11institutetext: Université Paris-Saclay, CNRS, Institut d’Astrophysique
Spatiale, 91405 Orsay, France22institutetext: Institut de Planétologie et
d’Astrophysique de Grenoble (IPAG), Université Grenoble Alpes, CNRS, F-38000
Grenoble, France33institutetext: Institut de Radioastronomie Millimétrique
(IRAM), 300 rue de la piscine, F-38406 Saint-Martin d’Hères,
France44institutetext: W.M. Keck Observatory, 65-1120 Mamalahoa Hwy, Kamuela,
HI, USA55institutetext: Department of Physics & Astronomy, The University of
Western Ontario, London ON N6A 3K7, Canada66institutetext: Institute for Earth
and Space Exploration, The University of Western Ontario, London ON N6A 3K7,
Canada77institutetext: Carl Sagan Center, SETI Institute, 339 Bernardo Avenue,
Suite 200, Mountain View, CA 94043, USA88institutetext: Institut de Recherche
en Astrophysique et Planétologie, Université de Toulouse, CNRS, CNES, UPS, 9
Av. du colonel Roche, 31028 Toulouse Cedex 04, France99institutetext:
Astronomy Department, University of Maryland, College Park, MD 20742,
USA1010institutetext: Instituto de Física Fundamental (IFF), CSIC, Calle
Serrano 121-123, 28006, Madrid, Spain1111institutetext: Department of Space,
Earth and Environment, Chalmers University of Technology, Onsala Space
Observatory, 439 92 Onsala, Sweden1212institutetext: LERMA, Observatoire de
Paris, PSL Research University, CNRS, Sorbonne Universités, F-92190 Meudon,
France1313institutetext: I. Physikalisches Institut der Universität zu Köln,
Zülpicher Straße 77, 50937 Köln, Germany

# High angular resolution near-IR view of the Orion Bar revealed by Keck/NIRC2

Emilie Habart 11 Romane Le Gal 2233 Carlos Alvarez 44 Els Peeters 556677
Olivier Berné 88 Mark G. Wolfire 99 Javier R. Goicoechea 1010 Thiébaut
Schirmer 1111 Emeric Bron 1212 Markus Röllig 1313

(2022)

###### Abstract

Context. Nearby Photo-Dissociation Regions (PDRs), where the gas and dust are
heated by the far UV-irradiation emitted from stars, are ideal templates to
study the main stellar feedback processes.

Aims. With this study we aim to probe the detailed structures at the
interfaces between ionized, atomic, and molecular gas in the Orion Bar. This
nearby prototypical strongly irradiated PDR will be among the first targets of
the James Webb Space Telescope (JWST) within the framework of the PDRs4All
Early Release Science program.

Methods. We employed the sub-arcsec resolution accessible with Keck-II NIRC2
and its adaptive optics system to obtain the most detailed and complete
images, ever performed, of the vibrationally excited line H2 1-0 S(1) at 2.12
$\mu$m, tracing the dissociation front, and the [FeII] and Br$\gamma$ lines,
at 1.64 and 2.16 $\mu$m respectively, tracing the ionization front. The former
is a powerful tracer of the FUV radiation field strength and gas density
distribution at the PDR edge, while the last two trace the temperature and
density distribution from the ionized gas to the PDR. We obtained narrow-band
filter images in these key gas line diagnostic over $\sim 40^{\prime\prime}$
at spatial scales of $\sim$0.1′′ ($\sim$0.0002 pc or $\sim$40 AU at 414 pc).

Results. The Keck/NIRC2 observations spatially resolve a plethora of
irradiated sub-structures such as ridges, filaments, globules and proplyds.
This portends what JWST should accomplish and how it will complement the
highest-resolution ALMA maps of the molecular cloud. A remarkable spatial
coincidence between the H2 1-0 S(1) vibrational and HCO+ J=4-3 rotational
emission previously obtained with ALMA is observed. This likely indicates the
intimate link between these two molecular species and highlights that in high
pressure PDR the H/H2 and C+/C/CO transitions zones come closer as compared to
a typical layered structure of a constant density PDR. The H/H2 dissociation
front appears as a highly structured dense region with over-dense sub-
structures with a typical thickness of a few $\sim$10-3 pc. This is in
agreement with several previous studies that claimed that the Orion Bar edge
is composed of very small, dense, highly irradiated PDRs at high thermal
pressure immersed in a more diffuse environment.

###### Key Words.:

¡photodissociation regions - interstellar medium - infrared emission - star
forming regions¿

##  1 Introduction

Stellar feedback influences the star formation activity through molecular
cloud dissolution, compression processes and increase in ionization fraction,
which slows down ambipolar diffusion. However, the precise nature and
importance of all theses mechanisms relative to other processes that influence
star formation remains largely unknown. Stellar feedback can take the form of
radiative heating and pressure, thermal expansion and evaporation, and stellar
winds and shocks (e.g., Pabst et al. 2020; Schneider et al. 2020, and
reference therein). The combined radiative and dynamical feedback of massive
stars on their parental cloud is not yet understood. Therefore, direct
observation and quantification of the radiative heating efficiency (e.g., the
coupling of gas and dust to the intense stellar-ultraviolet fields) and the
mechanical energy injection is necessary.

Recent near-infrared images obtained with the Gemini telescope at high angular
resolution ($\sim 0.06-0.11^{\prime\prime}$) revealed, at a spectacular level
of detail, unexpected structures within the strongly irradiated molecular
cloud at the Western Wall in Carina at a distance of 2.3 kpc (Hartigan et al.
2020). These authors found series of ridges, fragments, and waves with sizes
in the $\sim$200-2000 AU range that may result from the complex dynamical and
radiative processes that sculpt these systems. Indeed, while regularly-spaced
ridges that run parallel to the photodissociation front may suggest large-
scale magnetic fields are dynamically-important (Mackey & Lim 2011), several
fragments and waves could resemble Kelvin-Helmholtz instabilities. Berné et
al. (2010) reported the presence of a series of five surprisingly regular
wavelets (separated by 0.1 pc or 20000 AU) at the surface of the Orion
molecular cloud. These authors proposed that these waves formed by the
mechanical interaction of high-velocity plasma/gas, produced by massive stars,
with the dense molecular gas, which has provoked hydrodynamical instabilities.
Sub-arcsecond resolution is required to resolve detailed structures even for
the nearest regions of massive star formation. This capability now exists with
adaptive optics (AO) imaging, and will be further developed/expanded in the
near future with JWST.

The main goal of the present study is to observe and quantify the stellar
feedback in the closest site of ongoing massive star-formation: the Orion
molecular cloud. This region is located about 5 times closer than the Carina
star forming region. The dominant stellar feedback processes can be probed by
observations of Photo-Dissociation Regions (PDRs) where far-ultraviolet
photons of massive stars create warm regions of gas and dust in the neutral
atomic and molecular gas (e.g., for a recent review see Wolfire et al. 2022,
and references therein). Nearby, edge-on PDRs such as the Orion Bar are ideal
targets due to their wide extension on the sky, bright emission, and proximity
that allow to probe these processes on a small physical scale. PDRs are
particularly bright in the infrared (IR).

However, until now a very high angular (sub-arcsec resolution) IR molecular
view of the Orion Bar PDR was missing. In this study, we present observations
obtained with Keck/NIRC2 using AO, which provide the most complete and
detailed maps of the complex UV-irradiated region where the conversion from
ionized to atomic to molecular gas occurs. We mapped the vibrationally excited
line of H2 at 2.12 $\mu$m, tracing the dissociation front, and the [FeII] line
at 1.64 $\mu$m and the Br$\gamma$ line at 2.16 $\mu$m, tracing the ionization
front. The proximity of the region111The most commonly adopted distance to the
Bar is 414 pc (Menten et al. 2007) although more recent observations,
including Gaia, point to slightly lower values (Kounkel et al. 2017;
Großschedl et al. 2018). (414 pc) combined with recent advances in
instrumentation allows for the first time to conduct studies from the
(sub-)parsec scales to the smallest structures of $\sim$100 AU. Observations
with AO provide nearly diffraction-limited images in the near-IR over a field
of view of $1^{\prime}$ in size.

The paper is organized as follows. The target the Orion Bar is described in
Sect. 2. The observations and data reduction are described in Sect. 3. In
Sect. 4, the spatial morphology of the line intensities is discussed and
compared to previous observations. In Sects. 5 and 6, the observed line
intensities are corrected for dust extinction and compared to the model
predictions. Finally, a short summary and prospects for JWST are given in
Section 7.

##  2 The Orion Bar

The Orion Bar, a strongly ultraviolet (UV) irradiated PDR, is an escarpment of
the Orion molecular cloud (OMC), the closest site of ongoing massive star
formation. The Bar is illuminated by the O7-type star $\theta^{1}$ Ori C, the
most massive and luminous member of the Trapezium cluster at the heart of the
Orion Nebula (e.g., O’Dell 2001). The trapezium cluster creates a blister H ii
region that is eating its way into the parental cloud. A large cavity has been
carved out of the molecular gas and the inner concave structure tilts to form
the Orion Bar (Wen & O’dell 1995; O’Dell 2001). Weilbacher et al. (2015)
presented MUSE/VLT integral spectroscopic data of the central part of the
Orion Nebula with an angular resolution of $\sim$0.7 to 1.2′′. They derived an
extinction map and estimated physical properties (electron temperature and
density) of the Orion Nebula HII region. The Far-UV (FUV) radiation field
incident on the Orion Bar PDR is G${}_{0}=1-4\times 10^{4}$ in Habing units
(e.g., Marconi et al. 1998). Beyond the ionization front (IF), where the gas
converts from fully ionized to fully neutral, only FUV photons with energies
below 13.6 eV penetrate the cloud. This corresponds to the edge of the PDR.
Many previous works have studied the Orion Bar PDR’s spatial stratification.
The first PDR layers are predominantly neutral and atomic: [H] $>$ [H2] $\gg$
[H+]. They display NIR atomic emission lines from low ionization potential
elements (Walmsley et al. 2000) as well as carbon and sulfur radio
recombination lines (Wyrowski et al. 1997; Cuadrado et al. 2019; Goicoechea &
Cuadrado 2021). This warm and moderately dense gas ($n_{\rm H}$ of a few 104
cm-3) is mainly cooled by the very bright FIR [C+] 158 $\mu$m and [O0] 63 and
145 $\mu$m fine-structure lines (Tielens et al. 1993; Herrmann et al. 1997;
Bernard-Salas et al. 2012; Ossenkopf et al. 2013). The atomic PDR zone also
hosts the peak of the Mid-IR aromatic particles emission (e.g., Bregman et al.
1989; Sellgren et al. 1990; Tielens et al. 1993; Giard et al. 1994; Knight et
al. 2021; Schirmer et al. in prep).

At about 10-15′′ (or 0.02-0.03 pc) from the IF (at $A_{V}$ $\simeq$ 0.5-2 mag
of visual extinction into the neutral cloud), the dissociating FUV photons are
sufficiently attenuated and most of the hydrogen becomes molecular222This
range of extinction value is only value for high $G_{0}$/nH PDRs like the
Orion Bar, but not in lower $G_{0}$/nH PDRs where the H/H2 transitions occur
at much lower $A_{v}$ due to the H2 self-shielding. (e.g., van der Werf et al.
2013). This corresponds to the dissociation front (DF) where the H/H2
transition takes place. The DF displays a forest of IR rotational and
vibrationally excited H2 lines (e.g., Parmar et al. 1991; Luhman et al. 1994;
van der Werf et al. 1996; Allers et al. 2005; Shaw et al. 2009; Zhang et al.
2021), including FUV-pumped levels up to $v$ = 12 (Kaplan et al. 2017, 2021)
and HD rotational lines (Wright et al. 1999; Joblin et al. 2018). FUV-pumped
H2 drives the formation of molecular ions such as CH+ and SH+ through
reactions of C+ and S+ with vibrationally excited (e.g., Goicoechea et al.
2017; Parikka et al. 2017; Lehmann et al. 2022, and references therein).
Analysis of the IR H2 and 21 cm H i lines suggests warm temperatures ($T_{\rm
k}$ $\simeq$ 400-700 K) at the DF. Using stationary PDR models (i.e. PDR
models with stationary chemistry and without dynamics), the gas density in the
atomic gas of $n\rm{{}_{H}}=4-5\leavevmode\nobreak\ 10^{4}$ cm-3 is consistent
with the [OI] and [CII] line emission and the separation between the IF and DF
(Tielens et al. 1993; Hogerheijde et al. 1995; Marconi et al. 1998).

The IF and DF separation depends also on the dust extinction. Larger grains
than found in diffuse ISM that have lower FUV absorption cross-sections need
to be invoked in isobaric PDR models in order to be consistent with the
observed IF and DF separation of $\sim$10-15′′ (e.g., Allers et al. 2005).
Reduction in the FUV attenuation cross-section is in agreement with the recent
work of Schirmer et al. (in prep) modeling dust emission and extinction
throughout the Orion Bar PDR. Analyzing the Spitzer and Herschel observations
with the radiative transfer code SOC (Juvela 2019), together with the dust
THEMIS model (Jones et al. 2013, 2017), Schirmer et al. (in prep) found that
nano-grains are in fact strongly depleted compared to diffuse ISM (by a factor
$\geq$10), leading to a FUV attenuation reduction, and a minimum grain size
that is larger than in the diffuse ISM. In their model, the gas density is
estimated to be about 4 104 cm-3 at the mid-IR aromatic nano-dust emission
peak, and about 1.5 105 cm-3 on average between the mid-IR emission peak and
the H2 emission peak. This is consistent with previous estimates.

Beyond the DF, between $A_{V}$ = 2 and 4 mag, the C+/C/CO transition takes
place (Tauber et al. 1995) and the PDR becomes molecular. Some observations
and models suggest the presence of relatively large (0.01-0.02 pc) high
density clumps ($n_{\rm H}$ = 106–107cm-3) in the molecular PDR (e.g., Burton
et al. 1990; van der Werf et al. 1996; Young Owl et al. 2000; Lis & Schilke
2003; Andree-Labsch et al. 2017). These over-dense components must be embedded
in a lower density medium mainly responsible for the extended PDR emission.
Alternatively, the observed H2 and high-J CO lines emission close to the DF
may be explained by a roughly isobaric PDR, at high thermal-pressure $P_{\rm
th}/k$ $\approx$ 108 cm-3 K (e.g., Allers et al. 2005; Joblin et al. 2018). We
note that high density and pressure appear as a common feature in high FUV
field PDRs, as demonstrated by a number of observations (e.g., Ossenkopf et
al. 2010; Sheffer et al. 2011; Köhler et al. 2015; Wu et al. 2018). In the
high pressure isobaric model, a constant pressure from the atomic to the warm
molecular region results in an atomic region and a very narrow emission for
the warm molecular tracers. In the Joblin et al. (2018) model with P=2.8 108
cm-3 K the atomic region had a size of $\sim$3.5′′ while the emission zone of
the H2 (1-0) S(1) line has a width of $\sim$0.25′′. The predicted atomic
region width is nevertheless significantly smaller than the one observed
($\sim$10-15′′) and the very narrow molecular emission is unresolved in most
tracers until now.

While most of the previous molecular studies relied on modest angular
resolution observations, ALMA has provided $\sim$ 1 ′′ resolution images of
the molecular emission (Goicoechea et al. 2016). Instead of an homogeneous PDR
with well-defined and spatially separated H/H2 and C+/C/CO transition zones,
ALMA revealed rich small-scale ($\sim$0.004 pc) over-dense structures (akin to
filaments and globules), sharp edges, and bright emission from an embedded
proplyd (object 203-506; Champion et al. 2017). These observations have
challenged the traditional view of PDRs (and their models, e.g., Kirsanova &
Wiebe 2019) and revealed a steeply varying interface between the atomic and
the molecular gas (Fig. 1c, Goicoechea et al. 2016). The observed over-dense
substructures may have been induced by UV radiation-driven compression (Gorti
& Hollenbach 2002; Tremblin et al. 2012). Advection of the molecular gas
through the DF has been suggested by CO emission observed by ALMA in the form
of globules or plumes apparently extending into the atomic gas (Goicoechea et
al. 2016).

Recent FIR observations of the dust emission polarization from the Orion Bar
PDR suggest a relatively modest plane-of-the-sky magnetic field strength of
$B_{0}$ $\simeq$ 300 $\mu$G (e.g., Chuss et al. 2019; Guerra et al. 2021).
Hence, magnetic pressure of 3 107 K cm-3 (comparable to the ambient and inter-
clump thermal pressure of 1-3 ? 107 K cm-3) may also play a role in the PDR
dynamics (e.g., Pellegrini et al. 2009; Pabst et al. 2020).

Figure 1: Hubble Space Telescope WFPC2 mosaic of the Orion Bar (Credit:
NASA/STScI/Rice Univ./C.O’Dell et al. - Program ID: PRC95-45a). The NIRC2 wide
camera FoV is shown with the cyan square. The yellow square zooms into the two
proplyds lying in the targeted FoV. Figure 2: The PanSTARRS (z band) image
showing the NIRC2 wide camera FoV (cyan square, $40^{\prime\prime}\times
40^{\prime\prime}$) centered on RA=$05:35:20.662$, DEC=$-05:25:19.38$ (J2000).
The green circles enclose tip-tilt stars that can be used to perform the LGS
observations.

##  3 Observations and data reduction

###  3.1 Observations

On December 4, 2020 (Program ID N004), we used the NIRC2 wide field camera in
combination with the Keck-II AO Laser Guide Star (LGS) system to observe a
representative Field-of-View (FoV) of $40^{\prime\prime}\times
40^{\prime\prime}$ of the Orion Bar centered on RA=05:35:20.662,
DEC=-05:25:19.38 (J2000) with a pixel size of $0.04^{\prime\prime}$, as
illustrated in Figs. 1 and 2. This instrumental setup provides the optimal
combination of FoV and diffraction-limited imaging capabilities to fulfill our
science goals. The FoV was rotated by 52.5° (North to East). Observations were
obtained in the narrow-band filters H2 $v=1-0$ ($\lambda_{c}=2.128\,\mu$m,
$\Delta\lambda=0.034\,\mu$m), [FeII] ($\lambda_{c}=1.645\,\mu$m,
$\Delta\lambda=0.026\,\mu$m) and Br $\gamma$ ($\lambda_{c}=2.168\,\mu$m,
$\Delta\lambda=0.0326\,\mu$m). We also obtained observations in the Kcont
($\lambda_{c}=2.271\,\mu$m, $\Delta\,\lambda=0.033\,\mu$m) and Hcont
($\lambda_{c}=1.580\,\mu$m, $\Delta\lambda=0.023\,\mu$m) filters to subtract
the continuum from the H2 $v=1-0$, Br $\gamma$, and [FeII] line maps
respectively.

Fig. 2 shows the different point sources within 60′′ of the center of the
region that can be used as tip-tilt stars for the LGS system. The executed
observation sequence was a 5-point dither pattern using a $\sim
1^{\prime\prime}$ dither step with H2 $v=1-0$ and Kcont consecutive images on
each dither position. The same sequence was executed for the [FeII] and Hcont
filters, and the Br $\gamma$ and Kcont filters. The exposure time per image
was 150s (15s $\times$ 10 coadds) in multiple-correlated double-sampling mode
with 8 reads per coadd.

We integrated 750s on-source for each filter. The observing strategy was
successful although it was a bit challenging due to the variable nebular
background on the tip-tilt star. In fact, the nebular background can
significantly increase the effective magnitude of the tip-tilt star, which in
turn can degrade the AO correction. In an environment with such a complex
background as the Orion Bar, the automatic AO acquisition sequence may need to
be modified to manually take a background for the tip-tilt sensor away from
the nebular region. Such manual background acquisition reduces the efficiency
of the AO observations. We took images in the H2 $v=1-0$ and Kcont filters
with V377 Ori as the tip-tilt star. However, due to the high nebular
background, we used $\theta^{2}$ Ori A as the tip-tilt star for the
[FeII]/Hcont and Br-gamma/Kcont sequences. The factor of $\sim$2 larger
separation between $\theta^{2}$ Ori A and the science FoV with respect to V377
Ori was compensated by the fact that $\theta^{2}$ Ori A is 7.5 magnitudes
brighter on the wave front sensor. Our observations clearly benefited from
good seeing conditions and AO correction (K-band Strehl ratio $\sim$ 30%). The
full width at half maximum (FWHM) of the point-spread function (PSF) was $\sim
0.11^{\prime\prime}$. For comparison, JWST will achieve a resolution of 0.085”
in the K-band. In summary, these unusual bright extended source observations
for NIRC2 were successful.

###  3.2 Data reduction

The basic data reduction of the imaging frames (i.e., dark correction, flat
field, sky substraction) were performed using standard procedures for near-IR
imaging with a modified version of the reduction pipeline from the UCLA
Galactic Center group based on Pyraf (Lu et al. 2009). The set of frames
slightly offset in telescope position were realigned and co-added to produce
the final image. We calculated star centroids and offsets from one frame to
the other using the IRAF task IMALIGN in order to line up the images. Thus,
the images were co-added by weighted median which suppresses the ghosts and
the diffraction spike due to the bright $\theta^{2}$Ori A star. The final
images are of dimension of $38.64^{\prime\prime}\times 38.88^{\prime\prime}$
or 0.08 pc $\times 0.08$ pc at 414 pc.

In order to overcome the telescope pointing error (which is of the order of
$0.5^{\prime\prime}$) and determine the proper World Coordinate System (WCS),
we matched the stars in our NIRC2 image to Gaia coordinates. We used the Gaia
catalog data early release 3 (https://www.cosmos.esa.int/web/gaia).

For the flux calibration, we determined the conversion factor between the
detector counts and physical units using previous observations of the H2 1-0
S(1) line obtained with NTT/SOFI (Walmsley et al. 2000). We convolved the
continuum-subtracted Keck/NIRC2 H2 line emission to the beam of the NTT/SOFI
observation (seeing limited $\sim 1^{\prime\prime}$). We estimated the flux
conversion factor in regions of the maps with high signal to noise ratio.
Thus, the reduced science maps (in Analog Digital Unit per second) were
multiplied by this conversion factor to get the flux-calibrated science maps
in erg cm-2 s-1 sr-1. We assigned an accuracy of about 25% to the measurements
of the line intensity. The same conversion factor was used for the H2 $v=1-0$,
Br $\gamma$ and [FeII] lines maps since they were obtained with almost the
same weather conditions and the detector response is similar. We compared the
fluxes of each of the lines we obtained with those measured by Walmsley et al.
(2000) through the PDR (see their position C, Table 1) and found a good
agreement considering the different spatial resolution. Maps that are not
continuum-subtracted were divided by the filter width and are in units erg
cm-2 s-1 sr-1 $\mu$m-1. We must underline that we could have fluxed-calibrated
the observations using the photometric standard FS-7 observed in the H and Ks
filters. However, we would obtained similar uncertainties due to the sky
background variations between the standard star observations and the science
observations, which was significant in the K band.

##  4 Spatial distribution

In this section, the spatial morphology of the hydrogen Brackett $\gamma$,
iron and molecular hydrogen lines are presented and compared to previous
observations.

Figure 3: Integrated intensity maps of the [FeII] and continuum-subtracted
[FeII] line emission (left column) and of the Br$\gamma$ and continuum-
subtracted Br$\gamma$ line emission (right column). Units are erg cm-2 s-1
sr-1 $\mu{\rm m}^{-1}$ for the [FeII] and Br$\gamma$ maps and erg cm-2 s-1
sr-1 for the continuum-subtracted line emission map. The horizontal dashed
lines indicate the average position of the ionization and dissociation fronts
(as determined from the averaged emission cut over the entire FoV presented in
Fig. 5).

Figure 4: Same as for Fig. 3 for the H2 1-0 S(1) line emission.

Figure 5: Top row: Superposition of the four cuts perpendicular to the Orion
Bar described in Sect. 4.1 on the [FeII] 1.64$\mu$m and H2 2.12$\mu$m
continuum subtracted emission line maps. Cuts 1, 2, 3, 4 are positioned from
left to right. The squares area are used to compute the lines intensity in the
key regions presented in Table 1. Second and third rows: H2 (blue), Br$\gamma$
(red) and [FeII] (green) line intensity (in erg s-1 cm-2 sr-1) profiles shown
as function of the distance from the IF for each cut along with the HCO+ line
integrated intensity profile (in K km s-1, grey). The intensity profiles of
the Br$\gamma$ and [FeII] lines have been scaled by the factors indicated in
the legends. The line intensities have not been corrected for dust extinction.
Bottom row: The averaged emission cut calculated by taking the mean over the
entire FoV and perpendicular to the Orion Bar. The vertical dashed lines
indicate the average position of the IF, DF and HCO+ peak.

###  4.1 Br$\gamma$ and iron lines

The maps obtained in the Br$\gamma$ and [FeII] filters and the continuum-
subtracted emission are shown in Fig. 3, while the H2 filter maps are shown in
Fig. 4. Most of the structures seen in these lines and the continuum are very
similar to those visible in the H$\alpha$ HST map (Fig. 1). The ionization
front is clearly seen in the Br$\gamma$ and [FeII] line emission maps.
However, there are some differences between the Br$\gamma$ and [FeII] line
emission morphologies. In particular, in the area surrounding the two
identified proplyds near the Bar, 203-506 and 203-504 (Bally et al. 2000 and
located in the yellow squares in Fig. 1): both proplyds emit in [FeII] along
with bright streamers, whereas only the proplyd 203-504 shows strong
Br$\gamma$ emission as further described in Section 4.5.

The surface brightness profiles measured in the [FeII], Br$\gamma$ and H2
lines along 4 cuts perpendicular to the Bar are shown in Fig. 5. These cuts
use a 3-pixel average corresponding to the typical FWHM of the PSF. Cut 1 goes
through the left edge of bar, cut 2 through the position of the JWST/NIRSpec-
IFU and MIRI-IFU mosaics of the ERS program (see Fig. 3 in Berné et al. 2022),
cuts 3 and 4 through the right edge of the bar (see Fig. 5). To investigate
the stratification of the interfaces from ionized to molecular emission, we
also constructed averaged emission cut over the entire FoV and perpendicular
to the Orion Bar. As expected for a PDR seen edge-on, we found that the H2
emission is displaced further into the cloud than the Br$\gamma$ and [FeII]
line emission. A precise determination of the distance between the IF
delineated by the [FeII] and Br$\gamma$ lines and the DF delineated by the H2
line can be obtained. From the averaged emission cuts, we estimated that the
offset between the IF and the main peak of the H2 vibrational emission is
between 12 and 12.5′′ (0.024-0.025 pc). Finally, the [FeII] and Br$\gamma$
surface brightness profiles also show extended emission towards the PDR. This
emission may originate in the flattened region beyond the bar that is still
illuminated directly by the ionizing star (Wen & O’dell 1995; O’Dell 2001).

###  4.2 Vibrationally excited H2 line

The maps obtained in the H2 2.12$\mu$m filter and the continuum-subtracted H2
line emission are shown in Fig. 4 and also in Fig. 6 for comparison with the
ALMA HCO+ $J=4-3$ line emission map (see Section 4.4). In the H2 line emission
map, several bright H2 emission peaks are spatially resolved and show small
scale structures. The H/H2 dissociation front appears highly structured with
several ridges and extremely sharp filaments with a width of $1$ to
$2^{\prime\prime}$ (0.002-0.004 pc or 400-800 AU, see Figs. 4 and 5). Ridges
and filaments run parallel to the dissociation front but a succession of
bright sub-structures in H2 is also observed from the edge of the DF towards
the molecular region. The H2 emission peaks appear in an area that starts at
about $10^{\prime\prime}$ from the IF and up to $20$” and even 25-30′′ in some
places from the IF (see Figs. 4 and 5). The bright sub-structures result in
several peaks in the H2 brightness profiles shown in Fig. 5 obtained along the
cuts perpendicular to the Orion Bar. The peaks are roughly spaced by a few
arcseconds ($\sim$ 0.005-0.01 pc or $\sim$1000-2000 AU). The surface area
occupied by the bright sub-structures (ridges, filaments), i.e. with H2 line
intensity $>2\times 10^{-4}$ erg s-1 cm-2 sr-1, corresponds to about 40-45% of
the H2 emission zone in the Bar.

Since the H2 emission is very sensitive to both the FUV radiation field and
the gas density (as explained below), these very narrow and bright sub-
structures must be due to dense material directly irradiated. Towards more
tenuous material, the H2 emission is spatially much more extended and weaker.
The multiple H2 emission peaks along and across the Bar may be associated with
a multitude of small highly irradiated and dense PDRs. A single edge-on dense
PDR produces one narrow H2 emission peak. The slight tilt of the Bar along the
line of sight combined with the presence of over-dense structures may explain
the observed complex emission distribution, and especially the succession of
H2 peaks across the Bar.

The intensity variations in the different H2 emission peaks ranging from
$\sim$2 to $\sim$10 10-4 erg s-1 cm-2 sr-1 (Fig. 5) may result from a
combination of effects due to the local gas densities, geometry and dust
extinction effects. Density effects must important. In fact, PDR models show
that for the conditions prevailing in the Orion Bar, the intensity of the H2
v=1-0 S(1) line is approximately proportional to the gas density (e.g., Burton
et al. 1990). At equilibrium between the formation of H2 and the
photodissociation of H2 by FUV flux, the intensity of the 1-0 S(1) line is
proportional to $R_{f}n_{H}N(H_{0})$ where $R_{f}$ is the H2 formation rate,
$n_{H}$ is the total hydrogen gas density and $N(H_{0})$ the column density of
atomic H atoms from the PDR edge. For low value of $n_{H}/G_{0}$ ($<40$ cm-3),
which is the case in the atomic zone of the Orion Bar with $G_{0}\sim 10^{4}$
and $n_{H}$=104-105 cm-3, the H0/H2 is driven by dust opacity and N(H0) is a
constant equal to a few 1021 cm-2. The intensity is thus linearly proportional
to the density. Moreover, the H2 and HCO+ J=4-3 emission show a remarkable
similar spatial distribution as shown in Fig. 6 and further described in Sect.
4.4. This rotational line is a good indicator of dense gas (Goicoechea et al.
2016).

The dense sub-structures seen in H2 may be surrounded by a lower-density gas
component producing an extended emission. In the H2 data, a more widespread
and extended emission (with an intensity of about 2 10-4 erg s-1 cm-2 sr-1)
seems to be in fact observed at the photodissociation front at about 10-15′′
(0.02-0.03 pc) and up to 20-30′′ (0.04-0.06 pc) from the IF. Moreover, the H2
map and brightness profiles show some emission in front of the DF (see Fig. 5
and Table 1). Part of this emission likely originates from the surface of the
Orion molecular cloud-1 (OMC1). This surface is perpendicular to the line of
sight and is illuminated by the Trapezium cluster, making it a face-on PDR.
The emission from this background face-on PDR was also observed with Herschel
in other PDR tracers, especially in high-J CO lines (Parikka et al. 2018) and
[OI] 63 and 145 $\mu$m and [CII] 158 $\mu$m (Bernard-Salas et al. 2012). An
increase in the H2 emission at the ionisation front is also observed. This was
also visible in the previous data of Walmsley et al. (2000) and could
originate from the background molecular cloud.

###  4.3 Comparison with previous H2 observations

Our Keck observations convolved at the angular resolution of $\sim$1” of the
previous SOFI/NTT observations by Walmsley et al. (2000) show good agreement
in terms of line distribution and intensity (see Table 1). It can be noted
that in the SOFI/NTT observations, the brightest sub-structures were already
observed but not spatially resolved. The TEXES observations of the pure
rotational H2 0-0 S(1) and S(2) lines by Allers et al. (2005), with a
resolution of $\sim$2” cover the south-west part of our map. The comparison of
these observations with the H2 1-0 S(1) line map obtained previously by van
der Werf et al. (1996) show that the spatial distribution of the pure
rotational lines and the vibrationally excited line agree in remarkable detail
(see Fig. 2 in Allers et al. 2005). This is predicted by high pressure models
(Allers et al. 2005; Joblin et al. 2018), where a separation between the H2
lines is expected to be very small ($\lesssim$0.5′′). Thus, one would expect
to observe an overall spatial coincidence on the whole Keck map. Nevertheless,
detailed variations are expected because the pure rotational lines that result
from collisional excitation have a different dependence on the local physical
conditions. Future JWST-ERS observations (Berné et al. 2022) will allow such
an investigation in the parts of our maps observed with the IFU-MIRI
spectroscopy.

###  4.4 Comparison between H2 and HCO+ from ALMA

In this section, the distribution and correlation of the H2 line emission with
the ALMA observation of the HCO+ J=4-3 line are analysed. Considering the
position of the compact sources (e.g. proplyds 203-506), the ALMA observations
showed an offset to our Keck observations in coordinates of R.A.=-0.15” and
DEC.=0.75”. By correcting this offset, a good overlap of the position of the
compact sources and of the Bar is obtained.

In Fig. 6, we compare the maps obtained in the H2 1-0 S(1) and HCO+ J=4-3
lines across the same field of view. The middle and bottom figures zoom into
two parts of the map to be able to compare in detail the spatial distribution
of the emission from each of the detected sub-structures. Most of the sub-
structures are common to both maps and show a very similar distribution. Due
to a high-dipole moment and a high critical density, the HCO+ 4-3 line
(ncritical of a few 106 cm-3) is a good proxy of the gas density (Goicoechea
et al. 2016). Its integrated intensity is roughly proportional to the density
in the $n_{H}=10^{4}-10^{6}$ cm-3 range. The average density that reproduces
the mean HCO+ towards the dissociation front (at about 15′′ from the IF) is
about $n_{H}=0.5-1.5\leavevmode\nobreak\ 10^{6}$ cm-3. Thus, some of the
densest portions of the Bar lie along the dissociation front. We note that the
small H2 and HCO+ structures discussed here localized at the DF are shifted by
a about $\sim$20” relative to the bigger (5”-10”) condensations seen more
inside the molecular cloud (Young Owl et al. 2000; Lis & Schilke 2003).

Although there is a very good spatial coincidence between the H2 and HCO+ sub-
structures, the H2 line emission decreases faster in the Bar than the HCO+
line emission (see Fig. 5). This can be explained as follows. Firstly, the
vibrationally excited H2 line is more sensitive to the FUV field flux and the
most intense H2 emission must come from the transition region between the
diffuse and very dense medium where the FUV radiation is not yet attenuated.
The FUV shielding produced by the ridge of high-density sub-structures may
significantly decrease the vibrational excited H2 in the deeper regions.
Secondly, extinction due to dust in the Orion Bar and to foreground dust may
affect the apparent morphology of the near-IR H2 images. Small-scale dust
extinction differences could in fact result in morphological differences
between the near-IR and millimeter-wave images. Dust extinction effects on the
line intensities is discussed in Sect. 5.

The overall remarkable spatial coincidence between the H2 and HCO+ line
emission shows that they both come from high-densities but also indicates
their strong chemical link. Detection of both bright HCO+ and CO emission by
ALMA towards the H2 vibrational emission layers (Fig. 2c in Goicoechea et al.
2016) suggests that the C+/CO transition nearly coincides with the H/H2
transition. This fact was predicted in Joblin et al. (2018), where the best
fitting Orion Bar model has a separation between these transitions of
$\sim$0.25′′. We obtained a precise determination of the average offset
between the peak of the H2 vibrational emission (delineating the H/H2
transition) and the edge of the observed HCO+ emission (delineating the
C+/C/CO transition). From the averaged emission cuts, we estimated that this
average offset is less than $1"$, about $\sim$0.6” (or 0.0012 pc). However
considering that the angular resolution of the ALMA data is $\sim$1′′, higher
angular resolution observations are required to measure the exact value of
this offset. The presence of a large quantity of irradiated H2 may have
important consequences for the chemical structure. Due to the high densities
and enhanced H2 gas heating via formation and collisional de-excitation of FUV
pumped levels, the chemistry is triggered by high temperature and FUV pumped
levels. Endothermic reactions and reactions with energy barriers become faster
(Agúndez et al. 2010; Nagy et al. 2013). Reactions of H2 with abundant atoms
and ions, e.g. C+, shift the carbon bearing molecular gas towards the cloud
edge.

We note that although a spatial coincidence is observed between the H2 and
HCO+ over-dense sub-structures, a spatial shift of the emission peak is
measured for several sub-structures (e.g., sub-structure 3 in the middle
panels and sub-structures 2, 3 in the bottom panels of Fig. 6). This may
essentially result from the fact that the two emission lines vary differently
with the local conditions (FUV field flux and gas density) and that the H2
near-IR line is affected by dust extinction. The most important differences in
the spatial distribution of the H2 and HCO+ emission are found in the atomic
region. In fact, the brighter structures seen in the atomic regions in HCO+
(like globulettes) are faintly visible in H2 ro-vibrational emission (e.g.,
the sub-structures denoted 1 and 6 in the middle panels and the sub-structure
denoted 1 in the bottom panels of Fig. 6). These structures are probably
located in the background or foreground. Indeed, the emission velocity of
these HCO+ structures ($v_{LSR}$= 8-9 km s-1) is more consistent with emission
from the background OMC1 than from the Bar ($v_{LSR}$= 10.5 km s-1). Some
extended H2 line emission seen in the atomic zone to the south-west part of
the Bar (see bottom panel of Fig. 6) has also no counterpart in the HCO+ or CO
line emission maps. Finally, plume-like CO features seen with ALMA in the
atomic zone by Goicoechea et al. (2016) which may be advected from the surface
of the molecular cloud have no evident correspondences with the H2 emission
structures observed by Keck/NIRC2.

Figure 6: Left panels: Integrated intensity maps (continuum-subtracted) of the
H2 1-0 S(1) line emission in erg cm-2 s-1 sr-1. Right panels: Integrated
intensity maps of the HCO+ J=4-3 lines in K km s-1.

###  4.5 Proplyds and collapsing protostars

We are able to spatially resolve the FUV irradiated Orion Bar PDR edge but
also additional compact sources corresponding to over-dense irradiated sub-
structures such as proplyds near the IF, and perhaps collapsing protostars
near the DF. In the following, we briefly describe the observations towards
these sources.

####  4.5.1 Proplyds

Fig. 7 shows proplyds 203-504 and 203-506 (Bally et al. 2000) which are
present in the FoV of our Keck/NIRC2 observations. The star of 203-504 is
detected in all filters, however the disk/envelope is not clearly identifiable
in these images. The 203-506 proplyd is clearly visible in emission in both
the H2 and [FeII] lines, whereas it is not detected in the Br$\gamma$ line.

The H2 emission appears to have a similar morphology to the [OI] 6300 Å line
observed by Bally et al. (2000). This is expected since both lines trace warm
neutral gas ($\sim 1000$ K) near the dissociation front, inside the dense PDR
that is created at the disk surface (Champion et al. 2017). The [FeII] line
shows a very different morphology, with an elongated structure perpendicular
to the proplyd disk, and is reminiscent of a jet, such as those identified for
proplyds by Bally et al. (2015). The [FeII] emission would then be associated
with irradiated shocked gas. The absence of Br$\gamma$ emission could have
different explanations. The coming PDR4alls JWST data should bring additional
clues to better understand it.

####  4.5.2 Over-dense sub-structures

Numerous over-dense small structures (1-2”) appear in the H2 and HCO+ emission
that could be self-gravitating, or transient, turbulently compressed features
or compressed by FUV photoevaporation (Gorti & Hollenbach 2002; Tremblin et
al. 2012). Recently, Röllig & Ossenkopf-Okada (2022) showed that the intensity
levels of the HCO+ emission?map as well as its spatial distribution is
consistent with predictions from nonstationary, clumpy PDR model ensembles.
Whether they can become star-forming clumps (for example, by merging into
massive clumps) is uncertain. Gravitational collapse appears not apparent from
their density distribution (no high-density power-law tail, Goicoechea et al.
2016). In fact, the mass of a cylinder with a density $n_{H}\sim 10^{6}$ cm-3,
a width of 1” and a length of 2”-6” is $<0.005$ M⊙ (Goicoechea et al. 2016),
which is much lower than the virial and critical masses needed to make them
gravitationally unstable (approximately 5$M_{\odot}$ from the inferred gas
temperature, density, and velocity dispersion, Inutsuka & Miyama 1997).
However, the very bright substructure located in the northeast of our map and
denoted clump in Fig. 6 shows a very particular structure (with a size of
$\sim$1000 AU), likely a YSO candidate (Goicoechea et al. in prep).

Figure 7: Zoom on proplyds in the H2 2.12$\mu$m, [FeII] 1.64$\mu$m and
Br$\gamma$ 2.16$\mu$m lines (continuum substracted), as well as, in the Hcont
and Kcont filters with in addition the H$\alpha$ emission using the HST
observations from https://archive.stsci.edu/prepds/orion/acs_displaypage.html
which was adjusted in positions.

##  5 Line intensities and extinction correction

###  5.1 Line intensities in the key zones

In Table 1, we give the intensities of the [FeII], Br$\gamma$, and H2 lines
measured towards the ionised region, IF, PDR atomic region, DF, and from the
molecular region. The line intensities of each of these characteristic regions
have been estimated in the 2” by 2” square areas shown in Fig. 5 (top panels).
The areas for the atomic, DF, and molecular zones which are located at about
$5.5^{\prime\prime}$, $12.5^{\prime\prime}$, $21^{\prime\prime}$ from the IF,
are positioned within the FoV of the NIRSpec-IFU and MIRI-IFU mosaics (see
Fig. 3 of Berné et al. 2022) which are along the direction of cut 2 in Fig. 5.
On the other hand, the areas chosen for the ionized and IF regions are not
aligned along the JWST mosaics (i.e. cut 2) because the Keck maps do not
entirely cover these ionized gas and IF regions along the JWST mosaic (i.e.
cut 2). We therefore chose areas for the ionized gas and IF regions further
south-west (towards the direction of cuts 3 and 4, see Fig. 5).

Comparison with previous measurements of the intensities of these lines with
SOFI/NTT by Walmsley et al. (2000) in the ionized, IF, and DF regions are
given in Table 1. The measurements are in good agreement within a factor of
about 2 for the [FeII] and Br$\gamma$ lines at the IF and the H2 line at the
DF. However, we find some larger differences for Br$\gamma$ in the HII and DF
regions and H2 in the HII and IF regions. This might be mostly due to the fact
that the position regions of Walmsley et al. (2000) (shown as A, B, C in their
Fig. 1) do not correspond to our positions. Their HII and IF regions are
outside of the Keck/NIRC2 field-of-view.

###  5.2 Extinction correction

Corrections for extinction due to the foreground dust and internal dust in the
Bar itself of the line intensities were estimated and reported in Table 1. The
foreground visual extinction $A_{V}$ produced by the Veil was estimated to be
not greater than about 2 mag by O’Dell & Yusef-Zadeh (2000) using a radio-to-
optical surface brightness comparison. Using flux measurements of the Balmer
lines (H$\alpha$ to H$\beta$ flux ratio), Weilbacher et al. (2015) estimated
that the foreground extinction is about $A_{V}\sim$ 1.3 mag (or $A_{K}\sim$
0.15 mag) towards the ionized gas in the line of sight of the Orion Bar (see
their Fig. 15). The foreground dust structure appears smooth and devoid of
significant substructure. By this dust screen, the line emission will be
attenuated by $e^{-\tau_{\lambda}}$ with
$\tau_{\lambda}=0.921\leavevmode\nobreak\ A_{\lambda}$ the optical depth at
the wavelength of the line. To adopt a dust reddening appropriate to Orion, we
follow Goicoechea et al. (2015) and used the extinction curve of Cardelli et
al. (1989) as refined by Blagrave et al. (2007) with $R_{V}=A_{V}/E(B-V)=$5.5.
The reddening factors are 0.216, 0.143 and 0.138 at 1.64, 2.12 and 2.16 $\mu$m
respectively. Given this degree of foreground extinction, we estimated that
the [FeII], Br $\gamma$, and H2 lines are approximately 23%, 15%, and 16%
brighter respectively if foreground extinction correction is taken into
account.

For the H2 line in the PDR, internal extinction due to the dust in the Bar
itself may significantly attenuate the emission. An additional magnitude of
extinction due to dust in the Bar between the ionized gas and the region of
excited H2 may result in a stronger increase in line intensity. In order to
estimate this extinction, we assumed that the column density of gas along the
line of sight is equal to the column density between the IF and the region of
excited H2. Thus, we used the density profile towards the Bar as constrained
from comparison between Spitzer and Herschel observations and a radiative
transfer code with the THEMIS dust model (Schirmer et al. in prep). The
corresponding calculated column density is 1.5 1021 H cm-2 from the IF to the
beginning of the H2 emission (at 10” or 0.02 pc from the IF) and 10 1021 H
cm-2 from the IF to the end of the H2 emission (at 20” or 0.04 pc from the
IF). Adopting the same dust reddening as described before from Cardelli et al.
(1989) and $A_{V}/N_{H}=3.5\times 10^{-22}$ mag cm-2, we estimated an
extinction of $A_{V}=1$ to 4 or $A_{K}=0.13$ to 0.54. If this internal dust
extinction correction is taken into account and a correction factor of
$e^{-\tau_{\lambda}}$ is applied, the H2 line is approximately 12 to 40%
brighter. Regarding the assumed extinction law, the Cardelli extinction curve
with $R_{V}=$5.5 is similar to that calculated by the THEMIS dust model in the
Orion bar with nano-grains depletion (Schirmer et al. in prep). For this
model, the reddening factors are 0.224, 0.139 and 0.134 at 1.64, 2.12 and 2.16
$\mu$m respectively. The correction factor on the line intensities assuming
their extinction law will differ by less than 3%.

We must underline that if we assume that the gas and the dust are well mixed
in the H2 emission zone, one must apply a correction factor of
(1-$e^{-\tau_{\lambda}})/\tau_{\lambda}$ (e.g. Thronson et al. 1990). Assuming
a visual extinction of $A_{V}=3$ for the total H2 emission zone (including the
succession of H2 peaks) as calculated using the dust density model, we
computed the corresponding correction factor. This visual extinction is
equivalent to consider a gas density of 1-1.5 105 cm-3 and a length of 0.02 pc
(as the width of the H2 emission zone in Fig. 5). This visual extinction
corresponding to a large column density of UV pumped H2 can be considered as
an upper limit . With these assumptions, the line is approximately 18%
brighter after extinction correction in the H2 emission zone. Considering the
increase of 12% due to the extinction correction of the atomic zone from the
IF to the beginning of the H2 emission zone, the line will thus be 30%
brighter. This is relatively close to what we found previously assuming no
mixing which is of 40% (due to the internal extinction correction from the IF
to the end of the H2 emission zone).

In Table 1 and for the comparison to the model predictions in the following
section, we assumed that the H2 line will be in total 56% brighter after
correcting for foreground (16%) and internal extinction (40%) in the Bar. Our
total (foreground and internal) extinction corrections for H2 are thus about
$A_{K}=0.17+0.54=0.71$ which is very close to the one derived by Kaplan et al.
(2021) of $A_{K}=0.72\pm 0.1$. These authors used an effective way to measure
extinction which consists of comparing the observed to theoretical H2 ro-
vibrational line flux ratios from pairs of lines arising from the same upper
level that are widely separated in wavelength. Their errors on $A_{K}$ were
estimated from the assumptions made on the color correction. Their IGRINS
observation at high spectral resolution were made along a slit positioned
across the Bar and centered on at the southwest of the Bar (corresponding to
the position of the sub-structure 5 in the bottom zoom of Fig. 6). However, we
must underline that their extinction measurement is lower than the values
derived by Luhman et al. (1998) also using H2 ro-vibrational transitions with
common upper levels but observed a long a slit passing roughly through the
center of our Keck maps. Luhman et al. (1998) found averaged values of
$A_{K}$=2.6$\pm$0.7 and 2.3$\pm$0.8 respectively for the H2 peak and beyond.
The H2 line will be approximately 90% brighter if an extinction correction of
$A_{K}=2.6$ (or $A_{V}=19$) is taken into account. The internal extinction
might be variable depending on the sightline and the density of the region
crossed. From the radio and NIR H2 line maps, Walmsley et al. (2000) suggest
in fact that extinction can vary rapidly as a function of position in the Bar.
Specifically, precise spatial estimates of the internal PDR extinction are
needed. This will be possible with the high angular resolution near-IR line
maps that will be obtained with JWST’s NIRCAM and NIRSpec IFUs. This will
constrain in detail how dust extinction affects the apparent morphology of the
H2 line emission.

In summary, we estimated that the [FeII], Br $\gamma$, and H2 lines will be
$\sim$23%, 15%, and 16% brighter if foreground extinction correction is taken
into account. For the H2 line in the PDR, internal extinction due to the Bar
itself may also significantly attenuate the emission and the line could be
about $\sim$56% brighter in total. However, the extinction might vary in the
Bar due to due to density variations along the line of sight.

Table 1: Observed and predicted line intensities in erg cm-2 s-1 sr-1 in the ionized, IF, atomic, DF, and molecular regions. For Keck observations, the median and standard deviation of the intensities observed in the 2′′ by 2′′ square areas shown in Fig. 5 are given. The intensity peak of the lines is also given. The observed Keck intensities have been corrected for dust extinction and the correction factor applied is given in % (in the row ”Corr. Extinction”). Measurements of the intensities of these lines with SOFI/NTT by Walmsley et al. (2000) in the ionized, IF, and DF regions (corresponding to their A, B, and C regions in their Table 1) are also reported. Line |  $\lambda$ ($\mu$m) |  $A$ (s-1) |  $E_{u}$ (K) |  |  | Intensities |  |
---|---|---|---|---|---|---|---|---
|  |  |  | ionized | IF | atomic | DF | molecular
[FeII] | 1.64440 | 0.006 | 11445.9 |  |  |  |  |
|  |  | Obs. Keck | 3.6$\pm$0.7 10-4 | 7.0$\pm$1.6 10-4 | 1.7$\pm$0.6 10-4 | 1.1$\pm$0.6 10-4 | 0.7$\pm$0.6 10-4
|  |  | Max. Intensity | 6 10-4 | 1.2 10-3 |  |  |
|  |  | Corr. Extinction | +23% | +23% | +23% | +23% | +23%
|  |  | Obs. NTT | 4.7 10-4 | 6.0 10-4 |  | 1.2 10-4 |
|  |  | Cloudy model | 1.9 10-7 | 6 10-4 | - | - | -
H2 | 2.12183 | 3.47 10-7 | 6951.3 |  |  |  |  |
|  |  | Obs. Keck | 1.8$\pm$0.6 10-4 | 2.2$\pm$0.7 10-4 | 0.46$\pm$0.46 10-4 | 4.7$\pm$2.3 10-4 | 1$\pm$0.8 10-4
|  |  | Max. Intensity |  |  |  | 13.6 10-4 |
|  |  | Corr. Extinction | \+ 16% | +16% | +16% | +56% | +56%
|  |  | Obs. NTT | 0.3 10-4 | 0.7 10-4 |  | 3.0 10-4 |
|  |  | Meudon model | - | - | 0.1 10-4 | 22 10-4 | 3.7 10-9
Br $\gamma$ | 2.16612 | 3.045 105 | 154582.7 |  |  |  |  |
|  |  | Obs. Keck | 15.4$\pm$0.1 10-4 | 26.3$\pm$0.3 10-4 | 9.2$\pm$0.8 10-4 | 4.8$\pm$0.8 10-4 | 2.6$\pm$0.8 10-4
|  |  | Max. Intensity | 20.9 10-4 | 32.4 10-4 |  |  |
|  |  | Corr. Extinction | +15% | +15% | +15% | +15% | +15%
|  |  | Obs. NTT | 36.6 10-4 | 39.4 10-4 |  | 11.7 10-4 |
|  |  | Cloudy model | 4.7 10-4 | 36 10-4 | - | - | -

##  6 Comparison to model predictions

To guide our interpretation, in this section, we compare our extinction-
corrected observations of the emission gas lines to the model predictions in
the HII region, the IF, the atomic region, the DF, and the molecular zone. The
model predictions are those we used to make the template spectra described in
Berné et al. (2022) and to predict line intensities for the JWST Exposure Time
Calculator. The gas line intensities have been computed using (i) the Cloudy
code for the ionized gas in the H ii region and the ionization front (Ferland
et al. 2017); and (ii) the Meudon PDR code for the contribution from the
atomic and molecular lines in the neutral PDR gas (Le Petit et al. 2006). The
parameters and calculation requirements used for each model and region are
described in detail in Berné et al. (2022). In the following subsections, only
some computational results important for the comparison
predictions/observations are given.

In this comparison with model predictions, our primary goal was to ensure that
the models reproduce the observed intensity peak of the ionised and neutral
gas lines emission by Keck. This allowed us to adjust the required JWST
integration time in order to get a high signal-to-noise ratio and avoid
saturation problems, a challenging aspect for JWST observation of bright
targets. We emphasize that our model predictions were obtained by making
simple assumptions and by separately estimating the ionized and neutral
molecular gas lines. The radiative transfer and the thermal balance were not
calculated continuously from the HII region to the molecular region. We have
not attempted to reproduce the separation between the IF and the DF.

###  6.1 Predicted Br$\gamma$ and [FeII] lines emission

The input parameters of Pellegrini et al. (2009) and Shaw et al. (2009) were
adopted for the Cloudy model of the Orion Bar. This is an isobaric model with
initial electron density of $n_{e}\sim\leavevmode\nobreak\ 3500$ cm-3 and
temperature of $T_{e}\sim 9000$ K. The electron density reaches a maximum of
$n_{e}\sim$6600 cm-3 before the IF and drops sharply at the IF. At the IF, the
total proton density increases to $n$ =28,000 cm-3 while the electronic
temperature decreases to $T_{e}\sim$4000 K. The Br$\gamma$ 2.16 $\mu$m line
emissivity is spatially extended in the HII region, following the electronic
density profile, and then decreases strongly when H+ becomes H0 at the IF. On
the other hand, the [FeII] 1.64$\mu$m line emissivity peaks strongly at the
IF.

In Table 1, we report the predicted intensities of the lines. The [FeII] 1.64
$\mu$m and Br$\gamma$ 2.16 $\mu$m lines model predictions are in good
agreement with the observations at the IF front (by a factor less than 1.4).
On the other hand, the emission of these lines in the HII region are
significantly lower in the model predictions. This difference applies for
several other ionized gas lines predicted by Cloudy. The observations may
overlap the IF where the observed intensities are bright.

###  6.2 Predicted H2 line emission

For the Meudon code, we considered an isobaric model with a thermal pressure
$P=4\cdot 10^{8}$ K cm-3. This model exhibits gas physical conditions expected
near the dissociation front of the Orion Bar (e.g., Goicoechea et al. 2016;
Joblin et al. 2018). We fixed the radiation field impinging on the PDR so
that, at the edge of the PDR, $G_{0}\,=\,2\cdot 10^{4}$ in Mathis units. We
adopted the extinction curve of HD 38087 of Fitzpatrick1990 and
$R_{V}\,=\,5.62$ which is close to the value determined for Orion Bar of 5.5
(Marconi et al. 1998). The model includes an exact radiative transfer
calculation for the UV pumping lines originating from the first 30 levels of
H2, while the other lines are treated using the FGK approximation. This allows
to account for mutual shielding effects between overlapping H2 lines and can
significantly affect the position of the H/H2 transition. The H2 1-0 S(1) line
emissivity peaks near the H/H2 transition layer where the gas density is of
the order of few 105 cm-3. As in Joblin et al. (2018), the model does not
reproduce the observed width of the atomic region, i.e. the distance between
the position of the IF and the DF. It is significantly smaller than in the
observation. We note that as suggested by Allers et al. (2005), a PDR model
with a lower gas pressure in the atomic zone (i.e., a lower gas density) and a
reduction of the FUV dust cross section will better match the observed spatial
position of the H2 emission peak. In the Schirmer et al. (in prep) dust model
with nano-grain depletion (i.e., FUV extinction reduction), the visual
extinction integrated from the PDR edge to the observed H2 emission peak
position at 12-12.5′′ (or 0.024-0.025 pc) is of $A_{V}\sim 1$. The required
model medium density in the atomic zone is of 5 104 cm-3, close to the inter-
clump density.

We calculated the cumulative line intensities from the atomic and H0/H2
transition region (0$<A_{V}<$0.4 and 0.4$<A_{V}<$2.5) and from the molecular
region (which starts at the C/CO transition, $2.5<A_{V}<8.5$). The optically
thin line surface brightness are enhanced by a geometrical factor of
1/cos($\theta$)=2 relative to the face-on surface brightness. The viewing
angle $\theta$ between the line-of-sight and the normal to the PDR is taken
equal to $\sim$60∘ which gives an approximation of a nearly edge-on PDR and is
the maximum inclination that can be used to derive line intensities in the 1D
PDR Meudon code. The uncertainty on this angle could lead to an additional
scaling factor on the line intensity.

The H2 2.12 $\mu$m line intensity as predicted by the model in the DF is in
agreement with the measured peak intensity at the DF by a factor of 1.6 (too
high for the model). This could partly be due to a geometrical factor but also
to the fact that the isobaric model considered here with a high pressure of
$P=4\leavevmode\nobreak\ 10^{8}$ K cm-3 gives a too high density and over-
estimates the H2 1-0 S(1) line (see section 6.3). The H2 1-0 S(1) line
emissivity width predicted by the model is of $\sim$0.0006 pc or $\sim$0.3”.
This is lower that the observed thickness of the sharpest H2 filaments (see
Fig. 5). The observed width of the bright H2 ridge (about 1′′ to 2′′) may be
increased by geometrical effects or a lower thermal pressure.

In the atomic zone, the model predicts a much lower intensity by a factor of
$\sim$10 with respect to the DF because the H2 density is much lower. This is
in agreement with the data but the large uncertainties on the measured
intensity make a quantitative comparison difficult. In the molecular zone, the
predicted intensities are extremely low by a factor $>10^{4}$ with respect to
the DF. The measured intensity decreases much less. It is comparable to the
intensity measured in the HII region divided by a factor of 2. The observed H2
emission in the molecular zone must come from the flattened region behind the
main ionization front on the far side of the Orion Bar.

###  6.3 Thermal pressure and dynamic effects

Considering the TEXES H2 0-0 S(1) line observation with an angular resolution
of 2′′ (Allers et al. 2005) and the 1-0 S(1) line Keck observation convolved
at the same resolution and corrected for extinction, the 1-0 S(1) / 0-0 S(1)
line ratio is estimated to be about $\sim$1$\pm 0.4$ at the DF (position A in
Allers et al. 2005). The ratio predicted by the model is about 2.5 times
higher. A pressure of $4\leavevmode\nobreak\ 10^{8}$ K cm-3 is probably too
high to reproduce this ratio and more detailed modeling would be needed. The
previous H2 study by Allers et al. (2005) show in fact that an isobaric model
with $P=8\leavevmode\nobreak\ 10^{7}$ K cm-3 (with a pressure 5 times lower
that the one we assumed) matches the observed intensities of the ground-state
rotational lines, the H2 1-0 S(1) and 2-1 S(1) lines.

To determine the pressure and density variations at the PDR edge, future
detailed spatial studies of both the H2 pure rotational and rovibrational
lines are required. Excitation diagram from the numerous H2 lines observable
by JWST MIRI and NIRSpec will permit to trace the warm and hot (UV-pumped)
excitation temperatures, local gas density and pressure gradients at small
spatial scales. It will be possible to probe the physical conditions in most
of the dense sub-structures detected with Keck or ALMA as well as the very
thin surface layers that are sufficiently heated to photo-evaporate from the
PDR. On the other hand, one could marginally spatially resolve the temperature
gradient inside the over-dense substructures themselves. For a high pressure
PDR, the H2 emission thickness is predicted to be $<$1” and spatial shift
between the H2 rotational line emission peaks is comparable or smaller to the
JWST diffraction limit which is about 0.2” to 1” in the 5-28 $\mu$m range
where are the pure rotational lines.

These constraints on the physical conditions may allow to better understand
the dynamical effects in PDRs, e.g. compression waves, photo-evaporative
flows, and IF and DF instabilities. Recently, Maillard et al. (2021) modelled
the dynamical effects of the radiative stellar feedback on the H-to-H2
transition. These authors built a semi-analytical model of the H/H2 transition
in a 1D plane-parallel PDR illuminated by FUV radiation with advancing IF
resulting from the photoevaporation mechanism. For the high-excitation PDRs
such as the Orion Bar, moderate effects are however predicted. The H0/H2
transition will be slightly closer to the IF and sharper. Much stronger
effects of the advection dynamics with merged, or close to merged, IF and DF
are predicted for low excitation PDRs illuminated by late O stars such as the
Horsehead nebula.

##  7 Summary

In this section, a short summary and prospects for JWST are given.

  1. 1.

We obtained with Keck/NIRC2 using AO the most complete and detailed maps of
the complex UV-irradiated region of the Orion Bar where the conversion from
ionized to atomic to molecular gas occurs. We mapped the vibrationally excited
line of H2 at 2.12 $\mu$m, tracing the dissociation front, and the [FeII] line
at 1.64 $\mu$m and the Br$\gamma$ line at 2.16 $\mu$m, tracing the ionization
front. This allows for the first time to spatially resolve the dissociation
front with a resolution of 0.1′′ (40 AU) and obtain a very precise
determination of the offset between the peak of the ionization and
dissociation front of 12 and 12.5′′ (0.024-0.025 pc).

  2. 2.

The H0/H2 dissociation front appears highly structured with several ridges and
extremely sharp filaments with a width of $1-2^{\prime\prime}$ (0.002-0.004 pc
or 400-800 AU). Ridges and filaments run parallel to the dissociation front
but a succession of bright sub-structures in H2 is also observed from the edge
of the DF towards the molecular region. The multiple H2 emission peaks along
and across the Bar may be associated with a multitude of small highly
irradiated and dense PDRs.

  3. 3.

The comparison with ALMA data of the HCO+ J=4-3 line emission, a good
indicator of dense gas, show a remarkable similar spatial distribution between
the H2 and HCO+ emission. This suggests that they both come from high
densities but also indicates their strong chemical link and that the H/H2 and
C+/C/CO transition zones are very close.

  4. 4.

We spatially resolved additional compact sources corresponding to over-dense
irradiated sub-structures such as proplyds near the ionization front, and
perhaps collapsing protostars near the dissociation front.

  5. 5.

We compared our extinction-corrected observations of the emission gas lines to
the model predictions using the Cloudy code for the ionized gas and the Meudon
PDR code for the neutral PDR gas. The models reproduce well (by a factor less
than 2) the observed intensity peak of the gas lines emission. The predicted
vibrationaly excited H2 come from the H0/H2 transition layer where the gas
density is of the order of few 105 cm-3.

  6. 6.

This work confirms without ambiguity that one of the densest portions of the
Bar lie along the dissociation front and that the Orion Bar edge is composed
of small, dense sub-structures at high thermal pressure with P about 108 K
cm-3 immersed in a more diffuse environment. Further studies are required to
accurately determine the gas physical conditions (pressure and density
gradients) and dynamics of these over-dense irradiated sub-structures and
better understand their physical origin and future.

The JWST ERS proposal on the Orion Bar PDR (Berné et al. 2022) will very soon
give access to multiple spectroscopic images with a similar spatial resolution
to the Keck/NIRC2 observations but a signal-to-noise gain that will increased
contrast and allow a sharper detection of all less bright substructures. JWST
with IFU spectroscopy will give insight into the local gas physical conditions
(temperature, density and pressure) and chemical composition of the warm very
structured irradiated medium. It will be possible to probe the physical
conditions in most of the dense sub-structures detected with Keck or ALMA as
well as the very thin surface layers that are sufficiently heated to photo-
evaporate from the Orion Bar edge. Furthermore, JWST will spatially resolve at
near and mid-IR wavelengths dust emission and scattering simultaneously with
the gas lines. Variation of the dust properties (e.g., size distribution,
extinction) as function of PDR depth will be constrained and will be taken
into account in the UV shielding, thermal balance and H2 formation process.

Acknowledgements. The data presented herein were obtained at the W. M. Keck
Observatory, which is operated as a scientific partnership among the
California Institute of Technology, the University of California and the
National Aeronautics and Space Administration. The Observatory was made
possible by the generous financial support of the W. M. Keck Foundation.

The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
indigenous Hawaiian community. We are most fortunate to have the opportunity
to conduct observations from this mountain.

This research has made use of the Keck Observatory Archive (KOA), which is
operated by the W. M. Keck Observatory and the NASA Exoplanet Science
Institute (NExScI), under contract with the National Aeronautics and Space
Administration. Javier R. Goicoechea thanks the Spanish MCIYU for funding
support under grant PID2019-106110GB-I00.

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