ORION'S VEIL: MAGNETIC FIELD STRENGTHS AND OTHER PROPERTIES OF A PDR IN FRONT OF THE TRAPEZIUM CLUSTER

H i and OH absorption lines are observed against the radio free–free continuum of M42 and M43. An image of this continuum, derived by combining information from line-free channels in the Stokes I image cube, is a natural product of the data. Our 21 cm continuum image has a synthesized beamwidth of 25'' (0.05 pc); our 18 cm (1665 and 1667 MHz) OH images have a synthesized beamwidth of 40'' (0.09 pc). The peak brightness of our 21 cm image is 4.7 Jy beam⁻¹, equivalent to brightness temperature T_B = 5100 K. We do not present our continuum images as separate figures. Equivalent or higher spatial resolution Orion continuum images at similar wavelengths are available in the literature. See especially the 21 cm continuum image of vdWGO13. See also the 20 cm image of O'Dell & Yusef-Zadeh (2000) and the wide-field 330 MHz (90 cm) image of Subrahmanyan et al. (2001). We recover a total 21 cm continuum flux of 290 ± 15 Jy for M42. This value is to be compared with 335 ± 15 Jy found for M42 by vdWGO13. M43 contributes an additional 12 ± 2 Jy to our data, compared to 14 ± 2 Jy for vdWGO13. Errors reflect uncertainties in the allocation of flux between M42 and M43. See van der Werf & Goss (1989, hereafter vdWG89) and vdWGO13 for additional information about the total Orion 21 cm continuum flux density.

We constructed an H i optical depth image cube from the Stokes I image cube and the Stokes I continuum image. Toward the brightest part of M42, we measure peak H i optical depths as high as τ_{0, H i} ≈ 5. Over much of the Huygens region, we measure τ_{0,H i} of up to 4, and we measure H i optical depths out to the continuum brightness contour that is 3% of the peak. In general, H i optical depths increase from the southwest toward the northeast of the Veil, and the H i lines are saturated in the northeast sector of the image. Line saturation precludes measurement of τ_{H i} ∝ N(H⁰)/T_ex, where T_ex is the H i line excitation temperature. However, line saturation does not preclude detection of the H i Zeeman effect; see Section 3.4.

The spatial variation of H i optical depths has already been described by other authors beginning with Lockhart & Goss (1978). In particular, vdWG89 observed H i absorption in the Veil with the VLA C-array. Although their velocity resolution was half that of the present observations, they were able to identify several velocity components. Principal among them are components A and B (their designations, adopted here). Components A and B have typical LSR center velocities of 5.0 and 1.3 km s⁻¹, respectively, and typical FWHM of 2.5 and 3.6 km s⁻¹, respectively (Table 4). Clearly, there are multiple layers of H⁰ gas in the Veil. vdWG89 performed a Gaussian analysis of their H i optical depth data cube. From this analysis, they derived images of N(H⁰)/T_ex across the Veil for each component separately. They found that components A and B exist across the entire radio continuum source (M42 and M43), with peak optical depths generally higher in component A. However, an inspection of our more sensitive and higher velocity resolution H i optical depth profiles clearly reveals that the kinematical structure of the Veil is too complicated to be fully described by a two-component model. Nonetheless, the Gaussian decomposition done by vdWG89 provides a good qualitative idea of the distribution of H i velocity components A and B for which we have H i Zeeman effect images (Section 3.4). vdWGO13 also present extensive VLA data on H i absorption and emission in the Veil. However, these authors concentrate on small-scale structure, generally at velocities outside the range occupied by components A and B.

The OH optical depth cubes show that OH absorption across the Veil is qualitatively different from H i absorption in two ways. For one, OH absorption is only detected in four isolated regions, not across the entire Veil. The second difference is that the OH profiles usually consist of a single velocity component, compared to at least two components in the H i profiles. OH absorption is not detected toward the Trapezium Cluster. This absence is expected, given the very low H₂ abundance toward the Trapezium stars (N(H₂)/N(H⁰) ≈ 10^−6.5) measured by UV absorption lines (Abel et al. 2016). The Veil along this line of sight is almost completely atomic owing to the very high stellar radiation field from the Trapezium.

Four regions of OH absorption appear in Figure 2. Here we present a color-coded image of the velocity-integrated 1667 MHz OH optical depth, in units of [N(OH)/T_ex] × 10¹⁴ cm⁻² K⁻¹, where T_ex is the 1667 MHz excitation temperature. To calculate N(OH)/T_ex from the velocity-integrated optical depth profiles, we use the conversion factor given in Roberts et al. (1995), C₁₆₆₇ = 2.28 × 10¹⁴ cm⁻² K⁻¹ (km s⁻¹)⁻¹. This factor assumes LTE conditions. For reference, we overlay 1667 MHz continuum contours in the figure. These contours clearly show M42, as well as M43 to the northeast. Also note the circles in Figure 2 denoting five representative positions in the OH data discussed in the next paragraph. These five circles are also shown in the finder chart of Figure 1(b) (larger circles). The four OH absorption regions are as follows: (1) The most prominent absorption is toward the northeast Dark Lane along the northeast edge of M42. Here, peak 1667 MHz optical depths reach τ_0,1667 ≈ 1, perhaps higher in regions of saturation. (2) Much weaker OH absorption exists toward the Dark Bay. This absorption appears in Figure 2 as a tongue extending westward from the northeast Dark Lane toward the brightest region of radio continuum emission. OH optical depths are highest (τ_0,1667 ≈ 0.04) in the direction of Knot 1 identified by O'Dell & Yusef-Zadeh (2000) in their optical extinction image. (3) OH absorption (τ_0,1667 ≈ 0.12) is observed approximately 1' to the southwest of the peak continuum brightness. This direction closely coincides with the Orion-S molecular core (e.g., Henney et al. 2007), and the absorption appears as a distinct, nearly circular region, suggesting that it is barely resolved in the VLA data. We refer to this absorption as the Orion-S OH absorption, although the connection between OH and Orion-S bears further consideration. See Section 4.4. The Orion-S OH absorption feature has a clear counterpart in H i absorption, with peak optical depth τ_{0,H i} ≈ 0.2 in the present data and 0.45 in the higher spatial resolution data of vdWGO13. See Section 4.4 and Figure 10. Finally, (4) strong OH absorption (τ_0,1667 ≈ 0.6) appears along the eastern edge of M43. This absorption is clearly associated with the dark filament of optically obscuring material in Figure 1(a). This same filament is visible in the 800 μm OMC-1 dust continuum image of Johnstone & Bally (1999).

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To illustrate the nature of OH absorption toward Orion, we choose five representative positions in our image data. We label these positions OH1–OH5. Two of these positions are located in the northeast Dark Lane, and one is located in each of the Dark Bay, Orion-S, and M43 regions. The locations of these five positions are shown in Figures 1(a), 1(b), and 2 as circles of 40'' diameter, the 1665 and 1667 MHz synthesized beamwidth. Table 3 lists these positions and their relevant parameters; Table 2 lists the channel separation and resolution. Figure 3 shows 1667 MHz OH optical depth profiles for each position. Note that the optical depth profile for Orion-S is about a factor of two wider than any of the other profiles. Comparison of the OH optical depth profiles with H i optical depth profiles at these five positions (the latter not shown) indicates that the OH lines always lie within the velocity range of the saturated H i lines. Except for the Orion-S position (Figure 10), it is not possible to identify OH lines with specific H i velocity components owing to H i line saturation.

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Table 3.  Parameters for Positions with 18 cm OH Absorption toward Orion A

No.	Position Location	R.A.a	Decl.a	Vo,67b	ΔV67c	τo,67d	τo,67/τo,65e	N(OH)f	Avg	N(H)h
		(J2000)	(J2000)	(km s−1)	(km s−1)			(cm−2)	(mag)	(cm−2)
OH1	Northeast Dark Lane 1	05h35m322	−05°22'06''	6.4	2.7	0.37	1.7	4.7 × 1015	58	1.5 × 1023
OH2	Northeast Dark Lane 2	05h35m314	−05°20'46''	6.6	1.9	0.97	2.2	8.8 × 1015	110	2.7 × 1023
OH3	Dark Bay	05h35m234	−05°22'29''	3.7	2.7	0.04	1.9	5.6 × 1014	7	1.7 × 1022
OH4	Orion-S	05h35m121	−05°23'56''	6.9	5.2	0.12	1.2	3.8 × 1015	48	1.2 × 1023
OH5	M43	05h35m377	−05°15'46''	9.6	2.2	0.59	1.9	5.8 × 1015	72	1.8 × 1023

Notes.

^aPosition of the center of the 40'' synthesized beam at 18 cm. ^bCenter velocity of the 1667 MHz OH line. ^cFWHM width of the 1667 MHz OH line. ^dPeak optical depth of the 1667 MHz OH line. ^eRatio of peak optical depths of the 1667 and 1665 MHz OH lines. The LTE value is 1.8. ^fOH column density, taken as the average of OH column densities computed separately from the 1665 and 1667 MHz OH lines. Calculation of OH column densities from the individual OH lines was done with the relationships of Roberts et al. (1995), assuming T_ex = 20 K. ^gA_v estimated from the ratio N(OH)/A_v = 8 × 10¹³ cm⁻² mag⁻¹ of Crutcher (1979), who states that the ratio is valid over the range A_v = 0.4–7 mag. If the ratio N(OH)/A_v decreases for A_v > 7 mag, owing to freeze-out or chemical conversion of OH to other species, then some values of A_v in this column are underestimates. ^hN(H) estimated from the ratio A_v/N(H) = 4 × 10⁻²² mag cm² cited by Abel et al. (2004) for the Orion region. Some of these values could be underestimates; see note regarding A_v immediately above.

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For each of the five representative positions of OH absorption (Table 3), we derive N(OH) from the velocity-integrated 1665 and 1667 MHz optical depth profiles. To do so, we use the standard conversion factors C₁₆₆₅ and C₁₆₆₇ from Roberts et al. (1995, see above), and we assume T_ex = 20 K for both OH lines. However, N(OH) ∝ T_ex, and T_ex cannot be measured from our absorption-line data. T_ex can only be measured from a combination of absorption and emission lines along the same line of sight. Using such galactic data toward extragalactic continuum sources, Liszt & Lucas (1996) found T_ex ≈ 4–13 K for the OH main line transitions. Recently, C. Heiles (2016, private communication) analyzed a similar but more extensive data set from the Millennium Survey (Heiles & Troland 2005). Heiles found T_ex for the OH main lines in the range 2–15 K, with the majority of the values below 10 K and many less than 5 K. These OH data toward extragalactic continuum sources likely sample low-density molecular gas (n(H) ≈ 10^2–3 cm⁻³), where the OH lines are very subthermally excited (T_ex ≪ T_K). OH-bearing gas in the Veil is likely to be much denser (see note a to Table 6) and somewhat warmer, the latter owing to its proximity to the Trapezium. Therefore, we expect T_ex to be higher in the Veil than in the low-density molecular gas. According to the theoretical study of Guibert et al. (1978), T_ex for the OH main lines is rather insensitive to T_K. However, T_ex is sensitive to n(H). For a gas with T_K = 50 K, Guibert et al. calculate that T_ex increases from 5 K to an asymptotic value of 30 K in the range n(H) ≈ 10²–10⁴ cm⁻³ (see their Figure 2). Given this trend, we believe that our assumption of T_ex = 20 K for the Veil OH lines is reasonable and likely to be correct to within a factor of two.

Having estimated N(OH) as described above, we use standard conversion factors to scale N(OH) to N(H) and to A_v, where N(H) = N(H⁰) + 2 N(H₂). Results are given in Table 3 along with the conversion factors we have used. Note that values of A_v in Table 3 are not direct measures of optical extinction like those reported by O'Dell & Yusef-Zadeh (2000). Judging from Table 3, most of the OH absorption arises in high column density regions (A_v > 50). The only exception is the Dark Bay, for which A_v ≈ 7. Also, we note that the ratios of peak OH optical depths τ_0,1667/τ_0,1665 deviate from the LTE value of 1.8 for several of the positions in Table 3. Ratios greater than the LTE value indicate nonthermal excitation of the 18 cm OH levels, a common phenomenon (e.g., Crutcher 1977). Ratios less than the LTE value may also indicate nonthermal excitation and/or clumping of optically thick gas on scales smaller than the synthesized beamwidth.

A principal goal of these observations is to study the distribution of magnetic field strengths in the Veil. The strong radio continuum emission of the Orion H⁺ region leads to strong H i absorption lines, and, via the H i Zeeman effect, to measurements of B_los in the H⁰ layers of the Veil. Aperture synthesis data yield images of B_los across the Veil, and they do so independently for different velocity components. For the Veil data, we found evidence of the Zeeman effect in both velocity components A and B. Accordingly, we fitted separately over the channel ranges appropriate to component A (5.3–22 km s⁻¹) and component B (−14.7 to 3.6 km s⁻¹). Note that these velocity ranges include line-free channels necessary for the least-squares fits. We discuss below the images of B_los derived for these two components. We note that sensitivity to B_los is highly variable among pixels in the images. This variability arises from variations across the Veil in radio continuum brightness, line optical depth, and line width. Higher sensitivities to B_los arise in pixels where the radio continuum brightness and line optical depths are higher and where lines are narrower. Velocity component A has generally higher optical depths and narrower lines than component B. Therefore, the image of B_los for component A has better sensitivity over a larger number of pixels. In Figure 4, we show an example of 21 cm Stokes I/2 and V/2 profiles. These profiles are for a pixel in the images lying close to the center of the Trapezium. At this particular position, B_los is the same to about 1σ for the two velocity components. Table 1 lists the channel separation and resolution. The synthesized beamwidth is 25''.

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3.4.1. The H i Zeeman Effect in Component A

In Figure 5 we present an image of B_los in Veil H i velocity component A. Figure 5 (synthesized beamwidth 25'') is one of the most detailed images of interstellar magnetic field strengths published to date. B_los in component A is uniformly negative (magnetic field pointed toward the observer). For simplicity, we use the symbol B_los below to signify $| {B}_{\mathrm{los}}|$. Also, Figure 5 has been masked to include only those pixels for which $| {B}_{\mathrm{los}}|$/σ(B_los) > 3. Perhaps the most striking characteristic of Figure 5 is the relative uniformity of B_los over much of the Veil, with most values in the range 30–60 μG. However, there is a tendency for B_los to increase gradually from southwest to northeast, roughly similar to the increase in H i optical depths of components A and B (see vdWG89). Also, there appears to be a ridge of enhanced B_los extending from the southwest diagonally across the Veil to the northeast and widening toward the northeast. In this ridge, B_los ≈ 50–60 μG, whereas on either side of the ridge B_los ≈ 30–40 μG. The ridge of enhanced B_los coincides approximately with a ridge of enhanced N(H⁰)/T_ex in the image of component A presented by vdWG89. An indication of the ridge also appears in the H i optical depth image of vdWGO13 for a velocity of 8.4 km s⁻¹, on the unsaturated red wing of H i component A. Finally, there are isolated regions of higher B_los in Figure 5, most obviously in the northeast sector of the source. Here, B_los is typically >100 μG, reaching 300 μG in one small region about 30'' in size. Other isolated regions of higher B_los (75–100 μG) lie in the northern part of the Veil and near the southwest edges of the image in Figure 5. Overall, the image of B_los for component A is consistent with the equivalent image in Troland et al. (1989), where component A is labeled the high-velocity (HV) component. However, the present results in Figure 5, with their higher sensitivity and spatial resolution (25'' versus 40''), include values of B_los for more independent pixels, and they reveal high field strengths (B_los > 100 μG) in the northeast sector of the Veil, a region not included in the earlier results of Troland et al.

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3.4.2. The H i Zeeman Effect in Component B

In Figure 6 we present an image of B_los in Veil H i velocity component B (synthesized beamwidth 25''). Again, we have masked the figure to include only pixels for which $| {B}_{\mathrm{los}}|$/σ(B_los) > 3. As for component A, all values are negative, and we use the symbol B_los below to signify $| {B}_{\mathrm{los}}|$. Since component B is generally weaker and wider than component A, sensitivity to B_los is lower, and Figure 6 displays fewer values of B_los than Figure 5. Overall, the image of B_los for component B is remarkably similar to that for component A. In particular, B_los for component B is quite uniform over most of the image, with most values B_los ≈ 50–60 μG. Also, values for B_los in component B increase toward the northeast sector of the source, reaching 100 μG or more. This behavior, too, is similar to that for component A. In detail, however, there are differences in the distribution of B_los for the two H i velocity components. For example, a peak in B_los for component B in the southwest region of the image (90 μG) nearly coincides in position with a minimum in B_los for component A (30 μG). The image of B_los for component B is consistent with the equivalent image in Troland et al. (1989), where component B is labeled the low-velocity (LV) component. However, the earlier image of B_los for this component includes a very few independent measurements owing to severe sensitivity limitations.

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The present data provide the first aperture synthesis measurement of B_los in molecular regions of the Veil. Previously, Troland et al. (1986) detected the 1667 MHz OH Zeeman effect toward Orion A using the Nancay telescope. They found B_los,1667 = −125 ± 20 μG, positioning the Nancay 35 × 19' beam (FWHM, right ascension and declination, respectively) 3' east of the Orion A radio continuum peak (see contours in Figure 2). As for the H i data (Section 3.4), the OH data have highly variable sensitivities to the Zeeman effect. Careful examination of our 1667 MHz Stokes I and V profiles reveals the Zeeman effect reliably detected in only one independent position, OH1 in the northeast Dark Lane (Table 3). Here, B_los,1667 = −350 ± 47 μG and B_los,1665 = −151 ± 46 μG. At this same position, B_{los,H i} is −183 ± 32 μG in H i component A. In Figure 7 we present Stokes I/2 and V/2 profiles for the 1665 and 1667 MHz lines. The synthesized beamwidth is 40''; the channel separation is 0.27 km s⁻¹. The center velocity of the lines in this figure coincides quite well with the center velocity of the lines observed by Troland et al. (1986) at Nancay. Evidently, these authors sampled with a single dish nearly the same region of the Veil as we did with the VLA. The higher spatial resolution of the VLA likely accounts for the higher field strength detected with the aperture synthesis instrument.

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Values of B_los derived from the 1665 and 1667 MHz lines only agree to within 2σ. Also, the 1665 MHz Stokes V/2 profile in Figure 7 shows scant signs of the Zeeman effect. The Orion field of view includes OH masers that we attempted to remove in the uv-plane (Section 2). These masers are much stronger in the 1665 MHz line, and their effect cannot be completely removed from the synthesis data. Therefore, we suspect that residual maser contamination is present in the 1665 MHz Stokes V/2 profile of Figure 7. Troland et al. (1986) noted the same phenomenon. Their single-dish 1665 MHz Stokes V profile shows clear evidence for maser contamination near the thermal OH absorption line velocity. Yet they find no such contamination in their 1667 MHz Stokes V profile. With these considerations in mind, we assume that our Zeeman effect result at 1667 MHz is more reliable than that at 1665 MHz, so we use the former result in our energy analysis of Section 4.2.

The present data allow for a comparison among images of different physical parameters across the Veil. These images include B_los in H i components A and B, N(H⁰)/T_ex in components A and B, and optical extinction across the Veil. (For orientation purposes, recall that the dashed yellow rectangle in the optical image of Figure 1(a) corresponds to the fields of view of the B_los maps in Figures 5 and 6.) Comparisons among images are necessarily incomplete because images of the relevant parameters are incomplete over different parts of the Veil. For example, images of N(H⁰)/T_ex only provide information in the southwest regions of the Veil, where the H i line is unsaturated. Images of B_los are limited by sensitivity to the Zeeman effect, they only cover the inner parts of the Veil (especially for H i component B), and the images are only sensitive to one component of the magnetic field. The optical extinction images, likewise, only cover the inner Veil, where O'Dell & Yusef-Zadeh (2000) could measure extinctions.

Despite the limitations in image coverage, we find morphological similarities between the distributions of N(H⁰)/T_ex and magnetic fields across the Veil. In particular, there is a significant and previously established (vdWG89) tendency for the velocity-integrated N(H⁰)/T_ex to increase from the southwest toward the northeast of the Veil. This trend also applies individually to H i components A and B. Likewise, there is a significant tendency for B_los in H i component A to increase in the same direction, becoming highest in the direction of the northeast Dark Lane, where the H i line is deeply saturated (Figure 5, Section 3.4). The image of B_los in H i component B (Figure 6) is more limited in coverage, so this same trend is not so obvious. Nonetheless, the highest values of B_los for component B also occur in the northeast region of the image, just as they do for component A. Considering the morphology in slightly more detail, both N(H⁰)/T_ex in H i component A (vdWG89) and B_los in the same component display a ridge of higher values along a southwest to northeast axis. These morphological similarities between H i and B_los suggest a general tendency toward constant mass-to-flux ratio (∝ N(H⁰)/B_los) in the Veil. The similarities in morphology among N(H⁰)/T_ex in components A and B and B_los in components A and B imply a very close association between these two components despite their difference in center velocities.

The morphology of the optical extinction image (O'Dell & Yusef-Zadeh 2000) bears a more complex relationship to the morphologies of the N(H⁰)/T_ex and B_los images. As a result, it seems unlikely that the Dark Bay is directly associated with H i components A and B. Optical extinction increases from southwest to northeast across the image. Also, there is some indication of a ridge of enhanced extinction along this axis. This morphology is similar to those of B_los and N(H⁰)/T_ex in components A and B (see above). Indeed, the morphological similarities between optical extinction and N(H⁰)/T_ex across the Veil led O'Dell & Yusef-Zadeh (2000) to conclude that most of the optical extinction of the Orion Nebula arises in the H⁰ layers of the Veil rather than in the ionized gas itself. However, there is one obvious exception to these morphological similarities, the Dark Bay. No indication of the Dark Bay appears in the images of B_los (Figures 5 and 6). Therefore, it seems likely that the Dark Bay is physically separated from Veil H i components A and B. This suggestion is consistent with the morphology of optically obscuring material shown qualitatively in Figure 1(a). In this optical image, the Dark Bay appears to be a westward extension of very optically obscuring material to the east and northeast of the Orion Nebula. The optically obscuring material includes not only the Dark Bay but also the northeast Dark Lane and the filament of obscuring material partially covering M43. Perhaps this whole complex of optically obscuring material is a part of OMC-1 that lies in front of Veil H i components A and B.

Finally, we comment on the connection between OH absorption and the optical extinction image. OH absorption is only observed in four regions of the Veil (Section 3.3). Of these four regions, only two lie within the area covered by the optical extinction image of O'Dell & Yusef-Zadeh (2000). These regions are the Dark Bay and Orion-S, where A_v in the optical extinction image is about 5.5 and 1.4 mag, respectively. There is no detectable OH absorption toward the Trapezium stars (A_v ≈ 2). Also, there is no OH absorption toward the Southwest Cloud (SW Cloud in O'Dell & Yusef-Zadeh 2000) about 2' southwest of the Trapezium, where A_v ≈ 3. The Southwest Cloud appears in Figure 1(a) as a distinct, scorpion-shaped patch of extinction near the southwest edge of the bright H⁺ region. If we exclude Orion-S from consideration, as a different environment (see Section 4.4), then OH absorption is only observed in the Veil when A_v > 5. The absence of OH absorption except at relatively high A_v is not surprising since OH requires significant shielding to survive in an environment of such intense stellar radiation. This statement is consistent with the Cloudy spectral synthesis code model of Orion-S (O'Dell et al. 2009). In this model, significant OH does not form until A_v reaches about 4 mag. Although physical conditions in the Orion-S core differ significantly from those in the Veil, the Cloudy model incorporates the same intense stellar radiation field that is incident on the Veil. Therefore, the Cloudy predictions about OH formation as a function of A_v are likely to be relevant to the Veil in general, not just Orion-S.

The present observations offer insights into thermal, turbulent, magnetic, and gravitational energies in the Veil. Abel et al. (2006) performed an energy analysis for the single Veil line of sight toward the Trapezium stars (see their Table 5). Here we expand the analysis to many more lines of sight through the Veil, and we compare Veil energetics with those of other atomic and molecular regions in the ISM.

The energetics of the Veil and elsewhere can be characterized by the thermal, turbulent, and magnetic energy densities (erg cm⁻³), where E_therm = (3/2)nkT_K, E_turb = (3/2)$\rho {{\sigma }_{\mathrm{turb}}}^{2}$, and E_B = B²/8π. In these relationships, n is the particle density (cm⁻³) including He, ρ is the mass density (g cm⁻³) including He, σ_turb is the 1D turbulent velocity dispersion, and B is the total magnetic field strength (B_tot), not the measured B_los. Note that for velocity dispersions, σ = ΔV_FWHM/(8 ln 2)^½, where ΔV_FWHM is the velocity FWHM. Several other parameters relate to the ratios of energy densities. See the discussion in Heiles & Troland (2005) and in Crutcher (1999). These parameters include the turbulent Mach number M_turb, where (1/3)${{M}_{\mathrm{turb}}}^{2}$ = E_turb/E_therm, assuming isotropic turbulence. The conventional plasma parameter β_therm = (2/3)E_therm/E_B. Note that β_therm is sometimes defined to be one-half this value (Gammie & Ostriker 1996). The turbulent plasma parameter β_turb = (2/3)E_turb/E_B. Therefore, β_turb = ${{M}_{{\rm{A}}}}^{2}$, where M_A is the Alfvénic turbulent Mach number. Finally, the dimensionless mass-to-flux ratio λ is a measure of the ratio of gravitational to magnetic energies. If λ < 1, magnetic energy dominates gravity, and the material is magnetically subcritical. If λ > 1, gravity dominates magnetic energy, and the material is magnetically supercritical. We take λ = 5 × 10⁻²¹ N(H)/B, where B is in μG (Crutcher 1999). Note that β_therm and β_turb are defined as ratios of pressures rather than energy densities. In the discussion above, we take E_therm = (3/2) P_therm, E_turb = (3/2)P_turb, and E_B = P_B, where P_therm, etc., are the associated pressures.

Several difficulties arise in performing an energy analysis for the Veil. For one, relevant physical parameters such as N(H⁰)/T_ex and B_los are not uniformly sampled in the images (Section 4.1). Therefore, we have adopted a semi-quantitative approach in which we choose nine representative positions in the images to evaluate energy parameters in the H⁰ gas. These positions are labeled HI1 through HI9; they are shown in Figure 1(a) (blue circles), Figure 1(b) (smaller black circles), and Figure 5 (blue circles). A subset of these positions is shown in Figure 6. All positions lie in the southwestern region of the Veil, where the H i line is unsaturated, so N(H⁰)/T_ex is known. Coordinates and measured parameters for these positions are given in Table 4. We also choose five positions in the images to evaluate energy parameters in the molecular gas via OH absorption. These positions are listed in Table 3 and shown in Figure 1(a) (yellow circles), Figure 1(b) (larger black circles), and Figure 2 (black circles).

Table 4.  Parameters for Selected Positions with Unsaturated H i Absorption toward Orion A

No.	R.A.a	Decl.a	H i Component A				H i Component B
	(J2000)	(J2000)	Vob	ΔVc	N(H)d	Blos	Vob	ΔVc	N(H)e	Blos
			(km s−1)	(km s−1)	(cm−2)	(μG)	(km s−1)	(km s−1)	(cm−2)	(μG)
HI1	05h 35m 167	−05° 23' 25''	5.3	2.3	1.9 × 1021	−52 ± 4	1.0	3.2	2.7 × 1021	−47 ± 4
HI2	05h 35m 167	−05° 22' 37''	5.8	2.3	2.0 × 1021	−50 ± 5	2.3	3.6	3.1 × 1021	−35 ± 7
HI3	05h 35m 166	−05° 24' 13''	5.0	2.6	1.7 × 1021	−40 ± 4	−0.4	3.2	1.7 × 1021	−64 ± 6
HI4	05h 35m 199	−05° 23' 25''	5.5	3.0	2.7 × 1021	−60 ± 5	2.5	3.9	4.1 × 1021	−43 ± 6
HI5	05h 35m 135	−05° 23' 24''	4.4	2.4	1.3 × 1021	−48 ± 7	n/ag	n/ag	n/ag	n/ag
HI6f	05h 35m 121	−05° 23' 56''	3.8	3.2	1.3 × 1021	−27 ± 15	n/ag	n/ag	n/ag	n/ag
HI7	05h 35m 142	−05° 24' 45''	5.0	2.9	2.0 × 1021	−79 ± 7	0.6	3.9	1.2 × 1021	−35 ± 10
HI8	05h 35m 209	−05° 24' 25''	5.2	1.9	1.2 × 1021	−31 ± 5	n/ag	n/ag	n/ag	n/ag
HI9	05h 35m 215	−05° 23' 45''	5.7	2.4	1.7 × 1021	−73 ± 7	1.8	3.6	2.6 × 1021	n/ah

Notes.

^aPosition of the center of the 25'' synthesized beam at 21 cm. ^bCenter velocity of H i line component. ^cFWHM width of H i line component. ^dN(H) computed assuming T_ex = 90 K (Abel et al. 2006). ^eN(H) computed assuming T_ex = 135 K (Abel et al. 2006). ^fPosition coincides with Orion-S; however, velocity, N(H), and B_los values are for the unrelated H i component A. ^gH i component not clearly identifiable in the profile. ^hFitted value of B_los does not meet criterion of $| {{\rm{B}}}_{\mathrm{los}}|$/σ(B_los) > 3.

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A second difficulty in performing an energy analysis for the Veil lies in the uncertain systematic errors in many of the derived energy parameters. Energy parameters are calculated from direct measurements of line widths ΔV, as well as estimates of the quantities T_ex, T_K, N(H), n(H), and B_tot. Uncertainties exist in each of these parameters. For example, estimates of B_tot are based on statistical corrections to the measured values of B_los (see notes to Tables 5 and 6 for the statistical corrections we applied to estimate B_tot from B_los). Values of n(H) are based on PDR models of the Veil (Abel et al. 2006, 2016) or else on simple geometrical assumptions, as specified in notes to Tables 5 and 6. Estimates of N(H) in the molecular gas depend on an assumed value of T_ex (Section 3.3) and of the ratio N(OH)/N(H). No rigorous technique exists to quantify the propagation of systematic errors into the calculation of energies in the ISM. Therefore, conclusions drawn from these calculations must be regarded as approximate guides to the energetics of the region, accurate, perhaps, to a factor of two at best.

Table 5.  Estimated Energy Parameters for H i Gas Sampled by 21 cm H i Line

Parametera	H i Component A	H i Component B	CNMd
	(SW Sector)b	(SW Sector)c
Mturbe	2.7	3.8	3.0
βthermf	0.007	0.10	0.29
βturbg	0.017	0.46	0.88
λh	0.09	0.14	0.08
Etherm (%)i	1	8	16
Eturb (%)i	3	38	48
EB (%)i	96	54	36
Etherm + Eturb + EBj	3.2 × 10−10	4.4 × 10−10	3.9 × 10−12

Notes.

^aIn computing energy parameters involving magnetic fields, we take B_tot = 2B_los and ${{B}_{\mathrm{tot}}}^{2}=3{{B}_{\mathrm{los}}}^{2}$ (see Crutcher 1999). ^bEnergy parameters are computed from averages over positions 1–9 of relevant parameters (ΔV, B_los, N(H)) in Table 4. Also, we take n(H) = 300 cm⁻³ and T_K = 50 K (Abel et al. 2016). All positions included in the averages lie in the southwest sector of the Veil, where the H i line is unsaturated. ^cEnergy parameters are computed from averages over positions 1–4 and 7 of relevant parameters (ΔV, B_los, N(H)) in Table 4. Also, we take n(H) = 2500 cm⁻³ and T_K = 60 K (Abel et al. 2016). All positions included in the averages lie in the southwest sector of the Veil, where the H i line is unsaturated. ^dEnergy parameters for the cold neutral medium are computed from mean values of relevant parameters (ΔV, n(H), N(H), T_K, and B_tot = 6 μG) given by Heiles & Troland (2005). ^eTurbulent Mach number, measure of turbulent to thermal energy densities, (1/3)${{M}_{\mathrm{turb}}}^{2}$ = E_turb/E_therm. ^fConventional plasma parameter, measure of thermal to magnetic energy densities, β_therm = (2/3)E_therm/E_B. ^gTurbulent plasma parameter, measure of turbulent to magnetic energy densities, β_turb = (2/3)E_turb/E_B. ^hDimensionless mass-to-flux ratio, a measure of the gravitational to magnetic energies. ⁱPercent of (E_therm + E_turb + E_B) represented by the specified energy. ^{j Units of} ergs cm⁻³.

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Results of our energy analysis are listed in Tables 5 and 6. In Table 5 we list values of energy parameters in H i components A and B. For comparison purposes we also list energy parameters for the cold neutral medium (CNM) given by Heiles & Troland (2005). In Table 6 we list equivalent information for molecular gas in the Veil. For comparison purposes, we provide similar information for an ensemble of low-mass molecular cores and for molecular cores associated with three regions of massive star formation, M17, S106, and S88B. Information about magnetic field strengths in low-mass molecular cores and in the three regions of massive star formation comes from the literature of 1665 and 1667 MHz OH Zeeman effect observations. See notes to Table 6 for references. Note that Orion-S is included with the Veil in Table 6. However, this high-mass molecular core is likely to be quite different from the other Veil regions, and it is unlikely to be part of the Veil at all (Section 4.4). In both Tables 5 and 6 we also list the percent contributions of E_therm, E_turb, and E_B. See notes for these tables. With due regard for uncertainties, a variety of conclusions can be drawn from the energy parameters of Tables 5 and 6. We list these conclusions below, many of which are consistent with conclusions previously drawn for other regions of the neutral ISM:

• a.  
  Turbulent and thermal energies (M_turb).—Turbulent energy is greater than thermal energy in the atomic and molecular regions of the Veil (supersonic turbulence, M_turb > 1). H i components A and B are only mildly supersonic with M_turb ≈ 3 (E_turb/E_therm ≈ 3). In this sense, they are very similar to the CNM, although they are of order 1 dex denser. The molecular regions of the Veil are much more highly supersonic, with M_turb ≈ 4–6 (E_turb/E_therm ≈ 5–12). In this sense, the Veil molecular regions are very similar to molecular cores in other high-mass star-forming regions included in Table 6. High-mass star formation is associated with very turbulent molecular gas. However, low-mass molecular cores associated with low-mass star formation (Table 6) fall into a different category. These regions, when sampled in 1665 and 1667 MHz OH lines, are close to transonic, with M_turb ≈ 2 (E_turb/E_therm ≈ 1). As numerous previous studies have shown, the neutral ISM is a very turbulent environment in which thermal energy is relatively insignificant. An exception to this rule is the low-mass molecular core.
• b.  
  Thermal and magnetic energies (β_therm).—Thermal energy is insignificant compared to magnetic energy in H i components A and B and in the molecular northeast Dark Lane 1 position (β_therm, E_therm/E_B ≪ 1). The same statement applies to the three molecular cores associated with high-mass star formation listed in Table 6. Thermal energy is (at least on average) more significant in the CNM (β_therm ≈ 0.3, E_therm/E_B ≈ 0.5) and, especially, in low-mass molecular cores (β_therm ≈ 1.3, E_therm/E_B ≈ 2).
• c.  
  Turbulent and magnetic energies (β_turb, M_A).—A rough equipartition exists between turbulent and magnetic energies in most regions included in Tables 5 and 6 (trans-Alfvénic turbulence, β_turb ≈ 1, so M_A ≈ 1). Such a balance has been previously suggested for regions of the ISM sampled by the Zeeman effect (e.g., Myers & Goodman 1988; Crutcher 1999). In this sense, the atomic and molecular gas of the Veil is similar to atomic and molecular gas elsewhere in the ISM. However, there is one very notable exception to the equipartition rule, H i component A. Here, β_turb ≈ 0.02, so M_A ≈ 0.1 and E_turb/E_B ≈ 0.03. That is, this layer is very strongly dominated by magnetic energy over turbulence, i.e., very sub-Alfvénic turbulence. A similar conclusion was drawn by Abel et al. (2006) for the line of sight to the Trapezium alone. In Section 4.3.2 we comment further on the possible origin of sub-Alfvénic turbulence in H i component A. We note that Zeeman effect studies have yet to identify any examples of super-Alfvénic turbulence (β_turb, M_A ≫ 1) in the ISM. Evidently, super-Alfvénic turbulence is damped on short timescales.
• d.  
  The balance of thermal, turbulent, and magnetic energies.—Tables 5 and 6 list the percent contributions of these three energies to regions in the Veil and elsewhere. In general, magnetic and turbulent energies are comparable, with thermal energy relatively small. Obvious exceptions to this statement arise in (1) H i component A, where magnetic energy dominates the other two, and (2) low-mass molecular cores, where, on average, thermal energy is significant and comparable to the other two. The CNM is also a region where thermal energy is not negligible, although turbulent and magnetic energies are greater.
• e.  
  Thermal, turbulent, and magnetic energies combined (total pressure).—The sum of these three energy densities is a measure of the total support of a cloud or core against the confining effects of gravitation and external pressure. These sums are listed in the bottom rows of Tables 5 and 6. (For thermal and turbulent motions, pressures are 2/3 times energy densities.) Examination of Tables 5 and 6 leads to the identification of four distinct energy density or pressure regimes, with values ranging over 4 dex. These regimes, in order of increasing total energy density, are (1) the CNM; (2) low-mass molecular cores, 1 dex higher; (3) H i components A and B, 1 dex higher; and (4) molecular gas associated with high-mass star formation (Orion Veil, M17, S106, S88B), 2 dex higher. Note that the total energy densities in H i components A and B are approximately the same despite the different distribution among the energies. In effect, these two H⁰ regions are in approximate pressure equilibrium. Note also that the total energy density of the CNM (Table 5) is very comparable to the galactic midplane pressure of (3.9 ± 0.6) × 10⁻¹² dyn cm⁻² derived by Boulares & Cox (1990). That is, the CNM pressure is in equilibrium with the weight in the z-direction of the midplane gas.
• f.  
  Magnetic and gravitational energies (λ).—As listed in Table 5, λ < 1 in both H i components A and B (i.e., H⁰ is subcritical), and the value of λ is very similar to the average value for the CNM (λ ≈ 0.1). That is, magnetic energies dominate gravitational energies in both Veil H⁰ regions as they do in the CNM. However, λ ≈ 1 in the molecular northeast Dark Lane 1 position, where N(H) is about 2 dex higher than in H i components A and B (Table 6). This distinction between low-N(H) regions that are subcritical (λ < 1) and higher-N(H) regions that are critical to supercritical (λ ≥ 1) is consistent with a large body of Zeeman effect results covering N(H) ≈ 10^19–24 cm⁻² as described below.

To illustrate the relationship between λ and N(H), we present existing Zeeman effect data in Figure 8 on the log N(H)–log B_los plane. Veil data points are shown as filled colored circles; data for H i component A are in red, data for H i component B are in blue, and the data point for OH is in green. Other data points (black circles) were plotted by Crutcher (2012), who lists relevant references, or else they are from K. Thomson et al. (2016, in preparation). For N(H) ≤ 10²¹ cm⁻², the black circles sample diffuse H⁰ gas via the 21 cm H i line. For N(H) ≈ 10²¹–10²² cm⁻², the black circles represent molecular gas sampled by 18 cm (1665, 1667 MHz) OH lines. For N(H) > 10²³ cm⁻², the black circles denote dense molecular cores sampled by the 3 mm CN lines. (The N(H) ranges are approximate.) The diagonal line in Figure 8 represents λ = 1. Points above the line are magnetically subcritical (magnetically dominated, λ < 1); points below the line are magnetically supercritical (gravity dominated, λ > 1). Note that values of B_los are plotted directly without statistical correction. Therefore, a given point in Figure 8 represents an upper limit on the true value of λ ∝ N(H)/B_tot since a measured value of B_los represents a lower limit on B_tot. Given an ensemble of B_los measurements, as shown in Figure 8, the upper envelope is an indication of B_tot, as a function of N(H), assuming a random distribution of field angles relative to the line of sight.

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The Zeeman effect data of Figure 8 and of Tables 5 and 6 illustrate several key points. First, we exclude from consideration the colored points for the Veil. Then, magnetic field strengths (black circles) remain remarkably constant with increasing N(H) up to N(H) ≈ (1–2) × 10²² cm⁻². For higher N(H), field strengths increase. Otherwise stated, λ increases systematically with increasing N(H), remaining subcritical at lower values of N(H) in the diffuse H⁰ gas. Above N(H) ≈ (1–2) × 10²² cm⁻², λ in the molecular gas becomes nearly constant and slightly supercritical. The constancy of field strengths at lower N(H) has been noted in the past (e.g., Crutcher 2012). Lazarian et al. (2012) suggest that it is the result of the reconnection diffusion process that maintains approximately constant field strength in a gathering cloud until the free-fall timescale becomes shorter than the reconnection diffusion timescale. Once this threshold is reached, the gas contracts gravitationally, drawing in and strengthening the field in the process. We comment further on this process in Section 4.3.2.

Now considering the colored points in Figure 8 for the Veil, the green circle representing molecular gas in the northeast Dark Lane is quite consistent with other data points for molecular gas of comparable N(H). Very likely, this region of the Veil has been largely undisturbed by the star formation process, so it is typical of dense molecular gas associated with massive star formation elsewhere. However, the red and blue circles representing H i components A and B, respectively, lie a factor of 3–4 above the black circles for magnetic fields in other regions of the ISM with comparable N(H). Otherwise stated, these Veil H⁰ regions are more magnetically subcritical (i.e., λ smaller) than other regions of comparable N(H). See Section 4.3 for further comments about the low values of λ (i.e., high ratios B/N(H)) in these components.

The Orion Veil offers an unusual opportunity to explore PDR physics, as noted in the Introduction. The high field strengths in the Veil compared to those in the CNM, as well as a wealth of other observational evidence (e.g., vdWGO13), clearly establish that the Veil is closely associated with the Orion star-forming region, not unrelated diffuse gas along the line of sight. Also, the Veil has apparent plane-parallel geometry perpendicular to the line of sight, and it is located nearby, so it is susceptible to high spatial resolution studies. Abel et al. (2016) constructed detailed PDR models of the Veil (see also Abel et al. 2004, 2006). From these models, they estimate n(H) ≈ 10^2.5 and 10^3.4 cm⁻³ and T_K ≈ 50 and 60 K for components A and B, respectively. Strictly speaking, these parameters apply only to the line of sight toward the Trapezium. However, we assume that they apply to other Veil lines of sight where N(H) is comparable.

The magnetic field images in Figures 5 and 6 offer important additional perspectives on the natures of H i components A and B. These images reveal that B_los in the two H i components have very similar values and morphologies (Section 4.1). These magnetic similarities, together with the similarities in morphology of N(H⁰)/T_ex and in velocity gradients between the two components (see vdWG89), establish that components A and B are very closely associated. However, two questions must be addressed before a comprehensive understanding of the Veil is possible. One question is the distances of components A and B from the principal source of radiation, the Trapezium stars. The second question is the origin of the relatively high magnetic field strengths in components A and B. We consider these questions in the following two subsections.

4.3.1. Locations and Natures of H i Components A and B

Several authors have concluded that H i component B lies closer to the Trapezium stars than component A. For example, vdWG89 argued that component B consists of gas heated and photodissociated by non-H-ionizing stellar photons escaping from the H⁺ region. In this picture, H i component A is gas that has not yet been kinematically affected by the H⁺ region and makes up an envelope of H⁰ surrounding the molecular gas. These authors also noted that the blueshift of component B relative to A (≈4 km s⁻¹; see Section 3.2) can result from thermal expansion of the former owing to radiative heating. Recently, Abel et al. (2016) obtained high spectral resolution HST (STIS) spectra in the 1133–1335 nm wavelength range toward Theta ¹B Ori. These spectra resolve H i components A and B. Abel et al. detected Veil absorption lines of CI, CI*, CI**, and rotationally/vibrationally excited H₂. Based on these data, they constructed a PDR model for the Veil that yields estimates of the distances of components A and B from the Trapezium, as well as the temperatures, volume densities, and thicknesses of the two components. The model establishes that component B is, indeed, closer to the Trapezium, about 2 pc distant, as compared to 2.4 pc for component A.⁷ This relative placement is consistent with the facts that component B is warmer, thinner, denser, and more turbulent than component A. All of these properties point to more interactions of component B with the Trapezium environment than component A. At the same time, kinematic and magnetic similarities suggest a very close physical association between components A and B, as argued above.

One possible close physical association between the two components is that they lie on opposite sides of the shock preceding a weak-D ionization front. That is, component B is shocked gas, and component A is pre-shock gas. For this scenario to apply, we assume that the magnetic field lies nearly perpendicular to the plane of the shock (i.e., along the line of sight). Then, neglecting possible field tangling induced by motions within the shock layer itself, the shocked gas would slide along the field lines, increasing its density with no increase in magnetic field strength in component B, as observed. In such a case, standard, nonmagnetic jump conditions apply for the shock since the magnetic pressure is not relevant to motions along the field direction. We apply the equations for nonmagnetic shocks in Shu (1992), using values for n(H) and T_K in components A and B derived by Abel et al. (2016; see Section 4.3 above). We estimate a shock velocity of 2 km s⁻¹. The shock results in a blueshift of component B relative to component A of 1.7 km s⁻¹, to be compared with the observed value of 4 km s⁻¹. That is, the shock model underpredicts the velocity difference between the two components by a factor of about two. The predicted velocity difference is approximately proportional to [T_B × n(H)_B/n(H)_A]^½, where T_B is the kinetic temperature of component B. Therefore, a two times higher predicted velocity difference would require, for example, a two times higher temperature and two times higher density ratio. Abel et al. (2016) do not provide error estimates for their photoionization model-derived values of T_B, n(H)_B, and n(H)_A. As a result, we cannot estimate the likelihood of higher temperatures and density ratios. Also, the velocity difference between components A and B varies as a function of position across the Veil, with values closer to 3 km s⁻¹ in some positions. In short, the shock model is attractive because it accounts for kinematic and magnetic similarities between the components, and the shock passage may account for the higher turbulence in component B than in A. However, the shock model offers an uncertain quantitative fit to photoionization model densities and temperatures of Abel et al. (2016).

We illustrate the natures and locations of Veil components A and B with the cartoon of Figure 9. In this figure, the Earth is to the left, and north is up. Neutral gas is shown in blue, ionized gas, in red. The cartoon places component B closer to the Trapezium, and the cartoon shows the thicknesses of components A and B as derived from the Abel et al. (2016) Veil model, 1.6 and 0.40 pc, respectively. According to this same model, n(H) ≈ 10^2.5 and 10^3.4 cm⁻³ for components A and B, respectively. The higher density of component B is suggested in Figure 9 by darker shading. Three H⁺ regions are shown in the figure. One is the main Orion H⁺ region (Orion Nebula) with a scale height of 0.05 pc (O'Dell 2001), located 0.25 pc behind the Trapezium stars (Abel et al. 2006). The vertical extent of the Orion Nebula in the cartoon represents the size of the bright Huygens region, about 0.8 pc. (The vertical extent of the Veil is arbitrary.) The second H⁺ region in Figure 9 is labeled "Blue-shifted H⁺" ("blue component" in Abel et al. 2016; also described by Abel et al. 2006). This matter-bounded, ionized layer is shifted about −25 km s⁻¹ relative to OMC-1, and it is observed in optical emission lines and uv absorption lines. Abel et al. (2006) note that the blueshift can be ascribed to stellar radiative acceleration over a period of order 10⁵ yr. The third H⁺ region, labeled "Veil H⁺ region," is presumed to exist on the front face of the neutral Veil. However, optical and uv tracers of this layer would lie at velocities similar to those of the Orion Nebula; hence, they are unobservable. Immediately behind the Orion Nebula lies the OMC-1 filamentary cloud and the Orion-KL core. Also shown is the Orion-S molecular core embedded within OMC-1. However, this Orion-S location is only one possibility discussed in Section 4.4 below.

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Finally, we comment on the 21 cm H i excitation temperatures T_ex in components A and B in comparison with their kinetic temperatures. Under typical conditions in the galactic ISM, it is commonly expected that T_ex ≈ T_K. However, under conditions of low density and/or high stellar uv flux, resonant scattering of Lyα photons can pump the H i levels, increasing T_ex above T_K (Field 1959). Veil components A and B offer an unusual opportunity to study this effect since both T_ex and T_K are independently known along the line of sight to the Trapezium. In particular, T_ex ≈ 90 and 135 K for components A and B, respectively (Abel et al. 2006), while T_K ≈ 50 and 60 K for components A and B, respectively (Abel et al. 2016; see above). Therefore, the H i levels have been pumped in both components, and more so in component B, as one would expect if this component is closer to the Trapezium and subject to a higher stellar uv flux. However, it is not possible to be more quantitative about the pumping effect. The magnitude of the effect depends on the unknown strengths of the Lyman lines in the stellar spectral energy distribution (SED; Abel et al. 2016).

4.3.2. Magnetic Fields in the H i Components—Precursors and/or Products of Star Formation

Orion-S is one of two high-mass molecular cores in OMC-1; Orion-KL is the other. Orion-S is 90'' south of Orion-KL and about 60'' southwest of the Trapezium cluster (see Section 3.3 and Figure 2). Like Orion-KL, Orion-S is clearly visible in images of submillimeter dust emission (Lis et al. 1998; Johnstone & Bally 1999) and in molecular emission line images (e.g., Peng et al. 2012). The 850 μm dust emission image of Johnstone & Bally (see contour image in Peng et al. 2012) reveals an Orion-S core approximately 40'' (0.09 pc) in diameter, with N(H) ≈ (2–4) × 10²⁴ cm⁻² (A_v ≈ 800–1600 mag). The factor of two uncertainty reflects uncertainties in theoretically calculated values of the dust opacity κ_ν. Other uncertainties exist in this N(H) estimate, for example, in T_dust, which we have taken as 40 K (O'Dell et al. 2009). The implied total mass for Orion-S is 130–260 solar masses; the average density, assuming spherical symmetry, is (1–2) × 10⁷ cm⁻³. The virial mass of Orion-S, for an observed ΔV ≈ 5 km s⁻¹ and radius of 0.05 pc, is about 150 solar masses, suggesting that the core is close to virial stability.

It is logical to imagine that Orion-S lies behind the main Orion H⁺ region, just like the Orion-KL core. For example, there is no obvious optical extinction feature associated with this optically opaque core, just as there is none for Orion-KL. However, the situation for Orion-S is more complicated owing to several discoveries reported in the previous literature. Johnston et al. (1983) and Mangum et al. (1993) found 6 cm (4.8 GHz) H₂CO absorption toward Orion-S. The present OH data also reveal absorption (Section 3.3). The present data also show H i absorption toward Orion-S, and the data of vdWGO13 show this same absorption at higher spatial resolution (identified by these authors as H i component H). We illustrate the clear kinematical association between OH and H i absorption and Orion-S molecular emission in Figure 10. This figure presents H i and OH optical depth profiles from the present work and a CS (2-1) emission profile from Tatematsu et al. (1998). See the figure caption for beamwidths and channel separations. All three profiles are toward the center position of Orion-S. The OH and CS profiles have nearly identical center velocities (7 km s⁻¹) and velocity widths. The H i profile has a weak component on the high-velocity side of the main velocity component that appears to match the OH and CS features. (The low-velocity side of this weak H i component, at velocities 3–7 km s⁻¹, is presumably obscured by the main H i velocity component.) Evidently, a source of radio continuum emission lies behind all or part of Orion-S in order to account for the H i, OH, and H₂CO absorption. Most likely, this radio continuum emission comes from an H⁺ region. Another indication of the complexity of the Orion-S core comes from anomalies in the optical extinction reported by O'Dell et al. (2009). These anomalies suggest that part of the radio continuum observed toward Orion-S comes from an ionized layer from which we receive no Hα light. Presumably, this H⁺ layer lies behind an optically opaque layer associated with Orion-S. In short, previous and present observations point to the presence of two distinct layers of H⁺ along the line of sight to Orion-S. These layers are separated by an optically opaque region that consists of all or part of Orion-S.

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Apart from kinematics (Figure 10), there is an intriguing spatial correspondence between the H i absorption and the Orion-S core defined by dust emission. The vdWGO13 data offer a high spatial resolution image of this absorption. In Figure 11 we overlay contours of the 850 μm dust emission (dashed contours; Johnstone & Bally 1999) on an image of H i optical depth from the data of vdWGO13 (colors and light contours). The H i optical depth image has been integrated over the velocity range 8.4–9.7 km s⁻¹, a range over which optical depth associated with Orion-S is uncontaminated by unrelated velocity features (see Figure 10, top panel). The H i image has a synthesized beamwidth of 64. Figure 11 shows that the H i absorption arises from a partial shell just to the west of the peak in 850 μm dust emission associated with Orion-S. Although the morphologies of 850 μm dust emission and H i optical depth are far from identical, the general correspondence between the two provides strong evidence, along with the kinematical evidence (Figure 10), that the H i absorption is closely associated with Orion-S. The same conclusion holds for the H₂CO and OH absorption.

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O'Dell et al. (2009) propose that Orion-S is an isolated molecular core lying in front of the main ionization front (MIF) of the Orion Nebula (see their Figure 5). Therefore, the main H⁺ region provides radio continuum absorbed by H₂CO, OH, and H i. In this model, light from the Trapezium cluster ionizes the front face of Orion-S. As seen from the Earth, light from this ionized Orion-S layer fills in light from the main H⁺ region that is blocked by Orion-S. Therefore, Orion-S does not create an obvious optical extinction feature even though it lies in front of the MIF. O'Dell et al. also provide a detailed spectral synthesis calculation of Orion-S, predicting the run of density, dust and gas temperatures, and chemical composition into the core. This model establishes, for example, that T_dust in the core remains above the 30 K needed to keep H₂CO from freezing out onto grains.

Several objections can be raised to the O'Dell et al. (2009) model, none of which exclude it. These objections are related to the need for ionized gas behind Orion-S to account for the atomic and molecular absorption. In the O'Dell et al. (2009) model, the position of Orion-S must be carefully chosen so that it does not shadow the main Orion H⁺ region behind it. If Orion-S were to shadow this layer, then the layer would not be ionized, so it could not emit the radio continuum. Also, such a shadow would likely be visible in optical images of the Orion Nebula to the southwest of Orion-S (i.e., opposite to the direction toward the Trapezium). No such shadow is apparent (Figure 1(a), southwest of position OH4 that is coincident with Orion-S). Indeed, the existence of an isolated molecular core in Orion, surrounded by H⁺, seems unlikely. Most of the ionizing radiation in Orion comes from a single star, Theta 1C Ori. Therefore, Orion-S must cast a shadow, creating an elephant trunk of neutral gas similar to those observed in M16 (Hester et al. 1996). The postulated Orion-S elephant trunk would be seen from a different angle than those of M16. The Orion-S structure would point more nearly toward the observer in Orion and be seen against the bright background of the main H⁺ region. This geometry would be quite unlike that of the M16 elephant trunks that lie approximately in the plane of the sky and are viewed against a darker background. As a result, the Orion-S elephant trunk might be much less visible in optical images than those of M16. Nonetheless, an Orion-S elephant trunk would have to be carefully positioned to account for H⁺ behind the Orion-S core. With a suitable choice of geometry, this background H⁺ gas could be part of the main Orion H⁺ region, or it could lie along the skin of the elephant trunk on the side of the structure facing away from Earth. Either way, the geometry of the Orion elephant trunk would have to be rather optimally configured in order to place a significant amount of ionized gas directly behind Orion-S, while Orion-S itself lay in front of the MIF.

We now offer another explanation for the presence of H i, OH, and H₂CO absorption toward Orion-S that avoids the need to carefully position the molecular core in front of the MIF. In this model, the Orion-S molecular core lies entirely behind the MIF, just like Orion-KL. On the back side of Orion-S (i.e., facing away from Earth), an early-type star has created a small H⁺ region whose radio continuum emission is responsible for the observed atomic and molecular absorption. The small H⁺ region could be a blister-type region, similar to but smaller than the Orion Nebula, or it could be embedded within Orion-S. We have made a simple estimate of the type of star that could form such a small H⁺ region. We use the formalism described by Jackson & Kraemer (1999) and references therein. Consider an H⁺ region as large as Orion-S (0.1 pc) in the plane of the sky. Suppose that this H⁺ region has half the radio continuum brightness (in Jy beam⁻¹) as the main Orion H⁺ region. (Were the small H⁺ region much brighter, it would create an obvious peak in total brightness toward Orion-S, contrary to observation.) Given the assumed brightness and size of the small H⁺ region, its total 21 cm flux density is about 4 Jy. Assuming an electron temperature T_e ≈ 8000 K, the small H⁺ region could be created by a B0 zero-age main-sequence star, a star far less luminous than Theta ¹C Ori. Such a star, on the back side of Orion-S or embedded within it, would be invisible behind A_v ≈ 1000 from Orion-S. The postulated Orion-S H⁺ region is shown in Figure 9 as a red circle immediately behind Orion-S.

This second Orion-S model is ad hoc but plausible on several grounds. For one, Orion-S is well established as a star-forming region (e.g., Henney et al. 2007). Therefore, the presence of a B0 star in its vicinity would be no surprise. Also, the roughly circular region of enhanced optical extinction in the image of O'Dell & Yusef-Zadeh (2000) is easily explained as an artifact arising from background radio continuum emission of a small Orion-S H⁺ region from which no Hα emission is observed owing to the large optical extinction of Orion-S in front. (This is the anomalous extinction phenomenon cited above and described by O'Dell et al. 2009.) Finally, the partial shell of H i optical depth adjacent to Orion-S (see above) can be naturally explained as arising in a partial shell of H⁰ gas lying just outside the small Orion-S H⁺ region. In this simple model, the Orion-S core is just like the Orion-KL core, behind the main Orion H⁺ region. If this model is correct, then the Orion-S core may lie just barely behind the main Orion H⁺ region. Orion-S coincides spatially with a local maximum or bump in the H⁺ region surface that points toward Earth. This bump appears in the 3D map of Wen & O'Dell (1995). These authors note that the bump could be caused by dense gas behind the H⁺ region that retards the advance of the ionization front. This dense gas, of course, would be the Orion-S molecular core.

In short, two different models of Orion-S can account for existing observations, especially the presence of atomic and molecular absorption associated with the core. One model (O'Dell et al. 2009) places Orion-S in front of the MIF, as an isolated neutral region immersed in H⁺ gas. It is only a slight modification of this model (described above) to replace the isolated core with an elephant trunk having the core at its tip. The other model (present work) places Orion-S behind the MIF (like Orion-KL) with yet another, smaller H⁺ region behind Orion-S. Both models require ad hoc assumptions. However, we favor the placement of Orion-S behind the MIF since this placement avoids the necessity of rather specific geometry of an isolated molecular region or elephant trunk. Future high spatial resolution images of the atomic and molecular absorption regions associated with Orion-S might assist in distinguishing between these two models. For example, if the morphologies of H i and molecular absorption are found to trace a partial shell around the molecular core (a circumstance hinted at in Figure 11), this result would strengthen the hypothesis that a small H⁺ region lies behind Orion-S and a partial shell of neutral gas surrounds the ionized gas. That is, this result would strengthen the model placing Orion-S behind the MIF.