# FAUST XII. Accretion streamers and jets in the VLA 1623–2417 protocluster

C. Codella,1,2 L. Podio,1 M. De Simone,3,1 C. Ceccarelli,2 S. Ohashi,4 C.J.
Chandler,5 N. Sakai,4 J.E. Pineda,6 D.M. Segura-Cox,7 E. Bianchi,8 N. Cuello,2
A. López-Sepulcre,2,9 D. Fedele,1 P. Caselli,6 S. Charnley,10 D.
Johnstone,11,12 Z.E. Zhang,13,4 M.J. Maureira,6 Y. Zhang,4 G. Sabatini,1 B.
Svoboda,5 I. Jiménez-Serra,14 L. Loinard,15 S. Mercimek,1,16 N. Murillo,4 and
S. Yamamoto17,18
1INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125,
Firenze, Italy
2Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
3European Southern Observatory, Karl-Schwarzschild Str. 2, 85748 Garching bei
München, Germany
4RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama
351-0198, Japan
5National Radio Astronomy Observatory, PO Box O, Socorro, NM 87801, USA
6Max-Planck-Institut für extraterrestrische Physik (MPE), Gießenbachstr. 1,
D-85741 Garching, Germany
7Department of Astronomy, The University of Texas at Austin, 2515 Speedway,
Austin, TX 78712, USA
8Excellence Cluster ORIGINS, Boltzmannstraße 2, 85748, Garching bei München,
Germany
9Institut de Radioastronomie Millimétrique, 38406 Saint-Martin d’Hères, France
10Astrochemistry Laboratory, Code 691, NASA Goddard Space Flight Center, 8800
Greenbelt Road, Greenbelt, MD 20771, USA
11Department of Physics and Astronomy, University of Victoria, 3800 Finnerty
Road, Elliot Building Victoria, BC, V8P 5C2, Canada
12NRC Herzberg Astronomy and Astrophysics 5071 West Saanich Road, Victoria,
BC, V9E 2E7, Canada
13Department of Astronomy, University of Virginia, Charlottesville, VA
22904-4325, USA
14Centro de Astrobiologia (CSIC-INTA), Ctra. de Torrejon a Ajalvir, km 4,
28850, Torrejon de Ardoz, Spain
15Instituto de Radioastronomía y Astrofísica , Universidad Nacional Autónoma
de México, A.P. 3-72 (Xangari), 8701, Morelia, Mexico
16Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia, via
G. Sansone 1, 50019 Sesto Fiorentino, Italy
17The Graduate University for Advanced Studies (SOKENDAI), Shonan-village,
Hayama, Kanagawa 240-0193, Japan
18Research Center for the Early Universe, The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ; Accepted XXX. Received YYY;
in original form ZZZ)

###### Abstract

The ALMA interferometer has played a key role in revealing a new component of
the Sun-like star forming process: the molecular streamers, i.e. structures up
to thousands of au long funneling material non-axisymmetrically to disks. In
the context of the FAUST ALMA LP, the archetypical VLA1623-2417 protostellar
cluster has been imaged at 1.3 mm in the SO(56–45), SO(66–55), and SiO(5–4)
line emission at the spatial resolution of 50 au. We detect extended SO
emission, peaking towards the A and B protostars. Emission blue-shifted down
to 6.6 km s-1 reveals for the first time a long ($\sim$ 2000 au) accelerating
streamer plausibly feeding the VLA1623 B protostar. Using SO, we derive for
the first time an estimate of the excitation temperature of an accreting
streamer: 33$\pm$9 K. The SO column density is $\sim$ 1014 cm-2, and the SO/H2
abundance ratio is $\sim$ 10-8. The total mass of the streamer is 3 $\times$
10-3 $M_{\rm\sun}$, while its accretion rate is 3–5 $\times$ 10-7
$M_{\rm\sun}$ yr-1. This is close to the mass accretion rate of VLA1623 B, in
the 0.6–3 $\times$ 10-7 $M_{\rm\sun}$ yr-1 range, showing the importance of
the streamer in contributing to the mass of protostellar disks. The highest
blue- and red-shifted SO velocities behave as the SiO(5–4) emission, the
latter species detected for the first time in VLA1623-2417: the emission is
compact (100-200 au), and associated only with the B protostar. The SO
excitation temperature is $\sim$ 100 K, supporting the occurrence of shocks
associated with the jet, traced by SiO.

###### keywords:

ISM: kinematics and dynamics – astrochemistry – ISM: molecules – stars:
formation – ISM: Individual object: VLA 1623–2417

††pubyear: 2022††pagerange: FAUST XII. Accretion streamers and jets in the VLA
1623–2417 protocluster–FAUST XII. Accretion streamers and jets in the VLA
1623–2417 protocluster

##  1 Introduction

The low-mass star forming process takes a dense core of gas and dust inside a
molecular cloud and leaves a Sun-like star possibly surrounded by its
planetary system (Shu, 1977). Historically, the youngest two classes of Sun-
like protostars have beem classified in Class 0 and Class I objects (André et
al., 1993; Andre et al., 2000), being 104 yr and 105 yr old, respectivey. The
standard picture shows a collapse of the slowly infalling envelope (spatial
scale of $\sim$ 1000 au) accreting the protostellar mass through a rotating
equatorial accretion disk ($\sim$ 50 au). At the same time, angular momentum
is removed via fast ($\sim$ 100 km s-1) jets ejected from both the
protostellar poles (e.g. Terebey et al., 1984; Frank et al., 2014; Lee, 2020),
pushing in turn slower outflows. All these physical components, characterised
by different velocities, have been imaged using the proper combination between
spatial resolution and molecular tracer (e.g. Codella et al., 2019; Ceccarelli
et al., 2023, and references therein). As an example, envelopes and outflows
can be well traced by CO and its rarer isotopologues, while the classical jet
tracers are the SiO isotopologues. The so-called interstellar Complex Organic
Molecules (iCOMS, i.e. organic species with at least 6 atoms such as CH3OH,
Herbst & van Dishoeck, 2009; Ceccarelli et al., 2023, and references therein)
are able to trace the inner 100 au around the protostars where the temperature
is high enough ($\geq$ 100 K) to release species from dust mantles to the gas
phase. Finally, the protostellar disk has been traced by the chemical
enrichment (iCOMs, S-bearing species, such as SO) due to mild shocks occurring
near the centrifugal barrier, where the infalling envelope has to lose energy
to proceed on its journey to the protostar through the accretion disk (Sakai
et al., 2014a, b; Oya et al., 2016; Lee et al., 2019; Ceccarelli et al., 2023,
and references therein).

As matter of fact, the classic protostellar collapse picture predicted
axisymmetry of the protostellar structures with respect to the disk equatorial
plane, and/or the jet axis (Frank et al., 2014, e.g.), which was generally
supported by observations until recently. Nonetheless, a new component has
been detected thanks to high sensitivity interferometric images: the molecular
streamers, i.e. elongated structures revealed in the protostellar environment,
which could significantly contribute to the mass accretion of the newly born
stars (see the recent review by Pineda et al., 2023, and references therein).
Using IRAM-NOEMA, Pineda et al. (2020) discovered the presence of a large
scale (10000 au) accretion streamer in HC3N line emission towards the Class 0
object Per-emb-2. Successively, other streamers (as long as 6000 au) have been
imaged around well known Class 0 protostars with ALMA: Lupus3-MMS (CO
isotopologues, Thieme et al., 2022), and IRAS16293–2422 A (HNC, HC3N, HC5N,
Murillo et al., 2022). Thanks to ALMA, accretion streamers have been detected
also towards more evolved Class I objects, starting from the archetypical HL
Tau disk, where Yen et al. (2019) imaged in HCO+(3–2) a 200 au structure
rotating and infalling to the disk. In addition, (i) Garufi et al. (2021)
imaged a small ($\sim$ 150 au) CS(5–4) streamer towards DG Tau, while (ii)
Garufi et al. (2022) and Bianchi et al. (2023) showed evidence for shocks due
to the encounter between disks and infalling streamers in DG Tau, HL Tau, and
SVS13-A using SO, SO2, and HDO emission. Finally, using IRAM-NOEMA, Valdivia-
Mena et al. (2022) revealed a long ($\geq$ 2000 au) streamer in HCO+ and C18O
in the Class I object Per-emb-50, while Hsieh et al. (2023) imaged a DCN and
C18O streamer 700 au long accreting onto the SVS13-A binary.

In summary, there is evidence that molecular streamers are funneling fresh
material in an asymmetric way towards protostellar disks at the earliest
protostellar phases. This is even more important taking into account that one
of the main ALMA breaktrough results is that planet formation may start
already around protostars less than 1 Myr old (e.g. Sheehan & Eisner, 2017;
Fedele et al., 2018; Segura-Cox et al., 2020). The investigation of molecular
streamers has just started: the more efficient molecular tracers have not been
identified yet, as well as the typical lenghts of the elongated structures.
More observations are clearly needed to draw a more detailed picture (Pineda
et al., 2023). In this paper, in the context of the ALMA Large program FAUST
111http://faust-alma.riken.jp; Codella et al. (2021) (Fifty AU STudy of the
chemistry in the disk/envelope system of Solar-like protostars), we present a
survey in SO and SiO of the VLA 1623–2417 protostellar cluster in order to
reveal material associated with accretions streamers as well as protostellar
jets.

##  2 The VLA1623–2417 protostellar system

The VLA 1623–2417 (hereafter VLA 1623) region, located in Ophiucus A (d =
131$\pm$1 pc, Gagné et al., 2018) is one of the most studied protostellar
systems in the Southern hemisphere. VLA 1623 has several components imaged at
different spectral wavelengths (e.g. Andre et al., 1990; André et al., 1993;
Leous et al., 1991; Looney et al., 2000; Ward-Thompson et al., 2011; Murillo
et al., 2013, 2018a; Murillo et al., 2018b; Harris et al., 2018; Hsieh et al.,
2020; Ohashi et al., 2022; Codella et al., 2022; Mercimek et al., 2023, and
references therein): (i) a binary system made up of two Class 0 objects, A1
and A2, separated by less than 30 au, and surrounded by a circumbinary disk;
(ii) another Class 0, labelled B, lies outside of the A1+A2 circumbinary disk,
at a projected angular separation of $\simeq$ 1$\arcsec$ ($\sim$130 au); in
addition, a more evolved Class I object, labelled W, is located at $\sim$ 1200
au west of the VLA1623 A1+A2+B system.

Given its complexity, the VLA 1623 star forming region is a perfect laboratory
to study the interaction of the star forming process with the surrounding
medium. Figure 1 provides a sketch (not to scale) summarising some processes
imaged in VLA1623 and discussed here (see also Fig. 19 by Hsieh et al., 2020).
From the kinematic point of view, three main processes have been detected: (1)
outflowing motion, (2) gravitationally supported disks, and (3) infalling
molecular streamers. These processes are described further below.

  1. (1)

Extended ($>$ 1000 au) outflows along a NW-SE direction have been observed in
a number of species (e.g. CO isotoplogues) driven by the A+B multiple system
(e.g. Andre et al., 1990; Caratti o Garatti et al., 2006; Hsieh et al., 2020;
Hara et al., 2021, and references therein). Santangelo et al. (2015) imaged a
fast CO jet from VLA1623 B, while the number of flows driven by A1+A2 is
controversial. On the one hand, Hsieh et al. (2020) and Hara et al. (2021)
reported two cavities opened by two outflows along the same projected NW-SE
direction driven by A1 and A2. As part of ALMA-FAUST, Ohashi et al. (2022)
sampled (with a beam of 50 au) a unique, rotating, and low-velocity NW-SE
cavity opened by A1;

  2. (2)

C18O, CS, and CH3OH emission around both VLA1623-2417 A1 and B shows velocity
gradients (on 20-30 au scale) along the NE-SW direction (Murillo et al., 2013;
Ohashi et al., 2022; Codella et al., 2022), i.e. along the main axis of each
protostellar disk observed in continuum (Harris et al., 2018);

  3. (3)

Recently, the occurrence of molecular streamers have been reported by Hsieh et
al. (2020) imaging SO(88-77) at a spatial scale $\sim$ 100 au. The authors
support the occurrence of two blue-shifted northern flows accreting onto both
the circumbinary disk around the A binary and the B protostellar disk, plus a
red-shifted southern flow feeding B from the SW direction. The largest
recoverable scale of the SO maps by Hsieh et al. (2020) is
3$\aas@@fstack{\prime\prime}$5, calling for further observations imaging more
lines and larger spatial scales to confirm the occurrence of extended
accretion streamers.

##  3 Observations

The VLA1623 multiple system was observed between 2018 December, and 2020 March
with ALMA Band 6 (Setup 1: 214.0–219.0 GHz and 229.0–234.0 GHz, Setup 2:
242.5–247.5 GHz and 257.2–262.5 GHz) in the context of the FAUST Large Program
(2018.1.01:205.L, PI: S. Yamamoto), using the 12-m array (C43-1, C43-4, with
48 and 49 antennas, respectively) as well as the ACA (Atacama Compact Array)
7-m array (12 antennas). The baselines were between 9 m ($B_{\rm min}$) and
969 m ($B_{\rm max}$), for a maximum recoverable scale ($\theta_{\rm MRS}$
$\sim$ $0.6\,\lambda\,B_{\rm min}^{-1}$) of $\sim\,$29$\arcsec$. The
observations were centered at $\alpha_{\rm J2000}$ = 16h 26m
26$\aas@@fstack{s}$392, $\delta_{\rm J2000}$ = –24$\degr$ 24$\arcmin$
30$\aas@@fstack{\prime\prime}$178\. The lines here analysed are SO(56–45)
(219.9 GHz), SO(66–55) (258.3 GHz), and SiO(5–4) (217.1 GHz): the
spectroscopic parameters are reported in Table 1. The SO and SiO lines were
observed using spectral windows with a bandwidth/frequency resolution of 59
MHz/122 kHz ($\sim$80 km s-1/0.14–0.17 km s-1). The FWHM Field of View (FoV)
of the ALMA images are: 26$\arcsec$ for SO(56–45) and SiO(5–4), and
22$\arcsec$ for SO(56–45). A wide bandwidth (1.875 GHz) spectral window was
also included to support measurement of the continuum emission. Data were
calibrated using the quasars J1427-4206, J1517-2422, J1625-2527, J1924-2914,
and J1626-2951, reaching an absolute flux calibration uncertainty of
$\sim$10%. The data were self-calibrated using line-free continuum channels.
The primary beam correction has also been applied. We used the calibration
pipeline222https://github.com/autocorr/faust$\\_$line$\\_$imaging; Chandler et
al. (in preparation) within CASA 5.6.1-8 (CASA Team et al., 2022), including
an additional calibration routine to correct for $T_{\rm sys}$ issues and
spectral data normalization333https://help.almascience.org/kb/articles/what-
errors-could-originate-from-the-correlator-spectral-normalization-and-tsys-
calibration; Moellenbrock et al. (in preparation). As a consequence, the
dynamical range of the continuum data improved up to one order of magnitude.
Once the three array configurations were merged, the resulting continuum-
subtracted line-cubes were cleaned with a Briggs parameter of 0.5. The data
analysis was performed using the IRAM-
GILDAS444http://www.iram.fr/IRAMFR/GILDAS package. The continuum has been
imaged using uniform weighting, thus obtaining a beam of
0$\aas@@fstack{\prime\prime}$37 $\times$ 0$\aas@@fstack{\prime\prime}$34
($-65^{\circ}$), and 0$\aas@@fstack{\prime\prime}$43 $\times$
0$\aas@@fstack{\prime\prime}$32 ($-65^{\circ}$), for Setup 1 and Setup 2,
respectively. On the other hand, the r.m.s. noise is 0.22 mJy beam-1 (Setup
1), and 0.15 mJy beam-1 (Setup 2). The synthesized beams of the line datasets
are 0$\aas@@fstack{\prime\prime}$54$\times$0$\aas@@fstack{\prime\prime}$45
(PA=–75∘), for Setup 1, and
0$\aas@@fstack{\prime\prime}$48$\times$0$\aas@@fstack{\prime\prime}$45
(PA=+86∘), for Setup 2. The typical r.m.s. noise (per channel) is $\sim$3 mJy
beam-1. To decrease the noise, the SiO(5–4) datacube has been spectrally
smoothed to 1 km s-1, for an r.m.s. of 1 mJy beam-1.

Figure 1: Sketch (not to scale) of the VLA1623–2417 system (see also Fig. 19
by Hsieh et al., 2020). The figure shows: (i) the high-spatial resolution mm-
continuum map (Harris et al., 2018) revealing the A1+A2 binary system, its
circumbinary disk, and the protostar B, (ii) the extended rotating cavity (CS,
Ohashi et al., 2022), (iii) the directions of the multiple outflows (CO,
Santangelo et al., 2015; Hsieh et al., 2020; Hara et al., 2021), and (iv) the
rotating disks of A1 and B imaged in CH3OH (Codella et al., 2022). Figure 2:
Dust continuum emission at 216 GHz and 244 GHz (colour scale and contours)
from the VLA1623-2417 multiple system. First contours, in white, are 3$\sigma$
(0.8 mJy beam-1). Steps are 100$\sigma$. The synthesised beam (bottom-left
corners) are 0$\aas@@fstack{\prime\prime}$43 $\times$
0$\aas@@fstack{\prime\prime}$32 (PA = –65$\degr$), and
0$\aas@@fstack{\prime\prime}$38 $\times$ 0$\aas@@fstack{\prime\prime}$35 (PA =
+66$\degr$), for the 216 GHz and 244 GHz maps, respectively. The A1 and A2
protostars are not disentangled at the present angular resolutions. The B and
W protostars are also labelled. Table 1: Spectral Properties of the SO and SiO
lines observed towards VLA1623.

Transition | $\nu^{\rm a}$ | E${}_{\rm u}^{\rm a}$ | Log10(Aul/s${}^{-1})^{\rm a}$ | $S\mu^{\rm 2a}$
---|---|---|---|---
| (MHz) | (K) |  | (D2)
SO(56–45) | 219949.442 | 35 | –3.9 | 14.0
SO(66–55) | 258255.826 | 57 | –3.7 | 13.7
SiO(5–4) | 217104.980 | 31 | –3.3 | 48.0

a Spectroscopic parameters are from Klaus et al. (1996), and Bogey et al.
(1997) (SO), and Lowry Manson et al. (1977), for SiO, retrieved from the CDMS
database (Müller et al., 2005).

##  4 Results

###  4.1 Continuum emission

Figure 2 shows the VLA 1623 region as observed in dust continuum emission at
216 GHz (1.4 mm) and 244 GHz (1.2 mm). A 1.2 mm image has been already
reported in the context of the FAUST campaign by Codella et al. (2022), but
only using the C43-4 configuration of the 12m array. The 1.4 mm image has been
presented by Mercimek et al. (2023) in the context of the analysis of source
W.

The FAUST continuum images show the envelope containing the A1 and A2 binary
system (not disentangled by the present spatial resolution) and the B
protostar. The emission from the A1+A2 circumbinary disk is also revealed. At
about 1300 au west of the A+B system, the W protostar is also detected. The
J2000 coordinates of the A, B, and W protostars, as traced by the 2D fitting
of both the 1.2 mm and 1.4 mm images are A: 16h 26m 26$\aas@@fstack{s}$392,
–24∘ 24′ 30$\aas@@fstack{\prime\prime}$90; B: 16h 26m 26$\aas@@fstack{s}$307,
–24∘ 24′ 30$\aas@@fstack{\prime\prime}$76; W: 16h 26m 25$\aas@@fstack{s}$632,
–24∘ 24′ 29$\aas@@fstack{\prime\prime}$64\. In summary, the FAUST picture is
well in agreement with the ALMA image at 0.9 mm obtained by Harris et al.
(2018, see also the references therein) with a resolution of
0$\aas@@fstack{\prime\prime}$2\. A detailed analyis of continuum emission is
beyond the scope of this paper. Continuum images will contribute to the
analysis of the origin of the SO and SiO (Sect. 4) gas observed in the A+B
system.

###  4.2 Overall SO spatial distribution and spectra

Both SO(56–45) and SO(66–55) emission lines have been detected and imaged.
Figure 3 shows the SO(56–45) and SO(66–55) line profiles derived integrating
the emission over a region as large as the Field of View of the SO map at 258
GHz (22$\arcsec$). In Fig. 3 (Bottom panels) the zoom-in shows the weakest SO
emission, offset in velocity up to $\sim$ 10 km s-1 with respect to the
systemic velocity of the A+B system, i.e. $V_{\rm sys}$ = +3.8 km s-1 (Ohashi
et al., 2022). More precisely, the velocity range goes from –7.6 to +12.0 km
s-1. Emission due to SO has been recently reported by Hsieh et al. (2020), who
detected the SO(88–77) line at 344 GHz with ALMA, in a narrower velocity
range, from $\sim$ –2 km s-1 to $\sim$ +6 km s-1. Figure 4 reveals the spatial
distribution of the SO(56–45) and SO(66–55) emission as integrated over the
whole emitting velocity range (moment 0 maps). The present SO maps improve the
spatial resolution of the image collected by Hsieh et al. (2020), obtained
with a synthetised beam of 1$\aas@@fstack{\prime\prime}$11 $\times$
0$\aas@@fstack{\prime\prime}$76\. Figure 5 reports the SO(56–45) and SO(66–55)
spectra extracted at the positions of the A, and B peaks. Emission is also
detected towards the object W, located at the edge of the FoV of the SO(66–55)
image, but its analysis is out of the scope of the present paper. Those maps
show that SO has compact emission peaking on A and B, but also shows extended
and elongated structures not associated with the VLA1623 outflows. Both
components are discussed below.

###  4.3 SO emission close to the A and B protostars

The close association of the SO peaks with the protostellar positions suggest
a possible contribution from hot-corinos, where the temperature is high enough
($\geq$ 100 K) to allow evaporation into the gas phase of the icy mantles.
Recent observations (Codella et al., 2022) of VLA1623-2417 imaged methanol
emission rotating, on small-spatial scales, around the protostars A1 and B
(see Fig. 1).

The linewidth of the SO spectra extracted at the A continuum peak (see Figure
5) is 1.8 km s-1, narrower than the 4 km s-1 methanol profile observed by
Codella et al. (2022). However, the entire SO lines are broader, and they look
affected by absorption at velocities close to $V_{\rm sys}$, more specifically
at slightly red-shifted velocities, as found observing CS(5–4) by Ohashi et
al. (2022). As a consequence, the contribution of the SO emission by the hot-
corino in A cannot be assessed using the observed lines.

The line profiles extracted at the B continuum peak (Fig. 5) protostar are
more complex: the lines are very broad ($\sim$ 8 km s-1) with, in addition,
extended wings suggesting the occurrence of a high-velocity jet. An absorption
dip is observed at velocities close to the systemic one in the SO(56–45) line,
whereas a weak absorption is present in the SO(66–55) profile. A remarkable
absorption along the line of sight of B, down to negative brightness
temperatures, has been observed by Ohashi et al. (2022) using CS, CCH, and
H13CO+ low-excitation ($E_{\rm u}$ = 25–35 K) lines. Those profiles suggest
absorption against an optically thick continuum in the background, associated
with the protostar. The present SO profiles are also consistent with material
placed between the material surrounding the protostars and the observer. As
shown in Fig. 5, the absorption is more prominent for the SO(56–45) line
($E_{\rm u}$ = 35 K) with respect to the SO(66–55) one ($E_{\rm u}$ = 57 K),
suggesting low-excitation absorbing material or an optically thick continuum.

Figure 3: Upper panels: SO(56–45) (Left), and SO(66–55) (Right) spectra (in
brightness temperature, $T_{\rm B}$, scale) derived integrating the emission
over 480 arcsec2, i.e. a region 22$\arcsec$ wide centred around the A1+A2+B
protostars (see Fig. 4). In both panels, the brightness temperature r.m.s. is
$\sim$ 1 mK. The black vertical line is for the systemic velocity of the
triple system of $V_{\rm sys}$ = +3.8 km s-1 (Ohashi et al., 2022). The grey
vertical lines show the velocity range $\pm$ 1 km s-1 with respect to $V_{\rm
sys}$ (labelled S). The blue and red vertical lines delimitate the blue- and
red-shifted velocity ranges tracing different SO structures, as described in
Sect. 3. More precisely, the velocity range with a shift between 1.0 km s-1
and 6.6 km s-1 (blue) or 2.5 km s-1 (red) is labelled as LV. The label HV is
for the highest and weakest SO emission (see the results on kinematics of
Sect. 4). Bottom panels: Zoom-in of the same SO spectra of the Upper panels
shown to highlight the weak high-velocity emission.

###  4.4 Extended SO emission

The elongated SO structures can be compared with the spatial distribution of
the CS cavities (orange contours in Fig. 4), opened by the outflow located
along the NW-SE direction and driven by the VLA1623A1 object (Ohashi et al.,
2022). Figure 4 shows that two elongated structures lie outside the static CS
cavities: (i) a very long ($\sim$ 1500 au) one in the region south of the
multiple protostellar system, and (ii) one located north of A1+A2, $\sim$ 250
au long. The present large scale picture shows some differences with respect
to that drawn by Hsieh et al. (2020) using the SO(88–77) line: on the one hand
we confirm the occurrence of the elongated structure north of A1+A2; on the
other hand, the SW emission looks associated with the molecular cavity.

Figure 4: The VLA1623–2417 system as traced by the integrated intensity map
(moment 0, color scale and contours) of SO(56–45) (Left panel), SO(66–55)
(Middle), and SiO(5–4) (Right). The SO emission is integrated from –7.6 to
+12.0 km s-1, while that of SiO map from +0.6 to +5.2 km s-1. First contours
of both the SO maps start from 3$\sigma$ (27 mJy km s-1 beam-1) with intervals
of 9$\sigma$. First contour of the SiO image start from 5$\sigma$ (10 mJy km
s-1 beam-1) with intervals of 3$\sigma$. The synthesised beam (top-left
corners) are 0$\aas@@fstack{\prime\prime}$54 $\times$
0$\aas@@fstack{\prime\prime}$45 (PA = –74$\degr$), for SO(56–45) and SiO(5–4),
and 0$\aas@@fstack{\prime\prime}$47 $\times$ 0$\aas@@fstack{\prime\prime}$45
(PA = +86$\degr$), for SO(66–55). The dashed circles delimitate the FWHM Field
of View of the ALMA image: 26$\arcsec$ for SO(56–45) and SiO(5–4), and
22$\arcsec$ for SO(56–45). In the Right panel, white contours representing
selected intensities of the continuum map at 216 GHz (see Fig. 2) are drawn to
show the position of the A1+A2, and B protostars. The orange thick contour is
the CS(5–4) emission (25$\sigma$) which traces the outflow cavity walls
associated with VLA1623A1+A2 (from Ohashi et al., 2022).

Figure 5: SO(56–45) (Left-panels), and SO(66–55) (Middle), and SiO(5–4)
(Right) spectra (in brightness temperature, $T_{\rm B}$, scale) derived at the
two peaks of the continuum maps: A (Upper), and B (Bottom), see Fig. 2. The
black vertical lines are for the systemic velocity, i.e. +3.8 km s-1 (Ohashi
et al., 2022).

####  4.4.1 Southern region: the VLA1623 B accretion streamer

The analysis of kinematics allows us to disclose different molecular
components emitting at different velocities. Figure 6 shows the VLA1623-2417
A1+A2+B system as traced by both SO(56–45), and SO(66–55) emission integrated
over $\pm$ 1 km s-1 (velocity range labelled S, see Fig. 3) with respect to
the systemic velocity of the triple system of +3.8 km s-1 (Ohashi et al.,
2022). The emission at systemic velocity is mainly associated with the
cavities, with additional features plausibly related with the VLA1623-2417
envelope. Figure 7 shows the SO(56–45), and SO(66–55) maps of the blue-shifted
(by 1–6.6 km s-1 with respect to $V_{\rm sys}$) and red-shifted emission (by
1–2.5 km s-1), i.e. the intervals labelled as LV in Fig. 3. Note that the
blue- and red-shifted LV ranges are asymmetric with respect to $V_{\rm sys}$
because they have been defined a posteriori after inspecting the SO dataset to
identify velocity ranges tracing the same molecular structure. On these maps
the intensity-weighted velocity CS(5–4) map (moment 1 map), by Ohashi et al.
(2022), is overlapped. The CS map reveals the rotation of the outflow cavity,
with the southern sides red-shifted.

The red-shifted SO LV emission is quite compact, as highlighted in the zoom-in
of Figure 7. The emission peaks towards the B protostar, plus an additional
component starting at the position of A1+A2 and inclined towards the SE
direction, in agreement with the red-shifted outflow cavity (Ohashi et al.,
2022).

On the other hand, the blue-shifted SO LV emission is very extended and
clearly reveals a long ($\sim$ 1500 au) southern streamer pointing to the
central protostellar A+B system. Note that (i) the association with the
outflow cavity is excluded from both the curved morphology, and, most
importantly, (ii) by the fact that the outflow cavity in the southern region
is red-shifted. These findings are well summarised by Fig. 8, which shows the
Position-Velocity (PV) cut (obtained with a slice width equal to the beam) of
SO(56–45), black, and CS(5–4), magenta (Ohashi et al., 2022), along the
southern direction (PA $=0\degr$) from the position of VLA1623 A (upper panel)
and VLA1623 B (lower panel). The emission from the molecular cavity and the
streamer are located in different positions of the PV plot.

Crucial information on the streamer kinematics is also provided by Fig. 9,
which shows, for the blue-shifted LV emission of both SO lines: the moment 1
image as well as the intensity-weighted velocity dispersion map (moment 2).
More precisely, the zoom-in region in the Right panels of Figure 9 suggests
that the streamer, once at $\sim$ 100 au from the protostars, is directing its
gas mainly towards the B protostar, through an elongated feature well observed
in the velocity dispersion map. The moment 2 map also indicates that the
velocity dispersion is higher towards B, in agreement with an inclination
close to the edge-on geometry (74$\degr$, Harris et al., 2018; Ohashi et al.,
2022). Both the PV diagrams and the moment 1 maps show that the southern
streamer is a coherent structure and slightly accelerating from $V_{\rm
LSR}\sim 2$ km s-1 at $-8\arcsec$ distance from the protostar VLA1623 B to
$\sim 1.5$ km s-1 at $-2\arcsec$ offset. This suggests that the streamer is
conveying material towards the protostars.

To summarise, the analysis of the spatial distribution and velocity of the SO
emission indicate a streamer of gas extending from the outer envelope (out to
1500 au distance from A+B) to the central cluster plausibly feeding source B.
The velocity and velocity dispersion increase towards the protostellar
multiple system, possibly indicating accretion from the large scale envelope
to the protostellar disks. Note that the streamer is blue-shifted, but it is
on the side with red-shifted rotation of outflow and envelope (Ohashi et al.,
2022). To make this happen, the streamer needs to infall from the backside of
sources, and it will go behind the central sources.

Figure 6: The VLA1623–2417 A1+A2+B system as traced by SO(56–45) (Upper
panel), and SO(66–55) (Bottom) emission integrated over $\pm$ 1 km s-1
(labelled S in Fig. 3) with respect to the systemic velocity of the triple
system of +3.8 km s-1 Ohashi et al. (2022). The position of the A1+A2, B, and
W protostars are labelled. The dashed circles delimitate the FWHM Field of
View of the ALMA image: 26$\arcsec$ for SO(56–45), and 22$\arcsec$ for
SO(56–45). The dashed circles delimitate the FWHM Field of View of the ALMA
image. The synthesised beam (top-left corners) are
0$\aas@@fstack{\prime\prime}$54 $\times$ 0$\aas@@fstack{\prime\prime}$45 (PA =
–74$\degr$), for SO(56–45), and 0$\aas@@fstack{\prime\prime}$47 $\times$
0$\aas@@fstack{\prime\prime}$45 (PA = +86$\degr$), for SO(66–55). First
contours of both the SO maps start from 5$\sigma$ (35 mJy km s-1 beam-1,
Upper, 25 mJy km s-1 beam-1, Lower) with intervals of 10$\sigma$. The orange
thick contour is the CS(5–4) emission (25$\sigma$) which traces the outflow
cavity walls associated with VLA1623A1+A2 (from Ohashi et al., 2022). In
magenta we plot selected contours from the high spatial resolution ($\sim$
0$\aas@@fstack{\prime\prime}$2) continuum (0.9 mm) ALMA map by Harris et al.
(2018) to pinpoint the positions of A1, A2, and B.

####  4.4.2 Northern region: the VLA1623 A accretion streamer

Focusing on the region north of A+B, Figure 7 shows two small ($\sim$
1$\arcsec$) elongated features, which could be associated with the blue-
shifted cavity expected in these regions, plus a longer ($\sim$ 2$\arcsec$)
structure located along the N-S direction (see the zoom-in in the right
panels). The latter is not spatially associated with the outflow cavity,
therefore plausibly being an accretion streamer, in agreement with what Hsieh
et al. (2020) proposed using the SO(88–77) line. Again, instructive
information is provided by kinematics. Figure 9 shows that the northern LV
streamer has an increase of the intensity-weighted emission line width
coinciding (on the plane of the sky) with the outer regions of the
circumbinary disk around A1+A2. In conclusion, these findings are very
suggestive that material falls onto the circumbinary disk at the position
where SO emission is broader. No further information on the fate of the
material of the circumbinary disk is learned from the present data.

Figure 7: The VLA1623-2417 A1+A2+B system as traced by SO(56–45) (Left panel),
and SO(66–55) (Middle) emission blue-shifted by 1–6.6 km s-1 and red-shifted
by 1–2.5 km s-1 (labelled LV, see Fig. 3) with respect to the systemic
velocity of the triple system of +3.8 km s-1 (Ohashi et al., 2022). For sake
of clarity the contours of the red-shifted spatial distribution are reported
only in the zoom-in in the Right panels. The position of the A1+A2, and B
protostars are labelled. The dashed circles delimitate the FWHM Field of View
of the ALMA image: 26$\arcsec$ for SO(56–45), and 22$\arcsec$ for SO(66–55).
The synthesised beam (top-left corners) are 0$\aas@@fstack{\prime\prime}$54
$\times$ 0$\aas@@fstack{\prime\prime}$45 (PA = –74$\degr$), for SO(56–45), and
0$\aas@@fstack{\prime\prime}$47 $\times$ 0$\aas@@fstack{\prime\prime}$45 (PA =
+86$\degr$), for SO(66–55). First contours of both the SO maps start from
5$\sigma$ (25 mJy km s-1 beam-1, blue, 15 mJy km s-1 beam-1, red) with
intervals of 10$\sigma$. Colour image represents the moment 1 spatial
distribution of the molecular cavity as traced by CS(5–4) by Ohashi et al.
(2022): the cavities are rotating with the red-shifted emission coming from
the southern arms, while the blue-shifted emission (here in green to avoid
confusions with the SO blue contours) associated with the northern arms. In
black we plot selected contours from the high spatial resolution ($\sim$
0$\aas@@fstack{\prime\prime}$2) continuum (0.9 mm) ALMA map by Harris et al.
(2018) to pinpoint the positions of A1, A2, and B.

Figure 8: Position-Velocity cut (beam averaged) of SO(56–45), black, and
CS(5–4), magenta (Ohashi et al., 2022), along the southern direction (PA =
0$\arcsec$) centered on the position of VLA1623 A (Upper panel) and VLA1623 B
(Lower panel)

. Contour levels range from 5$\sigma$ (10 mJy beam-1) by steps of 8$\sigma$.
Dashed lines marks the systemic velocity (+3.8 km s-1, Ohashi et al., 2022).

Figure 9: Kinematics of the VLA1623–2417 A1+A2+B system as traced by the
SO(56–45) (Upper panels), and SO(66–55) (Bottom panels) emissions blue-shifted
with respect to systemic velocity (+3.8 km s-1, Ohashi et al., 2022) of 1–6.6
km s-1 (labelled LV, see Fig. 3). Left and Middle panels are for the moment 1
(intensity-weighted peak velocity), and moment 2 (intensity-weighted emission
width) maps, respectively (colour scale). First contours of both the SO maps
start from 5$\sigma$ (25 mJy km s-1 beam-1). The position of the A1+A2, and B
protostars are labelled. The dashed circles delimitate the FWHM Field of View
of the ALMA image: 26$\arcsec$ (Upper), and 22$\arcsec$ (Bottom). The
synthesised beam (top-left corners) are 0$\aas@@fstack{\prime\prime}$54
$\times$ 0$\aas@@fstack{\prime\prime}$45 (PA = –74$\degr$), for SO(56–45), and
0$\aas@@fstack{\prime\prime}$47 $\times$ 0$\aas@@fstack{\prime\prime}$45 (PA =
+86$\degr$), for SO(66–55). In red or black we plot selected contours from the
high spatial resolution ($\sim$ 0$\aas@@fstack{\prime\prime}$2) continuum (0.9
mm) ALMA map by Harris et al. (2018) to pinpoint the positions of A1, A2, and
B. The orange thick contour is the CS(5–4) emission (25$\sigma$) which traces
the outflow cavity walls associated with VLA1623A1+A2 (from Ohashi et al.,
2022). Right panels: Zoom-in of the inner region around the circumbinary A1+A2
disk and the protostellar B disk.

###  4.5 SO and SiO jet emission

Figure 10 shows the SO spatial distribution at the highest velocities with
respect to $V_{\rm sys}$ = +3.8 km s-1: blue-shifted by up to 11.2 km s-1, and
red-shifted by up to 8.2 km s-1. This velocity range has been labelled as HV
in Fig. 3. Note that the disk size derived from the high-spatial resolution
continuum by Harris et al. (2018) is plotted in magenta. Both the SO(56–45)
and SO(66–55) emissions are compact and overlap with the position of the
protostar B. The red-shifted and blue-shifted emission peaks are spatially
separated, and located along the SE-NW direction. This direction is
perpendicular to the disk position angle (42$\degr$, Harris et al., 2018). In
turn, these findings support the association of HV SO with outflowing motion
driven by VLA1623 B. The velocities once deprojected using the geometry of the
protostellar system (disk inclination $\simeq$ 74$\degr$, Harris et al., 2018)
reaches values $\sim$ 40 km s-1 with respect to the systemic velocity.

The SiO(5–4) line has been detected, for the first time, in the VLA1623 star
forming region. Fig. 4 shows the moment 0 map: the emission is in fact
spatially unresolved and it overlaps on the position of the B protostar. The
spectrum towards VLA1623 B is shown in Fig. 5: the line is centred at the
systemic velocity (+3.8 km s-1), and it extends up to about +6 km s-1 and down
to +2 km s-1. Figure 10 shows the blue- and red-shifted SiO emission: as for
SO at the highest velocities, SiO is associated with a velocity gradient, with
the red-shifted emission spatially offset towards SE (with respect to the
continuum emission), while the blue-shifted emission peaks at NW. As a typical
high-velocity shock tracer, SiO then probes the protostellar jet driven by
VLA1623 B. This is consistent with the CO(2–1) ALMA Band 6 images by
Santangelo et al. (2015): their maps have a lower spatial resolution
(0$\aas@@fstack{\prime\prime}$65) than the FAUST dataset, but they indicate
the same spatial offset for emission at velocities blue- and red- shifted by
at least 6 km s-1. The SiO radial velocities are lower than for SO. This could
be due to the fact that the SO emission probes a wider angle layer of the wind
with respect to SiO, which is expected to probe the inner collimated jet
portion, as seen, e.g., in the high resolution ALMA maps of HH 212 (see e.g.
Lee et al., 2019). In this scenario the SiO gas would lie closer to the plane
of the sky, which would explain lower observed radial velocities. Moreover,
the estimated jet velocity could be a lower limit since it is obtained by
deprojecting the SiO and SO radial velocity for the inclination derived for
the disk ($\sim 74\degr$). The estimate of disk inclination for systems that
are close to edge-on is affected by large uncertainty (e.g. Villenave et al.,
2020), and an inclination of larger than 85$\degr$ would lead to a typical jet
velocity of at least $100$ km s-1 (Podio et al., 2021). Finally, note that the
direction of the SiO velocity gradient is perpendicular (within the present
spatial resolution) to the rotating protostellar disk recently traced using
methanol by Codella et al. (2022) and at the C18O(2–1) HV emission (here
traced in Fig. 10). This comparison again supports that SiO traces the
protostellar jet ejected by VLA1623 B.

Figure 10: Kinematics of the VLA1623–2417 B protostar as traced by the
SO(56–45), and SO(66–55) (Left panels) emission at the highest velocities with
respect to systemic velocity (+3.8 km s-1, Ohashi et al., 2022): blue-shifted
by up to 11.2 km s-1 (Upper panels), and red-shifted by up to 8.2 km s-1
(Lower panels). These velocity ranges are labelled as HV in Fig. 3. First
contours of both the SO maps start from 5$\sigma$ (20 mJy km s-1 beam-1) by
steps of 10$\sigma$. The synthesised beam (top-right corners) are
0$\aas@@fstack{\prime\prime}$54 $\times$ 0$\aas@@fstack{\prime\prime}$45 (PA =
–74$\degr$), for SO(56–45), and 0$\aas@@fstack{\prime\prime}$47 $\times$
0$\aas@@fstack{\prime\prime}$45 (PA = +86$\degr$), for SO(66–55). In magenta
we plot a selected contour from the high spatial resolution ($\sim$
0$\aas@@fstack{\prime\prime}$2) continuum (0.9 mm) ALMA map by Harris et al.
(2018). The tilted black cross indicates the disk inclination (PA = 42$\degr$)
and the normal direction expected for the jet axis. (Right panels): SiO(5–4)
and C18O(2–1) blue- and red-shifted emission. The SiO(5–4) line is weaker than
the SO ones: first contours and steps correspond to 3$\sigma$: 9 mJy km s-1
beam-1), and 6 mJy km s-1 beam-1 for the blue- and red-shifted emission,
respectively. The velocity ranges are smaller fo SiO (see text), while for
C18O the highest velocities tracing emission around B have been selected and
reported in the labels. The beam is that of the SO(56–45) image.

##  5 Discussion

Figure 11: Left panel: The VLA1623–2417 southern molecular streamer as traced
by the C18O(2–1) emission at velocities blue-shifted by 1.4–3.2 km s-1 with
respect to $V_{\rm sys}$ = +3.8 km s-1. The velocities are those tracing, in
C18O, the blue-shifted streamer (see text). First contours start from
5$\sigma$ (30 mJy km s-1 beam-1) with intervals of 3$\sigma$. Right panels
SO(56–45), C18O(2–1), and SO(66–55) spectra (in brightness temperature,
$T_{\rm B}$, scale) derived at the position
(–0$\aas@@fstack{\prime\prime}$7,–3$\aas@@fstack{\prime\prime}$0) associated
with the streamer, and marked with a triangle in the Left panel. The black
vertical lines are for the systemic velocity. The blue vertical lines delimit
the velocities of the C18O used to obtain the image of the southern streamer
shown in the Left panel.

###  5.1 Excitation temperature of the VLA1623 B accretion streamer

In light of the SO results, and in order to constrain the physical parameters
of the molecular streamer detected in the VLA1623 A+B region, we inspected the
C18O(2–1) dataset, published by Mercimek et al. (2023). Figure 11 (Left panel)
shows the C18O(2–1) map integrated over the velocities tracing the blue-
shifted streamers, namely shifted by 1.4–3.2 km s-1 with respect to $V_{\rm
sys}$. The southern streamer accreting towards VLA1623 B is well revealed,
while in the northern portion of the map there is a clear contamination with
the blue-shifted outflow cavity. We then proceeded to analyse the southern
VLA1623 B streamer. We extracted the spectrum at the position offset by
–0$\aas@@fstack{\prime\prime}$7,–3$\aas@@fstack{\prime\prime}$0 (with respect
to the phase center of the map, see Sect. 2), i.e. at the emission peak
closest to the A+B system. The C18O(2–1) line profile shows the Gaussian-like
component associated with the accretion streamer. Figure 11 (Right panels)
compares the C18O(2–1) lines with those of both the SO lines, extracted at the
same position of the map. Also the SO spectra show a Gaussian-like profile
similar to that of C18O. Assuming an LTE (Local Thermodynamic Equilibrium)
population and optically thin lines, a crude estimate of the SO excitation
temperature ($T_{\rm ex}$) can be derived from the two SO observed lines:
33$\pm$9 K. To our knowledge, this is the first $T_{\rm ex}$ estimate of a
molecular streamer based on two lines of the same species, being usually
detected with one emission line of a molecular species (see the recent review
by Pineda et al., 2023). Based on a simple toy model where the gas and dust
are heated by the central protostars (without considering the outflow cavities
and the disks) (e.g. Ceccarelli et al., 2000), we estimate the expected gas
temperature at $\sim$ 390 au distance from the protostars (where the spectra
have been extracted). For a total bolometric luminosity of $\sim$ 1
$L_{\rm\sun}$, we find that the temperature is $\sim$ 20 K. The estimated
excitation temperature is higher, being in the 24–42 K range. However, the
comparison has to be taken with a pinch of salt, being based on two
transitions: more lines need to be observed to investigate the reliability of
the LTE assumption, as well as possible line opacity effects. In addition, (i)
if the emission is thermalised, the temperature is likely to increase near the
cavity walls, being thus closer to the SO excitation temperature, and (ii)
there are the uncertainties due to projection effects and to the length of the
material along the line of sight.

Note that the excitation temperature measured towards the SO region where the
northern streamer impacts with the circumbinary VLA1623 A disk (see Fig. 9 at
+0$\aas@@fstack{\prime\prime}$3,+1$\aas@@fstack{\prime\prime}$5 from the map
center) is higher than the value measured in the southern streamer, 55$\pm$12
K, a temperature plausibly increased due to a slow shock at the impact
location. The SO excitation temperature has been estimated also at the
position where the southern streamer seems to impact onto the disk of the B
protostar (see Fig. 9 at
–1$\aas@@fstack{\prime\prime}$4,–0$\aas@@fstack{\prime\prime}$2): the
temperature is high, 63$\pm$12 K, and it can be explained again by a shock.
Alternatively, given the proximity of the position to B, the high temperature
could be due to protostellar heating. Again, this has to be verified using
multiple SO lines for a more reliable temperature measurement.

###  5.2 Accretion and infalling rates

At a temperature of 33 K, the total SO column density is $N_{\rm SO}$ $\simeq$
2 $\times$ 1014 cm-2. To derive the uncertainty, $N_{\rm SO}$ increases by a
factor 2 assuming 20 K instead of 33 K. The total column density of C18O is 4
$\times$ 1015 cm-2. Using the classical 16O/18O = 560 and CO/H2 = 10-4 (Wilson
& Rood, 1994), the H2 total column density is 2 $\times$ 1022 cm-2. The total
mass of the blue-shifted southern streamer can be estimated from the emitting
region and the estimate of the average C18O (and consequently H2) column
density throughout the emitting region: Mstreamer $\simeq$ 3 $\times$ 10-3
$M_{\rm\sun}$. This estimate is lower with respect to the total mass of the
HC3N long (104 au) streamer detected by Pineda et al. (2020) towards the Class
0 object IRAS 03292+3039 (Mstreamer = 0.1–1 $M_{\rm\sun}$). On the other hand,
if we compare the VLA 1623–2417 southern streamer with the Class I streamers,
our estimates are similar: SVS13-A (4 $\times$ 10-3 $M_{\rm\sun}$, Hsieh et
al., 2023) and Per-emb-50 (1 $\times$ 10-2 $M_{\rm\sun}$, Valdivia-Mena et
al., 2022).

As the southern streamer is impacting on the disk of source VLA1623 B, we aim
to compare the mass infall rate of the streamer with the mass accretion rate
on source B, to understand how much streamers may contribute to set the final
mass of protostellar objects. This is indeed still an open question, given the
paucity of measurements of the physical properties of accretion streamers. On
the one hand, Pineda et al. (2020) and Valdivia-Mena et al. (2022) found that
the accretion rates of the streamers in IRAS 03292+3039 and Per-emb-50, are of
the same order of magnitude of the protostellar accretion rates. On the other
hand, Hsieh et al. (2023), found an accretion rate of the streamer lower by an
order of magnitude with respect to the protostellar accretion in the SVS13-A
source. An estimate of the free-fall timescale of the southern streamer
accreting VLA1623 B can be obtained using the classical equation (e.g Pineda
et al., 2020, 2023),

$t_{\rm ff}=\sqrt{R^{3}/GM_{\rm total}},$ (1)

where R is the streamer length, $M_{\rm total}$ is the mass inside R, and G is
the gravitational constant. Taking R = 1500 au, a total mass in the 1–2
$M_{\rm\sun}$ range (e.g. Murillo et al., 2018a; Ohashi et al., 2022), we
obtain, for the southern blue-shifted streamer, $t_{\rm ff}$ $\simeq$ 6–9
$\times$ 103 yr. Note that the free-fall velocity lies in the range 0.9–1.3 km
s-1, i.e. values quite close (56%–81%) to the difference in velocity, 1.6 km
s-1, observed within the southern streamer. By dividing the streamer mass with
the free-fall timescale we obtain an estimate of the accretion rate of the
southern streamer onto the B protostar: 3–5 $\times$ 10-7 $M_{\rm\sun}$ yr-1.

To estimate the mass accretion rate on source B, we assume that the source
bolometric luminosity is due to the gravitational energy released by the
accretion onto the protostar ($L_{\rm bol}$ = $L_{\rm acc}$), and estimate the
mass accretion as: $\dot{M}_{\rm acc}$ = $L_{\rm bol}$$R_{\rm*}$/G$M_{\rm*}$.
The bolometric luminosity of source B derived by Murillo et al. (2018a) based
on the source spectral energy distribution is 0.2–0.3 $L_{\rm\sun}$, while the
protostellar mass has been estimated from the fit of the rotation curve of the
disk by Ohashi et al. (2022), giving a dynamical mass of 1.7 $M_{\rm\sun}$.
Based on these values, and assuming that the stellar radius is $R_{\rm*}$ = 2
$R_{\rm\sun}$ (Stahler, 1988) we infer $\dot{M}_{\rm acc}$ = 10-8
$M_{\rm\sun}$ yr-1. The estimated mass accretion rate is highly uncertain
because it depends strongly on the protostellar properties, which may be
affected by large uncertainties, and because accretion may be episodic and
characterized by accretion bursts (Fischer et al., 2023). In particular, the
estimated dynamical mass is uncertain, due to the intermediate angular
resolution of the FAUST data (50 au, Ohashi et al., 2022). If we assume the
typical range of masses kinematically estimated for low-mass protostellar
objects, i.e. $M_{\rm*}$ = 0.05–0.25 $M_{\rm\sun}$ (Choi et al., 2010; Kwon et
al., 2015; Yen et al., 2017; Lee, 2020), we obtain a mass accretion rate up to
6 $\times$ 10-8 $M_{\rm\sun}$ yr-1 (for 0.25 $M_{\rm\sun}$) and 3 $\times$
10-7 $M_{\rm\sun}$ yr-1 (for 0.05 $M_{\rm\sun}$). In summary, as the streamer
infall rate is about 3–5 $\times$ 10-7 $M_{\rm\sun}$ yr-1 the mass fed by the
streamer is comparable with the total mass accretion rate.

###  5.3 SO abundances in the southern VLA1623 B streamer

The SO abundance relative to H2 can be derived for the LV southern streamer by
comparing the SO and H2 column densities extracted at the
(–0$\aas@@fstack{\prime\prime}$7,–3$\aas@@fstack{\prime\prime}$0) position,
where C18O emission is dominated by the streamer emission (see Sect. 5.1):
$X_{\rm SO}$ $\simeq$ 10-8. This value is larger than that measured in the gas
phase in molecular clouds located in Perseus, Taurus, and Orion (0.7–2
$\times$ 10-9, Navarro-Almaida et al., 2020; Rodríguez-Baras et al., 2021, and
references therein). On the other hand $X_{\rm SO}$ $\simeq$ 10-8 is at the
lower end of the SO abundance range derived for hot-corinos around protostars
up to $\sim$ 10-7 (e.g. Codella et al., 2021, and references therein).
However, the hot-corino nature, i.e. the thermal evaporation of the dust
mantle in the streamer, is here excluded (assuming LTE conditions),
considering the derived excitation temperature of $\sim$ 30 K. Even the
occurrence of strong shocks ($V_{\rm shocks}$ $\geq$ 10 km s-1) has to be
excluded given that they would increase the SO abundance up to higher values
than those observed in the southern streamer ($\sim$ 10-7, e.g. Bachiller &
Pérez Gutiérrez, 1997; Bachiller et al., 2001; Feng et al., 2020). A
possibility to explain an SO abundance larger than those typical in starless
molecular clouds is to speculate the occurrence of mild shocks ($V_{\rm
shocks}$ of a few km s-1), induced by the accretion of the gas through the
streamer, releasing part of the Sulphur on dust mantles. Interestingly, van
Gelder et al. (2021) modeled the Sulphur chemistry in low-velocity shocks
(down to $\sim$ 3–4 km s-1), showing that SO can be efficiently formed from SH
reacting with the O atom and/or S with OH. The SO chemistry in the streamer
could mimic that observed in the L1448-mm protostar (Jiménez-Serra et al.,
2005), where the weak shock precursor component increases the SO abundance by
one order of magnitude only.

###  5.4 VLA 1623B: the SiO jet

Here we estimate the beam-averaged column density in the HV SO component (see
Fig. 3) as well as of the SiO jet. Assuming LTE conditions and optically thin
emission, the excitation temperature of the HV SO ranges between 92$\pm$18 K
(emission red-shifted by up to 8.2 km s-1) and 102$\pm$19 K (emission blue-
shifted by up to 11.2 km s-1). This supports the association of HV SO with
shocked regions created by the propagation of the jet driven by VLA1623 B, as
observed in several protostellar regions (e.g. Bachiller et al., 2001; Taquet
et al., 2020; Feng et al., 2020; Podio et al., 2021, and references therein).
With these temperatures the SO column density is $\sim$ 5 $\times$ 1014 cm-2.
The SiO total column density has been derived assuming a typical jet
temperature of 100$\pm$50 K (e.g. Podio et al., 2021), obtaining $N_{\rm SiO}$
= 2–5 $\times$ 1012 cm-2. Unfortunately, the SO and SiO abundances cannot be
constrained because the C18O(2–1) emission at these highest detected
velocities (up to 6 km s-1 and down to 9 km s-1 with respect to $V_{\rm sys}$)
are tracing a compact structure rotating along a direction perpendicular to
the SiO jet axis (Fig. 10, Right panels). As a matter of fact, C18O observed
on spatial scales below 100 au is an efficient tracer of the inner
protostellar envelope and/or accretion disks (Murillo et al., 2015; Bergner et
al., 2019; Zhang et al., 2021; Mercimek et al., 2023). In the VLA1623 B case,
C18O(2–1) traces the same rotating gas observed as the CH3OH by Codella et al.
(2022) using the FAUST dataset.

##  6 Conclusions

In the context of the FAUST ALMA Large Program, the VLA1623-2417 protostellar
cluster has been imaged at 1.2–1.3 mm in the SO(56–45), SO(66–55), and
SiO(5–4) emissions at the spatial scale of 50 au. In particular, we focused on
VLA1623 A and its circumbinary disk, and on the VLA1623 B protostar. The main
findings are summarized as follows:

  * •

SO shows extended ($\sim$ 20$\arcsec$, 260 au) emission, peaking towards the A
and B protostars, where the observed spectra are consistent with the
association with the A and B hot-corinos. An absorption dip is present in the
VLA1623 B profile. The absorption is more prominent for SO(56–45), suggesting
the presence of a cold SO component along the line of sight;

  * •

The analysis of the SO kinematics allows us to reveal different structures
emitting at different velocities. At the systemic velocity (+3.8 km s-1)
elongated SO structures are associated with the outflow cavities previously
imaged in CS. Velocities blue-shifted by 1–6.6 km s-1 reveal a long ($\sim$
2000 au) southern streamer, with an increase in the mean velocity of $\sim$
1.6 km s-1 approaching the central A+B system, and apparently feeding the
VLA1623 B protostar. In addition, a $\sim$ 2$\arcsec$ (260 au) streamer,
previously observed by Hsieh et al. (2020), is imaged through the N-S
orientation, impacting from North the A circumbinary disk;

  * •

The SiO emission, detected for the first time in VLA1623-2417, is very compact
($\sim$ 100 au) and associated only with the B protostar. The HV SO emission,
red- and blue-shifted up to $\sim$ 10 km s-1 is also compact ($\leq$ 100 au),
and overlaps with the B protostar, as shown by SiO(5–4). Assuming LTE
conditions and optically thin lines, an estimate of the HV SO excitation
temperature can be derived: 92$\pm$5 K(red) and 102$\pm$6 K (blue), showing
the association of HV SO with shocks created by VLA1623 B jet. Using these
temperatures, the SO and SiO total column densities are $N_{\rm SO}$ = 5
$\times$ 1014 cm-2, and $N_{\rm SiO}$ = 2–5 $\times$ 1012 cm-2, respectively;

  * •

An estimate of the SO excitation temperature of the southern streamer can also
be derived (LTE, optically thin emission): 33$\pm$9 K. The total SO column
density is 2 $\times$ 1014 cm-2. Using C18O(2–1) FAUST data (Mercimek et al.,
2023), we estimated the SO abundance: $X_{\rm SO}$ $\simeq$ 10-8, a value
higher than what is usually found in molecular clouds. We speculate the
occurrence of weak shocks induced by the accretion through the shock which
could release into the gas-phase part of the dust mantles;

  * •

The total mass of the blue-shifted southern streamer is 3 $\times$ 10-3
$M_{\rm\sun}$. This estimate is in agreement with those observed in Class I
objects: 4 $\times$ 10-3 $M_{\rm\sun}$ for SVS13-A (Hsieh et al., 2023), and 1
$\times$ 10-2 $M_{\rm\sun}$ for Per-emb-50 (Valdivia-Mena et al., 2022). On
the other hand, our estimate is lower with respect to that measured in the
Class 0 object IRAS 03292+3039 (0.1–1 $M_{\rm\sun}$, Pineda et al., 2020). It
would be tempting to correlate the streamer mass with the evolutionary stage
of the acrreting protostars. However, beside the evident lack of statistics,
the comparison between the total mass of the streamers strongly depends on its
length, which looks not fully traced because it is larger than the FoV of the
interferometric (IRAM-NOEMA, ALMA) images;

  * •

The free-fall timescale of the southern streamer is 6–9 $\times$ 103 yr.
Consequently, the estimate of the the accretion rate of the streamer on the B
protostar is 3–5 $\times$ 10-7 $M_{\rm\sun}$ yr-1. This can be compared with
the mass accretion rate, $\dot{M}_{\rm acc}$, on source B, calculated between
6 $\times$ 10-8 $M_{\rm\sun}$ yr-1 and 3 $\times$ 10-7 $M_{\rm\sun}$ yr-1. In
conclusion, the mass fed by the streamer is a significative fraction of the
total mass accretion rate of VLA1623 B.

##  7 Epilogue: uniqueness of the VLA1623–2717 region

The ALMA high-sensitivity FAUST data contributed to chemically characterise
the already well studied VLA1623–2417 star forming region, imaging: CS, CCH,
and H13CO+ (Ohashi et al., 2022), CH3OH, and HCOOCH3 (Codella et al., 2022),
C18O (Mercimek et al., 2023), SO, and SiO (this paper). As matter of fact,
CH3OH, HCOOCH3, and SiO have been detected for the first time in VLA1623–2417.
In addition, the FAUST papers enlighted the multiple processes at work in
shaping a multiple protostellar system A1+A2+B. More specifically, there are
strong hints of misaligned accretion from the southern environment (this
paper), and the possible hierarchical decay of the multiple stellar system,
where the A1 and B protostellar disks are counter-rotating (Ohashi et al.,
2022; Codella et al., 2022), molecular envelope and outflows show a
misalignament rotation (Ohashi et al., 2022), and with the ejection of one
member of such an unstable system in the NE direction (Mercimek et al., 2023,
VLA1623 W).

## Acknowledgements

We thank the anonymous referee for their comments and suggestions definitely
improved the manuscript. This project has received funding from the EC H2020
research and innovation programme for: (i) the project "Astro-Chemical
Origins” (ACO, No 811312), (ii) the European Research Council (ERC) project
“The Dawn of Organic Chemistry” (DOC, No 741002), and (iii) the European
Research Council (ERC) project Stellar-MADE (No. 101042275, project Stellar-
MADE). CC, LP, and GS acknowledge the PRIN-MUR 2020 BEYOND-2p (Astrochemistry
beyond the second period elements, Prot. 2020AFB3FX), the PRIN MUR 2022
FOSSILS (Chemical origins: linking the fossil composition of the Solar System
with the chemistry of protoplanetary disks, Prot. 2022JC2Y93), the project
ASI-Astrobiologia 2023 MIGLIORA (Modeling Chemical Complexity,
F83C23000800005), and the INAF-GO 2023 fundings PROTO-SKA (Exploiting ALMA
data to study planet forming disks: preparing the advent of SKA,
C13C23000770005). GS also acknowledges support from the INAF-Minigrant 2023
TRIESTE ("TRacing the chemIcal hEritage of our originS: from proTostars to
planEts”). EB aknowledge the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany´s Excellence Strategy – EXC 2094 –
390783311. DJ is supported by NRC Canada and by an NSERC Discovery Grant. LL
acknowledges the support of UNAM DGAPA PAPIIT grants IN112820 and IN108324,
and CONAHCYT-CF grant 263356. SBC was supported by the NASA Planetary Science
Division Internal Scientist Funding Program through the Fundamental Laboratory
Research work package (FLaRe). IJ-S acknowledges funding by grants No.
PID2019-105552RB-C41 and PID2022-136814NB-I00 from the Spanish Ministry of
Science and Innovation/State Agency of Research MCIN/AEI/10.13039/501100011033
and by “ERDF A way of making Europe". This paper makes use of the following
ALMA data: ADS/JAO.ALMA#2018.1.01205.L. 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.

## DATA AVAILABILITY

The raw data are available on the ALMA archive at the end of the proprietary
period (ADS/JAO.ALMA#2018.1.01205.L).

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