11institutetext:  INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5,
50125 Firenze, Italy 22institutetext: Univ. Grenoble Alpes, CNRS, Institut de
Planétologie et d’Astrophysique de Grenoble (IPAG), 38000 Grenoble, France
33institutetext: Università degli Studi di Firenze, Dipartimento di Fisica e
Astronomia, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy 44institutetext:
Institut de Radioastronomie Millimétrique, 300 rue de la Piscine, Domaine
Universitaire de Grenoble, 38406, Saint-Martin d’Hères, France
55institutetext: Observatorio Astronómico Nacional (OAN-IGN), Alfonso XII 3,
28014 Madrid, Spain 66institutetext: Max-Planck-Institut für
extraterrestrische Physik (MPE), Giessenbachstrasse 1, 85748 Garching, Germany
77institutetext: RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-
shi, 351-0198 Saitama, Japan 88institutetext: Dipartimento di Chimica,
Biologia e Biotecnologie, Via Elce di Sotto 8, 06123 Perugia, Italy
99institutetext: Leiden Observatory, Leiden University, PO Box 9513, 2300 RA
Leiden, The Netherlands 1010institutetext: Department of Physics and
Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
1111institutetext: Department of Physics, The University of Tokyo, 7-3-1,
Hongo, Bunkyo-ku, Tokyo 113- 0033, Japan 1212institutetext: Research Center
for the Early Universe, The University of Tokyo, 7-3-1, Hongo, Bunkyo- ku,
Tokyo 113-0033, Japan

# The SVS13-A Class I chemical complexity as revealed by S-bearing species.
SOLIS XIII

C. Codella 1122 E. Bianchi 2211 L. Podio 11 S. Mercimek 1133 C. Ceccarelli 22
A. López-Sepulcre 2244 R. Bachiller 55 P. Caselli 66 N. Sakai 77 R. Neri 44 F.
Fontani 11 C. Favre 22 N. Balucani 881122 B. Lefloch 22 S. Viti 991010 S.
Yamamoto 11111212<EMAIL_ADDRESS>
(Received date; accepted date)

###### Abstract

Context. Recent results in astrochemistry revealed that some molecules such as
interstellar complex organic species and deuterated species represent precious
tools to investigate star forming regions. Sulphuretted species can also be
used to follow the chemical evolution of the early stages of the Sun-like star
forming process.

Aims. The goal is to obtain a census of S-bearing species using
interferometric images, towards SVS13-A, a Class I object associated with a
hot corino rich in interstellar complex organic molecules.

Methods. To this end, we used the NGC1333 SVS13-A data at3mm and 1.4mm
obtained with the IRAM-NOEMA interferometer in the framework of the Large
Program SOLIS. The line emission of S-bearing species has been imaged and
analysed using LTE and LVG approaches.

Results. We imaged the spatial distribution on $\leq$ 300 au scale of the line
emission of 32SO, 34SO, C32S, C34S, C33S, OCS, H2C32S, H2C34S, and NS. The low
excitation (9 K) 32SO line is tracing (i) the low-velocity SVS13-A outflow and
(ii) the fast (up to 100 km s-1 away from the systemic velocity) collimated
jet driven by the nearby SVS13-B Class 0 object. Conversely, the rest of the
lines are confined in the inner SVS13-A region, where complex organics have
been previously imaged. More specifically the non-LTE LVG analysis of SO, SO2,
and H2CS indicates a hot corino origin (size in the 60-120 au range).
Temperatures between 50 K and 300 K, and volume densities larger than 105 cm-3
have been derived. The abundances of the sulphuretted are in the following
ranges: 0.3–6 $\times$ 10-6 (CS), 7 $\times$ 10-9 – 1 $\times$ 10-7 (SO), 1–10
$\times$ 10-7 (SO2), a few 10-10 (H2CS and OCS), and 10-10–10-9 (NS). The
N(NS)/N(NS+) ratio is larger than 10, supporting that the NS+ ion is mainly
formed in the extended envelope.

Conclusions. The [H2CS]/[H2CO] ratio, once measured at high-spatial
resolutions, increases with time (from Class 0 to Class II objects) by more
than one order of magnitude (from $\leq$ 10-2 to a few 10-1). This suggests
that [S]/[O] changes along the Sun-like star forming process. Finally, the
estimate of the [S]/[H] budget in SVS13-A is 2%-17% of the Solar System value
(1.8 $\times$ 10-5), being consistent with what was previously measured
towards Class 0 objects (1%-8%). This supports that the enrichment of the
sulphuretted species with respect to dark clouds keeps constant from the Class
0 to the Class I stages of low-mass star formation. The present findings
stress the importance of investigating the chemistry of star forming regions
using large observational surveys as well as sampling regions on a Solar
System scale.

###### Key Words.:

Stars: formation – ISM: abundances – ISM: molecules – ISM: individual objects:
SVS13-A

††offprints: C. Codella,

##  1 Introduction

Molecular complexity builds up at each step of the process leading to Sun-like
star formation. Searches for exoplanets have shown a large degree of diversity
in the planetary systems111https://exoplanets.nasa.gov/, and it is unclear how
common a System like our own is. In this context, the role of the pre-solar
chemistry in the formation of the Solar System bodies is far from being
understood. A breakthrough question (see e.g. Ceccarelli et al., 2007; Herbst
& van Dishoeck, 2009; Caselli & Ceccarelli, 2012; Jørgensen et al., 2020, and
references therein) is to understand whether planetary systems inherited at
least part of the chemical composition of the earliest stages of the Sun-like
star forming process, such as prestellar cloud, Class 0 ($\leq$ 105 yr), Class
I ($>$ 105 yr), and Class II ($>$ 106 yr) objects. To progress, it is of
paramount importance: (i) to observe objects representing all the evolutionary
stages of the star forming process sampling regions on a Solar System scale,
and (ii) to combine high-sensitivity spectral surveys collecting a large
number of species and emitting lines to constrain their abundances.

In the last years, ALMA revolutionised our comprehension of planet formation,
delivering images of rings and gaps (see e.g., Sheehan & Eisner, 2017; Fedele
et al., 2018; Andrews et al., 2018) in the dust distribution around objects
with an age less than 1 Myr. This clearly supports that planet formation
occurs earlier than what was postulated before, more specifically already in
the Class I phase. This in turn stresses the importance of investigating Class
I objects, a sort of bridge between the prototellar phase and the
protoplanetary disks around Class II young objects. Several projects focused
on the chemical complexity of Class I objects have been recently performed,
mainly focusing the attention on interstellar small or complex (with at least
6 atom) organic molecules and/or deuteration using both single-dishes and
interferometer (see e.g., Öberg et al., 2014; Bianchi et al., 2017; Bergner et
al., 2017, 2019; Bianchi et al., 2019a, b, 2020; Le Gal et al., 2020; Yang et
al., 2021).

In the dense gas typical of star forming regions, [S]/[H] is far to the value
measured in our Solar System (1.8 $\times$ 10-5 Anders & Grevesse, 1989),
given sulphur is depleted by several orders of magnitude (e.g. Tieftrunk et
al., 1994; Wakelam et al., 2004a; Phuong et al., 2018; Laas & Caselli, 2019;
van ’t Hoff et al., 2020). On grains, sulphur is expected to be very
refractory, likely in the form of FeS (Kama et al., 2019) or S8 (Shingledecker
et al., 2020), while it is still debated which is the main reservoir on dust
mantles. For years, H2S and possibly OCS have been postulated to be the
solution, but so far they have never been directly detected in interstellar
ices (Boogert et al., 2015), so that it seems that other, not yet identified,
frozen species contain the majority of sulphur.

The abundance of gaseous S-bearing species drastically increases in the
regions where the species frozen out onto the dust mantles are injected into
the gas-phase either due to thermal evaporation in the heated central zone of
protostars (e.g. in the Class 0/I hot corinos) or because of gas-grain
sputtering and grain-grain shattering in shocked regions (e.g. Charnley et
al., 1997; Bachiller et al., 2001; Wakelam et al., 2004a; Codella et al.,
2005; Sakai et al., 2014b, a; Podio et al., 2014; Imai et al., 2016; Holdship
et al., 2016; Taquet et al., 2020; Feng et al., 2020). In both cases,
S-bearing species have proved to be extremely useful in the reconstruction of
both the chemical history and dynamics of the studied objects. In addition,
S-bearing species have been recently imaged in relatively older protoplanetary
disks using CS, SO, H2S, and H2CS line emission (e.g. Teague et al., 2018;
Booth et al., 2018; Phuong et al., 2018; Le Gal et al., 2019; Loomis et al.,
2020; Codella et al., 2020; Garufi et al., 2020, 2021; Podio et al., 2020a, b;
Oya & Yamamoto, 2020). All these studies (i) have shown that S-bearing species
are a powerful tool to follow the evolution of the chemistry until the latest
stages of star formation, and (ii) call for more studies of S-bearing species
towards the Class I protostars, which, as mentioned above, represent a crucial
transition from the youngest Class 0 protostars and the more evolved Class II
protoplanetary disk sources.

In the present paper, we report a survey of the S-bearing species in the Class
I source prototype SVS13-A observed in the framework of the IRAM-NOEMA SOLIS
(Seeds Of Life In Space)222https://solis.osug.fr/ (Ceccarelli et al., 2017).
The article is organised as follows. In Sect. 2, we report the description of
target source, SVS13-A. We describe the observations in Sect. 3 and the
results in Sect. 4. In Sect. 5, we carry out a non-LTE analysis of the
obtained data and derive the physical and chemical parameters of the detected
S-bearing in the molecules emitting gas. We discuss the implications of our
findings in Sect. 6 and summarise the conclusions of this work in Sect. 7.

##  2 The SVS13-A Class I prototypical source

The SVS13-A object is located in the NGC1333 cluster, in the Perseus region,
at a distance of 299 $\pm$ 14 pc (Zucker et al., 2018). SVS13-A is in turn a
0$\aas@@fstack{\prime\prime}$3 binary source (VLA4A, VLA4B; Anglada et al.
2000; Tobin et al. 2016, 2018), so far not disentangled using mm-wavelengths
observations (e.g. Lefèvre et al. 2017; Maury et al. 2019), located close
($\sim$ 4$\arcsec$) is a third object called VLA3. The three objects are
surrounded by a large molecular envelope (Lefloch et al., 1998). The
bolometric luminosity of SVS13-A is $\sim$ 50 $L_{\rm bol}$, and it is
considered as one of the archetypical Class I sources (at least 105 yr, e.g.
Chini et al. 1997), having been observed in the last decades at different
spectral windows (see e.g. Chini et al. 1997; Bachiller et al. 1998; Looney et
al. 2000; Chen et al. 2009; Tobin et al. 2016; Maury et al. 2019, and
references therein). SVS13-A is driving an extended molecular outflow (Lefloch
et al., 1998; Codella et al., 1999; Sperling et al., 2020; Dionatos et al.,
2020), associated with the Herbig-Haro (HH) chain 7–11 (Reipurth et al., 1993)
as well as younger flows moving towards Southern-Eastern directions (Lefèvre
et al., 2017).

A hot corino has been revealed towards SVS13-A using deuterated water observed
with the IRAM 30-m by Codella et al. (2016) and then imaged by De Simone et
al. (2017) using the IRAM PdBI and HCOCH2OH (glycolaldehyde) emission lines,
finding a 90 au diameter. The first iCOMs census of interstellar Complex
Organic Species (iCOMs; organic molecules with at least 6 atoms) has been
reported by Bianchi et al. (2019a) thanks to the ASAI (Astrochemical Surveys
At IRAM) Large Program (Lefloch et al., 2017) unbiased survey in the IRAM
spectral windows. In this context, Bianchi et al. (2017, 2019b) analysed
fractionation and deuteration of a large number of species. Several iCOMs have
been also detected by Belloche et al. (2020) using high-resolution PdBI
observations. Unfortunatly, even the interferometric campaigns did not allow
the observers to clearly identify which component of the binary system is
associated with a rich chemistry, noting only that the emission peak is offset
($\sim$ 1$\aas@@fstack{\prime\prime}$5 to West) from VLA4A (see also Lefèvre
et al., 2017).

##  3 Observations

The SVS13-A region was observed at 1.4mm and 3mm in two different setups
(hereafter labelled 5 and 6: see also: Ceccarelli et al., 2017) with the IRAM
NOEMA interferometer. The phase center of the obtained images is
$\alpha_{2000}$ = 03h29m03s.73, $\delta_{2000}$ = +31∘16′03′′.8.

Setup 6, at 3mm, was observed in A configuration (1 track) using 9 antennas in
March 2018. The frequency ranges are 80.2–88.3 GHz and 95.7–103.9 GHz. The
shortest and longest projected baselines are 64 m and 760 m, respectively. The
field of view is about 60$\arcsec$, while the Largest Angular Scale (LAS) is
$\simeq$ 8$\arcsec$. Line images were produced by subtracting continuum image,
using natural weighting, and restored with a clean beam, for continuum, of
1$\aas@@fstack{\prime\prime}$8 $\times$ 1$\aas@@fstack{\prime\prime}$1 (PA
$\simeq$ 41∘). Note that the scope of the present project is to focus on the
hot corino and not the extended emission. The Polyfix correlator was used,
with a total spectral band of about 8 GHz, and a spectral resolution of 2 MHz
($\simeq$ 7 km s-1). Setup 5, at 1.4mm, was observed in A and C configurations
(3 tracks) using 8 antennas in December 2016. The frequency range is
204.0–207.6 GHz. The shortest and longest projected baselines are 24 m and 760
m, respectively, for a field of view of 24$\arcsec$ and LAS $\sim$ 9
$\arcsec$. The clean beam is, for the continuum at 1.4 mm,
0$\aas@@fstack{\prime\prime}$6 $\times$ 0$\aas@@fstack{\prime\prime}$6 (PA
$\simeq$ –46∘). The WideX backend has been used providing a bandwidth of
$\sim$ 3.6 GHz with a spectral resolution of $\sim$ 2 MHz (2.8–2.9 km s-1). In
addition, 320 MHz wide narrowband backends providing a spectral resolution of
$\sim$ 0.9 km s-1 have been used.

For both setups, calibration was carried out following standard procedures,
using GILDAS-CLIC333http://www.iram.fr/IRAMFR/GILDAS. The bandpass was fixed
on 3C84, while the absolute flux was calibrated on LkH$\alpha$101, MWC249, and
0333+321. The final uncertainty on the absolute flux scale is $\leqslant$
10$\%$ (3mm) and $\leqslant$ 15$\%$ (1.4mm). The phase rms was $\leqslant$
50∘, and the typical precipitable water vapor (pwv) was $\sim$ 5-15 mm.
Finally, the system temperature was $\sim$ 50-200 K. The final rms noise in
the broadband cubes is $\sim$ 20–50 mJy beam-1 (3mm), and $\sim$ 700–1000 mJy
beam-1 (1.4mm).

Figures A.1-A.4 compares the NOEMA-SOLIS spectra with those derived at the
same frequency with the IRAM 30-m Lefloch et al. (2018), smoothed to the 2 MHz
spectral resolution of the SOLIS data). Red labels indicate the S-bearing
species analysed in this paper (see Table 1). As expected, the single-dish
observations are detecting the photons emitted by the multiple components
inside the IRAM 30-m HPBW (25$\arcsec$–30$\arcsec$ at 3mm, and 12$\arcsec$ at
1.4mm), such as the cold extended envelope or the large-scale SVS13-A outflow.
On the other hand, NOEMA-SOLIS, filtering out the emission at scales larger
than $\sim$ 8$\arcsec$ is well suited for the analysis of the inner 100 au
protostellar region as long as the filtering does not affect the line profile
which traces the hot corino.

##  4 Results

###  4.1 Continuum images

Figure 1–Left shows the the SVS13-A region as observed in dust continuum
emission at 3mm. Several protostars are detected: SVS13-A (without
disentangling the binary components VLA4A and 4B at the present
1$\aas@@fstack{\prime\prime}$3 angular resolution), VLA3, SVS13-B, and, out of
the primary beam, also SVS13-C. Figure 1-Right shows the 1.4mm map of the
inner 30$\arcsec$ (the primary beam is, in this case, 24$\arcsec$): while
there is a tentative 5$\sigma$ signature of VLA3, SVS13-A and SVS13-B are
clearly detected. Still, at an angular resolution of
0$\aas@@fstack{\prime\prime}$6, the SVS13-A binary system (separated by
0$\aas@@fstack{\prime\prime}$3) is not disentangled.

The J2000 coordinates of the protostars are in agreement with the previous
continuum imaging in both cm- and mm-wavelengths (see e.g. Looney et al. 2000;
Anglada et al. 2000; Tobin et al. 2018; Maury et al. 2019), namely: SVS13-A:
03h29m03s.757, +31∘16′03$\aas@@fstack{\prime\prime}$74; VLA3: 03h29m03s.386,
+31∘16′01$\aas@@fstack{\prime\prime}$56; SVS13-B: 03h29m03s.064,
+31∘15′51$\aas@@fstack{\prime\prime}$50; SVS13-C: 03h29m01s.947,
+31∘15′37$\aas@@fstack{\prime\prime}$71\. Finally, the peak fluxes, for the
sources imaged inside the primary beams, are: SVS13-A: 26.6$\pm$0.1 mJy beam-1
(90 GHz), and 94$\pm$1 mJy beam-1 (205 GHz); VLA3: 2.2$\pm$0.1 mJy beam-1 (90
GHz), and 5$\pm$1 mJy beam-1 (205 GHz); SVS13-B: 19.2$\pm$0.1 mJy beam-1 (90
GHz).

Figure 1: Left Panel: The SVS13-A region as observed in dust continuum
emission at 3mm (see Sect. 2) using IRAM NOEMA. Angular offset are with
respect to the phase center (see Sect. 3). First contour and steps are,
respectively, 5$\sigma$ (1$\sigma$ = 100 $\mu$Jy) and 50$\sigma$. The filled
ellipse shows the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6
$\times$ 1$\aas@@fstack{\prime\prime}$1 (PA= 41∘). The SVS13-B, SVS13-C, and
VLA3 protostars are also labelled. White dashed circle indicate the primary
beam: $\sim$ 55$\arcsec$. Right Panel: Zoom-in of the inner SVS13-A region as
observed in dust continuum at 1.3mm. First contour and steps are,
respectively, 5$\sigma$ (1$\sigma$ = 1 mJy) and 30$\sigma$. Symbols are as in
the Left panel. The synthesised beam (HPBW) is 0$\aas@@fstack{\prime\prime}$6
$\times$ 0$\aas@@fstack{\prime\prime}$6 (PA= –46∘), while the primary beam is
24$\arcsec$.

###  4.2 Line images and spectra

We imaged, at both 1.4 mm and 3mm, a large (32) number of lines of S-bearing
species, listed in Table 1. Namely, 4 32SO (hereafter SO) lines ($E_{\rm u}$
in the 9–39 K range), 2 34SO lines (9–19 K), 7 SO2 lines (37–549 K), 2 34SO2
lines (55–70 K), 1 C32S (hereafter CS) line (7 K), 1 C34S line (6 K), 1 C33S
line (7 K), 3 OCS lines (16–89 K), 9 H2C32S (hereafter H2CS) lines (including
two pairs blended at the present spectral resolution; 10–244 K), 1 H2C34S line
(48 K), and 1 NS line (27 K). In the following, for sake of clarity, the
results of each species will be reported separately. The overall picture will
be discussed in Sect. 6.

####  4.2.1 SO

Figure 2-Left shows the spatial distribution of the low-$E_{\rm u}$ (9 K)
SO(23–12) emission observed at 86 GHz. The emission peaks are towards SVS13-A
and SVS13-B (3mm continuum drawn in black) and are spatially unresolved. In
addition, a contribution from the extended envelope is suggested. Figure 3
reports the SVS13-A spectrum. The used low-spectral resolution (7 km s-1)
prevents us from a proper kinematical analysis. However, the peak velocity is
centred at the systemic velocity of +8.6 km s-1 (Chen et al., 2009). By
imaging the SO(23–12) per velocity range, Fig. 2-Left shows some blue-shifted
emission flowing towards South-East, i.e. tracing signatures of the well-known
extended ($\gg$ 8$\arcsec$) outflow associated with HH7-11 (see e.g. Lefloch
et al. 1998; Codella et al. 1999; Lefèvre et al. 2017). In addition, a well
collimated (and more compact) bipolar outflow driven by SVS13-B is observed.
Very high-velocity emission, up to +20 km s-1 and down to –94 km s-1, is
detected. This outflow, located along the NW-SE direction, had been discovered
by (Bachiller et al., 1998) using SiO, and recently imaged in the context of
the CALYPSO IRAM Large Program Maury et al. (2019) by Podio et al. (2021) in
the SiO(5–4), CO(2–1), and SO(56-45) lines. The outflow collimation is
consistent with SVS13-B being in an earliest evolutionary stage (Class 0) with
respect to SVS13-A (Class I) driving a more extended, and less collimated
flow.

Moving towards slightly higher excitation lines (up to 39 K), the SO lines
observed at 3mm with $\sim$ 1$\aas@@fstack{\prime\prime}$5 (450 au) angular
resolution appear spatially unresolved and centred on SVS13-A. SVS13-B is
detected only through the 22–11 and 23–12 lines. On the other hand, the images
of the SO lines at 1.4mm (synthesised beam $\sim$ 180 au) reveal a structure
with a size $\sim$ 300 au, plausibly associated with the molecular envelope.
An elongation (due to low-velocity blue-shifted emission) towards the blue-
shifted outflow SE direction is clearly visible. The SO(45–34) line ($E_{\rm
u}$ = 39 K) profile, observed with a spectral resolution of 2.8 km s-1, has a
FWHM line width of 9.2 km s-1.

Finally, the ratio between the integrated fluxes as derived towards SVS13-A of
the SO and 34SO 23–12 or 22–11 lines is $\sim$10–12, which, assuming optically
thin 34SO emission and 32S/34S = 22 (Wilson & Rood, 1994), leads to an SO
opacity $\sim$ 1.

Figure 2: Left Panel: Spatial distribution of the SVS13-A region obtained
using the SO(23–12) red- and blue-shifted emission overlaid with the 90 GHz
continuum map (see Fig. 1). Red-shifted emission maps have been derived by
integrating the SO emission from the systemic velocity (+8.6 km s-1, Chen et
al. (2009)) up to +20 km s-1. Blue-shifted image has been obtained by
integrating down to –94 km s-1 in absolute values). Angular offset are with
respect to the phase center (see Sect. 3). First contour and steps are,
respectively, 3$\sigma$, and 4$\sigma$, respectively. The 1$\sigma$ value is 5
mJy km s-1 and 14 mJy km s-1 for the red- and blue-shifted emission,
respectively. The filled ellipse shows the synthesised beam (HPBW):
1$\aas@@fstack{\prime\prime}$6 $\times$ 1$\aas@@fstack{\prime\prime}$1 (PA=
41∘). The SVS13-B protostar is also labelled. White dashed circle indicate the
primary beam: $\sim$ 55$\arcsec$. Upper-Right Panel: Zoom-in of the inner
SVS13-A region as observed using the SO(45–34) emission. Green contours are
for the emission in the 3 km s-1 around the systemic velocity. Red-shifted
emission maps has been derived by integrating the SO emission from the
systemic velocity up to +20 km s-1. Blue-shifted image has been obtained by
integrating down to –5 km s-1. First contour and steps are, respectively,
3$\sigma$, and 10$\sigma$. The 1$\sigma$ value is 10 mJy km s-1 (systemic
velocity), 13 mJy km s-1 (red), and 11 mJy km s-1 (blue). Symbols are as in
the Left panel. The black cross indicates the positions of the 205 GHz
continuum peak (see Fig. 1). The synthesised beam (HPBW) is
0$\aas@@fstack{\prime\prime}$65 $\times$ 0$\aas@@fstack{\prime\prime}$58 (PA=
–46∘). Middle-Right Panel: Zoom-in of the inner SVS13-A region as observed
using the SO(45–44) emission. The whole velocity emitting region has been used
(see Fig. 3). First contour and steps are, respectively, 3$\sigma$ (9 mJy km
s-1), and 10$\sigma$. Symbols are as in the Left panel. The synthesised beam
(HPBW) is: 1$\aas@@fstack{\prime\prime}$6 $\times$
1$\aas@@fstack{\prime\prime}$1 (PA= 41∘). Bottom-Right Panel: Zoom-in of the
inner SVS13-A region as observed using the 34SO(23–12) emission. First contour
and steps are, respectively, 3$\sigma$ (12 mJy km s-1), and 10$\sigma$.
Symbols are as in the Left panel. The synthesised beam is as in the Middle-
Right panel.

Figure 3: Observed SO, and 34SO spectra (in TB scale, see Table 1) extracted
at the emission peak: $\alpha_{2000}$ = 03h29m03s.75, $\delta_{2000}$ =
+31∘16′03′′.8. Transitions and corresponding upper level energies are
reported. The vertical dashed line stands for the ambient LSR velocity (+8.6
km s-1, Chen et al. (2009)). Note that the p-H2CS(62,4–52,3) appears close to
the SO(45–34) profile (see Tab. 1).

####  4.2.2 CS

We imaged the $J$ = 2–1 line emission of the CS, C34S, and C33S isotoplogues,
emitting in the 96.4–98.0 GHz spectral range (Table 1). Figure 4 shows how the
main isotopologue is tracing the molecular envelope around SVS13-A. The rarer
isotopologues are emitting towards the CS emission peak, having a spatially
unresolved structure ($\leq$ 450 au). The spectra corresponding to the CS peak
are drawn in Fig. 5. The line ratios observed towards SVS13-A are: CS/C34S
$\simeq$ 3 and CS/C33S $\simeq$ 11\. In turn, assuming the C33S emission to be
optically thin and 32S/33S = 138 (Wilson & Rood, 1994), this implies optically
thick ($\tau$ $\sim$ 14) CS emission. The C34S emission results to be
moderately thick ($\tau_{\rm C^{34}S}$ $\simeq$ 2).

Figure 4: Spatial distribution of the SVS13-A region obtained using the $J$ =
2–1 CS (Upper panel), C34S (Middle), and C33S (Bottom) line emission (contours
and colour). The whole velocity emitting region has been used (down to – 5 km
s-1 and up to +25 km s-1, depending on the line, see Fig. 5). Angular offset
are respect to the phase center (see Sect. 3). First contour and steps are,
respectively, 5$\sigma$, and 10$\sigma$, respectively. The 1$\sigma$ value is
10 mJy km s-1 (CS), and 4 mJy km s-1 (C34S, C33S). The filled ellipse shows
the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6 $\times$
1$\aas@@fstack{\prime\prime}$1 (PA= 41∘). The black crosses indicate the
positions of the VLA4A and VLA4B sources as imaged using the VLA array by
Tobin et al. (2018).

Figure 5: Observed CS, C34S, C33S, and NS spectra (in TB scale, see Table 1)
extracted at the emission peak: $\alpha_{2000}$ = 03h29m03s.75,
$\delta_{2000}$ = +31∘16′03′′.8. Transitions and corresponding upper level
energies are reported. The vertical dashed line stands for the ambient LSR
velocity (+8.6 km s-1, Chen et al. (2009)). The C33S(2–1) line consists of 6
hyperfine components with $S\mu^{2}$ in the 0.5–12.2 D2 range (Bogey et al.,
1981; Lovas, 2004; Müller et al., 2005) spread on a 9 MHz frequency interval.
The vertical red lines (in scales according to their $S\mu^{2}$) indicated
their relative offset in velocity scale with respect to the brightest
$F$=5/2–3/2 line. The NS 9/2–7/2 $\Omega$=1/2 line consists of 3 hyperfine
components (Lee et al., 1995) associated with $S\mu^{2}$ in the 10.9–17.4 D2
range spread on a 0.6 MHz frequency interval. The vertical red lines (in
scales according to their $S\mu^{2}$) indicated their relative offset in
velocity scale with respect to the brightest $F$=11/2–9/2 line (see Table 1).

####  4.2.3 SO2

A large number of SO2 (and 34SO2) lines has been detected at both 3mm and
1.4mm, covering a very large range of the upper level energies, from 37 K to
549 K. Figure 6 reports a selection of the spatial distributions of the SO2
lines, peaking towards SVS13-A. All the spectra are reported in Fig. 7: when
observed with a spectral resolution of 2.9 km s-1, the profiles peak close to
the systemic velocity (+8.6 km s-1, Chen et al. 2009), and are $\sim$ 7–8 km
s-1 broad.

Contrarily to SO and CS, the SO2 emission is spatially unresolved both at 3mm
and 1.4mm, indicating an emitting size less than 180 au. In other words, there
is neither signature of outflows (as for SO) nor of the envelope revealed by
SO and CS. The SO2 and 34SO2 emission is tracing the inner protostellar
region. By fitting the position of the brightest SO2 line (204.2 GHz) using a
Gaussian fit in the $uv$ domain444In the $uv$ domain, the error on centroid
positions is the function of the channel signal-to-noise ratio and atmospheric
seeing, and is typically much smaller than the beam size., we found
$\alpha_{2000}$ = 03h29m03s.755, $\delta_{2000}$ = +31∘16′03′′.782. The $uv$
fit error is 3 mas. This position lies between the coordinates of the binary
components VLA4A and VLA4B (see Fig. 6-Right panels), more specifically at
$\simeq$ 0$\aas@@fstack{\prime\prime}$13 (39 au) from both protostars. This
shift perfectly agrees with what was found using iCOMs emission as imaged with
an angular resolution of
0$\aas@@fstack{\prime\prime}$4–1$\aas@@fstack{\prime\prime}$3 (at 1.3–3mm) in
the context of the CALYPSO project (De Simone et al., 2017; Belloche et al.,
2020).

Finally, since we have not detected common SO2 and 34SO2 lines, the estimate
on the SO2 opacity will be discussed in Sect. 5 in light of the Large Velocity
Gradient (LVG) analysis.

Figure 6: Spatial distribution (contours and colour) of the SVS13-A region
obtained using different SO2, and 34SO2 line emission (see Table 1). Angular
offset are respect to the phase center (see Sect. 3). The whole velocity
emitting region has been used (from 0 km s-1 to +20 km s-1, see Fig. 7). The
SO2(112,10–111,11) profile has been deblended by the CH3OCHO line fitting the
profile with two Gaussians (see Table 1). First contour and steps are,
respectively, 5$\sigma$, and 10$\sigma$, respectively. The 1$\sigma$ value is:
7 mJy km s-1 for SO2(81,7–80,8 (Left panel), 14 mJy km s-1 for
SO2(112,10–111,11), SO2(183,15–182,16), and 34SO2(120,12–111,11). The filled
ellipse shows the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6
$\times$ 1$\aas@@fstack{\prime\prime}$1 (PA= 41∘) for the SO2(81,7–80,8) maps
(Left panel), and 0$\aas@@fstack{\prime\prime}$65 $\times$
0$\aas@@fstack{\prime\prime}$58 (PA= –46∘) for the the other images. The black
crosses indicate the positions of the VLA4A and VLA4B sources as imaged using
the VLA array by Tobin et al. (2018).

Figure 7: Observed SO2, 34SO2, and 33SO2 spectra (in TB scale, see Table 1)
extracted at the emission peak: $\alpha_{2000}$ = 03h29m03s.75,
$\delta_{2000}$ = +31∘16′03′′.8. Transitions and corresponding upper level
energies are reported. The vertical dashed line stands for the ambient LSR
velocity (+8.6 km s-1, Chen et al. (2009)). The 34SO2 line at $E_{\rm u}$ = 55
K could be contaminated by 13CCS emission with $E_{\rm u}$ = 22 K (see Table
1).

####  4.2.4 OCS

Figure 8 shows the spatial distribution of the three detected OCS lines. The
$J$ = 7–6 and 8–7 transitions fall in the 3mm band: the emitting size is
clearly unresolved with the spatial resolution of
1$\aas@@fstack{\prime\prime}$5\. Also the OCS(17–16) line, imaged with a
synthesised beam of 0$\aas@@fstack{\prime\prime}$6, is spatially unresolved.
The $uv$ analysis leads to a peak coordinates of $\alpha_{2000}$ =
03h29m03s.754, $\delta_{2000}$ = +31∘16′03′′.778, with an error of 5 mas. This
position is consistent with what found using SO2, lying between the VLA4A and
VLA4B positions. The OCS spectra are reported in Fig. 9: the peak velocity is
in agreement with the SVS13-A systemic velocity of +8.6 km s-1 (Chen et al.,
2009). In addition the OCS(17–16) profile, samples with a 2.8 km s-1, shows a
FWHM of 7 km s-1, consistent with those of the SO2 lines observed at the same
angular resolution.

Figure 8: Spatial distribution of the SVS13-A region obtained using the
OCS(7–6) (Upper panel), OCS(8–7) (Middle), and OCS(17–16) (Bottom) line
emission (contours and colour). The whole velocity emitting region has been
used (from 0 km s-1 to +20 km s-1, see Fig. 9). Angular offset are with
respect to the phase center (see Sect. 3). First contour and steps are,
respectively, 5$\sigma$, and 10$\sigma$, respectively. The 1$\sigma$ value is
5 mJy km s-1 ($J$ = 7–6, and 8–7), and 26 mJy km s-1 ($J$ = 17–16). The filled
ellipse shows the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6
$\times$ 1$\aas@@fstack{\prime\prime}$1 (PA= 41∘) for OCS(7–6) and OCS(8–7),
and and 0$\aas@@fstack{\prime\prime}$65 $\times$
0$\aas@@fstack{\prime\prime}$58 (PA= –46∘) for OCS(17–16). The black crosses
indicate the positions of the VLA4A and VLA4B sources as imaged using the VLA
array by Tobin et al. (2018).

Figure 9: Observed OCS spectra (in TB scale, see Table 1) extracted at the
emission peak: $\alpha_{2000}$ = 03h29m03s.75, $\delta_{2000}$ =
+31∘16′03′′.8. Transitions and corresponding upper level energies are
reported. The vertical dashed line stands for the ambient LSR velocity (+8.6
km s-1, Chen et al. (2009)).

####  4.2.5 H2CS

As reported in Table 1, ten H2CS and H2CS34S lines, with $E_{\rm u}$ in the
10–244 K range, have been revealed using both setups at 3mm and 1.4mm. Two
pairs of SO2 lines are blended at the present spectral resolution. Figure 10
shows examples of the spatial distributions of the H2CS lines: as SO2 and OCS,
the emission is peaking towards SVS13-A, being spatially unresolved at both
3mm and 1.4mm.

The peak coordinates, according to the $uv$ fit, are $\alpha_{2000}$ =
03h29m03s.752, $\delta_{2000}$ = +31∘16′03′′.786, with an error of 8 mas, in
agreement with the SO2 and OCS ones. The profiles at the peak emission are
shown in Fig. 11. Interestingly, o-H2C34S(61,5–51,4) has been observed with a
spectral resolution of 0.9 km s-1, i.e. definitely better than that of the
other lines (3–7 km s-1). For this line the profile is well sampled, peaking
at the SVS13-A systemic velocity (+8.6 km s-1, Chen et al. 2009), and with a
FWHM of 2.7 km s-1.

Figure 10: Spatial distribution (contours and colour) of the SVS13-A region
obtained using different H2CS, and H2C34S line emission (see Table 1). The
whole velocity emitting region has been used (from 0 km s-1 to +20 km s-1, see
Fig. 11). The p-H2CS(62,4–52,3) emission has been deblended from the SO
emission (see Table 1) applying two Gaussian profiles. Angular offset are
relative to the phase center (see Sect. 2). First contour and steps are,
respectively, 5$\sigma$, and 10$\sigma$, respectively. The 1$\sigma$ value,
from Left to Right, is 5, 13, 11, and 9 mJy km s-1, respectively. The filled
ellipse shows the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6
$\times$ 1$\aas@@fstack{\prime\prime}$1 (PA= 41∘) for the o-H2CS(31,3–21,2)
line (Left panel), and 0$\aas@@fstack{\prime\prime}$65 $\times$
0$\aas@@fstack{\prime\prime}$58 (PA= –46∘) for the p-H2CS(60,6–50,5),
p-H2CS(62,4–52,3), and o-H2C34S(61,5–51,4) lines (Middle and Right panels).
The black crosses indicate the positions of the VLA4A and VLA4B sources as
imaged using the VLA array by Tobin et al. (2018).

Figure 11: Observed H2CS, and H2C34S spectra (in TB scale, see Table 1)
extracted at the emission peak: $\alpha_{2000}$ = 03h29m03s.75,
$\delta_{2000}$ = +31∘16′03′′.8. Transitions and corresponding upper level
energies are reported. The vertical dashed line stands for the ambient LSR
velocity (+8.6 km s-1, Chen et al. (2009)). Red labels and red vertical
segments denote two H2CS profiles with the same $E_{\rm u}$ value and blended
at the present spectral resolution (Table 1). The black vertical labels
indicate that the line is reported in another panel of the present figure. The
H2CS doublets at $E_{\rm u}$ = 244 K could be contaminated by CH3OH emission
with $E_{\rm u}$ = 317 K (see Table 1). The H2C34S(61,5–51,4) profile has been
observed using both low- (black histogram) and high-spectral (blue) backends
(see Sect. 2: labelled Widex and NB, respectively).

####  4.2.6 NS

The NS(9/2–7/2) $\Omega$=1/2 line, with $E_{\rm u}$ = 27 K, has been detected
towards SVS13-A. The profile consists of three hyperfine components, blended
with the 2.8 km s-1 spectral resolution (see Fig. 5). The frequency
transitions is 207.4 GHz and the corresponding spatial distribution is shown
in Fig. 12. The emitting size is unresolved, being less than the
0$\aas@@fstack{\prime\prime}$6 synthesised beam. The emission peaks between
the positions of the VLA4A and VLA4B, namely at $\alpha_{2000}$ =
03h29m03s.750, $\delta_{2000}$ = +31∘16′03′′.808, with an error of 14 mas. In
summary, NS, OCS, SO2, H2CS, once observed with the present spatial resolution
($\sim$ 100 au) are tracing the same spatially unresolved region, being
consistent with what expected from a chemical enriched region around the
protostar(s), i.e. the hot corino(s). These findings will be discussed in
Sect. 6 in light of the physical parameters derived in Sect. 5.

Figure 12: Spatial distribution (contours and colour) of the SVS13-A region
obtained using the NS(9/2–7/2) $\Omega$=1/2 emission. The whole velocity
emitting region has been used (from 0 km s-1 to +15 km s-1. The line profile
consists of three hyperfine components, blended at the present spectral
resolution (see Fig. 5 and Table 1). Angular offset are relative to the phase
center (see Sect. 3). First contour and steps are, respectively, 5$\sigma$ (50
mJy km s-1), and 10$\sigma$, respectively. The filled ellipse shows the
synthesised beam (HPBW): 0$\aas@@fstack{\prime\prime}$65 $\times$
0$\aas@@fstack{\prime\prime}$58 (PA= –46∘). The black crosses indicate the
positions of the VLA4A and VLA4B sources as imaged using the VLA array by
Tobin et al. (2018). Table 1: List of transitions of S-bearing species
detected towards SVS13-A. The Gaussian fit parameters (in $T_{\rm MB}$ scale)
refer to the spectra extracted at the emission peak: $\alpha_{2000}$ =
03h29m03s.75, $\delta_{2000}$ = +31∘16′03′′.8.

Transition |  $\nu$a |  $E_{\rm up}$a |  $S\mu^{2}$a |  $d$v | rms | $T_{\rm peak}$ | $V_{\rm peak}$ | FWHM | $I_{\rm int}$
---|---|---|---|---|---|---|---|---|---
| (MHz) | (K) | (D2) | (km s-1) | (mK) | (mK) | (km s-1) | (km s-1) | (K km s-1)
SO
22–11 | 86093.95 | 19 | 3.5 | 7.0 | 22 | 2765(98) | +8.9(0.2) | 9.7(0.5) | 27.69(0.23)
23–12 | 99299.87 | 9 | 6.9 | 6.0 | 42 | 4191(42) | +8.7(0.2) | 9.4(0.7) | 44.30(1.99)
45–44 | 100029.64 | 39 | 0.8 | 6.0 | 23 | 1209(43) | +8.8(0.2) | 7.5(0.5) | 9.55(0.27)
45–34 | 206176.01 | 39 | 8.9 | 2.8 | 920 | 43142(777) | +8.3(0.2) | 9.2(0.2) | 422.00(7.38)
34SO
22–11 | 84410.69 | 19 | 3.5 | 7.1 | 54 | 296(12) | +9.2(4.2) | 7.2(5.1) | 2.29(0.68)
23–12 | 97715.32 | 9 | 6.9 | 6.1 | 120 | 436(4) | +8.2(1.1) | 9.7(7.0) | 4.48(1.20)
SO2
134,10–143,11 | 82951.94 | 123 | 5.1 | 7.1 | 57 | 751(23) | +7.6(1.7) | 9.9(1.5) | 7.96(0.68)
81,7–80,8 | 83688.09 | 37 | 17.0 | 7.2 | 72 | 2071(24) | +7.0(0.3) | 10.3(0.5) | 22.65(0.94)
325,27–316,26 | 84320.88 | 549 | 13.5 | 7.1 | 40 | 364(30) | +8.0(2.3) | 7.1(6.1) | 2.76(0.65)
83,5–92,6 | 86639.09 | 55 | 3.0 | 6.9 | 53 | 719(22) | +8.1(1.3) | 8.9(1.4) | 6.82(0.73)
183,15–182,16 | 204246.76 | 181 | 34.5 | 2.9 | 780 | 12609(160) | +8.2(0.2) | 7.6(0.5) | 102.64(5.5)
74,4–83,5 | 204384.30 | 65 | 1.7 | 2.9 | 540 | 2757(210) | +8.0(0.7) | 7.9(1.6) | 23.09(4.12)
112,10–111,11 | 205300.57 | 70 | 12.1 | 2.9 | 197 | 11235(230) | +8.7(0.8) | 7.3(1.9) | 87.28(19.24)
34SO2
101,9–92,8b | 82124.35 | 55 | 6.5 | 7.1 | 160 | 6998(55) | +9.4(1.2) | 8.3(3.2) | 63.29(3.03)
120,12–111,11 | 204136.23 | 70 | 22.7 | 2.9 | 1400 | 5982(780) | +9.1(0.7) | 5.4(2.0) | 34.56 (9.4)
CS
2–1 | 97980.95 | 7 | 7.6 | 6.1 | 38 | 5196(12) | +8.6(0.2) | 7.0(0.3) | 38.72(0.62)
C34S
2–1 | 96412.95 | 6 | 7.6 | 6.2 | 45 | 2088(27) | +7.8(1.4) | 6.4(4.8) | 14.26(4.38)
C33S
2–1 $F$=5/2–3/2c | 97171.84 | 7 | 12.2 | 6.2 | 29 | 388(32) | +8.2(0.5) | 8.6(1.2) | 3.56(0.33)
OCS
7–6 | 85139.10 | 16 | 3.5 | 7.0 | 36 | 3787(50) | +8.5(0.4) | 7.1(0.2) | 28.39(0.34)
8–7 | 97301.21 | 21 | 4.1 | 6.1 | 29 | 5031(86) | +8.6(0.2) | 7.6(0.2) | 40.73(1.18)
17–16 | 206745.16 | 89 | 8.7 | 2.8 | 471 | 40764(140) | +8.4(0.3) | 7.1(0.7) | 308.66(4.89)
H2CS
o-31,3–21,2 | 101477.81 | 23 | 21.8 | 5.9 | 20 | 1576(12) | +8.6(1.4) | 10.0(3.3) | 17.12(4.50)
p-30,3–20,2 | 103040.45 | 10 | 8.2 | 5.8 | 33 | 1603(93) | +8.5(1.3) | 6.2(3.3) | 10.49(2.26)
p-32,1–22,0 | 103051.87 | 63 | 4.5 | 5.8 | 46 | 318(18) | +7.8(4.7) | 9.9(4.5) | 3.79(1.15)
p–60,6–50,5 | 205987.86 | 35 | 16.3 | 2.8 | 159 | 7702(79) | +8.2(0.2) | 7.0(0.2) | 57.35(0.56)
p-64,3–54,2d | 206001.88d | 244 | 9.0 |  |  |  |  |  |
|  |  |  |  } 2.8 | 115 | 15074(260) | +8.8(0.2) | 7.3(0.2) | 116.65(1.84)
p-64,2–54,1d | 206001.88d | 244 | 9.0 |  |  |  |  |  |
o-63,4–53,3d | 206051.94d | 153 | 36.6 |  |  |  |  |  |
|  |  |  |  } 2.8 | 161 | 13512(120) | +7.1(0.8) | 7.6(2.1) | 108.84(24.75)
o-63,3–53,2d | 206052.24d | 153 | 36.6 |  |  |  |  |  |
p-62,4–52,3e | 206158.60e | 87 | 14.5 | 2.8 | 160 | 6004(120) | +7.9(0.2) | 7.7(0.5) | 48.87(0.49)
H2C34S
o-61,5–51,4 | 205583.13 | 48 | 47.5 | 0.9 | 560 | 3113(190) | +8.6(0.2) | 2.7(0.5) | 8.91(1.36)
NS
9/2–7/2 $\Omega$=1/2f l=e | 207436.05 | 27 | 17.4 | 2.8 | 1100 | 3968(840) | +7.9(0.8) | 5.7(1.7) | 24.22(6.41)
NS+
2–1 | 100198.55 | 7 | 8.7 | 6.0 | 28 | – | – | – |  $\leq$ 1g

a Spectral parameters from the Cologne Database for Molecular Spectroscopy
(Müller et al., 2001, 2005) for all the species, with the exception of those
of the H2CS isotoplogues, derived from the Jet Propulsion Laboratory (JPL
Pickett et al., 1998), and those of NS+, from Cernicharo et al. (2018). b
Possible contamination with 13CCS emission at 82123.376 MHz ($E_{\rm u}$ = 22
K, $S\mu^{2}$ = 0.7 D2). c The C33S(2–1) line consists of 6 hyperfine
components (Bogey et al., 1981; Lovas, 2004; Müller et al., 2005) in a 9 MHz
frequency interval. The line with the highest $S\mu^{2}$ is reported (see Fig.
5). d Lines blended at the present spectral resolution (2 MHz). Possible
contamination with CH3OH emission at 206001.30 MHz ($E_{\rm u}$ = 317 K,
$S\mu^{2}$ = 10.2 D2). e Contaminated by SO(45–34) high-velocity emission. f
The 9/2–7/2 $\Omega$=1/2 line consists of 3 hyperfine components (Lee et al.,
1995) in a 0.6 MHz frequency interval. The line with the highest $S\mu^{2}$
$F$=11/2–9/2 is reported (see Fig. 5). g 3$\sigma$ upper limit.

##  5 Physical parameters

We analysed the SO, SO2 and H2CS (and their isotopologues) spectra extracted
at the emission peak ($\alpha_{2000}$ = 03h29m03s.75, $\delta_{2000}$ =
+31∘16′03′′.8) via the non-LTE (Local Thermodynamic Equilibrium) Large
Velocity Gradient (LVG) approach using the code grelvg described in Ceccarelli
et al. (2003). We assumed a Boltzmann distribution for the H2 ortho-to-para
ratio. For SO, we used the collisional coefficients with p-H2 computed by
Lique et al. (2007) and retrieved from the BASECOL database (Dubernet et al.,
2013). For SO2, we used the collisional coefficients with ortho- and para-H2
computed by Balança et al. (2016) and retrieved from the LAMDA database
(Schöier et al., 2005). For H2CS, we used the H2CO-H2 collisional coefficients
with ortho- and para-H2 derived by Wiesenfeld & Faure (2013), scaled them for
the mass ratio, and provided by the LAMDA database (Schöier et al., 2005).

We assumed a semi-infinite slab geometry to compute the line escape
probability (Scoville & Solomon, 1974) and assumed a line width equal to 8 km
s-1. We used the 32S/34S equal to 22 (Wilson & Rood, 1994), and an H2CS ortho-
to-para ratio equal to 3. Finally, the errors on the observed line intensities
have been obtained adding the spectral r.m.s. to the uncertainties due to
calibration (see Sect. 3). We ran large grids of models varying the kinetic
temperature ($T_{\rm kin}$) from 20 to 500 K, the volume density ($n_{\rm
H_{2}}$) from 104 cm-3 to 109 cm-3, the emitting sizes from
0$\aas@@fstack{\prime\prime}$1 to 30$\arcsec$ and the SO, SO2 and H2CS column
densities from 1015 cm-2 to 1021 cm-2. The best fit for each species is
obtained by simultaneously minimizing the difference between the predicted and
observed integrated intensities of both used isotopologues (e.g. SO and 34SO;
SO2 and 34SO2; H2CS and H2C34S).

The results obtained for SO show a best solution, characterised by $\chi^{2}$
$\simeq$ 2, with a total column density NSO of 1017 cm-2, a kinetic
temperature $T_{\rm kin}$ equal to 280 K, and the volume density $n_{\rm
H_{2}}$ being 108 cm-3. The size is 0$\aas@@fstack{\prime\prime}$3 (90 au).
The line opacities lies between 0.1 and 1.4. If we consider an uncertainty of
1 $\sigma$, which correspond to a probability of 30% to exceeding $\chi^{2}$,
we have $T_{\rm kin}$ $\geq$ 150 K, $n_{\rm H_{2}}$ $\geq$ 6 $\times$ 106
cm-3, NSO = 0.2–3 $\times$ 1017 cm-2, and sizes in the
0$\aas@@fstack{\prime\prime}$2–0$\aas@@fstack{\prime\prime}$5 range.

The analysis of SO2 leads to a best solution ($\chi^{2}$ $\simeq$ 3) with the
N${}_{\rm SO_{2}}$ = 1018 cm-2, $T_{\rm kin}$ = 210 K, and 108 cm-3. The size
is 0$\aas@@fstack{\prime\prime}$2 ($\sim$ 60 au). The line emission is
moderately thick, being the opacity between 0.30 and 4.5. Once considered the
uncertainty of 1 $\sigma$, we obtain $T_{\rm kin}$ $\simeq$ 100–300 K, and
$n_{\rm H_{2}}$ $\geq$ 5 $\times$ 106 cm-3, N${}_{\rm SO_{2}}$ = 0.3–3
$\times$ 1018 cm-2, and the size between 0$\aas@@fstack{\prime\prime}$1 and
0$\aas@@fstack{\prime\prime}$3.

The best fit obtained for H2CS, identified by $\chi^{2}$ $\simeq$ 0.1,
indicates the total column density equal to 2 $\times$ 1015 cm-2, a size of
0$\aas@@fstack{\prime\prime}$4 (120 au), the kinetic temperature $T_{\rm kin}$
= 100 K, and the volume density $n_{\rm H_{2}}$ = $2\times$ 105 cm-3. The line
opacities are all in the 0.04–0.4 range but that of the 60,6–50,5 para line
which is 0.86. Taking into account 1 $\sigma$, the following constraints are
derived: $T_{\rm kin}$ $\geq$ 50 K, $n_{\rm H_{2}}$ $\geq$ 105 cm-3, N${}_{\rm
H_{2}CS}$ = 0.7–2 $\times$ 1015 cm-2, and sizes in the
0$\aas@@fstack{\prime\prime}$2–0$\aas@@fstack{\prime\prime}$8 range.

Figure 13 shows the comparison between observations and best-fit line
predictions for SO, SO2, and H2CS, while Table 2 summarises the excitation
ranges found for the three molecules. As a matter of fact, all the SO, SO2 and
H2CS analysis are consistent with the occurrence of hot corino emission. This
will allow us to compare the present results with what previously found using
iCOMs (see Sect. 6).

Table 2: 1$\sigma$ Confidence Level (range) from the Non-LTE LVG Analysis of
the SO, SO2, and H2CS lines towards SVS13-A as imaged with NOEMA. The OCS, CS,
and NS column densities, derived assuming LTE conditions, are also reported.
The last row with H2S, is based on IRAM 30-m data at 1.4mm. The last column is
for the abundance with respect to H2.

Species | Ntot | n${}_{\rm H_{2}}$ | Tkin | size | X${}_{\rm H_{2}}$d
---|---|---|---|---|---
| (cm-2) | (cm-3) | (K) | (arcsec) |
SO | 0.2-3 $\times$ 1017 |  $\geq$ 6 $\times$ 106 |  $\geq$ 150 K | 0$\aas@@fstack{\prime\prime}$2–0$\aas@@fstack{\prime\prime}$5 | 7 $\times$ 10-9 – 1 $\times$ 10-7
SO2 | 0.3-3 $\times$ 1018 |  $\geq$ 5 $\times$ 106 | 100–300 | 0$\aas@@fstack{\prime\prime}$1–0$\aas@@fstack{\prime\prime}$3 | 1–10 $\times$ 10-7
H2CS | 0.7-2 $\times$ 1015 |  $\geq$ 105 |  $\geq$ 50 K | 0$\aas@@fstack{\prime\prime}$2–0$\aas@@fstack{\prime\prime}$8 | 2–7 $\times$ 10-10
| Ntot | n${}_{\rm H_{2}}$ | Trot | size | X${}_{\rm H_{2}}$d
| (cm-2) | (cm-3) | (K) | (arcsec) |
OCSa | 1-2 $\times$ 1015 | – | 70–170 | 0$\aas@@fstack{\prime\prime}$3a | 3–7 $\times$ 10-10
CSb | 0.8-17 $\times$ 1018 | – | 37.5c–300 | 0$\aas@@fstack{\prime\prime}$3b | 0.3–6 $\times$ 10-6
NSb | 1-6 $\times$ 1015 | – | 37.5c–300 | 0$\aas@@fstack{\prime\prime}$3b | 0.2–3 $\times$ 10-9
NS+b |  $\leq$ 8 $\times$ 1014 | – | 37.5c–300 | 0$\aas@@fstack{\prime\prime}$3b |  $\leq$ 3 $\times$ 10-10
H2Sb,e | 0.5–1 $\times$ 1018 | – | 37.5c–300 | 0$\aas@@fstack{\prime\prime}$3b | 2–4 $\times$ 10-7

a Estimate derived using the RD approach, and assuming a source size of
0$\aas@@fstack{\prime\prime}$3 following the SO, SO2, and H2CS LVG analysis. b
Estimates derived using one line, and assuming: (i) a source size of
0$\aas@@fstack{\prime\prime}$3, and a temperature in the 37.5–300 K range
(from LVG analysis of SO, SO2, and H2CS). For CS, we took into account the
line opacity of 14 derived from the comparison with the emission of C34S and
C33S. c For Trot we conservatively used a lower limit of 37.5 K, according to
the partition function tabulated in the Jet Propulsion Laboratory (JPL,
Pickett et al., 1998) database. d We assume N${}_{\rm H_{2}}$= 3 $\times$ 1024
cm-2 (Chen et al., 2009). e Estimated based on the 22,0–21,1 line observed
with a HPBW = 11$\arcsec$ using the IRAM 30-m antenna (see Sect. 6.4).

Figure 13: Ratio of the observed and best-fit theoretical line integrated
intensities of SO (Upper panel), SO2 (Middle), and H2CS (Bottom) as a function
of the line upper-level energy (see the text and Table 2). Different symbols
indicate different isotopologues as well as ortho and para species.

For OCS, having detected three lines, two of them at very similar upper level
excitation (16 K and 21 K), we did not apply the LVG analysis, adopting
instead the rotational diagram (RD) approach, where LTE population and
optically thin lines are assumed. Under these assumptions, for a given
molecule, the relative population distribution of all the energy levels, is
described by a Boltzmann temperature, that is the rotational temperature
$T_{\rm rot}$. Given the OCS emission is peaking towards SVS13-A and spatially
unresolved (Fig. 8), we corrected the line intensities assuming a size of
0$\aas@@fstack{\prime\prime}$3, i.e. the average size obtained from the LVG
results for SO, SO2, and H2CS. The RD analysis which provides a column density
of 1–2 $\times 10^{15}$ cm-2, and a rotational temperature Trot = 120$\pm$50 K
(see Fig. 14).

Finally, for CS and NS, having detected only one transition, in light of the
previous LVG results we adopted again a source size of
0$\aas@@fstack{\prime\prime}$3 and conservatively assumed the overall
temperature range (37.5–300 K, see Table 2). We consequently derived: 0.8–17
$\times 10^{18}$ cm-2 for CS, and 1–6 $\times 10^{15}$ cm-2 for NS.

Figure 14: Rotational diagrams for OCS derived using the emission lines
observed towards SVS13-A (see Table 1 and Fig. 9). The parameters Nu, gu, and
$E_{\rm up}$ are, respectively, the column density, the degeneracy and the
energy (with respect to the ground state of each symmetry) of the upper level.
A source size of 0$\aas@@fstack{\prime\prime}$3 has been assumed, following
the SO, SO2, and H2CS LVG analysis. The derived values of the rotational
temperature are reported in the panels.

##  6 Discussion

###  6.1 The chemical census of the SVS13-A hot corino

The SVS13-A system has been recently subject of IRAM 30-m (ASAI: Lefloch et
al., 2018) and IRAM PdBI (CALYPSO: Maury et al., 2019) observations aimed to
obtain its chemical census. More specifically, Bianchi et al. (2017, 2019a)
reported the analysis of a large sample of iCOMs using the ASAI single dish
unbiased spectral survey: the large number of lines allowed the authors to:
(i) analyse using the LVG approach the methanol isotopologues, and (ii)
consequently derive the column densities of more complex organic species
(CH3CHO, H2CCO, HCOOCH3, CH3OCH3, CH3CH2OH, NH2CHO). On the other hand, De
Simone et al. (2017) and Belloche et al. (2020) used the PdBI images
(synthesised beams between 0$\aas@@fstack{\prime\prime}$5 and
1$\aas@@fstack{\prime\prime}$7) of iCOMs emitting in selected spectral windows
to derive the column densities in LTE conditions of, again, a large number of
iCOMs, namely those reported by Bianchi et al. (2019a) plus C2H5CN,
a-(CH2OH)2, and HCOCH2OH. Both the ASAI and the CALYPSO analysis led to an
emitting size, for iCOMs, of 0$\aas@@fstack{\prime\prime}$3, perfectly
consistent with what is found in the present analysis of S-bearing species
(see Table 2). The column densities are also well in agreement, being
different by less than a factor of 2 for all the iCOMs in common except for
methanol and formamide (a factor of 3–4). Very recently, also Yang et al.
(2021) reported the results of the PEACHES ALMA survey on the chemical content
of star forming regions in Perseus, SVS13-A among them. A large number of
iCOMs are detected, in agreement with the ASAI and CALYPSO results. Column
densities, measured in this case of a 0$\aas@@fstack{\prime\prime}$5 source
size, are also consistent considering the uncertainties. In conclusion, once
observed with a $\sim$ 1$\arcsec$ resolution, it looks that S-bearing species
are emitting from a region similar to that associated with the hot corino
chemistry.

In order to derive the abundances of S-bearing species we assumed N${}_{\rm
H_{2}}$ = 3 $\times$ 1024 cm-2 as the typical value for the inner
0$\aas@@fstack{\prime\prime}$3 region, following what was adopted by Bianchi
et al. (2019a) and Belloche et al. (2020) for the iCOMs analysis, using the
continuum images by Chen et al. (2009). The abundances are reported in Table
2: the most abundant S-species are CS (0.3–6 $\times$ 10-6), SO (7 $\times$
10-9 – 1 $\times$ 10-7), and SO2 (1–10 $\times$ 10-7). On the other hand, H2CS
and OCS have similar, lower, abundances (a few 10-10), while XNS $\sim$
10-10–10-9. Interestingly, the H2CS abundance in SVS13-A is four orders of
magnitude higher with respect to the recently measured in the H2CS ring in the
protoplanetary disk around the Class II HL Tau (Codella et al., 2020). This
strongly supports that sulfur chemistry is indeed definitely evolving during
the star-forming process.

Finally, Figure 15 summarises the abundances derived here for the sulfuretted
molecules as well as (i) those of iCOMs reported by Bianchi et al. (2019a),
(ii) and those derived using the CALYPSO datatset De Simone et al. (2017);
Belloche et al. (2020) applying the same H2 column density. For completeness,
we also added 5-atoms molecules such as H2CCO (Bianchi et al., 2019a), and
CH3CN, and NH2CN (Belloche et al., 2020). The present census of the S-bearing
molecules thus contribute to building up a suite of abundances representative
of the inner 90 au SVS13-A region, calling for modelling (out of the scope of
this paper) to constraint the chemical evolution in star-forming regions.
Obviously, any theoretical approach in modelling the SVS13-A chemical richness
will face the long-standing problem on the main reservoir of sulfuretted
molecules on dust mantles. A progress in that direction would surely unlock
the interpretation of the chemical richness (also) around protostars.
Meanwhile, a little step can be done by comparing the H2CS emission of H2CO,
which is not properly an iCOM, but is key molecule for the production of more
complex species (see e.g. Caselli & Ceccarelli, 2012; Jørgensen et al., 2020,
and references therein).

Figure 15: Summary of the abundances with respect to H2 derived for the hot
corino observed towards SVS13-A (N${}_{\rm H_{2}}$ = 3 $\times$ 1024 cm-2 Chen
et al., 2009). Blue points are for the S-species reported in the present
paper, while blue triangles (Bianchi et al., 2019a) and grey diamonds
(Belloche et al., 2020) are for iCOMs (see Sect. 6.1).

###  6.2 H2CS versus H2CO

One of the main reasons of astrochemical studies of protostellar regions is to
understand the chemical composition of the gas where planets start their
formation process. As a matter of fact, to understand if the planetary
composition has the marks of where planets formed would definitely be a
breakthrough result (e.g. Turrini et al., 2021, and references therein).
Obviously, several processes are expected to be at work to sculpt the
characteristics of planetary atmospheres. Many intermediate steps should
intervene between the interstellar chemistry and the planetary chemistry, and
consequently, a complete chemical reset cannot be excluded. Whatever is the
path leading to planets, the elemental abundance ratios are the root where the
atmospheric chemistry is anchored (e.g. Booth & Ilee, 2019; Cridland et al.,
2019, and references therein). Together with O, C, N, sulfur is playing a
major role in this aspect (e.g. Semenov et al., 2018; Fedele & Favre, 2020;
Turrini et al., 2021). With time, the number of S-bearing species around
protoplanetary disks is definitely increasing. First, several detections of CS
and SO has been reported (e.g. Dutrey et al., 1997, 2017; Fuente et al., 2010;
Guilloteau et al., 2013, 2016; Pacheco-Vázquez et al., 2016). More recently,
thanks to the advent of ALMA, also H2S, H2CS have been imaged towards disk
around Class I/II objects showing rings and gaps (Phuong et al., 2018; Le Gal
et al., 2019; Codella et al., 2020; Loomis et al., 2020). These findings allow
us to compare what we found for the Class I SVS13-A with more evolved star
forming regions, namely Class I/II (105–106 yr old).

In this context, as recently remarked by Fedele & Favre (2020), the abundance
ratio between H2CS and H2CO could be used to investigate the S/O abundance
ratio provided that both molecules in the gas-phase are mainly formed by
reacting O or S with the methyl group CH3. In order to estimate [H2CS]/[H2CO]
in SVS13-A, we used the emission of the o–H2CO(61,5–61,6) transition at
101332.991 MHz (Eu = 88 K; from the Cologne Database for Molecular
Spectroscopy (CDMS, Müller et al., 2001, 2005). falling in the present Setup 6
at 3mm. Figure 16 reports the H2CO spatial distribution as well as the
spectrum extracted at the peak emission, both perfectly consistent with that
of H2CS as observed with the same spatial and spectral resolution (see Figs.
10 and 11). We then adopted the same size and kinetic temperature range
inferred for H2CS (see Table 2), the ortho/para ratio equal to 3 and, assuming
LTE conditions, we derived a total column density N${}_{\rm H_{2}CO}$ = 2-8
$\times$ 1017 cm-2. The [H2CS]/[H2CO] ratio is then between 9 $\times$ 10-4
and 2 $\times$ 10-2.

The present values obtained for a Class I object can be compared with other
measurements obtained from interferometric observations sampling Solar System
scales around protostars at different evolutionary stages:

  * •

the prototypical Class 0 hot corino IRAS 16293-2422B as revealed with ALMA on
a 60 au scale (PILS project: Jørgensen et al., 2016; Persson et al., 2018;
Drozdovskaya et al., 2018, 2019): 7 $\times$ 10-4;

  * •

late Class I or II protoplanetary disks as imaged with ALMA on a 40 au scale
(ALMA-DOT project: Podio et al., 2020a; Codella et al., 2020; Garufi et al.,
2021): 0.1–0.2 (HL Tau), and 0.4–0.7 (IRAS 04302+2247).

The comparison suggests an increase with time of the [H2CS]/[H2CO] ratio in
the gaseous compositions around stars by more than one order of magnitude.
Obviously, we cannot quantify [S]/[O] from [H2CS]/[H2CO] given the complexity
of the overall S and O chemistry, but the present findings suggest that
[S]/[O] could change along the Sun-like star forming process.

Finally, we inspected what has been measured with the ROSINA spectrometer
towards the comet 67P/Churyumov-Garasimenko (C-G) in the context of the ESA
Rosetta space mission Rubin et al. (2020). ROSINA derived the chemical
composition of the volatiles in the coma, reporting the H2CS and H2CO
abundance with respect to water. The corresponding [H2CS]/[H2CO] ratio ranges
in the 7 $\times$ 10-4 – 4 $\times$ 10-2 range, i.e. a quite wide spread which
does not allow us to verify if a relic of the early stages of our Solar System
supports the tentative [H2CS]/[H2CO] dependence on time from Class 0 to Class
II objects. Clearly, more measurements are needed to perform a statistical
study.

Figure 16: Upper panel: Spatial distribution of the SVS13-A region obtained
using the o–H2CO(61,5–61,6) emission. The whole velocity emitting region has
been used (from –5 km s-1 to +20 km s-1). The angular offsets are relative to
the phase center (see Sect. 2). First contour and steps are, respectively,
5$\sigma$ (25 mJy km s-1), and 20$\sigma$, respectively. The filled ellipse
shows the synthesised beam (HPBW): 1$\aas@@fstack{\prime\prime}$6 $\times$
1$\aas@@fstack{\prime\prime}$1 (PA= 41∘). The black crosses indicate the
positions of the VLA4A and VLA4B sources as imaged using the VLA array by
Tobin et al. (2018). Lower panel: Observed o–H2CO(61,5–61,6) spectrum (in TB
scale, see Table 1) extracted at the emission peak: $\alpha_{2000}$ =
03h29m03s.75, $\delta_{2000}$ = +31∘16′03′′.8. The upper level energy is
reported. The vertical dashed line stands for the ambient LSR velocity (+8.6
km s-1, Chen et al. (2009)).

###  6.3 NS versus NS+

The cation NS+ has been very recently discovered in interstellar space using
IRAM 30-m observations in the mm-spectral window of a sample of low-mass star-
forming regions (Cernicharo et al., 2018). More specifically, NS+ has been
revealed towards cold molecular clouds and prestellar cores as well as in
shocked protostellar regions and in the direction of hot corinos (e.g.
NGC1333-IRAS4A). Cernicharo et al. (2018) derived the NS/NS+ ratio, lying in
the 30–50 range, which has been modelled adopting the following chemical
routes (see e.g. Agúndez & Wakelam, 2013): NS is formed by reaction of SH with
N or of NH with S, while NS+ is formed when the atomic nitrogen reacts with
the SO+ and SH+ ions. On the other hand, both NS and NS+ should be destroyed
via reactions with the O, N, or C atoms. NS+ should go first through
dissociative recombination. Cernicharo et al. (2018) fit the observations by
using a relatively cold gas, even for the NGC1333-IRAS4A region (Tkin $\simeq$
30 K), which in turn means that NS+ is not released in the hot corino, but
instead from a more extended molecular envelope.

In the present SOLIS observations of SVS13-A, NS is clearly tracing the
protostellar region with a source size less than 100 au, then it is plausibly
emitted in the hot corino (see Fig. 12). In fact, in Sect. 4 we derived the NS
column density by assuming a kinetic temperature in the 50–300 K range.

Interestingly, the present SOLIS NOEMA setup is covering (with a $\sim$
1$\aas@@fstack{\prime\prime}$3 spatial resolution) the frequency of the
NS+(2–1) line (100198.55 GHz), characterised by Eu = 7 K, $S\mu^{2}$ = 9 D2
(Cernicharo et al., 2018). However, this line was not detected and only an
upper limit on NS+ column density can be derived by assuming the same emitting
size as well as the same kinetic temperatures adopted for the NS analysis (see
Table 2). The 3$\sigma$ upper limit on the velocity integrated emission is 1 K
km s-1, which in turn allows us to fix an upper limit on N${}_{\rm NH^{+}}$
$\leq$ 8 $\times$ 1014 cm-2. In summary, we can derive N(NS)/N(NS+) $\geq$ 10,
a number in agreement with those reported by Cernicharo et al. (2018), in
particular for the NGC1333-IRAS4A hot corino ($\sim$ 40). Note that these
findings are also consistent with the inspection of the spectra of the IRAM
30-m ASAI Legacy (Lefloch et al., 2018), which provides an unbiased spectral
survey at 1, 2, and 3mm of SVS13-A. ASAI covered not only the NS+(2-1) line,
but also the $J$ = 3–2 and 5–4 ones, at 150295.607 MHz and 250481.463 MHz,
respectively (Cernicharo et al., 2018). No detection has been found, providing
an upper limit on the NS+ column density of a few 1014 cm-2, similarly to what
was obtained with NOEMA SOLIS. The present findings, providing the first
constraint on the N(NS)/N(NS+) ratio based on interferometric data, call for a
comparison with predictions from astrochemical modelling at work at kinetic
temperatures typical of hot corinos ($\geq$ 100 K).

###  6.4 SO versus SO2

The importance of the SO2 over SO abundance ratio in star forming regions has
been discussed since the end of the last century. The starting assumption was
that H2S is the main S-bearing species in the dust mantles. As a consequence,
the injection of the material frozen on ices due either to thermal heating
(hot cores, hot corinos) or due to sputtering (shocks), or even for chemical
desorption caused by the excess energy of an exothermic reaction (Oba et al.,
2018), increases the H2S abundance in the gas-phase, which in turn forms first
SO and successively SO2 (e.g. Pineau des Forets et al., 1993; Charnley et al.,
1997; Hatchell et al., 1998). As a result, [SO2]/[SO] has been proposed to be
a chemical clock to date the evaporation/sputtering process. However,
successive attempts to apply this tool in young ($\geq$ 103 yr) shocked
regions did not result to be efficient (Codella et al., 1999; Wakelam et al.,
2004a; Codella et al., 2005) given all the uncertainties associated with the
S-chemistry starting from the still open question on the main S-bearing
species frozen on ices (e.g. Laas & Caselli, 2019; Taquet et al., 2020, and
references therein). On the other hand, a Kitt Peak single-dish (HPBW =
43$\arcsec$) survey of Class 0 and Class I hot corinos (104–105 yr) by Buckle
& Fuller (2003) suggested an evolutionary trend, with [SO2]/[SO] $\simeq$ 0.1
for Class 0 and [SO2]/[SO] $\simeq$ 0.4 for Class I.

Moving to interferometric observations, the present dataset shows for the
Class I SVS13-A target [SO2]/[SO] $\sim$ 10, a value larger than what measured
with ALMA towards the Class 0 IRAS16293-2422 hot corino (PILS: Drozdovskaya et
al., 2018, 2019): [SO2]/[SO] ratios $\sim$ 3\. Both measurements are higher
than what measured using IRAM-NOEMA (in the SOLIS context) of the young
shocked regions L1157 and L1448 outflows: [SO2]/[SO] $\simeq$ 0.2
(NGC1333-IRAS4A Taquet et al., 2020), and 0.1–0.3 (L1157 Feng et al., 2020).
In conclusion, these recent findings support the use the [SO2]/[SO] ratio to
date gas enriched in sulphur around protostars, using high-spatial
interferometric images to disentangle contributions due to different physical
components.

###  6.5 On the sulfur budget in SVS13-A

The recent results by Kama et al. (2019) and Shingledecker et al. (2020)
indicates that a large fraction ($\sim$ 90%) of sulphur in dense star forming
regions is in very refractory forms such as FeS or S8. In this context, in
order to evaluate the sulfur budget in the Class I SVS13-A hot corino, we need
an estimate of the abundance of H2S, which, as reported in the Sect. 1, is
postulated to be a major S-bearing molecule on dust mantles. Unfortunately,
the NOEMA SOLIS spectral windows do not cover H2S line frequencies. However,
the H2S column density can be measured using the line of the para 22,0–21,1
transition observed at 1.4mm in the context of the IRAM 30-m ASAI Large
Program (Lefloch et al., 2018). The line is emitting at 216710.4365 MHz: the
HPBW is 11$\arcsec$ and the energy of the upper level is quite high, 84 K
555The Frequencies and spectroscopic parameters have been provided by Cupp et
al. (1968), Burenin et al. (1985), and Belov et al. (1995) and retrieved from
the Cologne Database for Molecular Spectroscopy (Müller et al., 2001, 2005).
This combination minimises the contaminations expected from the cold envelope
with respect to the SVS13-A hot corino, and excludes any possible contribution
due to SVS13-B (see Fig. 1). Figure 17 reports the observed spectra, with the
p–H2S(22,0–21,1) profile peaking at +8.1(0.1) km s-1, with a FWHM line width
equal to 3.2(0.1) km s-1, and an integrated area (in TMB scale) of 534(14) mK
km s-1. Given S$\mu^{2}$ = 2.1 D2, assuming LTE conditions, an emitting size
equal to 0$\aas@@fstack{\prime\prime}$3 and a temperature range of 50–300 K
(as for the other S-species here imaged by NOEMA), an ortho/para ratio equal
to 3, we obtain a total column density of 0.5–1 $\times$ 1018 cm-2. Assuming
again N${}_{\rm H_{2}}$ = 3 $\times$ 1024 cm-2 (Chen et al., 2009), the H2S
abundance results to be 2–4 $\times$ 10-7. Table 2 and Fig. 15 summarises the
column density and abundances of the S-bearing molecules observed in the
SVS13-A hot corino. Overall, if we take all of them into account we reach
[S]/[H] = 3.0 $\times$ 10-7 – 3.8 $\times$ 10-6, i.e. 2%–17% of the Solar
System [S]/[H] value (1.8 $\times$ 10-5; Anders & Grevesse, 1989). Obviously,
not all the S-species observed around low-mass protostars have been revealed
in the present survey, missing mainly CCS as well as the SO+ and HCS+ ions.
However, we can reasonably assume that the contribution due to CCS (a standard
envelope tracer), and the SO+ and HCS+ ions (two orders of magnitude less
abundant than CS in the warm shocked gas in the L1157 outflow Podio et al.
(2014)) do not significantly contribute to the total S budget in SVS13-A.

The present measurements can be compared with what obtained in surveys of
other prototypical regions associated with Sun-like star-forming regions:

  * •

the Taurus dark cloud TMC 1 has been recently investigated in the context of
the GEMS project (Fuente et al., 2019) using the IRAM 30-m and Yebes 40-m
antennas in CS, SO, and HCS+ (plus rarer isotoplogues of these molecules). The
authors found a strong sulfur depletion both in the traslucent low-density
phase (where [S]/[H] is 2%–12% of the Solar System one, very similar to what
is found in SVS13-A) and in the dense core (where this percentage falls down
to 0.4%). Additional GEMS H2S observations reported by Navarro-Almaida et al.
(2020) did not significantly change these results;

  * •

the L1689N star forming region, hosting the well known Class 0 hot corinos
IRAS16293-2422A and B has been sampled using SO, and SO2, and H2S as observed
by Wakelam et al. (2004b) with the IRAM 30-m single-dish. The authors
estimate, for the hot corino region, the [S]/[H] ratio to be $\sim$ 8% of the
Solar System value. Successively, in the context of the PILS Large Program
(Jørgensen et al., 2016), Drozdovskaya et al. (2018, 2019) report the census
of S-bearing species as observed with ALMA towards the hot corino
IRAS16293-2422B (SO, SO2, H2S, CS, H2CS, and CH3SH). Assuming an H2 column
density of 1025 cm-2 derived in the PILS context by (Jørgensen et al., 2016),
the [S]/[H] ratio is then $\sim$ 1% of the Solar System measurement;

  * •

Holdship et al. (2019) measured the sulfur budget in the $\sim$ 100 K shocked
regions associated with the protostellar L1157 jet. In this case, the sampled
region is chemically enriched due to sputtering and shuttering induced by a
shock with a velocity of $\simeq$ 20–40 km s-1 (e.g. Flower et al., 2010; Viti
et al., 2011). For the bright L1157-B1 shock Holdship et al. (2019) report
[S]/[H] $\sim$ 10% of the Solar System, a value in agreement with what found
in SVS13-A.

Figure 17: Spectrum of the p–H2S(22,0–21,1) line (in TMB scale) as observed
towards SVS13-A at 1.4mm using the IRAM 30-m antenna. Transition and
corresponding upper level energy are reported. The HPBW is also indicated. The
vertical dashed line stands for the ambient LSR velocity (+8.6 km s-1, Chen et
al. (2009)).

In summary, the measurements of percentage of the [S]/[H] value with respect
to the Solar System value are: 0.4% (dense core), 1%-8% (Class 0 object),
2%-17% (Class I object), 10% (shock). Obviously, these estimates are strongly
dependent on the uncertainties associated with the adopted H2 column
densities. For instance Jørgensen et al. (2016) use N(H2) = 1025 cm-2 for
IRAS16293-2422B, while Bianchi et al. (2019a) and Belloche et al. (2020) adopt
3 $\times$ 1024 cm-2 for SVS13-A. With these caveats in mind, we can speculate
that (i) the increase of S-bearing molecules in the gas-phase due to thermally
evaporation in a Class 0 hot corino seems to keep constant also in the more
evolved Class I stage; (ii) the enrichment of sulfuretted molecules (with
respect to dense cold clouds) due to thermal evaporation seems to be
quantitatively the same than that in shocks, where sputtering rules.

##  7 Summary and conclusions

In the context of the IRAM NOEMA SOLIS Large Program we observed the SVS13-A
Class I object at both 3mm (beam $\simeq$ 1$\aas@@fstack{\prime\prime}$5) and
1.4mm (beam $\simeq$ 0$\aas@@fstack{\prime\prime}$6) in order to obtain a
census of the S-bearing species. The main results can be summarised as
follows:

  * •

We obtained 32 images of emission lines of 32SO, 34SO, C32S, C34S, C33S, OCS,
H2C32S, H2C34S, and NS, sampling $E_{\rm u}$ up to 244 K. The low-excitation
(9 K) SO is peaking towards SVS13-A. This emission traces also the molecular
envelope and the low-velocity outflow emission driven by SVS13-A. SO is also
imaging the collimated high-velocity (up to 100 km s-1 shifted with respect to
the systemic velocity) jet driven by the nearby SVS13-B Class 0. In general,
the molecular envelope contributes to the low-excitation (less than 40 K) SO
and CS emission. Conversely, all the rest of the observed species and
transitions show a compact emission around the SVS13-A coordinates indicating
the inner $\sim$ 100 au protostellar region.

  * •

The non-LTE LVG analysis of SO, SO2, and H2CS indicates a hot corino origin.
The emitting size is about 90 au (SO), 60 au (SO2), and 120 au (H2CS). For SO,
we have $T_{\rm kin}$ $\geq$ 150 K, and $n_{\rm H_{2}}$ $\geq$ 6 $\times$ 106
cm-3. The analysis of SO2 leads $T_{\rm kin}$ $\simeq$ 100–300 K, and $n_{\rm
H_{2}}$ $\geq$ 5 $\times$ 106 cm-3. Finally, for H2CS, $T_{\rm kin}$ $\geq$ 50
K, and $n_{\rm H_{2}}$ $\geq$ 105 cm-3. For OCS we used the rotation diagram
approach using LTE obtaining a $T_{\rm rot}$ of 120$\pm$50 K, consistent with
the temperatures expected for a hot corino.

  * •

The bright emission from S-bearing molecules is confirmed to arise from the
SVS13-A hot corino, where the iCOMs, previously imaged, are abundant De Simone
et al. (2017); Bianchi et al. (2019a); Belloche et al. (2020). The abundances
of the sulphuretted species are in the following ranges: 0.3–6 $\times$ 10-6
(CS), 0.7–10 $\times$ 10-7 (SO), 1– 10 $\times$ 10-7 (SO2), a few 10-10 (H2CS
and OCS), and 10-10–10-9 (NS).

  * •

Also NS is tracing a region with a size less than 100 au. We constrain for the
first time the N(NS)/N(NS+) using interferometric observations: $\geq$ 10\.
This is in agreement with what is previously reported for the NGC1333-IRAS4A
hot corino by Cernicharo et al. (2018) using single-dish measurements,
supporting that NS+ is mainly formed in the extended envelope.

  * •

Once measured using the NOEMA array, the [SO2]/[SO] ratio towards SVS13-A is
$\sim$ 10, a value slightly larger (by a factor 3) than what measured with
ALMA towards the Class 0 IRAS16293-2422B hot corino (PILS: Drozdovskaya et
al., 2018, 2019). This is clearly not enough to support the use of the
[SO2]/[SO] as chemical clock. However, after several unsuccessful attempts
done in the past using observations sampling gas on large scales (mainly using
single-dish antennas), the present measurements suggest to verify the use of
[SO2]/[SO] as chemical clock, but sampling the inner 100 au around the
protostars.

  * •

Considering that in the gas-phase H2CS and H2CO (i) are mainly formed by
reacting O or S with the methyl group CH3, and (ii) they are among the fews
species detected from protostars to protoplanetary disks, we derived their
abundance ratio in SVS13-A, obtaining 0.9 $\times$ 10-3 – 2 $\times$ 10-2. The
comparison between the few interferometric observations sampling Solar System
scales (IRAS 16293-2422B, SVS13-A, HL Tau, and IRAS 04302+2247) suggests an
increase with time of the [H2CS]/[H2CO] ratio in the gaseous compositions
around stars by more than one order of magnitude. It is then tempting to
speculate that [S]/[O] could vary along the Sun-like star forming process.

  * •

The estimate of the [S]/[H] budget in SVS13-A is 2%-17% of the Solar System
value (1.8 $\times$ 10-5). This number is consistent with what was previously
measured towards Class 0 objects (1%-8%). As a matter of fact, it seems that
the enrichment of the S-bearing molecules in Class 0 hot corinos (with respect
to dense and cold clouds) remain in the Class I stage.

To conclude, the present results are in agreement with the results reported by
Kama et al. (2019), who analysed a sample of young stars photospheres
concluding that 89%$\pm$8% of elemental sulfur in their disks is locked in
refractory form. Kama et al. (2019) conclude that the main S-carrier in the
dust has to be more refractory than water, suggesting sulfide minerals such as
FeS. Note also that recently (Shingledecker et al., 2020) have shown that
radiation chemistry converts a large fraction of S in allotropic form, in
particular S8, which cannot be detected (except for possible desorption
products due to photo-processes or shocks, such as S2, S3 and S4, as also
detected in the coma of the 67P/Churyumov-Gerasimenko comet (Calmonte et al.,
2016). Indeed, this is supported by the fact that even in a shocked region
such as L1157-B1, associated with both C and J-shocks (Benedettini et al.,
2012) and indeed rich in water (H2O/H2 = 10-4; Busquet et al., 2014), the
[S]/[H] ratio is not significantly larger than what is found in both Class 0
and Class I hot corinos.

###### Acknowledgements.

We thank the referee M. Drozdovskaya for her careful and instructive report,
that definitely improved the manuscript. We are also very grateful to all the
IRAM staff, whose dedication allowed us to carry out the SOLIS project. This
work was supported by (i) the European MARIE SK$\L$ODOWSKA-CURIE ACTIONS under
the European Union’s Horizon 2020 research and innovation programme, for the
Project “Astro-Chemistry Origins” (ACO), Grant No 811312, (ii) the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme, for the Project ”The Dawn of Organic Chemistry” (DOC),
grant agreement No 741002, and (iii) the project PRIN-INAF 2016 The Cradle of
Life - GENESIS-SKA (General Conditions in Early Planetary Systems for the rise
of life with SKA). This work is also supported by the French National Research
Agency in the framework of the Investissements d’Avenir program
(ANR-15-IDEX-02), through the funding of the ”Origin of Life” project of the
Univ. Grenoble-Alpes.

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##  Appendix A Comparison between NOEMA-SOLIS and IRAM 30m-ASAI

Figures A.1 and A.2 show the comparison between the IRAM 30-m 1.4mm and 3mm
spectrum obtained in the context of the ASAI Large Program Lefloch et al.
(2018) and the spectra derived by integrating the emission in the NOEMA-SOLIS
images in a region equal to the HPBW of the IRAM 30-m. The output is clearly
different, with the single-dish observations collecting not only the emission
imaged with NOEMA (LAS $\simeq$ 8$\arcsec$–9$\arcsec$), but also the large
scale structure (e.g. molecular envelope around SVS13-A, extended outflow.).
More specifically, Figs. A.3 and A.4 report zoomed-in portions of the 3mm and
1.4mm spectra to enlight lines of selected S-bearing molecules. The comparison
confirms that, as expected, the NOEMA-SOLIS maps are well suited to image hot
corinos. A particular case is represented by the SO single-dish spectra, which
are collecting a considrable amount of flux due to extnded emission. On the
other hand, the lines due to e.g. SO2 and H2CS are less affected by emission
filtering.

Figure 18: Comparison (in flux density scale) of the 3mm spectrum as observed
using the IRAM 30-m antenna (grey; in the ASAI LP context Lefloch et al.
(2018)) and that extracted from the present NOEMA SOLIS maps (red) from a
circular region equal to the IRAM 30-m HPBW (24$\arcsec$ at 104 GHz,
31$\arcsec$ at 80 GHz). The ASAI spectrum has been smoothed to match the SOLIS
velocity resolution (2 MHz, see Sect. 2). Red labels indicate the S-bearing
species analysed in this paper (see Table 1).

Figure 18: Continued. Comparison (in flux density scale) of the 3mm spectrum
as observed using the IRAM 30-m antenna (grey; in the ASAI LP context Lefloch
et al. (2018)) and that extracted from the present NOEMA SOLIS maps (red) from
a circular region equal to the IRAM 30-m HPBW (24$\arcsec$ at 104 GHz,
31$\arcsec$ at 80 GHz). The ASAI spectrum has been smoothed to match the SOLIS
velocity resolution (2 MHz, see Sect. 3). Red labels indicate the S-bearing
species analysed in this paper (see Table 1).

Figure 19: Comparison (in flux density scale) of the 1.4mm spectrum as
observed using the IRAM 30-m antenna (grey; in the ASAI LP context Lefloch et
al. (2018)) and that extracted from the present NOEMA SOLIS maps (red) from a
circular region equal to the IRAM 30-m HPBW (12$\arcsec$). The ASAI spectrum
has been smoothed to match the SOLIS velocity resolution (2 MHz, see Sect. 3).
Red labels indicate the S-bearing species analysed in this paper (see Table
1).

Figure 20: Zoom-in of Fig. A.1 to enlight selected emission lines of S-bearing
species: comparison (in flux density scale) of the 3mm spectrum as observed
using the IRAM 30-m antenna (grey; in the ASAI LP context Lefloch et al.
(2018)) and that extracted from the present NOEMA SOLIS maps (red) from a
circular region equal to the IRAM 30-m HPBW (25$\arcsec$ at 100 GHz,
29$\arcsec$ at 84 GHz). The ASAI spectrum has been smoothed to match the SOLIS
velocity resolution (2 MHz, see Sect. 3). Red labels indicate the S-bearing
species analysed in this paper (see Table 1).

Figure 21: Zoom-in of Fig. A.2 to enlight selected emission lines of S-bearing
species: comparison (in flux density scale) of the 1.4mm spectrum as observed
using the IRAM 30-m antenna (grey; in the ASAI LP context Lefloch et al.
(2018)) and that extracted from the present NOEMA SOLIS maps (red) from a
circular region equal to the IRAM 30-m HPBW (12$\arcsec$). The ASAI spectrum
has been smoothed to match the SOLIS velocity resolution (2 MHz, see Sect. 3).
Red labels indicate the S-bearing species analysed in this paper (see Table
1).