Structure of the Orion Nebula

© 2001. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.
, , Citation C. R. O'Dell 2001 PASP 113 29 DOI 10.1086/317982

1538-3873/113/779/29

ABSTRACT

The nature of the structure of the Orion Nebula has become clearer but more complex. Quantitative application of simple photoionization theory has allowed construction of a three‐dimensional model of the main ionization front, while high‐resolution study of the flow of [O i], [O ii], [O iii], and [S iii] has allowed determination of how this material moves. Material in a "foreground lid" of H i is seen in absorption lines in the 21 cm continuum and in optical spectra of Na i and Ca ii. There remain many unsolved and possibly basic questions, among them the source of nonthermal broadening of all lines, which carries as much energy as the thermal content of the gas. We have also found that varying amounts of emission‐line light scattered by the dust particles immediately behind the main ionization front introduces a nonphotometric scatter of up to 25% in spectral intensities.

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1. INTRODUCTION

Our understanding of the physical structure of the Orion Nebula has continued to evolve and become more detailed than at the time it was described in the Symposium on the Orion Nebula to Honor Henry Draper by M. Peimbert (1982). By that time the current basic model, where the nebula that we see as M42 is a thin photoionized layer on the surface of the giant molecular cloud OMC‐1, had been widely accepted. The model was advocated at about the same time by several authors (Zuckerman 1973; Balick, Gammon, & Hjellming 1974; Balick, Gull, & Smith 1980; Meaburn 1975; Pankonin et al. 1979); Zuckerman and Balick et al. (1974) are usually given credit for the defining argument in favor of the model, that one observes a gradient of progressively more blueshifted emission lines, with the highest ionization lines being the most blueshifted. In fact, a slab model for the emission goes back much farther. It was originally invoked by Münch (1958) to explain the statistical properties of the fine‐scale motions across the face of the nebula and also by Wurm (1961) to explain the monochromatic emission‐line and broadband scattered light images that he was obtaining (Wurm & Rosino 1959, 1965). The Wurm article appeared only in German and apparently was not widely read, and Münch & Wilson (1962) later advocated a nonslab model, so that the question of the three‐dimensional structure remained unclear up until the middle 1970s. Once the paradigm shift occurred, many known features fell into place. Progress since the 1981 meeting has been considerable, largely due to the increase in the number of investigations of a quantitative nature, using CCD detectors for both imaging and high‐resolution spectroscopy. These studies show that M42 has a myriad of features not anticipated two decades ago.

In the succeeding sections I will discuss what we know of the main ionization zone (§ 2), the nature of the lid that covers the front (§ 3), the bright bar (§ 4), velocities in the nebula and its associated stars (§ 5), and the role of scattered light (§ 6); I then summarize with a discussion of unresolved problems (§ 7). Questions of the exact physical conditions, such as electron temperature, are discussed in a companion article by Ferland (2001), who presents a description of the closely related subject of the atomic abundances.

2. THE MAIN IONIZATION ZONE

The paradigm shift that occurred nearly 30 years ago was the recognition that M42 was a thin blister of photoionized gas on the surface of OMC‐1. Such a structure would be dynamic, in the sense that the overpressure situation produced by heating of the gas would cause material to be lost by almost unconstrained expansion. This process is often labeled as a champagne phase flow, although that is not rigorously correct, since the champagne phase flow more exactly describes the emptying of a previously enclosed H ii region when its constraining neutral boundary is breached. However, the Tenorio‐Tagle (1979) models do capture the important element, that an ionized layer at the surface of a giant molecular cloud is a nearly static phenomenon, rather than a fixed feature. The molecular cloud has a large reserve of material, in this case of about 103 M. New molecular cloud material is added to the ionized gas as some is lost through expansion. There is theoretical and observational evidence (Tielens & Hollenbach 1985; Escalante, Sternberg, & Dalgarno 1991) that a shocked, highly compressed zone (the photon‐dominated region, or PDR) exists immediately behind the ionization front (IF), meaning that there is so much material that the specific location of the exact IF will change only slowly. However, the flow of gas away from the IF may not be absolutely unconstrained, since the radiation pressure from the stars of the Trapezium approximately equals the pressure at the base of the ionization front, which means that if the material becomes optically thick to the stellar soft radiation, then ionized material may expand more slowly at the substellar point. We now have the radial velocity material to test whether an exact theoretical model with and without partial radiation pressure confinement best fits these observations. What is lacking is the realistic theoretical calculation for the conditions in M42. The expectation is that material would be accelerated away from the IF, i.e., become more blueshifted with respect to the observer, and that the density should decrease as this acceleration occurs. Independent of the details of this process, it is important to understand that this spectacular object is produced with only about 2 M of material (Wilson et al. 1997).

There should be an ionization stratification that occurs within the ionized level. Fortunately this is easy to predict since there is only one important source of ionizing photons and the opacity of UV photons is primarily determined by only hydrogen and helium. The spectral type of θ1 Ori C, the brightest and hottest star in M42, is O7 (Conti & Alschuler 1971), which means that its photoionizing luminosity (above 13.6 eV) is about 3–4 times greater than the closest competitor θ2 Ori A, which is spectral type O9 V (Conti & Alschuler 1971) and lies away from the Trapezium. As pointed out in Osterbrock's (1989) text, the range of absorption coefficients of various atoms and ions varies little as compared with the abundances of the elements. This means that radiative transfer in the region immediately above 13.6 eV will be dominated by hydrogen absorption, that above 24.6 eV by He i, and that above 54.4 eV by He ii. This means that the heavy elements such as carbon, nitrogen, and oxygen, which produce many observable lines, should be found in zones whose primary structure is determined by the ionic state of H and He. The ionization front itself will give rise to [O i] and [S ii] emission, since they require both the presence of these low‐ionization states and electrons of several eV to cause the collisional excitation of the forbidden lines. The next zone out from the IF will have H+ but neutral helium (He0) and produce emission from [N ii] and [O ii]. Outside of that zone the helium will exist as He+, and its emission in recombination will be accompanied by collisionally excited [O iii] and [Cl iii]. Higher states of ionization are not important because of the temperature of θ1 Ori C. This simple stratification of ionization states agrees well with our observations, with Table 1 giving the range of velocities and electron densities that are observed, which agrees well with an an emitting layer of stratified ionization, with the material farthest from the IF having the lowest densities and the greatest blueshifts.

For several decades the discrepancy between the high densities measured by indicators such as the [O ii] λ3727 doublet and the surface brightness [S(Hα)] in Hα was resolved by introducing a "filling factor." The need for this concept disappears with the recognition that the emitting layer is thin as compared with the overall size of the H ii region and that, in fact, one can calculate the thickness of the emitting layer. Baldwin et al. (1991) first showed how their calibrated slit spectra surface brightnesses could be used to calculate a formal thickness for the emitting layer, when the local density was known. This method was extended by Wen & O'Dell (1995) across the brightest parts of the nebula, and they found that the layer thickness was about 0.13 pc under the assumption that the density is constant. If the density is assumed to fall exponentially, the e−1 scale height is half of this value. Since the emissivity of all of the observed lines scales as the square of the density, this means that the e−1 scale height of the observed emission is only 0.13/4 = 0.03 pc; this corresponds to an angular distance of 14 '', which is small when compared with the dimension of the nebula (it is 135 '' between θ1 Ori C and θ2 Ori A) if the distance to the nebula is the same as that of the associated stars, 430 pc (Warren & Hesser 1977).

Ferland (2001) also showed in the Baldwin et al. (1991) paper that one could also calculate the separation distance between the photoionizing star and the IF. In the case of photoionization equilibrium by a thin layer at a distance r from a star of ionizing luminosity Q (photons s−1), the total number of recombinations in a column of material must be exactly equal to the photon flux (Q/4πr2). Since a fixed fraction of the recombinations will produce an observable Hα photon, then the extinction‐corrected Hα surface brightness in photons s−1 sr−1 will be

where αeffHα and αB are the hydrogen recombination coefficients defined and given values by Osterbrock (1989). Ferland's formulation is rigorously valid only for the substellar point, where the photons enter along the same line of sight as the observer's view; the basic process was expanded to cover the entire inner region by Wen & O'Dell (1995), who made detailed calculations of the effect of the incident and observed directions when they differed. This required knowledge of the density distribution across the nebula, for which they utilized the densities determined from the [S ii] doublet ratios by Pogge, Owen, & Atwood (1992). They found that the separation at the substellar point was about 0.3 pc and that the nebula was a highly irregular concave surface, which is unusually high to the southwest of θ1 Ori C, where the nebula is brightest, and curves up abruptly along the northeast‐southwest bright bar that runs just north of θ2 Ori A. Their substellar separation is confirmed by an independent calculation from the surface brightness of the nebula in scattered starlight (O'Dell 1994).

The bottom‐line result of these calculations is that the nebula is really quite a low‐mass object (2 M), whose primary emission occurs from a glowing layer that is thin (0.03 pc) as compared with the minimum stellar distance (0.3 pc) and the characteristic dimension of the object in the plane of the sky (0.6 pc, which is about twice the θ1 Ori C–θ2 Ori A distance).

3. THE FOREGROUND LID

One of the most significant investigations concerning the structure of the M42 region since the Henry Draper Symposium was that of van der Werf & Goss (1989). In this study they used the 21 cm thermal continuum emission from M42 as a background source and searched for H i absorption lines. The region covered was centered on the Trapezium stars and extended to a diameter of about 10 '. Superb velocity resolution was employed (0.64 km s−1), and the spatial resolution (18 '') was sufficient to resolve most of the features detected. Clumped neutral hydrogen absorption was detected in front of much of the nebula, generally showing an increase of column density N(H i) toward the northeast, where the optically dominant Dark Bay feature is seen to the east of the Trapezium. A follow‐up investigation was made by O'Dell et al. (1992) to determine if the H i column density correlates with the amount of extinction. Extinction was determined by comparing the Hα/Hβ ratio point by point from calibrated images (Hester et al. 1991) of the nebula. It was found that there was an excellent correlation of N(H i) with extinction, which indicates that most of the extinction suffered by the nebula and its nearby cluster arises in the material producing the 21 cm absorption.

The location of this material is hard to pinpoint. However, it probably lies quite close to the nebula as the velocities of the material are close to but always blueshifted with respect to the OMC‐1 velocity. None of the velocities have the high blueshifts associated with the outermost parts of the entire Orion Complex which are commonly referred to as Orion's Cloak (Cowie 1982), so that the new H i material is probably best called the "foreground lid" to M42. "Veil" might be a more accurate description, since the visual optical depth is about 2, diminishing to the southwest and becoming much larger in the Dark Bay, which is a continuous part of the Foreground Lid. It is difficult to place the Lid exactly. The S(Hα) versus stellar distance equation should also apply to the IF that lies on the side of the Lid closest to θ1 Ori C, and a considerable effort has been made to detect emission from the lid. Unfortunately, the thermal width of the Hα lines is about 15 km s−1, which is larger than the velocity difference of the Lid from the main IF, with the result that emission from the inside of the Lid has not been detected. There is an extended region of [S ii] emission which may mark that IF, but one cannot locate the position from its intensity. Recent work on Herbig‐Haro type shocks in the vicinity of the Trapezium cluster indicates that a number of shocks, such as HH 203–204 and HH 269, are features marking where outflow from cluster stars are colliding with the Lid (O'Dell et al. 1997b), and the placement of these objects argues that the Lid separation is approximately the size of the optical nebula. This means that the Lid lies about 0.6 pc in front of θ1 Ori C. The Lid seems to be composed of three systems, each distinct in its characteristic velocity even though highly irregular in N(H i). In the terminology of van der Werf & Goss, the systems and their heliocentric velocities are A (24 km s−1), B (21 km s−1), and C (16 km s−1). These three systems are also evident in a study of the interstellar absorption lines of Ca ii in the four Trapezium stars plus θ2 Ori A (O'Dell et al. 1993) and of Na i in θ1 Ori C and θ2 Ori A (Hobbs 1978). The spectra of these heavy elements show multiple velocity components, with coinciding Ca ii components at 22.0, 19.8, and 15.3 km s−1 and Na i components at 23.0, 18.3, and 14.9 km s−1. All of the absorption‐line data are presented in Table 2, and the velocity systems identified with the Lid are designated there as V7 and V8. The additional noncoinciding components are discussed in § 7.6. Even though neither ion is the most populous species of the atom, they produced measurable lines because one can observe transitions from the highly populated ground state. Ca ii is produced by 6.1 eV photons and is in turn photoionized by 11.9 eV photons, which means that Ca iii is the most populous species of calcium, since photons of less than 13.6 eV will penetrate into the neutral hydrogen clouds. A similar situation applies for Na i, which is photoionized by 5.1 eV photons. It should be possible to determine the approximate displacements from θ1 Ori C from the relative abundances of Na i and Ca ii, which have been measured accurately.

Van der Werf & Goss (1990) also report the presence of a few rapidly moving H i clouds, characteristically blueshifted about 15 km s−1 with respect to the Lid systems. They explain these as having been accelerated by the rocket effect of photoablation, where clouds much more massive would not have been accelerated enough to be displaced and detected and clouds less massive would have been destroyed by photoionization. Unfortunately, no optical counterparts to these clouds have been seen. This could be used as an argument against the rocket acceleration interpretation; however, the ionization boundaries producing the push would be weak as compared with the background nebular emission of the main IF.

4. THE BRIGHT BAR

An IF will typically produce a shocked high‐density region on its neutral side (the PDR). This region will have a gradient of conditions basically determined by the extinction in the ultraviolet continuum on the low‐energy side of 13.6 eV, the cutoff imposed by H i. As nicely described by Tielens et al. (1993), this leads one to expect a series of layers. The closest to the IF will be C ii as a result of seeing photons in the 11.3–13.6 eV range (Wyrowski et al. 1997), with the next layer being of H2, and the deeper layer being optimally traced by CO emission. They also point out that the polycyclic aromatic hydrocarbon molecules, with a strong emission feature at 3.3 μm, will also occur in the region immediately behind the IF. All of these spectral features are observed when looking at M42 in the radio and infrared regions, but the interpretation of the data is usually not clear because one is looking along a line of sight passing about perpendicular to the IF. Fortunately, this is not the case for the Bright Bar, a region of enhanced Hα surface brightness that runs about 6 ' from the northeast to the southwest and passes about 30 '' north of θ2 Ori A. Not only is this remarkable linear feature brighter, but it also shows an enhanced [N ii]/Hα ratio, generally being greater on the side facing θ1 Ori C. This led to the early recognition that the Bright Bar is caused by the main IF being tipped almost along the observer's line of sight (Dopita, Dyson, & Meaburn 1974; Balick et al. 1974). This position has been taken as a point of departure by each study since then. Wen & O'Dell's (1995) three‐dimensional model of the nebula showed that this view of the Bright Bar is basically correct; however, their calculations indicate that the IF is not exactly perpendicular, although it must be admitted that their method tends to smooth the nebula and reduce the gradients in the surface. A detailed study of Hubble Space Telescope WFPC2 images along the bar (O'Dell & Wong 1996) shows that there are a number of peculiar features, which include crenellated structures (O'Dell & Wen 1994) on the side away from θ1 Ori C (which should not be observed if we are looking at an IF viewed exactly along its edge) and even regions where the [O iii] emission is enhanced on the side away from θ1 Ori C. Although the first‐order structure is caused by our viewing an IF almost edge‐on, there are obviously many questions to be resolved.

5. STRUCTURAL FEATURES DERIVED FROM VELOCITY OBSERVATIONS

The fact that the emission‐line radiation is packed into a narrow wavelength interval has allowed the application of very high spectral resolution in some studies of the nebula, and the brightness of the Trapzeium stars and θ2 Ori A has also allowed similar high resolutions for investigation of absorption lines formed in material lying between the observer and those stars. The FWHM broadening of an ion of atomic weight M in a gas of electron temperature 8000 K will be FWHM = 19.2 × M-1/2 km s−1 and will increase as the square root of the temperature. This means that resolutions of a few km s−1 are as high as necessary for studying the hot nebular gas, although better resolution will benefit absorption studies of a cooler gas.

The ultimate data set of velocity information would be coverage of every major ion at a spectral resolution that well resolves the line profiles and at a spatial resolution matching that of the best images. We are well short of that goal but are slowly making progress. A series of papers by the author and his students has provided adequate velocity resolution studies in [O iii] (O'Dell & Castañeda 1987; Castañeda 1988), [O ii] (Jones 1992), [O i] (O'Dell & Wen 1992), [S iii] (Wen & O'Dell 1993), and [S ii] (Hu 1996) using slit spectroscopy. Although multiple slit settings were employed, the spectra cover only a small, but probably representative, sample of the central 5 ' diameter region of the nebula. Radio observations of H ii have covered the entire nebula at superb velocity but low spatial resolution (Wilson et al. 1997). The central 10 ' region has been covered continuously at 50 km s−1 resolution in [O iii] and [S ii] using a Fabry‐Perot imaging system (O'Dell et al. 1997a). This latter study is quite adequate for identifying very high velocity features, which abound as a result of outflows from many pre–main‐sequence stars. However, these interesting features do not play an important role in the dynamics of the nebula as a whole and fall outside the scope of the present paper.

Only the brightest stars can be used for study of absorption lines caused by intervening gas. The early studies of θ1 Ori C and θ2 Ori A (Münch & Wilson 1962; Münch 1985) have recently been supplemented by studies of all four members of the Trapezium (Oudmaijer et al. 1997) and the Trapezium members plus θ2 Ori A (O'Dell et al. 1993).

5.1. The Large‐Scale Velocities of M42

The entire nebula has been mapped in the H64α line at 1.4 km s−1 and 42 '' by Wilson et al. (1997) using the 100 m telescope of the Max‐Planck‐Institut für Radioastronomie. The central 3 ' diameter region was also studied using the Balmer H12 optical line by Jones (1992) at a resolution of 20 '' with very similar results. Since the H ii emission comes from all ionized zones, it is the least discriminating ion for study of the acceleration of material away from the IF but the best guide to the overall flow of gas. The radio maps have a particular advantage in studying the flow in the eastern part of the nebula where the Dark Bay extinguishes much of the optical radiation, especially so as the nebula also becomes of lower intrinsic surface brightness there (Yusef‐Zadeh 1990). The H ii data show that there is a central most positive velocity of about 20 km s−1 centered about 30 '' east‐southeast of θ2 Ori A. Throughout this paper all velocities will be heliocentric, which are 18.3 km s−1 more positive than the local standard of rest velocities favored by radio astronomers and students of Galactic structure. There is a global trend for the velocities to become about 6 km s−1 more blueshifted as the radial distance increases from θ1 Ori C out to a distance of about 2farcm5. In addition, there are two nonradially symmetric trends. About 3 ' to the southwest the flow is an extra 2 km s−1 more blueshifted. About 3 ' due west of θ1 Ori C, well behind the Dark Bay, the velocity abruptly shifts back to the central values and perhaps becomes slightly more positive (see Fig. 1).

Fig. 1.—

Fig. 1.— This is a depiction of the center of the Orion Nebula Cluster and M42 as viewed from the southwest. The escarpment which produces the Bright Bar feature is on the far left, and the brightest region, which lies over the Orion S molecular outflow source, is in the low middle. The relative positions of the stars and proplyds have been determined from the assumption of a symmetric distribution in three dimensions as determined by Hillenbrand & Hartmann (1998) except where there is specific evidence for the position. The shocks associated with outflows from low‐mass stars are shown in positions developed in O'Dell & Bally (2000) and Bally, O'Dell, & McCaughrean (2000). The distance to the inner side of the Foreground Lid (horizontal bright feature above the brightest star, θ1 Ori C) is probably the most uncertain dimension in this depiction. This image was rendered by the San Diego Supercomputer Center under contract with the American Museum of Natural History as part of the Three‐D Galaxy project of the new Hayden Planetarium.

The optical studies are limited in the area of coverage by the decreasing surface brightness away from θ1 Ori C and also the extinction due to the Lid material. The central 2farcm5 diameter region shows an almost constant velocity at 25.5 km s−1 in [O i] (O'Dell & Wen 1992). The [O ii] emission has a central value of about 19 km s−1 and becomes several km s−1 bluer to the southwest of θ1 Ori C. [O iii] emission is about 22 km s−1 in the central region, generally becoming a few km s−1 more blueshifted at increasing radial distance with an asymmetry of even greater blueshift to the southwest.

Within the paradigm that all of the neutral gas has the velocity of OMC‐1 (28 km s−1) and that there is a local flow of gas perpendicular to and away from the local IF, then one can use these velocities to discuss the three‐dimensional structure of M42. The radially symmetric increasing blueshift with distance from θ1 Ori C is the opposite to what one would expect from a concave surface (which is indicated by the three‐dimensional model of Wen & O'Dell). It is as if the rate of acceleration of material away from the IF is much lower in the regions closest to θ1 Ori C, which probably is the case, since the radiation pressure from the stellar continuum will be highest there and the gas will be held back. The asymmetric blueward flow to the southwest has been interpreted by O'Dell & Wen (1994) and Wilson et al. (1997) as an indication that this is where the ionized material is escaping the confinement of the Lid, which is consistent with the fact that the Lid becomes very thin or perhaps even vanishes in that region. The abrupt increase of H ii velocities 3 ' west of θ1 Ori C was interpreted by Wilson et al. as being due to the IF curving abruptly toward the observer, thus removing the expansion component of velocity. This interpretation is consistent with the 21 cm continuum map of van der Werf & Goss (1989), at 22 '' resolution, which shows the surface brightness diminishing less with distance. Since the radio surface brightness contours behind the Dark Bay region (van der Werf & Goss 1989; Yusef‐Zadeh 1990) decrease asymmetrically fast, this indicates that the IF is less concave than in the optically visible region. The observations of Wilson et al. may be showing us the region where the IF curves around toward the observer and joins up with the Lid.

5.2. Turbulence in the Main IF

The availability of the slit spectra of M42 has made it possible to investigate the statistical properties of the main IF velocities and to compare these with the expectation of turbulence theory. Each long‐slit spectrum could be divided into multiple spectra, each representing a spatial sample of about 2'' × 5'', thus providing an adequate sample of several hundred accurate points. The theoretical framework has existed for nearly half a century. Von Hörner (1951) solved the problem of relating observable radial velocities to the intrinsic distribution of velocities, where it was assumed that the relative velocity (v) of two points separated by a distance (r) will be v2rn. For the common case of Kolmogorov turbulence, n = 2/3. Von Hörner's model was that of a thin slab nebula, and he determined the properties of the radial velocity V(ϕ) derived along various lines of sight. The cleanest method of analysis is through the statistical property called the structure function [B(ϕ)], which is defined as B(ϕ) = 〈V') - V'')|2〉, where φ refers to the angular separation of two samples located at positions φ ' and φ '' and B(ϕ) is calculated for all combinations of velocity samples. At small values of φ, B(ϕ)∝ϕn-1; at large values, B(ϕ)∝ϕn. The transition to "large" occurs at the angular distance that is equivalent to the thickness of the emitting layer.

The value of B(ϕ) was calculated for the radial velocities of each of the ions ([O i], [O ii], [O iii], and [S ii]) that was studied with the slit spectrograph. Three of the ions showed the theoretically predicted steep power law at small φ‐values and a transition to flatter power laws at large φ‐values. [O ii] and [S iii], which should arise from similar levels of ionization, were very similar, being slopes near unity for small φ‐values and essentially constant for large φ‐values, with the transition occurring at about 22 ''. [O iii] made a transition from a power law of 0.8 to one of 0.3 at about 15 ''. It is remarkable that the transitions occurred at about the same φ, since the [O ii] layer should be very thin as compared with the [O iii] layer, as shown in Table 1. Moreover, the well‐defined large φ power laws were much less than the Kolmogorov theory value of 2/3. One can summarize these results by saying that these ions show results that resemble, but do not agree with, the predictions of von Hörner's models. This result is different from the older analysis of Münch (1958), who applied a similar technique to a set of photographic M42 spectra (Wilson et al. 1959).

The one ion whose structure function agrees well with the prediction of the model is [O i], which shows a constant power law of 0.7 ± 0.1 over the entire range of φ that was observed (6 ''–180 ''). The power law agrees with Kolmogorov theory, and the lack of a break in the slope is consistent with even the smallest values of φ being much larger than the thin [O i] emitting layer (Table 1).

There is, however, another discrepancy with theory which applies to all of the ions observed. According to the turbulence model there will be a turbulent broadening of the emission line along each line of sight, effectively representing random motions along a line. The magnitude of that broadening can be estimated from the absolute value of B(ϕ), and in each case the turbulent broadening should be a small fraction of 1 km s−1. Von Hörner and Münch found the same result for the early [O iii] observations. In fact, each of the lines studied shows a nonthermal broadening of about 9 km s−1. By nonthermal, I mean that after one quadratically subtracts the expected thermal broadening, there always remains a component of broadening with FWHM ≃ 9 km s−1. A very similar result was found by Wilson et al. (1997) for H i radio emission.

Such an extra line broadening may be very significant, because it means that along each line of sight as much or more energy is being carried by this nonthermal turbulence as is contained in the Maxwellian random motion of the individual atoms. However, it is not obvious that this is important in determining the energy balance of the nebula. We know that the thermal gas loses its energy in a characteristic time of about 100,000/Ne years, where Ne is the electron density (cm−3), which means a timescale of about 10 years for the densest part of M42. Without knowing the mechanism producing the extra broadening, we cannot derive the power necessary to sustain it. O'Dell & Wen (1992) argue that it is due to fine‐scale irregularities in the shape of the main IF, an interpretation discussed in another context in § 7.3.

5.3. The He i Absorption‐Line System

The presence of a metastable level in He i gives rise to a large optical depth in some He i emission lines formed near the main IF and also the potential for formation of absorption lines in the stellar continua. The lowest lying triplet state (2 3S) is populated by He+ recombinations and depopulated by two‐photon emission to the ground‐state singlet, collisions to the 11P state, and photoionizations by Lyα photons of hydrogen. Very early observations of θ1 Ori C revealed the He i λ3889 line in absorption, which has been followed by many subsequent observations (Münch & Wilson 1962; O'Dell et al. 1993; Oudmaijer et al. 1997). The 3889 Å line is formed by the 2 3S–3 3P transition and is instrinsically weaker than the more difficult to observe the 10830 Å line of the 2 3S–2 3P transition. However, improved near‐infrared detectors have led to the measurement of that line too (Vaughan 1968; Münch 1985; Oudmaijer et al. 1997). Our primary source of information lies with the 3889 Å line, although any observation of the central stars is made against the He i emission lines produced by the nebula. The much greater brightness of θ1 Ori C at 3889Å more than compensates for its lower oscillator strength, although Münch & Pitz (1981) have used a chopping technique that compensates for much of the nebular emission at 10830 Å. This contrast effect means that the determination of the absorption spectrum will be less well determined for the fainter stars in the Trapezium.

The two modern CCD studies (O'Dell et al. 1993; Oudmaijer et al. 1997) have produced similar results for the four Trapezium stars, while only the earlier study included θ2 Ori A. O'Dell et al. used a velocity resolution of 3.3 km s−1, while that of Oudmaijer et al. was ∼7 km s−1. Table 2 gives the average results of these studies for the Trapezium stars and O'Dell et al.'s values for θ2 Ori A. The component reported by Oudmaijer et al. at −60 km s−1 in θ2 Ori A was also seen in the O'Dell et al. study, although it did not reach their credibility threshold for publication. It is certainly there, as it appears in these two very independent studies. The Oudmaijer et al. values for this line are given in Table 2.

The primary feature is at 3 km s−1 which is common to all of the Trapezium stars. The 3889 Å line in θ2 Ori A has absorption features close to this velocity, but very clearly the θ2 Ori A line requires two components to fit the line profile.

O'Dell et al.'s spectra also allowed measurement of the nearby [Ca ii] line, and Hobbs (1978) measured [Na i] in θ1 Ori C and θ2 Ori A. O'Dell et al. found a strong [Ca ii] component at 7.5 km s−1 in the Trapezium stars and another at 0.5 km s−1 in θ2 Ori A. These are also included in Table 2, where the various systems are grouped by similar velocities.

5.4. Where Are the Absorption Lines Formed?

Only the two velocity systems (7 and 8) associated with the foreground lid seem to have an established region of formation. The origin of the other velocity systems is quite uncertain with the exception of the 21 km s−1 component of He i, which could arise from absorption in the main IF. This would mean that θ1 Ori D would have to lie closer to the main IF than the other Trapezium stars, an interpretation that is consistent with the fact that the Ney‐Allen infrared source is centered on this star.

There is no He i emission‐line counterpart of any of the He i absorption systems, which is not surprising since it takes very few atoms in the 2 3S state to produce the observed λ3889 line. This argument is most clearly given in Baldwin et al. (1991) and repeated in a slightly different form by Münch & Wilson (1962) and Oudmaijer et al. There are emission‐line components of [O ii] near the Trapezium at 3.1 km s−1 (Jones 1992) and of [O iii] at 2.8 km s−1 near θ2 Ori A (Castañeda 1988), so perhaps those are arising from the same sources.

The most difficult thing to decipher in interpretation of the absorption lines is that system 5 seems to produce both the high‐ionization He i lines and the low‐ionization Na i and Ca ii lines. If indeed all of these velocity features have the same region of origin, it will be a parcel of material if they lie within the boundary of the main IF (on the back) and the Lid (on the front) unless they are short‐lived. A relative velocity with respect to OMC‐1 and the main IF of 25 km s−1 means that 1 pc is traversed in about 40,000 years, a time short compared with the (0.5–1) × 106 yr age of the cluster. There is indeed a wealth of fine‐scale features in the nebula that move within this velocity range. These are the shocked material produced by outflows from low‐mass pre–main‐sequence stars, some of which have previously been detected as Herbig‐Haro objects, while most of them have been revealed through the new HST images (O'Dell et al. 1997b) and Fabry‐Perot discrimination of their high velocities (O'Dell et al. 1997a). These short‐lived features have sizes from a few arcseconds to many tens of arcseconds, which means that they could cover the entire Trapezium region and produce multiple velocity systems. The idea of producing observable absorption lines of Na i and Ca ii in shocks within an H ii region seems to have not been considered, so that it is difficult to say if this interpretation is plausible.

5.5. The Relative Velocity of Various Systems

Membership and association of the stars in Orion are usually determined from proper‐motion data. These are not available for the nebular components of M42 and are notoriously inaccurate for the Trapezium stars because of their brightness, a condition that is not changed by the new Hipparcos data because the four bright stars of the Trapezium are too close together. One can, however, obtain some useful information from the radial velocities. The radial velocity of the molecular components of OMC‐1 is 28 km s−1 (as determined from the compilation in Table 3.3.VII of Goudis 1982). The nebular values are as blue as 25.5 km s−1 at the IF, with the main body at about 18 km s−1. The average of θ1 Ori A, θ1 Ori B, and θ1 Ori D is 24 ± 3 km s−1 if one uses the values from Abt, Wang, & Cardona (1991). Both θ1 Ori A and θ1Ori B are spectroscopic binaries, where one must use their systemic velocities, while θ1 Ori D is a broad‐line B0.5 V star. The low‐mass stars of the cluster give an average radial velocity of 27 ± 3 km s−1 (R. Mathieu & L. Marschall 1998, private communication). All of these numbers are consistent with the cluster having no more than a few km s−1 relative velocity with respect to OMC‐1 and the fact that the nebula's blueshift is a result of expansion of the ionized gas away from the surface of OMC‐1.

5.6. The Riddle of the Radial Velocity of θ1 Ori C

The radial velocity of θ1 Ori C is extremely important in understanding what has happened, what is happening, and what will happen in M42. The recombination time for photoionized hydrogen is about 100,000/N years (where Ne is the electron density in units of cm−3), which means that very close to the IF this is only about 10 years and most of the main emission has a timescale of less than a century. Therefore, variations in the UV luminosity or distance of θ1 Ori C can produce changes in the nebula. If one simply accepts the Yale Bright Star Catalogue (Hoffleit 1964) value of +33 km s−1, then θ1 Ori C is moving into OMC‐1 at a rate of 6 km s−1 and would travel to the present position of the main IF in only 50,000 years. It is very difficult to accept such a radial velocity because it would have a corresponding proper motion much larger than the other cluster stars (Jones & Walker 1988), and it is hard to understand why the most massive star in this cluster (Hillenbrand & Hartmann 1998) could have such a large spatial velocity. This precipitated a literature search by the author for various determinations of the radial velocity and an attempt to assess their accuracies.

Quite different radial velocities have been obtained by different observers. Moore's (1932) catalog of radial velocities gives 23.1 ± 1.8 km s−1, which is similar to the less accurate value of 24 ± 16 km s−1 of Plaskett (1924). The latter gives a value of 16 ± 5 km s−1 for the Ca ii lines, whose average modern value is about 20 ± 4 km s−1 with the uncertainty arising from how the complex profile of the absorption by multiple narrow lines (O'Dell et al. 1993) would have been treated in the measurement by eye of low‐resolution spectra. Hoffleit's value seems primarily driven by the study of Struve & Titus (1944), who measured all of the stars of the Trapezium. They found 37.5 ± 2.0 km s−1 for θ1 Ori C,0.5 ± 2.3 km s−1 for the nebula, and 20.3 ± 2.9 km s−1 for Ca ii; i.e., their Ca ii values agree with modern values, but the nebular value is low by about 18. The latter difference raises fundamental questions about the small probable errors they claim. A more recent high‐resolution study by Conti (1972) found 26 ± 3 km s−1, while a lower resolution study by Abt et al. (1991) found 17 ± 11 km s−1. A program of monitoring the spectrum of θ1 Ori C at high resolution by Stahl et al. (1993) gave a value of 14 ± 1 km s−1, although a brief period of a significantly lower velocity was seen. The author and his assistant David Brown measured the stellar absorption lines in the spectra obtained for studying the interstellar absorption lines (O'Dell et al. 1993) and found 14 ± 1 km s−1. The most recent set of observations by Stahl (1997) gives radial velocities with an accuracy of a few km s−1 over an interval of about 1900 days. During this interval he saw nonperiodic short‐timescale variations of about 10 km s−1 and values through the range of 5–43 km s−1. This indicates that the earlier observations were not anomalous but are part of a currently not understood pattern of change. Certainly there is not a monotonic secular change.

The explanation of the remarkable radial velocity behavior of θ1 Ori C probably lies with the intrinsic nature of the star. Conti (1972) established that the He ii λ4686 line was asymmetric, being of a P Cygni type. Walborn (1981) first established that there were systematic variations in the spectrum of θ1 Ori C, a conclusion verified and extended by the first study of Stahl et al. (1993) and additional observations (Stahl et al. 1996). The object even seems to vary in its X‐ray luminosity (Gagné et al. 1997). All of the authors agree that there is a 15.4 day periodic variation, although there is no short‐term radial velocity variation. An oblique magnetic rotator model is usually invoked to explain the spectroscopic and X‐ray changes, which would be consistent with demonstrating no detectable radial velocity changes. Stahl (1997) favors an interpretation of the radial velocity changes as patterns of change in the profiles of the stellar absorption lines, although the lack of periodicity of the velocity changes can be used as a counterargument to this interpretation, leaving open the chance that the variations are due to the motion of the star. At this point in time the important issue of the velocity of θ1 Ori C remains quite unresolved.

6. SCATTERED LIGHT AS A USEFUL AND CONFUSING FACTOR

Scattered starlight dominates the spectrum of the continuum, being about 5 times stronger than the atomic component of the gas. This fact has been known from the early images of Wurm & Rosino (1956, 1957) and was one of the contributing factors in Wurm's argument for a slab model of the nebula. The strength of the continuum was also measured by photoelectric filter photometry (O'Dell & Hubbard 1965) and then more recently by Baldwin et al. (1991) in their slit spectra. An extensive set of calculations by Schiffer & Mathis (1974) tried to explain the observations, but these models assumed that the dust was distributed close to the source stars, and are probably not relevant.

The fact that starlight is scattered by dust in the nebula should not be a surprise. We know that the visual optical depth behind the main IF is very large, so that as long as the albedo of the dust particles is nonzero, there should be a measurable scattered light continuum. In effect, the facing side of OMC‐1 acts as a diffuse mirror, a fact that was appreciated by Münch (1985) but published only in a publication that was not widely circulated. Many of the elements of his discussion of the effect of scattering of the He i λ10830 line were independently introduced by the author (O'Dell, Walter, & Dufour 1992).

In his study of the [O iii] λ5007 line, Castañeda (1988) made a multiple Gaussian component fit to each of his spectra. In this analysis he identified three strong velocity systems. System A was the strongest and represents emission near the IF. His deconvolutions also yielded a second system shifted by just a few km s−1 blueward, which was never fully resolved. This type of deconvolution into multiple components was made because we were seeing for the first time multiple higher velocity systems, and it was thought that the asymmetries in the main emission were due to unresolved components. Henney (1998) has shown that this second component is artificial, simply representing the acceleration of gas away from the IF. However, the third systematic component cannot be explained in this way. This component is characteristically twice the FWHM of the main component and has a ratio of brightness of about 25%. Its peak is also typically redshifted with respect to the main component. The interpretation applied by O'Dell et al. (1992) is that this is the reflection of the main component, with the line being slightly redshifted because the light has been reflected from a mirror that is moving away from the emitting layer, which produces a doubling of the velocity shift in the reflected light (of course it is actually the emitting layer that is moving away from the stationary OMC‐1). They interpret the broadening as being caused by light being reflected (scattered) from a variety of relative velocities, since both the scattering and emitting layers are extended. Light scattered from directly below the emitting point will have the greatest redshift. Detailed models of this process are included in a recent paper by Henney (1998).

This is not simply a second‐order effect. Independent of our understanding of the details of the blister model, this model unavoidably says that a certain significant fraction of the radiation emitted in the direction of OMC‐1 will be backscattered toward the observer. This factor must be included in our interpretation of all facets of the nebula. For example, the calculation of an equivalent thickness of the emitting layer from the known surface brightness and electron density assumes that the emission occurs isotropically into 4π steradians. In the case of the dust being a perfect reflector (albedo unity), then the emission is radiated into 2π steradians. Without knowing the detailed processes involved with this scattered light, it is not possible to make accurate corrections. The problem is even more complex, since the fraction of light that is backscattered probably depends upon wavelength and the separation between the emitting and scattering layers. The wavelength dependence (which would arise from the effective change in optical depth, albedo, and phase function with wavelength) would mean that on the average a different fraction of the light is scattered at different wavelengths. If this fraction increased with decreasing wavelength, then it means that the physical interpretation of the observed spectrum would be skewed by artificially enhancing the bluer lines. If the blue lines are artificially enhanced, this could provide an explanation of the the anomalous extinction law for M42 found by Costero & Peimbert (1970), although this would not remove the peculiarity of the Orion extinction law found by investigations of the stars lying in front of the nebula. The case becomes even more complex if the fraction of light that is scattered depends upon the separation of the emitting and scattering layers. This separation would be quite small for ions such as [O i] and [S ii], which arise from close to the IF, while it would be large for high‐ionization emission from [O iii]. This correction introduces a new level of complexity into analysis of spectrophotometry of M42 and must be causing a misinterpretation of the observed lines. Without understanding the details of this process, we must assume that errors in the relative values of emission lines can be as much as 25%.

7. MAJOR UNRESOLVED QUESTIONS ABOUT THE STRUCTURE OF M42

Although there have been many advances in our knowledge of the structure of M42 since the Henry Draper Symposium, a number of fundamental issues remain unresolved. This closing compilation is basically a list of the ones that are the author's favorites, and their solution should help clarify what is actually happening in this important object.

7.1. Why Is the Bright Bar So Linear?

It is easy to cause small‐scale linear features, with jets and shadows being obvious mechanisms; but these cannot be invoked to explain this major feature in M42. Clearly the Bright Bar is a warp in the main IF of M42 which we view from nearly edge‐on, but this means that the radiation field that has sculpted this part of the nebula has been constant over a long length or that the underlying density of neutral material is nearly constant.

7.2. Why Can We See Such Fine‐Scale Structure?

The main piece of physics that describes the brightness of the material near the main IF is the fact that the local surface brightness will depend only on the flux of ionizing photons from θ1 Ori C and the viewing angle. The surface brightness together with knowledge of the emitting region densities give the result that the e−1 scale for emission is 14 ''. This means that we would expect the nebula to be smooth at this scale, whereas the observed nebula shows structure down to a few arcseconds. The explanation cannot lie with density differences of the material, because if the object is ionization bounded, the surface brightness depends only on the ionizing flux. Perhaps the answer has its source with density in the sense that the advance of the IF into OMC‐1 will proceed more rapidly where the density is low, leaving behind columns of un‐ionized material (the much publicized pillars seen in M16 are the most dramatic example, which has been known since at least the time of the Palomar Sky Survey). Irregularities in OMC‐1 at the scale of 0.01 pc would then show up as roughness in M42's main IF, which would become visible through variations of the local flux and viewing angle. There are several arguments that such irregularities exist in the PDR (Hollenbach & Tielens 1997), as high‐density knots are necessary to produce the CO millimeter line profiles (Stacey et al. 1993).

7.3. What Is the Source of the Extra Line Broadening?

It is remarkable that all of the emission lines studied to date have an unexplained line‐width component of about 9 km s−1, this being true for the [O i] emission that must originate exactly in the IF and the [O iii] that must arise from a more extended zone closer to θ1 Ori C and farther from the IF. It is as if ionizing gas is moving in random directions at about this velocity on a scale of less than a few arcseconds. What physical model can explain this and possibly what nebular physics is being left out of what we are doing in building these models? If the timescale for driving this extra line broadening is short, then this is an important element in the determination of the energy balance of M42. The unexplained line broadening may be produced by the same small‐scale structure discussed in the previous section. In this case the broadening would be caused by free flow of material in all directions from around isolated knots and pillars in the IF (O'Dell & Wen 1992). An attractive alternative is that of Ferland (2001), who invokes the presence of Alfvén waves.

7.4. How Is Scattered Emission‐Line Radiation Affecting Analysis of the Spectra?

We now know that not only is the visual starlight from the Trapezium stars scattered by the concentration of particles immediately behind the IF in the associated PDR, but that this scattering also occurs for the emission lines. Short of observing every line of interest at velocity resolutions sufficient to deconvolve the original and scattered components, this mechanism introduces a nonphotometric "noise" into the analysis of emission‐line ratios. Many of the problems dealing with interpretation of the spectrum of M42 will not be changed by photometric uncertainties at the level of 25%, but others will, and this needs to be considered in all spectral analysis.

7.5. Is There a Central Cavity?

We certainly know that θ1 Ori C is the source of a strong stellar wind (Howarth & Prinja 1989), which raises the expectation that there would be a central cavity of highly shocked material. This has been invoked by many of the early models of M42 and as recently as the paper by Wilson et al. (1997) to explain the more redshifted velocities near the center of the nebula. However, the author favors an interpretation of that feature as being due to radiation pressure constraining flow away from the main IF in that region. Furthermore, there is no evidence for the high‐temperature shocked material that would be formed behind the shock that leads this wind. The most likely explanation is that the flow of material through the IF and into the region that produces the visible M42 is energetically much more important than the stellar wind of θ1 Ori C. This is supported by the fact that the energy flux in particles is 1.3 × 1035 ergs s−1 while the energy flux of ionizing photons is 1.7 × 1038 ergs s−1. There certainly are large‐scale structures in the central part of M42, but none of these are centered on θ1 Ori C (O'Dell et al. 1997a).

7.6. Where Are the Non‐Lid Absorption Lines Being Formed?

The riddle of the location of the material forming the He i absorption lines has been with us for half a century without resolution. We have now added the problem of also explaining Na i and Ca ii lines at both blueshifts and redshifts. There are sources for pushing nebular material around at these velocities in the form of the outflows from pre–main‐sequence low‐mass stars, but at this point we do not have the theoretical knowledge that links the two.

7.7. Where Is the Lid Located?

The presence of a lid seems well established, being seen in H i, Na i, and Ca ii absorption, indicating that there must be a second IF on the side of the Lid facing θ1 Ori C. The important question is one of how far from θ1 Ori C it is located. The answer has broad application not only in study of the nebula proper but also in study of the Trapezium cluster, as a close‐in Lid would indicate that some of the observed cluster stars are probably located within or on the near side, while most lie within the photoionized main cavity.

It is the author's pleasure to acknowledge the independent work, assistance, and discussions of his former students Hector O. Castañeda, Michael R. Jones, Leisa K. Townsley, Zheng Wen, Xihai Hu, and Wendy M. Lane in formulating the view of M42 that appears here. My more senior colleagues Gary Ferland, Patrick Hartigan, Will Henney, and John Meaburn have also been generous of their material and ideas over the last many years. This review is based on an oral paper presented at the 1997 June Ringberg Castle conference on "The Orion Complex Revisited" sponsored by the the Max Planck Society. The original draft of this review was done while supported by the German Alexander von Humboldt Foundation and hosted by the Max Planck Institute for Astronomy in Heidelberg, Germany. Final preparation of the manuscript was supported in part by the Space Telescope Science Institute grant GO‐8121.

The figure depicting a close‐up view of M42 was directed by Carter Emmert, with technical production by Erik Wesselak, both from the American Museum of Natural History in New York. Volumetric rendering software was done by Dave Nadeau and Jon Genetti of the San Diego Supercomputer Center. Their professionalism and cooperation are gratefully acknowledged.

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