# Mapping physical parameters in Orion KL at high spatial resolution

Olivia H. Wilkins Division of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, CA 91125 USA  P. Brandon Carroll Center for
Astrophysics $\mid$ Harvard & Smithsonian, Cambridge, MA 02138 USA  Geoffrey
A. Blake Division of Chemistry and Chemical Engineering, California Institute
of Technology, Pasadena, CA 91125 USA  Division of Geological and Planetary
Sciences, California Institute of Technology, Pasadena, CA 91125 USA

(Received August 12, 2021; Revised September 28, 2021; Accepted October 18,
2021)

###### Abstract

The Orion Kleinmann-Low nebula (Orion KL) is notoriously complex and exhibits
a range of physical and chemical components. We conducted high angular
resolution (sub-arcsecond) observations of ^13CH3OH $\nu=0$ (${\sim}0\farcs 3$
and ${\sim}0\farcs 7$) and CH3CN $\nu_{8}=1$ (${\sim}0\farcs 2$ and
${\sim}0\farcs 9$) line emission with the Atacama Large
Millimeter/submillimeter Array (ALMA) to investigate Orion KL’s structure on
small spatial scales (${\leq}350$ au). Gas kinematics, excitation
temperatures, and column densities were derived from the molecular emission
via a pixel-by-pixel spectral line fitting of the image cubes, enabling us to
examine the small-scale variation of these parameters. Sub-regions of the Hot
Core have a higher excitation temperature in a $0\farcs 2$ beam than a
$0\farcs 9$ beam, indicative of possible internal sources of heating.
Furthermore, the velocity field includes a bipolar ${\sim}7{-}8$ km s-1
feature with a southeast-northwest orientation against the surrounding
${\sim}4{-}5$ km s-1 velocity field, which may be due to an outflow. We also
find evidence of a possible source of internal heating toward the Northwest
Clump, since the excitation temperature there is higher in a smaller beam
versus a larger beam. Finally, the region southwest of the Hot Core (Hot Core-
SW) presents itself as a particularly heterogeneous region bridging the Hot
Core and Compact Ridge. Additional studies to identify the (hidden) sources of
luminosity and heating within Orion KL are necessary to better understand the
nebula and its chemistry.

astrochemistry — ISM: abundances — ISM: individual objects (Orion KL) — ISM:
molecules

††journal: ApJ††facilities: ALMA††software: CASA (McMullin et al., 2007), CDMS
(Müller et al., 2001), LMFIT (Newville et al., 2019), APLpy (Robitaille &
Bressert, 2012; Robitaille, 2019), Gaussian16 (Frisch et al., 2016)

##  1 Introduction

Molecules are useful tools for characterizing the physical structure of dense
interstellar environments (e.g., Herbst & van Dishoeck, 2009; Ginsburg et al.,
2017; Moscadelli et al., 2018; Gieser et al., 2019; Law et al., 2021). As has
been illustrated repeatedly with the Orion Kleinmann-Low nebula (Orion KL,
$d\sim 388$ pc)—the closest region of high-mass star formation to the Earth
(Kounkel et al., 2017)—, different types of molecules can be used to trace
different types of environments and conditions in interstellar material. In
Orion KL, the complex interplay of dense molecular gas and star formation is
traced by several components, such as the Hot Core, the Compact Ridge, the
Extended Ridge, and the Plateau regions, each of which has varying chemical
and physical properties (e.g., Blake et al., 1987; Friedel & Widicus Weaver,
2011; Feng et al., 2015; Tercero et al., 2018; Luo et al., 2019; Cortes et
al., 2021). Figure 1 shows a schematic representation of Orion KL illustrating
regions discussed in this work. The variety of chemical and physical
properties, as well as the readily detectable emission lines from
isotopologues (e.g., Neill et al., 2013), observed toward Orion KL make it an
excellent laboratory for studying the formation and subsequent chemistry of
molecules in high-mass star-forming regions.

Figure 1: Illustration of Orion KL’s morphology, as seen in the plane of the
sky. Regions of interest include Source I (I), the Hot Core (HC), the Hot
Core-Southwest (HC-SW), the Compact Ridge (CR) and the Northwest Clump (NWC).
The crosses indicate specific emission regions that are discussed in the text.
The scale bar in the top left corresponds to a linear scale of $\sim$1000 au
(2.6″) at Orion KL’s distance of 388 pc.

Generally, the two dominant sub-regions of Orion KL that harbor complex
chemistry are the so-called “Hot Core” which contains denser and warmer gas
($n_{\mbox{\scriptsize\ce{H2}}}\sim 10^{7}$ cm-3, $T_{kin}\sim 200$ K) and the
“Compact Ridge” that lies to the southwest of the Hot Core, and which is both
cooler and less dense ($n_{\mbox{\scriptsize\ce{H2}}}\utilde{<}10^{6}$ cm-3,
$T_{kin}\sim 100{-}150$ K) (Blake et al., 1987; Genzel & Stutzki, 1989). The
regional variation in physical conditions has also resulted in large-scale
variation in the chemistry, with the Hot Core and Compact Ridge being the
sites of prominent emission from nitrogen-bearing and oxygen-bearing species,
respectively (e.g. Blake et al., 1987; Friedel & Widicus Weaver, 2011).

The variation in both the physical conditions and chemistry of Orion KL has
been well-documented across various spatial scales, e.g. $\sim$20″$-$43″ with
Herschel/HIFI by Wang et al. (2011); $\sim$0$\farcs$5$-$5$\farcs$0 with CARMA
by Friedel & Widicus Weaver (2011); and $\sim$2$\farcs$6$-$3$\farcs$7 with
combined SMA and IRAM 30m data by Feng et al. (2015). There has also been
high-angular-resolution millimeter continuum imaging of the nebula, e.g. by
Hirota et al. (2015) at $\sim$0$\farcs$5 with ALMA. Ginsburg et al. (2018) and
Wright et al. (2020) imaged continuum and line emission specifically toward
the disk and outflow of Source I alone down to 0$\farcs$03.

Observations of molecular line emission have shed light on both the velocity
structure and sources of heating within Orion KL. Ammonia (NH3) and methyl
formate (HCOOCH3), for example, have been used to trace the velocity fields
throughout the nebula at sub-arcsecond angular scales (e.g., Goddi et al.,
2011; Pagani et al., 2017). CH3OH, HCOOCH3, thioformaldehyde (H2CS), and
cyanoacetylene (HC3N) are included in the suite of molecules used to probe
whether Orion KL’s different components are internally or externally heated, a
question that remains the subject of debate toward the Hot Core specifically
(de Vicente et al., 2002; Goddi et al., 2011; Zapata et al., 2011; Crockett et
al., 2014b; Orozco-Aguilera et al., 2017; Peng et al., 2017; Li et al., 2020).

Even with these studies, many questions remain about the nature of Orion KL.
Investigations of the nebula’s three-dimensional (3-D) structure, for example,
have mostly looked at the so-called high-energy “fingers” and “bullets”
emanating on arcminute scales from an explosion that took place in the nebula
about 500 years ago (Nissen et al., 2007; Bally et al., 2015; Youngblood et
al., 2016; Bally et al., 2017). However, a more small-scale view of the 3-D
structure of the dense molecular gas in Orion KL is largely absent in the
literature, despite continuum and molecular line emission imaging showing that
both the physical and chemical complexity of Orion KL are not simply regional
but are manifest on more localized scales as well. That is, while the physical
and chemical aspects of Orion KL can be divided into large areas such as the
dense, nitrogen-rich Hot Core and the less dense, oxygen-rich Compact Ridge,
there is growing evidence suggesting that this heterogeneity extends to within
these subregions of the nebula as well (e.g., Friedel & Widicus Weaver, 2011;
Crockett et al., 2014b).

Thus far, the results of high-angular-resolution imaging of Orion KL have
generally focused on distinct regions or line emission peaks. Such
observations at various spatial scales are imperative to understanding the
physical and chemical conditions of star-forming regions, and they reveal that
there is still much to uncover in Orion KL.

Here we present a more localized ($\sim$0$\farcs$9-0$\farcs$2) view of Orion
KL using a combination of ground-state ^13CH3OH and vibrationally-excited
CH3CN line emission with the Atacama Large Millimeter/submillimeter Array
(ALMA). These compounds are both complex (i.e., have at least six atoms) and
(near) symmetric top molecules, which means they have spectra that are both
abundant in lines and relatively simple, such that deriving their abundances
and temperatures is rather straightforward. We specifically target methanol to
trace colder, less dense gas; the carbon-13 methanol isotopologue was
specifically targeted because it serves as an optically thin proxy for the
primary carbon-12 isotopologue, which is optically thick toward Orion KL.
Similarly, CH3CN $\nu_{8}=1$ was selected to trace hotter and denser gas, to
probe high energy emission excited by massive embedded protostars, and because
ground-state CH3CN is optically thick toward the Orion KL Hot Core.

The observations presented here complement previous studies of Orion KL to
further elucidate the small-scale physical structure of the nebula. The
angular resolutions (from 0$\farcs$9 down to 0$\farcs$2) were deliberately
chosen to enable observations of at the expense of resolving out extended
emission that is already widespread in the existing literature. Combining both
molecular tracers in a single analysis is needed to characterize the wide
range of environments in Orion KL, especially in light of the longstanding
observations that nitrile and oxygen-bearing organic emission lines are
kinematically and spatially distinct, even at 10-30′′ spatial resolution (e.g.
Blake et al., 1987; Crockett et al., 2014b). We find that our observations
agree overall with previous studies toward Orion KL; however, we resolve
spatial structure at scales on the order of protoplanetary disks, which lie
within radii typically associated with molecular abundance enhancements caused
by heating from embedded protostars (Boonman et al., 2001; Schöier et al.,
2002). Furthermore, our results provide new insights to the kinematics and
thermal profile of the nebula.

The ALMA observations and an overview of the data analysis are described in
Sections 2 and 3, respectively. The chemical distribution, including column
density measurements, is discussed in Section 4. A discussion of the physical
and chemical structure in Orion KL, including line width and velocity field
maps, is presented in Section 5. Section 6 provides a discussion of derived
temperature maps and possible sources of heating. The results of this work are
summarized in Section 7.

##  2 Observations

Observations of Orion KL were taken in ALMA Cycles 4 and 5 with a pointing
center of $\alpha_{\mbox{\scriptsize J2000}}=05$${}^{\mbox{\scriptsize
h}}$35${}^{\mbox{\scriptsize m}}$14$\fs$50, $\delta_{\mbox{\scriptsize
J2000}}=-05\arcdeg 22\arcmin 30\farcs 9$. All observations were carried out
the 12-meter array.

The Cycle 4 observations (project code #2016.1.01019, PI: Carroll) include the
CH3CN $\nu_{8}=1$ lines used in these analyses. These observations comprised
two epochs, each with one execution block and and one spectral window covering
a frequency range of 146.83-147.77 GHz in Band 4 at a spectral resolution of
488.28 kHz ($\sim$1.0 km s-1). The Cycle 4 data taken on 2 October 2016 used
44 antennas with projected baselines between 18.6 m and 3.2 km (9.3k$\lambda$
and 1600k$\lambda$) and a primary beam (field of view) of 39.8″. The on-source
integration time was 455 s. The precipitable water vapor was 2.1 mm, and
typical system temperatures were around 50-100 K. The observations taken on 28
November 2016 used 47 antennas with projected baselines between 15.1 m and
704.1 m (7.6k$\lambda$ and 350k$\lambda$) and a primary beam of 39.8″. The on-
source integration time was 151 s. The precipitable water vapor was 1.9 mm,
and typical system temperatures were around 50-100 K.

The Cycle 5 observations (project code #2017.1.01149, PI: Wilkins) include the
^13CH3OH $\nu=0$ lines used in these analyses. These observations comprised
one execution block and 10 spectral windows, three of which contained the
targeted ^13CH3OH lines. These three windows covered frequency ranges of
155.13-155.37 GHz, 155.57-155.80 GHz, and 156.06-156.29 GHz in Band 4 at
spectral resolutions of 244 kHz ($\sim$0.5 km s-1). These observations were
carried out on 14 December 2017 and used 49 antennas with projected baselines
between 15.1 m and 3.3 km (7.6k$\lambda$ and 1650k$\lambda$) and a primary
beam of 39.1″. The on-source integration time was 2062 s. The precipitable
water vapor was 3.7 mm, and typical system temperatures were around 75-125 K.

The spectra for each molecular probe analyzed here were confined to a single
correlator sub-band; as such, the uncertainties for quantities derived from
for these molecular probes are dominated by the thermal and phase noise and
are mostly unaffected by systemic calibration uncertainties. Calibration was
completed using standard CASA calibration pipeline scripts using CASA 4.7.0
for Cycle 4 data and CASA 5.1.1-5 for Cycle 5 data. source J0423$-$0120 was
used as a calibrator for amplitude, atmosphere, bandpass, pointing, and WVR
(Water Vapor Radiometer) variations, while J0541$-$0211 was used as a phase
and WVR calibrator.

The image cubes presented here were created with continuum emission estimated
from line-free channels subtracted in the UV-plane using the uvcontsub task in
CASA.

###  2.1 Cycle 4 Data Reduction

The Cycle 4 data were processed in CASA 4.7.0 using the Cycle 4 ALMA data
processing pipeline,111 which used the tclean algorithm with Briggs weighting
and a pipeline-generated mask . A robust parameter of 0.5 was used for
deconvolution. The resulting continuum and line images are primary-beam-
corrected and have a noise-level of $\sigma_{\mbox{\scriptsize RMS}}\sim 1.2$
mJy beam-1. Comprising two epochs, that yield images of CH3CN $\nu_{8}=1$ at
two angular resolutions, the Cycle 4 data taken on 2016 October 2 have a
0$\farcs$23$\times$0$\farcs$21 synthesized beam (hereafter identified using
the shorthand 0$\farcs$2), which corresponds to linear scales of $\sim$90 au
in Orion KL, with a position angle of PA $=$ -8∘. Images from observations on
2016 November 28 have a synthesized beam of 1$\farcs$13$\times$0$\farcs$72
(hereafter 0$\farcs$9), which corresponds to linear scales of $\sim$350 au in
Orion KL, with PA $=$ -71∘.

The targeted CH3CN $\nu_{8}=1$ lines in these data were also detected in Cycle
2 observations (project #2013.1.01034, PI: Crockett, Carroll (2018)) toward
Orion KL but at an angular resolution of $\sim$2$\farcs$0 ($\sim$800 au).
Comparing the integrated intensities for the CH3CN lines listed in Table 1, we
find that we recover $\sim$28% and $\sim$16% of the flux integrated over the
whole Orion KL region in the 0$\farcs$2 and 0$\farcs$7 images, respectively,
compared to what is recovered in the 2$\farcs$0 observations.

###  2.2 Cycle 5 Data Reduction

The Cycle 5 data were similarly processed in CASA 5.1.1-5 using the tclean
algorithm (interactive) with Briggs weighting and the ‘auto-multithresh’
masking algorithm (Kepley et al., 2020). A robust parameter of 1.5 (i.e.,
semi-natural weighting) was used for deconvolution to overcome significant
artifacts that obstructed analysis of the images when using a robust parameter
of 0.5. One possible explanation for these artifacts is that the ^13CH3OH
emission is extended such that it is difficult to image at longer baselines,
thus requiring a robust parameter that gave higher weights to shorter
baselines. The images are primary-beam-corrected and have a noise-level of
$\sigma_{\mbox{\scriptsize RMS}}\sim 1.0$ mJy beam-1.

There was only one set of observations taken, on 14 December 2017, toward
Orion KL during the Cycle 5 program. These images have a synthesized beam of
0$\farcs$34$\times$0$\farcs$20 (hereafter 0$\farcs$3), which corresponds to
linear scales of $\sim$110 au in Orion KL, with PA $=$ -56∘. To compare the
^13CH3OH emission on multiple spatial scales, we re-imaged these data
splitting the measurement set to include only baselines of $\leq$500 m,
resulting in a synthesized beam of 0$\farcs$74$\times$0$\farcs$63 (hereafter
$0\farcs 7$), which corresponds to linear scales of $\sim$270 au in Orion KL,
with PA $=$ -72∘. The image cube generation was otherwise done in the same
fashion as that used for the full ^13CH3OH data set.

The $J=5$ transition of ^13CH3OH at 156.3 GHz in these data was also detected
in the aforementioned Cycle 2 observations toward Orion KL but at
$\sim$2$\farcs$0 angular resolution ($\sim$800 au). Comparing the integrated
intensities for this line, we find that we recover $\sim$9% and $\sim$14% of
the ^13CH3OH flux integrated over the whole Orion KL region in the 0$\farcs$3
and 0$\farcs$7 images, respectively, compared to what is recovered in the
2$\farcs$0 observations. Moreover, we estimate that we recover about 4% and 6%
of the total ^13CH3OH $J=5$ flux based on rough estimates of the flux derived
from abundances and rotation temperature measurements made using Herschel
(Crockett et al., 2014b). We attribute this to extended being resolved out in
our observations, which have maximum recoverable scales equivalent to about
930-2400 au in Orion KL. In this work, however, we focus on probing the small-
scale structure rather than large-scale features of the nebula. Thus we
emphasize that these observations complement the existing lower-angular-
resolution studies of Orion KL and that observations at multiple spatial
scales are imperative for a holistic picture of star-forming regions such as
Orion KL.

##  3 Methods

As noted in Section 1, different molecular tracers can be used as probes of
different conditions in star-forming regions. The spectra from the ten
spectral windows in the ALMA Cycle 5 observations, which are shown in Figure
2, illustrate this, with distinct profiles observed in the Hot Core (red) and
the Compact Ridge (blue). While some transitions emit with similar intensities
across the nebula, some lines show up in either the Hot Core or the Compact
Ridge, but not both, while others have lines in both regions but at
substantially different intensities. Using three transitions of ^13CH3OH and
eight transitions of CH3CN $\nu_{8}=1$, which we list in Table 1, we resolve
detailed profiles of velocity, temperature, and line widths of these tracers
toward Orion KL. As discussed in Section 2, these lines were chosen because
they were observed within a single correlator set-up (across three spectral
windows for ^13CH3OH and in one spectral window for CH3CN $\nu_{8}=1$), hence
minimizing the uncertainties for the derived parameters. While there were
additional lines present in the data, the selected lines represent a subset of
consistently strong and unblended emission lines across the nebula.

Figure 2: Spectra from ten ALMA Cycle 5 Band 4 spectral windows toward Orion
KL, displaying the plethora of molecular line emission toward the Compact
Ridge (blue) and the Hot Core (red, offset by 10 mJy beam-1 for better
visibility). Solid lines show transitions of ^13CH3OH (black), ^12CH3OH
$v_{t}=0$ (teal), and ^12CH3OH $v_{t}=1$ (orange). All tick marks are
separated by 0.1 GHz. Continued on next page. Figure 2: Continued from
previous page.

Line width, velocity, excitation temperature, and column density of ^13CH3OH
$\nu=0$ and CH3CN $\nu_{8}=1$ as a function of position were derived by a
pixel-by-pixel fit of the data.222Python script available at
https://github.com/oliviaharperwilkins/LTE-fit. Because all lines used in the
fit for each molecule were observed simultaneously, the uncertainties in
excitation temperature, which are derived from relative fluxes, should be
dominated by thermal noise rather than by multiple sources of calibration
uncertainty. For the column density estimates, the relative differences across
the images should again be dominated by thermal (and phase) noise, while the
overall calibration error budget does impact the total column densities
derived but by $\leq$5% in Band 4 (Andreani et al., 2018).

The pixel-by-pixel fit of the data was achieved by extracting spectra in a
single synthesized beam centered on each pixel, in succession. To avoid
erroneous fits, only lines with peak amplitudes of
$\geq$3$\sigma_{\mbox{\scriptsize RMS}}$ were considered. Line
parameters—namely line width, velocity shift, excitation temperature, and
column density—were determined simultaneously by least-squares fitting with
LMFIT333LMFIT (Newville et al., 2019) is a non-linear least-squares
minimization and curve-fitting algorithm for Python that can be accessed at
https://doi.org/10.5281/zenodo.598352. (version 0.9.15) to model the spectra
assuming optically thin lines at local thermodynamic equilibrium (LTE)444For
the rationale behind the assumption of optically thin lines at LTE, see
Appendix A. using Equation 1 (adapted from Remijan et al., 2003):

$N_{tot}=2.04\times
10^{20}C_{\tau}\frac{1}{\Omega_{S}(\Omega_{S}+\Omega_{B})}\frac{\int{I_{\nu}d\nu}}{\theta_{a}\theta_{b}}\frac{Q(T_{ex})e^{E_{u}/T_{ex}}}{\nu^{3}S_{ij}\mu^{2}}\mbox{
cm}^{-2}$ (1)

where $N_{tot}$ is the total column density [cm-2] and $T_{ex}$ is the
excitation temperature [K]. Line width and velocity were extracted from the
Gaussian fits used in the $\int I_{\nu}d\nu$ term, which is the integrated
intensity of the line [Jy beam-1 km s-1]. The optical depth correction factor
$C_{\tau}=\tau/(1-e^{-\tau})$ was assumed to be unity, since the optical depth
$\tau$ is known to be small for the isotopologue transitions selected (see
Appendix A). The $\Omega_{S}$ and $\Omega_{B}$ terms are the solid angles of
the source and beam respectively; we assume that the source completely fills
the beam at all positions and that $\Omega\approx\pi\theta^{2}$ since $\theta$
is small. The remaining terms are known: $\theta_{a}$ and $\theta_{b}$ are the
FWHM beam sizes [″], $Q$ is the partition function, $E_{u}$ is the upper-state
energy level [K], $\nu$ is the rest frequency of the transition [GHz], and
$S_{ij}\mu^{2}$ is the product of the transition line strength and the square
of the electric dipole moment [Debye2].

Table 1: Transitions used for line fits. Transition | $\nu$ | $E_{u}$ | $S_{ij}\mu^{2}$ |  | $A_{ul}$ | $g_{u}$
---|---|---|---|---|---|---
(GHz) | (K) | (Debye2) |  | ($\times 10^{-5}$ s-1)
^13CH3OHaaSpectroscopic data for ^13CH3OH comes from CDMS. |
$8_{(0,8)}-8_{(-1,8)}$ | 155.6958 | 94.59 | 6.86 |  | 1.77 | 17
$6_{(0,6)}-6_{(-1,6)}$ | 156.1866 | 60.66 | 5.70 |  | 1.94 | 13
$5_{(0,5)}-5_{(-1,5)}$ | 156.2994 | 47.08 | 4.98 |  | 2.01 | 11
CH3CN $\nu_{8}=1$bbSpectroscopic data for CH3CN $\nu_{8}=1$ comes from the JPL spectroscopic database. |
$J=8_{-5}-7_{-5}$ | 147.5123 | 802.03 | 278.88 |  | 15.32 | 68
$J=8_{-4}-7_{-4}$ | 147.5439 | 724.50 | 171.63 |  | 18.87 | 34
$J=8_{-3}-7_{-3}$ | 147.5698 | 661.23 | 196.67 |  | 21.64 | 34
$J=8_{5}-7_{5}$ | 147.5756 | 668.87 | 139.43 |  | 15.34 | 34
$J=8_{-2}-7_{-2}$ | 147.5899 | 612.23 | 429.03 |  | 23.61 | 68
$J=8_{4}-7_{4}$ | 147.5954 | 618.01 | 343.26 |  | 18.89 | 68
$J=8_{-1}-7_{-1}$ | 147.6040 | 577.50 | 225.29 |  | 24.80 | 34
$J=8_{2}-7_{2}$ | 147.6199 | 559.01 | 214.52 |  | 23.62 | 34

The transitions of ^13CH3OH and CH3CN used for the fits are summarized in
Table 1. One other ^13CH3OH transition is present in our observations at
155.262 GHz but was not included in the fits due to line blending. The
^13CH3OH lines are ground vibrational state c-type transitions with upper
state energies $E_{u}$ between 47 and 95 K and $J=5,6,8$. The $J=7$ line at
$\nu_{rest}=155.994$ GHz is expected to be unblended but was excluded in our
observations to optimize the spectral setup. Three other ^13CH3OH transitions
fall within our spectral setup at $\nu_{rest}=141.381$ GHz, $155.262$ GHz, and
$156.149$ GHz. The 141.381 GHz and 155.262 GHz lines appear to be blended:
with CH3OH $v_{t}=1$ at 141 GHz and an unknown contaminant at 155 GHz. The
line at 156.149 GHz is high $J$ ($J=26-25$) with $E_{u}=988$ K and thus a
strong detection of this transition would not be expected especially toward
the Compact Ridge. An example spectrum of the ^13CH3OH lines fitted in our
analyses is shown in Figure 4.

The CH3CN lines analyzed are all strong, vibrationally-excited ($\nu_{8}=1$)
$J=8-7$ transitions. Their upper state energies between 559 K and 803 K make
these lines appropriate tracers of high-energy (or radiatively pumped)
emission, in and near the Hot Core. There are other, weaker CH3CN $\nu_{8}=1$
lines in Figure 5; however, these lines were excluded from the fits because
they are blended, which prevented good line fits. Nevertheless, the fitted
parameters characterizing the CH3CN emission come with reasonable propagated
uncertainties of $\leq$20% for much of the Hot Core (and up to $\sim$30% near
the region’s edges where emission drops off).

Figure 4: Example spectrum of ^13CH3OH $\nu=0$ toward the center of the
Compact Ridge showing the Gaussian fits to the unblended transitions by the
red dashed line over the data in black. Figure 5: Example spectrum of CH3CN
$\nu_{8}=1$ toward the center of the Hot Core showing the Gaussian fits to the
included transitions by the red dashed line over the data in black.

Because the synthesized beams are small compared to the extent of molecular
emission toward Orion KL, we assume the sources completely fill the beam at
all positions. The $E_{u}$, $\nu$, $S_{ij}\mu^{2}$, and $Q(T_{ex})$ values for
^13CH3OH and CH3CN $\nu_{8}=1$ were obtained from the Cologne Database for
Molecular Spectroscopy (CDMS, Müller et al., 2001) and the JPL molecular
spectroscopy database (Pickett et al., 1998), respectively, via the
Splatalogue555http://splatalogue.online database for astronomical
spectroscopy. Values and uncertainties (standard errors calculated using
LMFIT) for $N_{tot}$, $T_{ex}$, and local standard of rest velocity $V_{LSR}$
were extracted from the line fits using Equation 1 and are presented
throughout the rest of the paper.

The figures presented herein show color maps of the derived parameters from
CH3CN $\nu_{8}=1$ and ^13CH3OH $\nu=0$ line emission with contours of the
continuum at both the full and tapered angular resolution (Figures 7-10). In
general, the estimated uncertainty is $<$30% for the column density and
excitation temperature and $<$5% for the velocity and width fields. Maps of
the propagated uncertainty are given in Appendix B. The continuum contours are
the same as those plotted over the Cycle 5 Band 4 ($\sim$150 GHz) continuum
images in Figure 6. The continuum images obtained from the Cycle 4 data
exhibit similar profiles and are not shown here.

Figure 6: ALMA Cycle 5 continuum in Band 4 ($\sim$150 GHz) toward Orion KL at
full (left) and tapered (right) angular resolution. The synthesized beam is
shown by the black oval in the bottom left. The warmer, denser Hot Core region
is shown by HC, and the cooler, less dense Compact Ridge region is indicated
by CR. The locations of source I and IRc7 are shown by the red star and red
plus, respectively. The yellow circles correspond to millimeter/submillimeter
continuum sources identified by Hirota et al. (2015). The embedded millimeter
source C22 (Friedel & Widicus Weaver, 2011) and the protostar SMA1 (Beuther et
al., 2006) are shown by the teal triangles. Both the greyscale and contours
plot the continuum with contours at $3\sigma_{\mbox{\scriptsize
RMS}},6\sigma_{\mbox{\scriptsize RMS}},12\sigma_{\mbox{\scriptsize
RMS}},24\sigma_{\mbox{\scriptsize RMS}},\dots$ where
$\sigma_{\mbox{\scriptsize RMS}}=1.3$ mJy beam-1 is the noise level for the
full resolution image and $\sigma_{\mbox{\scriptsize RMS}}=1.0$ mJy beam-1 is
the noise level for the tapered resolution image.  Figure 7: Parameter maps
for the full angular resolution images of CH3CN $\nu_{8}=1$. Contours show the
2 mm ($\sim$150 GHz) continuum from the left panel of Figure 6. The color
plots show, from left to right: (top row) velocity field, line width field,
(middle row) total column density, excitation temperature, and (bottom row)
integrated intensity (moment-0). All panels have the same field of view.
Figure 8: Parameter maps for the full angular resolution images of ^13CH3OH
$\nu=0$. Contours show the 2 mm ($\sim$150 GHz) continuum from the left panel
of Figure 6. The color plots show, from left to right: (top row) velocity
field, line width field, (middle row) total column density, excitation
temperature, and (bottom row) integrated intensity (moment-0). All panels have
the same field of view. Figure 9: Parameter maps for the tapered angular
resolution images of CH3CN $\nu_{8}=1$. Contours show the 2 mm ($\sim$150 GHz)
continuum from the right panel of Figure 6. The color plots show, from left to
right: (top row) velocity field, line width field, (middle row) total column
density, excitation temperature, and (bottom row) integrated intensity
(moment-0). All panels have the same field of view. Figure 10: Parameter maps
for the tapered angular resolution images of ^13CH3OH $\nu=0$ (bottom
cluster). Contours show the 2 mm ($\sim$150 GHz) continuum from the right
panel of Figure 6. The color plots show, from left to right: (top row)
velocity field, line width field, (middle row) total column density,
excitation temperature, and (bottom row) integrated intensity (moment-0). All
panels have the same field of view.

##  4 Chemical Distributions

The bottom-most panels of Figures 7-10 show the integrated intensities of
^13CH3OH and CH3CN $\nu_{8}=1$ throughout Orion KL. While ^13CH3OH emission is
present throughout the nebula, most of the emission arises from the region
extending southwest from the Hot Core and toward the Compact Ridge, which fits
the profile of this region being the site of oxygen-bearing chemistry (e.g.
Blake et al., 1987; Favre et al., 2017; Tercero et al., 2018). CH3CN
$\nu_{8}=1$ is found predominantly in the region surrounding the Hot Core and
Source I, as well as IRc7.

In our analyses, ^13CH3OH $\nu=0$ was selected to trace colder, less dense gas
such as that in the Compact Ridge, a component that is also rich in oxygen-
bearing chemistry (Blake et al., 1987; Friedel & Widicus Weaver, 2011).
Furthermore, ^13CH3OH serves as an optically thin proxy for the primary
carbon-12 isotopologue of methanol, which is often optically thick in star-
forming regions and which is known to be optically thick toward the Hot Core
and Compact Ridge in Orion KL specifically, from Herschel Space Telescope
observations (Crockett et al., 2014b). Compared to lower angular resolution
images (e.g., CARMA images by Friedel & Widicus Weaver, 2011), the methanol
emission in our observations is much more compact. We attribute this to the
extended emission of the nebula being resolved out in our images. As stated in
Section 2.2, we recover $\sim$9% and $\sim$14% of the ^13CH3OH flux in the
0$\farcs$3 and 0$\farcs$7 images compared to observations at 2$\farcs$0\. Even
between Figures 8 and 10, the (fittable) ^13CH3OH emission is generally more
compact in the full angular resolution images (Figure 8) than in the tapered
angular resolution images (Figure 10).

The derived ^13CH3OH column densities are shown in the middle left panel
Figures 8 and 10. We derive ^13CH3OH column densities on the order of
$10^{16}$ cm-2 throughout the Compact Ridge and the region southwest of the
Hot Core (Hot Core-SW) at 0$\farcs$3, which is in agreement with the ^13CH3OH
column densities reported by Crockett et al. (2014b). In the Compact Ridge and
the edges of the Hot Core-SW, the column density is ${\sim}1.0\times 10^{16}$
cm-2; toward the center of the Hot Core-SW, there are pockets of higher column
density, as much as ${\sim}3.0\times 10^{16}$ cm-2. At 0$\farcs$7 angular
resolution, the derived column density is as much as four times higher,
particularly in elongated structures extending south from SMA1 and C22. This
is perhaps due to emission, which is resolved out in the 0$\farcs$3 images,
from material that is being blown southward by the explosive event that took
place north of Source I 500 years ago (e.g., Bally et al., 2015).

CH3CN $\nu_{8}=1$ was selected for similar reasons, but to trace the hotter
and denser gas toward the Hot Core region, which is also rich in nitrogen-
bearing molecules (Blake et al., 1987; Friedel & Widicus Weaver, 2011). The
vibrationally excited lines were specifically targeted to probe high energy
emission excited by far-IR pumping associated with particularly dense gas from
massive embedded protostars (e.g. Genzel & Stutzki, 1989) while also
overcoming the fact that CH3CN $\nu=0$ has been observed to be optically thick
toward the Hot Core, Compact Ridge, and Plateau regions in Orion KL (Crockett
et al., 2014b).

The column density of CH3CN $\nu_{8}=1$ is on the order of $10^{16}{-}10^{18}$
cm-2 in the Hot Core and Source I region, with the column density derived from
the 0$\farcs$9 data being about an order of magnitude greater than that
derived from the 0$\farcs$2 data. Crockett et al. report CH3CN $\nu_{8}=1$
column densities of $3.7\times 10^{15}$ cm-2, which is almost two orders of
magnitude less than what we generally find in our fits, toward the Hot Core in
a $\geq$9″ beam. The discrepancy may be the result of probing vastly different
spatial scales ($\geq$9″ versus sub-arcsecond angular scales) or because
Crockett et al. use a different analytical method, including a wideband survey
whereas our analyses includes $J=8$ transitions of CH3CN $\nu_{8}=1$ only. We
suspect that the former is the likely source of the difference between the two
sets of measurements because CH3CN $\nu_{8}=1$ traces dense gas, in particular
gas affected by far-IR pumping associated with massive embedded protostars. In
other words, we can expect the CH3CN $\nu_{8}=1$ to be more compact such that
its emission was perhaps diluted in a much larger beam.

Alternatively, the $\nu_{8}=1$ mode is not necessarily in thermal equilibrium
with the CH3CN ground state at the same effective rotational temperature
(i.e., $T_{vib}\neq T_{rot}$). However, Crockett et al. report that the
$\nu=0$ and $\nu_{8}=1$ models are consistent toward the Hot Core, or that
$T_{rot}=T_{vib}$, and we find that the rotational LTE models employed in this
work fit the data well (see Appendix A). Thus we proceed under the assumption
of thermal equilibrium, with the caveat that the derived excitation
temperatures for the $\nu_{8}=1$ lines do not necessarily reflect the actual
kinetic temperature. However, previous measurements for ground-state CH3CN at
$0\farcs 33\times 0\farcs 35$ (Carroll, 2018) yield similar temperature values
as what we see in our 0$\farcs$9 data. These values are also similar to the
temperature measurements in our 0$\farcs$2 data cube except at the very center
of the Hot Core over an area presumably resolved out in the larger beam.

##  5 Physical Properties

The (sub)mm continuum of Orion KL is mostly dominated by thermal dust emission
(e.g., Masson et al., 1985; Wright & Vogel, 1985; Wright & Plambeck, 2017);
however, some regions—namely Source I—may have significant contributions from
free-free emission (Beuther et al., 2006). It is well-established that the Hot
Core region is denser than the Compact Ridge, and this is evident by the
greater thermal dust emission toward the Hot Core in our continuum images as
well, as seen in Figure 6. The velocity maps derived here, consistent with
previous results, show that the Hot Core and Source I regions have a lower LSR
velocity than the Compact Ridge, one that is blue shifted with respect to the
large scale molecular cloud complex, perhaps showing a profile resulting from
the recent Orion KL explosive event.

The top left panel of each set of Figures 7-10 show the velocity fields
derived from ^13CH3OH $\nu=0$ and CH3CN $\nu_{8}=1$ line emission. The
velocity fields for each tracer were derived from the frequency offset in the
pixel-by-pixel fits of the lines. Deriving the velocity offsets from a fixed
frequency offset results in only a modest level of uncertainty because of
Orion KL’s low $V_{LSR}$, the high frequency of these observations, and the
close proximity of the included lines (Table 1): within 0.6 GHz for ^13CH3OH
and 0.1 GHz for CH3CN. This adds negligible uncertainty ($\ll 1\%$) to the
derived frequency offsets. This is confirmed by consistently low velocity
uncertainties: the uncertainty on these measurements is ${\leq}3.5\%$, except
for a few regions in the 0$\farcs$2 CH3CN map, in which some regions near the
edges of the emission region have uncertainties as high as $\sim$8%.
Generally, the uncertainty is ${<}0.5$% in all maps, and places with higher
uncertainties often occur at the edges of emission regions and thus may be the
result of the flux dropping off, giving rise to weak or noisy lines.

The velocity gradients mapped by ^13CH3OH in this work agree well with past
methanol observations, as summarized in Table 2. In brief, our derived
velocity field in the Compact Ridge spans $\sim$7-9 km s-1, and previous
measurements have yielded an LSR velocity of $7.6{-}8.6$ km s-1.

Table 2: Velocity profiles traced by molecular emission in Orion KL. Molecule | $V_{LSR}$ | Reference
---|---|---
(km s-1)
Compact Ridge
^13CH3OH | ${\sim}7{-}9$ | This work
^13CH3OH | 7.8 | Crockett et al. (2014b)
CH3OH | 8.6 | Wang et al. (2011)
CH3OH | 7.6 | Wilson et al. (1989)
Hot Core
^13CH3OH | ${\sim}6$ | This work
^13CH3OH | 7.5 | Crockett et al. (2014b)
CH3OH | $6{-}9$ | Wang et al. (2011)
CH3OH | ${\sim}7$ | Wilson et al. (1989)
CH3CN $\nu_{8}=1$ | ${\sim}6{-}8$ | This work
CH3CN $\nu_{8}=1$ | $6{-}9$ | Wang et al. (2011)

Our derived velocity toward the Hot Core region is slightly lower at $\sim$6
km s-1 in the ^13CH3OH images. Likewise, the LSR velocity derived from CH3CN
$\nu_{8}=1$ spans $\sim$6-8 km s-1, which agrees with Wang et al. (2011), who
report a $V_{LSR}$ of 6-9 km s-1 toward the Hot Core.

The velocity field provides insight into the physical structure of Orion KL at
spatial scales of ${\leq}350$ au. Specifically, we find possible evidence of a
molecular outflow in the Hot Core and a velocity gradient in the Hot Core-SW.

###  5.1 Hot Core

In our CH3CN 0$\farcs$2 velocity map, the Hot Core mm/submm emission peak
(alternatively designated SMM3 by Zapata et al., 2011) is characterized by a
radial velocity gradient that runs from $\sim$5 km s-1 (the LSR velocity of
Source I) around the edge of its signature heart shape to values closer to 7-8
km s-1to both the north and south of Source I. This velocity gradient is
centered about 0.45″ to the south of the Hot Core’s 865 $\mu$m emission peak,
as seen by the light orange region near the center of Figure 11. This
contrasts with the location of the peak excitation temperature and column
density of CH3CN, which are centered approximately at the location of the 865
$\mu$m emission peak. Opposite the Hot Core mm/submm peak, to the north, the
velocity approaches $\sim$8 km s-1.

Restated in terms of 3-D structure, the velocity field in the north is close
to the systemic velocity of Orion KL (9 km s-1, e.g., Hall et al., 1978) but
becomes more blue-shifted for the emission to the south associated with the
Hot Core and Source I. With increasing blue shift, the velocity width also
increases, as is seen in the top right panel of Figure 7. The combination of
the relative blue shift of the gas and the broader line widths may indicate
that this dense gas is being pushed away from the putative explosive event.
Areas throughout the Hot Core and Source I region where the velocity is closer
to the systemic velocity, then, may be acting as a buffer to slow the gas,
whereas a lower LSR velocity shows where that gas is pushed outward with fewer
obstacles.

Figure 11: The same as the $V_{LSR}$ (top left) panel of Figure 7 but with a
close-up view of the Hot Core region. The red cross shows the mm/submm
emission peak, and the red star denotes Source I. Contours show the 2 mm
($\sim$150 GHz) continuum from the left panel of Figure 6.

Another explanation for the elongated velocity structure is that it may be the
result of a low-velocity outflow emanating from a source east of Source I.
Goddi et al. (2011) detect a similar elongated velocity structure toward IRc7
in Expanded Very Large Array (EVLA) observations of high-excitation NH3 lines
in a 0$\farcs$8 beam. They conclude that the elongated velocity structure,
coupled with line-width enlargements, is evidence of a low-velocity outflow.
As seen in the bottom right panel of Figure 7, CH3CN $\nu_{8}=1$ has narrower
line widths ($\sim$ 1.5 km s-1) at the location of the Hot Core mm/submm peak,
but broader lines ($\sim$3 km s-1) in the region surrounding the peak. The
fact that the mm/submm peak is co-spatial with a region of relatively narrow
line widths and peaks in CH3CN excitation temperature and column density but
the elongated velocity structures are co-spatial with broader lines supports
the conclusion that the elongated velocity structure to the north and south of
this mm/submm peak is the result of a low-velocity outflow.

###  5.2 SMA1

SMA1 is a submillimeter source first identified by Beuther et al. (2004) at
346 GHz (865 $\mu$m). It has since been observed to have a 3 mm emission peak
and a HCOOCH3 emission peak (Friedel & Widicus Weaver, 2011; Favre et al.,
2011). Beuther & Nissen (2008) suggest that SMA1 hosts the driving source of
the high-velocity outflow that runs northwest-southeast in Orion KL, but the
nature of this object otherwise remains not well-understood.

The structure surrounding SMA1 is particularly dynamic in our images. The
velocity fields derived from the CH3CN $\nu_{8}=1$ emission line at both
0$\farcs$2 and 0$\farcs$9 angular resolution show a gradient that seems to
emanate from just southeast of the SMA1 submm emission center. As seen in
edit1Figure 7, the velocity peaks at around 8 km s-1. The velocity gradient
decreases gradually moving to the southeast (seen in the 0$\farcs$2 map only)
and northwest but changes abruptly in the orthogonal direction. This agrees
with previous conclusions that SMA1 is the location of a driver of the
northwest-southeast outflow.

###  5.3 Hot Core-SW

The Hot Core-SW, the region to the southwest of the Hot Core and east of the
Compact Ridge, is distinct from, but shares characteristics with, both the Hot
Core and the Compact Ridge. The velocity fields in this region, traced by
^13CH3OH, show a gradient from lower LSR velocity toward SMA1 ($\sim$6.5 km
s-1) to higher velocities ($\sim$7.8 km s-1) toward the south near the Compact
Ridge. This gradient can be explained by the interaction between gas emanating
from the center of the explosion northwest of Source I with the clumps
distributed throughout the nebula. As the gas travels away from the explosion
center toward the east and south, it first interacts with the denser Hot Core
and Source I regions, which act as a buffer to slow the gas. Toward the
Compact Ridge in the south, there is less dust to act as a buffer, allowing
the gas to pass through more easily and thus become more blue-shifted.

In this sense, the Hot Core-SW region is like the Hot Core and Source I in
that it is denser than the Compact Ridge. Moreover, the Hot Core-SW contains
higher column densities of ^13CH3OH than the Compact Ridge, a characteristic
that is evident in both the 0$\farcs$3 and 0$\farcs$7 maps. This region also
has higher excitation temperatures than the Compact Ridge.

It is curious, then, that the Hot Core-SW region is not traced by nitrogen-
bearing compounds, which is evident here from the lack of CH3CN $\nu_{8}=1$
emission and from previous observations (e.g., Friedel & Snyder, 2008).
Despite having velocity, density, and temperature profiles more akin to the
Hot Core region, the Hot Core-SW region appears to be more chemically similar
to the Compact Ridge.

Previous interferometric observations show strong emission in the Hot Core-SW
from the oxygen-bearing species dimethyl ether ((CH3)2O, CARMA, Friedel &
Snyder, 2008) and methyl formate (HCOOCH3, IRAM PdBI, Favre et al., 2011).
Friedel & Snyder (2008) also found acetone ((CH3)2CO) emission toward the Hot
Core-SW, part of which overlaps with ethyl cyanide (C2H5CN) emission near SMA1
and C22 in the north. In their observations, (CH3)2CO was detected only toward
the Hot Core-SW and IRc7, both of which have overlapping oxygen- and nitrogen-
bearing chemistry. Subsequent observations of (CH3)2CO show that this molecule
is much more extended than reported by Friedel & Snyder and that it is an
oxygen-bearing species that has a distribution similar to that of large
nitrogen-bearing molecules (Peng et al., 2013).

It would appear, then, that the Hot Core-SW is a hybrid of the Hot Core and
Compact Ridge regions, and thus the Hot Core-SW presents itself as a possible
location for bridging the oxygen-bearing chemistry of the less dense, colder
Compact Ridge and the nitrogen-bearing chemistry of the denser, warmer Hot
Core region. Sutton et al. (1995) suggest that the chemical differentiation
between the Hot Core and Compact regions is not so stark as originally thought
and that the chemical emission from both nitrogen-bearing and oxygen-bearing
species is spatially extended. Nevertheless, such chemical differentiation has
also been observed in other sources, such as the ultracompact H II region
W3(OH) (Wyrowski et al., 1997), the high-mass protostar AGAL 328.25 (Csengeri
et al., 2019), and cluster-forming clumps in NGC 2264 (Taniguchi et al.,
2020). In a sample of seven high-mass protostars, Bisschop et al. (2007) found
that complex organics could be classified as either cold ($<$100 K) or hot
($>$100 K) based on their rotation temperatures, and that nitrogen-bearing
species were exclusively “hot” molecules whereas different oxygen-bearing
species were found in both categories. Fayolle et al. (2015) found chemical
differentiation in a sample of three massive young stellar objects (YSOs); in
their sample, CH3CN and CH3OCH3 originated from the central cores, CH3CHO and
CH3CCH emission came from the extended envelope, and CH3OH (and sometimes HNCO
straddled both regimes. While the origin(s) of this chemical differentiation
are not well understood, it may may be influenced by the precursor content
(e.g., H2O, NH3, CH4) in icy grain mantles (e.g., Fayolle et al., 2015) and
prestellar core evolutionary time-scales (e.g., Laas et al., 2011; Sakai &
Yamamoto, 2013). In Orion KL, this may translate to a scenario in which, on
large spatial scales, the Hot Core-SW is analogous to the region between an
embedded YSO core and its extended envelope, which would begin to explain the
observed distribution of ^13CH3OH in this work and (CH3)2CO by Friedel &
Snyder (2008). However, a better understanding of complex organic
formation—and of the initial conditions in Orion KL before the putative
explosive event—is likely needed to explain the observed chemical and physical
patterns.

##  6 Thermal Structure

In considering the thermal structure of Orion KL, we assume local
thermodynamic equilibrium (LTE, see Appendix A) and that the kinetic
temperature in the nebula is approximated by the excitation temperature of the
molecular gas due to the nebula’s high density. The derived temperature maps
for ^13CH3OH $\nu=0$ and CH3CN $\nu_{8}=1$ are shown in the middle right
panels of each group of plots in Figures 7 and 10, respectively. Because we
have temperature maps on two different angular scales, we can get information
about possible sources of heating throughout the nebula. In particular, the
higher angular resolution ($\sim$0$\farcs$2$-$0$\farcs$3) images probe spatial
scales on the order of $\sim$78$-$116 au, which is within the protostellar
radius of 150 au where the gas-phase chemistry is expected to be driven by
thermal submlimation from the young stellar object (e.g., Schöier et al.,
2002). Conversely, the tapered angular resolution
($\sim$0$\farcs$7$-$0$\farcs$9) images correspond to spatial resolutions of
$\sim$272$-$350 au, which is greater than the typical radius of a protostellar
core. That is, our angular resolutions enable us to look at possible heating
sources on scales that straddle the boundary of whether thermal sublimation is
expected to be driven by an embedded protostar.

We consider possible sources of heating in Orion KL by mapping the difference
between the excitation temperatures derived in a larger versus smaller beam.
That is, we subtract the excitation temperature derived within the smaller
beam $T_{ex,S}$ from that derived within the larger beam $T_{ex,L}$ to give
$\Delta T_{ex}=T_{ex,L}-T_{ex,S}$ at each pixel. It follows then that $\Delta
T_{ex}>0$ suggests an external source of heating whereas $\Delta T_{ex}<0$
suggests an internal source of heating. In other words, $\Delta T_{ex}<0$
indicates that the warmer temperature, potentially from a compact heating
source, measured in a smaller beam is diluted by colder temperatures in the
more extended larger beam. Similarly, $\Delta T_{ex}>0$ indicates that a
colder region detected in a smaller beam is in the presence of nearby warmer
gas.

We note that whether the sign of $\Delta T_{ex}$ accurately reflects the
source of heating depends on the assumed source radius and proximity to the
source peak. As such, we ran simple Gaussian temperature distribution models
for externally and internally heated material with approximate temperatures
and radii of sources described in this section. In these toy models, briefly
described in Appendix C, the sign of $\Delta T_{ex}$ consistently reflected
whether a modeled compact source was internally or externally heated.
Furthermore, we note that, as mentioned in Section 2.2, we recover about the
same amount of ^13CH3OH flux in both the full and tapered image cubes,
indicating that $\Delta T_{ex}$ is not affected by flux recovery in the
0$\farcs$3 and 0$\farcs$7 synthesized beams.

The resulting maps for $\Delta T_{ex}$ are presented in Figures 12 and 13 for
^13CH3OH and CH3CN $\nu_{8}=1$, respectively. In these maps, regions where
$\Delta T_{ex}>0$, indicative of an external source of heating, are shaded
red. Regions where $\Delta T_{ex}<0$, indicative of a possible internal
heating source, are shaded blue.

Figure 12: Maps showing $\Delta T_{ex}=T_{ex,0\farcs 7}-T_{ex,0\farcs 3}$,
i.e., the difference between the derived excitation temperature from a
0$\farcs$7 and 0$\farcs$3 beam for ^13CH3OH. From left to right, the panels
show $\Delta T_{ex}-\sigma$, $\Delta T_{ex}$, and $\Delta T_{ex}+\sigma$ where
$\sigma$ is the propagated uncertainty. Red represents an external source of
heating, and blue represents internal heating. Contours show the 2 mm
($\sim$150 GHz) continuum. Figure 13: Maps showing $\Delta
T_{ex}=T_{ex,0\farcs 9}-T_{ex,0\farcs 2}$, i.e., the difference between the
derived excitation temperature from a 0$\farcs$9 and 0$\farcs$2 beam, for
CH3CN $\nu_{8}=1$. From left to right, the panels show $\Delta T_{ex}-\sigma$,
$\Delta T_{ex}$, and $\Delta T_{ex}+\sigma$ where $\sigma$ is the propagated
uncertainty. Red represents a possible external source of heating, and blue
represents possible internal heating. Contours show the 2 mm ($\sim$150 GHz)
continuum.

###  6.1 Hot Core

Our analyses suggest possible internal sources of heating in the Hot Core. As
seen in Figure 13, $\Delta T_{ex}<0$ at the mm/submm emission peak of the Hot
Core. We also see ^13CH3OH in the 0$\farcs$3 images only and not in the
0$\farcs$7 images, implying a highly compact methanol source, which would also
be consistent with an internally heated core. This, along with a possibility
of a low-velocity outflow, as discussed in Section 5.1, matches the profile of
an embedded young star.

Sources of heating in the Hot Core region of Orion KL remain the topic of
ongoing debate. In a more general sense, the term “hot core” describes a
compact, molecule-rich region with temperatures between 100 and 300 K
resulting from the warm-up of young massive stars (e.g., Evans, 1999; Kurtz et
al., 2000; Herbst & van Dishoeck, 2009). Moreover, the nearly two dozen hot
cores presented in the literature typically are characterized as being
internally heated by embedded massive stars (Hernández-Hernández et al., 2014;
Fayolle et al., 2015). However, there have been a couple of hot molecular
cores—namely the Orion KL Hot Core and G34.26$+$0.15 (Mookerjea et al.,
2007)—for which definitive evidence of an embedded heating source has eluded
observations. Despite the expectation that a region of hot molecular gas would
have an internal source of heating, the source of heating in Orion KL’s Hot
Core region is currently unknown.

The so-called Hot Core was first identified by Ho et al. (1979), who observed
it as a compact source of hot NH3 emission. Blake et al. (1996) found no
evidence for a (strong) source of internal heating there, and since then,
there have been multiple studies that support an externally-heated “hot core”
(e.g. Goddi et al., 2011; Zapata et al., 2011; Bally et al., 2017; Orozco-
Aguilera et al., 2017; Peng et al., 2017). Zapata et al. (2011), for example,
favor an externally heated Hot Core model (SMM3 in their work) because they do
not find hot molecular gas emission associated with self-luminous
submillimeter, radio, or infrared sources. Furthermore, they find that hot
HC3N gas seems to form a shell around the northeastern edge of the Hot Core,
which suggests the Hot Core is illuminated from the edges—that is, externally
heated, specifically by shockwaves.

Alternatively, Kaufman et al. (1998) show that large, warm columns of
molecular gas are more easily produced in internally heated cores. They
conclude that, while Source I may externally heat some of the material in the
area surrounding the Hot Core, there are likely young embedded star(s) heating
the core. de Vicente et al. (2002) further suggest that the Hot Core is
internally heated by an embedded massive star obscured by an edge-on disk.
Their speculation is based on vibrationally excited HC3N observed in the Hot
Core at energy levels that would require a heating source with too large a
luminosity to come from nearby external sources. Furthermore, Crockett et al.
(2014a) conclude that H2S emission, which is pumped by far-IR radiation, in
the Hot Core region signals the presence of a hidden source of luminosity.
Another hybrid hypothesis is that the Hot Core might have been a typical hot
core around Source I prior to Orion’s explosive event, and that, as a result
of this, even the dense gas of the Hot Core were spatially separated from the
protostars, especially Source I (Nickerson et al., 2021), giving us the
enigmatic molecular core we observe today.

We stress that our evidence in support of an internal heating source does not
preclude external heating in the Hot Core. Other studies that have looked at
whether the Hot Core is externally or internally heated have made use of a
range of angular resolutions. For example, Zapata et al. used Submillimeter
Array (SMA) observations with an angular resolution of
3$\farcs$28$\times$3$\farcs$12, which corresponds to spatial scales of $>$1200
au in Orion KL. They suggest that external heating of the Hot Core comes from
energetic shocks from the Orion KL explosion that are now passing through the
Hot Core region. Goddi et al. (2011) drew similar conclusions but with EVLA
observations at sub-arcsecond angular resolutions.

Heating from a combination of shocks and embedded young stars may explain the
line width profiles observed for CH3CN $\nu_{8}=1$. At 0$\farcs$2 angular
resolution, the CH3CN $\nu_{8}=1$ line widths are narrower, with $\Delta V\sim
1.5$ km s-1, at the mm/submm Hot Core peak and are surrounded by CH3CN
$\nu_{8}=1$ emission marked by slightly broader lines of $\Delta V\sim 2.0$ km
s-1. While this is only a modest difference, the fact that the line width
field is not uniform, specifically at the mm/submm peak, and that shocked
material is marked by broader line widths are evidence that the conditions at
this site are distinct from the surrounding region.

Crockett et al. (2014b) demonstrate that, relative to other components, the
Hot Core is the most heterogeneous thermal structure in Orion KL given the
spread of excitation temperatures derived for a spread of cyanides, sulphur-
bearing molecules, and oxygen-bearing complex organics. Therefore, it is
likely that the Hot Core region is heated by a multitude of sources, both
internally and externally. Based on mass estimates of $1001\pm 791\;M_{\odot}$
(Pattle et al., 2017) and a 10% star formation efficiency combined with a mean
stellar mass of ${\sim}2\;M_{\odot}$ (Hillenbrand & Hartmann, 1998), the Orion
KL/BN region could be expected to have enough mass to form $50\pm 40$ stars.
In other words, Orion is a dense protostellar cluster in which additional
protostellar sources beyond Source I are expected. Further observations are
needed to confirm whether there is, in fact, an embedded massive star at the
Hot Core site as predicted by and supported by our analyses.

###  6.2 Compact Ridge

Figure 12 shows that the Compact Ridge, as traced by ^13CH3OH emission, is
externally heated. This conclusion agrees with past studies of ground-state
methanol in Orion KL . The derived excitation temperature for a HCOOCH3
emission peak in the Compact Ridge—denoted by the teal diamond labeled ‘MF1’
in Figure 12—was also measured to be higher in a larger beam than in a smaller
one (Favre et al., 2011).

###  6.3 Hot Core-SW

As discussed in Section 5.3, the region southwest of the Hot Core is
interesting because it seems to exhibit, broadly speaking, the physical
parameters of the Hot Core but the chemical composition of the Compact Ridge.
The thermal structure of this region is also interesting because of its
heterogeneity.

The average ^13CH3OH excitation temperature in the Hot Core-SW (i.e., the mean
derived $T_{ex}$ across all pixels in the range of $\alpha_{\mbox{\scriptsize
J2000}}=05$${}^{\mbox{\scriptsize h}}$35${}^{\mbox{\scriptsize
m}}$14$\fs$21-14$\fs$64 and $\delta_{\mbox{\scriptsize J2000}}=-05\arcdeg
22\arcmin 32\arcsec{-}38\arcsec$ in the 0$\farcs$3 map) is 140 K, which agrees
with methanol excitation temperatures toward the Compact Ridge reported by
Crockett et al. (2014b). As seen in the full angular resolution ^13CH3OH
excitation temperature map, the Hot Core-SW exhibits pockets of higher
temperature, with some areas having temperatures as warm as $\sim$225 K. The
sizes of these pockets range from $\sim$0$\farcs$15 to $\sim$0$\farcs$50
across, which corresponds to approximately 60 and 200 au, respectively, at
Orion KL’s distance. Thus, the pockets have the same spatial scales as
embedded YSOs.

Furthermore, Figure 12 shows that the pockets of higher temperature align with
regions where $\Delta T_{ex}<0$. This suggests that there could be internal
sources of heating at these sites, and that these warm pockets could house
embedded YSOs which are heating the gas.

However, these pockets are irregularly shaped and do not have temperature
gradients resembling a localized “spot heating” effect, in which the gas
temperature decreases radially outward from the center of an embedded YSO
(e.g. van ’t Hoff et al., 2018, 2020). As such, we cannot definitively say
whether these anomalous temperature pockets in the Hot Core-SW can be
attributed to embedded sources of heating. Determining the nature of these
pockets may require detailed radiative transfer modeling or additional
continuum observations to complement the existing data sets.

One of these pockets is co-spatial with a strong HCOOCH3 emission peak,
reported as MF2 ($\alpha_{\mbox{\footnotesize
J2000}}=05$${}^{\mbox{\scriptsize h}}$35${}^{\mbox{\scriptsize m}}$14$\fs$44,
$\delta_{\mbox{\footnotesize J2000}}={-}05\arcdeg 22\arcmin 34\farcs 4$) by
Favre et al. (2011). Favre et al. report $T_{ex}\sim 130$ K in both a
1$\farcs$8$\times$0$\farcs$8 ($T_{ex}=128\pm 9$ K) and a
3$\farcs$6$\times$2$\farcs$2 ($140\pm 14$ K) beam. As such, their results at
this site do not agree with ours; however, their observations use larger beam
sizes than our analysis, which likely contributes to this discrepancy.

Like the Hot Core, the thermal structure of the Hot Core-SW region is likely
affected by a mix of internal and external heating sources. At 0$\farcs$7
angular resolution, we see high temperatures of $\sim$300 K typical of hot
cores adjacent to SMA1 and C22 and along the western edge of the Hot Core-SW.
This may show the edge of this region being heated by the shocks from the
Orion KL explosion propagating through the gas. This part of the Hot Core-SW
is also marked by $\Delta T_{ex}>0$, further supporting some source of
external heating.

###  6.4 IRc4

IRc4 is a compact emission region north of the Compact Ridge that is
associated with a high-density core on the order of $\sim$200-300 au (Hirota
et al., 2015). The heating source of IRc4 remains uncertain. Okumura et al.
(2011) propose that IRc4 is a simple, externally heated dust cloud, whereas de
Buizer et al. (2012) suggests that it is self-luminous.

The ^13CH3OH $\Delta T_{ex}$ profile is ambiguous toward IRc4. East of the
emission peak center, $\Delta T_{ex}<0$ K, including when accounting for
uncertainty, suggesting a source of internal heating. However, just west of
center, $\Delta T_{ex}>0$ within radii where simple Gaussian models of an
internally heated source predict $\Delta T_{ex}<0$ K. These ambiguous results
may indicate that IRc4 is indeed heated both internally close-in to the core
and externally everywhere else. However, dedicated follow-up observations are
necessary to confirm this hypothesis.

###  6.5 Northwest Clump

IRc6 is a mid-IR source toward the northwestern part of the Northwest Clump
(NWC). In our observations, we do not detect vibrationally excited CH3CN,
which traces material pumped by far-IR radiation from massive stars, toward
IRc6, and other studies have reported that there is no evidence of an embedded
young star there (e.g. Shuping et al., 2004).

Curiously, we find $\Delta T_{ex}<0$ K from the ^13CH3OH temperature measured
toward IRc6. This signals that there is perhaps a source of internal heating
in this region. Further evidence in support of IRc6 being internally heated
can be seen in the ^13CH3OH excitation temperature maps, particularly the
tapered angular resolution map (Figure 10). The Northwest Clump exhibits a
radial temperature gradient from $\sim$95 K in the center to $\sim$65 K near
the edges of that region. This localized “spot heating” effect, in which the
gas temperature decreases radially outward from the center of an embedded
young stellar object, has been observed toward the warm embedded disk in L1527
(van ’t Hoff et al., 2018) and the deeply embedded protostellar binary IRAS
16293-2422 (van ’t Hoff et al., 2020). If there is, in fact, an internal
heating source in the Northwest Clump, it likely does not play a dominant role
in the thermal profile of the region (Li et al., 2020).

##  7 Summary

We have used ground-state ^13CH3OH and vibrationally-excited CH3CN emission in
ALMA Band 4 from Cycles 4 and 5 observations to map the velocity and thermal
structure of Orion KL at angular resolutions of ${\sim}0\farcs 2{-}0\farcs 3$
and ${\sim}0\farcs 7{-}0\farcs 9$. Overall, our results agree with the
previous work at lower angular resolutions (e.g., by Wang et al., 2011;
Friedel & Widicus Weaver, 2011; Feng et al., 2015). The angular resolution
employed in this work probes spatial scales ${\leq}350$ au in Orion KL, giving
us a more localized look at the nebula’s physical structure, specifically that
induced by YSOs.

  1. 1.

We find evidence of possible sources of internal heating in the Hot Core. The
velocity field exhibits an elongated structure centered on the Hot Core
mm/submm emission peak. This elongated structure may be a low-velocity outflow
with an LSR velocity of $\sim 7{-}8$ km s-1, which is slightly higher than the
ambient velocity ($V_{LSR}\sim 5$ km s-1) of the Hot Core region. Furthermore,
the derived CH3CN $\nu_{8}=1$ excitation temperature in the Hot Core is higher
in a smaller beam than in a larger beam, suggesting an internal heating
source. The thermal profile and apparent outflow structure emanating from the
Hot Core may be evidence of an embedded protostar in the Hot Core.

  2. 2.

The Hot Core-SW appears to have an exceptionally heterogeneous thermal
structure. The average excitation temperature in the region is 140 K, and
there are pockets of higher temperature as much as 225 K throughout. These
pockets have higher temperatures in a smaller beam versus a larger beam,
suggesting that they are internally heated. However, these pockets are not
associated with compact mm/submm emission sources. The Hot Core-SW is also
externally heated on the northeastern edge, presumably by the Orion KL
explosion that took place about 500 years ago northwest of Source I.

  3. 3.

The thermal structure of IRc6 in the Northwest Clump suggests that this region
has an internal heating source. Specifically, the temperature there is higher
in a smaller beam, and the excitation temperature profile decreases radially
from 95 K in the center to 65 K near the edges, resembling a spot heating
effect found in embedded YSOs elsewhere. If there is an internal source of
heating at IRc6, however, it does not play a dominant role in the Northwest
Clump.

As we uncover more about Orion KL, it is becoming increasingly apparent that
is a dynamic and heterogeneous region, and that each of its spatial components
is not accurately described by one set of parameters. Furthermore, identifying
the heating sources within Orion KL, and in particular the sources of internal
heating, are critical to better understanding the nebula and its chemistry.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.01149,
ADS/JAO.ALMA#2016.1.01019, and ADS/JAO.ALMA#2013.1.01034. ALMA is a
partnership of ESO (representing its member states), NSF (USA), and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Tawain), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio
Astronomy Observatory (NRAO) is a facility of the National Science Foundation
(NSF) operated under Associated Universities, Inc. (AUI). This research made
use of APLpy, an open-source plotting package for Python (Robitaille &
Bressert, 2012; Robitaille, 2019). This work has been supported by the NSF
Graduate Research Fellowship Program under Grant No. DGE-1144469 and NRAO
Student Observing Support under Award No. SOSPA6-014. OHW is additionally
supported by an ARCS Los Angeles Founder Chapter scholarship. GAB gratefully
acknowledges support from the NSF AAG (AST-1514918) and NASA Astrobiology
(NNX15AT33A) and Exoplanet Research (XRP, NNX16AB48G) programs. This work
benefited from discussions with Cam Buzard, Dana Anderson, Griffin Mead, Kyle
Virgil, and Sadie Dutton. The authors thank Susanna Widicus Weaver and the
anonymous referee for feedback on the prepared manuscript. OHW thanks Erica
Keller, Sarah Wood, and the NRAO North American ALMA Science Center (NAASC)
for their assistance with the data reduction. OHW also thanks the custodial
staff at Caltech, especially Cruz Martinez.

##  Appendix A Assuming optically thin lines at local thermodynamic
equilibrium

The ^13CH3OH $\nu=0$ and CH3CN $\nu_{8}=1$ transitions used in our analyses
should be well-described by a local thermodynamic equilibrium (LTE). A rough
collisional cross-section based on molecular geometry and van der Waals radii
(2.096 Å for ^13CH3OH and 2.408 Å for CH3CN, based on geometry optimization
conducted through density functional theory (DFT) with the B3LYP level of
theory and 6-31G basis set available in the Gaussian 16 computational
chemistry software program) give critical densities on the order of
$10^{4}{-}10^{5}$ cm-3 for both compounds. The reported densities toward Orion
KL are ${\geq}10^{5}$ cm-3, suggesting that an LTE assumption is appropriate
for these data. Moreover, LTE has been assumed in previous observations of
complex organics toward Orion KL due to the high density of Orion KL’s
substructures (e.g. Feng et al., 2015).

We assume optically thin lines at LTE following guidelines set forth by
Goldsmith & Langer (1999). They write the optical depth $\tau$ of a transition
as

$\tau=\frac{h}{\Delta V}N_{u}B_{ul}(e^{h\nu/kT}-1)$ (A1)

where $\Delta V$ is the full-width at half-maximum line width in velocity
units, $N_{u}$ is the column density in the upper state, $B_{ul}$ is the
Einstein B coefficient for the transition, $\nu$ is the frequency of the
transition, and $T$ is the excitation temperature for the molecule (Goldsmith
& Langer, 1999, Eqn. 6). This can be rewritten in terms of the Einstein A
coefficient, which is related to $B_{ul}$ by

$B_{ul}=\frac{A_{ul}c^{3}}{8\pi h\nu^{3}}.$ (A2)

Moreover, $N_{u}$ can be written in terms of the total column density
$N_{tot}$ as

$N_{u}=\frac{N_{tot}}{Q(T)}g_{u}e^{-E_{u}/T}$ (A3)

where $Q(T)$ is the excitation partition function, $g_{u}$ is the upper state
degeneracy, and $E_{u}$ is the energy level of the upper state (Goldsmith &
Langer, 1999, adapted from Eqn. 19). Substituting Eqns. A2 and A3 into Eqn.
A1, the optical depth can be expressed as

$\tau=\frac{g_{u}}{\Delta
V}\frac{N_{tot}}{Q(T)}\frac{A_{ul}c^{3}}{8\pi\nu^{3}}e^{-E_{u}/T}(e^{h\nu/kT}-1).$
(A4)

To test whether each transition of each molecular tracer is optically thin in
our data, we calculated $\tau$ at each transition using the constants from
Splatalogue listed in Table 1. For ^13CH3OH, we selected a spectrum extracted
from a single beam area near the center of the Compact Ridge, which has a
total column density $N_{tot}$ of $2.4\times 10^{16}$ cm-2, a temperature of
196 K, and line width of 1.2 km s-1; for CH3CN, we selected a spectrum
extracted from a single beam area near the center of the Hot Core, where
$\Delta V=2.9$ km s-1, $N_{tot}=3.9\times 10^{16}$ cm-2, and $T_{ex}=275K$.
All lines have $\tau\leq 0.02\ll 1$ thus are optically thin.

Furthermore, we ran $\chi^{2}$ tests as an additional check for whether the
LTE model is appropriate for the data presented in this work. The average
$\chi^{2}$ values for the ^13CH3OH fits are 1.02 and 1.85 for the 0$\farcs$3
and 0$\farcs$7 data, respectively. For CH3CN $\nu_{8}=1$, $\chi^{2}$ is 3.60
and 0.15 for the 0$\farcs$2 and 0$\farcs$9 maps, respectively. These are
slightly better than the $\chi^{2}$ calculations for these molecules by
Crockett et al. (2014b), who calculated 1.9 for ^13CH3OH and 4.0 for CH3CN
$\nu_{8}=1$.

##  Appendix B Uncertainty maps

Percent uncertainty maps were calculated from the derived LMFIT standard
errors. These maps are presented in Figures 14 and 15 for the full and tapered
angular resolution images, respectively.

Figure 14: Propagated percent error uncertainty maps for Figures 7 and 8,
showing uncertainties for full resolution (first row) CH3CN $\nu_{8}=1$
velocity field and line width field; (second row) CH3CN $\nu_{8}=1$ total
column density and excitation temperature; (third row) ^13CH3OH velocity field
and line width field; and (fourth row) ^13CH3OH total column density and
excitation temperature. Contours show the 2 mm ($\sim$150 GHz) continuum from
the left panel of Figure 6.

Figure 15: Propagated percent error uncertainty maps for Figures 9 and 10,
showing uncertainties for tapered resolution (first row) CH3CN $\nu_{8}=1$
velocity field and line width field; (second row) CH3CN $\nu_{8}=1$ total
column density and excitation temperature; (third row) ^13CH3OH velocity field
and line width field; and (fourth row) ^13CH3OH total column density and
excitation temperature. Contours show the 2 mm ($\sim$150 GHz) continuum from
the right panel of Figures 6.

##  Appendix C Internal versus external heating profile models

We ran simple models for different source sizes (with radii between 100 and
1000 au) and temperature gradients to test whether internally and externally
heated sources are consistently characterized by $\Delta T_{ex}<0$ and $\Delta
T_{ex}>0$, respectively. The models calculated the temperature inside a full
and tapered synthesized beam at various radii across 2-D Gaussian temperature
profiles (both circular and elliptical). The models were run assuming both a
smooth (unchanging) temperature background and a linear temperature gradient
background. In all models, the sign of $\Delta T_{ex}$ accurately reflected
whether a source of radius $r_{src}$ was internally or externally heated at
radii within $0.67r_{src}$ of the source center, with ‘higher contrast’ source
profiles (i.e., sources that have either much higher peak temperatures than
their surroundings or particularly steep temperature gradients) being more
likely to deviate from the predicted sign of $\Delta T_{ex}$ toward their
outer radii. Smaller sources (e.g., with radii of 100 au) consistently had
$\Delta T_{ex}$ values in agreement with their source of heating regardless of
temperature contrast. In other words, within 100 au or more of a source’s
center (e.g., mm emission peak), the $\Delta T_{ex}$ sign is expected to
accurately reflect whether that source is internally or externally heated. An
example of the simple models used to test the sign of $\Delta T_{ex}$ is shown
in Fig. C1.

Figure C1: Example of the simple models used to test the sign of $\Delta
T_{ex}$. These plots show the temperature $T_{ex}$ profile for an internally
(a) and an externally (b) heated source with a radius of 250 au. The value of
$\Delta T_{ex}$ (c) for each profile was measured at different radii from the
source center. Here, the plot shows $\Delta T_{ex}$ with a small beam of
0$\farcs$2 and a large beam of 0$\farcs$9 (same as that used in the CH3CN
$\nu_{8}=1$ images.)

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