# Early Planet Formation in Embedded Disks (eDisk) III: A first high-
resolution view of sub-mm continuum and molecular line emission toward the
Class 0 protostar L1527 IRS

Merel L.R. van ’t Hoff Department of Astronomy, University of Michigan, 1085
S. University Ave., Ann Arbor, MI 48109-1107, USA  John J. Tobin National
Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22903 USA
Zhi-Yun Li Department of Astronomy, University of Virginia, 530 McCormick Rd.,
Charlottesville, VA 22904, USA  Nagayoshi Ohashi Academia Sinica Institute of
Astronomy & Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU, No.1,
Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.  Jes K. Jørgensen Niels
Bohr Institute, University of Copenhagen, Øster Voldgade 5–7, 1350, Copenhagen
K, Denmark  Zhe-Yu Daniel Lin Department of Astronomy, University of Virginia,
530 McCormick Rd., Charlottesville, VA 22904, USA  Yuri Aikawa Department of
Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan  Yusuke Aso Korea Astronomy and Space Science
Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of Korea
Itziar de Gregorio-Monsalvo European Southern Observatory, Alonso de Cordova
3107, Casilla 19, Vitacura, Santiago, Chile  Sacha Gavino Niels Bohr
Institute, University of Copenhagen, Øster Voldgade 5–7, 1350, Copenhagen K,
Denmark  Ilseung Han Division of Astronomy and Space Science, University of
Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of
Korea  Korea Astronomy and Space Science Institute, 776 Daedeok-daero,
Yuseong-gu, Daejeon 34055, Republic of Korea  Patrick M. Koch Academia Sinica
Institute of Astronomy & Astrophysics, 11F of Astronomy-Mathematics Building,
AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.  Woojin Kwon
Department of Earth Science Education, Seoul National University, 1 Gwanak-ro,
Gwanak-gu, Seoul 08826, Republic of Korea  SNU Astronomy Research Center,
Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of
Korea  Chang Won Lee Division of Astronomy and Space Science, University of
Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of
Korea  Korea Astronomy and Space Science Institute, 776 Daedeok-daero,
Yuseong-gu, Daejeon 34055, Republic of Korea  Jeong-Eun Lee Department of
Physics and Astronomy, Seoul National University, 1 Gwanak-ro, Gwanak-gu,
Seoul 08826, Korea  Leslie W. Looney Department of Astronomy, University of
Illinois, 1002 West Green St, Urbana, IL 61801, USA  Suchitra Narayanan
Institute for Astronomy, University of Hawai‘i at Mānoa, 2680 Woodlawn Dr.,
Honolulu, HI 96822, USA  Adele Plunkett National Radio Astronomy Observatory,
520 Edgemont Rd., Charlottesville, VA 22903 USA  Jinshi Sai (Insa Choi)
Academia Sinica Institute of Astronomy & Astrophysics, 11F of Astronomy-
Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei 10617,
Taiwan, R.O.C.  Alejandro Santamaría-Miranda  European Southern Observatory,
Alonso de Cordova 3107, Casilla 19, Vitacura, Santiago, Chile  Rajeeb Sharma
Niels Bohr Institute, University of Copenhagen, Øster Voldgade 5–7, 1350,
Copenhagen K, Denmark  Patrick D. Sheehan National Radio Astronomy
Observatory, 520 Edgemont Rd., Charlottesville, VA 22903 USA  Shigehisa
Takakuwa Department of Physics and Astronomy, Graduate School of Science and
Engineering, Kagoshima University, 1-21-35 Korimoto, Kagoshima, Kagoshima
890-0065, Japan  Academia Sinica Institute of Astronomy & Astrophysics, 11F of
Astronomy-Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei
10617, Taiwan, R.O.C.  Travis J. Thieme Institute of Astronomy, National Tsing
Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan
Center for Informatics and Computation in Astronomy, National Tsing Hua
University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan
Department of Physics, National Tsing Hua University, No. 101, Section 2,
Kuang-Fu Road, Hsinchu 30013, Taiwan  Jonathan P. Williams Institute for
Astronomy, University of Hawai‘i at Mānoa, 2680 Woodlawn Dr., Honolulu, HI
96822, USA  Shih-Ping Lai Institute of Astronomy, National Tsing Hua
University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan  Center
for Informatics and Computation in Astronomy, National Tsing Hua University,
No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan  Department of
Physics, National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road,
Hsinchu 30013, Taiwan  Academia Sinica Institute of Astronomy & Astrophysics,
11F of Astronomy-Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd,
Taipei 10617, Taiwan, R.O.C.  Nguyen Thi Phuong Korea Astronomy and Space
Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of
Korea
Department of Astrophysics, Vietnam National Space Center, Vietnam Academy of
Science and Techonology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam  Hsi-Wei
Yen Academia Sinica Institute of Astronomy & Astrophysics, 11F of Astronomy-
Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei 10617,
Taiwan, R.O.C.

###### Abstract

Studying the physical and chemical conditions of young embedded disks is
crucial to constrain the initial conditions for planet formation. Here, we
present Atacama Large Millimeter/submillimeter Array (ALMA) observations of
dust continuum at $\sim$0$\farcs$06 (8 au) resolution and molecular line
emission at $\sim$0$\farcs$17 (24 au) resolution toward the Class 0 protostar
L1527 IRS from the Large Program eDisk (Early Planet Formation in Embedded
Disks). The continuum emission is smooth without substructures, but asymmetric
along both the major and minor axes of the disk as previously observed. The
detected lines of 12CO, 13CO, C18O, H2CO, c-C3H2, SO, SiO, and DCN trace
different components of the protostellar system, with a disk wind potentially
visible in 12CO. The 13CO brightness temperature and the H2CO line ratio
confirm that the disk is too warm for CO freeze out, with the snowline located
at $\sim$350 au in the envelope. Both molecules show potential evidence of a
temperature increase around the disk–envelope interface. SO seems to originate
predominantly in UV-irradiated regions such as the disk surface and the
outflow cavity walls rather than at the disk–envelope interface as previously
suggested. Finally, the continuum asymmetry along the minor axis is consistent
with the inclination derived from the large-scale (100′′ or 14,000 au)
outflow, but opposite to that based on the molecular jet and envelope
emission, suggesting a misalignment in the system. Overall, these results
highlight the importance of observing multiple molecular species in multiple
transitions to characterize the physical and chemical environment of young
disks.

,

##  1 Introduction

Planets form in disks around young stars, starting with the growth of dust
grains beyond interstellar medium sizes. Evidence for planet formation already
being underway when the disk is still embedded in its natal envelope has been
inferred from low dust opacity spectral indexes in Class 0 sources (Kwon et
al., 2009; Shirley et al., 2011), dust polarization (e.g., Kataoka et al.,
2015, 2016; Yang et al., 2016), decreasing dust masses derived from
(sub-)millimeter observations for more evolved systems (e.g., Williams et al.,
2019; Tychoniec et al., 2020), and the lack of CO isotopologue emission toward
the protostellar position due to grain growth in the Class I system TMC1A
(Harsono et al., 2018). In addition, rings in continuum emission, which could
be a signpost of forming planets (e.g., Bryden et al., 1999; Zhu et al., 2014;
Dong et al., 2018), are observed in disks as young as only $\sim$0.5 Myr (ALMA
Partnership et al., 2015; Segura-Cox et al., 2020; Sheehan et al., 2020).
Characterizing the physical and chemical conditions in young disks is thus
crucial in understanding disk evolution and planet formation.

L1527 IRS (also known as IRAS 04368+2557) is the first Class 0 source toward
which a Keplerian rotating disk was established (Tobin et al., 2012). This
low-mass protostar is located in the L1527 dark cloud in the Taurus star-
forming region and has been observed extensively from the near-infrared to
centimeter wavelengths. Based on Gaia Data Release 2 (DR2), Luhman (2018)
measured a distance of 139–141 pc for L1527, consistent with the analysis of
Gaia DR2 and very long baseline interferometry (VLBI) data by Galli et al.
(2019). Roccatagliata et al. (2020) group L1527 into the much larger Taurus B
region with an average distance of 131.0 $\pm$ 1.0 pc, but sources in L1527
have parallaxes closer to the lower end of the range for Taurus B ($\sim$6.95
mas, corresponding to 143.9 pc). We therefore adopt a distance of 140 pc,
which is also consistent with the distance used in earlier works by Kenyon et
al. (1994) and Zucker et al. (2019).

Table 1: Overview of molecular lines.

Species | Transition | Frequency |  $E_{\rm{up}}$ a |  $A_{ij}$ b |  $\Delta v$ c | RMS d | Velocity range e
---|---|---|---|---|---|---|---
|  | (GHz) | (K) | (s-1) | (km s-1) | (mJy beam-1) | (km s-1)
12CO | 2–1 | 230.538000 | 16.6 | 6.910$\times 10^{-7}$ | 0.635 | 0.95 |  $-$11.30 – $-$1.13, 0.77 – 9.04
13CO | 2–1 | 220.398684 | 15.9 | 5.066$\times 10^{-7}$ | 0.167 | 1.96 |  $-$4.38 – $-$0.21, 0.46 – 3.97
C18O | 2–1 | 219.560354 | 15.8 | 6.011$\times 10^{-7}$ | 0.167 | 1.49 |  $-$3.55 – 3.64
DCN | 3–2 | 217.238538 | 20.9 | 4.575$\times 10^{-4}$ | 1.340 | 0.55 |  $-$3.84 – 1.53 g
SO | 65–54 | 219.949442 | 35.0 | 1.335$\times 10^{-4}$ | 0.167 | 1.78 |  $-$4.05 – 3.30
SiO | 5–4 | 217.104980 | 31.3 | 5.196$\times 10^{-4}$ | 1.340 | 0.58 |  $-$13.45 – 1.30
H2CO | 30,3–20,2 | 218.222192 | 21.0 | 2.818$\times 10^{-4}$ | 1.340 | 0.51 |  $-$3.84 – 2.87
H2CO | 32,1–22,0 | 218.760066 | 68.1 | 1.577$\times 10^{-4}$ | 0.167 | 1.42 |  $-$3.05 – 3.14
H2CO | 32,2–22,1 | 218.475632 | 68.1 | 1.571$\times 10^{-4}$ | 1.340 | 0.48 |  $-$2.50 – 2.87
c-C3H2 | 60,6–51,5 f | 217.822148 | 38.6 | 5.396$\times 10^{-4}$ | 1.340 | 0.54 |  $-$1.16 – 1.53
c-C3H2 | 61,6–50,5 f | 217.822148 | 38.6 | 5.396$\times 10^{-4}$ | 1.340 | 0.54 |  $-$1.16 – 1.53
c-C3H2 | 51,4–42,3 | 217.940046 | 35.4 | 4.026$\times 10^{-4}$ | 1.340 | 0.52 |  $-$1.16 – 1.53
c-C3H2 | 52,4–41,3 | 218.160456 | 35.4 | 4.041$\times 10^{-4}$ | 1.340 | 0.50 |  $-$1.16 – 1.53
CH3OH | 42–31, E | 218.440063 | 45.6 | 4.686$\times 10^{-5}$ | 1.340 | 0.49 | –

aafootnotetext: Energy of the transition’s upper level.

bbfootnotetext: Einstein A coefficient of the transition.

ccfootnotetext: Velocity resolution of the observations.

ddfootnotetext: RMS level per channel in the data cubes imaged with a robust
parameter of 2.0, measured within a 10′′ region over five empty channels.

eefootnotetext: Velocity range over which emission is detected ($>3\sigma$)
with the system velocity of 5.9 km s-1 shifted to 0 km s-1 (Caselli et al.,
2002; Tobin et al., 2011).

fffootnotetext: These two transitions are blended.

ggfootnotetext: DCN is only detected at the 3–4$\sigma$ level.

L1527 IRS (hereafter L1527) is often classified as a borderline Class 0/I
object, as classification is challenging due to the edge-on orientation. Its
bolometric temperature and submillimeter luminosity to bolometric luminosity
ratio are typical of a Class 0 source, but at a lower inclination it would be
classified as a Class I object (Tobin et al., 2008). The large envelope mass
and extended outflow cavities suggest that L1527 is younger than typical Class
I sources, but it lacks the collimated outflow of typical Class 0 sources (see
e.g., the discussion in Tobin et al. 2013). Recent re-analysis of the spectral
energy distribution (SED) classified L1527 as a Class 0 source with a
bolometric luminosity of 1.3 $L_{\sun}$ and a bolometric temperature of 41 K
(Ohashi et al., 2022a).

Single-dish sub-millimeter observations of L1527 have identified a bipolar
outflow in 12CO emission with an orientation almost perfectly in the plane of
the sky (Tamura et al., 1996; Hogerheijde et al., 1998). Bright bipolar
scattered light nebulae extending $\sim$10,000 au along the east–west outflow
axis are visible in infrared observations with the Spitzer Space Telescope and
ground-based telescopes (Tobin et al., 2008, 2010), as well as in the recently
released JWST NIRCam image (release id 2022-055, PI: K.
Pontoppidan111https://webbtelescope.org/contents/news-releases/2022/news-
2022-055). The eastern outflow lobe harbors a compact ($\sim$1′′ long) radio
continuum jet close to the protostellar position at centimeter wavelengths
(Reipurth et al., 2004).

Ohashi et al. (1997) identified a flattened infalling and rotating envelope
with a radius of 2000 au from 6′′ resolution C18O observations. The presence
of a rotationally supported disk was initially inferred from 13CO observations
with the Combined Array for Millimeter-wave Astronomy (CARMA; Tobin et al.
2012) that also resolved the continuum at 0$\farcs$35 resolution, and was
later confirmed by observations with the Atacama Large Millimeter/sub-
millimeter Array (ALMA; Ohashi et al. 2014; Aso et al. 2017). High-resolution
(0$\farcs$15) continuum observations with ALMA have suggested that the disk is
warped with the inner and outer disk boundary between 40 and 60 au (Sakai et
al., 2019). Even higher resolution (0$\farcs$08) observations with the Karl G.
Jansky Very Large Array (VLA) initially revealed clumpy substructures in
$Q$-band (Nakatani et al., 2020), but these structures were not confirmed in
later observations with higher sensitivity (Sheehan et al., 2022).

Molecular line observations have shown that the disk is warm ($\gtrsim$ 20 K),
based on the presence of CO gas out to at least 75 au (van ’t Hoff et al.,
2018). The water snowline is suggested to be located between $\sim$2–4 au (van
’t Hoff et al., 2022), but only a tentative detection of a complex molecule
(methanol, CH3OH) in the inner disk has been reported (Sakai et al., 2014a;
van ’t Hoff et al., 2020). Observations by Sakai et al. (2014a, b) reveal
different morphologies and kinematics for several molecular species,
suggesting that they trace different components of the protostellar system. In
particular, SO seems to be enhanced in a ring at the disk-envelope interface
(see also Ohashi et al. 2014).

While L1527 has been studied at high resolution at multiple wavelengths in
continuum emission (0$\farcs$045 at cm wavelengths and 0$\farcs$08 at mm
wavelengths; Sheehan et al. 2022; Ohashi et al. 2022b, respectively),
molecular line observations have been limited to a resolution of
$\sim$0.3–0$\farcs$5\. Here, we present high angular resolution 1.3 mm
continuum (0$\farcs$06) and molecular line images (0$\farcs$17) obtained with
the ALMA Large Program eDisk (Early Planet Formation in Embedded Disks). The
molecular lines detected toward L1527 are 12CO, 13CO, C18O, H2CO, c-C3H2, SO,
SiO and DCN. A notable nondetection is CH3OH. The observations are described
in Sect. 2. The structure of the 1.3 mm continuum is presented in Sect. 3.1
and the morphology and spatial origin of the molecular lines in Sect. 3.2. The
system’s inclination is discussed in Sect. 4.1, a dynamical estimate of the
central mass is made in Sect. 4.2, and the temperature structure is described
in Sect. 4.3. In Sect. 4.4 we discuss the physical and chemical reasons behind
the different molecular distributions. Finally, our conclusions are summarized
in Sect. 5.

Figure 1: Overview of 1.3 mm continuum and line observations (integrated
intensity maps) toward L1527. For H2CO the $3_{0,3}-2_{0,2}$ transition is
shown, and for c-C3H2 the blended $6_{0,6}-5_{1,5}$ and $6_{1,6}-5_{0,5}$
transitions are shown. The images are centered on the source position (R.A. =
04:39:53.9, Dec. = +26:03:09.4). The spatial scale is the same in each panel,
with the white scale bar denoting 250 au. The size of the 12CO image is 24′′
$\times$ 24′′. All color scales are linear, start at zero, and are saturated
to highlight weaker, more extended emission. Intensity scales are shown in
Fig. 3. All images are made with a robust parameter of 2.0, and the beam size
is depicted in the lower left corner of each panel.

##  2 Observations

L1527 has been observed as part of the ALMA Large Program eDisk
(2019.1.00261.L; PI N. Ohashi) on 14 and 15 October 2022, sampling baselines
between 91 and 11,469 m. Observations in a more compact configuration with the
purpose of recovering larger spatial scales were carried out through a DDT
program (2019.A.00034.S; PI J. Tobin) on 3 December 2021, 16 December 2021 and
3 July 2022. These observations used baselines between 15 and 2617 m. The
correlator setup for both programs is centered around $\sim$225 GHz (1.3 mm)
and includes 2 low spectral resolution windows at 976.56 kHz (1.34 km s-1)
resolution, 1 spectral window at 488.28 kHz (0.635 km s-1) resolution, and 4
higher spectral resolution windows at 122.07 kHz (0.167 km s-1) resolution.
More details about the observations are provided by Ohashi et al. (subm.), and
an overview of the molecular lines discussed in this paper is provided in
Table 1.

Standard calibration of the data was done using the ALMA Pipeline and a script
developed for the eDisk Large Program, as described in Ohashi et al. (subm.)
was used for subsequent data reduction and imaging. In short, the continuum
emission peaks of all execution blocks were first aligned to a common phase
center after which an amplitude rescaling was applied to the shifted
visibilities. The amplitude calibration uncertainty is expected to be
$\sim$5–10%. Two rounds of continuum self-calibration were then performed on
the aggregate continuum data, first on the short-baseline data only and then
on the short- and long-baseline data combined. For L1527, phase and amplitude
self-calibration were performed on the short baseline data, while only phase
self-calibration was used for the combined data set. The final gain tables
were also applied to the line data.

Figure 2: ALMA 1.3 mm continuum image of L1527. The left panel shows the full
extent of the continuum imaged with a robust parameter of $-$0.5 (color scale;
beam size of 0$\farcs$056 $\times$ 0$\farcs$029, PA = 9.3∘), with the solid
white contour marking the 5$\sigma$ level (0.15 mJy beam-1). The dotted white
contour marks the 5$\sigma$ level (0.11 mJy beam-1) of the map imaged with a
robust parameter of 2.0 (beam size of 0$\farcs$123 $\times$ 0$\farcs$111, PA =
-13.7∘). The white cross marks the source position derived from a Gaussian fit
in the image plane (R.A. = 04:39:53.9, Dec. = +26:03:09.4). The black dashed
square shows the region depicted in the top middle panel, where the brightness
temperature of the continuum is displayed. The top right panel shows the
normalized intensity along the disk minor axis at source position (orange
curve) and at 10 au to the north (top black curve) and south (bottom black
curve). The bottom right panel shows the normalized intensity along the disk
major axis at source position (orange curve) and at 3 au to the east (left
black curve) and west (right black curve). Black and orange triangles in the
continuum image (top middle panel) mark the locations of the intensity
profiles. The black curves are shifted by 0.2 in intensity scale with respect
to the orange curves for better visibility. The shaded region depicts the
3$\sigma$ level and the dotted lines are the mirror images of the solid lines
to highlight the asymmetries.

The standard eDisk image products were created with tclean using a range of
robust parameters ($-$2.0, $-$1.0, $-$0.5, 0.0, 0.5, 1.0 and 2.0) for the
continuum and robust = 0.5 for the line images. For L1527, line images were
also created with a robust value of 2.0 to increase the signal-to-noise ratio,
and those images are presented here. The resulting beam size for the line
images is approximately 0$\farcs$17 $\times$ 0$\farcs$14 (PA = -20∘), and the
noise levels for the different line cubes are listed in Table 1. Unless noted
otherwise, we present the continuum image created with a robust value of
$-$0.5 as a compromise between resolution and sensitivity. This image has a
resolution of 0$\farcs$056 $\times$ 0$\farcs$029 (PA = 9.3∘), and an rms of 29
$\mu$Jy beam-1. The full range of continuum images is presented in Fig. 17. An
overview of the continuum and molecular line observations toward L1527 is
presented in Fig. 1.

Figure 3: Overview of molecular lines detected toward L1527, shown on scales
of the disk and inner envelope. The first and fourth column present integrated
intensity (moment zero) maps (in mJy beam-1 km s-1), the second and fifth
column present peak intensity (moment eight) maps (in mJy beam-1), and the
third and sixth column present velocity maps made with bettermoments (in km
s-1, centered at the systemic velocity of 5.9 km s-1). The velocity map is
only showing pixels above the $>3\sigma$ level of the moment zero map. The
molecular line is indicated above the panels, and the beam is depicted in the
lower left corner of each panel.

##  3 Results

###  3.1 Continuum

The 1.3 mm continuum image of L1527 obtained with a robust parameter of $-$0.5
is shown in Fig. 2, and a gallery of images made with different robust
parameters is presented in Fig. 17. The continuum image displays an edge-on
disk with the major axis along the north–south direction, as previously
observed (e.g., Ohashi et al., 1997; Loinard et al., 2002; Tobin et al., 2008,
2010, 2012, 2013; Sakai et al., 2014b; Aso et al., 2017; Nakatani et al.,
2020; Ohashi et al., 2022b; Sheehan et al., 2022). The flared nature of the
disk inferred by radiative transfer modeling of multi-wavelength continuum
emission (Tobin et al., 2013) is now clearly visible at this high resolution.
The emission extends out to a radius of $\sim$0$\farcs$5 (70 au) along the
major axis, and in the east–west direction to $\sim$0$\farcs$1 (14 au) above
the midplane near the source position and up to $\sim$0$\farcs$2 (28 au) at a
radial offset of $\sim$0$\farcs$3 (42 au). Fainter emission extending out to a
radius of $\sim$1′′ (140 au) and to $\sim$0$\farcs$5 (70 au) above the
midplane is visible in the image obtained with a robust parameter of 2.0. This
is most likely due to more faint envelope emission being picked up by the
higher sensitivity of the robust = 2.0 image, because the vertical extent of
the bright central region is not much more extended (Fig. 17). The brightness
temperature for the majority of the disk is 40–60 K (for a robust parameter of
$-$0.5), suggesting that the continuum may be optically thick.

The continuum emission appears smooth with no sign of substructures. However,
an asymmetry between the north and south side, with the south side being
brighter than the north side, is visible for all robust parameters (see radial
cuts for a robust value of $-$0.5 in Fig. 2). At the highest resolutions
(robust values $\leq$ 0.0 or beam sizes of 0$\farcs$062$\times$0$\farcs$038
and smaller), an asymmetry between the east and west side becomes also clear,
with the east side being brighter than the west side. The north–south
asymmetry is then also more pronounced in the east. The east–west asymmetry is
stronger in the south but visible along the entire major axis. The difference
in maximum brightness temperature between the southeast and the northeast or
southwest is about 10 K.

Because of the flared nature of the disk, a simple 2D Gaussian fit does not
represent the emission morphology and total flux density. Therefore, we sum
over all pixels with values $>3\sigma$, which yields a flux density of 192.57
$\pm$ 0.05 mJy (compared to 139.04 $\pm$ 0.73 mJy from the Gaussian fit). This
is only 9% higher than the 1.3 mm flux reported by Aso et al. (2017) obtained
within a 4′′ $\times$ 4′′ box from 0$\farcs$47 $\times$ 0$\farcs$37 resolution
observations. Using a similar aperture, we obtain a slightly lower flux
density of 188.78 mJy, which is within 7% of the previously reported value.

For isothermal and optically thin emission, the continuum flux density,
$S_{\nu}$, can be converted into a dust mass using

$M_{\rm{dust}}=\frac{D^{2}S_{\nu}}{\kappa_{\nu}B_{\nu}(T_{\rm{dust}})},$ (1)

where $D$ is the distance (140 pc), $\kappa_{\nu}$ the dust opacity at the
observed frequency, and $B_{\nu}(T_{\rm{dust}})$ the Planck function at the
observed frequency for a dust temperature of $T_{\rm{dust}}$. We adopt a dust
opacity of 2.3 cm2 g-1 at the observed frequency of 225 GHz (Beckwith et al.,
1990), and an average temperature of $T=43\,(L/L_{\sun})^{0.25}$ K = 46 K
(with $L$ = 1.3 $L_{\sun}$; Ohashi et al. subm.), based on a suite of
radiative transfer models by Tobin et al. (2020). This results in a dust mass
of $\sim$41 $M_{\earth}$. Adopting a temperature of 20 K, as typically done
for Class II disks (e.g., Ansdell et al., 2016), results in a dust mass of
$\sim$112 $M_{\earth}$. For a gas-to-dust ratio of 100, the total disk mass is
then $\sim$0.01–0.03 $M_{\sun}$, consistent with previous estimates at
different wavelengths given different choices for temperature and dust opacity
(e.g. Tobin et al., 2013; Aso et al., 2017; Nakatani et al., 2020; Sheehan et
al., 2022). The here derived mass is a lower limit because the continuum
emission is likely optically thick.

Figure 4: Overview of CO isotopologue emission at scales larger than depicted
in Fig. 3. The first column presents integrated intensity (moment zero) maps
(in mJy beam-1 km s-1), the middle column presents peak intensity (moment
eight) maps (in mJy beam-1), and the right column presents velocity maps made
with bettermoments (in km s-1, centered at the systemic velocity of 5.9 km
s-1). The color scale of the moment zero and moment eight maps are capped to
highlight emission at large scales. The velocity map is only showing pixels
above the $>3\sigma$ level of the moment zero map. The beam is shown in the
bottom left corner of each panel. The white arrows in the 12CO peak intensity
map (top middle panel) highlight the kinks discussed in the main text (Sect.
3.2.1), and the black arrow in the 12CO velocity map marks the potential jet.

###  3.2 Molecular lines

An overview of all molecular lines detected towards L1527 is listed in Table 1
and presented in Fig. 3. In addition to moment zero maps (integrated
intensity), we show moment eight maps (peak intensity) and velocity maps
(similar to moment nine maps) created with the quadratic method of the
bettermoments package222https://github.com/richteague/bettermoments (Teague &
Foreman-Mackey, 2018). It is evident from Fig. 3 that each molecular species
and for H2CO, each transition, exhibits a different spatial and velocity
distribution. Each species and its spatial origin (e.g., outflow, envelope,
disk) is therefore discussed individually below (Sect. 3.2.1–3.2.6), before
the full molecular structure and the underlying physical and/or chemical
structure are discussed in Sects. 4.3 and 4.4.

####  3.2.1 12CO, 13CO, C18O

In addition to the images on disk-scales shown in Fig. 3, moment zero, moment
eight and velocity maps on larger scales are presented in Fig. 4 for the CO
isotopologues. The large-scale 12CO emission displays an hour glass
morphology, with emission originating along and inside the outflow cavity
walls. The cavity walls deviate from a parabolic shape and display a kink
(highlighted with white arrows in Fig. 4). This kink occurs at larger offsets
from the source for the northwestern and southeastern cavity walls. The most
prominent feature inside the cavity walls is visible $\sim$3–6′′ (420–840 au)
west of the source position at blueshifted velocities (highlighted with an
arrow in the velocity map in Fig. 4 and in the channel maps in Fig. 20).

12CO emission is detected over a velocity range of $-$11.3 – $-$1.13 and 0.77
– 9.04 km s-1 (with respect to the systemic velocity of 5.9 km s-1 Caselli et
al. 2002; Tobin et al. 2011), while most of the emission is resolved out at
velocities close to the systemic velocity. There is no clear velocity gradient
visible in the outflow direction (east–west), but the southern outflow cavity
walls are more pronounced at blueshifted velocities, while the northern cavity
walls are stronger at redshifted velocities. This velocity pattern is more
clearly visible at smaller scales (Fig. 3) and is similar to the rotation
direction of the disk and inner envelope.

The 13CO and C18O emission are dominated by the disk and inner envelope (Fig.
3), but they also have a contribution from material inside and along the
cavity walls. Emission inside the cavity walls is clearly visible in the 13CO
images in Fig. 4 (at offsets larger than $\sim$4′′ in the east–west
direction), while for C18O it is only visible in the individual velocity
channels (see Fig. 22). Large-scale emission is seen out to velocity offsets
of $\sim|7.5|$ km s-1 in 12CO emission, while this is only visible out to
$\sim|2.0|$ km s-1 in 13CO and C18O, maybe due to the lower sensitivity at the
higher velocity resolution. For both 13CO and C18O, there is a narrow arc of
emission in both outflow cavities that moves outward with increasing velocity
offsets (Figs. 21 and 22). A similar moving “front” of emission is also
visible in a range of 12CO channels (Fig. 20), but at smaller spatial scales
($\sim$2–3′′ off source, compared to $\sim$2–$>$16′′ for 13CO and C18O) and
higher velocity offsets ($\sim|2.5-7|$ km s-1, compared to $\lesssim|2.0|$ km
s-1 for 13CO and C18O). This differences between 12CO and 13CO/C18O is likely
because most 12CO emission is resolved out at the velocities where the
13CO/C18O moving “front” is detected and the sensitivity is not high enough to
detect 13CO/C18O emission at velocities as high as for 12CO.

The large-scale C18O moment eight map (Fig. 4) displays X-shaped emission
($\lesssim$8′′), while very faint and narrow X-shaped emission is visible in
some 13CO velocity channels (Fig. 19) and very weakly in the moment zero map
on smaller spatial scales ($\lesssim$4′′). This structure was previously
observed for 13CO $J=1-0$ emission (Ohashi et al., 1997). One of the reasons
for the difference between the 13CO and C18O moment maps is that while 13CO
(and 12CO) emission is resolved out near the systemic velocity, C18O is
detected in all low-velocity channels. Therefore, to better compare the
spatial origin of the emission from the different CO isotopologues, 13CO and
C18O images are created at the same velocity resolution as the 12CO image, and
velocity channels with emission from all three isotopologues overlaid are
presented in Fig. 5. Channel maps for each individual isotopologue are shown
in Fig. 19. The overlay in Fig. 5 reveals a layered structure, with 12CO
tracing the surface layer of the cavity wall and 13CO and C18O tracing deeper
and deeper into the envelope. The faint and narrow X-shaped emission visible
in 13CO channels coincides with 12CO emission from the cavity wall (visible in
yellow), while the broad X-shape in the C18O moment maps is caused by emission
at velocities close to the systemic velocity. A similar structure is visible
for 13CO at $-$0.5 km s-1, and this velocity channel clearly shows that the
13CO emission originates from layers closer to the outflow cavity. The
emission from the inner envelope and disk, as traced by 13CO and C18O
($-$1.77, $-$1.13, 0.77, 1.41 km s-1 in Fig. 5), is present in between the
12CO emission features. Here too, the 13CO emission is peaking in higher
layers compared to C18O. The C18O channel maps at the original velocity
resolution (Fig. 22) clearly show that the emission has a contribution from
outflowing material as well as from the surface layer of the envelope or
cavity wall. At velocities close to the systemic velocity ($\pm$ $\sim$0.5 km
s-1), these components start to overlap.

(a)

(b)

Figure 5: Selected velocity channel maps showing 12CO (red), 13CO (green) and
C18O (blue) emission overlaid. The bottom row is zoomed in on the central part
of the channels shown in the top row. The velocity with respect to the
systemic velocity is listed in the top right corner of each panel. The beam
(nearly identical for all three isotopologues) is shown in the bottom left
corner of the right most panels. The same channels are shown for each
individual molecule in Fig. 19.

While both 13CO and C18O trace emission from the disk and inner envelope, the
contributions from the different components are not exactly the same for both
isotopologues. The difference in origin between 13CO and C18O emission becomes
more clear from position-velocity (pv) diagrams, as presented in Fig. 6.
Emission at angular offsets $\gtrsim$2′′ as well as emission in the non-
Keplerian quadrants (top left and bottom right) is relatively stronger for
C18O than for 13CO. Together with the fact that 13CO emission is resolved out
in the central channel while C18O emission is not, this suggests that C18O
traces emission from the infalling envelope out to larger scales than 13CO
emission. This is probably because 13CO becomes optically thick faster due to
its higher abundance and hence gets resolved out more heavily near line
center. Close to the central protostar, the C18O emission is concentrated on
scales $\lesssim$ 1′′ and velocities $\gtrsim$ 1 km s-1, while 13CO emission
extends out to slightly larger scales and slightly lower velocities. This
suggests that the contribution from the innermost envelope is stronger for
13CO than it is for C18O, likely due to the higher 13CO abundance. A similar
conclusion can be drawn from the velocity maps (Fig. 3), where 13CO displays a
stronger contribution from blueshifted envelope emission in the north and
redshifted envelope emission in the south, that is, opposite to the disk
velocity structure.

The intensity ratio between 13CO and C18O in channels with disk and inner
envelope emission ($|\Delta v|\gtrsim$ 1 km s-1) is $\sim$1–3 instead of the
canonical ratio of $\sim$7 (Wilson & Rood, 1994). This suggests that 13CO is
generally optically thick and that C18O is probably optically thick in the
midplane region where the line ratio is lowest ($\sim$1), consistent with
earlier observations (van ’t Hoff et al., 2018). The central negative “gap”
visible in the 13CO and C18O moment zero map (and low-velocity channels, e.g.,
Fig. 5 and most clearly visible in Fig. 19) is therefore likely the result of
continuum oversubtraction from optically thick line emission, potentially in
combination with absorption by cold outer envelope material that is being
resolved out.

Figure 6: Position-velocity diagrams extracted along the major axis (averaged
over the size of the beam) for 12CO (first panel) and the molecular lines
observed at 0.167 km s-1 resolution: 13CO (second panel), C18O (third panel),
H2CO $3_{2,1}-2_{2,0}$ (fourth panel), and SO (fifth panel). For 12CO, a
cropped velocity range is shown for better visibility of the structure of the
other molecular lines. The horizontal and vertical dotted white lines mark the
source position and systemic velocity (which is shifted to 0 km s-1),
respectively.

####  3.2.2 SiO

Very compact, mostly unresolved SiO emission is detected just west of the
source position, peaking at an offset of $-$0$\farcs$08 ($\sim$11 au; Fig 7).
The emission is predominantly blueshifted and is detected at velocities
ranging between $-$13.45 and 1.30 km s-1 with respect to the systemic
velocity, and peaks at $-$2.72 km s-1. This component is not seen in any of
the other molecular lines. 12CO emission typically peaks towards the northwest
or southwest, rather than directly west, and emission close to source is only
detected out to $-$10.18 km s-1 in individual velocity channels (see also Fig.
7, right panel). SiO is a shock tracer and is typically observed in
protostellar jets. A jet origin of the SiO emission observed toward L1527 is
consistent with the high velocities of the emission.

####  3.2.3 c-C3H2

All four c-C3H2 transitions (two are blended, see Table 1) display strong
emission features along the north–south direction out to offsets of $\sim$2′′
(280 au; Fig. 3), which is more extended than the bright components seen in
13CO and C18O ($\sim$1′′). The blueshifted emission in the south is stronger
than the redshifted emission in the north. In contrast, the total extent in
the east–west direction is only $\sim$0$\farcs$3, compared to $\sim$1$\farcs$0
and $\sim$2$\farcs$0 for C18O and 13CO, respectively. In addition, a weak
large scale emission component is visible (most clearly seen in Fig. 1).

At the velocity resolution of 1.34 km s-1, the c-C3H2 transitions are detected
in only three channels, spanning a velocity range of $-$1.16 – 1.53 km s-1,
except for the blended $6_{0,6}-5_{1,5}$ and $6_{1,6}-5_{0,5}$ transitions
that display weak (3–4$\sigma$) emission at $-$2.5 km s-1 (Fig. 23). The faint
extended component is only visible in the central channel. The combination of
emission morphology and narrow velocity range indicates that c-C3H2 is tracing
envelope emission. A central absorption feature is only present in the central
velocity channel and is likely due to absorption of the warm continuum
emission by cold envelope material.

Figure 7: Integrated intensity (moment zero) map of SiO in the inner
0$\farcs$5 (left panel) and spectra extracted in a 0$\farcs$2 aperture (middle
panel) centered on the SiO peak 0$\farcs$08 west of the source position
(orange) and at the same angular offset to the east (blue). In the right panel
the normalized spectrum toward the SiO peak (orange) is compared to the
normalized 12CO spectrum extracted in the same aperture (black). The color
scale of the integrated intensity map is in mJy beam-1 km s-1. The beam is
depicted in the lower left corner and the cross marks the source position.

####  3.2.4 DCN

Very weak DCN emission is tentatively detected at the 3–4$\sigma$ level in the
central velocity channel (Fig. 24). The emission is extended surrounding a
central region with negative emission and bears the most resemblance to the
faint large scale emission component seen in c-C3H2 (as shown in Fig. 1).
There is a hint of a narrow emission feature north of the source extending in
the north–south direction in the first redshifted channel (1.53 km s-1), but
such a feature is absent in the south in the first blueshifted channel (-1.16
km s-1). This is reflected in the peak intensity map shown in Fig. 3. DCN is
thus at least present in the envelope and the central absorption feature is
likely due to absorption of the warm continuum.

####  3.2.5 H2CO

Three H2CO transitions are observed, with upper level energies of 21 K
($3_{0,3}-2_{0,2}$) and 68 K ($3_{2,1}-2_{2,0}$ and $3_{2,2}-2_{2,1}$). The
low-energy transition displays stronger and more extended emission than the
higher energy transitions. All transitions display X-shaped emission,
extending about 0$\farcs$8 toward the north and south, and 0$\farcs$4 toward
the east and west (Fig. 3; most clearly visible in the peak intensity maps).
The low-energy transition ($3_{0,3}-2_{0,2}$) shows an emission peak along the
north–south axis at $\sim$1′′ offsets. This feature is smaller and less
evident for the higher energy transitions. Only the $3_{0,3}-2_{0,2}$
transition displays weak extended emission in the north–south direction as
well as inside the outflow cavity walls ($\gtrsim$8′′).

The difference in emission morphology between the H2CO transitions, as well as
the origin of the emission can be more clearly seen in the individual velocity
channels. In Fig. 8 we compare the $3_{0,3}-2_{0,2}$ and $3_{2,2}-2_{2,1}$
transitions because they are observed at the same low velocity resolution of
1.34 km s-1. In order to provide a qualitative description of the origin of
the H2CO emission we also present velocity channel maps of a model with a
Keplerian disk (125 au radius) embedded in a rotating and infalling envelope
(CMU; Ulrich 1976; Cassen & Moosman 1981)333The CMU model describes the
collapse of an isothermal, spherically symmetric, and uniformly rotating
cloud. The assumption of free fall with each particle conserving angular
momentum results in particles moving along parabolic paths. Details about the
implementation can be found in Appendix C of van ’t Hoff et al. (2018).. The
temperature and density structure are based on radiative transfer modeling of
multi-wavelength continuum observations of L1527 by Tobin et al. (2013) and
this model has been used by van ’t Hoff et al. (2018, 2020, 2022) to study
molecular line observations toward L1527. The model images are created with
the radiative transfer code LIME (Brinch & Hogerheijde, 2010). Our goal here
is not to reproduce the observed emission exactly, but to illustrate the
emission features expected for emission originating in different parts of the
protostellar system. The model presented in Fig. 8 has emission originating in
the inner 250 au of the envelope and in the surface layers of the disk.

The low-energy $3_{0,3}-2_{0,2}$ transition is detected over a velocity range
of $-$3.84 – 2.87 km s-1, while the high-energy transition is only marginally
detected at $-$3.84 km s-1 (Fig. 8). The $3_{2,1}-2_{2,0}$ transition is
observed at a higher velocity resolution (0.167 km s-1) and emission is
detected over a velocity range of $-$3.05 – 3.14 km s-1 (Fig. 25), suggesting
that the asymmetry in velocity for the other transitions is likely due to the
low spectral resolution. The V-shaped emission pattern responsible for the
X-shape in the integrated intensity map (Fig. 3) is visible in all channels,
except the central channel, and is characteristic of emission originating in
the surface layers of the disk. In contrast, the emission features $\sim$1′′
north and south of the source position seen most strongly for
$3_{0,3}-2_{0,2}$ are only present in the $-$1.16 and 1.53 km s-1 channels and
not at higher velocities, and likely originate in the inner envelope. Both
transitions differ in the central velocity channel; where the
$3_{2,2}-2_{2,1}$ emission extends to the east and west in a bow-tie pattern,
the $3_{0,3}-2_{0,2}$ transition shows absorption surrounded by compact
emission features to the southeast and northwest. The bow-tie pattern of
$3_{2,2}-2_{2,1}$ is indicative of disk emission, while the asymmetric
features, as well as the more extended features at low velocities in the north
and south of $3_{0,3}-2_{0,2}$, are consistent with envelope emission. The
$3_{2,2}-2_{2,1}$ bow-tie extends as far in the east and west direction as the
$3_{0,3}-2_{0,2}$ emission features, so the absence of the bow-tie for the
$3_{0,3}-2_{0,2}$ transition is not due to the central absorption. The warm
$3_{2,2}-2_{2,1}$ transition thus originates predominantly in the disk surface
layers, while the colder $3_{0,3}-2_{0,2}$ transition also has a strong
contribution from the envelope. Absorption of continuum emission by the outer
envelope is then the likely origin of the absorption in the central velocity
channel of the $3_{0,3}-2_{0,2}$ transition.

Figure 8: Velocity channel maps for the H2CO $3_{0,3}-2_{0,2}$ (top row) and
$3_{2,2}-2_{2,1}$ (middle row) transitions, and for a model of a 125 au
(radius) Keplerian rotating disk embedded in a rotating infalling envelope
with molecular line emission originating in the disk surface layers and the
inner envelope (bottom row; Tobin et al. 2013; van ’t Hoff et al. 2018, 2020,
2022). In the model panels, the contribution from the disk is shown in an
orange color gradient and the envelope contribution is shown in a blue color
gradient. For visualization purposes, the disk emission is depicted on top of
the envelope emission. The model is meant as a qualitative comparison to
determine the origin of the H2CO emission. Observed emission features most
likely originating in the disk surface are marked by orange arrows, and
envelope features by white arrows. The black cross marks the source position.
The velocity with respect to the systemic velocity is listed in the top right
corner of each panel. The beam is shown in the bottom left corner of the right
most panels. Figure 9: Moment eight (peak intensity) maps for 12CO (left
panels), C18O (middle panels) and SO (right panels) on a scale of 24′′ (top
panels) and 6′′ (bottom panels). For C18O and SO, only the five central
velocity channels ($-$0.37 – 0.29 km s-1) are used to highlight the large-
scale emission features, while for 12CO the full velocity range ($-$11.3 –
9.04 km s-1) has been used. The dashed and dotted lines are the same in all
three bottom panels and are meant to help guide the eye with respect to the
location of the emission. The white arrows point to features described in the
main text. The beam is shown in the bottom left corner of each panel.  Figure
10: Selected velocity channel maps of the 0.167 km s-1 resolution data cubes
for SO (top group of panels), C18O (second group of panels), and H2CO
$3_{2,1}-2_{2,0}$ (third group of panels). The black contour marks the
3$\sigma$ level of the SO emission in all panels. The fourth and fifth group
of panels show velocity channel maps for a model with emission arising in the
surface layers of both the disk (orange) and envelope (i.e., along the cavity
wall; blue), and for a model with emission arising at the disk–envelope
interface, i.e., in the inner envelope (125–150 au), respectively. The black
cross marks the source position. The velocity with respect to the systemic
velocity is listed in the top right corner of each panel. The beam is shown in
the bottom left corner of the right most panels.

####  3.2.6 SO

Emission from the SO $6_{5}-5_{4}$ transition ($E_{\rm{up}}$ = 35 K) is
detected over a velocity range of $-$4.05 – 3.30 km s-1 (Fig. 26), and extends
about 1′′ north and south of the source position in the integrated and peak
intensity maps (Fig. 3). At low velocities ($-$0.54 – 0.46 km s-1), weak more
extended emission is visible (see Figs. 9 and 27). These narrow arc-like
emission features extend predominantly towards the southwest and are
blueshifted, but less extended ($\lesssim$4′′) X-shaped emission is visible.
This large scale emission overlaps with the surface layer of the envelope
traced in C18O. However, the SO emission originates in a more narrow layer in
individual velocity channels. Due to the rotating, infalling velocity profile
of the envelope, emission from the surface layer has a slightly different
spatial location at different velocities, resulting in the double layered
feature in the southwest in the peak intensity map (Fig. 9, arrow in top right
panel). The narrow SO emission feature visible in the southeastern outflow
cavity in the peak intensity map (Fig. 9, arrow in bottom right panel) is not
visible in the C18O map, but it is formed by small SO emission patches over a
velocity range of $-$0.54 – 0.13 km s-1 that coincide with the outward moving
emission front visible in 13CO and C18O channels (Figs. 22 and 21). Several
more of such SO emission spots coinciding with the outflowing material traced
in 13CO and C18O are visible at higher velocities and larger spatial offsets,
especially in the western outflow cavity (Fig. 27).

The SO emission on 1′′ scales does not resemble the morphology of any of the
other lines (Fig. 3). The north–south emission features east and west of the
source position are more parallel to each other than the X-shape seen in H2CO
and do not extend as far east–west as 13CO and C18O. In addition, the SO
emission peaks directly east and west of the source in the integrated
intensity map (with the west side being brighter), while 13CO and C18O clearly
peak north and south of source with less emission originating directly to the
east and west. From the pv-diagram (Fig. 6) it becomes clear that the
redshifted emission is brighter than the blueshifted emission. Based on the
channel maps (Fig. 10), this is most likely because there is redshifted
emission present along the midplane at an offset of $\sim$1′′, while this is
not the case at blueshifted velocities (e.g. 0.46 km s-1 versus -0.54 km s-1).

The velocity structure as shown in Fig. 3 deviates from pure Keplerian
rotation with blueshifted velocities extending north of the source in the west
and redshifted velocities extending south in the east. A similar pattern is
seen for 13CO, C18O, c-C3H2, and H2CO $3_{0,3}-2_{0,2}$ and indicates the
presence of envelope emission. The pv-diagrams (Fig. 6) show that this
envelope component is less extended than for 13CO and C18O as the SO emission
is confined to smaller angular offsets. The SO pv-diagram consists of two
components, most clearly distinct at blueshifted velocities, that seem to
anti-correlate with the C18O emission. The first component is a narrow feature
at low spatial offsets ($\lesssim$ 0$\farcs$4) that extends over the entire
detected velocity range. A similar, but stronger, feature is also visible for
H2CO that originates predominantly in the disk surface layers, suggesting that
this feature traces emission from the disk surface. The second feature is
located at lower velocities ($\lesssim$ 2 km s-1) and larger spatial offsets
and is just offset from the region with bright C18O emission, suggesting that
it originates in the inner envelope or outer disk.

To look at the spatial origin of the SO emission in more detail we present
selected velocity channel maps in Fig. 10 (the full velocity range is
presented in Fig. 26) and overlay the 3$\sigma$ contour of the SO emission on
C18O and H2CO ($3_{2,1}-2_{2,0}$) channels. At high redshifted velocities
(1.13 – 2.47 km s-1), the SO emission displays a V-shape resembling the H2CO
emission and coinciding with the outermost layer of C18O emission. A similiar
pattern is visible at blueshifted velocities ($-$2.38 – $-$1.88 km s-1),
although the emission is more asymmetric and dominated by the west side of the
disk. This morphology is consistent with the conclusion drawn from the pv-
diagrams that part of the SO emission originates in the disk surface layers.

At lower velocities the emission is predominantly located in two narrow bands
extending north–south both east and west of source. Similar features are
present in C18O channels on top of more extended emission. Only at low
redshifted velocities (0.29 – 0.69 km s-1) SO emission is visible along the
midplane between $\sim$0$\farcs$5–1$\farcs$0 north of source, coinciding with
the low energy H2CO ($3_{0,3}-2_{0,2}$) transition. A model with emission
originating solely in the surface layers of both the disk and envelope can
explain the vertical emission bands at intermediate velocity offsets (e.g.,
$-$1.54 and 1.46 km s-1), but not at velocities close to the systemic velocity
(Fig. 10). This could be because there is a disconnect at the disk–envelope
interface between the velocity structure in a model with a pure Keplerian disk
and CMU envelope. Figure 10 also shows results for a model with emission
arising solely from the disk–envelope interface. In this scenario, the
majority of the emission is expected along the major axis of the system, which
does not resemble the observed emission morphology. Overall, the SO emission
thus seems to originate in the disk and inner envelope, and in both components
the emission seems to originate predominantly in the surface layers.

##  4 Analysis and discussion

###  4.1 Continuum sub-structures and inclination

The L1527 disk displays smooth, but asymmetric continuum emission, with the
southern side brighter than the northern side along the major axis, and the
eastern side brighter than the western side. The image does not show the
clumps previously reported in 7 mm VLA images (Nakatani et al., 2020),
consistent with more recent higher signal-to-noise VLA images at the same
wavelength and spatial resolution (Sheehan et al., 2022).

The north–south asymmetry was previously observed at 7 mm and 1.3 cm with the
VLA, and confirmed through analytic modeling (Sheehan et al., 2022). As
discussed by those authors, determining the underlying physical nature of this
asymmetry is difficult due to the edge-on nature of the disk, and could depend
on where the emission at different wavelengths becomes optically thick.
Detailed modeling of multi-wavelength data is therefore required to assess
whether there is an enhancement in surface density in the southern part of the
disk and if so, whether this is related to for example a vortex, spiral or
pressure bump. The east–west asymmetry was not visible in the VLA data, even
though they have comparable spatial resolution, potentially because at these
longer wavelengths the vertical extent of the disk is smaller and the emission
is less optically thick.

Both asymmetries were recently observed with ALMA in Band 7 (0.87 mm) and Band
3 (3.3 mm), although with the western side brighter in Band 3 (Ohashi et al.,
2022b). The same Band 3 data was presented by Nakatani et al. (2020), but they
show that the brightness temperature peaks slightly southeast of the source
position. We therefore re-imaged the archival Band 3 data with the eDisk data
reduction and imaging scripts, which results in an image with the eastern side
brighter than the western side (Fig. 18), similar to the Band 6 and 7 images.
For a near-edge on disk like L1527, the disk can either be orientated such
that eastern side faces us, in which case the emission east of source traces
the back side of the disk, that is, the half of the disk furthest away from us
along our line of sight, or such that the western side faces us, in which case
the emission west of source traces the back or far side of the disk (see e.g.,
Fig. 6 in Oya et al. 2015). An asymmetry along the minor axis of a near-edge
on disk can be explained by a vertically extended optically thick dust disk.
In this scenario, warmer material is observed toward the back side of the disk
because the emission would get optically thick already in the colder outer
disk on the near side (e.g., Ohashi et al. 2022b and Fig. 3 therein, Lin et
al. subm., Takakuwa et al. in prep.). The north–south asymmetry appears
stronger at 3.3 mm, especially in the east, while the east–west asymmetry is
less pronounced at longer wavelengths and only visible in the south. A
stronger east–west asymmetry at shorter wavelengths hints that it is indeed
due to optically thick emission, as the disk becomes less optically thick at
longer wavelengths. However, the resolution of the Band 3 data is slightly
lower than the here presented Band 6 data (0$\farcs$086 $\times$ 0$\farcs$043
versus 0$\farcs$056 $\times$ 0$\farcs$029) and detailed modeling of the
continuum emission at multiple wavelengths in the visibility plane is required
to confirm the origin of east–west asymmetry. Nonetheless, the images
presented here suggest that the continuum presents a coherent picture at
different ALMA wavelengths, implying that the eastern side is the back side of
the disk under the assumption of optically thick emission.

Figure 11: Comparison between the ALMA 1.3 mm continuum and 12CO images and
the JWST NIRCam 4.4 $\mu$m image. The 4.4 $\mu$m image is shown on different
spatial scales in the first and second panel, with the 1.3 mm continuum
overlaid in contours in the first panel. The dashed yellow square in the
second panel marks the region shown in the first panel. The 12CO peak
intensity (moment 8) map is shown in the third panel, and an overlay of the
4.4 $\mu$m image (red) and the 12CO map (blue) is shown in the fourth panel.

The brightness asymmetry of the disk previously observed in the Gemini L′ (3.8
$\mu$m) scattered light image, with the eastern side nearly twice as bright as
the western side, also suggests that the eastern side is the side facing us
(Tobin et al., 2010). Deconvolution of the Spitzer IRAC image (3.6 $\mu$m)
results in the western side being brighter (Velusamy et al., 2014), but the
brightness of the cavities in scattered light has been shown to be variable
over time (Tobin et al., 2008; Cook et al., 2019). The recently released JWST
NIRCam image (release id 2022-055, proposal id 2739, PI: K.
Pontoppidan444https://webbtelescope.org/contents/news-
releases/2022/news-2022-055) also suggests that the eastern side is facing us.
The JWST 4.4 $\mu$m image (Fig. 11) is consistent with the Gemini image555The
ALMA continuum seems slightly rotated with respect to the JWST 4.4 $\mu$m
image and is not located in the center of the dark lane between the two bright
regions east and west of the source position in the 4.4 $\mu$m image. The JWST
image aligns with the Spitzer IRAC image presented by Tobin et al. (2008) and
there is no rotation evident based on the location of background stars. The
east–west misalignment is not due to proper motion as L1527 is moving south,
but the displacement is too small to rule out a systematic offset in the
NIRCam image using the Spitzer image. and there is more short wavelength
emission (2 $\mu$m) in the eastern cavity, which indicates less extinction and
hence that the eastern cavity is the blue-shifted outflow cavity.

The orientation inferred from the dust continuum and scattered light is at
odds with the orientation derived from molecular line emission from the
envelope (CS; Oya et al. 2015), which suggests that the western side is the
back side. In this orientation, the blueshifted envelope emission is stronger
in the southwest than in the southeast, while redshifted emission is stronger
in the northeast than in the northwest. For a system with the eastern side
being the back side, the blueshifted and redshifted envelope components would
be strongest in the southeast and northwest, respectively. The velocity
patterns of 13CO, C18O, c-C3H2, H2CO $3_{0,3}-2_{0,2}$ and SO observed here
(Fig. 3) are consistent with the earlier CS observations and suggest that the
western side of the envelope is the far side.

However, a small inclination toward the west, as suggested by the continuum
observations, is consistent with the large scale ($\sim$100′′) outflow
observed in 12CO, which shows blueshifted emission predominantly toward the
east and redshifted emission toward the west (Hogerheijde et al., 1998).
Consistent with previous observations, on smaller scales as observed here, the
12CO emission displays both blueshifted and redshifted emission on both sides
of the source, making it hard to infer the systems inclination. The potential
blueshited jet feature in the west (Fig. 4), as well as the blueshifted SiO
emission in the west (Fig. 7), would suggest an orientation opposite of that
based on the large scale outflow. However, in the 12CO velocity channels, weak
features are visible at high redshifted velocities in the extension of the
potential jet.

Overall, the continuum emission on small scales ($\lesssim$0$\farcs$5), the
scattered light images, and the large-scale 12CO outflow ($\sim$100′′) suggest
that the eastern side of the system is facing us, while molecular line
emission on small scales (SiO jet) and intermediate scales (envelope) are
consistent with the opposite orientation of the western side facing us.
Differences in orientation based on outflowing material on small and large
scales could be due to precession of the outflow, as discussed in more detail
by Oya et al. (2015). The continuum asymmetry is observed at scales of
$\sim$0$\farcs$1, while the orientation derived from the line emission is
based on envelope scales. This suggests that there is either a misalignment
between the disk and the envelope, or a warp in the inner disk (Cook et al.,
2019; Sakai et al., 2019). A detailed analysis of the molecular line emission
on disk-scales may be able to help constrain the system’s orientation.
Moreover, an overlay of the 12CO outflow cavity on the JWST NIRCam 4.4 $\mu$m
image shows that the asymmetry in the scattered light cavity shapes is not
reflected in the 12CO cavity walls, and may thus be the result of shadowing on
the northwestern and southeastern cavity wall (Fig.11). A comprehensive study
including the molecular line emission, the multi-wavelength continuum
emission, and the scattered light images is therefore required to fully
unravel the structure of the system.

Figure 12: Rotation curves derived from the pv-diagrams along the disk major
axis (Fig. 6) for 13CO (left panel) and C18O (right panel). Points tracing the
outer edge of the pv-diagrams are shown as circles and points tracing the peak
of the emission (the ridge) are shown as squares. Blue and red symbols denote
blueshifted and redshifted emission, respectively. The dashed lines show power
laws with indices, $p_{\mathrm{in}}$, of $-0.5$ (for Keplerian rotation), and
the dotted lines show power laws with the best-fit indices,
$p_{\mathrm{out}}$, as listed in Table 2. The radius where the two power laws
cross, $r_{\rm{b}}$, is listed in Table 2. The velocity is with respect to the
systemic velocity. Table 2: Results from the pv-diagram analysis.

|  | Double power law | Inner power law fixed ($p_{\rm{in}}$ = 0.5)
---|---|---|---
Method |  $v_{\rm{sys}}$ a |  $p_{\rm{in}}$ b |  $p_{\rm{out}}$ c |  $r_{\rm{b}}$ d |  $p_{\rm{out}}$ c |  $r_{\rm{b}}$ d |  $M_{\star}$ e
| (km s-1) |  |  | (au) |  | (au) | ($M_{\sun}$)
13CO edge | 5.955 $\pm$ 0.005 | 0.43 $\pm$ 0.02 | 0.89 $\pm$ 0.03 | 114 $\pm$ 4 | 0.89 $\pm$ 0.02 | 125 $\pm$ 3 | 0.53 $\pm$ 0.02
13CO ridge | 6.024 $\pm$ 0.006 | 0.63 $\pm$ 0.01 | 1.57 $\pm$ 0.08 | 131 $\pm$ 3 | 1.25 $\pm$ 0.03 | 100 $\pm$ 2 | 0.29 $\pm$ 0.01
C18O edge | 5.958 $\pm$ 0.006 | 0.47 $\pm$ 0.03 | 0.86 $\pm$ 0.04 | 102 $\pm$ 6 | 0.86 $\pm$ 0.02 | 109 $\pm$ 5 | 0.49 $\pm$ 0.03
C18O ridge | 5.995 $\pm$ 0.007 | $-$ | $-$ | $-$ | 0.98 $\pm$ 0.02 | 54 $\pm$ 2 | 0.32 $\pm$ 0.02

Notes. a Systemic velocity. b Power-law index of the inner power law. c Power-
law index of the outer power law. d Transition radius between the inner and
out power law. e Central mass.

###  4.2 Dynamical mass and disk radius

The stellar mass and disk radius can be derived by fitting a double power law
to the rotation curve (e.g., Seifried et al., 2016; Aso & Machida, 2020; Maret
et al., 2020). We use the publicly available Spectral Line Analysis/Modeling
(SLAM) code666https://github.com/jinshisai/SLAM to extract the rotation curves
from the 13CO and C18O pv-diagrams (Aso et al., 2015; Sai et al., 2020) and to
do the fitting. The signal-to-noise ratio of the H2CO and SO emission is not
high enough for this analysis and 12CO is dominated by outflow emission.
Details of the methods employed by SLAM are described by Ohashi et al.
(subm.), but the main steps are as follows.

First, the (position,velocity) coordinates are determined either for points
tracing the outer edge (5$\sigma$ level) of the pv-diagram or for points
tracing the peak of the emission (also called the “ridge” of the pv-diagram).
Next, a double power law is fit to the (position,velocity) coordinates using
the Markov Chain Monte Carlo (MCMC) algorithm implemented in the emcee package
(Foreman-Mackey et al., 2013). For an infalling rotating envelope conserving
angular momentum, the velocity is proportional to $r^{-1}$, while for a
Keplerian disk, $v\propto r^{-0.5}$. In the latter case the stellar mass can
be derived from $v_{b}=\sqrt{GM_{*}/r_{b}}\sin i$, where $v_{b}$ is the
velocity at the transition radius, $r_{b}$, between disk and envelope velocity
profiles. We first perform the fits with the systemic velocity and inner
power-law index as free parameters and confirm that the power-law index for
the inner region is indeed $\sim$ $-$0.5. We then fix the systemic velocity to
the best-fit value and the inner power-law index to $-$0.5 to derive the
dynamical stellar mass. The results are listed in Table 2 and the rotation
curves are shown in Fig. 12.

The dynamical mass derived from the two isotopologues is consistent within
1-2$\sigma$, and is $\sim$0.3 $M_{\sun}$ using the ridge method and $\sim$0.5
$M_{\sun}$ using the edge method. This is higher than the 0.2 $M_{\sun}$
derived by Tobin et al. (2012) from 13CO and consistent with 0.45 $M_{\sun}$
derived by Aso et al. (2017) from C18O, who used the ridge method on lower
resolution data. For the edge points, the transition radius found from 13CO
and C18O is also consistent with each other within error bars, while the
results from the ridge points are different for the two isotopologues and
different from the edge point derived values. The reason is most likely that
the ridge is not well defined at this high resolution (see the pv-diagrams in
Fig. 6). The difference between 13CO and C18O for the ridge points could also
be due to the difference in optical depth between the two isotopologues
resulting in both isotopologues tracing a different layer. An average radius
of 108 au from the edge points is only slightly larger than the radius derived
from the C18O pv-diagram by Aso et al. (2017) (75 au). Tobin et al. (2012)
derived a 125 au disk radius from multi-wavelength continuum modeling, but the
5$\sigma$ contour of the 1.3 mm image extends only out to $\sim$85 au. A
detailed analysis of the continuum emission is required to better constrain
the dust-disk size, but it seems not very different from the gas-disk size.
Overall, the analysis for L1527 seems most robust using the edge method and
suggests a stellar mass of $\sim$0.5 $M_{\sun}$ and a gas-disk radius of
$\sim$110 au.

###  4.3 Temperature structure

####  4.3.1 The disk is too warm for CO freeze out

On scales of a few arcseconds, both 13CO and C18O display an X-shaped emission
morphology (most clearly visible in the peak intensity maps in Fig. 4), with
emission arising from the surface of the envelope along the outflow cavity
wall out to larger radii than emission from the midplane. Along the midplane,
the emission starts to disappear at offsets of $\sim$2$\farcs$5 ($\sim$350
au), suggesting that CO starts to freeze out. This is consistent with the
analysis of 13CO, C18O and C17O by van ’t Hoff et al. (2018, 2020), which
showed that CO was present in the gas phase throughout the entire disk
($\sim$100 au), as well as with the temperature profile derived from modeling
the multi-wavelength continuum emission by Tobin et al. (2013) in which the
temperature drops below 20 K at a radius of 360 au.

A more detailed temperature structure can be obtained from the optically thick
13CO brightness temperature as presented in Fig. 13. For all channels with
velocities $\gtrsim|1|$ km s-1 and with resolved emission, the brightness
temperature is higher than 20 K, with temperatures increasing in the surface
layers up to $\sim$50 K. The temperature in the radially and vertically most
extended regions is $<$20 K, but this is likely due to the emission becoming
optically thin (especially in the upper most surface layers) and beam dilution
as this region typically fills only half of the beam. Beam dilution is also
the reason why temperatures decrease at velocities $\gtrsim|3|$ km s-1, where
the emission solely originates in the inner half of the disk. Based on the
13CO/C18O line ratio, the C18O emission is only optically thick in the
midplane at angular offsets $\lesssim$ 0$\farcs$5\. Consequently, the midplane
brightness temperatures are consistent with those for 13CO, while the
brightness temperature in the surface layers is lower ($\sim$30–35 K). These
results are also in agreement with the disk midplane temperature profile
derived by van ’t Hoff et al. (2018) from observations with lower resolution
and sensitivity.

The temperature structure can also be assessed using H2CO. The resolution is
high enough to spatially resolve a decrease in H2CO toward the midplane, as
observed before for the edge-on young disk IRAS 04302 (Podio et al., 2020; van
’t Hoff et al., 2020). Assuming this is due to freeze out, the base of the
V-shape provides an estimate of the H2CO snowline at $\sim$70 K (Noble et al.,
2012; Fedoseev et al., 2015). The tip of the V is unresolved, suggesting that
the snowline is at a radius less than 24 au. In addition, the ratios of H2CO
lines are good probes of temperature (e.g., Mangum & Wootten, 1993). Fig. 14
(top row) presents the $3_{0,3}-2_{0,2}$/$3_{2,2}-2_{2,1}$ line ratio per
channel, and shows that the ratio is $\lesssim$3 in all pixels with a
$>3\sigma$ detection of the weaker $3_{2,2}-2_{2,1}$ transition.

Figure 13: Brightness temperature of 13CO in selected 0.167 km s-1 velocity
channels. Only pixels above the 3$\sigma$ level are shown. The red line marks
the 20 K contour. The velocity with respect to the systemic velocity is listed
in the top right corner of each panel. The beam is shown in the bottom left
corner of the right most panel. Figure 14: Line ratio of the H2CO
$3_{0,3}-2_{0,2}$ and $3_{2,2}-2_{2,1}$ transitions in the observed velocity
range (top panels) and the corresponding temperature for optically thin
emission (bottom panels). Ratios lower than 2 indicate optically thick
emission and those regions are shown in grey in the temperature maps (bottom
panels). Only pixels with a $>3\sigma$ detection of the $3_{0,3}-2_{0,2}$
transition are shown, and the contours depict the 3, 6 and 9$\sigma$ levels of
the $3_{2,2}-2_{2,1}$ transition. The color scale is such that blue indicates
low temperatures (corresponding to high ratios) and red indicates high
temperatures (corresponding to low ratios). The black cross marks the source
position. The velocity with respect to the systemic velocity is listed in the
top right corner of each panel. The beam is shown in the bottom left corner of
the right most panels.

The $3_{0,3}-2_{0,2}$/$3_{2,2}-2_{2,1}$ ratio as observed here is particularly
sensitive to temperatures $\lesssim$ 90 K (see Fig. 28). For optically thin
emission in Local Thermodynamic Equilibrium (LTE), the ratio drops from
$\sim$20 to $\sim$5 for temperatures between 20 and 40 K. Around 90 K the
ratio has dropped to $\sim$3, and the ratio remains higher than 2 for
temperatures up to 300 K. If the emission is optically thick, the ratio drops
below 2. The observed line ratio is $>2$, except in the inner
$\sim$0$\farcs$3, where the emission thus becomes optically thick. A
conservative estimate of the uncertainty on the line ratio in the optically
thin regions (ratio $>$ 2) with a $>6\sigma$ detection of the
$3_{2,2}-2_{2,1}$ transition is then 18% when propagating the individual rms
noise levels of the observations. This means that for line ratios of $\sim$3,
the temperature is at least 60 K, but the upper limit is not well constrained.
As can be seen from Fig. 14, the temperature in the regions where both H2CO
lines are detected is then at least 60 K. At velocity offsets of $-$1.16 and
1.53 km s-1, no $3_{2,2}-2_{2,1}$ emission is detected from the midplane and
the ratio becomes $\gtrsim$4, suggesting temperatures below $\sim$40 K. In the
inner envelope midplane where both transitions are detected (angular offsets
of $\sim$0$\farcs$75-1$\farcs$0) temperatures of at least 60 K are found. A
similar temperature was derived in this region from a non-LTE large-velocity-
gradient (LVG) analysis of SO by Ohashi et al. (2014); Sakai et al. (2014b).

The temperatures derived from the H2CO line ratio are $\sim$10–20 K higher
than the 13CO brightness temperature. This difference is likely caused by two
dominant effects. First, the brightness temperature from 13CO traces the
radius where the emission gets optically thick. This is not necessarily the
same as the observed angular offset, which means that colder material further
out may be projected closer to the star. Second, the brightness temperature of
the 13CO emission gets smeared out over the size of the beam, while the
effects of beam dilution cancel out for the H2CO line ratio. Since both
effects work to lower the observed brightness temperature of 13CO, the
physical temperature is likely closer to that measured with H2CO. In addition,
while the brightness temperature of the continuum drops steeply at radii
$\gtrsim$0$\farcs$3, continuum subtraction may have lowered the 13CO
brightness temperature a little. A higher midplane temperature than derived
from the 13CO brightness temperature would be consistent with the analysis by
van ’t Hoff et al. (2018) that showed that the temperature profile as derived
by Tobin et al. (2013) from the multi-wavelength continuum emission needed to
be increased by at least 30% to reproduce the observations. Such a warm
temperature profile was also adopted by Aso et al. (2017) for analysis of C18O
observations of L1527.

Finally, if the dust is optically thick, as suggested by the brightness
asymmetry along the minor axis, the continuum brightness temperature provides
a third temperature probe. The continuum brightness temperature is $\sim$40 K
out to $\sim$25 au, after which it steeply drops to temperatures below
$\sim$20 K (Fig. 2), probably because the emission becomes optically thin. A
midplane temperature of $\sim$40 K at 25 au is consistent with the 13CO
brightness temperatures at larger radii and the temperature profile derived by
van ’t Hoff et al. (2018). However, the continuum brightness temperature
suffers from the same effects as the 13CO brightness temperature, so it may
also underestimate the real temperature. Overall, all results point to the
L1527 disk being warm, with midplane temperatures too high for CO freeze out
throughout the disk (20–40 K), but low enough for H2CO freeze out outside
$\sim$24 au.

Moreover, the similarity between the temperature derived from the continuum
and the molecular lines suggests that the grains do not scatter efficiently,
as this would decrease the brightness temperature (Birnstiel et al., 2018).
Since grains only scatter appreciably when the size of the grain is comparable
to the observing wavelength, this suggests that L1527 mainly contains grains
much smaller than $\sim$1 mm. The lack of large grains is consistent with the
vertical extent of the dust disk which indicates that the grains have not yet
settled.

####  4.3.2 A potential temperature enhancement around the disk–envelope
interface

At intermediate redshifted velocities (e.g., the 1.8 km s-1 channel shown in
Fig. 13), the 13CO brightness temperature increases from $\sim$25 K to
$\sim$35 K at angular offsets $\gtrsim$ 0$\farcs$5 (1$\sigma$ = 2 K). A
similar effect is derived from the H2CO line ratio, but at both redshifted and
blueshifted velocities. This suggests that there may be an increase in
temperature around the disk–envelope interface. Such a rise was invoked by
Sakai et al. (2014b) based on SO observations. Temperatures of $\sim$60 K and
$\sim$200 K were derived from SO emission at angular offsets between
$\sim$0$\farcs$6–1$\farcs$0 (Ohashi et al. 2014; Sakai et al. 2014b, 2017,
resp.), but these studies did not have high enough spatial resolution and
signal-to-noise ratio to derive a temperature at smaller offsets. However,
there is no increase in 13CO brightness temperature at blueshifted velocities,
so several factors have to be taken into account before a temperature
enhancement can be concluded from the observations presented here.

Relating the brightness temperature observed at a certain position in a
certain velocity channel to a physical location is non-trivial, because it
depends on where in the system the emission becomes optically thick (see e.g.,
Fig. 6 in van ’t Hoff et al. 2018). For example, if the emission along a line
of sight close to the protostar becomes optically thick in the outer envelope,
the brightness temperature at a small angular offset will reflect the
temperature in the cold outer envelope instead of in the warm disk. Since
redshifted emission originates in the rotating-infalling envelope in front of
the disk, and blueshifted emission in the envelope behind the disk, a
comparison between redshifted and blueshifted velocity channels can help
constrain the origin of the emission. If the emission becomes optically thick
in the disk, the redshifted and blueshifted channels should be similar.
However, this is inconsistent with the observations. The two simplest possible
scenarios are then that either the 13CO emission is just optically thick
($\tau\gtrsim$ 1), or that the 13CO is very optically thick ($\tau>>$1).

The first scenario ($\tau\gtrsim$ 1) could explain the observations if the
13CO emission becomes optically thick in the envelope behind the disk at
blueshifted velocities, and in the disk at redshifted emission. In other
words, if the disk itself does not contain enough CO to make the emission
optically thick. The observations would then suggest that the envelope
midplane (seen at blueshifted velocities) is colder than the outer disk
midplane (seen at redshifted velocities). A potential issue with this scenario
is that it may not be able to reproduce the (marginally) optically thick C18O
emission.

The second scenario ($\tau>>$1) may explain the observations if the 13CO
emission already becomes optically thick in the envelope at redshifted
velocities and in the disk at blueshifted velocities. In this case there is
enough material in both the envelope and the disk to make the emission
optically thick. This would then suggest that the disk midplane (seen at
blueshifted velocities) is colder than the inner envelope (seen at redshifted
velocities). If the C18O emission does not become optically thick yet in the
envelope (at redshifted velocities), this temperature increase would not be
visible in C18O, consistent with the observations. A potential inconsistency
is that you would expect to observe warm emission from the inner envelope at
angular offsets larger than the extent of the disk at both blueshifted and
redshifted velocities. The fact that this is not observed, suggests then that
either the temperature or the optical depth drops quickly in the inner
envelope. However, a rapid decrease in temperature is inconsistent with the
temperature derived from H2CO, which shows $\sim$60 K out to
$\sim$1$\farcs$1–1$\farcs$4 ($\sim$150–200 au projected from the source), and
a rapid decrease in optical depth is inconsistent with the observed 13CO/C18O
line ratio, which suggests 13CO is optically thick out to
$\sim$1$\farcs$1–1$\farcs$4 as well.

An alternative explanation for the 13CO observations is that there is a
north–south asymmetry in the temperature, but this would be opposite to the
north–south asymmetry observed for the continuum emission and not clearly
visible in H2CO. In conclusion, both the 13CO and H2CO show potential evidence
of an increase in the temperature in the outer disk and/or inner envelope.
However, observations of H2CO at higher spectral resolution and for higher
energy transitions are required to better constrain the temperature. Moreover,
detailed radiative transfer modeling is required to derive a temperature
structure for the disk and envelope from the observed emission and to confirm
whether an increase in temperature occurs at the disk–envelope interface.

Figure 15: Schematic overview of the chemical and temperature structure of the
inner few hundred au of the L1527 protostellar system based on the
observations presented here. The potential temperature enhancement is seen in
both the north and south in H2CO, but only in the north in 13CO.

###  4.4 Molecular structure

A cartoon illustrating which components of the L1527 protostellar system are
traced by which molecules is presented in Fig. 15. Outflowing material is
visible in 12CO, 13CO, C18O, and H2CO $3_{0,3}-2_{0,2}$ with 12CO tracing the
highest velocity gas. A blueshifted jet is visible in the western outflow
cavity in SiO and potentially 12CO. The SiO jet is compact and located close
to the protostar (peak position is 0$\farcs$08 offset from source), while the
12CO jet is further away from the source ($\sim$3–6′′) and extended in the
east–west direction. The outflow cavity wall is clearly outlined in 12CO, but
also faintly in 13CO (at small scales), C18O and SO. The large scale envelope
is visible in c-C3H2 and weakly in DCN. Emission from the inner envelope is
most strongly visible in 13CO. In addition, while weak envelope emission is
seen in H2CO $3_{0,3}-2_{0,2}$, all H2CO transitions display bright emission
in the inner envelope midplane. The disk is traced by 13CO, C18O and H2CO,
where H2CO only originates in the disk surface layers. SO also traces surface
layers in the disk and inner envelope, that is, in layers along the outflow
cavity wall. The physical and/or chemical reason behind the different emission
morphologies is further discussed in the following sections.

####  4.4.1 Outflowing material

All three CO isotopologues display a moving front of emission in the outflow
cavity with material at higher velocities located further away from the star
(marked with dotted lines in the channel maps in Figs. 20-22). This is in
agreement with both a jet/bow shock driven outflow as well as a wind-driven
outflow (e.g., Lee et al., 2000; Arce et al., 2007, and references therein).
The velocity maps in Fig. 3 show that the 12CO emission has higher velocities
along the outflow cavity walls close to source ($\lesssim$1′′) compared to the
disk emission traced by 13CO and C18O, suggesting that there may be a disk
wind in this system. The velocity structure can be shown more clearly in pv-
diagrams obtained parallel to the disk minor axis at different offsets along
the major axis, that is, north and south of the source position (Fig. 16).
13CO and C18O show Keplerian emission on one side of the diagram and a low-
velocity contribution from the envelope in the other half. In contrast, 12CO
shows extended emission in all four quadrants but peaks near the 13CO and C18O
disk emission. However, the bright 12CO emission has velocities higher than
the expected Keplerian velocity. The fainter extended 12CO emission may be
explained by material moving away in a conical or parabolic shape. Because the
outflow is in the plane of the sky, the near side of this shell would move
toward us and the far side would move away from us, resulting in both
redshifted and blueshifted emission. This poloidal expansion coupled with the
super-Keplerian rotation suggests that 12CO may trace a rotating, expanding
disk wind. A more detailed analysis is left for future work.

The outward moving front is present in both outflow cavities for 13CO and
C18O, while 12CO only shows this in the eastern cavity (Figs. 20-22, but
outside of the angular range shown in the pv-diagrams in Fig. 16). Instead,
there is an indication of a blueshifted 12CO jet $\sim$3–6′′ ($\sim$ 400–800
au) off source (Figs. 4 and 20). However, the velocity is lower than the
velocity of the SiO jet closer to source ($\sim$ 11 au). 12CO emission has
been observed before with CARMA ($\sim$3′′ resolution) and ALMA (0$\farcs$8
resolution) in the $J=1-0$ transition (Flores-Rivera et al., 2021), which
displays a similar outflow morphology as the $J=2-1$ transition presented
here. Flores-Rivera et al. (2021) referred to the narrow ‘neck’ between the
two outflow cavities (see Figs. 3, 11, 20, fourth row) as a jet extending out
to $\sim$75 au. However, the channel maps in Fig. 20 (fourth row) suggest a
widening of the outflow opening angle with the north-south extension (making
up the ‘neck’) originating from emission cospatial with the disk and/or inner
envelope (potentially tracing a wind) with redshifted emission north of the
source and blueshifted emission south of the source. At larger scales (Fig.
20), there is a hint of a redshifted jet-like emission feature along the line
of the blueshifted jet at larger offsets ($\sim$8–12′′). This may signal that
the jet has precessed. Precession may also explain the kinks seen in the
outflow cavity walls (marked by white arrows in Fig. 4). Alternatively, this
could be due to widening of the outflow opening angle over time, or due to
inhomogeneity of the surrounding medium.

Figure 16: Position-velocity diagrams of the CO isotopologues (different
columns) extracted parallel to the disk minor axis (averaged over the size of
the beam) at offsets of $\pm$0$\farcs$3 (first and second row) and
$\pm$0$\farcs$6 (third and fourth row) along the major axis (i.e., north and
south of the source position). The horizontal dotted line marks the disk
midplane, with larger angular offsets corresponding to the disk surface
layers. The vertical dotted line marks the systemic velocity, which is shifted
to 0 km s-1. The red curve shows the expected Keplerian velocity for a 0.5
$M_{\sun}$ star (based on the pv-diagram analysis described in Sect. 4.2) at
each radial offset, $r$, as function of disk height, $z$:
$V_{\rm{Keplerian}}=\sqrt{\frac{GMr^{2}}{(r^{2}+z^{2})^{3/2}}}$ (e.g.
Rosenfeld et al., 2013).

####  4.4.2 Disk versus envelope

Studying whether changes occur in the composition of the volatile material as
it transitions from the envelope to the disk is crucial for understanding the
origin of chemical complexity in planet-forming material. Moreover,
identifying molecular species or transitions that exclusively trace the disk
environment would aid in identifying and studying the conditions in young
disks. In recent years, chemical changes across the disk–envelope interface
have been observed for multiple sources (e.g., L1527, L1489, IRAS 16293 A,
IRAS 16293 B, IRAS 15398; Sakai et al. 2014b; Yen et al. 2014; Oya et al.
2016, 2018; Okoda et al. 2018, resp.), but so far no molecule or transition
has been uniformly identified that reliably traces the disk or the
disk–envelope interface.

In the observations presented here, c-C3H2 emission originates solely in the
envelope. The c-C3H2 observations are consistent with previous ALMA
observations of different transitions (Sakai et al., 2014b) and the
distribution of C2H (Sakai et al., 2014a). These hydrocarbons are often
associated with UV irradiation and therefore typically observed in photo-
dissociation regions (PDRs; e.g., van der Wiel et al. 2009; Guzmán et al.
2015) and along outflow cavity walls, especially in Class 0 sources (e.g.,
Murillo et al., 2018; Tychoniec et al., 2021). At the spectral resolution of
1.34 km s-1, strong c-C3H2 emission is only detected in three 1.34 km s-1
velocity channels ($-$1.16 - 1.53 km s-1), but weak (3$\sigma$) emission is
detected at $-$2.5 km s-1 for the blended $6_{0,6}-5_{1,5}$ and
$6_{1,6}-5_{0,5}$ transitions, which is at a higher velocity offset than
detected before ($-$2.2 km s-1; Sakai et al. 2014b). Higher spectral
resolution observations are required to constrain the distribution in the
envelope, and higher sensitivity observations are needed to establish whether
c-C3H2 is really absent in the disk. The presence or absence of c-C3H2 in the
disk is interesting as bright hydrocarbon emission in Class II protoplanetary
disks is associated with high C/O ratios ($>$ 1; Bergin et al. 2016; Miotello
et al. 2019). A comparison between embedded and mature disks could thus
provide information about the chemical evolution during the disk stage.

The H2CO transitions observed here predominantly originate in the disk surface
layers, where the temperature as determined from the line ratio is $\gtrsim$60
K. The higher energy transitions ($3_{2,1}-2_{2,0}$ and $3_{2,2}-2_{2,1}$) are
not detected in the midplane, while weak emission from the lower energy
transition ($3_{0,3}-2_{0,2}$) is present. The $3_{0,3}-2_{0,2}$ flux is
expected to increase at lower temperatures (for a given column density), so
this is not an excitation effect. The observed distribution could instead be
due to freeze out of H2CO in the midplane as the freeze-out temperature is
$\sim$70 K (Noble et al., 2012; Fedoseev et al., 2015). A low residual
midplane abundance could be due to gas-phase formation of H2CO or nonthermal
desorption (e.g., Aikawa et al., 2002; Loomis et al., 2015; Öberg et al.,
2017; Terwisscha van Scheltinga et al., 2021). Alternatively, the
$3_{0,3}-2_{0,2}$ emission along the midplane originates in the envelope that
is visible between the disk surface layers. These results substantiate the
analysis of the temperature profile of the young disk IRAS 04302 based on a
similar V-shaped emission pattern of one H2CO transition toward that source
(van ’t Hoff et al., 2020). The increase in H2CO intensity in the inner
envelope (or outer disk, as detailed modeling is required to determine the
exact location) could then be due to a lower freeze-out temperature at lower
densities or an increase in temperature at the disk–envelope interface (as
discussed in Sect. 4.3.2).

SO has been suggested to be enhanced at the centrifugal barrier in L1527, due
to elevated temperatures in this region caused by an accretion shock (e.g.,
Sakai et al., 2014b, 2017). While the concept of a centrifugal barrier is not
supported by hydrodynamic simulations, the physics and dynamics at the
disk–envelope interface are complex (Jones et al., 2022; Shariff et al.,
2022), and models show that SO can be enhanced if a shock occurs (Aota et al.,
2015; Miura et al., 2017; van Gelder et al., 2021). Consistent with previous
observations, SO emission is strong at scales $\lesssim$1′′, and in the region
of the pv-diagram consistent with the outer disk and/or inner envelope.
However, a careful examination of the individual velocity channels suggests
that the emission is coming from surface layers of the envelope (i.e., along
the cavity wall) rather than the midplane. This is, for example, clearly
visible at $-$1.54 km s-1, where H2CO $3_{2,1}-2_{2,0}$ displays emission from
the disk surface layers and the envelope midplane, while the SO emission
surrounds the H2CO envelope midplane emission (Fig. 10, but see also Fig. 8).
The SO emission pattern is also inconsistent with a simple model with emission
from the inner envelope (Fig. 10, fifth set of panels), and shows better
agreement with a model where the emission solely originates in the surface
layers of the disk and envelope (Fig. 10, fourth set of panels).

Based on the H2CO line ratio, the temperature in the disk surface layers is
$\gtrsim$60 K, so the origin of the SO emission could be thermal sublimation
of SO ice as the freeze out temperature of SO is $\sim$40–60 K (Hasegawa &
Herbst, 1993; Garrod & Herbst, 2006). Thermal sublimation may also explain why
there is some SO emission present along the midplane at $\sim$0$\farcs$7 at
low redshifted velocities (0.46-0.96 km s-1), as the 13CO brightness
temperature is increased in this region. However, the increase in 13CO
brightness temperature is visible at higher velocities ($\sim$1.8 km s-1; Fig.
13), while there is no SO emission along the midplane at those velocities.
Alternatively, SO may trace UV irradiated environments, either because of UV
heating of the gas causing SO ice to desorb, or because its formation becomes
possible in these regions through photodissociation of H2O. It is possible to
form SO in shocks, which may occur at the disk–envelope interface and/or along
the outflow cavity wall, but this still requires the presence of a UV field
(van Gelder et al., 2021). If the distribution of SO is set by the UV field,
this may naturally lead to an enhancement in the inner envelope as UV
radiation may penetrate deeper into the envelope than into the disk. However,
a detailed study is required as the disk could shadow parts of the inner
envelope. An SO distribution along the outflow cavity wall was also inferred
for the embedded disk TMC1A (Harsono et al., 2021). Observations of multiple
SO transitions are needed to derive the temperature of the emitting gas and
detailed modeling will be required to fully constrain the spatial and
physical/chemical origin of the SO emission.

##  5 Conclusions

We have presented high resolution (0$\farcs$06–0$\farcs$17 or 8–24 au) ALMA
observations (taken as part of the Large Program eDisk) of the 1.3 mm
continuum and molecular line emission toward the Class 0 protostar L1527, and
provided a qualitative description of the different emission morphologies and
their potential underlying physical and/or chemical conditions. The main
conclusions are summarized below:

  * •

The continuum emission is smooth, but asymmetric along both the major
(north–south) and minor axis (east–west), with emission being brighter in the
south and east. The flaring nature of the disk and the comparable brightness
temperature of the dust and 13CO emission suggest that the grains have not yet
grown beyond $\sim$1 mm and settled to the midplane.

  * •

Although the disk is viewed nearly edge-on, there is evidence of misalignment
between different components as the continuum asymmetry along the minor axis
(on scales of $\lesssim$0$\farcs$05) and the large-scale outflow ($\sim$100′′)
suggest that the east side of the system is the far side, while the SiO jet
($\lesssim$0$\farcs$1) and envelope emission (a few arcsec) suggest that the
west side is the far side.

  * •

Different molecules trace different components of the protostellar system.
Outflowing material is most clearly visible in 12CO, but also in 13CO, C18O
and H2CO, while SiO traces a compact jet in the western outflow cavity. The
outflow cavity wall is also visible in SO. Super-Keplerian 12CO emission in
the inner $\sim$1′′ may trace a disk wind. c-C3H2 and DCN only show emission
from the envelope, although higher sensitivity is required to rule out their
presence in the disk. 13CO, C18O, H2CO and SO trace the disk and inner
envelope, with H2CO emission arising predominantly in the disk surface layers.
SO emission is dominated by the envelope surface along the outflow cavity wall
and the disk component originates in the surface layers. This suggests that SO
may be tracing UV irradiated regions.

  * •

Analysis of the pv-diagrams of 13CO and C18O results in a $\sim$100 au
Keplerian rotating disk around a $\sim$0.5 $M_{\sun}$ star.

  * •

The disk is warm, with temperatures of 20–40 K throughout the midplane and
$\gtrsim$50–60 K in the surface layers. The disk is therefore too warm for CO
freeze out, which occurs at a midplane radius of $\sim$350 au in the envelope,
while H2CO is frozen out in the midplane down to $\lesssim$25 au.

  * •

The 13CO brightness temperature and H2CO line ratio suggest a potential
temperature increase around the disk–envelope interface. However, this
increase is only seen at redshifted velocities for 13CO and more detailed
modeling is required to determine whether the higher temperature occurs in the
outer disk or inner envelope, and whether it is associated with an accretion
shock.

High resolution observations of multi-wavelength continuum and multiple
molecular species are required to study young disks. Given the complex nature
of molecular line emission from a disk–envelope system, these observations
need to be combined with source-specific radiative transfer modeling to
provide a detailed picture of the physical and chemical structure. The eDisk
observations and the work presented here highlight the potential of such
studies, and a comparison between the ALMA and JWST NIRCam images already
shows the synergy between the two observatories.

We thank the referee for carefully reading the manuscript. This paper makes
use of the following ALMA data: ADS/JAO.ALMA#2019.1.00261.L,
ADS/JAO.ALMA#2019.A.00034.S and ADS/JAO.ALMA#2017.1.00509.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), 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 is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. M.L.R.H
acknowledges support from the Michigan Society of Fellows. J.J.T. acknowledges
support from NASA XRP 80NSSC22K1159. Z.-Y.L. is supported in part by NASA
NSSC20K0533 and NSF AST-1910106. N.O. acknowledges support from National
Science and Technology Council (NSTC) in Taiwan through the grants NSTC
109-2112-M-001-051 and 110-2112-M-001-031. J.K.J., S.G., and R.S. acknowledge
support from the Independent Research Fund Denmark (grant No. 0135-00123B).
Z.-Y.D.L. acknowledges support from NASA 80NSSC18K1095, the Jefferson Scholars
Foundation, the NRAO ALMA Student Observing Support (SOS) SOSPA8-003, the
Achievements Rewards for College Scientists (ARCS) Foundation Washington
Chapter, the Virginia Space Grant Consortium (VSGC), and UVA research
computing (RIVANNA). Y.A. acknowledges support by NAOJ ALMA Scientific
Research Grant code 2019-13B, Grant-in-Aid for Scientific Research (S)
18H05222, and Grant-in-Aid for Transformative Research Areas (A) 20H05844 and
20H05847. I.d.G. acknowledges support from grant PID2020-114461GB-I00, funded
by MCIN/AEI/10.13039/501100011033. P.M.K. acknowledges support from NSTC
108-2112- M-001-012, NSTC 109-2112-M-001-022 and NSTC 110-2112-M-001-057. W.K.
was supported by the National Research Foundation of Korea (NRF) grant funded
by the Korea government (MSIT) (NRF-2021R1F1A1061794). C.W.L. is supported by
the Basic Science Research Program through the National Research Foundation of
Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-
2019R1A2C1010851), and by the Korea Astronomy and Space Science Institute
grant funded by the Korea government (MSIT; Project No. 2022-1-840-05). J.E.L.
was supported by the National Research Foundation of Korea (NRF) grant funded
by the Korean government (MSIT) (grant number 2021R1A2C1011718). L.W.L.
acknowledges support from NSF AST-2108794. S.N. acknowledges support from the
National Science Foundation through the Graduate Research Fellowship Program
under Grant No. 2236415. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the authors and do not
necessarily reflect the views of the National Science Foundation. S.T. is
supported by JSPS KAKENHI Grant Numbers 21H00048 and 21H04495. This work was
supported by NAOJ ALMA Scientific Research Grant Code 2022-20A. S.P.L. and
T.J.T. acknowledge grants from the National Science and Technology Council of
Taiwan 106-2119-M-007-021-MY3 and 109-2112-M-007-010-MY3. J.P.W. acknowledges
support from NSF AST-2107841. H.-W.Y. acknowledges support from the National
Science and Technology Council (NSTC) in Taiwan through the grant NSTC
110-2628-M-001-003-MY3 and from the Academia Sinica Career Development Award
(AS-CDA-111-M03).

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##  Appendix A Additional continuum images

Figure 17 presents an overview of the 1.3 mm continuum toward L1527 imaged
with different robust parameters in addition to the image made with a robust
value of $-$0.5 as presented in Fig. 2 (left panel). In addition, Fig. 18
presents a similar image for the 3.3 mm continuum image from archival ALMA
data (2017.1.00509.S, PI: N. Sakai) as shown in Fig. 2 for 1.3 mm.

Figure 17: ALMA 1.3 mm continuum image of L1527 imaged with different robust
parameters as listed in the top left corner of each panel. The robust = $-$0.5
image is shown in the left panel of Fig. 2. The beam size is depicted by the
white ellipse in the bottom left corner of each panel. The solid white contour
marks the 5$\sigma$ level and the white cross indicates the source position.
Figure 18: ALMA 3.3 mm continuum image of L1527 from archival data created
with the eDisk data reduction script. The left panel shows the full extent of
the continuum imaged with a robust parameter of $-$1.0 (color scale; beam size
of 0$\farcs$086 $\times$ 0$\farcs$043), with the solid white contour marking
the 5$\sigma$ level (0.13 mJy beam-1). The dotted white contour marks the
5$\sigma$ level (0.04 mJy beam-1) of the map imaged with a robust parameter of
2.0 (beam size of 0$\farcs$225 $\times$ 0$\farcs$173). The black dashed square
shows the region depicted in the top middle panel, where the brightness
temperature of the continuum is displayed. The top right panel shows the
normalized intensity along the disk minor axis at source position (orange) and
at 15 au to the north (top black curve) and south (bottom black curve). This
is a slightly different offset compared to what is shown for the 1.3 mm image,
as the asymmetry is strongest at larger radii at 3.3 mm. The bottom right
panel shows the normalized intensity along the disk major axis at source
position (orange) and at 3 au to the east (left black curve) and west (right
black curve). Black and orange triangles in the continuum image (top middle
panel) mark the locations of the intensity profiles. The black curves are
shifted by 0.2 in normalized intensity with respect to the orange curves for
better visibility. The shaded region depicts the 3$\sigma$ level and the
dotted lines are the mirror images of the solid lines to highlight the
asymmetries.

##  Appendix B Additional molecular line images

The individual 12CO, 13CO, and C18O channel maps used to make the RGB overlay
(Fig. 5) are shown in Fig. 19. In addition, Figs. 20–22 present 12CO, 13CO,
and C18O channel maps to highlight the outflowing material visible in the
three CO isotopologues. Velocity channel maps for the c-C3H2 transitions are
displayed in Fig. 23, for DCN in Fig. 24, for H2CO $3_{2,1}-2_{2,0}$ in Fig.
25, and for SO in Fig. 26. Figure 27 shows the SO moment eight (peak
intensity) map.

Figure 19: Selected velocity channel maps of 12CO (first and fourth row), 13CO
(second and fifth row) and C18O (third and sixth row) as used for the RGB
overlay in Fig. 5. The top three rows display the emission on scales of 24′′
(corresponding to the top row in Fig. 5) and the bottom three rows display the
emission on scales of 6′′ (corresponding to the bottom row in Fig. 5). Figure
20: Velocity channel maps of 12CO. The color scale is capped to highlight the
large scale emission. A vertical white dotted line is drawn at the same
position in the top and bottom panels to guide the eye with respect to the
outward moving emission front at the highest velocity offsets. The white
arrows at $-$3.67 – $-$1.77 km s-1 and 2.68 – 3.95 km s-1 highlight the
potential jets. The beam is depicted in the bottom left corner of the bottom
right panel, and the velocity with respect to the system velocity is listed in
the top right corner of each panel.  Figure 21: Low and intermediate velocity
channel maps of 13CO highlighting the emission in the outflow cavity. Two
vertical white dotted lines are drawn at the same position in each panel to
guide the eye with respect to the outward moving emission fronts with higher
velocity offsets. The beam is depicted in the bottom left corner of the bottom
right panel, and the velocity with respect to the system velocity is listed in
the top right corner of each panel. Figure 22: As Fig. 21, but for C18O.
Different components are outlined in three velocity channels ($-$0.54 –
$-$0.21 km s-1), with dashed red lines indicating outflowing material and
dashed black lines marking the envelope surface or cavity wall. These curves
are drawn by hand and merely serve as a guide for the eyes.

Figure 23: Velocity channel maps of c-C3H2 $6_{0,6}-5_{1,5}$ blended with
$6_{1,6}-5_{0,5}$ (top row), $5_{1,4}-4_{2,3}$ (middle row) and
$5_{2,4}-4_{1,3}$ (bottom row).

Figure 24: Velocity channel maps of DCN on a 24′′ scale (top row) and 6′′
scale (bottom row). Figure 25: Velocity channel maps of H2CO
$3_{2,1}-2_{2,0}$. Figure 26: Velocity channel maps of SO Figure 27: Peak
intensity (moment eight) map of SO.

##  Appendix C Additional figures

Figure 28 presents the H2CO $3_{0,3}-2_{0,2}$/$3_{2,2}-2_{2,1}$ line ratio as
function of temperature for optically thin emission in LTE.

Figure 28: Line ratio of the H2CO $3_{0,3}-2_{0,2}$ and $3_{2,2}-2_{2,1}$
transitions as function of temperature for optically thin emission in LTE. The
shaded area marks the uncertainty for a signal-to-noise ratio of 6 for the
$3_{2,2}-2_{2,1}$ transition and 12 for the $3_{0,3}-2_{0,2}$ transition.
Horizontal dotted lines marking line ratios of 3 and 5 are drawn for
reference.