it is another ionized region. The more southerly region of large c^dif_hβ is probably similar, but it must not be as dense as the Orion-S feature since one does not see H₂CO in absorption.

Nature provides a way of probing where material is located within the Orion Nebula through the ionization shadows created beyond the proplyds. In a study of linear features within the Orion Nebula and the Helix Nebula, O'Dell (2000) established that these features can occur when there is a single dominant ionizing star and an intervening object optically thick to the EUV Lyman continuum (LyC) radiation. The first-order theory for this situation had already been determined (Cantó et al. 1998). Gaseous material lying beyond an object like a proplyd (in the Orion Nebula) or a knot (in the Helix Nebula) will be shadowed from photoionizing LyC photons coming directly from the ionizing star, but will be exposed to LyC photons produced through the recombination of surrounding nebular gas. This diffuse radiation field will be a small fraction of the direct radiation from the ionizing star and there will be fewer higher energy photons than in the direct radiation. The difference in the radiation field is because the recombinations occur preferentially to energy states just above hydrogen's ionization threshold. The lower density of ionizing photons means a lower rate of photoionization and the different energy distribution means that any shadowed gas will equilibrate at a lower electron temperature. The lower temperature means that forbidden line radiation will have a reduced emissivity and recombination lines will have an increased emissivity. This shows up particularly well when looking at the ratio of images in [O iii] and Hα, as shown in Figures 2 and 3. O'Dell (2000) established that the linear rays seen in the [O iii]/Hα image occurred along lines of sight passing through θ¹ Ori C and a proplyd, but not all proplyds have visible radiation shadows.

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These shadowed regions will only appear when there is material present. This means that the absence of a radiation shadow indicates that only low-density gas lies within that conic column. In the case where the radiation shadow does not begin at the proplyd, then the gas occupying the space between the proplyd and the start of the radiation shadow must be of low density.

Figure 2 has had all the linear and nearly linear features traced, solid lines being used for the indistinguishably linear features and dashed lines for the nearly linear features (which cannot be radiation shadows unless second-order effects discussed in O'Dell 2000 are in play). One sees that in essentially every case of a linear feature there is an identified shadowing proplyd and, again, that not all proplyds have radiation shadows. In many cases, the associated proplyd is well inside the radiation shadow (closer to θ¹ Ori C). The general pattern is clear, none of the proplyds near θ¹ Ori C have radiation shadows extending close to them and the proplyds with closely approaching radiation shadows are distant from θ¹ Ori C. We interpret this to mean that there is a region of low-density (or very different ambient condition) gas lying within the approximate boundary shown in Figure 2. This irregular boundary in the plane of the sky is the projection along the line of sight and the central cavity is probably somewhat larger than the outlined boundary. The irregular boundary drawn indicates that there is an asymmetric distribution about the dominant ionizing star θ¹ Ori C.

It should be noted that the high-velocity feature HH 202-S (O'Dell & Henney 2008) also casts a radiation shadow. This indicates that this shock produces a sufficiently high-density gas that it is optically thick to LyC photons and becomes a local ionization front within a generally ionized volume. This vitiates any argument that HH 202 was caused by high-velocity material from the Orion-S region impinging on either the foreground Veil or a section of the MIF that had curved toward the observer and intercepted the collimated outflow.

Within the paradigm of the Orion Nebula being described to first order as a relatively thin blister of ionized gas on the θ¹ Ori C side of the MIF, one expects that the [N ii] emitting zone will be quite narrow as compared with the Hα emitting zone, which includes all of the ionized gas. [O iii] emission must arise from closer to θ¹ Ori C and over a larger volume since the effective temperature of θ¹ Ori C is insufficient to produce a He⁺⁺ zone (where O⁺⁺ has been ionized and [O iii] is not emitted). This means that the [N ii]/Hα ratio is a good indicator of when the MIF is highly tilted with respect to the plane of the sky. This is the reason why the bright bar feature is so well delineated in the left panel of Figure 3. Although there are many unexplained features of the bright bar, the overwhelming evidence is that it is an escarpment in the MIF where we see almost along the local ionization front. This is probably also the correct interpretation of the low-ionization zone to the southwest of the Trapezium that lies on the northeast side of Orion-S.

2.6.1. A Previously Unrecognized High-Ionization Structure within the Inner Huygens Region

2.6.2. Physical Conditions in the [O iii] Shell

The average hydrogen number density of the [O iii] shell, n, can be estimated from the Hα surface brightness (photons cm² s^-1 sr⁻¹) given by

$$\begin{equation} S(\mathrm{H\alpha }) = x_\mathrm{e}\alpha _\mathrm{eff}n^2 L / 4\pi, \end{equation} \tag{ 1 }$$

where L is the path length of the line of sight through the shell and x_e is the electron fraction. Both hydrogen and helium are assumed to be singly ionized, with He/H = 0.0977 (Esteban et al. 1998), so that x_e = 1.0977. The effective line recombination coefficient α_eff has a very weak density dependence and can be approximated in the Case B limit as 1.16 × 10⁻¹³T⁻¹₄ cm³ s^-1 (Osterbrock & Ferland 2006), where T₄ = T/10⁴ K. For a spherical shell of radius R and fractional thickness Δ ≪ 1, the maximum path length through the shell is L ≃ 2Δ^1/2R. The observed radius and thickness of the [O iii] shell vary with position angle (P.A.) by about 50% but we will take R = 2 × 10¹⁷ cm, Δ = 0.28 as typical of the well-defined northern arm of the shell, so that L ≃ R.

The surface brightness of the shell is most easily estimated from the sharp brightness jump at the inner edge of its limb-brightened northern arm. Using WFPC2 images (O'Dell & Wong 1996), flux-calibrated following O'Dell & Doi (1999), and extinction-corrected following O'Dell & Yusef-Zadeh (2000), we find S(Hα) = 2.85 × 10¹⁰photons cm² s^-1 sr⁻¹, which represents about 25% of the total nebular surface brightness at the shell position. We also find [O iii]/Hα = 1.62 and no evidence of any [N ii] emission from the shell ([N ii]/Hα < 0.01).

For the shell temperature, we use the results of Mesa-Delgado et al. (2008) who find T ≃ 8300 K at the position of the shell from the ratio of the 4363 Å and 5007 Å [O iii] lines (the upper-right panel of their Figure 6). This temperature represents an average of the emission from the shell and the background nebula at that position, but there is no evidence for any significant jump in T at the inner edge of the shell, so we can be confident in using it for the shell temperature, giving an effective recombination coefficient of 1.36 × 10⁻¹³cm³s^-1.

Combining all of the above, we find a shell-emission measure of EM = x_en²L = 2.56 × 10²⁴cm^-5 and hence a density n = 3400 cm^-3. The ionizing flux at the position of the shell is Φ_H = Q_H/4πR² ≃ 3.6 × 10¹³ cm^-2 s⁻¹, where Q_H is the ionizing luminosity of θ¹ Ori C, assumed to be 1.8 × 10⁴⁹ s⁻¹ (Henney et al. 2005).

The ionization parameter in the shell (Φ_H/nc = 0.35) is very large when compared with typical values for the nebula as a whole (0.01–0.02). Therefore, if dust grains are not significantly underabundant, the grains will dominate the ultraviolet opacity of the shell. Assuming a dust extinction cross section of σ_d = 10⁻²¹ cm² per H nucleon (Baldwin et al. 1991), the optical depth of grains in the shell to ionizing radiation is nσ_dRΔ ≃ 0.2. For comparison, the neutral hydrogen optical depth is much smaller: α_BEM/Φ_H ≃ 0.022. Thus, the shell is optically thin to EUV radiation, which, combined with the high-ionization parameter, means that low-ionization lines such as [N ii] are expected to be very weak. Indeed, no detectable [N ii] emission is observed from the shell.

In spite of its brightness, it has been difficult to determine the 3D space motion of θ¹ Ori C, the dominant ionizing star. This is true for both the tangential and radial velocity components that are needed for deriving this motion.

The brightness relative to the other cluster members presents particular challenges in determining the tangential velocity. The most accurate study is that of van Altena et al. (1988), who determined that θ¹ Ori C was moving at 4.8 ± 0.5 km s⁻¹ toward P.A. 142° and that this was significantly larger than the dispersion value of 1.5 ± 0.1 km s⁻¹ found for the other cluster stars (49 cluster members in the sample). Jones & Walker (1988) did not include the brightest members of the ONC in their astrometric study, but did find a velocity dispersion of 1.5 ± 0.7 km s⁻¹ for the brighter stars in their study. Tan (2004) interpreted this high tangential velocity away from the direction of the imbedded BN–KL cluster stars as evidence that θ¹ Ori C shares a point of origin with the radio source Becklin–Neugebauer (BN), which is moving in the opposite direction at a high velocity (38 km s⁻¹ at P.A. = 322°), and that the present tangential velocity would have placed the BN object in the vicinity of the Trapezium about 4000 years ago. However, subsequent studies (Rodríguez et al. 2005; Gómez et al. 2005, 2008) of the radio sources within the BN–KL region show that three radio sources in the center of the BN–KL region are moving away from a common center with a timescale of 500 years and that the BN–KL source I used for reference by Tan (2004) was one of the moving objects. Gómez et al. (2005) found that BN was moving toward the northwest at 24 km s⁻¹ in the Orion cluster rest frame. The separation of θ¹ Ori C and the dynamic center of BN–KL is 63'', which means that a backward projection of θ¹ Ori C's tangential motion as determined by van Altena et al. (1988) would cross that position in about 28,000 years. Even if it is moving away from the BN–KL center, this timescale indicates that it is unlikely that θ¹ Ori C is a runaway object from the BN–KL region event that produced the three escaping radio sources and the bipolar outflow with an upper limit age of 1000 years (Doi et al. 2002) that has produced the well-known H₂ fingers.

Even the modest anomalous tangential velocity of 4.8 km s⁻¹ may be too high. The data of van Altena et al. (1988) indicate that θ¹ Ori C and θ¹Ori B are moving in opposite directions at about 3.5 mas year⁻¹. In a compilation of visual astrometric measurements of the relative positions of the Trapezium stars, Allen et al. (1974) present results for these two stars over a time interval of 125 years, during which time the stars would have separated by 043, but there is no detectable change to an accuracy of about 015.

Determination of the radial velocity of θ¹ Ori C is also difficult (O'Dell 2001b; Vitrichenko 2002). In this case the brightness of the star aids the collection of high-velocity resolution spectra, but the star is complex, being an oblique-rotation magnetic star which shows a bewildering pattern of periodic and erratic spectral changes. It has a resolved early-type star companion. The properties of the system are summarized in Muench et al. (2008). Utilizing only spectroscopic radial-velocity data, Vitrichenko (2002) determined a systemic radial velocity of 10.9 ± 2 km s⁻¹ and by combining spectroscopic and astrometric (Kraus et al. 2007; Patience et al. 2008) data, Stahl et al. (2008) have determined the systemic radial velocity of θ¹ Ori C as 13 km s⁻¹, which is quite different from that of the other Trapezium stars and the lower mass ONC members, as summarized in Table 1, and indicating that it is moving rapidly away from the OMC and its host star cluster (relative velocity about 13 km s⁻¹). In Section 3.4, we examine the effect that such a rapid motion for θ¹ Ori C would have on the present structure and evolution of the Orion Nebula.

This special characteristic (high spatial velocity) may not be all that unexpected. Stone (1991) concludes that in general 40% of all O stars are runaways, although only one in 10 OB stars has a known binary companion. There is an observational selection effect operating in the ONC that favors detection of blueshifted radial velocities. A redshifted runaway would be moving into the obscured portion of the OMC and we would not be seeing the photoionized Orion Nebula at visual wavelengths. This means that if we are going to detect an anomalous radial velocity, it is going to be a blueshift. The difference in radial velocity with respect to the other Trapezium stars would mean that either this juxtaposition of massive stars is coincidental or perhaps that dynamical interactions with the other stars has produced θ¹ Ori C's anomalous radial velocity.

Certainly, runaway stars are expected from a grouping like the Trapezium (Pflamm-Altenburg & Kroupa 2006) and have been created previously in the ONC. The divergence from Orion of the two high-velocity stars AE Aur and μ Col has been known for over a half century (Blaauw & Morgan 1954). Calculations of the trajectories of these stars and ι Ori (Hoogerwerf et al. 2001) indicate that they all originated about 2.5 million years ago from a position now occupied by the ONC. This is not to argue that these stars arose in the Trapezium grouping, however, it is evidence that there was an earlier epoch of massive star formation in this vicinity. Given today's presence of three centers of star formation (the ONC, BN–KL, and Orion-S), it is not hard to accept that there was at least one earlier similar center. Likewise, the earlier creation of runaways argues that this could have again occurred and θ¹ Ori C is the product.

The presence of a high-velocity SW from θ¹ Ori C is characteristic of early spectral type stars and will certainly affect the conditions of the nearby nebular gas. In this section we address the nature of the wind, its expected interactions, and compare the expectations with what is observed.

The radiatively driven SW is modified by the star's strong dipolar magnetic field (Donati et al. 2002), leading to a very anisotropic outflow (Smith & Fullerton 2005). However, the large inclination between the magnetic and rotation axes (Wade et al. 2006) means that much of this anisotropy is smoothed out over the 15.422 day rotational period (Stahl et al. 1993, 1996), so that it is reasonable to assume that the wind is approximately isotropic when considering its interaction with the Orion Nebula. Angle-averaged values for the mass-loss rate and terminal velocity of $\dot{M}_\mathrm{w}= 4 \times 10^{-7} M_\odot \mathrm{yr}^{-1}$ and V_w = 1400 km s⁻¹ have been determined from modeling the X-ray emission from the base of the wind (Gagné et al. 2005).

A totally independent measurement of the strength of the fast SW is provided by the [O iii]/MIR arcs seen in front of the closest proplyds to θ¹ Ori C (Hayward et al. 1994; Bally et al. 1998; Robberto et al. 2005; Smith et al. 2005), which are interpreted as the stationary stand-off bowshocks that result from the interaction of the proplyd photoevaporation flow (PF) with the SW (García-Arredondo et al. 2001). The position of these bowshocks is determined by the balance between the ram pressures of the proplyd outflow and the fast wind from θ¹ Ori C, so that they can be used as probes of $\dot{M}_\mathrm{w}V_\mathrm{w}$ so long as the proplyd parameters can be determined with sufficient precision. Application to the best-studied proplyd 167-317 (García-Arredondo et al. 2001, 2002; Henney et al. 2002) yields a value of $(\dot{M}_\mathrm{w}/ 10^{-7} M_\odot \mathrm{yr}^{-1}) (V_\mathrm{w}/ 1000\; \mathrm{km\ s}^{-1}) = 4.6 \pm 1.4$, which is consistent with the Gagné et al. (2005) values given above.

3.1.1. Theoretical Predictions of the Wind/Nebula Interaction

The interaction of the fast wind from θ¹ Ori C with its surroundings differs from the standard spherical hot-shocked wind bubble scenario (see e.g., Dyson & Williams 1997) due to the effects of geometry, density gradients, mass loading from embedded sources, and possibly thermal conduction. The different wind interaction regions are summarized in Figure 4, which synthesizes findings from many recent theoretical and observational studies. Each region is discussed further below, starting from the inside. We concentrate on the inner parts of the nebular that are relevant to the observational material presented in this paper, leaving aside considerations of the EON from which X-ray evidence of SW interaction has recently been reported (Güdel et al. 2008).

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Mass-loading zone. Mass loading of an SW by embedded sources lowers the SW velocity of the unshocked wind and consequently reduces the temperature and modifies the cooling properties in the hot-shocked wind region (Hartquist et al. 1986). In the Orion Nebula, the sources of mass are the photoevaporated flows from the close-in proplyds (PB in the figure) and the SWs from the other Trapezium stars (SB). Of these sources, the proplyds are the most important (García-Arredondo et al. 2001), since the mass-loss rate from each proplyd is of the same order as $\dot{M}_\mathrm{w}$ (Henney & O'Dell 1999; Henney et al. 2002), whereas the most massive of the other Trapezium stars are early B-type, with winds at least an order of magnitude weaker than that of θ¹ Ori C (MS in the figure). Unfortunately, the efficiency of the mixing between the SW and the proplyd PFs is poorly constrained (García-Arredondo et al. 2002), leading to large uncertainties in the degree of deceleration of the wind. However, as long as the mixed wind remains highly supersonic, its momentum $\dot{M}_\mathrm{w}V_\mathrm{w}$ is conserved.

Shocked wind. When this mass-loaded, but still supersonic, wind interacts with the nebula, a two-shock flow pattern is formed (Pikel'ner 1968; Dyson & de Vries 1972): an outer shock that accelerates the nebular gas and an inner shock (the blue double-dashed line in Figure 4) that decelerates the SW. The two shocked regions are separated by a contact discontinuity (blue dotted line), across which the pressure is continuous. If the inner wind shock is nonradiative (as is usually the case), the shocked SW will have a temperature T/10⁶ K ≃ 0.15(V_w/100 km s⁻¹)² and a thermal pressure roughly equal to the ram pressure at the inner shock.

Large-scale density gradients in the adjoining MC mean that the inner shock is much closer to the star in the cloud direction (upper-left in Figure 4) than in the opposing direction (off-picture to the lower-right), leading to a higher pressure of the shocked SW in the cloud-facing direction, which therefore flows toward the low-density end of the bubble (Arthur & Hoare 2006) in a transonic wind exhaust (WE in Figure 4). A simple steady-state model then gives the radius of the wind shock as 0.73 times the radius of the contact discontinuity.

Shocked nebula. In the early evolution of an H ii region, the ionization front is likely to be trapped inside the dense shell swept up by the outer wind-driven shock (García-Segura & Franco 1996; Arthur & Hoare 2006). The density in the shell decreases with time, so that the ionization front eventually escapes from the shell and drives a low-velocity neutral shock ahead of itself into the molecular gas (Arthur 2007). After this time, the outer wind-driven shock will be interacting with photoionized nebular gas, as shown in Figure 4. If this gas is static, with a constant hydrogen number density n cm^-3, then the outer shock will degenerate into a sound wave after ≃1.3/n^1/2 million years (Dyson & Williams 1997), leading to dissipation of the shocked nebular shell, after which one will have approximate static pressure equilibrium between the H ii region and the shocked wind. In the cloud-facing direction, where the ionized density is n = 10³–10⁴ cm^-3, this will occur on a timescale much shorter than the age of the nebula, so that stagnant zones of ionized gas (SI in Figure 4) can be confined by the wind (Arthur & Hoare 2006). In the direction away from the cloud, the ionized density is much lower, n < 100 cm^-3 (Felli et al. 1993), so that one may still have a dynamic shell (DS) of swept-up H ii region that moves outward at a few tens of km s⁻¹.

Additional structures will arise due to the internal dynamics of the ionized gas in the H ii region. Turbulence and gravitational collapse in MCs (Vázquez-Semadeni et al. 2005) produce density concentrations on multiple scales (idealized as dense cores, DC, in Figure 4), which retard the progress of the ionization front. In regions where the ionization front is locally convex or flat, PFs will develop (Henney et al. 2005; Mellema et al. 2006), which reach mildly supersonic velocities of 20–40 km s⁻¹ (Dyson 1968; Bertoldi 1989). Where one of these PFs interacts with the SW bubble, a stationary shell (SS) of shocked ionized gas will form at a position where the ram pressure of the PF balances the thermal pressure of the shocked wind.

3.1.2. Observational Evidence for the Effects of the Wind on the Ionized Nebula

The several pieces of published and newly derived evidence require that we revise the accepted picture that Orion-S is simply a local rise in the MIF caused by dense underlying material in the OMC. Certainly, this is a region of enhanced density as determined from H¹³CO⁺ observations. The recently published 21'' resolution H¹³CO⁺ maps that include the Huygens region (Ikeda et al. 2007) show that the most massive cores lie about 30'' north of BN–KL and within Orion-S, but these observations cannot discriminate between cores that lie within a foreground optically thick feature and something that lies behind the MIF and within the main OMC filament. However, the presence of H₂CO absorption in the radio continuum (as discussed in Section 2.3) clearly places a high density, very optically thick object in front of an ionized volume and this object could also be the source of the peak in rotationally excited CO emission that lies between the H₂CO absorption feature and the Trapezium (Wilson et al. 2001). The disparity in the extinction derived from radio-to-optical and optical line ratios (as discussed in Section 2.4) further confirms that the optical features we see lie in the foreground of an ionized volume. The low ionization seen on the northeast side of Orion-S is most easily explained as an inclined face analogous to the escarpment causing the bright bar, but not as tilted. Otherwise it is impossible to explain the [N ii] surface brightness this close to the ionizing star.

There are arguments that the foreground Orion-S Cloud hosts the embedded stars that are the sources of several optical features and outflows. A dark rectangular form lies almost exactly on the redshifted SiO outflow and the IR source 139-357. It is not certain which (or if both) of these two features is associated, but an association of an optical feature with either places that feature in the foreground, rather than something within the OMC. There is a suggestive notch in the H₂CO absorption contour coincident with both the blueshifted outflows in SiO and CO, so that one or both of these must be in the foreground feature. The presence of high-ionization, high tangential velocity features symmetric with the Dark Arc (O'Dell & Yusef-Zadeh 2000; O'Dell et al. 2008) indicates that it is also part of the foreground structure.

The H₂CO absorption indicates very high optical depths in the near ultraviolet and it is unlikely that the obscuration by the foreground feature stops at the lowest contour of detection of H₂CO absorption. This high extinction allows us to comment on the location of the sources that give rise to optical outflows. The sources of the large-scale optical outflows have been isolated to a small region shown as the dark dashed-line ellipse in Figure 1 (O'Dell et al. 2008). These outflows are all blueshifted. The east-oriented HH 529 shocks are high ionization and are seen very close to the source, indicating that this flow emerges quickly from behind the local ionization front. The west-oriented HH 269 shocks and jet also emerge close to their sources and are seen visually, arguing that they too originate in the foreground Orion-S Cloud. The emergence further from the source region (O'Dell et al. 2008) of the high-velocity gas driving the northwest-oriented HH 202 and the southeast-oriented HH 203 and HH 204 could either indicate that their sources are more deeply imbedded in the Orion-S Cloud or lie within the background OMC. The latter interpretation would imply that the lack of visibility near the source region is due to the high optical extinction of the Orion-S Cloud, but it seems more likely that all the sources lie at a similar distance along the line of sight.

There is a question about the location of the strongest IR and radio sources in this region: 137-408 (CS 3 in earlier, low-resolution studies) and 134-411 (FIR 4 in earlier, low-resolution studies). The symmetry axis of the nearby HH 530 shocks points to either of these sources and the proximity of such an optical feature argues that its source lies in the foreground Orion-S Cloud.

The far-IR emission from dust heated by embedded strong IR sources (Houde et al. 2004) indicates (Figure 1) a peak in the vicinity of BN–KL and a weaker elongated peak in the Orion-S feature. The northerly extension of this southern feature coincides with the source region for the optical outflows and the southerly extension coincides with the 137-408 and 134-411 sources. Unfortunately, this does not tell us if the southerly extension belongs to the foreground feature or lies within the OMC.

The most likely geometry for this region is shown in Figure 5. In this model, we have placed the Orion-S Cloud far enough into the foreground that the MIF extends continuously behind it. The exact placement of the Orion-S Cloud in the foreground is uncertain, but it must be close to the distance of θ¹ Ori C in front of the local MIF because if it were much further from the observer it could not be distinguished from the MIF. In the same way that the bright bar probably represents where the ionization front of the nebula encounters a long high-density condensation within the host OMC, it is likely that the Orion-S Cloud was a high-density feature within the OMC, which has been isolated as the ionization front progressed into the host MC. This conclusion is compatible with the fact that the velocity of the H₂CO extinction feature $(V_{\rm H_{2}CO} = 28.6\pm2)$ is essentially the same as the host MC (V_OMC = 25.9± 1.7).

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Distinctly different heating processes are important in various regions of the Orion environment. Starlight is the most important heating/ionization process in the bright H⁺ region and its associated PDR. Wind-driven shocks are responsible for much of the geometry and emission of the BN object. Cosmic rays and heating by dissipative MHD waves may be important in deeper regions of OMC1. Given the assortment of possible dynamical and microphysical processes involved, two approaches to numerical simulations of the ISM can be taken. Hydrodynamics codes follow the motions of the gas but must compromise on the microphysics to solve the problem on today's computers. A microphysics code (like Cloudy, which we use here) will not compromise on the microphysics but must do something simple for the structure of the cloud. Atomic processes are usually much faster than dynamical timescales so the physics that determines the spectrum is often not affected by the dynamics and a static geometry can be assumed.

In this section, we wish to understand several overall features of the Orion-S Cloud via a simulation of the ionization, thermal, and chemical state of the cloud. The primary question we want to answer is "can we explain the presence of H₂CO in absorption?" Furthermore, can we do so in the context of other molecules seen in emission and the geometrical constraints imposed by the projected size of Orion-S? There are estimates of the gas column density, particle density, temperature, and gas pressure (which is surprisingly high). Can starlight from the Trapezium cluster account for these general properties, or are other processes at play? Here, we test whether starlight from the Trapezium cluster can account for several of the observed properties of Orion-S.

3.3.1. Observational Constraints and Geometry

The most important constraints to modeling the Orion-S Cloud are the H₂CO absorption measurements, the total column density, and the projected size of Orion-S. In cold, dark MCs, chemical models, which include the effects of accretion of molecules onto grain surfaces (Hasegawa et al. 1992; Hasegawa & Herbst 1993), show that H₂CO will reside almost exclusively on the surface of grains (henceforth "freeze out") at temperatures at or below 10 K. A temperature of 10 K is also consistent with the ionized and molecular gas in Orion-S being in gas-pressure equilibrium (see below). However, since H₂CO is observed in the gas phase in Orion-S, the temperature must be higher, such that the rate of evaporation of H₂CO from grain surfaces, k_evap = 1.7 × 10¹²exp(−1760/T_d), must be large enough to produce a significant gas-phase abundance of H₂CO. Figure 6 shows that this rate will be fast (>10⁻¹⁰s⁻¹) for T_d > 34 K. Therefore, H₂CO observations imply that the dust temperature (which should be nearly in equilibrium with the gas temperature for deeper regions of the cloud) needs to be roughly 30 K or higher in order to explain the presence of H₂CO. The total H column density is given in McMullun et al. (1993), who through 1.3 and 3.1 mm dust continuum emission found N(H) ∼ 4 × 10²⁴ cm^-2 for the region 12'' N of the 3.1 mm continuum peak, corresponding to a region they referred to as the local quiescent cloud. The projected separation of the Trapezium stars from Orion-S is 2.2 × 10¹⁷ cm, and the projected diameter of the cloud is ∼2.8 × 10¹⁷ cm. Assuming an approximately spherical shape then gives a total cloud mass of 280 M_☉ (McMullun et al. 1993).

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The close proximity of Orion-S to the Trapezium means there must be an H⁺ region on the side of Orion-S facing the Trapezium. Optical emission lines suggest that it has a density of ∼6000 cm^-3 (Pogge et al. 1992; García-Díaz & Henney 2007), corresponding to a gas pressure of P/k = 2nT = 1.08 × 10⁸ cm^-3 K, assuming a gas temperature of 8500 K. For the assumed thickness of Orion-S, and the above estimate of N(H), the density deep in the MC of Orion-S is 3 × 10⁷ cm^-3. If the environment were in gas-pressure equilibrium, then the corresponding MC pressure, 0.5nT = 2 × 10⁷Tcm^-3 K, would correspond to a temperature of 7 K. However, as noted above, this is inconsistent with the presence of gas-phase H₂CO, indicating that the gas pressure in the molecular gas must be several times higher than that in the ionized gas.

There are at least four different factors that may account for this overpressure of the molecular gas:

• 1.  
  If the ionization front on the surface of the cloud is D-critical, then the transonic ionized flow from the front contributes an additional ram pressure term, which is roughly equal to the thermal pressure. On the neutral/molecular side, the net flow toward the front is highly subsonic, so the ram pressure term there is negligible. In a steady-state equilibrium, this gives a molecular gas pressure twice that of the ionized gas.
• 2.  
  Absorption of the momentum of the stellar photons produces an outwardly directed effective gravity. In a steady-state configuration, in which the molecular gas is forced to remain at rest with respect to the star, this must be balanced by a pressure gradient between the optically thin and optically thick portions of the cloud.
• 3.  
  If the cloud is self-gravitating and hydrostatic, then the deeper gravitational potential in the center of the cloud will produce a higher pressure for the molecular gas there than for the ionized gas at the cloud surface.
• 4.  
  If the cloud is a transient phenomenon, formed from the dynamic interaction of converging flows, then there is no reason to expect it to be in pressure equilibrium at all.

On the other hand, there are two factors that would tend to work in the other direction:

• 5.  
  Magnetic fields tend to be relatively weak in ionized nebulae (Heiles et al. 1981), with magnetic pressure smaller than the gas pressure. In MCs, on the other hand the reverse is frequently true, with the magnetic pressure typically exceeding the gas pressure by a factor of 10 or more (Crutcher 1999).
• 6.  
  Turbulent internal motions in MCs are frequently supersonic, with turbulent ram pressure approximately equal to the magnetic pressure.

Therefore, the increase in gas pressure, when going from ionized to molecular gas, indicates that one or more of the first four factors must outweigh factors 5 and 6.

3.3.2. An Equilibrium Cloudy Model of Orion-S

We perform calculations with version 8.0 of the spectral synthesis code Cloudy, described by Ferland et al. (1998). Extensions to PDR physics and chemistry are described by Abel et al. (2005, 2008). The gas-phase composition and dust properties of the Orion environment are well known and are given in Abel et al. (2004a).

Our choice of ionizing continuum is characteristic of the dominant source of ionizing photons, the O7 star θ¹ Ori C. We assume a Kurucz stellar atmosphere with a temperature of 39,600 K, and Q(H) = 1.7 × 10⁴⁹photons s^-1. We include X-ray emission from the SW (see Section 3.1), modeled as a 10⁶ K bremsstrahlung component, although this does not affect the results presented below.

For simplicity, we consider a time-independent, magnetostatic equilibrium for the Orion-S Cloud, as has been recently employed to account for the structure and observed magnetic field in M17 (Pellegrini et al. 2007). The current version of Cloudy does not treat self-gravity, and we also ignore gas motions and time-dependent effects, so the model cannot directly address factors 1, 2, or 4, listed in the previous section. In the model, the total pressure increases as one proceeds into the cloud in such a way that the local pressure gradient exactly counterbalances the acceleration due to absorption of radiation. The total pressure is the sum of the thermal, magnetic, turbulent, and trapped resonance line radiation contributions. For simplicity, we assume that the turbulent pressure is in equipartition with the magnetic field and that the magnetic field is tangled on small scales and well coupled to the gas, so that the magnetic stress tensor reduces to an isotropic pressure that is polytropic, with index γ_m = 4/3 (Henney et al. 2005). The magnetic field of the entire cloud is then set by the field at the illuminated face, increasing as B ∼ ρ^2/3. The magnetic field in Orion-S is not known but fields are important elsewhere in the Orion environment (Abel et al. 2004a). The initial magnetic field was taken as 3μG, which rises to 850μG deep inside the cloud, where the combined magnetic and turbulent pressures become roughly equal to the thermal pressure. We found that models with stronger magnetic fields were not capable of reproducing the observed molecular hydrogen density deep in the cloud of n ≃ 3 × 10⁷ cm^-3, since factors 5 and 6 of Section 3.3.1 were too effective in counteracting factor 3.

We assume a closed geometry, in which all radiation must eventually escape in the direction away from the central star cluster, which is appropriate if optically thick gas fully surrounds the cluster. Under this assumption, inwardly directed diffuse emission is compensated by symmetric emission from the other side of the star cluster. Light can undergo multiple scatterings as it diffuses outward though the cloud, so that the total rate of momentum transfer exceeds the single scattering limit, L_*/c, by a few factors. We use the McMullun et al. (1993) deduced hydrogen column density to set the total thickness of the cloud.

The entire structure and properties of the cloud follows from these assumptions. Cloudy computes the kinetic temperature, ionization, chemistry, optical depths, and emission properties of the gas at each point. The density and radiation field striking the illuminated face are set by observations and the gas pressure at this point is computed. The calculation follows the starlight as it penetrates the cloud. The transmitted continuum sets the pressure and physical conditions. The magnetic field follows from our flux-freezing assumption. The total pressure is set by the assumption of magnetostatic equilibrium. The calculation stops when the observed column density is reached.

Figure 7 shows the results of our calculations for the density, temperature, molecular abundances, and pressure as a function of depth into the cloud. The first criterion we demand our model reproduce is clearly satisfied: that the model yields a temperature high enough to allow H₂CO to evaporate off of grain surfaces and remain in the gas phase. The dust temperature (Figure 7(b)) remains above 38 K throughout the model, which, as discussed above in Section 3.3.1, is high enough to inhibit freeze-out of H₂CO. This is achieved in our model purely through external heating by starlight from the Trapezium.

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Although we can explain the presence of gas-phase H₂CO using our model, the chemistry of Orion-S is extremely complex. At our MC temperature of 38 K, some molecules, such as SiO, CS, and SO₂, will freeze out onto grains. Figure 7(c) shows the predicted CO, CN, OH, and SiO abundance as a function of A_V. Our prediction of SiO, once the full effects of freeze out and molecular evaporation off grain surfaces are included, will likely be quite different. The current version of Cloudy only treats freeze-out and evaporation processes involving CO, OH, and H₂O, with the goal of making accurate predictions of gas-phase oxygen deep in MCs. The freeze-out of other atoms/molecules, such as SiO, is not considered by our models, and neither are grain-surface reactions, other than those that form H₂. So, while our current analysis is sufficient to deduce that H₂CO remains in the gas phase, a full treatment of gas-grain and time-dependent chemical effects is necessary to fully understand all the rich chemical environment of Orion-S. ¹²CO and ¹³CO lines are optically thick and not sensitive to gas properties such as pressure or column density. C¹⁷O and C¹⁸O should be optically thin and therefore potentially a good diagnostic of physical properties. However, as Orion-S and OMC1 lie along the same sightline with similar kinematic properties, the optically thin CO emission from OMC1 and Orion-S is difficult to disentangle. Therefore, we do not present CO comparisons because of these complexities.

While our current analysis is sufficient to deduce H₂CO remains in the gas phase, a full treatment of gas-grain and time-dependent chemical effects is necessary to fully understand the chemical environment of Orion-S. Such a treatment, while beyond the scope of this work and the current version of Cloudy (Cloudy currently only treats freeze-out of CO, OH, and H₂O), will be the subject of a future investigation.

One appealing aspect of our model is how we succeed in reproducing the projected dimensions of Orion-S under the assumption of magnetostatic equilibrium, with an effective gravity provided by the momentum of the absorbed starlight. The density (Figure 7(a)) varies by ∼4dex over the physical extent of our model, yet our calculation reaches N(H) ∼ 4 × 10²⁴ cm^-2 at a depth of 2.4 × 10¹⁷ cm, or within 20% of the observed projected thickness. Despite this success, there are arguably some deficiencies in our model assumptions, of which the most serious are the neglect of self-gravity and the rather weak magnetic field. Using the observed mass and size of the cloud (Section 3.3.1), one finds the escape speed at the cloud surface to be 7.3 km s⁻¹, meaning that the molecular gas is gravitationally bound, while the ionized gas is gravitationally unbound. Thus, factor 3 of Section 3.3.1 is likely to contribute significantly to the overpressure of the molecular gas, so that a self-gravitating model would allow the magnetic field in the cloud to be significantly higher, while still satisfying the observational constraints. However, it is not clear that any equilibrium self-gravitating model is possible. Unless the turbulent and magnetic pressures are more than 100 times greater than given by our model, the cloud mass is higher than both the Jeans critical value and the magnetic critical value, and so the cloud may be dynamically collapsing on a free-fall timescale of a few times 10⁴ years.

In summary, our equilibrium Cloudy model represents a necessary compromise, including as it does a detailed simulation of the relevant microphysics, but at the expense of a simplified treatment of some of the relevant macrophysics. As such, although it is broadly successful in accounting for the observed properties of the Orion-S Cloud using almost no free parameters, it should not be considered the last word in modeling this region, especially in the light of the uncertainties outlined in the previous paragraph.

In Section 2.7, we saw that θ¹ Ori C appears to be moving away from the OMC at about 13 km s⁻¹. Since this star is only about 0.2 pc in front of the local MIF, θ¹ Ori C would have been at the present location of the MIF only 15,000 years ago. This is simply a reference number for the dynamic timescale as one would expect that θ¹ Ori C would have continuously ionized the gas immediately surrounding it, thus producing a constantly changing structure. It does appear that θ¹ Ori C has only recently entered a region of low-density gas and has just begun to photoionize a much larger volume of space (the Huygens region and the EON). This is a dramatically new way of viewing the Orion Nebula and means that the object need not be in quasi-dynamic equilibrium. A short illumination age of the ONC stars is quite attractive because the well-determined mass-loss rates of the proplyds close to θ¹ Ori C indicate that they should have been destroyed through photoablation within the last 1.5 × 10⁴ to 1.1 × 10⁶ years (Churchwell et al. 1987; Henney et al. 2002; Smith et al. 2005; O'Dell & Henney 2008). The absence of any evidence for destruction indicates that their illumination ages by θ¹ Ori C are no more than a few times 1.5 × 10⁴ years.

If one accepts the scenario that θ¹ Ori C has emerged from a much higher density environment during the last 10,000 years, then it is worth considering how this picture would change the expected ionization, density, and dynamics of the present-day nebula. If the surrounding density was much higher in the past, then the H ii region would have been much smaller. For example, in an ambient density of n = 10⁶ cm^-3, the Strömgren radius would be only 0.007, or 32. As θ¹ Ori C left the high-density environment, an R-type ionization front would propagate into the low-density gas at a speed of Φ_H/n ⩾ 1000 km s⁻¹, where Φ_H is the ionizing flux, defined in Section 2.6.2. This speed is much larger than the stellar velocity, so that deviations from static photoionization equilibrium would be fleeting and difficult to detect. Assuming a density n = 100 cm^-3 for the low-density gas, the ionization front would reach its equilibrium Strömgren value (≃3 pc) in only 1000 years. The maximum recombination front velocity is also of order 1000 km s⁻¹ so that the gas would recombine effectively instantaneously in the high-density regions vacated by the star. The timescale for molecular hydrogen formation on dust grains is approximately 1000(10⁶ cm^-3/n) yr (Tielens & Hollenbach 1985), so that, unless the previously ionized gas was of rather low density, there has been time for it to return to a fully molecular state.

The density structure of the ionized gas is intimately tied to its dynamics, with typical internal velocities of order the ionized sound speed, which is very similar to the putative stellar velocity of 13 km s⁻¹. It seems likely, therefore, that the ionized density structure will not be greatly affected by the stellar motion. Numerical simulations confirm (Henney et al. 2005; Arthur & Hoare 2006) that an approximately steady-state champagne flow is established on a timescale equal to the sound crossing time. It is therefore at the largest scales in the nebula (>1) that one would expect to find the clearest evidence for nonequilibrium dynamics induced by the stellar motion. However, uncertainties in the exact ambient density distribution and the effect of the SW would make it difficult to draw clear conclusions. Another possible observational diagnostic of a moving ionized star would be the dense neutral wake, which numerical simulations predict should form behind the star (Raga et al. 1997; Kraus et al. 2007). Again, observational detection of such a wake would be very challenging, chiefly due to confusion brought on by the rich profusion of structures at all scales in the MC behind the nebula.

A very young age for the present configuration of the Orion Nebula could also remove the dilemma presented by the fact that the H⁺ layer lying between θ¹ Ori C and the Veil is moving toward the Veil with a closure velocity of about 18 km s⁻¹ and there is no evidence of an interaction with the Veil. Abel et al. (2006) calculate that the collision time with the Veil is about 40,000 years. Without a detailed model of the expected very time-dependent structure, one cannot assess the importance of this number except that it too indicates that the present configuration is quite young.

In conclusion, it seems impossible to definitively confirm or rule out the moving star hypothesis, based on existing observational evidence. The strongest argument in favor remains the short mass-loss lifetimes derived for the proplyds in the inner nebula. The strongest arguments against are (1) the required coincidence that θ¹ Ori C currently resides so close to the center of the Trapezium cluster, despite not being dynamically bound to the cluster and (2) the difficulty in explaining how θ¹ Ori C acquired such a high velocity. The mass of the current θ¹ Ori C multiple system is ≃50 M_☉ (Kraus et al. 2007), so assuming that it originally had a velocity typical of ONC members, then to achieve its current velocity it must have ejected a ≃10 M_☉ companion at 65 km s⁻¹, or even faster for a less-massive star. Note that these high stellar velocities mean that many-body interactions at the level of the star cluster are unlikely to play a role since the velocity dispersion of the cluster is only a few km s⁻¹(Jones & Walker 1988) and disruption of binaries by the cluster potential has been shown to be ineffective for binary separations <05 (Reipurth et al. 2007).

One further possibility examined is that the velocity kick of the ionizing star was acquired much more recently. This would sidestep most of the arguments discussed above, both for and against the moving star hypothesis. For example, Tan (2004, 2008) has proposed that the runaway B star known as the BN object (Becklin & Neugebauer 1967) was ejected from the θ¹ Ori C multiple system 4500 years ago (but see Gómez et al. 2005, 2008 for an alternative viewpoint). If the anomalous velocity of θ¹ Ori C is due to this event, then it will only have moved about 0.05 pc since then, which is very small compared with the size of the nebula, so that observable consequences are unlikely. However, one serious problem with this proposal is that the measured radial velocity of BN is +13 km s⁻¹ with respect to the ONC rest frame (Scoville et al. 1983), which is the same absolute value as that recently determined for θ¹ Ori C (Stahl et al. 2008), but in the opposite direction. BN's mid-IR luminosity of 2600L_☉ (Gezari et al. 1998; re-adjusted to a distance of 440 pc) is consistent with a dust-enshrouded main-sequence B2 to B3 star, implying a mass of 9 ± 1M_☉, which is more than five times less than the mass of θ¹ Ori C. Therefore, as discussed in the previous paragraph, momentum conservation means that BN ought to have a much higher redshifted velocity than is observed if it has truly been ejected from the θ¹ Ori C system in the recent past.

In this paper, we have been able to establish several remarkable new properties of the Orion Nebula. (1) There is an incomplete shell of high-ionization gas shaped by the high-velocity wind arising from θ¹ Ori C and open in the direction of detected X-ray emission. (2) The highest surface brightness portion of the Orion Nebula occurs to the southwest of the Trapezium stars, in the region called Orion-S, a center of star formation and stellar outflow. (3) The Orion-S region is caused by an optically thick MC which lies within the ionized cavity of the Orion Nebula. This Orion-S Cloud is the host of a separate region of star formation and is sufficiently cold in the middle that it can produce H₂CO lines in absorption. (4) It is possible that θ¹ Ori C has a large radial velocity with respect to the ONC and other members of the Trapezium. The observations of the nebula do not contradict such a possibility, and the presence of a large radial velocity would resolve the conundrum of the lack of destruction of the disks in proplyds close to θ¹ Ori C and would explain why the inner H⁺ layer expanding toward the observer has not yet reached the Veil feature.