11institutetext: IRAP, Université de Toulouse, CNRS, UPS, CNES, 31400
Toulouse, France, 11email<EMAIL_ADDRESS>22institutetext: Max-Planck-
Institut für extraterrestrische Physik, Gießenbachstraße 1, D-85748 Garching,
Germany 33institutetext: Université Grenoble Alpes, CNRS, Institut de
Planétologie et d’Astrophysique de Grenoble (IPAG), 38000 Grenoble, France
44institutetext: Centro de Astrobiologia (CSIC-INTA), Ctra. de Torrejon a
Ajalvir, km 4, 28850, Torrejon de Ardoz, Spain 55institutetext: Graduate
School of Informatics and Engineering, The University of Electro-
Communications, Chofu, Tokyo 182-8585, Japan 66institutetext: INAF-
Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125, Florence,
Italy 77institutetext: National Radio Astronomy Observatory, PO Box O,
Socorro, NM 87801, USA 88institutetext: European Southern Observatory, Karl-
Schwarzschild Str. 2, 85748 Garching bei München, Germany 99institutetext:
RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama
351-0198, Japan 1010institutetext: Department of Physics, The University of
Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 1111institutetext:
Research Center for the Early Universe, The University of Tokyo, 7-3-1, Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan 1212institutetext: Institut de
Radioastronomie Millimétrique, 38406 Saint-Martin d’Hères, France
1313institutetext: Department of Astronomy, The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 1414institutetext: Department of
Chemistry, Biology, and Biotechnology, The University of Perugia, Via Elce di
Sotto 8, 06123 Perugia, Italy 1515institutetext: Astrochemistry Laboratory,
Code 691, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD
20771, USA 1616institutetext: Cergy Paris Université, Sorbonne Université,
Observatoire de Paris, PSL University, CNRS, LERMA, F-95000, Cergy, France
1717institutetext: Instituto de Radioastronomía y Astrofísica, Universidad
Nacional Autónoma de México, A.P. 3-72 (Xangari), 8701, Morelia, Mexico
1818institutetext: Department of Astronomy, Xiamen University, Zengcuo’an West
Road, Xiamen, 361005, Peoples Republic of China 1919institutetext: National
Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka-shi, Tokyo 181-8588,
Japan 2020institutetext: NRC Herzberg Astronomy and Astrophysics, 5071 West
Saanich Road, Victoria, BC, V9E 2E7, Canada 2121institutetext: Department of
Physics and Astronomy, University of Victoria, Victoria, BC, V8P 5C2, Canada
2222institutetext: Komaba Institute for Science, The University of Tokyo,
3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan 2323institutetext: Center for
Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522,
Japan 2424institutetext: Department of Chemistry, University of Virginia,
McCormick Road, PO Box 400319, Charlottesville, VA 22904, USA
2525institutetext: Department of Physics and Astronomy, Rice University, 6100
Main Street, MS-108, Houston, TX 77005, USA 2626institutetext: Instituto de
Astronomía, Universidad Nacional Autónoma de México, Ciudad Universitaria,
A.P. 70-264, Cuidad de México 04510, Mexico 2727institutetext: Institute of
Low Temperature Science, Hokkaido University, N19W8, Kita-ku, Sapporo,
Hokkaido 060-0819, Japan 2828institutetext: Departament de Química,
Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2929institutetext:
Steward Observatory, 933 N Cherry Ave., Tucson, AZ 85721 USA
3030institutetext: Leiden Observatory, Leiden University, PO Box 9513, 2300 RA
Leiden, The Netherlands 3131institutetext: Department of Physics and
Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
3232institutetext: Materials Science and Engineering, College of Engineering,
Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan
3333institutetext: Departament de F sica Quàntica i Astrof sica, Institut de
Ciències del Cosmos, Universitat de Barcelona (IEEC-UB), Martí Franquès, 1,
E-08028 Barcelona, Catalunya, Spain 3434institutetext: Astronomical Institute,
Graduate School of Science, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku,
Sendai, Miyagi, 980-8578, Japan,

# Hot methanol in the [BHB2007] 11 protobinary system: hot corino versus shock
origin? : FAUST V

C. Vastel 11 F. Alves 22 C. Ceccarelli 33 M. Bouvier 33 I. Jiménez-Serra 44 T.
Sakai 55 P. Caselli 22 L. Evans 1166 F. Fontani 66 R. Le Gal 331212 C. J.
Chandler 77 B. Svoboda 77 L. Maud 88 C. Codella 3366 N. Sakai 99 A. López-
Sepulcre 331212 G. Moellenbrock 77 Y. Aikawa 1313 N. Balucani 1414 E. Bianchi
33 G. Busquet 3434 E. Caux 11 S. Charnley 1515 N. Cuello 33 M. De Simone 33 F.
Dulieu 1616 A. Durán 1717 D. Fedele 66 S. Feng 1818 L. Francis 20202121 T.
Hama 2222 T. Hanawa 2323 E. Herbst 2424 T. Hirota 1919 M. Imai 1010 A. Isella
2525 D. Johnstone 20202121 B. Lefloch 33 L. Loinard 17172626 M. Maureira 22 N.
M. Murillo 99 S. Mercimek 66 S. Mori 3434 F. Menard 33 A. Miotello 88 R.
Nakatani 99 H. Nomura 1919 Y. Oba 2727 S. Ohashi 99 Y. Okoda 1010 J. Ospina-
Zamudio 33 Y. Oya 10101111 J. E. Pineda 22 L. Podio 66 A. Rimola 2828 D.
Segura Cox 22 Y. Shirley 2929 L. Testi 6688 S. Viti 30303131 N. Watanabe 2727
Y. Watanabe 3232 A. Witzel 33 C. Xue 2424 Y. Zhang 99 B. Zhao 22 S. Yamamoto
10101111

(Received March 4th, 2022; accepted June 17th, 2022)

###### Abstract

Aims. Methanol is a ubiquitous species commonly found in the molecular
interstellar medium. It is also a crucial seed species for the building-up of
the chemical complexity in star forming regions. Thus, understanding how its
abundance evolves during the star formation process and whether it enriches
the emerging planetary system is of paramount importance.

Methods. We used new data from the ALMA Large Program FAUST (Fifty AU STudy of
the chemistry in the disk/envelope system of Solar-like protostars) to study
the methanol line emission towards the [BHB2007] 11 protobinary system
(sources A and B), where a complex structure of filaments connecting the two
sources with a larger circumbinary disk has been previously detected.

Results. Twelve methanol lines have been detected with upper energies in the
range [45–537] K along with one 13CH3OH transition and one methyl formate
(CH3OCHO) line blended with one of the methanol transitions. The methanol
emission is compact (FWHM $\sim$ 0.5′′) and encompasses both protostars, which
are separated by only 0.2′′ (28 au). In addition, the overall methanol line
emission presents three velocity components, not spatially resolved by our
observations. Nonetheless, a detailed analysis of the spatial origin of these
three components suggests that they are associated with three different
spatial regions, with two of them close to 11B and the third one associated
with 11A. A non-LTE radiative transfer analysis of the methanol lines gives a
kinetic temperature of [100-140] K, an H2 volume density of 106–107 cm-3 and
column density of a few 1018 cm-2 in all three components with a source size
of $\sim$ 0.15′′. Thus, this hot and dense gas is highly enriched in methanol
with an abundance as high as 10-5. Using previous continuum data, we show that
dust opacity can potentially completely absorb the methanol line emission from
the two binary objects.

Conclusions. Although we cannot firmly exclude other possibilities, we suggest
that the detected hot methanol is resulting from the shocked gas from the
incoming filaments streaming towards [BHB2007] 11 A and B, respectively.
Higher spatial resolution observations are necessary to confirm this
hypothesis.

###### Key Words.:

astrochemistry - ISM: abundance - ISM: molecules - line: identification

##  1 Introduction

The rich chemistry observed in Solar-type protostars is triggered at earlier
stages of the protostellar evolution (e.g. Ceccarelli et al., 2007; Caselli &
Ceccarelli, 2012). Methanol (CH3OH) is a key ingredient in the enhancement of
this chemical complexity from prestellar cores to protoplanetary disks (Vastel
et al., 2014; Bizzocchi et al., 2014; Maret et al., 2005; Walsh et al., 2016;
Spezzano et al., 2020, 2022; Punanova et al., 2022). It is the seed from which
interstellar Complex Organic Molecules (iCOMs: Ceccarelli et al., 2017) sprout
(e.g. Charnley et al., 1992; Garrod et al., 2008; Balucani et al., 2015;
Taquet et al., 2016; Aikawa et al., 2020; Jin & Garrod, 2020).

iCOMs have been detected towards prestellar cores (Bacmann et al., 2012;
Vastel et al., 2014; Jiménez-Serra et al., 2016, 2021; Scibelli & Shirley,
2020), where their presence in the gas has been explained by non-thermal
desorption processes such as photodesorption from UV photons (Bertin et al.,
2016), chemical desorption (Minissale et al., 2016), sputtering caused by a
gentle shock (Flower & Pineau des Forets, 1995), or cosmic-ray induced
chemistry (Shingledecker et al., 2018; Wakelam et al., 2021) and reactive
desorption of methanol followed by gas-phase reactions (Vasyunin et al.,
2017). iCOMs have also been found at a later stage, the Class 0/I protostars
(André et al., 1993). Here, the central protostar is embedded in a dense
envelope as the parental dense core undergoes gravitational collapse. The
iCOMs are observed in the lukewarm region where the dust temperature is
between the CO and H2O sublimation temperatures ($\sim$ 30–100 K (e.g. Jaber
et al., 2014) and in the compact hot corino region where the dust temperatures
are larger than $\sim$100 K and densities larger than $\sim 10^{7}$ cm-3 (e.g.
Ceccarelli et al., 2000b; Cazaux et al., 2003; Bottinelli et al., 2004;
Jørgensen et al., 2016; Yang et al., 2021; Chahine et al., 2022). Finally,
iCOMs are also detected in protoplanetary disks (Öberg et al., 2015, 2021;
Favre et al., 2018; Lee et al., 2019).

The gas phase is therefore chemically enriched in iCOMs, due to either direct
release from dust mantles or gas phase formation from simpler molecules
released from the mantles. Two possibly distinct classes of Solar-like Class
0/I protostars have been found: the hot corinos (Ceccarelli et al., 2007) and
the warm carbon chain chemistry sources (WCCC: Sakai & Yamamoto, 2013),
although intermediate situations are also possible (e.g. Yang et al., 2021).
An intermediate (hybrid) source was also found by Oya et al. (2017).

Since the chemical composition of the planetary systems depends on the
chemical evolution starting from the earliest phases of the protostar
formation, it is crucial to understand how the molecular complexity is
transferred from the large-scale envelope (a few thousand au) to the small-
scale structures of the protostellar system, and how it is maintained in the
inner disk system ($\leq$ 50 au).

In this context, the ALMA (Atacama Large Millimeter/submillimeter Array) Large
Program FAUST (Fifty AU STudy of the chemistry in the disk/envelope system of
Solar-like protostars)111http://faust-alma.riken.jp is designed to survey the
chemical composition of a sample of 13 Class 0/I protostars at the scale of
about 50 to 1000 au (all sources have a distance lower than 250 pc). The
description of the project is reported in Codella et al. (2021). The selected
sources represent the protostellar chemical diversity observed at large scales
and have been observed in three frequency setups chosen to study both
continuum and line emission from specific molecules: 85.0–89.0 GHz, 97.0–101.0
GHz, 214.0–219.0 GHz, 229.0–234.0 GHz, 242.5–247.5 GHz, and 257.5–262.5 GHz.
The FAUST survey provides a uniform sample in terms of frequency setting,
angular resolution and sensitivity. We report the first results obtained
towards the [BHB2007] 11 Class 0/I protostar system focused on the most simple
iCOM, methanol.

##  2 The [BHB2007] 11 protobinary system

The [BHB2007] 11 source was originally identified as a single object in the
Barnard 59 (B59) molecular cloud, which is located at a distance of 163 $\pm$
5 pc (Gaia second data release: Dzib et al., 2018). B59 hosts a proto-cluster
of low-mass young stellar objects (YSOs) at different evolutionary stages as
first shown by Onishi et al. (1999) using the 1–0 transition of 12CO, 13CO,
and C18O with the NANTEN telescope with a 2.7′ beam. Following this, the
proto-cluster was extensively observed in infrared bands (Brooke et al., 2007;
Forbrich et al., 2009; Covey et al., 2010; Román-Zúñiga et al., 2010; Sandell
et al., 2021), ammonia (NH3) emission (Rathborne et al., 2008; Redaelli et
al., 2017) and X-rays (Forbrich et al., 2010). The protostellar nature of the
youngest and most embedded member of the cluster, [BHB2007] 11 , was confirmed
by several studies reporting bipolar outflows (Riaz et al., 2009; Duarte-
Cabral et al., 2012), hints of dynamical infall (Hara et al., 2013; Alves et
al., 2017) and a Spectral Energy Distribution (SED) consistent with a Class
0/I protostar with bright far-infrared emission and $L_{\mathrm{bol}}\sim 4.4$
$L_{\mathrm{\odot}}$ (Sandell et al., 2021).

Alves et al. (2017) used ALMA in its extended configuration to observe the
dust continuum emission at 1.3 mm and molecular transitions of CO, C18O and
H2CO lines (angular resolution of 0.22′′). The dust distribution reveals a
$\sim 180$ au disk surrounded by a fainter, elongated structure tracing the
inner component of the core envelope. The spectral line data reveal a bipolar
outflow launched at the edge of the inner disk at a radial distance of 90–130
au from the central source. The disk is rotationally supported, with Keplerian
rotation revealed by H2CO lines (Alves et al., 2017, 2019). At much higher
angular resolution ($\sim 0.04\arcsec$), Alves et al. (2019) uncovered a young
binary protostar system embedded in circumstellar disks that have radii of 2
to 3 au. The protostars are named [BHB2007] 11 A (hereafter 11A) for the
Northern source ($\alpha$ (2000) = 17h11m23.097s, $\delta$ (2000) =
-27∘24′32.85′′) and [BHB2007] 11 B (hereafter 11B) for the Southern source
($\alpha$ (2000) = 17h11m23.09s, $\delta$ (2000) = -27∘24′33′′). These systems
are surrounded by a complex filamentary structure (the so-called streamers)
connecting to the larger circumbinary disk. Note that streamers have recently
been seen in other more evolved objects Alves et al. (2020) and modeled as
mostly free-falling (Pineda et al., 2020; see Pineda et al., 2022, for a
review). The binary mass ratio is $\gtrsim 1$, since the 11A disk is slightly
more massive (of the order of a Jupiter mass) than the 11B disk and the system
has a projected separation of 28 au ($\sim$ 0.2′′). Source 11B is located
between high velocity components of the CO emission (VLSR ¡ -1.5 km s-1 and
VLSR ¿ 9 km s-1), which is interpreted as enhanced gas accretion towards 11B
from the circumbinary disk. Both protostars are accreting from their
individual circumstellar disks as inferred from centimetric continuum emission
observed from both sources. The radio data are consistent with free-free
emission from ionised jets launched by the disk-star system (Alves et al.,
2019). The dynamical mass of the protobinary system has been estimated as an
upper limit from the Keplerian model of the H2CO data with a value of 2.25
$\pm$ 0.13 M⊙.

In this paper, we report high-$J$ methanol emission (45 K ¡ Eup ¡ 537 K ) from
[BHB2007] 11 obtained in the framework of the FAUST collaboration observed in
a $\sim$ 0.4′′ beam. These data unveil the hot corino nature of the source
seen over multiple velocity components. From these data, we derive the hot gas
properties (column density and temperature) for each velocity component.

##  3 Observations

[BHB2007] 11 has been observed with ALMA (FAUST Large Program 2018.1.01205.L)
with two frequency setups in Band 6 (setup 1 and 2) and one frequency setup in
Band 3 (setup 3). The data exploited here were acquired between 2018 and 2020
using the 12-m and 7-m array for setup 1 and 2, and the 12-m array for setup
3. The baseline length in the configurations of the 12-m array for setup 1 and
2 (C43-4 and C43-1) ranges from 15 m to 1.3 km, and the baseline length in the
configuration of the 7-m array ranges from 8.9 m to 48.9 m. For setup 3, the
baseline length in the configurations of the 12 m array (C43-6 and C43-3)
ranges from 15 m to 3 km. The observations were centred at $\alpha$ (2000) =
17h11m23.125s, $\delta$ (2000) = -27∘24′32.87′′. J2056-4714 and J1427-4206
were used as bandpass calibrators for setup 2 (12-m array), and J1700-2610 as
phase calibrator and flux calibrator. J1427-4206 and J2056-4714 were used as
bandpass calibrator and flux calibrator for setup 1 (12-m array), and
J1700-2610 as phase calibrator.
The data were reduced in the Common Astronomy Software Applications package
(CASA) version 5.6.1 (McMullin et al. 2007) using a modified version of the
ALMA calibration pipeline and an additional in-house calibration routine to
correct for the system temperature and spectral line data
normalisation222https://help.almascience.org/kb/articles/what-errors-could-
originate-from-the-correlator-spectral-normalization-and-tsys-calibration.
Self-calibration was carried out using carefully-selected, line-free,
continuum channels for each configuration. The complex gain corrections
derived from the self-calibration were then applied to all channels in the
data, and the continuum model derived from the self-calibration was then
subtracted from the data to produce continuum-subtracted line data. A self-
calibration technique was also used to align both amplitudes and phases across
the multiple configurations, to correct for any remaining offsets in the flux
density scales, and to correct for systematic position offsets that may be
caused by either source proper motion or other system issues.
For each setup, iterative phase self-calibration using a very long solution
interval was then used to do the position alignment across multiple
configurations. In addition, amplitude offsets between datasets needed to be
corrected. To do this, a model derived from a very deeply-cleaned and masked
image was used to obtain amplitude corrections per execution block. The
dynamic range of the resulting self-calibrated image was improved by a factor
of three for setup 1, without reduction in the peak flux density of the
source. Fig. 1 shows an amplitude versus uv-distance plot of the data from the
different configurations before and after this amplitude alignment for setup 1
in the continuum spectral window (least noisy). The data have been averaged
per baseline across the entire dataset. The improvement in the dynamic range
was less significant for setup 2 (around 10%), because for setup 2, the
amplitude scale of the 12-m (TM 1 and TM 2) was much better aligned coming out
of the calibration pipeline and per-configuration self-calibration process
than they were for setup1.

Figure 1: Amplitude versus uv-distance plots, before (top) and after (below)
self-calibration.

The resulting continuum-subtracted line-cube has been made using a Briggs
robust parameter of 0.5 and we obtained a synthesised beam of 0.44′′ $\times$
0.37′′ Position Angle (PA) = -82∘ at 261.687 GHz, and 0.41′′ $\times$ 0.39′′
PA = 47∘ at 218 GHz. We estimate an overall systematic uncertainty of 10% for
each dataset. The observed spectral windows (spw) are centred on the
frequencies listed in Table 1. The bandwidth is 59 MHz for 12-m (62 MHz for
7-m) except for the continuum window with a 1.875 GHz (2 GHz for 7-m)
bandwidth. Spectral line imaging was performed with the
CASA333https://casa.nrao.edu/ package, while the data analysis was performed
using the IRAM/GILDAS444http://www.iram.fr/IRAMFR/GILDAS package as well as
the CASSIS555http://cassis.irap.omp.eu package.

Table 1: Observed spectral windows in the observed FAUST data.

Spectral window | setup 1 | setup 2 | setup 3
---|---|---|---
| (GHz) | (GHz) | (GHz)
spw 25 | 216.113 | 243.916 | 93.181
spw 27 | 216.563 | 244.049 | 94.405
spw 29 | 217.105 | 244.936 | 95.000
spw 31 | 217.822 | 245.606 | 107.014
spw 33 | 218.222 | 246.700 | 108.040
spw 35 | 218.440 | 260.189 | 104.239
spw 37 | 219.560 | 260.255 | 105.799
spw 39 | 219.949 | 261.687 |
spw 41 | 231.061 | 262.004 |
spw 43 | 213.221 | 257.896 |
spw 45 | 231.322 | 258.256 |
spw 47 | 231.410 | 258.549 |
spw 49a | 233.796 | 259.035 |
666a: continuum window

Figure 2: Dust continuum maps obtained in each setup. The rms noise level is
50 $\mu$Jy beam-1 for Band 3 observations (setup 3, left panel), 90 $\mu$Jy
beam-1 for setup 1 in Band 6 (middle panel) and 70 $\mu$Jy beam-1 for setup 2
in Band 6 (right panel). The intensity contour levels in the left panel are
-5, 5, 10, 30, 50, 70, 90 $\times$ the noise level, while the intensity
contours in the middle and right panels are -5, 5, 50 and from 100 to 1000 (in
steps of 100) $\times$ 70 $\mu$Jy beam-1, the noise level in setup 2. The
colour scale at the top is the same for all panels. The red dots indicate the
positions of 11A (North) and 11B (South) as reported by Alves et al. (2019).
The sources are not resolved with the present resolution. The left panel also
shows the integrated intensity contours from CO ($2\rightarrow 1$) emission
from the bipolar outflow powered by [BHB2007] 11 (Alves et al., 2017). The
synthesised beam is displayed in the bottom left corner of each panel
($0.36\arcsec\times 0.34\arcsec,0.39\arcsec\times 0.33\arcsec$ and
$0.42\arcsec\times 0.29\arcsec$ for Setups 3, 1 and 2, respectively). Figure
3: Radial profile of the dust continuum emission at 252 GHz (setup 2) towards
[BHB2007] 11 . The profile is centred on the continuum peak. The red line
shows a Gaussian fit to the disk brightness distribution. The dashed line
indicates the synthesised beam size. The grey line shows the rms noise level
of the continuum emission. Figure 4: Spectral Energy Distribution determined
for the dust emission within the circumbinary disk ($\alpha=3.0$, black line)
and in the envelope ($\alpha=3.4$, dotted dashed line). The flux densities for
disk and envelope are indicated as filled circles and open triangles,
respectively. The errors are dominated by the uncertainty in the flux
calibration, which is assumed to be $\sim 10\%$. The dashed line shows the SED
determined from the free-free (centimetric) emission detected with the Very
Large Array (Alves et al., 2019).

##  4 Line identification

The line identification has been performed using the CASSIS software that
connects to the JPL and CDMS databases. This is a standalone software, written
in Java, freely delivered to the community to help with visualising, analysing
and modelling observations from ground or space-based observatories. CASSIS
has been developed at IRAP since 2005 and is part of the OVGSO777https://ov-
gso.irap.omp.eu/ data centre that aims at promoting the Virtual Observatory
(VO) technology. CASSIS displays any spectrum (ASCII, FITS or GILDAS/CLASS
format or the result from the query to any Simple Spectral Access Protocol
(SSAP) VO or EPN-TAP888Europlanet-Table Access Protocol VO service from
IVOA999International Virtual Observatory Alliance registries) and identifies
atomic and molecular species through its link to the databases such as CDMS
(Müller et al., 2005) or JPL (Pickett et al., 1998) via a SQLite database, or
via a direct access to VAMDC101010http://www.vamdc.org/ for any available
spectroscopic database.
The systemic velocity of [BHB2007] 11 with respect to the local standard of
rest is VLSR = 3.6 km s-1 (Onishi et al., 1999). We identified and detected
twelve methanol transitions in the observed spectral windows of the three
spectral setups (dust peak emission), and only one 13CH3OH transition (234 GHz
but not at 94.4 GHz where the rms reached 0.9 K). No deuterated counterparts
such as CH2DOH at 261.7 GHz have been detected. We list, in Table 2, the
spectroscopic parameters of the detected transitions using the CDMS database.
The spectral resolutions are also quoted as $\delta$V (km s-1) for each
detected transition. The methanol transitions cover a broad range in energy
from Eup $\sim$ 45 to 537 K.

Table 2: Spectroscopic Parameters of the methanol transitions (using the CDMS
database) detected towards [BHB2007] 11 and results from the Gaussian fits.

|  |  |  |  CH3OH |  |  |  |  |
---|---|---|---|---|---|---|---|---|---
Frequency | QN |  Eup |  Aij | beam, PA | rms |  $\delta$V |  Tmb | FWHM |  VLSR
(MHz) |  | (K) |  (s-1) |  ${}^{\prime\prime}\times^{\prime\prime}$,∘ | (mK) |  (km s-1) | (K) |  (km s-1) |  (km s-1)
218440.063(0.013) |  4-2,3 – 3-1,2 E | 45.46 |  4.69 $\times$ 10-5 |  0.41 $\times$ 0.39, 47 | 158 | 0.17 | 1.57(0.06) | 3.2(0.1) | -2.0
|  |  |  |  |  |  | 1.46(0.04) | 6.1(0.3) | 2.8
|  |  |  |  |  |  | 1.16(0.04) | 5.4(0.2) | 9.9
243915.788(0.004) |  51,4 – 41.3 A | 49.66 |  5.97 $\times$ 10-5 |  0.47 $\times$ 0.40, -84 | 59 | 0.15 | 2.01(0.04) | 3.2(0.1) | -2.0
|  |  |  |  |  |  | 1.67(0.02) | 5.9(0.1) | 2.8
|  |  |  |  |  |  | 1.41(0.02) | 4.9(0.1) | 9.9
247228.587(0.013) |  42,2 – 51,5 A | 60.92 |  2.12 $\times$ 10-5 |  0.46 $\times$ 0.39, -80 | 34 | 1.18 | 1.49(0.06) | 2.9(0.2) | -2.0
|  |  |  |  |  |  | 1.01(0.04) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.99(0.04) | 5.0(0.0) | 9.9
234683.37(0.012) |  42.3 – 51,4 A | 60.92 |  1.87 $\times$ 10-5 |  0.38 $\times$ 0.34, 70 | 74 | 0.62 | 1.32(0.07) | 2.9(0.1) | -2.0
|  |  |  |  |  |  | 0.92(0.04) | 6.2(0.5) | 2.8
|  |  |  |  |  |  | 0.92(0.04) | 5.3(0.3) | 9.9
234698.519(0.015) |  54.2 – 63,3 E | 122.72 |  6.34 $\times$ 10-6 |  0.38 $\times$ 0.34, 70 | 73 | 0.63 | 0.85(0.05) | 3.1(0.2) | -2.0
|  |  |  |  |  |  | 0.53(0.03) | 5.1(0.5) | 2.8
|  |  |  |  |  |  | 0.56(0.03) | 5.7(0.5) | 9.9
232945.797(0.012) |  103,7 – 112,9 E | 190.37 |  2.13 $\times$ 10-5 |  0.38 $\times$ 0.34, 70 | 79 | 0.62 | 1.12(0.07) | 3.1(0.2) | -2.0
|  |  |  |  |  |  | 0.84(0.04) | 5.9(0.6) | 2.8
|  |  |  |  |  |  | 0.91(0.04) | 5.6(0.4) | 9.9
247161.95(0.015) |  16-2,15 – 153,13 E | 338.14 |  2.57 $\times$ 10-5 |  0.46 $\times$ 0.39, -80 | 29 | 1.18 | 1.00(0.05) | 3.0(0.2) | -2.0
|  |  |  |  |  |  | 0.62(0.03) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.72(0.03) | 5.0(0.0) | 9.9
261704.409(0.015) |  12-6,7 – 13-5,8 E | 359.77 |  1.78 $\times$ 10-5 |  0.44 $\times$ 0.37, -82 | 104 | 0.14 | 1.41(0.05) | 3.9(0.2) | -2.0
|  |  |  |  |  |  | 0.53(0.05) | 3.6(0.5) | 2.8
|  |  |  |  |  |  | 0.81(0.04) | 5.2(0.3) | 9.9
233795.666(0.012) |  183,15 – 174,14 A | 446.58 |  2.20 $\times$ 10-5 |  0.38 $\times$ 0.34, 70 | 89 | 0.63 | 0.67(0.09) | 2.6(0.4) | -2.0
|  |  |  |  |  |  | 0.48(0.05) | 6.3(1.2) | 2.8
|  |  |  |  |  |  | 0.51(0.06) | 4.4(0.7) | 9.9
247610.918(0.014) |  183,15 – 182,16 A | 446.58 |  8.29 $\times$ 10-5 |  0.46 $\times$ 0.39, -80 | 49 | 1.18 | 1.16(0.06) | 2.9(0.2) | -2.0
|  |  |  |  |  |  | 0.67(0.04) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.82(0.04) | 5.0(0.0) | 9.9
246873.301(0.015) |  193,16 – 192,17 A | 490.65 |  8.27 $\times$ 10-5 |  0.46 $\times$ 0.39, -80 | 19 | 1.18 | 1.01(0.06) | 2.7(0.2) | -2.0
|  |  |  |  |  |  | 0.62(0.04) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.73(0.04) | 5.0(0.0) | 9.9
246074.605(0.016) |  203,17 – 202,18 A | 537.04 |  8.25 $\times$ 10-5 |  0.46 $\times$ 0.39, -80 | 29 | 1.19 | 0.93(0.08) | 3.2(0.3) | -2.0
|  |  |  |  |  |  | 0.65(0.05) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.66(0.05) | 5.0(0.0) | 9.9
|  |  |  |  13CH3OH |  |  |  |  |
234011.58(0.05) |  51,5 – 41,4 A+ | 48.25 |  5.27 $\times$ 10-5 |  0.38 $\times$ 0.34, 70 | 76 | 0.62 | 0.41(0.05) | 2.9(0.4) | -2.0
|  |  |  |  |  |  | 0.47(0.03) | 5.6(0.0) | 2.8
|  |  |  |  |  |  | 0.30(0.03) | 5.0(0.0) | 9.9

111111 The spectral resolution is indicated as $\delta V$. The 1$\sigma$ error
are quoted in parenthesis for the main beam temperature, the full width half
maximum and velocity in the standard of rest. The spectra were extracted over
the region above 4$\sigma$ in the integrated intensity map for each
transition.

##  5 Results

###  5.1 Dust emission

Figure 2 shows the dust continuum maps obtained in the three setups (ACA+12m
combined). The dust distribution is consistent with the previous maps of Alves
et al. (2017), showing bright emission from the circumbinary disk (inclined
$\sim 56\degr$ with respect to the line-of-sight) at the centre of the
elongated envelope emission. The apparent misalignment between the envelope
major axis and the disk major suggests a warped disk. This is consistent with
the velocity structure previously revealed by H2CO lines, where low upper
energy level (Eup) transitions trace envelope rotation/infall misaligned with
the disk rotation seen in high-Eup transitions (Alves et al., 2017, 2018). At
the present resolution, the proto-binary system reported by Alves et al.
(2019) is not resolved, but faint, extended emission oriented in a north-west
south-east direction is detected (at a 3$\sigma$ level) in the $\sim 1$ mm
bands (setups 1 and 2) beyond the envelope. The radial profile of the
continuum emission, taken from increasing elliptical annuli oriented at a
position angle of 167° East of North (the orientation of the inner envelope),
is displayed in Fig. 3. The contribution from the disk is distinguishable from
the fainter structure that surrounds it, as the disk brightness is well
represented by a Gaussian distribution whose wings do not encompass the
extended emission.

With the continuum data aligned in position across the three FAUST setups, we
reconstructed the continuum maps with a common clean beam of $0.35\arcsec$. We
then computed the Spectral Energy Distribution (SED) from a linear fit (in
log-log scale) over the fluxes observed in the three setups (Fig. 4). Note
that the flux density (and error) used to construct the SED are derived from
2D Gaussian fits over the disk emission, where the emission is centrally
peaked, while the envelope flux is derived from a contour excluding the
disk.121212The circumbinary disk emission over which the SED was computed is
determined as the first closed contour around it (i. e., not encompassing the
extended N-S emission): 15, 120 and 230 times the rms noise of the beam-
matched maps in setups 3, 1, and 2, respectively. The SED for the envelope
uses the integrated flux higher than 5 times the rms noise but lower than the
contours listed above (i .e, it excludes the circumbinary disk). Table 3
reports the peak flux and flux density for the circumbinary disk, for which we
find a spectral index of $3.0\pm 0.1$. The same index is reported by Alves et
al. (2019), whose observations cover ALMA Bands 3, 6 and 7. In contrast, the
dust emission from the inner envelope has a spectral index of $3.4\pm 0.2$,
which is slightly lower than the canonical value of the Interstellar Medium
($\alpha_{\mathrm{ISM}}=3.7$, Testi et al., 2014), implying that the grains in
the envelope are potentially mildly larger than in the ISM ($\lesssim
10\,\mu$m, Agurto-Gangas et al., 2019).

Table 3: Peak flux and flux density for the circumbinary disk.

Setup | Frequency | Peak Flux | Flux Density
---|---|---|---
| (GHz) |  (mJ beam-1) | (Jy)
3 | 100.6 |  5.4 $\pm$ 0.2 |  20.9 $\pm$ 0.9
1 | 225.4 |  49 $\pm$ 1 |  233 $\pm$ 7
2 | 253.0 |  76 $\pm$ 2 |  331 $\pm$ 12
131313Uncertainties refer to the 2D Gaussian fit error.

###  5.2 Molecular emission

Figure 5 shows the moment 0 maps (in Jy beam km s-1) of the CH3OH high
spectral resolution lines at 218, 244 and 262 GHz using the 12m array. These
three transitions are the only ones observed at high spectral resolution
(0.1–0.2 km s-1). The contours start at 4$\sigma$ at every 10$\sigma$ for
218.440 and 243.916 GHz, and every 3$\sigma$ at 261.704 GHz. The ellipse in
the bottom left corner represents the ALMA synthesised beam. The emission is
compact (less than 1′′) and centred at the same location, which means that, in
this region, the gas is co-existent, from the low energy transition to the
higher energy transition. The beam encompasses both 11A and 11B, separated by
0.2′′, which therefore cannot be resolved. The other transitions where the
spectral resolution is lower (0.6 – 1.2 km s-1) also show a centred compact
emission.

From Fig. 5 it is obvious that all methanol transitions do not necessarily
trace the same extended structure. The 218 GHz and 244 GHz transitions, which
have an upper energy of 45 K and 50 K respectively, are tracing a more
extended region (around 1′′) compared to the highest energy levels at 540 K
for the 246.074 GHz transition tracing a seemingly more compact region (around
0.5′′).

Figure 5: Moment 0 map of the high spectral resolution methanol transitions at
218.440 GHz ($\rm E_{u}$=45.46 K), 243.916 GHz ($\rm E_{u}$=49.66 K) and
261.704 GHz ($\rm E_{u}$=359.77 K). Contours start at 4$\sigma$ at every
10$\sigma$ for 218.440 and 243.916 GHz, and every 3$\sigma$ at 261.704 GHz.
The ellipse in the bottom left corner represents the ALMA synthesised beam.
Both source A and B identified by Alves et al. (2019) are indicated as white
filled circles.

####  5.2.1 CH3OH line identification

We extracted the average spectrum over the region above 4$\sigma$ in the
integrated intensity map for each molecular transition (either in Jy beam-1 or
in Kelvin) into the CASSIS software and the high spectral resolution
transitions are presented in Fig. 6 while the lower spectral resolution
transitions of methanol are presented in Fig. 7 and 8. From these figures we
can clearly distinguish three components, which are visible at -2 km s-1, 2.8
km s-1 and 9.9 km s-1. Table 2 shows the results of the best-fit adjustment
using the Levenberg-Marquardt fitting within CASSIS using a large number of
iterations (Tmb in Kelvin, FWHM and VLSR in km s-1).

Figure 6: Tb (K) spectra for the high spectral resolution Methanol transitions
at 218.440, 243.916 and 261.704 GHz. The dashed lines correspond to the
results of the best-fit Gaussian at -2 km s-1, 2.8 km s-1 and 9.9 km s-1. The
-2 km s-1 component of the 261.704 GHz transition is blended with a transition
of methyl formate (see text). Figure 7: Spectra (in mJy beam-1) for the low
spectral resolution Methanol transitions. The dashed lines correspond to the
results of the best-fit Gaussian of the high spectral resolution transitions
at -2 km s-1, 2.8 km s-1 and 9.9 km s-1. Figure 8: Spectra (in mJy beam-1) for
the low spectral resolution methanol transitions in the 234 GHz spectral
windows. The dashed lines correspond to the results of the Gaussian components
obtained from each of the high spectral resolution transitions at -2 km s-1,
2.8 km s-1 and 9.9 km s-1.

The maximum recoverable scale of the 12-m array data is 9′′–11′′. Since the
CH3OH emission is compact and its size is less than 3′′, the missing flux in
the 12 m array data is negligible. In fact, we confirmed that the flux of the
data combined with the 7-m and 12-m array data (maximum recoverable scale:
16′′–19′′) is comparable with that of the 12-m array data (see Fig. 9 for the
243.916 GHz transition). We therefore used in the following the 12-m array
data only.

Figure 9: Difference between the 12 m-only data and the joint data for the
A-CH3OH transition at 243.916 GHz.

Fig. 10 shows the velocity field (moment 1) of the two extreme (in upper
energy values) high spectral resolution methanol transitions at $\sim 50$ K
(243.916 GHz) and $\sim 350$ K (261.704 GHz) upper energy levels (Eup). The
velocity structure ranges from -5 to 15 km s-1 in both low and high
transitions, and it has a northwest-southeast gradient centred on the 11B
source at the systemic velocity of the source. Although we cannot resolve the
protostars in these maps, this could indicate that the methanol maps are more
sensitive to the kinematics of the southern source.

Figure 10: Velocity field determined from methanol transitions at low and high
energy levels. The contours indicate the continuum intensity levels from the
high spatial resolution observations of Alves et al. (2019). The compact
emission contours arise from the circumstellar disks around each protostar of
the binary system: 11A (northern component) and 11B (southern component). The
dashed line in the left panel shows the direction of the cut used to produce
the position-velocity diagram displayed in Fig. 17. The cut position angle is
140$\degr$ and its width is $0.5^{\prime\prime}$, encompassing both
protostars.

Due to the molecular complexity of this source we explored the line blending
from other species. The CH3OH transition at 261.704 GHz is indeed clearly
blended, as shown in Fig. 6, with the 21(7,14)- 20(7,13) E transition of
methyl formate (CH3OCHO) at 261715.5180 MHz. Figure 11 shows the methyl
formate transition with the three components at -2 km s-1, 2.8 km s-1 and 9.9
km s-1 indicated as thin dashed lines. It is clear that the -2 km s-1 methanol
transition is blended with the 9.9 km s-1 transition of methyl formate. A
subsequent analysis of the iCOMs detected in our [BHB2007] 11 FAUST data will
be published at a later time.

Figure 11: Spectra at the 3.6 km s-1 VLSR of the [BHB2007] 11 source showing
the E-CH3OCHO 21(7,14)- 20(7,13) transition at 261.715 GHz blended with the
CH3OH transition at 261.704 GHz. The dashed lines correspond to the results of
the best-fit Gaussian components obtained from the high spectral resolution
methanol transitions at -2 km s-1, 2.8 km s-1 and 9.9 km s-1 for the methyl
formate transition.

Within CASA (imfit command), we fitted a 2D gaussian to the integrated
intensity maps of the three high spectral resolution transitions, taking into
account the three velocity components. At 243.916 GHz, the image component
size (deconvolved from beam) for (i) the 9.9 km s-1 velocity component
(channel 195) is 0.27′′ $\times$ 0.23′′ (major axis FWHM $\times$ minor axis
FWHM), (ii) the -2 km s-1 (channel 274) is 0.27′′ $\times$ 0.16′′ (major axis
FWHM $\times$ minor axis FWHM), (iii) the 2.8 km s-1 (channel 242) is 0.53′′
$\times$ 0.36′′ (major axis FWHM $\times$ minor axis FWHM). The 218.440 GHz
give similar results and the 261.704 GHz non-blended components at +9.9 and
2.8 km s-1 tend to a point source deconvolved source size. Therefore, the two
extreme velocity components seem slightly more compact than the 2.8 km s-1.

####  5.2.2 13CH3OH line identification

Only one transition of the 13C methanol isotopologue has been detected at 234
GHz with $\rm E_{up}$ = 48 K, and it presents the same characteristics as
methanol and methyl formate with three components, as shown in Figure 12. We
present in Table 2 the results from the best-fit Gaussian adjustments for this
transition. Figure 13 shows that the integrated line intensity is much noisier
than the other methanol moment 0 maps but still compact and centred on the
same position.

Figure 12: Spectrum (in mJ beam-1) of the only detected transition of 13CH3OH
at 234 GHz. The dashed lines correspond to the results of the best-fit
Gaussian components obtained from the high spectral resolution transitions at
-2 km s-1, 2.8 km s-1 and 9.9 km s-1. Figure 13: Moment 0 map of the 13CH3OH
transition at 234 GHz. Contours start at 4$\sigma$ at every 2$\sigma$. The
ellipse in the bottom left corner represents the ALMA synthesised beam. Both
source 11A and 11B identified by Alves et al. (2019) are indicated as white
filled circles.

##  6 Modelling of the methanol and dust emission

We first performed a local thermodynamic equilibrium (LTE) analysis to
estimate the excitation temperature and column density for our methanol
transitions. To achieve that, we defined a polygon extracted from the average
spectrum over a region above 4$\sigma$ in the integrated intensity map of the
218.440 GHz methanol transition. This polygon was then used to extract the
average spectrum for each methanol transition. We then performed a best-fit of
the three components and obtained a rotational diagram (RD) analysis followed
by a non-LTE analysis to estimate the H2 volume density, the column density,
kinetic temperature and size of the source. The integrated line intensities
used in the following are presented in Table 4.

Table 4: Integrated intensities used for the LTE and non-LTE analysis,
extracted over a region above 4$\sigma$ in the integrated intensity map of the
218.440 GHz methanol transition.

| W(-2 km s-1) | W(2.8 km s-1) | W(9.9 km s-1)
---|---|---|---
GHz | K km s-1 | K km s-1 | K km s-1
CH3OH |  |  |
218.440∗ | $5.4\pm 0.2$ | $9.5\pm 0.2$ | $6.7\pm 0.2$
243.916∗ | $5.2\pm 0.1$ | $7.9\pm 0.1$ | $5.6\pm 0.1$
247.229∗ | $3.4\pm 0.1$ | $4.3\pm 0.1$ | $3.9\pm 0.1$
234.683∗ | $3.1\pm 0.1$ | $4.0\pm 0.1$ | $3.8\pm 0.1$
234.698∗ | $1.8\pm 0.1$ | $2.5\pm 0.1$ | $2.5\pm 0.1$
232.946∗ | $2.7\pm 0.1$ | $3.6\pm 0.1$ | $4.2\pm 0.1$
247.162 | $3.2\pm 0.2$ | $3.7\pm 0.2$ | $3.8\pm 0.2$
261.704∗ | $1.1\pm 0.1$ | $1.5\pm 0.1$ | $1.9\pm 0.1$
233.796 | $1.9\pm 0.4$ | $3.2\pm 0.4$ | $2.4\pm 0.4$
247.611 | $3.6\pm 0.1$ | $4.0\pm 0.1$ | $4.4\pm 0.1$
246.873 | $2.9\pm 0.1$ | $3.7\pm 0.1$ | $3.9\pm 0.1$
246.075 | $3.2\pm 0.1$ | $3.9\pm 0.1$ | $3.5\pm 0.1$
13CH3OH |  |  |
234.011∗ | $0.9\pm 0.1$ | $2.3\pm 0.2$ | $1.4\pm 0.2$
141414Transitions used in the LVG are indicated by the star symbol.

###  6.1 LTE Rotational Diagram analysis

For a molecule in LTE, all excitation temperatures are the same, and the
population of each level is given by:

$\rm N_{u}=\frac{N_{tot}}{Q(T_{rot})}g_{u}e^{-E_{u}/kT_{rot}},$ (1)

where Q is the partition function, Trot is the rotational temperature, gu is
the statistical weight in the upper level, Eu is the energy of the upper
level, k is the Boltzmann constant, Nu is the column density in the upper
level and Ttot is the column density of the species. We can rewrite this
equation to obtain:

$\rm
ln\frac{N_{u}}{g_{u}}=ln\frac{N_{tot}}{Q(T_{rot})}-\frac{E_{u}}{kT_{rot}}.$
(2)

A rotational diagram can be useful to determine whether the emission is
optically thick or thin, whether the level populations are described by LTE,
and to determine what temperature describes the population distribution in the
event that LTE applies (Goldsmith & Langer, 1999). Equation 2 can be written
in terms of the observed integrated area W when the lines are optically thin:

$\rm ln\frac{8\pi
k\nu^{2}W}{hc^{3}A_{ul}g_{u}}=ln\frac{N_{tot}}{Q(T_{rot})}-\frac{E_{u}}{kT_{rot}},$
(3)

where h is the Planck constant, Aul is the Einstein coefficient between level
$up$ and level $low$, $\nu$ is the frequency for each observed transition and
c is the celerity of light. The error bars should be taken into account for
the order 1 polynomial fit, in order to obtain a reliable value for the
uncertainty on the rotational temperature as well as the total column density.
From the CASSIS Line Analysis module, the user can fit the lines and produce a
detailed .rotd file with the integrated area and rms values for each
transition. The user is required to give a value for the instrumental
calibration uncertainty. The uncertainty ($\Delta$W) of the integrated area is
computed though the following formula:

$\rm\Delta W=\sqrt{(\rm cal/100\times W)^{2}+(rms\sqrt{2\times\rm
FWHM\times\delta V})^{2}},$ (4)

where cal is the calibration value ($\%$), W is the integrated area (in K km
s-1), rms is the noise around the selected species (in K), FWHM is the full
width at half maximum (km s-1) and $\delta$V is the bin size (in km s-1).
Therefore, the plotted uncertainties are simply:

$\rm\Delta\left(ln\frac{N_{u}}{g_{u}}\right)=\frac{\Delta W}{W}.$ (5)

From the fitted straight line ($y=ax+b$) the slope $a$ is related to the
rotational excitation temperature as $T_{rot}=-1/a$. Then $\Delta
T_{rot}=\Delta a/a^{2}$. The intercept $b$ is related to the total column
density as Ntot = Q(Trot) $\times$ eb. Therefore $\Delta N_{tot}$ = Q(Trot)
$\times\Delta b\times e^{b}$.

The RD analysis is presented in Figure 14 along with the resulting column
densities and excitation (also called rotational) temperature. All the
transitions are shown, although the blended transition of the 261.7 GHz
methanol transition at -2 km s-1 is not used in the fit. A large dispersion
can be seen in the Figures. The low energy transitions are also tracing the
more extended and colder envelope compared to the higher energy transitions.
Removing the transitions with upper energy less than 150 K does not change the
results because of the wide dispersion in these points.

Figure 14: Rotational Diagrams of the detected methanol lines for the -2 km
s-1 (top panel), 2.8 km s-1 (middle panel) and 9.9 km s-1 (bottom panel)
components, respectively.

The estimated parameters for the three components are similar:
-2 km s-1: N = (1.0 $\pm$ 0.4) 1016 cm-2, $\rm T_{rot}$ = (167 $\pm$ 31) K,
2.8 km s-1: N = (1.1 $\pm$ 0.3) 1016 cm-2, $\rm T_{rot}$ = (152 $\pm$ 16) K,
9.9 km s-1: N = (1.2 $\pm$ 0.4) 1016 cm-2, $\rm T_{rot}$ = (165 $\pm$ 27) K,
where the column density is the beam-averaged one and the lines are predicted
to be optically thin.

###  6.2 Non-LTE LVG analysis

In order to better take into account the possible/probable non-LTE effects, we
modelled the methanol line emission via the Large Velocity Gradient (LVG) code
grelvg, developed by Ceccarelli et al. (2003). We used the collisional
coefficients with para-H2, computed by Rabli & Flower (2010) between 10 and
200 K for the first 256 levels and provided by the BASECOL database (Dubernet
et al., 2012, 2013). We therefore used the methanol transitions up to J=15 for
the non-LTE analysis. We assumed an A-/E- CH3OH ratio equal to 1 and the
12C/13C equal to 68 (e.g. Milam et al., 2005). To compute the line escape
probability as a function of the line optical depth we adopted a spherical
geometry and a linewidth equal to 3.2 km s-1 for the -2 km s-1 component, 6 km
s-1 for the 2.8 km s-1 component and 5 km s-1 for the 9.9 km s-1 component,
following the observations.

We ran a large grid of models ($\sim 10000$) to cover the $\chi^{2}$ surface
in the parameters space: the total (A- plus E- ) methanol column density
N(CH3OH) from $1\times 10^{13}$ to $2\times 10^{18}$ cm-2, the H2 density nH2
from $1\times 10^{5}$ to $1\times 10^{9}$ cm-3 and the temperature T from 15
to 200 K. We then simultaneously fitted the measured 12C and 13C -A- and 12C
E- line intensities extracted from the 4$\sigma$ polygon of the 218.440 GHz
methanol transition, by comparing them with those predicted by the model,
leaving N(CH3OH), nH2 and T. Since the line emission is unresolved with our
spatial resolution, we also left the emitting size $\theta_{s}$ as a free
parameter. We performed this same procedure for the three velocity components
separately.

##### Component at -2 km s-1:

We obtained a good fit (reduced $\chi^{2}$ = 1.2 for 5 degrees of freedom) for
all lines with the following values: N(A+E CH3OH) = ($1.4\pm 0.6$) $\times
10^{18}$ cm-2, T = ($110\pm 10$) K and nH2 = ($1.0^{+3}_{-0.5}$) $\times
10^{7}$ cm-3 and $\theta_{s}$ = ($0.15^{\prime\prime}\pm
0.10^{\prime\prime}$). Fig. 15 reports (i) the minimum $\chi^{2}$, with
respect to the temperature T and density nH2, as a function of the methanol
column density N(CH3OH-A). The same figure also shows the temperature-density
$\chi^{2}$ contour plot at the best fit N(CH3OH) (note that the x-axis reports
N(CH3OH)/2). Finally, the third panel of Fig. 15 shows the observed/predicted
line intensity ratio as a function of the line upper level energy $E_{up}$.

Figure 15: Upper panel: Results from the $\chi^{2}$ minimisation for the -2 km
s-1 component fitting simultaneously the A and E forms with a ratio equal to
unity and the 13C E methanol transition with a ratio of 68. The minimum has to
therefore be multiplied by two to obtain the A+E forms of methanol. Middle
panel: density and temperature range obtained for the best fit methanol column
density of 2 $\times$ (7 $\times$ 1017) cm-2 and source size of 0.15′′. Bottom
panel: Observed integrated intensities versus modelled ones as a function of
the upper energy level value with respect to the lowest value: 7.9 K for E
methanol (red filled circles) and 0 K for A methanol (red filled stars). The
13C E methanol is represented as a red filled triangle.

The 12C lines are predicted to be from moderately (the 234.69 GHz line has the
smallest value, $\tau=0.64$) to heavily (the 243.91 GHz line has the largest
value, $\tau\sim 12$) optically thick, while the 13C line is optically thin
($\tau=0.25$).

##### Component at +9.9 km s-1:

The best fit (reduced $\chi^{2}$ = 1.9) of the +9.9 km s-1 gives values very
similar to those obtained for the -2 km s-1 component, namely: N(CH3OH) =
($3.0\pm 0.8$) $\times 10^{18}$ cm-2, T = ($130\pm 10$) K and nH2 = ($2.5\pm
2.2$) $\times 10^{7}$ cm-3 and $\theta_{s}$ = (0.12′′ $\pm$ 0.10′′).

##### Component at +2.8 km s-1:

The best fit (reduced $\chi^{2}$ = 2.7) of the +2.8 km s-1 gives the following
values: N(CH3OH) = ($4.0\pm 1.0$) $\times 10^{18}$ cm-2, T = ($130\pm 10$) K
and nH2 = ($2.0\pm 0.5$) $\times 10^{6}$ cm-3 and $\theta_{s}$ =
($0.13^{\prime\prime}\pm 0.10^{\prime\prime}$).

##### Summary of the non-LTE analysis:

The three velocity components trace gas with similar characteristics: hot
(with a temperature around 110–130 K), dense (with a H2 density 2–20 $\times
10^{6}$ cm-3), enriched in methanol (with a methanol column density [1–5]
$\times 10^{18}$ cm-2) and relatively compact (0.12′′–0.15′′). Table 5 lists
the results of the analysis for the three components. Assuming that the
emission in each velocity component originates in a spherically symmetric
region, one can estimate the approximate H2 column density ($\sim 2\times
10^{23}$ cm-2) and, then, the methanol abundance, whose value ends up to be
very high, $\sim 10^{-5}$.
Compared to the results of the LTE RD analysis (see § 6.1), the non-LTE
analysis predicts slightly lower gas temperatures and much higher methanol
column densities, by about two orders of magnitude. These differences are due
to two major effects. First, the column densities calculated with the RD are
beam-averaged whilst the LVG analysis, where the emitting size is derived,
shows that the methanol emission is relatively compact. This explains the
large difference between the two estimates. Second, the RD in Fig. 14 show a
clear scatter of the points around the best-fit straight line, which indicates
optically thick lines and/or non-LTE effects. They both lead to a misleading
evaluation of the gas temperature (and, to a lesser extent, methanol column
density). Finally, even though the source size and the optical depths of the
lines can be corrected a posteriori (using the rotational diagram analysis),
non-LTE effects (e.g. sub-thermally populated lines), if present, cannot be
corrected unless performing a non-LTE analysis. In summary, in the RD
analysis, all of the above mentioned effects lead to an underestimation of the
methanol column density and incorrect gas temperature.

Table 5: Results from the non-LTE analysis.  | -2 km s-1 | 2.8 km s-1 | 9.9 km s-1
---|---|---|---
N(CH3OH) (cm-2) | ($1.4\pm 0.6$) $\times 10^{18}$ | ($4.0\pm 1.0$) $\times 10^{18}$ | ($3.0\pm 0.8$) $\times 10^{18}$
T (K) | $110\pm 10$ | $130\pm 10$ | $130\pm 10$
n${}_{H_{2}}$ (cm-3) | ($1.0^{+3}_{-0.5}$) $\times 10^{7}$ | ($2.0\pm 0.5$) $\times 10^{6}$ | ($2.5\pm 2.2$) $\times 10^{7}$
$\theta_{S}$ (′′) | $0.15^{\prime\prime}\pm 0.10^{\prime\prime}$ | $0.13^{\prime\prime}\pm 0.10^{\prime\prime}$ | 0.12${}^{\prime\prime}\pm 0.10^{\prime\prime}$

###  6.3 Dust opacity towards the binary system objects, 11A and 11B

As described in Sect. 2, [BHB2007] 11 is a binary system where the two objects
(11A and 11B) are embedded in their respective circumstellar disks (Alves et
al., 2019). The disks are both detected in the continuum at 0.94 cm with the
Karl G. Jansky Very Large Array (JVLA) and at 1.3 mm with ALMA. Following the
findings by De Simone et al. (2020) that the dust in front of the hot corino
of NGC1333 IRAS4A1 completely absorbs its methanol lines in the millimeter
wavelengths, here we aim to estimate the possible absorption of the methanol
emission specifically related to the compact disk scales around each of the
sources 11A and 11B. To this scope, we use the dust continuum observations by
Alves et al. (2019) at 225 GHz, who found a flux density $F_{225}$ equal to
$5.2\pm 0.53$ mJy towards 11A and $5.62\pm 0.45$ mJy towards 11B. The
deconvolved sizes are $7.3(\pm 1.3)\times 5.4(\pm 1.1)$ au2 and $4.9(\pm
1.1)\times 3.7(\pm 1.0)$ au2 for 11A and 11B, respectively. Thus, the 225 GHz
continuum emission is more compact in 11B than 11A, despite having a similar
flux density.

We can constrain the dust optical depth $\tau_{\nu}$ and temperature towards
each of the two sources using the equation:

$F_{\nu}=B_{\nu}(T_{d})\leavevmode\nobreak\
(1-e^{-\tau_{\nu}})\leavevmode\nobreak\ \Omega_{s}\leavevmode\nobreak\ ,$ (6)

where $B_{\nu}(T_{d})$ is the Planck function, which depends on the dust
temperature $T_{d}$, and $\Omega_{s}$ is the source solid angle, derived from
the continuum observations. The source solid angle is defined as $\sim
A/d^{2}$ where A is the source emitting area (derived from the sources size)
and $d^{2}$ is the distance to the sources. The dust optical depth can be
estimated by inverting Eq. 6, as follows:

$\tau_{\nu}=-\text{ln}\left(1-\frac{F_{\nu}}{B_{\nu}(T_{d})\leavevmode\nobreak\
\Omega_{s}}\right)\leavevmode\nobreak\ .$ (7)

Finally, using Eq. 7, we can estimate the possible dust absorption coefficient
using the following equation:

$e^{\tau_{\nu}}=\frac{I_{\nu}^{\text{pred}}}{I_{\nu}^{\text{obs}}}\leavevmode\nobreak\
.$ (8)

As we do not know the dust temperature, $T_{d}$, of the sources we derived the
dust optical depth for temperatures ranging between 100 and 500 K with steps
of 10 K from 100 K to 200 K, and by steps of 20 K from 200 to 500 K, following
the method described in Bouvier et al. (2021). The observed 225 GHz flux
provides a lower limit to $T_{d}$. Specifically, the condition
$F_{\nu}$/$\Omega_{s}\leq B_{\nu}(T_{d})$ implies $T_{d}\geq 130$ K in 11A and
$T_{d}\geq 300$ K in 11B (as it is more compact). Then, for each dust
temperature, we can derive the dust opacity at 225 GHz, reported in Fig. 16.

Figure 16: Dust optical depth $\tau_{\nu}$ at 225 GHz as a function of the
dust temperature Td, derived from the observations of Alves et al. (2019) and
following the method described in Bouvier et al. (2021). The lines show
$\tau_{\nu}$ as derived from Eq. 7. The errors are calculated using the error
propagation method described in Appendix C.2. of Bouvier et al. (2021), and
include the calibration uncertainty of 15$\%$ (Alves et al., 2019) and the
source size uncertainty. The left and right panels refer to 11A and 11B,
respectively.

The figure shows that $\tau_{\nu}$ is well constrained in the two sources,
except around the minimum Td for each of them, where the error bars become
very large. Specifically, in 11A $\tau_{\nu}$ varies from $5^{+48}_{-5}$ at
$T_{d}\sim 130$ K to $0.3^{+0.2}_{-0.1}$ at $T_{d}=500$ K; in 11B,
$\tau_{\nu}$ varies from $3^{+9}_{-3}$ at $T_{d}\sim 300$ K to
$0.8^{+0.7}_{-0.6}$ at $T_{d}=500$ K. The dust opacities tend to be optically
thick and, taking the largest dust optical depths gives $\tau_{\nu}\leq 53$
and $\tau_{\nu}\leq 12$ in 11A and 11B, respectively. Therefore, the possible
methanol lines from the hot corinos associated with 11A and 11B, if they
exist, can be completely attenuated by the foreground dust.

##  7 Origin of the observed methanol components

In the following, we discuss the possible origin of the three velocity
components detected in our methanol spectra. In order to better understand
this point, we created a position-velocity (PV) diagram for the methanol
transition at 243.916 GHz (E${}_{\mathrm{up}}\sim 50$ K), displayed in Fig.
17.

Figure 17: Position-velocity (PV) diagram obtained from the CH3OH emission at
243.916 GHz. The position angle (PA) and width of the PV cut is indicated in
the figure. Note that the direction of the cut used to produce the position-
velocity diagram is shown in Fig. 10 as a grey dashed line. The three velocity
components observed in the methanol spectra are also indicated.

The PV plot is produced from a cut oriented parallel to the velocity gradient
observed in the moment 1 map of the methanol emission (Fig. 10), whose
position angle (PA) is 140° East of North. The cut width is 0.5′′, whose value
is comparable to the angular resolution of the FAUST data, and encompasses
both core 11A and core 11B, separated by only 0.2′′. Unlike the H2CO PV plot,
which shows a smooth Keplerian profile over the velocity range (Alves et al.,
2019), a fragmented profile is clearly seen in the methanol PV plot. The three
substructures correspond to the three velocity components observed in the
methanol spectra (a similar distribution is observed at the higher Eup
transition).

Although we cannot locate the methanol emission with respect to the binary
system due to our limited angular resolution, we notice that blue- and red-
shifted emission in the high velocity channels where SNR is larger than 5
(-4.89 km s-1 in blue and 13.3 km s-1 in red) tends to be aligned with source
11B (Fig. 18, left panel), alike the high-velocity components of the CO
emission shown by Alves et al. (2019). The methanol emission at velocity
channels near the systemic velocity of the source ($\sim$ 3.6 km s-1) also
tends to peak near 11A. The three methanol components appear in a compact
configuration which is compatible with the compact methanol seen in the moment
0 maps (Fig. 5).

Figure 18: Left panel: Methanol intensity contours at 243.916 GHz plotted over
the dust continuum map of Alves et al. (2019). The contours show the methanol
emission at extreme velocity channels detected at a 3$\sigma$ level
(1$\sigma=1.8$ mJy beam-1). The blue and red contours correspond to emission
at the $-4.89$ km s-1 and $13.3$ km s-1 velocity channels, respectively. White
contours show emission (from a 20$\sigma$ level) from velocity channels near
the systemic velocity of the source (2.91 km s-1). The synthesised beam of the
methanol (FAUST) data is shown in the lower left corner. Right panel: Position
of intensity peaks (circles) from the two-dimensional Gaussian fit in each
velocity channels separated by $\sim 0.15$ km s-1 from each other . Colour
code for the edges of the circle is red for the 9.9 km s-1 methanol component,
green for the 2.8 km s-1 methanol component and blue for the -2 km s-1
methanol component, while the CO (2–1) high-velocity components have cyan. The
circle size is defined by the uncertainty on the absolute position of the
emission peak in each velocity component (largest circle has $\sim
0.02^{\prime\prime}$)

It is clear from Fig. 6, 7 and 8 that the three velocity components are not
completely spectrally independent and that they are affected by blending from
one another. We present in Fig. 19 the integrated intensity and velocity field
maps from the 243 GHz methanol transition, for the three velocity components
in the [-7–0] km s-1 range for the -2 km s-1 component, the [0–6] km s-1 range
for the 2.8 km s-1 component and the [6–16] km s-1 range for the 9.9 km s-1
component. The three positions are clearly identified in the moment 0 maps:
the 2.8 km s-1 component in between [BHB2007] 11 A and [BHB2007] 11 B, while
the -2 and 9.9 km s-1 are located North-West and South-East from [BHB2007] 11
B, respectively. There is no clear evidence of velocity structure in these two
velocity range, which points to the conclusion of the results from a compact
shock emission (see Sec. 7.3). The 2.8 km s-1 seems to be more sensitive to
the disk rotation (like the H2CO centroid map in Alves et al., 2019) and that
could explain the gradient that is seen more clearly than in the other two
components. Also, Fig. 18 (right panel), must be analysed with caution as the
overlap of velocity ranges from one component to another can be misleading to
conclude that we have an elongated structure for the methanol emission. We
added, on this Figure, coloured borders to identify the three velocity
components observed in our methanol observations. However, higher spatial
resolution observations of methanol are necessary to determine the velocity
structure of methanol accurately.

Figure 19: Top: Moment 0 map of the high spectral resolution methanol
transition at 243.916 GHz ($\rm E_{u}$=49.66 K) for the three components
([-7–0] km s-1 for the -2 km s-1 component, [0–6] km s-1 for the 2.8 km s-1
component and [6–16] km s-1 for the 9.9 km s-1 component,). Contours start at
4$\sigma$ at every 4$\sigma$. The ellipse in the bottom left corner represents
the ALMA synthesised beam. Both source A and B identified by Alves et al.
(2019) are indicated as white filled circles. Bottom: Moment 1 map of the high
spectral resolution methanol transition at 243.916 GHz ($\rm E_{u}$=49.66 K)
for the three components.

Since the emission in each velocity channel is compact and centrally peaked,
we performed two-dimensional (2D) Gaussian fits on the emission in each
channel to obtain the position of their intensity peak. The accuracy on the
relative position is given by $\Theta/\mathrm{(2\times SNR)}$, where $\Theta$
is the synthesised beam size and SNR is the signal-to-noise ratio of the peak
with respect to the map noise (Condon, 1997; Condon et al., 1998). Thus the
uncertainty in the position is inversely proportional to the SNR in each
velocity channel. Centroid fitting to the compact molecular emission yields
astrometry with precisions better than those of the spatial resolution in the
case of high SNR. For this calculation, we considered only intensity peaks
brighter than 5 times its Gaussian fit error and SNR larger than 10.0 (which
corresponds to a position accuracy better than 0.02′′). The right panel of
Fig. 18 shows the 2D Gaussian centroid map with the location of each methanol
emission peak (black circle) as a function of velocity. The velocity
components satisfying the conditions above span from $-$4.1 to 12.7 km s-1.
It is noticeable that the methanol emission with velocities between 0 and 8 km
s-1 tends to lie in the region in between sources 11A and 11B, while the gas
with velocities $<$0 km s-1 and $>$8 km s-1 seems to approach source B, as
also seen in the CO (2–1) observations presented in Alves et al. (2017) and
Alves et al. (2020). Their analysis shows an increasing velocity towards 11 B
that seems to indicate acceleration of infalling gas from the circumbinary
disk onto 11 B. This can be shown on the right side of Fig. 18 where we also
present the CO emission as circles with green borders, as opposed to the
methanol emission as circles with black borders. The CO emission observed by
Alves et al. (2017) and shown in the left panel of our Fig. 2 traces primarily
large-scale outflowing gas emission, launched from a distance of $\sim$ 100 au
from the disk centre and propagating perpendicular to the envelope major axis.
However, velocity components faster than the outflows are detected within the
circumbinary disk at only a few au. These high-velocity CO components reach up
to 15 km s-1 and the blue- and red-shifted velocities (VLSR $<$ -1.5 km s-1
and VLSR $>$ 9 km s-1 respectively) are centred on and aligned with 11 B, the
higher velocities being closest to the position of the protostar. Note that no
high velocity components are seen near 11 A. The increasing velocity toward
[BHB2007] 11 B indicates acceleration of infalling gas from the circumbinary
disk onto [BHB2007] 11 B.
From our methanol analysis, an increasing velocity is not as clear as in CO,
possibly due to our lower spatial resolution, but also due to the fact that
the three velocity components identified in our methanol spectra are partially
overlapping. The informations provided by the PV diagram and centroid maps
provide constrains on the origin of the three velocity components, as follows.

###  7.1 The -2.0 and +9.9 km s-1 components:

Based on the arguments above, these two velocity components are likely
associated with the gas streaming towards 11B. The most extreme components,
$-5$ km s-1 and 13 km s-1, are consistent with the high-velocity components
observed in CO lines distributed along the filaments and confined within the
circumbinary disk (see also higher spatial resolution observations by Alves et
al., 2019, and their Fig. 2 and S2). These components exceed the Keplerian
velocities observed in the H2CO maps of Alves et al. (2019), -3 km
s${}^{-1}\lesssim\mathrm{v}_{Kep}\lesssim 12$ km s-1), and are distributed
around 11B. Our non-LTE analysis of the methanol lines indicates that this gas
is very warm (100–140 K), dense ($\sim 10^{7}$ cm-3) and very enriched in
methanol (abundance w.r.t H${}_{2}\sim 10^{-5}$). We will discuss the physical
origin of gaseous methanol later in this section.

###  7.2 The +2.8 km s-1 component:

This component seems rather associated with 11A when considering the arguments
based on the velocity field, position-velocity diagram and centroid maps
above. This gas is also warm (120–140 K), dense ($\sim 2\times 10^{6}$ cm-3)
and very enriched in methanol (abundance w.r.t H${}_{2}\sim 10^{-5}$), which
would point to a similar origin of the methanol emission to the other two
components. Moreover, the H2CO (E${}_{\mathrm{up}}\sim 70$ K) observations of
Alves et al. (2019), taken at comparable spectral resolution but a factor
$\sim 2$ better angular resolution, show relatively warm gas associated with
11A. In fact, the emission observed in the velocity range of 2.5 – 5.0 km s-1
is spatially coincident with 11A, which is consistent with our findings (see
figure S3 in Alves et al., 2019). This component is close to the systemic
velocity of 3.6 km s-1 and could be tracing (partially) the keplerian motion
of the disk (similar to H2CO), so a velocity gradient is expected and
identified in our Fig. 19 (middle Figure, bottom panel).

Nevertheless, due to the limited angular resolution of our maps, we should not
completely discard that this velocity component has some contribution from 11B
or from gas located in between sources.

###  7.3 Origin of the gaseous methanol: shock versus thermal desorption

Methanol is known to have a very low abundance $\leq 10^{-8}$ in cold objects
(e.g. Friberg et al., 1988; Nagy et al., 2019) while its abundance is high
(10-7–105) in hot cores/corinos (e.g. Gibb et al., 2000; Cazaux et al., 2003)
and molecular outflow shocks (e.g. Bachiller et al., 1995; Codella et al.,
2020). It is commonly accepted that methanol is indeed synthesised on the
grain surfaces (e.g. Watanabe & Kouchi, 2002; Rimola et al., 2014) during the
cold prestellar phase and released from the grain mantles into the gas phase
by thermal and non-thermal processes. Hot cores/corinos are therefore the
results of thermal processes (e.g. Maret et al., 2005; Taquet et al., 2016)
while molecular outflow triggers non-thermal desorption via shocks (e.g.
Caselli et al., 1997; Jiménez-Serra et al., 2008).

The temperature derived from the non-LTE analysis of the methanol lines tells
us that the gas is hot and dense. The latter would also imply that the dust
and gas are thermally coupled (e.g. Goldsmith, 2001) and, hence, also the dust
is warm enough for methanol to be thermally desorbed, based on the recent
estimates of the methanol binding energy by (Ferrero et al., 2020). These
authors found the CO binding energy ranges between $\sim$4400 and $\sim$6500
K, which would correspond to a dust sublimation temperature of about 80 to 120
K, assuming that the grain mantles have been warmed up since $\sim 10^{4}$
yr151515Note that these sublimation temperatures could be lower by less than
10 K if the heating of the ices is 1 Myr instead.. Of course, it is possible
that methanol is trapped in the water-rich ices, so that the sublimation
temperature could be dominated by the co-desorption of methanol with water.
Again based on the Ferrero et al. (2020) work, this would happen at about 110
K, namely in between the dust sublimation temperature of a pure methanol ice.

A first question to answer is whether the measured temperature, 110–130 K (§
6.2), is compatible with the warming of the dust from the two sources or it
necessitates a non-thermal mechanism. To this end, we can estimate the
approximate dust temperature of a dust grain heated by a $L_{\star}$ source at
a distance $r$ from it. When the dust is optically thin, the dust temperature
profile heated by a central source can be approximated by the following
equation (Ceccarelli et al., 2000a):

$\rm
T_{d}[K]=75\left[\frac{L_{\star}}{27L_{\odot}}\right]^{0.25}\left[\frac{r}{150au}\right]^{-0.5}.$
(9)

Considering that the two sources 11A and 11B have a total bolometric
luminosity of 4.4 L⊙ Sandell et al. (2021) and that the distance between them
is 28 au (0.2′′), the dust temperature would be $\sim$93 K. As already stated
in Sec. 6.3, the dust is optically thick, therefore the dust temperature
should be above $\sim$93 K. This means that all the dust in between 11A and
11B could be warm enough for the methanol to sublimate, within the
uncertainties discussed above on the frozen methanol sublimation temperature.
A fortiori, if 11A and 11B host one or two hot corinos, the observed methanol
could just originate from them. However, the above analysis on the location of
the gas (§ 7.1 and 7.2) and the dust optical depth towards 11A and 11B (§ 6.3)
is not in favour of the hypothesis that the observed hot methanol originates
in the 11A or 11B cores, therefore invalidating their hot corino nature.

Alternatively, the observed methanol could be the result of the sputtering of
the grain mantles in shocks (e.g. Caselli et al., 1997; Jiménez-Serra et al.,
2008; De Simone et al., 2020; Codella et al., 2020) created by the streaming
of the gas towards 11A and 11B and impacting the quiescent gas of the
circumbinary envelope/disk or, possibly, the two circumstellar disks. The mass
contained in the shocked gas traced by methanol would then be about 10-6 M⊙,
namely a very minor fraction of the dynamical mass ($\sim$ 2.2 M⊙) or even the
mass of the larger circumbinary disk ($\sim$ 0.08 M⊙ Alves et al., 2019).

Indeed, the gas kinematics in a binary system is expected to be more complex
compared to a simple protostar formation, with accretion shocks and structures
which are related to the transition from the circumbinary material to the
circumstellar disks (Matsumoto et al., 2019). Alves et al. (2019) computed a
mass accretion rate from the circumbinary disk into the circumstellar disk of
$\sim 1.1\times 10^{-5}$ M⊙ yr-1, which is also consistent with other Class
0/I protostars. Also, the infall motion, traced by the high velocity CO, is
perfectly consistent with the dynamical mass of the system. A similar
situation as in [BHB2007] 11 is seen in the young binary system IRAS16293 A
where some molecular tracers such as HNCO, NH2CHO and t-HCOOH coincide with
the location of the dust substructures detected in the continuum emission,
away from the the two binaries (Maureira et al., 2020). Also, the CH3OH
emission and the HCOOCH3 molecular emission detected by Oya et al. (2016)
likely originate in the ring-like region with a radius of 50 au surrounding
the protostar, based on their kinematic structures (Oya & Yamamoto, 2020),
with temperatures rising to more than 300 K. The evidence presented here (dust
opacity, compactness of the three components, centroid analysis) would seem to
point to the hypothesis of a shocked region due to the large scale streaming
material feeding the proto-binary system (see Fig. 18). However, since the
beam of our observations is relatively large with respect to the supposed
shock structures, this hypothesis will need to be confirmed by future high-
angular resolution observations.

##  8 Conclusions

We have analysed the emission of methanol measured towards the Class 0/I
protostar system [BHB2007] 11 and obtained within the ALMA FAUST large
program. The Band 3 and Band 6 continuum images show that the dust continuum
emission is faint and it extends beyond the northwest-southeast envelope
previously detected by Alves et al. (2019). A series of methanol transitions
are detected towards this source and reveal the presence of hot methanol gas
arising from three different velocity components centred at VLSR = -2, 2.8 and
9.9 km s-1. The overall emission of hot methanol peaks at the location of the
circumbinary disk. The moment 1 maps of the methanol emission show a velocity
gradient with the blue-shifted gas located towards the northwest and the red-
shifted gas peaking towards the southeast, consistent with the gas kinematics
previously detected in H2CO (Alves et al., 2019). Non-LTE analysis shows that
the methanol emission is compact ($\sim$ 0.15′′), the gas is hot (100–140 K)
and dense (2 $\times$ 106– 2 $\times$ 107 cm-3) and the inferred methanol
column densities are a few 1018 cm-2. Although the binary system, [BHB2007] 11
A and [BHB2007] 11 B, cannot be resolved in the FAUST images, the 2D Gaussian
centroid map of the hot methanol line at 243.916 GHz shows that this emission
arises from the region associated with [BHB2007] 11 A and North-West and
South-East from [BHB2007] 11 B. This could either be due to the fact that the
dust emission is very optically thick towards the hot corinos and/or the hot
methanol gas is associated with shocked gas within an accretion streamer
falling onto source [BHB2007] 11 B. This idea is supported by the fact that
the methanol emission is compact, located nearby sources [BHB2007] 11 A and B,
within the infalling CO gas detected at extreme velocities $<-$1.5 km s-1 and
$>$9 km s-1. However, higher angular resolution observations are needed to
disentangle between these two possibilities.

###### Acknowledgements.

This project has received funding within the European Union’s Horizon 2020
research and innovation program from the European Research Council (ERC) for
the project The Dawn of Organic Chemistry (DOC), grant agreement No 741002,
and from the Marie Sklodowska-Curie for the project Astro-Chemical Origins
(ACO), grant agreement No 811312. I.J.-S. has received partial support from
the Spanish State Research Agency (project number PID2019-105552RB-C41). D.J.
is supported by NRC Canada and by an NSERC Discovery Grant. SY thanks the
support by Grant-in-Aids from Ministry of Education, Culture, Sports, Science,
and Technologies of Japan (18H05222). 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.

## References

  * Agurto-Gangas et al. (2019) Agurto-Gangas, C., Pineda, J. E., Szűcs, L., et al. 2019, A&A, 623, A147
  * Aikawa et al. (2020) Aikawa, Y., Furuya, K., Yamamoto, S., & Sakai, N. 2020, ApJ, 897, 110
  * Alves et al. (2019) Alves, F. O., Caselli, P., Girart, J. M., et al. 2019, Science, 366, 90
  * Alves et al. (2020) Alves, F. O., Cleeves, L. I., Girart, J. M., et al. 2020, ApJ, 904, L6
  * Alves et al. (2017) Alves, F. O., Girart, J. M., Caselli, P., et al. 2017, A&A, 603, L3
  * Alves et al. (2018) Alves, F. O., Girart, J. M., Padovani, M., et al. 2018, A&A, 616, A56
  * André et al. (1993) André, P., Ward-Thompson, D., & Barsony, M. 1993, ApJ, 406, 122
  * Bachiller et al. (1995) Bachiller, R., Liechti, S., Walmsley, C. M., & Colomer, F. 1995, A&A, 295, L51
  * Bacmann et al. (2012) Bacmann, A., Taquet, V., Faure, A., Kahane, C., & Ceccarelli, C. 2012, A&A, 541, L12
  * Balucani et al. (2015) Balucani, N., Ceccarelli, C., & Taquet, V. 2015, MNRAS, 449, L16
  * Bertin et al. (2016) Bertin, M., Romanzin, C., Doronin, M., et al. 2016, ApJ, 817, L12
  * Bizzocchi et al. (2014) Bizzocchi, L., Caselli, P., Spezzano, S., & Leonardo, E. 2014, A&A, 569, A27
  * Bottinelli et al. (2004) Bottinelli, S., Ceccarelli, C., Lefloch, B., et al. 2004, ApJ, 615, 354
  * Bouvier et al. (2021) Bouvier, M., López-Sepulcre, A., Ceccarelli, C., et al. 2021, A&A, 653, A117
  * Brooke et al. (2007) Brooke, T. Y., Huard, T. L., Bourke, T. L., et al. 2007, ApJ, 655, 364
  * Caselli & Ceccarelli (2012) Caselli, P. & Ceccarelli, C. 2012, A&A Rev., 20, 56
  * Caselli et al. (1997) Caselli, P., Hartquist, T. W., & Havnes, O. 1997, A&A, 322, 296
  * Cazaux et al. (2003) Cazaux, S., Tielens, A. G. G. M., Ceccarelli, C., et al. 2003, ApJ, 593, L51
  * Ceccarelli et al. (2017) Ceccarelli, C., Caselli, P., Fontani, F., et al. 2017, ApJ, 850, 176
  * Ceccarelli et al. (2007) Ceccarelli, C., Caselli, P., Herbst, E., Tielens, A. G. G. M., & Caux, E. 2007, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil, 47
  * Ceccarelli et al. (2000a) Ceccarelli, C., Castets, A., Caux, E., et al. 2000a, A&A, 355, 1129
  * Ceccarelli et al. (2000b) Ceccarelli, C., Loinard, L., Castets, A., Faure, A., & Lefloch, B. 2000b, A&A, 362, 1122
  * Ceccarelli et al. (2003) Ceccarelli, C., Maret, S., Tielens, A. G. G. M., Castets, A., & Caux, E. 2003, A&A, 410, 587
  * Chahine et al. (2022) Chahine, L., López-Sepulcre, A., Neri, R., et al. 2022, A&A, 657, A78
  * Charnley et al. (1992) Charnley, S. B., Tielens, A. G. G. M., & Millar, T. J. 1992, ApJ, 399, L71
  * Codella et al. (2020) Codella, C., Ceccarelli, C., Bianchi, E., et al. 2020, A&A, 635, A17
  * Codella et al. (2021) Codella, C., Ceccarelli, C., Chandler, C., et al. 2021, Frontiers in Astronomy and Space Sciences, 8, 227
  * Condon (1997) Condon, J. J. 1997, PASP, 109, 166
  * Condon et al. (1998) Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693
  * Covey et al. (2010) Covey, K. R., Lada, C. J., Román-Zúñiga, C., et al. 2010, ApJ, 722, 971
  * De Simone et al. (2020) De Simone, M., Ceccarelli, C., Codella, C., et al. 2020, ApJ, 896, L3
  * Duarte-Cabral et al. (2012) Duarte-Cabral, A., Chrysostomou, A., Peretto, N., et al. 2012, A&A, 543, A140
  * Dubernet et al. (2012) Dubernet, M., Nenadovic, L., & Doronin, N. 2012, in Astronomical Society of the Pacific Conference Series, Vol. 461, Astronomical Data Analysis Software and Systems XXI, ed. P. Ballester, D. Egret, & N. P. F. Lorente, 335
  * Dubernet et al. (2013) Dubernet, M. L., Alexander, M. H., Ba, Y. A., et al. 2013, A&A, 553, A50
  * Dzib et al. (2018) Dzib, S. A., Loinard, L., Ortiz-León, G. N., Rodríguez, L. F., & Galli, P. A. B. 2018, ApJ, 867, 151
  * Favre et al. (2018) Favre, C., Fedele, D., Semenov, D., et al. 2018, ApJ, 862, L2
  * Ferrero et al. (2020) Ferrero, S., Zamirri, L., Ceccarelli, C., et al. 2020, ApJ, 904, 11
  * Flower & Pineau des Forets (1995) Flower, D. R. & Pineau des Forets, G. 1995, MNRAS, 275, 1049
  * Forbrich et al. (2009) Forbrich, J., Lada, C. J., Muench, A. A., Alves, J., & Lombardi, M. 2009, ApJ, 704, 292
  * Forbrich et al. (2010) Forbrich, J., Posselt, B., Covey, K. R., & Lada, C. J. 2010, ApJ, 719, 691
  * Friberg et al. (1988) Friberg, P., Madden, S. C., Hjalmarson, A., & Irvine, W. M. 1988, A&A, 195, 281
  * Garrod et al. (2008) Garrod, R. T., Widicus Weaver, S. L., & Herbst, E. 2008, ApJ, 682, 283
  * Gibb et al. (2000) Gibb, E., Nummelin, A., Irvine, W. M., Whittet, D. C. B., & Bergman, P. 2000, ApJ, 545, 309
  * Goldsmith (2001) Goldsmith, P. F. 2001, ApJ, 557, 736
  * Goldsmith & Langer (1999) Goldsmith, P. F. & Langer, W. D. 1999, ApJ, 517, 209
  * Hara et al. (2013) Hara, C., Shimajiri, Y., Tsukagoshi, T., et al. 2013, ApJ, 771, 128
  * Jaber et al. (2014) Jaber, A. A., Ceccarelli, C., Kahane, C., & Caux, E. 2014, ApJ, 791, 29
  * Jiménez-Serra et al. (2008) Jiménez-Serra, I., Caselli, P., Martín-Pintado, J., & Hartquist, T. W. 2008, A&A, 482, 549
  * Jiménez-Serra et al. (2016) Jiménez-Serra, I., Vasyunin, A. I., Caselli, P., et al. 2016, ApJ, 830, L6
  * Jiménez-Serra et al. (2021) Jiménez-Serra, I., Vasyunin, A. I., Spezzano, S., et al. 2021, ApJ, 917, 44
  * Jin & Garrod (2020) Jin, M. & Garrod, R. T. 2020, ApJS, 249, 26
  * Jørgensen et al. (2016) Jørgensen, J. K., van der Wiel, M. H. D., Coutens, A., et al. 2016, A&A, 595, A117
  * Lee et al. (2019) Lee, C.-F., Codella, C., Li, Z.-Y., & Liu, S.-Y. 2019, ApJ, 876, 63
  * Maret et al. (2005) Maret, S., Ceccarelli, C., Tielens, A. G. G. M., et al. 2005, A&A, 442, 527
  * Matsumoto et al. (2019) Matsumoto, T., Saigo, K., & Takakuwa, S. 2019, ApJ, 871, 36
  * Maureira et al. (2020) Maureira, M. J., Pineda, J. E., Segura-Cox, D. M., et al. 2020, ApJ, 897, 59
  * Milam et al. (2005) Milam, S. N., Savage, C., Brewster, M. A., Ziurys, L. M., & Wyckoff, S. 2005, ApJ, 634, 1126
  * Minissale et al. (2016) Minissale, M., Dulieu, F., Cazaux, S., & Hocuk, S. 2016, A&A, 585, A24
  * Müller et al. (2005) Müller, H. S. P., Schlöder, F., Stutzki, J., & Winnewisser, G. 2005, Journal of Molecular Structure, 742, 215
  * Nagy et al. (2019) Nagy, Z., Spezzano, S., Caselli, P., et al. 2019, A&A, 630, A136
  * Öberg et al. (2015) Öberg, K. I., Guzmán, V. V., Furuya, K., et al. 2015, Nature, 520, 198
  * Öberg et al. (2021) Öberg, K. I., Guzmán, V. V., Walsh, C., et al. 2021, ApJS, 257, 1
  * Onishi et al. (1999) Onishi, T., Kawamura, A., Abe, R., et al. 1999, PASJ, 51, 871
  * Oya et al. (2016) Oya, Y., Sakai, N., López-Sepulcre, A., et al. 2016, ApJ, 824, 88
  * Oya et al. (2017) Oya, Y., Sakai, N., Watanabe, Y., et al. 2017, ApJ, 837, 174
  * Oya & Yamamoto (2020) Oya, Y. & Yamamoto, S. 2020, ApJ, 904, 185
  * Pickett et al. (1998) Pickett, H. M., Poynter, R. L., Cohen, E. A., et al. 1998, J. Quant. Spec. Radiat. Transf., 60, 883
  * Pineda et al. (2022) Pineda, J., Arzoumanian, D., Andr , P., et al. 2022, To appear in Protostars and Planets VII [arXiv:2205.03935]
  * Pineda et al. (2020) Pineda, J. E., Segura-Cox, D., Caselli, P., et al. 2020, Nature Astronomy, 4, 1158
  * Punanova et al. (2022) Punanova, A., Vasyunin, A., Caselli, P., et al. 2022, ApJ, 927, 213
  * Rabli & Flower (2010) Rabli, D. & Flower, D. R. 2010, MNRAS, 406, 95
  * Rathborne et al. (2008) Rathborne, J. M., Lada, C. J., Muench, A. A., Alves, J. F., & Lombardi, M. 2008, ApJS, 174, 396
  * Redaelli et al. (2017) Redaelli, E., Alves, F. O., Caselli, P., et al. 2017, ApJ, 850, 202
  * Riaz et al. (2009) Riaz, B., Martín, E. L., Bouy, H., & Tata, R. 2009, ApJ, 700, 1541
  * Rimola et al. (2014) Rimola, A., Taquet, V., Ugliengo, P., Balucani, N., & Ceccarelli, C. 2014, A&A, 572, A70
  * Román-Zúñiga et al. (2010) Román-Zúñiga, C. G., Alves, J. F., Lada, C. J., & Lombardi, M. 2010, ApJ, 725, 2232
  * Sakai & Yamamoto (2013) Sakai, N. & Yamamoto, S. 2013, Chemical Reviews, 113, 8981
  * Sandell et al. (2021) Sandell, G., Reipurth, B., Vacca, W. D., & Bajaj, N. S. 2021, ApJ, 920, 7
  * Scibelli & Shirley (2020) Scibelli, S. & Shirley, Y. 2020, ApJ, 891, 73
  * Shingledecker et al. (2018) Shingledecker, C. N., Tennis, J., Le Gal, R., & Herbst, E. 2018, ApJ, 861, 20
  * Spezzano et al. (2020) Spezzano, S., Caselli, P., Pineda, J. E., et al. 2020, A&A, 643, A60
  * Spezzano et al. (2022) Spezzano, S., Fuente, A., Caselli, P., et al. 2022, A&A, 657, A10
  * Taquet et al. (2016) Taquet, V., Wirström, E. S., & Charnley, S. B. 2016, ApJ, 821, 46
  * Testi et al. (2014) Testi, L., Birnstiel, T., Ricci, L., et al. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning, 339
  * Vastel et al. (2014) Vastel, C., Ceccarelli, C., Lefloch, B., & Bachiller, R. 2014, ApJ, 795, L2
  * Vasyunin et al. (2017) Vasyunin, A. I., Caselli, P., Dulieu, F., & Jiménez-Serra, I. 2017, ApJ, 842, 33
  * Wakelam et al. (2021) Wakelam, V., Dartois, E., Chabot, M., et al. 2021, A&A, 652, A63
  * Walsh et al. (2016) Walsh, C., Loomis, R. A., Öberg, K. I., et al. 2016, ApJ, 823, L10
  * Watanabe & Kouchi (2002) Watanabe, N. & Kouchi, A. 2002, ApJ, 571, L173
  * Yang et al. (2021) Yang, Y.-L., Sakai, N., Zhang, Y., et al. 2021, ApJ, 910, 20