11institutetext:  Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp - CNRS -
Université Paris Diderot, 91191 Gif-sur-Yvette Cedex, France 22institutetext:
SOFIA Science Center, Universities Space Research Association, NASA Ames
Research Center, Moffett Field, California 94035, USA 22email:
<EMAIL_ADDRESS>33institutetext: European Southern Observatory,
Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago , Chile
44institutetext: Harvard-Smithsonian Center for Astrophysics, Cambridge, MA
02138, USA 55institutetext: National Astronomical Observatory of Japan, NAOJ
Chile, Alonso de Córdova 3788, Office 61B, 7630422, Vitacura, Santiago, Chile
66institutetext: Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura,
Santiago, Chile 77institutetext: NAOJ Fellow

# Physical conditions for dust grain alignment in Class 0 protostellar cores

I. Observations of dust polarization and molecular irradiation tracers

V. J. M. Le Gouellec 112233 A. J. Maury 1144 C. L. H. Hull 556677

###### Abstract

Context. High angular resolution observations of Class 0 protostars have
produced detailed maps of the polarized dust emission in the envelopes of
these young embedded objects. Interestingly, the improved sensitivity brought
by ALMA has revealed wide dynamic ranges of polarization fractions, with
specific locations harboring surprisingly large amounts of polarized dust
emission.

Aims. Our aim is to characterize the grain alignment conditions and dust
properties responsible for the observed polarized dust emission in the inner
envelopes ($\leq\,1000$ au) of Class 0 protostars.

Methods. We analyzed the polarized dust emission maps obtained with ALMA and
compared them to molecular line emission maps of specific molecular tracers,
mainly C2H, which allowed us to probe one of the key components in dust grain
alignment theories: the irradiation field.

Results. We show that C2H peaks toward outflow cavity walls, where the
polarized dust emission is also enhanced. Our analysis provides a tentative
correlation between the morphology of the polarized intensity and C2H
emission, suggesting that the radiation field impinging on the cavity walls
favors both the grain alignment and the warm carbon chain chemistry in these
regions. We propose that shocks happening along outflow cavity walls could
potentially represent an additional source of photons contributing to dust
grain alignment. However, some parts of the cores, such as the equatorial
planes, exhibit enhanced polarized flux, although no radiation driven
chemistry is observed, for example where radiative torques are theoretically
not efficient enough. This suggests that additional physical conditions, such
as source geometry and dust grain evolution, may play a role in grain
alignment.

Conclusions. Comparing chemical processes with grain alignment physics opens a
promising avenue to develop our understanding of the dust grain evolution
(i.e., their origin, growth, and structure) in the interior of Class 0
protostars. The source geometry and evolution can represent important factors
that set the environmental conditions of the inner envelope, determining
whether the radiation field strength and spectrum can drive efficient dust
grain alignment via radiative torques.

###### Key Words.:

ISM: jets and outflows — ISM: magnetic fields — polarization — stars:
formation — stars: protostars — radiation mechanisms: thermal — radiative
transfer

##  1 Introduction

Located in the densest parts of molecular clouds, Class 0 protostars are the
youngest low-mass star forming objects (Andre et al., 1993; Andre & Montmerle,
1994). They are composed of a growing protostellar embryo at the center, which
accretes material from the surrounding cold protostellar envelope. These
objects have yet to accrete the main part of their future main sequence star
mass as most of their mass is still located in the envelope, such that
$L_{\textrm{sub-mm}}/L_{\textrm{bol}}\gg 0.5\%$ and $M_{\textrm{env}}\gg
M_{\star}$. The Class 0 protostellar phase thus corresponds to a period of
vigorous accretion activity whose physical characteristics will set the
properties of the future star and protoplanetary disk. At this stage the
accretion is ruled by a variety of physical processes, and it remains unclear
if, for example, the accretion is disk-regulated, as it is in later stage T
Tauri stars (Hartmann et al., 2016), or if it occurs directly from the
infalling flows of the envelope (Lee et al., 2021). The accretion is
responsible for the vigorous ejection of material in the form of (bi)polar
jets (Bachiller & Tafalla, 1999; Arce et al., 2007; Bally, 2016), and for an
important irradiation feedback on the envelope caused by the accretion shock
onto the central protostellar embryo (Spaans et al., 1995). Outflow cavities
surrounding the jets are also formed, potentially powered by the collimated
jet (Raga & Cabrit, 1993) and/or by the ejection of low-velocity winds
launched at disk scales (Louvet et al., 2018; de Valon et al., 2020).

Outflow cavities are directly subject to the radiation field emanating from
the accretion activity (Krumholz et al., 2012), which may highly influence the
chemistry of the inner envelope (Stäuber et al., 2004, 2005). For instance,
far-infrared rotational lines of CO and H2O from the bulk of the emission of
young protostars (Spaans et al., 1995; Hogerheijde et al., 1998; van Kempen et
al., 2009a; Kristensen et al., 2013), were reproduced by models accounting for
UV-heated gas and/or shocks along outflow cavity walls (Goicoechea et al.,
2012; Visser et al., 2012; Lee et al., 2015). The UV photons coming from the
accretion disk around the central protostellar embryo, which are reprocessed
or are scattered into cavities, are responsible for heating the gas and thus
creating photon dominated region (PDR) conditions in outflow cavity walls,
which can also be probed by [CI] and [CII] lines; the presence of these lines
suggests the presence of UV-irradiated shocks (van Kempen et al., 2009b;
Goicoechea et al., 2012; Yıldız et al., 2012). Farther away from the central
object, additional UV photons can be produced in bow shocks of the outflow
(Böhm et al., 1993), if $J$-shocks are present (Neufeld & Dalgarno, 1989a, b),
and/or by small-scale shocks along the walls of the cavities (Curiel et al.,
1995; Saucedo et al., 2003; Walter et al., 2003). The presence of irradiating
photons was also confirmed by observations along the outflow cavity walls of
molecules tracing warm chemistry processes involving UV photons, such as C2H
and $c$-C3H2 (Murillo et al., 2018; Tychoniec et al., 2021), because the
formation pathway of these molecules requires a significant amount of UV
irradiation. The corresponding chemistry is similar to what is encountered at
the edge of PDR zones, for example the Horsehead PDR (Cuadrado et al., 2015;
Guzmán et al., 2014, 2015).

On the other hand, recent observations have revealed that outflow cavity walls
also seem to harbor specific grain alignment conditions as strong polarized
dust emission along the walls of the bipolar outflow cavities were detected
(Hull et al., 2017a; Cox et al., 2018; Maury et al., 2018; Ko et al., 2020;
Kwon et al., 2019; Le Gouellec et al., 2019; Hull et al., 2020). In regions of
optically thin thermal dust emission, which is the case for the typical
spatial scales resolved by ALMA toward protostellar envelopes (i.e., $\sim$ 50
to 1000 au), the polarization is caused by the thermal emission of aligned and
aspherical dust grains. In the typical conditions prevailing in protostellar
envelopes, the most likely grain alignment process is caused by radiative
alignment torques (RATs; Draine & Weingartner 1996, 1997; Lazarian & Hoang
2007; Andersson et al. 2015), which aligns the dust grains’ minor axis
parallel to the ambient magnetic field lines. This causes the linear
polarization of the dust thermal emission to be orthogonal to the magnetic
field component projected on the plane of the sky. The RAT mechanism is
subject to the local environmental conditions (i.e., the mean wavelength,
strength, and degree of anisotropy of the radiation field), the dust
characteristics (size, shape, composition), and the gas temperature and
density. Understanding the causes for the strong polarized dust emission
detected in outflow cavity walls and within the inner envelope ($\leq 500$ au)
is thus crucial to further developing the knowledge we have of the impacts
that accretion has on what surrounds the central protostellar embryo. Because
it governs the gaseous collisional rate that randomizes the orientation of the
dust grains, gas density is one of the key parameters that set the grain
alignment conditions (see, e.g., Reissl et al. 2020). However, the
polarization fraction maps are irregular with nonhomogeneous spatial
distribution in protostellar envelopes. The high values exhibited in outflow
cavity walls may point toward the total intensity not being a good proxy for
the local gas volume density and/or specific grain alignment conditions such
as favored irradiation. In this work, divided into two papers, we make a joint
effort to analyze both the UV-sensitive chemistry and the efficiency of the
dust grain alignment in the interiors of Class 0 protostars. This paper
focuses on comparing the location of strongly irradiated molecular gas with
the spatial distribution of aligned grains in the envelope of Class 0
protostellar cores through tracers of warm chemistry and polarized dust
emission. In this first work, which relates to observations alone, we use
preferentially the polarized intensity as a proxy for the morphology of the
favorable grain alignment conditions to qualitatively address the role of the
radiation field. The polarization fraction values taken into account with the
levels of magnetic field organization will be discussed in Paper II, which
will focus on reproducing the observed grain alignment efficiency via
comparisons with radiative transfer modeling, where the role of the radiation
field is investigated.

This paper is structured as follows. In Section 2 we present ALMA dust
polarization observations alongside ALMA molecular line observations of the
UV-sensitive C2H molecule and the shock-tracer SO in a sample of Class 0
protostars. In Section 3 the spatial distribution of polarized dust emission
is qualitatively compared with the distributions of the molecular emission
lines. Finally, in Section 4 we discuss the comparisons between the dust
polarization and irradiation tracer observational results. We draw our
conclusions in Section 5.

##  2 ALMA observations of the polarized dust emission and molecular gas
tracers

Table 1: Sources and ALMA dust polarization observations details Name | $\alpha_{\textrm{J2000}}$ | $\delta_{\textrm{J2000}}$ |  $M_{\textrm{env}}$a |  $L_{\textrm{bol}}$a |  Dist.b |  $\lambda$c |  $\theta_{\textrm{res}}$d |  Referencee
---|---|---|---|---|---|---|---|---
|  |  | $M_{\odot}$ | $L_{\odot}$ | pc | (mm) | (au) |
B335 | 19:37:00.91 |  -07:34:09.60 |  01.44 |  002.7 | 165 |  1.30 | 101 |  Maury et al. (2018), in prep.
L1448 IRS2 | 03:25:22.41 |  -30:45:13.21 |  01.30 |  007.0 | 294 |  1.30 | 135 | Kwon et al. (2019)
NGC1333 IRAS4A | 03:29:10.55 |  -31:13:31.00 |  12.30 |  014.2 | 294 |  1.30 | 112 | Ko et al. (2020)
Serpens Emb 8 | 18:29:48.09 |  -01:16:43.30 | 12.80 | 007.3 | 484 | 0.87 | 161 | Hull et al. (2017b)
Serpens Emb 8(N) | 18:29:48.73 |  -01:16:55.61 | 484 | 0.87 | 161 | Le Gouellec et al. (2019)
For the CCH spectral lines presented in the figures below, we integrated over
the two hyperfine structures in order to construct the moment 0 maps.
a Envelope mass $M_{\textrm{env}}$ and bolometric luminosity
$L_{\textrm{bol}}$ values. The values calculated for Serpens Emb 8 and Emb
8(N) include the two sources together (Enoch et al., 2009, 2011). Kurono et
al. (2013); Maury et al. (2018) for B335. Sadavoy et al. (2014); Karska et al.
(2018) for L1448 IRS2. Karska et al. (2018); Galametz et al. (2019) for
IRAS4A.
b Distance reported in the literature. Zucker et al. (2019) for Perseus and
Serpens. Watson (2020) for B335. We scale the masses and luminosities found in
the literature to the distances listed here.
c Wavelength of dust polarization observations.
d Angular resolution in au. We took the effective synthesized beam size of the
ALMA maps.
e Reference of the publication(s) presenting the ALMA dust polarization dataset(s).  Table 2: ALMA molecular line observations details Name |  Spectral Lines a |  $\nu$b |  Referencec
---|---|---|---
|  | (GHz) |
B335 |  C2H ($J_{N,F}$=7/23,4–5/22,3) | 262.004260 | Imai et al. (2016)
C2H ($J_{N,F}$=7/23,3–5/22,2) | 262.006482
CS ($J$=5–4) | 244.935644
$c$-C3H2 (52,3–43,2) | 249.054368
L1448 IRS2 |  C2H ($J_{N,F}$=5/23,3–3/22,2) | 262.064986 | Zhang et al. in prep.
C2H ($J_{N,F}$=5/23,2–3/22,1) | 262.067469
CS ($J$=5–4) | 244.935644
NGC1333 IRAS4A |  C2H ($J_{N,F}$=7/23,4–5/22,3) | 262.004260 | Chuang et al. (2021)
C2H ($J_{N,F}$=7/23,3–5/22,2) | 262.006482
CS ($J$=5-4) | 244.935644
SO ($N_{J}$=7(6)–6(5)) | 261.843684
Serpens Emb 8 |  C2H ($J_{N,F}$=7/23,4–5/22,3) | 262.004260 | van Gelder et al. (2020)
C2H ($J_{N,F}$=7/23,3–5/22,2) | 262.006482
SO ($N_{J}$=7(6)–6(5)) | 261.843684
Serpens Emb 8(N) |  C2H ($J_{N,F}$=7/23,4–5/22,3) | 262.004260 | Le Gouellec et al. (2019)
C2H ($J_{N,F}$=7/23,3–5/22,2) | 262.006482
SO ($N_{J}$=6(5)–5(4)) | 219.949433 | Tychoniec et al., in prep.
For the CCH spectral lines presented in the figures below, we integrated over
the two hyperfine structures in order to construct the moment 0 maps.
a Spectral lines that we present in this study.
b Frequency of spectral line observations.
b Reference of the publication(s) presenting the ALMA molecular line
dataset(s).

Figure 1: Observations of magnetic fields, polarized intensity, and molecular
lines around the B335 Class 0 protostellar core. Left panel: Line segments
represent magnetic field lines, rotated by 90∘ from the dust polarization
angle (the length of a segment does not represent a quantity). They are
plotted where the polarized intensity $P\,>\,3\sigma_{P}$. The gray scale is
the total intensity (Stokes $I$) of the thermal dust emission, shown from
3$\sigma_{I}$. The white contours trace the total intensity at levels of 5, 8,
11, 16, 24, 44, 74, 128, 256 $\times\,\sigma_{I}$. The blue and red contours
trace the moment 0 map of the blueshifted (by integrating emission from –25 to
7 km s-1) and redshifted (by integrating emission from 10 to 35 km s-1) CO
($J$ = 2 $\rightarrow\,$1) map at levels of 3, 5, 7, 9, 11, 16, 24, 44, 74,
128, 256, 400 $\times$ the rms noise level of the map. Right panel: In each
panel the color scale is the dust polarization intensity, shown from
3$\sigma_{P}$. The crosses indicate the peak of the dust continuum map. The
thin gray contours trace the dust polarization intensity, at levels of 3, 5,
7, 9, 11, 16, 24, 44 $\times\,\sigma_{P}$. The thick light blue contours trace
the moment 0 map of the C2H (by integrating emission from 7 to 12.5 km s-1)
molecular emission spectral line (see Table 2 for details of the line
transitions) at levels of 3, 5, 7, 9, 11, 16, 24, 44 $\times$ the rms noise
level of each map. In the bottom left corner of each panel the ellipses
represent the beam resolution element of a given dataset: yellow for polarized
dust emission, red for CO bipolar outflow emission, and white for the CCH
spectral emission line. The ALMA 1.3mm dust polarized emission is from Maury
et al. (2018) and Maury et al. (in preparation). The ALMA CO ($J$ = 2
$\rightarrow\,$1) bipolar outflow emission is from Cabedo et al. (2021). The
C2H emission line is from Imai et al. (2016).

Figure 2: Same as Figure 1, but for the L1448 IRS2 Class 0 protostellar core.
The blue and red contours trace the moment 0 map of the blueshifted (by
integrating emission from –16.5 to 3 km s-1) and redshifted (by integrating
emission from 6 to 21.5 km s-1). The thick light blue contours (top right and
bottom panels) trace the moment 0 map of the C2H (by integrating emission from
3 to 8 km s-1) molecular emission spectral line. The ALMA 1.3mm dust polarized
emission is from Kwon et al. (2019). The ALMA CO ($J$ = 2 $\rightarrow\,$1)
bipolar outflow emission is from Tobin et al. (2018). The C2H emission line is
from ALMA project 2016.1.01501.S, Y. Zhang (in preparation).

Figure 3: Same as Figure 1, but for the NC1333 IRAS4A Class 0 protostellar
core. The blue and red contours trace the moment 0 map of the blueshifted (by
integrating emission from –30 to 4 km s-1) and redshifted (by integrating
emission from 10 to 55.5 km s-1). The thick light blue contours (top right and
bottom panels) trace the moment 0 map of the C2H (by integrating emission from
2.5 to 15.5 km s-1) and SO (by integrating emission from -10 to 19.5 km s-1)
molecular emission spectral line. The two crosses are located at the two peaks
of the dust continuum map. IRAS4A1 is to the southeast of IRAS4A2. The ALMA
1.3mm dust polarized emission is from Ko et al. (2020). The ALMA CO ($J$ = 2
$\rightarrow\,$1) bipolar outflow emission is from T.C. Ching 2016.1.01089.S.
The SO emission is line from Chuang et al. (2021).

Figure 4: Same as Figure 1, but for the Serpens Emb 8 Class 0 protostellar
core. The blue and red contours trace the moment 0 map of the blueshifted (by
integrating emission from –10 to 6.5 km s-1) and redshifted (by integrating
emission from 10 to 21 km s-1). The thick light blue contours (top right and
bottom panels) trace the moment 0 map of the C2H (by integrating emission from
4.4 to 12.6 km s-1) and SO (by integrating emission from -1.5 to 15.5 km s-1)
molecular emission spectral line. ALMA band 0.87mm dust polarized emission is
from Hull et al. (2017a). ALMA CO ($J$ = 2 $\rightarrow\,$1) bipolar outflow
emission is from Le Gouellec et al. (2019). C2H and SO emission line is from
van Gelder et al. (2020) and Tychoniec et al. (2021).

Figure 5: Same as Figure 1, but for the Serpens Emb 8(N) Class 0 protostellar
core. The blue and red contours trace the moment 0 map of the blueshifted (by
integrating emission from –10 to 6.5 km s-1) and redshifted (by integrating
emission from 10 to 21 km s-1). The thick light blue contours (top right and
bottom panels) trace the moment 0 map of the C2H (by integrating emission from
5.4 to 12.8 km s-1) and SO (by integrating emission from -16 to 8 km s-1, and
from 10.5 to 35.5 km s-1) molecular emission spectral line. The ALMA band
0.87mm dust polarized emission, ALMA CO ($J$ = 2 $\rightarrow\,$1) bipolar
outflow emission, and C2H emission line are from Le Gouellec et al. (2019).
The SO emission line is from ALMA project 2019.1.00931.S, Tychoniec et al. (in
prep.).

We collected and analyzed observations of six Class 0 protostars carried out
with the ALMA interferometer: B335, L1448 IRS2, NGC1333 IRAS4A1 & IRAS4A2,
Serpens Emb 8, Serpens Emb 8(N). We present in Figures 1, 2, 3, 4, and 5 the
maps of the dust continuum emission, the polarized dust emission, and the
molecular gas emission obtained toward six sources. We use molecular line
observations to either trace the bipolar outflow (with the CO ($J$ = 2
$\rightarrow\,$1) transition), or to probe the irradiation field in the inner
core with the C2H and SO molecular species (two other molecules $c$-C3H2 and
CS, potentially tracing the radiation field, are presented in Appendix A as
additional material). As introduced above, the C2H molecule has been detected
in PDRs, and the role of the irradiation field (enhancing the ionization) in
its chemical formation pathway has been well established. In addition, SO is a
tracer of shocks, which can be sources of UV photons. We compare the maps of
polarized flux with those of moment 0 molecular emission lines to investigate
whether the dust polarization is enhanced in highly irradiated zones. The goal
is to understand the physical conditions that favor efficient grain alignment.
We discuss the chemistry of these molecules in Section 4.3.

Details of the sources and dust polarization observations we present can be
found in Table 1, while the details of the spectral lines studied can be found
in Table 2. These sources were selected because the interferometric maps
exhibit extended polarized dust emission throughout the inner envelope
($\sim$10-2000 au), and ALMA datasets of the chemical tracers we target were
publicly available, offering similar $uv$-coverage to the dust polarization
observations111Another source, the Class 0 B1-c in Perseus, originally
triggered our interest. The ALMA C2H molecular emission line published in van
Gelder et al. (2020); Tychoniec et al. (2021) exhibit an extended emission
toward the bipolar outflow cavity and cavity walls. However, the 1.3 mm ALMA
dust polarization observations published in Cox et al. (2018) suffers from a
lack of sensitivity; only a few patches of polarized intensity are detected at
the base of the outflow cavity.. The polarized dust emission maps of B335,
Serpens Emb 8, and Serpens Emb 8(N) are from Hull et al. (2017b), Le Gouellec
et al. (2019), and Le Gouellec et al. (2020), and details of the data
reduction can be found in the corresponding references. For this project we
calibrated and imaged the ALMA dust polarization observations toward L1448
IRS2, and NGC1333 IRAS4A. To produce the polarized dust continuum emission
maps we used the tclean task of the CASA software version 5.8 (McMullin et
al., 2007). We applied three to four rounds of consecutive phase-only self-
calibration (Brogan et al., 2018), using the total intensity (Stokes I)
solutions as the model, with a Briggs weighting parameter of 0.5 to 1,
depending on the source, and the appropriate integration time intervals. The
three Stokes parameters $I$, $Q$, and $U$ were cleaned separately after the
last round of self-calibration, using an appropriate residual threshold and
number of iterations. We then created the debiased polarized intensity maps
following the method from Wardle & Kronberg (1974) and Hull & Plambeck (2015).

A variety of ALMA 12m datasets at 1.3 mm were used to target the molecular
emission lines of C2H and SO, whose angular resolutions are about
0.3$\aas@@fstack{\prime\prime}$–0.8$\aas@@fstack{\prime\prime}$. The datasets
were pipeline calibrated and manually phase-only self-calibrated222For the
self-calibration of the spectral lines, we apply the phase self-calibration
solutions calculated with the continuum maps devoid of spectral lines on the
individual spectral line measurement sets., with the CASA software version 5.8
(McMullin et al., 2007). The images were made with the tclean task. The images
were produced with an adapted mask constructed manually in each channel
covering the entire emission. For the outflow traced by the CO molecular line,
we pipeline calibrated and manually phase-only self-calibrated ALMA 12m
observations of the CO ($J$ = 2 $\rightarrow\,$1) transition for L1448 IRS2
and NGC1333 IRAS4A. The CO molecular line observations are from Cabedo et al.
(2021) in B335, Hull et al. (2017b) in Serpens Emb 8, Le Gouellec et al.
(2019) and Tychoniec et al. (2019) in Serpens Emb 8(N), and Tobin et al.
(2018) in L1448 IRS2.

B335: Figure 1 presents the dust polarization observations from Maury et al.
(2018) and Maury et al. (in preparation) overlaid with contours following the
intensity levels of the integrated emission of the C2H molecular line from
Imai et al. (2016). The dataset also includes the SO
($N_{J}$=6${}_{7}\rightarrow 5_{6}$) transition, which we do not show here as
the line is only detected at the dust continuum peak. As pointed out in Maury
et al. (2018), the polarized dust emission in B335 is bimodal. The polarized
flux is either enhanced along the outflow cavity walls with the average
magnetic fields orientated east–west following the walls of the cavities or
enhanced toward the equatorial plane of the core (the northern patch of
polarized dust emission) where the magnetic field orientations are
north–south. This bi-modality is also found in the histogram of polarization
position (Maury et al., 2018), and is actually present in a few other
published observations of Class 0 cores (Le Gouellec et al., 2020). The
emission of the carbon chain molecule C2H is clearly enhanced toward the
outflow cavities. C2H emission appears across the bulk of the bipolar cavity
traced by the CO emission, with enhancement along the cavity walls, up to
$\sim$1500 au for the southern edges. The polarized flux and these molecular
emission lines thus appear to spatially overlap toward the outflow cavity
walls. However, the equatorial plane to the north of the dust continuum peak,
which is strongly polarized, seems to be devoid of molecular line emission
tracing irradiated conditions, suggesting a different nature of the
irradiation conditions in the mid-plane, compared to the outflow cavity walls.
This applies only to the northern part of the core, as the southern part is
much less polarized.

L1448 IRS2: Figure 2 presents the dust polarization observations from (Kwon et
al., 2019) overlaid with contours following the intensity levels of the
integrated emission of the C2H molecular line from Y. Zhang et al. (in
preparation) (ALMA project 2016.1.01501.S, PI: N. Sakai). The dataset also
includes the SO ($N_{J}$=6${}_{7}\rightarrow 5_{6}$) and SO
($N_{J}$=6${}_{6}\rightarrow 5_{5}$) transitions, which we do not show here as
the emission only peaks at the dust continuum peak. The polarized dust
emission is enhanced on each side of blue- and redshifted outflow, embracing
the cavities. The magnetic field lines exhibit a very pinched hourglass-like
morphology. The depolarization in the mid-plane is likely due to beam smearing
effects. The C2H molecular emission line appears enhanced toward the walls of
the cavities, as is the case for the polarized dust emission.

NGC1333 IRAS4A: Figure 3 presents the dust polarization observations from Ko
et al. (2020) overlaid with contours following the intensity levels of the
integrated emission of the C2H and SO molecular lines from Chuang et al.
(2021). Similarly to the SMA dust polarization of this wide binary (Girart et
al., 2006), the magnetic field global morphology exhibits a pinched hourglass-
like morphology aligned with the direction of the bipolar outflows. The maps
shown here, however, suggest that the polarized emission is enhanced along the
outflow cavities of both protostars IRAS4A1 (southeast) and IRAS4A2
(northwest) as well as the infalling equatorial planes. The SO molecular line
peaks toward the blue- and redshifted outflow of IRAS4A2, and only in the
blueshifted lobe of the IRAS4A1 outflow. In such a bright Class 0 object,
where dust polarization is strong and extended across the inner $\sim$2000 au
of the core, C2H emission is surprisingly not extended compared to the first
two objects we described. The C2H molecular emission line is mostly associated
with two compact emission features in the outflow of IRAS4A2, and a weak
$\sim$5$\sigma$ detection toward the eastern wall of the IRAS4A1 redshifted
cavity. The lower S/N emission shown in Chuang et al. (2021) exhibits a more
extended emitting region, consistent with the outflow cavity.

Serpens Emb 8: Figure 4 presents the dust polarization observations from Hull
et al. (2017a) overlaid with contours following the intensity levels of the
integrated emission of the C2H and SO molecular lines from van Gelder et al.
(2020). In this core the scenario seems to be surprising, given the drastic
difference between the extent of the C2H emission with respect to the
polarized dust emission. The C2H emission extends much farther than the
polarized dust emission in the central regions of the envelope. Where it
overlaps with the polarized dust emission, the C2H emission morphology seems
to show a morphology following closely that of the polarized intensity,
especially to the southeast of the core. At the base of the cavity walls of
the blueshifted outflow, the C2H emission is also enhanced and exhibits a
V-shaped pattern, confirming that the cavity walls are the ideal conditions to
form and/or excite the rotational transitions of C2H. The SO and C2H peaks are
also $\sim$ 2000 au away from the center, toward the cavity of the blueshifted
outflow in the northwest, where faint dust emission is also detected. The
surprising morphology of the C2H emission in this source, which is more
extended than the emission in the other protostars analyzed here, could be
explained by the recent accretion activity of this source. With near-infrared
spectroscopy, Greene et al. (2018) showed that the properties of the central
protostellar embryo (i.e., low surface gravity and effective temperature)
suggest that Serpens Emb 8 has recently undergone a period of high accretion
activity, which may explain the spatial extent of the irradiation-sensitive
chemistry in the core. The emission from the SO line exhibits an elongated
structure toward the center of the core that overlaps with one patch of
polarized dust emission. Finally, SO also peaks on the southern side of the
redshifted outflow lobe.

Serpens Emb 8(N): Figure 5 presents the dust polarization observations from Le
Gouellec et al. (2019) overlaid with contours following the intensity levels
of the integrated emission of the C2H and SO molecular lines from Le Gouellec
et al. (2019) and Tychoniec et al. (in preparation). C2H peaks in the outflow
cavities, with an asymmetry in the emission strength (it is stronger on the
redshifted side); it is slightly spatially shifted from the polarized dust
emission. On the redshifted side C2H peaks farther away than the polarized
dust emission, and on the blueshifted side C2H peaks inside the cavity, while
the polarized dust emission is enhanced toward the walls of the cavity. The
disorganization of the structures in dust and polarized dust emission of
Serpens Emb 8, relative to Serpens Emb 8(N), which is much more symmetric and
organized, suggests that irradiation may have escaped more easily throughout
the inner core in Emb 8. This would explain why the C2H emission is so
different between the two sources: it only peaks in the walls of the cavity in
Emb 8(N) versus everywhere in the inner envelope and in the blueshifted
outflow lobe in Emb 8. In Serpens Emb 8(N), the SO molecular emission line
peaks toward the walls of the blueshifted cavity, from the center of the
source up to $\sim$ 2000 au. It also peaks in the redshifted cavity, but much
farther away, at $\sim$ 2000 au from the source, likely spotting the bow shock
studied in Tychoniec et al. (2019). Toward the northern wall of the
blueshifted cavity, the SO emission coincides with a patch of highly polarized
dust emission.

Figure 6: Spectra of molecular emission lines in NGC1333 IRAS4A2, Serpens
Emb8, and Serpens Emb 8N. The solid lines show the spectra of the C2H, CS, and
SO molecular emission lines, toward the north (top left panel) and the south
(top right panel) of IRAS4A2. The spectra of the C2H and SO molecular emission
lines toward the redshifted cavity of Serpens Emb 8, and the blueshifted
cavity of Serpens Emb 8(N), are shown in the bottom left and bottom right
panel, respectively. For IRAS4A, the emission is summed over a circle of
2.5$\aas@@fstack{\prime\prime}$ in diameter, centered on the two peaks of C2H
visible in the integrated moment 0 map seen in Figure 3. For Serpens Emb 8 and
Serpens Emb 8(N), the spectra are from a circle of
1$\aas@@fstack{\prime\prime}$ in diameter located at 800 au from the center,
in the redshifted and blueshifted cavity, respectively. In all cases, while
the C2H hyperfine structure is detected at the $v_{\rm{lsr}}$, the spectra of
CS and SO are clearly broader, suggesting material linked to the outflowing
gas.

In summary, the carbon chain molecule C2H seems preferentially associated with
outflows and cavity walls in some sources, and is widely distributed in
others. Such different spatial segregation may suggest that the source
geometry plays an important role in the heating of the inner envelope (see
Section 4.1). Another spatial segregation among various irradiation conditions
is also suggested by the emission line spectra in IRAS4A, Serpens Emb 8, and
Serpens Emb 8(N) shown in Figure 6. In these four spectra, while the velocity
of the C2H associated hyperfine structure is distributed around the systemic
velocity of the source, SO exhibits a much broader range of gas velocities.
This indicates to what extent the molecular species we target belong to the
outflow (or the material entrained by the outflow), like SO, or if it belongs
to the envelope–cavity walls, like C2H. In addition, the spectra of CS is
distributed toward a broader range of gas velocities than the C2H spectra, but
narrower compared to the SO spectra (see Appendix A for the moment 0 maps of
CS). Hence, while C2H seems to trace the irradiated walls of the cavity,
located between the outflowing gas of the outflow and the infalling gas from
the envelope, SO seems to be linked with the outflowing gas, and as a shock
tracer its emission emanates from the interaction zone between cavity walls
and the jet–outflow system.

These molecular lines are expected to trace the regions with abundant UV
photons in the gas. We thus investigate whether the polarized dust emission
presents different properties in these areas, which would allow us to
characterize the role played by such energetic photons in the mechanisms
producing the polarized dust emission. However, significant dust polarization
signals are observed toward locations that are likely not under a strong
radiation field, for example in equatorial mid-planes and envelope emission in
the north of B335 and mid-planes of IRAS4A. Therefore, the local physical
conditions need to be further explored in order to understand how dust grain
alignment is efficient in this kind of environment. This is addressed with the
help of radiation transfer calculations presented in Paper II.

##  3 Comparing the spatial distribution of the emissions maps

Figure 7: Results from the two-sided 1D and 2D KS tests between the $P$ and
C2H moment 0 maps of B335, performed with $N$=100 and $n$=1000. Top row (left
and middle): $P$ and C2H moment 0 emission maps in color scale, respectively.
Both maps are overlaid with the $N$ lines, where the white lines correspond to
the $N^{\prime}$ sample of selected profiles. The red lines correspond to the
profiles where the S/N selection criteria was not reached, and the black lines
correspond to the profiles where the 1D Gaussian fit does not converge.
(right): Obtained ($\sigma$,$\mu$) values from these 1D Gaussian fits in the
form of a 2D diagram, with a linear regression line fitting both the $\sigma$
and $\mu$ values. Middle row: Results of the two-sided 2D KS tests, where each
pixel corresponds to a given Gaussian distribution of width $\Sigma$, added on
the sample of $\sigma$ values ($x$-axis) and $\mu$ values ($y$-axis), obtained
from the $P$ map. The gray scale corresponds to the $p$-values obtained after
$n$ realizations. The left, middle, and right panels, show the mean $p$-value
minus the standard deviation of $p$-values, the mean $p$-value, and the mean
$p$-value plus the standard deviation of the obtained $p$-values,
respectively. The blue contours correspond to $p\,=\,0.2$. Bottom row: Results
of the two-sided 1D KS tests performed on the $\mu$ values (left panel) and on
the $\sigma$ values (right panel). In each panel the solid line and markers
represent the resulting mean $p$-value as a function of $\Sigma$, which is the
width of the Gaussian distribution added on the $\sigma$ and $\mu$ values
obtained from the $P$ map. At each point, the shaded area shows the complete
range of obtained $p$-values, while the error bars indicate the standard
deviation of the distribution of $p$-values after $n$ tries. Given our $p$
rejection criteria of 0.2, we can infer that the two ($\sigma$,$\mu$)
distributions between the C2H moment 0 and $P$ maps could come from a common
parent distribution.

We present a quantitative comparison between the spatial distribution of the
UV-sensitive tracer C2H and that of the polarized dust emission. A simple flux
to flux comparison did not appear to be the most relevant method to compare
the morphology of the moment 0 of the C2H molecular emission and the polarized
intensity $P$. We chose to use two-sided Kolmorogov-Smirnov (KS) tests between
these two maps. Only B335 and L1448 IRS2 have high enough sensitivity in both
the C2H and $P$ maps for the emissions to overlap sufficiently, the main
condition to run the KS tests. Therefore, we performed the tests only on these
two sources. In order to match the spatial frequency of emission, both
datasets were reduced again using a common uv-range. The C2H moment 0 and $P$
maps were then smoothed to the same angular resolution, and regridded to a
Nyquist pattern (4 pixels per beam surface area).

We now describe the method used to characterize the morphology of the emission
in both maps. We follow the propagation path of photons emanating from the
central region, and investigate whether a common cause (i.e., the irradiation
field) can be responsible for both the emission of UV-sensitive molecules and
the polarized dust emission. To do so, we draw a number $N$ of lines starting
from the peak of the total intensity map and going up to the outer edge of the
maps over 360∘ to obtain a set of 1D emission profiles along those $N$ lines.
Among the profiles that have a sufficient number of high signal-to-noise (S/N)
pixels in both the C2H moment 0 and polarized intensity maps (we require in
this selection that at least five pixels have S/N $\geq$ 3), a 1D Gaussian fit
of the profile is attempted. If the 1D Gaussian fits converge in both the C2H
moment 0 and $P$ maps, we retain two parameters, the standard deviation
$\sigma$ and the position of the center of the Gaussian $\mu$, for each map.
We now have a set of $N^{\prime}$ (with $N^{\prime}\leq N$, given that we
selected profiles for S/N and 1D Gaussian fit convergence reasons) couples
($\sigma$,$\mu$) for both the C2H moment 0 and $P$ maps.

Before computing the KS tests, we draw sets of perturbations (i.e., adding
dispersion in the values) from a Gaussian distribution of a given width
$\Sigma$ on these ($\sigma_{i}$,$\mu_{i}$)${}_{i\in\llbracket
i,..,N^{\prime}\rrbracket}$, ($\sigma_{i}$)${}_{i\in\llbracket
i,..,N^{\prime}\rrbracket}$, and ($\mu_{i}$)${}_{i\in\llbracket
i,..,N^{\prime}\rrbracket}$ distributions obtained with the $P$ map333The same
results are obtained if we apply these dispersions on the ($\sigma$,$\mu$)
values derived from the C2H map.. We then perform two-sided 2D KS tests
between $\\{(\sigma_{i},\mu_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}\\}_{\textrm{C}_{2}\textrm{H}}$ and
$\\{(\sigma_{i},\mu_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}+\textrm{T}(\Sigma)\\}_{P}$, where
$\textrm{T}(\Sigma)$ is a Gaussian distribution of width $\Sigma$. We also
perform two-sided 1D KS tests between $\\{(\mu_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}\\}_{\textrm{C}_{2}\textrm{H}}$ and
$\\{(\mu_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}+\textrm{T}(\Sigma)\\}_{P}$, and between
$\\{(\sigma_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}\\}_{\textrm{C}_{2}\textrm{H}}$ and
$\\{(\sigma_{i})_{i\in\llbracket
i,..,N^{\prime}\rrbracket}+\textrm{T}(\Sigma)\\}_{P}$. For each value of
$\Sigma$ (tested in the range 0-4′′) we repeat this process $n$ times.

To evaluate if they are drawn from a common parent distribution, KS tests are
performed with these distributions. Each test results in a value $p$, with low
values corresponding to different distributions. We reject the hypothesis that
two distributions are drawn from the same parent distribution when $p$ ¡ 0.2
(Peacock, 1983; Fasano & Franceschini, 1987; Press et al., 2007). At a given
$\Sigma$ we evaluate the distributions of the $n$ $p$-values obtained (i.e.,
we derive the mean $p$-value and the standard deviation).

Figure 7 presents the results of these 1D and 2D KS tests toward B335 (see
Appendix B for the tests performed on L1448 IRS2), with $N=100$, $n=1000$. The
$N^{\prime}$ S/N selected profiles and corresponding Gaussian fits from the
C2H moment 0 and $P$ maps are shown in Figure 11. In the top left and top
middle panels of Figure 7, the $P$ and C2H moment 0 maps are overlaid with the
$N$ profiles respectively, where the white lines represents the $N^{\prime}$
sample of selected profiles (the red lines correspond to the profiles where
the S/N selection criteria was not reached, and black lines correspond to the
directions where the 1D Gaussian fit does not converge). The top right panel
shows the obtained ($\sigma$,$\mu$) sample in the form of a 2D diagram. The
middle and bottom rows show the results of the 2D and 1D KS tests,
respectively. Given our $p$ rejection criteria of 0.2, our 2D KS tests
performed on B3335 suggest that the two distributions of
($\sigma_{i}$,$\mu_{i}$)${}_{\textrm{C}_{2}\textrm{H}}$ and
($\sigma_{i}$,$\mu_{i}$)P may be drawn from the common parent distribution
when we consider dispersion values of $\Sigma\,\lesssim 1.4^{\prime\prime}$
and $\Sigma\,\lesssim 1.8^{\prime\prime}$, applied on the $\sigma$ and $\mu$
distributions, respectively (see the blue contour in the central panel of
Figure 7). For L1448 IRS2, the same conclusion can be made for
$\Sigma\,\lesssim 1^{\prime\prime}$ and $\Sigma\,\lesssim 1.2^{\prime\prime}$,
applied on the $\sigma$ and $\mu$ distributions, respectively (see Figure 12).
The selected $N^{\prime}$ lines, 38 lines in B335 and 43 lines in L1448 IRS2,
lie mostly toward the outflow cavity walls of the two protostars, and cover
most of the regions where both emission (polarized intensity and C2H moment 0
maps) are sufficiently high. Therefore, we propose that the spatial
distribution of the dust polarization and C2H molecular emission maps can have
a common origin, assuming that our approach describes the morphology of these
emissions sufficiently well.

In order to investigate the role of the irradiation field in the observed
chemistry and the efficiency of the grain alignment, we would need to build
models simulating the involved physical and chemical processes. While we
perform the modeling of conditions leading to dust grains to align with
different efficiencies in Paper II, the modeling of the effect of irradiation
on the chemistry is beyond the scope of this work and is left for a future
study. We restrict ourselves here to this quantitative comparison, which
suggests that the morphology of the $P$ and C2H moment 0 emission maps, are
comparable in B335 and L1448-IRS2.

##  4 Discussion

###  4.1 Dust grain polarization and tracers of irradiated molecular gas

The spatial distribution of the polarized dust emission and C2H molecular
emission suggests that the heating occurs preferentially along the outflow
cavities. The accretion activity onto the central protostellar embryo likely
represents the major source of photons responsible for triggering the observed
warm carbon chain chemistry (Sakai et al., 2009; Sakai & Yamamoto, 2013) and
for increasing the grain alignment efficiency by extending the population of
dust grains subject to alignment by the radiative torques (Le Gouellec et al.,
2020). These processes can explain the highly polarized dust emission and C2H
molecular emission observed toward the dense walls of outflow cavities, as
suggested by our statistical tests described in Section 3. However, we note
that this analyzis relies on two sources, and other Class 0s presented in
Sect. 2 may show different behaviors.

Several reasons can justify why, in some regions of Class 0s protostellar
envelopes, the spatial distribution of the irradiation tracers and polarized
dust emission appears to differ. The morphology of the inner envelope density
structures directly dictates the propagation scheme of energetic photons
emanating from the central source. For example, Serpens Emb 8 and Serpens Emb
8(N) exhibit drastic morphological differences in the ALMA dust continuum and
polarized dust emission (Hull et al., 2017b; Le Gouellec et al., 2019).
Serpens Emb 8(N) appears much more axisymmetric than Serpens Emb 8, which can
significantly affect the map of the radiation field in the inner core. The
disorganized structures of Serpens Emb 8 could thus favor the propagation of
the radiation field throughout the entire inner envelope rather than along
outflow cavities, which appear preferentially polarized in Serpens Emb 8(N).
In addition, the various timescales of the physical and chemical processes
involved here (i.e., grain alignment and warm carbon chain chemistry
timescales) may vary from one source to another. For example, the precession
timescale of the IRAS4A2 outflow (Chuang et al., 2021) may prevent the warm
carbon chain chemistry from developing farther out in the cavities, explaining
why the spatial distribution of the C2H molecular emission is limited compared
to the polarized dust emission. In Serpens Emb 8 the increase in irradiation
due to the recent accretion burst suggested by Greene et al. (2018) can
explain why the C2H molecular emission appears so extended and bright.
However, the polarized dust emission within the envelope exhibits a sparse
distribution and no significant detection down to the detection levels allowed
by the sensitivity of the observations. This could be due to either a more
disorganized magnetic field along the line of sight (e.g., Valdivia et al.
2022) or to a mean magnetic field orientation closer to the line of sight.
Finally, the last element that is crucial while investigating the role of
irradiation in the chemistry and grain alignment, is the properties of dust
grains. The structure and size distribution of dust grains could vary
throughout the envelope, depending on their spatial origin and the radiation
field strength, as dust grains can become rotationally disrupted by radiative
torques (Hoang et al., 2021). This point is further explored in Section 4.3.3
and in our Paper II. For example, this argument could explain why the northern
equatorial mid-plane of B335 is so polarized.

###  4.2 Contribution of shocks to illumination in cavities

Ultraviolet photons can be produced by mechanical processes, such as at bow
shocks in outflows and jets or potentially at smaller shocks along the outflow
cavity walls. Herschel observations of far-infrared spectral lines of CO and
H2O revealed evidence of irradiated shocks located along outflow cavity walls,
associated with a hot ($\geq\,500K$) gas component (Kristensen et al., 2017a;
Karska et al., 2018). Observations of SO (see Section 2), a candidate tracer
of the shocks developed at the interaction zones between the outflow–jet
system and the ambient envelope gas (Lefloch et al. 2005), also suggest the
presence of shocks in outflow cavities. These shocks could be an additional
source of UV photons (Neufeld & Dalgarno, 1989a, b) propagating in the
cavities (van Kempen et al., 2009a). SO can also trace the weak accretion
shock of the infalling gas onto the circumstellar disk (Sakai et al., 2014b,
a; Miura et al., 2017; van Gelder et al., 2021). It originates from reactions
of atomic S released from the grains with OH, and from H2S converted to SO
with atomic oxygen and OH. The fact that we notice spatial overlap of SO
emission with dust polarization in the outflow cavities of IRAS4A, Serpens Emb
8, and Serpens 8(N) (see Section 2) tends to suggest that the shock activity
plays a role in the alignment of dust grains (see, e.g., Hoang & Tram 2019).
To quantify the amount of self-irradiation in the candidate shocks, one
possibility could be to model the surface geometry of the cavity walls (see a
similar work performed for a bow shock in Gustafsson et al. 2010), and to
implement self-consistently the shock models that account for self-irradiation
(Lehmann et al., 2020).

###  4.3 Conditions for development of UV-irradiated gas and efficient grain
alignment in protostellar envelopes

Le Gouellec et al. (2020) showed that the grain alignment efficiency is high
and roughly constant with respect to column density in a prototypical Class 0
protostellar core. However, they could not entirely reproduce it; their
radiative transfer calculations show an alignment efficiency that is too low.
However, irradiation seems to be an important factor that drives the extent of
the regions where grain alignment produces polarized dust emission efficiently
(i.e., where the irradiation is high enough to align grains). The wide variety
of the observed spatial extent of the molecular emission lines we presented in
Section 2 can bring additional clues to the nature and morphology of the
radiation field in the inner core.

####  4.3.1 Using UV-sensitive chemistry and its associated radiation field to
explain the observed ALMA dust polarization maps

Interactions between UV radiation from shocks in jets and/or outflows and in
cavity walls (see above) and the ambient material could cause the growth of
regions of PDR-like conditions (Lee et al., 2015). The identification of PDR
tracers toward outflow cavity walls suggests that the UV radiation field is
significant in these regions. As mentioned above, one of the limitations of
our radiative transfer calculations is the fact that the radiative energy
derived in each cell only originates from the reprocessing of the radiative
energy escaping from the sink. Analyzing the UV-sensitive chemistry of the
inner core could allow us to confirm or rule out the radiation field we
implement in our models.

The molecule C2H is usually seen in PDRs, for example the Orion Bar (Teyssier
et al., 2004; Pety et al., 2005; van der Wiel et al., 2009; Nagy et al., 2015)
and the Horsehead Nebula (Cuadrado et al., 2015; Guzmán et al., 2014, 2015),
located at the irradiated, and thus warmer, edge of these regions. C2H was
also found enhanced in the presence of UV radiation toward molecular clouds
(Fuente et al., 1993; Hogerheijde et al., 1995; Jansen et al., 1995). This
molecule involves C, C+, and CH+ in its chemical formation pathway, which is
maintained in high abundance in the gas phase in the presence of strong UV
radiation (Stäuber et al., 2004; Benz et al., 2016). C2H could thus be
expected to trace the (UV-irradiated) outflow cavity walls. C2H has been
detected in a variety of Class 0/I protostellar cores, especially toward
outflow cavity walls (Jørgensen et al., 2013; Oya et al., 2014; Imai et al.,
2016; Higuchi et al., 2018; Oya et al., 2018; Okoda et al., 2018; Bjerkeli et
al., 2016a; Zhang et al., 2018; Bergner et al., 2020; Lee et al., 2020; Okoda
et al., 2020; Tychoniec et al., 2021; Ohashi et al., 2022). In particular,
Murillo et al. (2018) exhibited the anti-correlation between the cold gas
tracer DCO+ (Murillo et al., 2015; Le Gouellec et al., 2019) and the warm
irradiated regions traced by C2H (and also $c$-C3H2) in two Class 0 cores.
Finally, due to an increase in atomic C and C+ in the gas phase, C2H is also
commonly observed and modeled at the upper layer of protoplanetary disks where
UV and X-ray photons from the stellar irradiation field can propagate more
easily (Henning et al., 2010; Kastner et al., 2014, 2015; Bergin et al., 2016;
Cleeves et al., 2018; Kastner et al., 2018; Bergner et al., 2019; Miotello et
al., 2019; Cleeves et al., 2021). Another candidate mechanism to explain the
presence of carbon chain molecules in the gas phase is the top-down
destruction of polycyclic aromatic hydrocarbons (PAHs) photo-eroded by the
radiation field (Teyssier et al., 2004; Pety et al., 2005; van der Wiel et
al., 2009; Pety et al., 2012; Guzmán et al., 2015). However, this proposition
is challenged by the lack of observational detections of PAHs in protostellar
cores (Geers et al., 2009).

The presence of C2H (but also $c$-C3H2 and CS; see Appendix A) toward the
outflow cavities and cavity walls thus suggests that a significant UV
radiation field can survive in the inner $\sim$500 au region of Class 0
protostellar cores. Given the average penetration path length of UV photons
through the dense cavity walls, these photons are reprocessed quickly. These
reprocessed photons can still contribute to the alignment of small grains, as
the mean wavelength of the corresponding radiation spectrum is shorter than
the longer-wavelength photons responsible for the alignment of dust grains
with sizes $\geq\,1\,\mu$m. The equatorial mid-planes, which presumably do not
experience a similar radiation field (the equatorial mid-planes B335 are
depleted in C2H emission line for example), would be dense enough to be
protected by rotational disruption (depending of the opacity of the inner
circumstellar disk; see Paper II), but would require large grains to produce
the observed polarized dust emission. The case of Serpens Emb 8 is, however,
paradoxical. The C2H emission that peaks all over the inner core could be due
to significant leaks of irradiation from the very disorganized envelope. In
this source dust grains might be rotationally disrupted along a variety of
directions, which, along with the disorganized magnetic field orientations,
can explain the undetected dust polarization in a large portion of the dense
regions.

Previous chemical studies constrained the irradiated field in Class 0
protostellar cores. On scales of $\sim\,1000$ au, comparing atomic line fluxes
such as [CII] or [OI] with PDR models, Karska et al. (2018) found that for
typical low-mass protostars the UV field was $\sim\,$102 G0 (where G0 is the
radiative flux in the range $\sim$ 90-200 nm), and 103 G0 for protostars in
the regime of SMM1, the brightest protostar in Serpens Main with
$L_{\textrm{bol}}\,\gtrsim\,120$ (Enoch et al., 2011; Kristensen et al.,
2012). Using UV-irradiated shocks models, they found a UV field of 1-10 G0
using pre-shock densities of 105 cm-3. In addition, comparing the observed
fluxes and line ratios of several ionized hydrides such as C+, CH+, OH+, H2O+,
and HCO+ with chemical models, Benz et al. (2016) constrained values of
200-400 G0 for NGC1333 IRAS4A and 2-8 G0 for SMM1 at the Herschel half-power
beam radius at 300 $\mu$m, which corresponds to a radius of 3000 and 5000 au
from the center of the protostar at the distance of Perseus and Serpens,
respectively. Using the IRAM 30m observations, similar G0 values were derived
in Serpens Main by Mirocha et al. (2021), who computed ratios of CN to HCN
column densities, a good tracer of UV fields around around low- and
intermediate-mass protostellar cores. In our radiative transfer calculations,
the radiation field spectrum computed in these regions has been entirely
reprocessed toward longer wavelength photons (IR to millimeter wavelengths),
which means the G0 is negligible there.

As suggested above, in outflow cavities the high-energy (UV) part of the
radiation field spectrum must originate from the shocks occurring between the
outflowing gas and the envelope. Therefore, it is not possible to precisely
compare the radiation field obtained from radiative transfer calculations
(where the radiation field emanating from the center is heavily reprocessed)
with these chemical studies that only discuss the impact of the UV field on
the chemistry. For reference, at 1000 au from the protostar our fiducial model
(see Paper II) yields an irradiation field of
$u_{\textrm{rad}}/u_{\textrm{ISRF}}\,\simeq\,3\times 10^{3}$ in the direction
of the outflow and $\sim\,5\times 10^{2}$ in the direction of the equatorial
planes. At 3000 au from the protostar the ratio
$u_{\textrm{rad}}/u_{\textrm{ISRF}}$ is $\sim\,3.5\times 10^{2}$ in the
direction of the outflow and $\sim\,1\times 10^{2}$ in the direction of the
equatorial planes. The resulting grain alignment efficiency does not seem to
be high enough to reproduce the results obtained with ALMA observations
obtained in Le Gouellec et al. (2020). In addition, the higher values of
irradiation we explore may favor the rotational disruption of grains and thus
deteriorate the conditions for grain alignment removing the large grains. This
latter point is quantitatively addressed in our Paper II. While irradiation
appears to locally affect the grain alignment conditions, the global
efficiency of the grain alignment mechanisms is also important to take into
account. Le Gouellec et al. (2020) also noted that the paramagneticity of dust
grains strongly affects the grain alignment efficiency. Recently detailed
modeling by Hoang (2022), Hoang et al. (2022), and Chau Giang et al. (2022)
have shown that to ensure the alignment of large dust grains ($\geq$10 $\mu$m;
necessary to reproduce the observed polarized dust emission), grains
containing embedded iron inclusions are required to ensure efficient grain
internal and external alignment processes with respect to the gas
randomization (i.e., short Barnett relaxation and Larmor precession timescales
with respect to the gaseous damping timescale).

####  4.3.2 Effect of C/O in the gas phase and the CCH abundance

In protoplanetary disks only models implementing C/O¿1 can reproduce the high
abundance of C2H (Bergin et al., 2016; Kama et al., 2016; Cleeves et al.,
2018; Kastner et al., 2018; Miotello et al., 2019; Alarcón et al., 2020;
Anderson et al., 2021; Cleeves et al., 2021; Facchini et al., 2021), otherwise
CO would carry most of the carbon content. In disks, to obtain a high C/O
ratio, one possible explanation is the enhancement of carbon via destruction
(and/or photodesorption) of carbon grains and PAHs (Anderson et al., 2017),
while a deficit in oxygen can be caused by grain growth and dust settling
(Hogerheijde et al., 2011; Du et al., 2015; Salinas et al., 2016; Du et al.,
2017; Cleeves et al., 2018). However, Bergner et al. (2020) did not find that
C2H formation is favored by CO depletion in a few of Class 0/I systems,
suggesting that CO can already be quite depleted in the gas phase. In outflow
cavity walls, PDR-like modeling is required to fully understand the exact role
of the UV radiation field in the enhancement of C2H, but the C/O ratio is a
parameter that may also play a role in the C2H enhancement, in this active
region separating the warm outflow material from the dense cold infalling
envelope. In this region the temperature gradient is expected to be large
because of the large gas density gradient across cavity walls and reprocessing
of the local irradiation field. It is possible that in these specific
conditions, the gas experiences a rather sharp transition from cold envelope
conditions to temperatures allowing the CO sublimation out of dust grains
(Anderl et al., 2016). C2H might be detected where a high C/O ratio could be
explained by a limited CO sublimation. This is illustrated by the dichotomy
found in BHR71 IRS2 between the outflow cavity and inner envelope traced by CO
and C18O, respectively, and the cold envelope traced by N2D+ where CO freezes
out onto dust grains (Hull et al. 2020; see also the unpolarized southern
region of B335 in Figure 1 compared to these same molecular lines presented in
Cabedo et al. 2021, 2022). The dust polarization detected in the outflow
cavity walls of IRS2 lies precisely between the regions where the N2D+ and CO
emission lines peak, suggesting that dust grains cannot become aligned in
these areas. This can be explained by the attenuation of the irradiation
field, which is able to align far fewer grains. In addition, another cause of
the drop in polarized intensity where CO freezes out onto grains could be that
CO ices on grain surfaces decrease the helicity of the dust grains, and thus
the polarization. Modeling dust grain surfaces and volatile chemistry toward
the outflow cavity walls will be required to constrain the role played by the
C/O ratio and the radiation field spectrum and strength in the observed warm
carbon chemistry, and potentially the grain alignment conditions.

####  4.3.3 Understanding the origin of polarized dust in cavity walls via gas
kinematic studies

The regions traced by C2H and CS around the lobes of bipolar outflows are
thought to correspond to outflow cavities walls, because of their irradiated
nature. Assuming that the polarized dust emission and the UV-sensitive
molecular emission lines both come from these cavity walls, it is necessary to
characterize the kinematic nature of outflow cavity walls to further constrain
the physical conditions that favor grain alignment. Zhang et al. (2016) have
proposed tentative evidence of a slowly moving rotating outflow using CS,
suggesting that cavity walls are entrained by a rotating disk wind launched at
large radii from the source. Further evidence of rotation toward Class 0
objects was found by Zhang et al. (2018) and Ohashi et al. (2022) using CS and
C2H. The authors argue that these molecules should trace the gas entrained by
the outflow along the cavity walls, or the magneto-centrifugal wind itself
launched from the disk, rather than the gas infalling from the envelope to the
central object. Even if the rotation of the outflow cavity walls is minimal,
it has been suggested from observations of a few objects that the specific
angular momentum of the corresponding gas is greater than that of the
infalling-rotating envelope (Oya et al., 2018; Zhang et al., 2018). We note,
however, that Okoda et al. (2018) have concluded that the C2H emission in a
warm carbon-chain chemistry (WCCC) protostar was preferentially tracing gas
from the infalling-rotating envelope. They attribute the C2H emission, also
detected around outflow cavity, to the infalling-rotating envelope.

In Class 0 protostars it is thus still unclear whether the emission from the
C2H molecule originates from the regions surrounding outflow cavities rather
than from the outflowing gas itself. However, outflow cavity walls regions are
subject to a significant shear. The material located at the interface between
the outflowing gas and the infalling envelope material must experience
turbulent mixing. The mixing layer is replenished by outflowing material and
infalling envelope at a rate that is proportional to the mass outflow rate,
but the mass brought to the mixing layer by the outward shocked wind should be
larger than the mass brought by the infalling envelope (see Canto & Raga 1991;
Liang et al. 2020, where this result was quantified via analytical models).
Liang et al. (2020) developed a model of a steady-state cavity caused by the
interaction of a wind with an infalling rotating envelope, whose size is
dictated by the equilibrium between the wind ram pressure and envelope thermal
pressure. They were able to match their predictions of the warm turbulent
mixing layer with the broad-line profile of high-$J$ CO line observed with
Herschel toward Serpens SMM1 (Kristensen et al., 2017b). In this source the
mixing layer is made of warm gas (T$\,\sim\,$250 K), due to the competition
between turbulent heating, expansion, and CO cooling.

It is still unclear whether the regions of high dust polarization and C2H
emission belong to the outflowing gas, the mixing layer, or the infalling
envelope. This question is of great importance given the local physical
conditions required by grain alignment, especially the maximum size of aligned
dust grains (Valdivia et al., 2019; Le Gouellec et al., 2019; Hull et al.,
2020). To discuss the presence of large grains ($\geq$10 $\mu$m) in cavity
walls, we must address the question of where and when the required dust grain
growth has occurred. Dust growth may be efficient in situ, within the
infalling material of the protostellar envelope (Galametz et al. 2019; Bate
2022; infalling structures such as streamers may also favor dust grain growth
thanks to their higher density). However, if the material producing the
polarized dust emission in outflow cavity walls is entrained by a disk wind,
large dust grains in cavities could originate from the much denser regions of
the inner circumstellar disk where the outflow originates, and where grains
grow more quickly. Recent studies have investigated the possibility of dust
ejection from the inner disk (Wong et al., 2016; Liffman et al., 2020;
Vinkovic & Čemeljić, 2021; Hutchison & Clarke, 2021; Booth & Clarke, 2021;
Tsukamoto et al., 2021; Rodenkirch & Dullemond, 2022). Kinematic studies via
observations of the spectral lines tracing those highly polarized regions
could thus clarify which of these two scenarios can explain the spatial origin
of these large grains.

Additionally, mechanical grain alignment may also play a role in regions
harboring anisotropic (supersonic) gas-dust drift velocity streams.
Originally, the Gold alignment (Gold, 1952) was proposed to align the grains
with long axes along the flow in supersonic conditions. More recently, the
alignment of irregular grains induced by gaseous collisions was introduced in
Lazarian (2007). This mechanical torque (MET) alignment mechanism acts
similarly to that caused by RATs, where mechanical torques are applied by gas
particle momentum instead of the photon momentum. Recent numerical
quantification have shown a large range of grain spin-up efficiencies by METs
for different grain shapes and gas-dust drift velocities (Hoang et al., 2018;
Reissl et al., 2022). Alignment would occur with respect to the orientation of
the average gas-dust drift velocity component or the magnetic field, depending
on the amount of the iron inclusions and the gas-dust drift velocity (Lazarian
& Hoang, 2021; Hoang et al., 2022). In protostellar environments, unlike the
infalling streams of gas located within the envelope, the outflow cavity walls
are next to high velocity outflowing gas. The shocked layers defining the
interaction between the outflowing gas and the envelope may exhibit favorable
conditions for the mechanical alignment of dust grains. However, the width of
the shock fronts would likely be small compared to the angular resolution of
the observations presented here (see, e.g., Mottram et al. 2014; Kristensen et
al. 2017b), such that the polarized dust emission would not be dominated by
the shock front. The turbulent mixing layer (see Canto & Raga 1991; Liang et
al. 2020), marking the transition between the outflowing and infalling
velocities, could extend to a larger area. The gas-dust drift would be less
anisotropic, but the (sub)millimeter polarized dust emission more likely
emanates from this region. It is still unclear what the relative contributions
of RATs and METs are in outflow cavity walls. Revealing this question would
require precisely constraining the gas-dust drift velocities and irradiation
conditions undergone by the dust grains responsible for the observed
(sub)millimeter polarized dust emission.

##  5 Conclusions and summary

We compared the spatial distribution of polarized dust emission with molecular
emission line of UV-sensitive species in the envelope of Class 0 protostars
(B335, L1448 IRS2, NGC1333 IRAS4A, Serpens Emb 8, and 8(N)). The goal was to
use the warm chemistry processes to characterize the role of the radiation
field in grain alignment within the dense envelope of protostars. The main
results and conclusions of this paper are as follows:

  1. 1.

We qualitatively compare the observed maps of dust polarization with maps of
the irradiated regions probed by UV-driven chemistry traced by the emission of
the C2H hydrocarbon. The emission of this molecule is seen to be enhanced
along outflow cavities walls, where in the case of the axisymmetric cores the
polarized dust emission is also enhanced.

  2. 2.

In the case of a more turbulent core, such as Serpens Emb 8, the energetic
photons probed by the C2H emission seem to propagate throughout the entire
inner core. In this source, the polarized intensity exhibits very localized
detections, with only tentative correlations with the location of C2H
molecular gas emission.

  3. 3.

We show that the shock tracer SO also peaks toward outflow cavities where
polarized dust emission is enhanced. Shocks happening along cavity walls can
represent an additional source of high-energy photons that may contribute to
the anisotropic radiation field aligning grains via radiative torques.

  4. 4.

In the two protostars presenting the best detection of both the polarized dust
emission and the C2H emission, we find a quantitative correlation between the
morphology of the polarized intensity and C2H moment 0 integrated emission
maps, suggesting that the radiation field impinging on the cavity walls may
favor both the grain alignment and the warm carbon chain chemistry in these
regions.

  5. 5.

However, some regions of Class 0 protostellar envelopes, which are thought to
be under a weaker radiation field, still exhibit enhanced polarized intensity,
such as the the northern equatorial mid-plane of B335, contrary to the
southern one. This may suggest that a fraction of dust grains contributing to
the millimeter dust continuum emission may be aligned even in the absence of
an ultraviolet radiation field, but with a strongly reddened radiation field.

Comparing the ambient chemistry that develops where dust polarization is
observed opens a promising avenue to further constrain grain alignment, given
that the modeling of the results from these two fields can constrain crucial
parameters together, such as radiation field, dust temperature, and the
subsequent sublimation radii beyond which gas species can freeze onto dust
grains, potentially modifying their alignment properties. We highlight the
importance of source geometry and evolution in setting the environmental
conditions of the envelope of protostars, which in turn govern the capability
of radiative torques to align dust grains depending on the spectrum of local
photons.

Acknowledgments V.J.M.L.G. thanks Ł. Tychoniec, N. Sakai, and J. M. Girart for
their help and support regarding the ALMA molecular lines and dust
polarization observations presented in this paper. V.J.M.L.G. and C.L.H.H.
acknowledge the ESO Studentship Program, and the guidance and support of Eric
Villard. C.L.H.H. acknowledges the support of both the NAOJ Fellowship as well
as JSPS KAKENHI grant 18K13586. This work has received support from the
European Research Council (ERC Starting Grant MagneticYSOs with grant
agreement no. 679937). This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2013.1.01102.S, ADS/JAO.ALMA#2016.1.01552.S,
ADS/JAO.ALMA#2017.1.01392.S, ADS/JAO.ALMA#2013.1.01380.S,
ADS/JAO.ALMA#2018.1.01873.S, ADS/JAO.ALMA#2016.1.01501.S,
ADS/JAO.ALMA#2016.1.00604.S, ADS/JAO.ALMA#2013.1.00031.S,
ADS/JAO.ALMA#2016.1.01089.S, ADS/JAO.ALMA#2013.1.01102.S,
ADS/JAO.ALMA#2016.1.01089.S, ADS/JAO.ALMA#2015.1.00546.S.,
ADS/JAO.ALMA#2017.1.01174.S, ADS/JAO.ALMA#2016.1.00710.S,
ADS/JAO.ALMA#2013.1.00726.S, ADS/JAO.ALMA#2015.1.00768.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.

Facilities: ALMA

Software: APLpy, an open-source plotting package for Python hosted at
http://aplpy.github.com (Robitaille & Bressert, 2012). CASA (McMullin et al.,
2007). Astropy (Astropy Collaboration et al., 2018). POLARIS (Reissl et al.,
2016)

## References

  * Alarcón et al. (2020) Alarcón, F., Teague, R., Zhang, K., Bergin, E. A., & Barraza-Alfaro, M. 2020, ApJ, 905, 68
  * Anderl et al. (2016) Anderl, S., Maret, S., Cabrit, S., et al. 2016, A&A, 591, A3
  * Anderson et al. (2017) Anderson, D. E., Bergin, E. A., Blake, G. A., et al. 2017, ApJ, 845, 13
  * Anderson et al. (2021) Anderson, D. E., Blake, G. A., Cleeves, L. I., et al. 2021, ApJ, 909, 55
  * Andersson et al. (2015) Andersson, B.-G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A, 53, 501
  * Andre & Montmerle (1994) Andre, P., & Montmerle, T. 1994, ApJ, 420, 837
  * Andre et al. (1993) Andre, P., Ward-Thompson, D., & Barsony, M. 1993, ApJ, 406, 122
  * Arce et al. (2007) Arce, H. G., Shepherd, D., Gueth, F., et al. 2007, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil, 245
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Bachiller & Tafalla (1999) Bachiller, R., & Tafalla, M. 1999, in NATO Advanced Study Institute (ASI) Series C, Vol. 540, The Origin of Stars and Planetary Systems, ed. C. J. Lada & N. D. Kylafis, 227
  * Bally (2016) Bally, J. 2016, ARA&A, 54, 491
  * Bate (2022) Bate, M. R. 2022, MNRAS, 514, 2145
  * Benz et al. (2016) Benz, A. O., Bruderer, S., van Dishoeck, E. F., et al. 2016, A&A, 590, A105
  * Bergin et al. (2016) Bergin, E. A., Du, F., Cleeves, L. I., et al. 2016, ApJ, 831, 101
  * Bergner et al. (2019) Bergner, J. B., Öberg, K. I., Bergin, E. A., et al. 2019, ApJ, 876, 25
  * Bergner et al. (2020) —. 2020, ApJ, 898, 97
  * Bjerkeli et al. (2016a) Bjerkeli, P., Jørgensen, J. K., & Brinch, C. 2016a, A&A, 587, A145
  * Bjerkeli et al. (2016b) Bjerkeli, P., Jørgensen, J. K., Bergin, E. A., et al. 2016b, A&A, 595, A39
  * Böhm et al. (1993) Böhm, K. H., Noriega-Crespo, A., & Solf, J. 1993, ApJ, 416, 647
  * Booth & Clarke (2021) Booth, R. A., & Clarke, C. J. 2021, MNRAS, 502, 1569
  * Brogan et al. (2018) Brogan, C. L., Hunter, T. R., & Fomalont, E. B. 2018, arXiv e-prints, arXiv:1805.05266
  * Cabedo et al. (2021) Cabedo, V., Maury, A., Girart, J. M., & Padovani, M. 2021, A&A, 653, A166
  * Cabedo et al. (2022) Cabedo, V., Maury, A., Girart, J. M., et al. 2022, arXiv e-prints, arXiv:2204.10043
  * Canto & Raga (1991) Canto, J., & Raga, A. C. 1991, ApJ, 372, 646
  * Chau Giang et al. (2022) Chau Giang, N., Hoang, T., Kim, J.-G., & Tram, L. N. 2022, arXiv e-prints, arXiv:2210.01036
  * Chuang et al. (2021) Chuang, C.-Y., Aso, Y., Hirano, N., Hirano, S., & Machida, M. N. 2021, ApJ, 916, 82
  * Cleeves et al. (2018) Cleeves, L. I., Öberg, K. I., Wilner, D. J., et al. 2018, ApJ, 865, 155
  * Cleeves et al. (2021) Cleeves, L. I., Loomis, R. A., Teague, R., et al. 2021, arXiv e-prints, arXiv:2102.09577
  * Cox et al. (2018) Cox, E. G., Harris, R. J., Looney, L. W., et al. 2018, ApJ, 855, 92
  * Cuadrado et al. (2015) Cuadrado, S., Goicoechea, J. R., Pilleri, P., et al. 2015, A&A, 575, A82
  * Curiel et al. (1995) Curiel, S., Raymond, J. C., Wolfire, M., et al. 1995, ApJ, 453, 322
  * de Valon et al. (2020) de Valon, A., Dougados, C., Cabrit, S., et al. 2020, A&A, 634, L12
  * Draine & Weingartner (1996) Draine, B. T., & Weingartner, J. C. 1996, ApJ, 470, 551
  * Draine & Weingartner (1997) —. 1997, ApJ, 480, 633
  * Du et al. (2015) Du, F., Bergin, E. A., & Hogerheijde, M. R. 2015, ApJ, 807, L32
  * Du et al. (2017) Du, F., Bergin, E. A., Hogerheijde, M., et al. 2017, ApJ, 842, 98
  * Enoch et al. (2009) Enoch, M. L., Evans, II, N. J., Sargent, A. I., & Glenn, J. 2009, ApJ, 692, 973
  * Enoch et al. (2011) Enoch, M. L., Corder, S., Duchêne, G., et al. 2011, ApJS, 195, 21
  * Facchini et al. (2021) Facchini, S., Teague, R., Bae, J., et al. 2021, arXiv e-prints, arXiv:2101.08369
  * Fasano & Franceschini (1987) Fasano, G., & Franceschini, A. 1987, MNRAS, 225, 155
  * Fuente et al. (1993) Fuente, A., Martin-Pintado, J., Cernicharo, J., & Bachiller, R. 1993, A&A, 276, 473
  * Galametz et al. (2019) Galametz, M., Maury, A. J., Valdivia, V., et al. 2019, A&A, 632, A5
  * Geers et al. (2009) Geers, V. C., van Dishoeck, E. F., Pontoppidan, K. M., et al. 2009, A&A, 495, 837
  * Girart et al. (2006) Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science, 313, 812
  * Goicoechea et al. (2012) Goicoechea, J. R., Cernicharo, J., Karska, A., et al. 2012, A&A, 548, A77
  * Gold (1952) Gold, T. 1952, MNRAS, 112, 215
  * Greene et al. (2018) Greene, T. P., Gully-Santiago, M. A., & Barsony, M. 2018, ApJ, 862, 85
  * Gustafsson et al. (2010) Gustafsson, M., Ravkilde, T., Kristensen, L. E., et al. 2010, A&A, 513, A5
  * Guzmán et al. (2015) Guzmán, V. V., Pety, J., Goicoechea, J. R., et al. 2015, ApJ, 800, L33
  * Guzmán et al. (2014) Guzmán, V. V., Pety, J., Gratier, P., et al. 2014, Faraday Discussions, 168, 103
  * Hartmann et al. (2016) Hartmann, L., Herczeg, G., & Calvet, N. 2016, ARA&A, 54, 135
  * Henning et al. (2010) Henning, T., Semenov, D., Guilloteau, S., et al. 2010, ApJ, 714, 1511
  * Higuchi et al. (2018) Higuchi, A. E., Sakai, N., Watanabe, Y., et al. 2018, ApJS, 236, 52
  * Hoang (2022) Hoang, T. 2022, ApJ, 928, 102
  * Hoang et al. (2018) Hoang, T., Cho, J., & Lazarian, A. 2018, ApJ, 852, 129
  * Hoang & Tram (2019) Hoang, T., & Tram, L. N. 2019, ApJ, 877, 36
  * Hoang et al. (2021) Hoang, T., Tram, L. N., Lee, H., Diep, P. N., & Ngoc, N. B. 2021, ApJ, 908, 218
  * Hoang et al. (2022) Hoang, T., Tram, L. N., Phan, V. H. M., et al. 2022, arXiv e-prints, arXiv:2205.02334
  * Hogerheijde et al. (1995) Hogerheijde, M. R., Jansen, D. J., & van Dishoeck, E. F. 1995, A&A, 294, 792
  * Hogerheijde et al. (1998) Hogerheijde, M. R., van Dishoeck, E. F., Blake, G. A., & van Langevelde, H. J. 1998, ApJ, 502, 315
  * Hogerheijde et al. (2011) Hogerheijde, M. R., Bergin, E. A., Brinch, C., et al. 2011, Science, 334, 338
  * Hull et al. (2020) Hull, C. L. H., Le Gouellec, V. J. M., Girart, J. M., Tobin, J. J., & Bourke, T. L. 2020, ApJ, 892, 152
  * Hull & Plambeck (2015) Hull, C. L. H., & Plambeck, R. L. 2015, Journal of Astronomical Instrumentation, 4, 1550005
  * Hull et al. (2017a) Hull, C. L. H., Girart, J. M., Tychoniec, Ł., et al. 2017a, ApJ, 847, 92
  * Hull et al. (2017b) Hull, C. L. H., Mocz, P., Burkhart, B., et al. 2017b, ApJ, 842, L9
  * Hutchison & Clarke (2021) Hutchison, M. A., & Clarke, C. J. 2021, MNRAS, 501, 1127
  * Imai et al. (2016) Imai, M., Sakai, N., Oya, Y., et al. 2016, ApJ, 830, L37
  * Jansen et al. (1995) Jansen, D. J., Spaans, M., Hogerheijde, M. R., & van Dishoeck, E. F. 1995, A&A, 303, 541
  * Jørgensen et al. (2013) Jørgensen, J. K., Visser, R., Sakai, N., et al. 2013, ApJ, 779, L22
  * Kama et al. (2016) Kama, M., Bruderer, S., van Dishoeck, E. F., et al. 2016, A&A, 592, A83
  * Karska et al. (2018) Karska, A., Kaufman, M. J., Kristensen, L. E., et al. 2018, ApJS, 235, 30
  * Kastner et al. (2014) Kastner, J. H., Hily-Blant, P., Rodriguez, D. R., Punzi, K., & Forveille, T. 2014, ApJ, 793, 55
  * Kastner et al. (2015) Kastner, J. H., Qi, C., Gorti, U., et al. 2015, ApJ, 806, 75
  * Kastner et al. (2018) Kastner, J. H., Qi, C., Dickson-Vandervelde, D. A., et al. 2018, ApJ, 863, 106
  * Ko et al. (2020) Ko, C.-L., Liu, H. B., Lai, S.-P., et al. 2020, ApJ, 889, 172
  * Kristensen et al. (2017a) Kristensen, L. E., Gusdorf, A., Mottram, J. C., et al. 2017a, A&A, 601, L4
  * Kristensen et al. (2013) Kristensen, L. E., van Dishoeck, E. F., Benz, A. O., et al. 2013, A&A, 557, A23
  * Kristensen et al. (2012) Kristensen, L. E., van Dishoeck, E. F., Bergin, E. A., et al. 2012, A&A, 542, A8
  * Kristensen et al. (2017b) Kristensen, L. E., van Dishoeck, E. F., Mottram, J. C., et al. 2017b, A&A, 605, A93
  * Krumholz et al. (2012) Krumholz, M. R., Klein, R. I., & McKee, C. F. 2012, ApJ, 754, 71
  * Kurono et al. (2013) Kurono, Y., Saito, M., Kamazaki, T., Morita, K.-I., & Kawabe, R. 2013, ApJ, 765, 85
  * Kwon et al. (2015) Kwon, W., Fernández-López, M., Stephens, I. W., & Looney, L. W. 2015, ApJ, 814, 43
  * Kwon et al. (2019) Kwon, W., Stephens, I. W., Tobin, J. J., et al. 2019, ApJ, 879, 25
  * Lazarian (2007) Lazarian, A. 2007, J. Quant. Spec. Radiat. Transf., 106, 225
  * Lazarian & Hoang (2007) Lazarian, A., & Hoang, T. 2007, MNRAS, 378, 910
  * Lazarian & Hoang (2021) —. 2021, ApJ, 908, 12
  * Le Gouellec et al. (2019) Le Gouellec, V. J. M., Hull, C. L. H., Maury, A. J., et al. 2019, ApJ, 885, 106
  * Le Gouellec et al. (2020) Le Gouellec, V. J. M., Maury, A. J., Guillet, V., et al. 2020, A&A, 644, A11
  * Lee et al. (2020) Lee, S., Lee, J.-E., Aikawa, Y., Herczeg, G., & Johnstone, D. 2020, ApJ, 889, 20
  * Lee et al. (2015) Lee, S., Lee, J.-E., & Bergin, E. A. 2015, The Astrophysical Journal Supplement Series, 217, 30
  * Lee et al. (2021) Lee, Y.-N., Charnoz, S., & Hennebelle, P. 2021, A&A, 648, A101
  * Lefloch et al. (2005) Lefloch, B., Cernicharo, J., Cabrit, S., & Cesarsky, D. 2005, A&A, 433, 217
  * LeGal et al. (2019) LeGal, R., Öberg, K. I., Loomis, R. A., Pegues, J., & Bergner, J. B. 2019, ApJ, 876, 72
  * Lehmann et al. (2020) Lehmann, A., Godard, B., Pineau des Forêts, G., & Falgarone, E. 2020, A&A, 643, A101
  * Liang et al. (2020) Liang, L., Johnstone, D., Cabrit, S., & Kristensen, L. E. 2020, ApJ, 900, 15
  * Liffman et al. (2020) Liffman, K., Bryan, G., Hutchison, M., & Maddison, S. T. 2020, MNRAS, 493, 4022
  * Lindberg & Jørgensen (2012) Lindberg, J. E., & Jørgensen, J. K. 2012, A&A, 548, A24
  * Louvet et al. (2018) Louvet, F., Dougados, C., Cabrit, S., et al. 2018, A&A, 618, A120
  * Martín-Doménech et al. (2019) Martín-Doménech, R., Bergner, J. B., Öberg, K. I., & Jørgensen, J. K. 2019, ApJ, 880, 130
  * Maury et al. (2018) Maury, A. J., Girart, J. M., Zhang, Q., et al. 2018, MNRAS, 477, 2760
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Miotello et al. (2019) Miotello, A., Facchini, S., van Dishoeck, E. F., et al. 2019, A&A, 631, A69
  * Mirocha et al. (2021) Mirocha, A., Karska, A., Gronowski, M., et al. 2021, A&A, 656, A146
  * Miura et al. (2017) Miura, H., Yamamoto, T., Nomura, H., et al. 2017, ApJ, 839, 47
  * Mottram et al. (2014) Mottram, J. C., Kristensen, L. E., van Dishoeck, E. F., et al. 2014, A&A, 572, A21
  * Murillo et al. (2015) Murillo, N. M., Bruderer, S., van Dishoeck, E. F., et al. 2015, A&A, 579, A114
  * Murillo et al. (2018) Murillo, N. M., van Dishoeck, E. F., van der Wiel, M. H. D., et al. 2018, A&A, 617, A120
  * Nagy et al. (2015) Nagy, Z., Ossenkopf, V., Van der Tak, F. F. S., et al. 2015, A&A, 578, A124
  * Neufeld & Dalgarno (1989a) Neufeld, D. A., & Dalgarno, A. 1989a, ApJ, 340, 869
  * Neufeld & Dalgarno (1989b) —. 1989b, ApJ, 344, 251
  * Ohashi et al. (2022) Ohashi, S., Codella, C., Sakai, N., et al. 2022, ApJ, 927, 54
  * Okoda et al. (2018) Okoda, Y., Oya, Y., Sakai, N., et al. 2018, ApJ, 864, L25
  * Okoda et al. (2020) Okoda, Y., Oya, Y., Sakai, N., Watanabe, Y., & Yamamoto, S. 2020, ApJ, 900, 40
  * Oya et al. (2018) Oya, Y., Sakai, N., Watanabe, Y., et al. 2018, ApJ, 863, 72
  * Oya et al. (2014) Oya, Y., Sakai, N., Sakai, T., et al. 2014, ApJ, 795, 152
  * Peacock (1983) Peacock, J. A. 1983, MNRAS, 202, 615
  * Pety et al. (2005) Pety, J., Teyssier, D., Fossé, D., et al. 2005, A&A, 435, 885
  * Pety et al. (2012) Pety, J., Gratier, P., Guzmán, V., et al. 2012, A&A, 548, A68
  * Podio et al. (2020a) Podio, L., Garufi, A., Codella, C., et al. 2020a, A&A, 642, L7
  * Podio et al. (2020b) —. 2020b, A&A, 644, A119
  * Press et al. (2007) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & P., F. B. 2007, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press)
  * Raga & Cabrit (1993) Raga, A., & Cabrit, S. 1993, A&A, 278, 267
  * Reissl et al. (2020) Reissl, S., Guillet, V., Brauer, R., et al. 2020, arXiv e-prints, arXiv:2002.11792
  * Reissl et al. (2022) Reissl, S., Meehan, P., & Klessen, R. S. 2022, arXiv e-prints, arXiv:2201.03694
  * Reissl et al. (2016) Reissl, S., Wolf, S., & Brauer, R. 2016, A&A, 593, A87
  * Rivière-Marichalar et al. (2019) Rivière-Marichalar, P., Fuente, A., Goicoechea, J. R., et al. 2019, A&A, 628, A16
  * Robitaille & Bressert (2012) Robitaille, T., & Bressert, E. 2012, APLpy: Astronomical Plotting Library in Python, Astrophysics Source Code Library, ascl:1208.017
  * Rodenkirch & Dullemond (2022) Rodenkirch, P. J., & Dullemond, C. P. 2022, A&A, 659, A42
  * Ruíz-Rodríguez et al. (2021) Ruíz-Rodríguez, D., Kastner, J., Hily-Blant, P., & Forveille, T. 2021, A&A, 646, A59
  * Sadavoy et al. (2014) Sadavoy, S. I., Di Francesco, J., André, P., et al. 2014, ApJ, 787, L18
  * Sakai et al. (2009) Sakai, N., Sakai, T., Hirota, T., Burton, M., & Yamamoto, S. 2009, ApJ, 697, 769
  * Sakai & Yamamoto (2013) Sakai, N., & Yamamoto, S. 2013, Chemical Reviews, 113, 8981
  * Sakai et al. (2014a) Sakai, N., Oya, Y., Sakai, T., et al. 2014a, ApJ, 791, L38
  * Sakai et al. (2014b) Sakai, N., Sakai, T., Hirota, T., et al. 2014b, Nature, 507, 78
  * Salinas et al. (2016) Salinas, V. N., Hogerheijde, M. R., Bergin, E. A., et al. 2016, A&A, 591, A122
  * Saucedo et al. (2003) Saucedo, J., Calvet, N., Hartmann, L., & Raymond, J. 2003, ApJ, 591, 275
  * Spaans et al. (1995) Spaans, M., Hogerheijde, M. R., Mundy, L. G., & van Dishoeck, E. F. 1995, ApJ, 455, L167
  * Spezzano et al. (2016) Spezzano, S., Bizzocchi, L., Caselli, P., Harju, J., & Brünken, S. 2016, A&A, 592, L11
  * Stäuber et al. (2005) Stäuber, P., Doty, S. D., van Dishoeck, E. F., & Benz, A. O. 2005, A&A, 440, 949
  * Stäuber et al. (2004) Stäuber, P., Doty, S. D., van Dishoeck, E. F., Jørgensen, J. K., & Benz, A. O. 2004, A&A, 425, 577
  * Taquet et al. (2020) Taquet, V., Codella, C., De Simone, M., et al. 2020, A&A, 637, A63
  * Teyssier et al. (2004) Teyssier, D., Fossé, D., Gerin, M., et al. 2004, A&A, 417, 135
  * Tobin et al. (2018) Tobin, J. J., Looney, L. W., Li, Z.-Y., et al. 2018, ApJ, 867, 43
  * Tsukamoto et al. (2021) Tsukamoto, Y., Machida, M. N., & Inutsuka, S.-i. 2021, ApJ, 920, L35
  * Tychoniec et al. (2019) Tychoniec, Ł., Hull, C. L. H., Kristensen, L. E., et al. 2019, A&A, 632, A101
  * Tychoniec et al. (2021) Tychoniec, Ł., van Dishoeck, E. F., van’t Hoff, M. L. R., et al. 2021, A&A, 655, A65
  * Valdivia et al. (2019) Valdivia, V., Maury, A., Brauer, R., et al. 2019, MNRAS, 488, 4897
  * Valdivia et al. (2022) Valdivia, V., Maury, A., & Hennebelle, P. 2022, arXiv e-prints, arXiv:2203.14505
  * van der Wiel et al. (2009) van der Wiel, M. H. D., van der Tak, F. F. S., Ossenkopf, V., et al. 2009, A&A, 498, 161
  * van Gelder et al. (2021) van Gelder, M. L., Tabone, B., van Dishoeck, E. F., & Godard, B. 2021, A&A, 653, A159
  * van Gelder et al. (2020) van Gelder, M. L., Tabone, B., Tychoniec, Ł., et al. 2020, arXiv e-prints, arXiv:2005.06784
  * van Kempen et al. (2009a) van Kempen, T. A., van Dishoeck, E. F., Güsten, R., et al. 2009a, A&A, 501, 633
  * van Kempen et al. (2009b) —. 2009b, A&A, 507, 1425
  * Vinkovic & Čemeljić (2021) Vinkovic, D., & Čemeljić, M. 2021, MNRAS, 500, 506
  * Visser et al. (2012) Visser, R., Kristensen, L. E., Bruderer, S., et al. 2012, A&A, 537, A55
  * Walter et al. (2003) Walter, F. M., Herczeg, G., Brown, A., et al. 2003, AJ, 126, 3076
  * Wardle & Kronberg (1974) Wardle, J. F. C., & Kronberg, P. P. 1974, ApJ, 194, 249
  * Watson (2020) Watson, D. M. 2020, Research Notes of the American Astronomical Society, 4, 88
  * Wong et al. (2016) Wong, Y. H. V., Hirashita, H., & Li, Z.-Y. 2016, PASJ, 68, 67
  * Yıldız et al. (2012) Yıldız, U. A., Kristensen, L. E., van Dishoeck, E. F., et al. 2012, A&A, 542, A86
  * Zhang et al. (2016) Zhang, Y., Arce, H. G., Mardones, D., et al. 2016, ApJ, 832, 158
  * Zhang et al. (2018) Zhang, Y., Higuchi, A. E., Sakai, N., et al. 2018, ApJ, 864, 76
  * Zucker et al. (2019) Zucker, C., Speagle, J. S., Schlafly, E. F., et al. 2019, ApJ, 879, 125

##  Appendix A Additional tracers of warm chemistry in outflow cavities.

We present here maps of two additional tracers of warm chemistry, CS and
$c$-C3H2 (see Table 2 for the transition information). The molecule $c$-C3H2
has a similar chemistry to that of C2H. Like C2H, it has been detected toward
the PDR edges (Teyssier et al., 2004; Pety et al., 2005; Cuadrado et al.,
2015; Guzmán et al., 2014, 2015), and is likely an irradiation tracer.
Detections of $c$-C3H2 have been found at the scale of cores
($\sim\,2000-4000$ au) toward proto-stellar and pre-stellar cores irradiated
by external sources, suggesting irradiation driven chemistry (a nearby star,
for example, or the interstellar radiation field itself; see Lindberg &
Jørgensen 2012; Spezzano et al. 2016). $c$-C3H2 (and C2H) can also probe the
disk–envelope interface, at the limit between the centrifugal barrier and the
infalling-rotating envelope (Sakai et al., 2014a, b). CS is also a molecule
whose emission can be enhanced at the edges of PDR (Rivière-Marichalar et al.,
2019). Commonly seen toward outflow cavities tracing the warm molecular layer
(Kwon et al., 2015; Bjerkeli et al., 2016b; Oya et al., 2018; Zhang et al.,
2016; Martín-Doménech et al., 2019; Zhang et al., 2018; Okoda et al., 2020;
Taquet et al., 2020), CS may trace the UV-irradiated regions of disks as well
(Podio et al., 2020a, b). We note, however, in disks seen edge-on that CS can
appear below CN, whose production is favored by the irradiation of the disk
surface (Ruíz-Rodríguez et al., 2021). The chemical formation route of CS may
require strong UV radiation as it can trigger reactions between S/S+ and small
hydrocarbons to produce carbonated S-species, or photodesorption from dust
grains (LeGal et al., 2019; Podio et al., 2020b). In the protostars we study,
CS is less obviously tracing the PDR-like outflow cavity wall layer because
its spectral emission has a narrower profile than SO, but a broader extent
compared to that of C2H that only peaks at the $v_{\textrm{lsr}}$ (see the
kinematic study present in Figure 6; see also Tychoniec et al. 2021; Ohashi et
al. 2022). In addition, applying the method presented in Section 3 on the $P$
and CS moment 0 maps of B335 and L1448 IRS2 does not result in any probing
results (especially for L1448 IRS2), suggesting that the morphology of the CS
moment 0 map is less linked to outflow cavity walls.

B335: Figure 8 presents the $c$-C3H2 and CS moment 0 integrated emission maps
from Imai et al. (2016). The emission of the carbon chain molecule $c$-C3H2,
and the CS molecular emission, are clearly enhanced toward the outflow
cavities. The $c$-C3H2 emission is very faint, however, and is located
exclusively at the base of outflow cavity walls.

L1448 IRS2: Figure 9 presents the CS moment 0 integrated emission map (from Y.
Zhang in preparation, ALMA project 2016.1.01501.S, PI: N. Sakai) The C2H
molecular line shown in Figure 2, is more extended than CS, but emission from
both molecular lines appears enhanced toward the walls of the cavities.

NGC1333 IRAS4A: Figure 10 presents the CS moment 0 integrated emission map
from Chuang et al. (2021). The polarized dust emission along the outflow
cavity walls seems to overlap precisely with the CS molecular emission line in
the southern cavity of IRAS4A1 and IRAS4A2, and in the northern cavity of
IRAS4A1.

Figure 8: Polarized intensity and molecular line observations around the B335
Class 0 protostellar core (as in Figure 1). The thick light blue contours
trace the moment 0 map of the CS (from 6 to 11 km s-1) and $c$-C3H2 (from 7 to
9.5 km s-1) molecular emission spectral line, at levels of 3, 5, 7, 9, 11, 16,
24, 44 $\times$ the rms noise level of each map. In the bottom left corner of
each plot the ellipses represent the beam resolution element of a given
dataset: yellow for polarized dust emission; white for the CS and $c$-C3H2
spectral emission lines. ALMA 1.3mm dust polarized emission from Maury et al.
(2018) and Maury et al. (in preparation). The CS and $c$-C3H2 emission lines
are from Imai et al. (2016).

Figure 9: Magnetic fields, polarized intensity, and molecular line
observations around the L1448 IRS2 Class 0 protostellar core (as in Figure 2).
The thick light blue contours (top right and bottom panels) trace the moment 0
map of the CS (by integrating emission from 2 to 6 km s-1) molecular emission
spectral line. The ALMA 1.3mm dust polarized emission is from Kwon et al.
(2019) and the CS emission line is from ALMA project 2016.1.01501.S, Y. Zhang
(in preparation).

Figure 10: Magnetic fields, polarized intensity, and molecular line
observations around the NC1333 IRAS4A Class 0 protostellar core (as in Figure
3). The thick light blue contours (top right and bottom panels) trace the
moment 0 map of the CS (by integrating emission from -10 to 19.5 km s-1)
molecular emission spectral line. The two crosses are located at the two peaks
of the dust continuum map. IRAS4A1 is to the southeast of IRAS4A2. The ALMA
1.3mm dust polarized emission is from Ko et al. (2020). The CS emission line
is from Chuang et al. (2021).

##  Appendix B Details about our geometrical comparisons between the maps of
polarized intensity and integrated molecular emission line

Figure 11 presents the emission profiles of the S/N selected lines obtained in
the C2H moment 0 and $P$ maps of B335 from the method presented in Section 3.
These profiles correspond to the black and white lines in Figure 7.

Figures 12 and 13 present the same tests presented in Section 3, but applied
to L1448 IRS2, using $N$=100 and $n$=1000. This time the departure of the
lines is offset by $\sim$ 50 au from the peak of the total intensity map. We
chose this because the central region is thought to be optically thick and the
corresponding polarized emission to be contaminated by self-scattering (Kwon
et al., 2019). As in B335, the KS test results suggest that the two
distributions ($\sigma$,$\mu$) between the C2H moment 0 and $P$ maps in L1448
IRS2 could come from a common parent distribution. Therefore, in this core the
morphology of the emission in these two maps could also have a common origin.

Figure 11: Emission profiles of the S/N selected lines obtained in the C2H
moment 0 and $P$ maps of B335. The red and green solid line corresponds to the
emission profile along a given line of the C2H moment 0 and $P$ map,
respectively, shown in Figure 7. The angle in each panel is the position angle
(taken from the north) of the line (see Figure 7). When the 1D Gaussian fit
converges (for the white lines in Figure 7), it is shown as a dashed line.

Figure 12: Results from the two-sided 1D and 2D KS tests between the $P$ and
C2H moment 0 maps of L1448 IRS2, performed with $N$=100 and $n$=1000. Same as
Figure 7.  Figure 13: Emission profiles of the S/N selected lines obtained in
the C2H moment 0 and $P$ maps of L1448 IRS2. Same as Figure 11.