11institutetext: Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS,
Laboratoire Lagrange, France 22institutetext: European Southern Observatory,
Alonso de Córdova, 3107 Vitacura, Santiago, Chile 33institutetext: Department
of Astrophysics, University of Vienna, Türkenschanzstrasse 17 44institutetext:
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany 55institutetext: European Southern Observatory, Karl-Schwarzschild-
Str. 2, 85748 Garching, Germany 66institutetext: Konkoly Observatory, Research
Centre for Astronomy and Earth Sciences, Eötvös Loránd Research Network
(ELKH), Konkoly-Thege Miklós út 15-17, H-1121 Budapest, Hungary
77institutetext: Max Planck Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany 88institutetext: Leiden Observatory, Leiden University,
Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands 99institutetext: I.
Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937, Köln,
Germany 1010institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000, Grenoble,
France 1111institutetext: NASA Goddard Space Flight Center, Astrophysics
Division, Greenbelt, MD 20771, USA 1212institutetext: Anton Pannekoek
Institute for Astronomy, University of Amsterdam, Science Park 904, 1090 GE
Amsterdam, The Netherlands 1313institutetext: Nicolaus Copernicus Astronomical
Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland
1414institutetext: Department of Astrophysics/IMAPP, Radboud University, P.O.
Box 9010, 6500 GL Nijmegen, The Netherlands 1515institutetext: SRON
Netherlands Institute for Space Research Sorbonnelaan 2, 3584 CA Utrecht, The
Netherlands 1616institutetext: Institut für Theoretische Physik und
Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24118,
Kiel, Germany

# Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE

J. Drevon , Corresponding author: Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE<EMAIL_ADDRESS>F. Millour,
Corresponding author: Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE<EMAIL_ADDRESS>P. Cruzalèbes Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE C. Paladini
Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE J. Hron Locating dust and molecules
in the inner circumstellar environment of R Sculptoris with MATISSELocating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSE A. Meilland Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE F. Allouche
Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE K.-H. Hofmann Locating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE S. Lagarde Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
B. Lopez Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE A. Matter Locating dust
and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE R. Petrov Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
S. Robbe-Dubois Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE D. Schertl
Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE P. Scicluna Locating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE M. Wittkowski Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
G. Zins Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE
P. Ábrahám Locating dust and molecules in the inner circumstellar environment
of R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE P. Antonelli Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE U. Beckmann Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
P. Berio Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE F. Bettonvil Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE A. Glindemann Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
U. Graser Locating dust and molecules in the inner circumstellar environment
of R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE M. Heininger Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE Th. Henning Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
J. W. Isbell Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE W. Jaffe Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE L. Labadie Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
C. Leinert Locating dust and molecules in the inner circumstellar environment
of R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE M. Lehmitz Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE S. Morel Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
K. Meisenheimer Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE A. Soulain , Now
at the Sydney Institute for Astronomy (SIfA), School of Physics, The
University of Sydney, NSW 2006, AustraliaLocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
J. Varga Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE G. Weigelt Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
J. Woillez Locating dust and molecules in the inner circumstellar environment
of R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE J.-C. Augereau Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE R. van Boekel Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
L. Burtscher Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE W.C. Danchi
Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE C. Dominik Locating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE V. Gámez Rosas Locating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
V. Hocdé Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE M.R. Hogerheijde
Locating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
L. Klarmann Locating dust and molecules in the inner circumstellar environment
of R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE E. Kokoulina Locating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE J. Leftley Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with MATISSE
P. Stee Locating dust and molecules in the inner circumstellar environment of
R Sculptoris with MATISSELocating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSE F. Vakili Locating dust
and molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSE R. Waters Locating dust and molecules in the inner
circumstellar environment of R Sculptoris with MATISSELocating dust and
molecules in the inner circumstellar environment of R Sculptoris with
MATISSELocating dust and molecules in the inner circumstellar environment of R
Sculptoris with MATISSELocating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSE S. Wolf Locating dust and molecules
in the inner circumstellar environment of R Sculptoris with MATISSELocating
dust and molecules in the inner circumstellar environment of R Sculptoris with
MATISSE G. Yoffe Locating dust and molecules in the inner circumstellar
environment of R Sculptoris with MATISSELocating dust and molecules in the
inner circumstellar environment of R Sculptoris with MATISSE

(Received 22 June 2021 / Accepted 10 June 2022)

###### Abstract

Context. Asymptotic giant branch (AGB) stars are one of the main sources of
dust production in the Galaxy. However, it is not yet clear what this process
looks like and where the dust happens to be condensing in the circumstellar
environment.

Aims. By characterizing the location of the dust and the molecules in the
close environment of an AGB star, we aim to achieve a better understanding the
history of the dust formation process.

Methods. We observed the carbon star R Scl with the thermal-infrared
VLTI/MATISSE instrument in $L$\- and $N$-bands. The high angular resolution of
the VLTI observations (as small as 4.4 mas in the $L$-band and 15 mas in the
$N$-band with ATs), combined with a large uv-plane coverage allowed us to use
image reconstruction methods. To constrain the dust and molecules’ location,
we used two different methods: one using MIRA image reconstruction algorithm
and the second using the 1D code RHAPSODY.

Results. We found evidence of C2H2 and HCN molecules between 1 and 3.4
$R_{\star}$ which is much closer to the star than the location of the dust
(between 3.8 and 17.0 $R_{\star}$). We also estimated a mass-loss rate of
$1.2\pm 0.4\times 10^{-6}M_{\odot}\leavevmode\nobreak\ \rm{yr}^{-1}$. In the
meantime, we confirmed the previously published characteristics of a thin dust
shell, composed of amorphous carbon (amC) and silicon carbide (SiC). However,
no clear SiC feature has been detected in the MATISSE visibilities. This might
be caused by molecular absorption that can affect the shape of the SiC band at
11.3 $\mu$m.

Conclusions. The appearance of the molecular shells is in good agreement with
predictions from dynamical atmosphere models. For the first time, we co-
located dust and molecules in the environment of an AGB star. We confirm that
the molecules are located closer to the star than the dust. The MIRA images
unveil the presence of a clumpy environment in the fuzzy emission region
beyond 4.0 $R_{\star}$. Furthermore, with the available dynamic range and
angular resolution, we did not detect the presence of a binary companion. To
solve this problem, additional observations combining MATISSE and SAM-VISIR
instrument should enable this detection in future studies.

###### Key Words.:

techniques: interferometric - stars: AGB and post-AGB - stars: carbon - stars:
atmospheres - stars: mass-loss - stars: individual: R Scl

##  1 Introduction

R Scl is a bright infrared source known to be a semi-regular pulsating C-rich
asymptotic giant branch (AGB) star (Srb) with a pulsation period of about 370
days (Samus et al., 2009) and a mass-loss rate (published in the literature)
ranging from $2\times 10^{-10}\,M_{\sun}\leavevmode\nobreak\ \rm{yr}^{-1}$
(Brunner et al., 2018) up to $1.6\times 10^{-6}\,M_{\sun}\leavevmode\nobreak\
\rm{yr}^{-1}$ (De Beck et al., 2010). Carbon stars are spectrally classified
in R or N-type stars supplementing the classical hotter O, B, A, F, G, K, and
M spectral types. While the N-type stars are colder than R stars, they are
marked with a number identifying the effective temperature range of the star’s
location. Barnbaum et al. (1996) classified R Scl as a C-N5-type star in the
revised MK classification of Keenan (1993), with C/O$\approx 1.4$ (Hron et
al., 1998). Its distance is estimated to be $360\pm 50$ pc by Maercker et al.
(2018), and measured as 440$\pm$30 pc (DR2) and $393\pm 12$ pc (DR3) by Gaia
Collaboration (2018). These two Gaia distances are marginally compatible
within 1.5 $\sigma$ with the values from Maercker et al. (2018) and with each
other; therefore, we retained the conservative value of Maercker et al. (2018)
($360\pm 50$ pc) for the purposes of this work.

R Scl is one of just a few detached shell objects (Olofsson et al., 1996) and
ALMA observations revealed a spiral structure and the presence of clumpy and
non-centrosymmetric structures inside the shell. Maercker et al. (2012)
suggested it could be explained by the presence of a so far unseen companion
of $0.25\,M_{\odot}$ hidden at $60$ au ( 34 R⋆) in the dusty shell.
VLTI/PIONIER images do not show that companion, but instead show an extended
photosphere with a dominant spot that is very likely to be of a convective
origin (Wittkowski et al., 2017). Polarimetric observations confirm the clumpy
structure of the dust forming region (Yudin & Evans, 2002). However, such
clumps were not detected in the MIDI observations of Sacuto et al. (2011).
Such a non-detection was very likely due to the limitations in terms of uv-
coverage and visibility sampling of MIDI, which is not optimized for the
detection of large-scale asymmetric structures (Paladini et al., 2012, 2017).

This paper is organized as follows. In Section 2, we present new VLTI/MATISSE
observations in $L$\- and $N$-bands of the AGB star R Scl, as well as the data
reduction processes. In Section 3, we present the photometric data of this
star and we derived a hydrostatic model to describe the central source. The
resulting best-fit model is used as input for the DUSTY modeling used to
interpret both the photometry and the interferometric MATISSE data. In
Sections 4 and 5, we present the very first chromatic images in the $L$ (3–4
$\mu$m) and $N$ (8–13 $\mu$m) mid-infrared (mid-IR) bands of the star’s
photosphere and its immediate vicinity. In addition, to locate the molecules
and the dust in the circumstellar shell, we modeled the measured visibility
data with a combination of ring-shaped layers within the close environment of
the star and discuss our results. Finally, in Section 6, we provide our
conclusions.

##  2 Observations and data processing

The Multi Aperture Interferometric SpectroScopic Experiment (MATISSE) is a
four-telescope interferometric beam combiner that disperses the coherent light
from four telescopes of the Very Large Telescope Interferometer (VLTI) in the
$L$ (3–4 $\mu$m), $M$ (4.5–5 $\mu$m), and $N$ (8–13 $\mu$m) mid-infrared bands
(Lopez et al., 2022). It can combine either the four 1.8 m telescopes
(auxiliary telescopes, AT), or the four 8 m telescopes (unit telescopes, UT).
MATISSE delivers coherent fluxes, closures phases, differential phases, and
photometry which can be used with the coherent flux to derive the relevant
visibilities.

The four ATs can be moved along rails on the VLTI site, allowing for the
baselines (separation vector between two telescopes with coordinates (u,v)) to
more densely populate the (u,v)-plane than when only 4 fixed telescopes are
used. This makes MATISSE an imaging instrument that offers an exquisite
spatial resolution: reaching, in the $L$-band, up to $\lambda_{L}=3\,\mu$m,
$\lambda_{L}/B=4.4$ mas, and in the $N$-band up to $\lambda_{N}=10\,\mu$m,
$\lambda_{N}/B=15$ mas for a baseline of $B=140$ m. The reliability of the
image reconstruction process, the signal-to-noise-ratio (S/N), and the dynamic
range of the image depend on the completeness of the (u,v)-plane coverage.

The observations of R Scl were conducted using the ATs of the VLTI during the
commissioning run of MATISSE in December 2018. Table 3 presents the logbook of
the observations with the used AT configurations. Since on December 5 and 6,
the observing nights were of poor quality characterized by technical glitches,
only a fraction of the data from these two nights are used here.

Figure 1: SED of R Scl (log-log scales). Orange spectra: MATISSE data-sets in
$L$\- and $N$-bands with their associated error bars. Blue spectra: the
ISO/SWS spectrum. Red points: photometric data from the literature. The solid
black line is the best COMARCS+DUSTY model (see Section 3). Spectral features
are labeled with arrows. Insets zoom onto the MATISSE spectrum (linear
scales). SiC is marked as boldface as it is solid state, unlike the other
gaseous species. Figure 2: Plot of the MATISSE squared calibrated visibilities
(grey dots) at 3.10 $\mu m$ around the C2H2+HCN absorption feature (panel a),
3.52 $\mu m$ in the $L$-band pseudo-continuum (panel b), 11.30 $\mu m$ around
the SiC feature (panel c), and 12.00 $\mu m$ in the $N$-band pseudo-continuum
(panel d). We over-plotted the data with several models: Hankel profile
(blue), DUSTY model (orange), and MIRA mean 1D radial profile (red) and its
dispersion (solid red interval).

The data are processed using the MATISSE data reduction software drsmat
version 1.5.0 (Millour et al., 2016), which adopts a classical Fourier
transforms scheme (Perrin, 2003), with photometric calibration in the case of
the $L$-band (V. Coudé du Foresto et al., 1997). Chopping correction
(subtracting sky frames from target frames) and optical path difference (OPD)
demodulation procedures are applied before summing up the spectral densities,
bispectra, and interspectra, leading to estimates of the spectro-
interferometric observables: spectral distributions in squared visibility,
closure phase, and differential phase, in a similar way as was done with the
AMBER instrument (Tatulli et al., 2007). This leads to four reduced OIFITS2
files per pointed target (one for each beam commutation), which contains as
many observables as exposures on the target.

In the next step, an interferometric calibration procedure is applied to the
data: the targets used as calibrators (CAL) are corrected from their expected
observables given the predicted value of their angular diameters, and each
science target (SCI) is corrected from this transfer function estimate, owing
to a calibrated OIFITS2 file for each CAL-SCI pair111the calibrated data used
in this work can be found at
http://oidb.jmmc.fr/collection.html?id=12803c68-6124-40ad-803c-68612470ad3d.
It is important to notice that calibrators have been chosen with no IR excess
(see Cruzalèbes et al. (2019) for a description of the IR excess-free
criterion) to avoid bias on the infrared measurements and in the calibration
process. The drsmat has been developed in C with the ESO-specific library CPL,
and is interfaced with the ESO recipes environment esorex. A graphical user
interface can be used in the form of python tools developed by the
consortium222made freely available at
https://gitlab.oca.eu/MATISSE/tools/wikis/home to handle the data and recipes,
and display the results. Table 4 lists the stars used as calibrators for R Scl
during the MATISSE commissioning run.

##  3 Matching hydrostatic photosphere and 1D dust envelope model with the SED

Following the approach of Sacuto et al. (2011), we performed an estimation of
the spectral energy distribution (SED) of R Scl at the pulsation phase of the
MATISSE observations. Indeed, the SED is formed by selected photometric data
points listed in Table 5 and by the ISO/SWS spectra convolved at the same
spectral resolution as MATISSE ($R\sim 30$) and chosen at a pulsation phase
that is as close as possible to that of the MATISSE observations ($\varphi\sim
0.95$, see Figure 1).

###  3.1 Stellar pulsation

To estimate the pulsation phase of the MATISSE data, we made a periodogram
analysis of the AAVSO $V$-band photometry. For this purpose, we downloaded
data from between JD 2411972.3 and 2458893.5, and we selected only the best-
quality data (based on the AAVSO data flag system). The periodogram not shown
in this article is produced using the Lomb-Scargle method, an efficient
algorithm for detecting and characterizing periodicity in unevenly-sampled
time-data (VanderPlas, 2018). The primary peak was detected at $P=372\pm 5$
days which is consistent with the period 376 days from Wittkowski et al.
(2017). We also detected a secondary peak at 15000 days ($\approx$ 41 years),
which was previously unknown. We ensured this was not an alias of the shorter
period by checking that the secondary peak remains after we removed the
primary pulsation from the data. Furthermore, the 41-year pulsation period is
consistent with long secondary periods detected in several AGB stars (Wood et
al., 1999; Soszyński et al., 2021). Henceforth, we refer to the ”pulsation” as
the first 372-day period and ”variability” as the long-term variability of 41
years. The zero-phase time is set at 2456245.5 days (=2012-11-14). The MATISSE
observations were carried out close to maximum luminosity.

###  3.2 Photometric data and dereddening

The V, R, and I magnitudes reported in Table 5 are taken from the catalog of
Johnson et al. (1966). The errors on the flux are the results of errors in the
magnitude, the color index, and the extinction. The J, H, K, L band magnitudes
at the same pulsation phase as MATISSE data are taken from Whitelock et al.
(2006).

The photometric data are corrected from reddening using the visual extinction
equation of Bagnulo et al. (1998). To retrieve the extinction at each fiducial
wavelength, we assumed a total-to-selective extinction ratio in the visible of
$R=3.1$ (Fitzpatrick, 1999a). We notice that the dereddening effect induced by
the interstellar medium on the observed photometric data points is small.

###  3.3 Stellar contribution: COMARCS model fitting

In this section, the stellar contribution will be described using hydrostatic
models. The detailed fit of the spectral energy distribution which would
require more advanced models such as dynamic ones (Höfner et al., 2005) is
beyond the scope of the current paper. Our aim here is to derive the stellar
parameters and get a hydrostatic model that will be used in the following
section as central source for the radiative transfer equation solver DUSTY
333made freely available at http://faculty.washington.edu/ivezic/dusty_web/ in
order to model the total emission of R Scl.
We fit the photometric data with the grid of precomputed low-resolution
synthetic spectra COMARCS (Aringer et al., 2016, 2019). The spectra are
calculated starting from 1D hydrostatic model atmospheres that take into
account atomic and molecular absorption directly computed using the opacity
generation code from the Copenhagen Opacities for Model Atmospheres (COMA)
program (Aringer et al., 2009).
The fit is limited to the wavelength region where the dust contribution is
negligible, namely, between the V and I-bands (after dereddening). In such a
wavelength domain, we could expect strong absorption from the circumstellar
envelope (CSE) which is not considered in the models. Such dust extinction
could, in principle, impact the effective temperature estimation of the
COMARCS model. However, the bias described above is not significant for our
purpose, as previously discussed in Brunner et al. (2018).
Only a subset of 2600 COMARCS spectra matching metallicity, effective
temperature, and stellar mass was selected from the original grid of 11248
models available in the official COMARCS
repository444http://stev.oapd.inaf.it/atm/lrspe.html (Aringer et al., 2016).
After computing $\chi^{2}$ on the spectra subset, we selected one of the
models within 3$\sigma$ of the minimum $\chi^{2}$.
Using Equation 2 from Cruzalèbes et al. (2013) we estimated the Rosseland
radius associated to the model chosen in the previous step. Our result
R${}_{\star}=5.3\pm 0.6$ mas of the star is consistent with Cruzalèbes et al.
(2013) stellar limb-darkened radius of $R_{\star,C}=5.03\pm 0.03$ mas, based
on hydrostatic MARCS model, and it is also consistent with the Rosseland
radius $R_{\star,W}=4.45\pm 0.15$ mas of Wittkowski et al. (2017), obtained
using dynamic atmosphere models. Even using different models, the latter two
estimations are consistent within 1.5 $\sigma$ with our Rosseland radius,
meaning that the differences are not statistically significant. Finally, we
also tested the COMARCS model against a distance of 393 pc (Gaia
Collaboration, 2018), following the same steps than described previously, and
we did not notice any significant change in the SED and the stellar
contribution.

###  3.4 Dust contribution: DUSTY model fitting

To describe the circumstellar envelope of the star, we use the 1D radiative
transfer code DUSTY (Ivezić & Elitzur, 1997). We set: (1) the central source
as our best-fitting COMARCS model; (2) the dust grain-size distribution
following the classical MRN (Mathis Rumpl Nordsieck) distribution (Mathis et
al., 1977). For the latter, we assumed a minimum and maximum grain size
$a_{min}$ = 0.005 $\mu$m and $a_{max}$ = 0.25 $\mu$m, respectively, which are
largely adopted for size distribution among stellar envelopes and interstellar
dust; (3) the inner shell temperature was set to 1200 K, which aptly
represents the sublimation-condensation temperature of dust in particular AmC
(Gail & Sedlmayr, 1999). Such a temperature is affected, in practice, by
unknowns related to dust grain optical and physical properties. As a
consequence, we refer to the DUSTY radius where the dust grains condensate as
the ”DUSTY inner radius;” (4) then, we arbitrarily set the outer radius of the
envelope to 1000 $R_{in}$ consistently to Sacuto et al. (2011); (5) finally,
we assumed the density distribution driven by the pressure on dust grains.
Indeed, the Radiatively Driven Winds Analytic (RDWA) approximation (Elitzur &
Ivezić, 2001) was used for the dust density profile. The approach is
appropriate for AGB stars (in most cases) and according to the DUSTY manual,
it offers the advantage of a much shorter computing time. Then, fitting the
model on both observed SED and the MATISSE visibilities, we finetuned the
amount of silicone carbide (SiC) and amorphous carbon (amC), as well as the
optical depth at 1 $\mu$m. Thus, we estimated the inner shell radius and the
mass-loss rate. We assume that the main error sources in the DUSTY fitting
process come from the stellar temperature and luminosity. We used the lower
and higher temperatures and luminosities of the COMARCS grid of models based
on the error bars computed in Sect. 3.3. We repeated the process described in
Sect. 3.4 and deduced the confidence interval of the DUSTY parameters. The
summary of the DUSTY parameters are given in Table 1.

Table 1: Physico-chemical parameter values of the COMARCS (top part) and DUSTY (bottom part) models. Model parameter | Parameter value | Fixed
---|---|---
Distance |  $360\pm 50$ pc 555Maercker et al. (2018) | Yes
Surface gravity |  $-0.50\pm 0.10$ cm.s-2 | No
Stellar surface temperature |  $2700\pm 100$ K | No
Stellar Luminosity |  $8000\pm 1000$ $L_{\odot}$ | No
Stellar mass |  $2.0\pm 0.5$ $M_{\odot}$ | No
C/O ratio |  2${}^{+2.0}_{-0.6}$ | No
Microturbulent velocity |  2.5 km.s-1 666Aringer et al. (2009) | Yes
Rosseland Radius | $1.91\pm 0.20\,au$ | No
|  $5.3\pm 0.6$ mas |
Shell chemical composition |  AmC 777Hanner (1988) and SiC 888Pegourie (1988) | No
|  $88\pm 11$% of AmC |
|  $12\pm 11$% of SiC |
Dust grain-size distribution |  $n(a)\propto a^{-3.5}$ 999Mathis et al. (1977) | Yes
Optical depth at $\lambda=1\leavevmode\nobreak\ \mu$m | $0.19\pm 0.05$ | No
Inner boundary temperature |  $1200\pm 100$ K 101010Sacuto et al. (2011) | Yes
Inner radius |  $24.5\pm 9.0$ mas | No
|  $4.6\pm 1.7\,R_{\star}$ |
Outer radius |  1000 $R_{in}$ e | Yes
Mass-loss rate | $1.2\pm 0.4\times 10^{-6}M_{\odot}\leavevmode\nobreak\ \rm{yr}^{-1}$ | No

###  3.5 Results of the composite model fitting

Table 1 summarizes the parameters of the composite COMARCS+DUSTY best-fit
model. The fractional abundance of the relevant grains in the dust shell
resulting from this fit is a mixture of amorphous carbon (AmC, 88 $\pm$ 11%)
and silicon carbide (SiC, 12 $\pm$ 11%), with the optical depth at $1\mu$m
$\tau_{\lambda=1\mu m}=0.19\pm 0.05$. Our results are consistent with the
findings of Sacuto et al. (2011), who used a grid of DUSTY models and least-
squares fitting minimization to find a mixture of 90 $\pm$ 10% AmC and 10
$\pm$ 10% of SiC and an optical depth at $1\leavevmode\nobreak\ \mu$m of
$\tau_{\lambda=1\mu m}=0.18\pm 0.05$. Then, we also estimated a mass-loss rate
of $\dot{M}=(1.2\pm 0.4)\times 10^{-6}M_{\odot}\leavevmode\nobreak\
\rm{yr}^{-1}$, using a dust grain bulk density $\rho_{s}=1.85\,\rm{g.cm}^{-3}$
(Rouleau & Martin, 1991) and a gas-to-dust-ratio of $r_{gd}=590$ (Schöier et
al., 2005). Our estimation of the mass-loss rate is also consistent with that
of De Beck et al. (2010), namely, $1.6\times
10^{-6}M_{\odot}\leavevmode\nobreak\ \rm{yr}^{-1}$.

In Fig. 1, we display the selected photometry data sets and the composite
model of the SED. The MATISSE and the ISO/SWS spectra clearly show signatures
possibly associated to acetylene (C2H2) and hydrogen cyanide (HCN) molecules
at 3.1 $\mu$m as well as the solid state SiC at 11.3 $\mu$m (Yang et al.,
2004). We suspect the vertical-axis offset of the MATISSE spectrum with
respect to the ISO observations and COMARCS+DUSTY models is due to calibration
issues in terms of the MATISSE absolute flux or a field-of-view effect
(Paladini et al., 2017). We note that COMARCS + DUSTY models cannot reproduce
properly the CO + C3 absorption feature at 5.2 $\mu$m. Part of this
discrepancy can be linked to a well known problem about the opacity data and
equilibrium constants involved in the C3 band chemical description (Aringer et
al., 2019).

Since DUSTY does not handle molecules, and knowing the coexistence of
molecules and dust, we expected to see strong discrepancies between the DUSTY
model and the MATISSE data in the $L$-band, where strong molecular features
are located. Although dust emission usually dominates the $N$-band, molecular
contributions are also expected there, namely: CS and possibly SiO at 8
$\mu$m; HCN+C2H2 molecular bands between 11 and 16 $\mu$m (Chubb et al., 2020)
which can affect the shape of the SiC band at 11.3 $\mu$m.

The resulting fit to the SED (black curve in Fig. 1) provides results that are
in reasonable agreement with the above expectations: a satisfactory fit to the
$N$-band visibilities from MATISSE is found (orange curves in Fig. 2 c and d),
but the $L$-band visibilities are not well matched with this star+dust model
alone (Fig. 2 a and b). We therefore need to refine this model, introducing
additional ingredients for the $L$-band.

##  4 R Scl as seen by MATISSE

To locate the dusty and molecular regions, we used two independent methods:
the first one based on the MIRA image reconstruction algorithm and the second
one a new approach that is presented in this paper and based on an intensity
radial profile reconstruction method using the Hankel transform. The Hankel
method has the advantage of requiring less parameters than image
reconstruction, leading to fewer solution non-uniqueness problems, a better
convergence, and a better dynamic range, given that the source is centro-
symmetric at approximately all wavelengths.

###  4.1 MIRA image reconstruction

In Appendix. 8, we show the (u,v)-plane coverage obtained during the observing
run. The coverage is very dense, allowing us to reconstruct high-fidelity
monochromatic images of R Scl. For that purpose, we fed the calibrated
visibilities and closure phases into the MIRA software of Thiébaut (2008).
Additional scripts written by Millour et al. (2012) allowed us to slice the
wavelengths, and improve the image quality by low-frequencies filling.

The images were reconstructed with 128 pixel size, using total variation
regularization, a hyperparameter value of 10,000 (as suggested in Renard et
al., 2011), a random start image for the first wavelength, and the median
image of all previous wavelengths for the subsequent ones. In rows c and d of
Fig. 3, we show a subset of the reconstructed images.

Since the reconstructed interferometric image has a finer resolution than the
diffraction-limited resolution, we also show in Fig. 10 the reconstructed
images convolved by an interferometer clean beam with a Gaussian profile.
Furthermore, our MIRA image reconstruction effectively reproduces the closure
phase of MATISSE data at all wavelengths – even at 3.11 $\mu$m, as shown in
Appendix 9, where strong asymmetries are observed.

Figure 3: Reconstructed Hankel distribution from radial profiles (row a), the
same with the identified features highlighted (row b), images reconstructed
with MIRA (row c), and the same with features highlighted (row d). Each panel
shows the reconstructed image at the wavelength shown at its left top corner,
covering the $L$-band (3–4 $\mu$m) and the $N$-band (8–13 $\mu$m). In these
panels, the blue dashed circle in the center shows the calculated Rosseland
radius of the stellar photosphere, the green circles represent the inner and
outer boundary of the distinct molecular shell (seen here only at 3.52 $\mu$m
and only clearly identifiable in the Hankel reconstruction), the blue circle
represents the inner boundary of the dust envelope predicted by DUSTY, while
the white circle at each bottom left corner shows the theoretical angular
resolution of the interferometer. The white arrow shows the north-west arc
structure referenced in Sect. 4.3.3.

###  4.2 Hankel Profile reconstruction

The Hankel profile method uses a large number of concentric uniform narrow
rings of same width as that given by the angular resolution of the instrument.
A detailed description of the RHAPSODY tool is given in Appendix B. Although
it is built on simple models, RHAPSODY is not a simple model-fitting tool;
rather, it is a radial profile reconstruction tool based on a Bayesian
approach.

Figure 4: Spectra of the intensity profiles in $L$\- and $N$-bands. Upper
panels correspond to the observed MATISSE spectrum normalized by the median
and then divided by a black body spectra at T=2700 K to underline the observed
emission and absorption features. Lower panels are the spectro-radial maps in
$L$\- and $N$-band obtained by plotting the best intensity Hankel profile
normalized at one for each observed wavelength. The faint red structures
highlighted with the inclined dashed-white lines are reconstruction artifacts
(see Sect. 4.2 for details). The dashed and solid blue horizontal lines show
the position of the Rosseland radius and the DUSTY inner radius respectively.
The solid green horizontal lines delimit the extension of a hot distinct
molecular layer (see Sect. 5.3). The grey vertical bands cover the spectral
ranges where the centro-symmetric Hankel profile is not able to properly
reproduce the asymmetric shape of R Scl revealed by non-zero closure phases.

In this work, we reconstructed monochromatic radial profiles from visibilities
using this technique. Each radial profiles is generated varying several
parameters, including the number of rings, $N_{\rm step}$, the number of
iterations in the minimization routine, the initial radial profile, and the
value of the hyperparameter $\mu$ that we varied between $\mu=1$ and
$\mu=10^{10}$, in increments of the power of ten. The L-curve ($\chi^{2}$ as a
function of $\mu$) provides us a guideline to select the optimal value using
both regularization methods: 1) the quadratic smoothness $f_{\rm smooth}$,
which tends to minimize the intensity variations between consecutive radii;
and 2) the total variation $f_{\rm var}$ which tends to reconstruct uniform
intensities with sharp edges. Then we obtain the best radial profile
reconstructions (shown in Figs. 3 and 4) with $\mu=10^{4}$ and a median value
of the minimum reduced $\chi^{2}$ of 3.3, using the total variation
regularization method.

Images of the reconstructed Hankel profiles at selected wavelengths (i.e.,
pseudo-continuum (3.52 $\mu$m) and in C2H2 and/or HCN absorption bands (3.10
$\mu$m, ¿ 12 $\mu$m), as well as the SiC signature (11.30 $\mu$m)) are shown
in Fig. 3. The estimated Rosseland diameter is marked as a dashed circle and
the typical angular resolution of the interferometer for the fiducial
wavelength, computed as $0.5\,\lambda/B$ (Monnier, 2003), is marked as a white
circle in the bottom-left corner.

In Fig. 4, we show the obtained spectro-radial maps of the Hankel profile in
the $L$\- and $N$-bands. Profile reconstruction artifacts, coming from the
(u,v)-plane sampling voids, are clearly identifiable as their distance from
the star depends on the wavelength across the two $L$\- and $N$-bands (traced
as dashed white lines in Fig. 4). Spatially well-constrained structures show
no dependence of the distance on wavelength ($d=\text{Const}[\lambda]$). We
refer to Appendix C for more details on the fidelity of the profiles. The two
grey vertical bands from 3.05 to 3.30 $\mu$m and from 3.75 to 4.00 $\mu$m
cover the spectral ranges where the centro-symmetric Hankel profile is not
able to properly reproduce the asymmetric shape of R Scl, revealed by non-zero
closure phases and by the reconstructed images (see the following section).
The Rosseland radius is represented as a dashed blue line, the DUSTY inner
radius in solid blue line, and a new, so far unexpected emission discussed in
Section 5.3, which is between 12 and 18 mas ($\sim$ 2.3–3.4 $R_{\star}$)
within the two solid green lines.

As seen in Fig. 4, the extent of the inmost circumstellar shell is not
identical at all wavelengths but this variation is not coming from any
instrumental or data reduction issue. The shell is significantly larger
between 2.9 $\mu$m and 3.3 $\mu$m, and also 3.6 $\mu$m and 4.0 $\mu$m, and
except for those specific bandwidths, it steadily increases towards longer
wavelengths all the way up to 12 $\mu$m. Furthermore, this is in good
agreement with Paladini et al. (2009): from dynamical model, the pseudo
continuum radius is larger than the Rosseland radius because of the
atmospheric extension and the pseudo-continuous molecular opacity. Notably,
even at 3.525 $\mu$m, where we are expecting to find only the pseudo-continuum
(Paladini et al., 2009), the radial profile extent is slightly larger than the
value of the Rosseland radius. Therefore, our observations are qualitatively
supportive of the synthetic observations derived on the basis of dynamic
models described in Paladini et al. (2009).

The two reconstruction processes (profile and image) are different and,
therefore, they produce different results that must be interpreted adequately:
the Hankel profiles are computed using the visibilities across all position
angles altogether, reconstructing only the centro-symmetric information of the
object, whereas the MIRA images are computed using the visibilities and the
closure phases as a function of position angles and they bear the asymmetry
information. As a consequence, it is not surprising to find asymmetric
structures in the MIRA images while not seeing these asymmetries in the Hankel
profiles. Therefore, we should not go too far in the comparison of images
coming from both methods: what can be compared are the radial positions of
features, but not their relative intensities (except for azimuthally
integrated profiles of MIRA images compared to the Hankel profiles shown in
Fig. 6 and described in the following subsection). Furthermore, since it is
difficult to estimate the true angular resolution and the shape of the PSF,
the pixel size used to reconstruct the images is not meant to be the exact
angular resolution of the image for both methods.

###  4.3 Description of the R Scl environment in the mid-IR

In this section, we describe the observations, while the interpretations can
be found in Sect. 5. In Fig. 5, we provide a sketch of the region of the
circumstellar envelope close to the star R Scl based on the Hankel profiles
and the MIRA images, which we describe in more detail in the following
sections. Such a circumstellar envelope is mainly composed of: i) the central
component from 0 to 5 mas from the center of the star; ii) an inmost layer
from 5 to 10 mas (i.e., $\sim$ 1–2 $R_{\star}$); iii) a distinct layer from 12
to 18 mas (i.e., $\sim$ 2.3–3.4 $R_{\star}$); iv) a fuzzy emission in the
stellar outskirts at 20 to 90 mas (i.e., $\sim$ 3.8–17.0 $R_{\star}$).

Figure 5: Shell structure detected in the close envelope of R Scl (stellar
radii shown ranges).

####  4.3.1 Central component (0 – 5 mas)

In the first region between 0 and 5 mas from the center of the star (Figs. 3
and 4), we see a nearly round source dominating the flux in the pseudo-
continuum (3.52 $\mu$m and 10 $\mu$m). Figure 6 shows spectra extracted from
the Hankel profiles and the MIRA images in different regions around the star.
These separated spectra allow us to better understand the nature and the
composition of the different layer around the star. In Fig. 6, we see that the
spectrum of the central source is very similar to the total one: an absorption
feature at 3.05 $\mu$m and two bumps in the $N$-band at 8.7 $\mu$m and around
11.1 $\mu$m. This central part is clearly asymmetric in the 3.1 $\mu$m
C2H2/HCN absorption band in the MIRA images.

####  4.3.2 Inmost layer (5 – 10 mas)

A layer beyond the estimated Rosseland radius of R Scl is seen as a faint
environment between 5 and 7 mas ($\sim$ 1.0–1.3 $R_{\star}$), assuming that
the border of the photosphere is at 5 mas from the center of the star, as also
seen in the images in Fig. 3. The $N$-band images also exhibit a larger
central object compared to the $L$-band central star, meaning that we see the
contributions from the star and the inmost layer, but we cannot disentangle
them due to the lower angular resolution at these longer wavelengths.

We also observe a similar structure extending up to 10 mas (1.8 $R_{\star}$)
and attached to the central component, visible in the MIRA images at 3.1
$\mu$m and 3.9 $\mu$m as an irregular extended layer attached to the central
component (Fig. 3) and as a ring around the central object in the Hankel
profiles. In the spectra of Fig. 6, this is seen as two emissions bumps at
3.05 $\mu$m and 3.9 $\mu$m.

####  4.3.3 Distinct layer (12 – 18 mas)

A layer that is apparently distinct from the previous one (i.e., continuum at
3.52 $\mu$m) is detected between 12 and 18 mas, below the DUSTY inner radius
of 24.5 mas. Such layer is seen in the $L$-band in the MIRA image
reconstruction (Figs. 3 and 11) as a fuzzy arc to the north-west of the star
and a few blobs at the same distance from the photosphere. The RHAPSODY
intensity profile reconstruction shows also such layer as a continuous ring.
The nature of such layer is further discussed in Sect.5.3.

####  4.3.4 Fuzzy emission in the outer skirts (beyond 20 mas)

A fuzzy emission above 20 mas (marked as a solid blue line in Figs. 3 and 4)
is detected with MIRA and RHAPSODY. This emission is present both in $L$\- and
$N$-band. In the RHAPSODY images, the dynamic range of this emission is so low
that only flux artifacts are reconstructed (see Appendix C). In the MIRA
images, the (u,v)-coverage does not allow us to meaningfully reconstruct the
shape of the brightness distribution. As a consequence, the fuzzy emission
appears as blobs or artifacts in the north-eastern and south-western
directions.

##  5 Discussion

In this paper, we describe 2D images that are projections of the actual R Scl
3D environment. Consequently, the distances mentioned in the following
sections refer by default to distances projected onto the plane of the sky.

Figure 6: MATISSE spectrum (black line) together with spectra extracted from
circumstellar regions located at 0–5 mas (pink), 5–10 mas (green), 12–18 mas
(blue), and 20–90 mas (golden) for both the Hankel (solid lines) and MIRA
reconstructed images (dashed lines).

###  5.1 Central part: Star veiled by molecules

The data show a structure between 0–5 mas which can be interpreted as the
star’s photosphere. At the wavelengths where molecular bands are expected, the
photosphere is no longer visible due to the presence of molecular shells in
front of it. In the $L$-band at 3.05 $\mu$m, we can see a spectral feature
which, according to, for instance, Aringer et al. (2019), could be attributed
to C2H2 \+ HCN. The feature detected at 3.9 $\mu$m is associated to C2H2.

The bump near 11.3 $\mu$m in the $N$-band (see Figs. 1 and 6) resembles the
SiC signature. Two hypothesis are able to explain such feature: i) The
signature is not from dust but rather from a pseudo-continuum between adjacent
molecular features; ii) The signature is produced by an optically thick layer
of SiC dust located along the line of sight. In the case where the layer
temperature is lower than the one of the background (i.e., the stellar
surface), an optically thin layer scenario would produce an absorption
(Rutten, 2000); hence, this would not be compatible with the emission
observed. The limited angular resolution and the dynamic range of the MATISSE
$N$-band data do not allow us to correctly probe the SiC emission region,
which provides key information in making the choice of one scenario over the
other.

###  5.2 Inmost hot molecular layer (5–10 mas)

The inmost layer has clear spectral features (seen in the green curve of Fig.
6), appearing as two emission bumps at 3.05 $\mu$m and 3.9 $\mu$m, namely, the
signatures of C2H2 and HCN. The hypothesis of the existence of an absorption
band between these bumps is unlikely because spectral features at 3.05 $\mu$m
and 3.9 $\mu$m should therefore also be in absorption. In addition, the data
angular resolution in the $L$-band is high enough to avoid any contamination
from the stellar emission. Furthermore, the existence of these emission bands
is consistent with the lack of a strong continuum emission coming from the
back hemisphere of the envelope, in the ring between 5 and 10 mas. On the
other hand, C2H2 and HCN are already formed in the stellar atmosphere at a
temperature between 2500 K and 3000 K (Eriksson et al., 1984); thus, we
suggest that this layer is attached to the star and could be part of the
extended stellar atmosphere.

The inmost hot molecular layer is also visible at all other wavelengths in the
$L$-band as a faint environment between 5 and 7 mas ($\sim$ 1.0–1.3
$R_{\star}$), as seen in the images in Fig. 3. It may also be seen in the
$N$-band, as the images show a larger central object with respect to the
photosphere of the star.

###  5.3 Possibility of a distinct hot molecular layer (12–18 mas)

In $L$-band panels of Fig. 3, the MIRA images indicate the presence of
irregular emissions between 12 and 18 mas while RHAPSODY images (as also seen
in Fig. 4) shows clearly the presence of a layer in emission. In contrast, in
the $N$-band, neither MIRA nor RHAPSODY show any trace of such layer, but
there is still a noticeable enlargement with regard to the angular diameter of
the photosphere. The non-detection of such layer might be induced by the
limited dynamic range and $N$-band angular resolution of the data (see
Appendix C). The composition of this layer can then be of two different
natures: either formed by dust or filled with molecules.

####  5.3.1 Dust hypothesis

The dust hypothesis, based on the assumption the 12–18 mas layer (2.3–3.4
$R_{\star}$) is formed by dust, offers three possibilities: i) Dust grains in
the layer are only made of amorphous carbon. According to our estimation using
Equation 1 in Ivezić & Elitzur (1996), such layer should radiate at a mean
temperature of 1500 K. This temperature is in accordance with the condensation
temperature of amC in dynamic models (Nowotny et al., 2010). Wittkowski et al.
(2017) also confirmed the presence of amC in the line of sight of their R Scl
PIONIER images; ii) Dust grains in the layer are made of SiC. If we assume, as
the temperature for the SiC dust condensation, Teff = 1350 K from Yasuda &
Kozasa (2012), then such a scenario would be discarded because the estimated
temperature of the layer in this work is higher than the latter. On the other
hand, we should keep in mind that the condensation temperature of SiC is not
well known. Yasuda & Kozasa (2012) used select data on the condensation of
SixCy onto SiC dust grains that are affected by large errors. Gobrecht et al.
(2017) analyzed part of the chemical reactions used by Yasuda & Kozasa (2012)
and found significant differences. Agúndez et al. (2020) gave a condensation
temperature for SiC of $\approx$ 1300–1400 K, while Men’shchikov et al. (2001)
provided a temperature of 2000 K. Given these uncertainties, the scenario
cannot be fully discarded; iii) Dust grains in the layer are made of titanium
carbide (TiC). TiC also condenses at those temperatures (Agúndez et al.,
2020), however such a chemical species is not included in this paper since
there is no clear spectral signature of TiC in the MATISSE spectral range (von
Helden et al., 2000).

Figure 7: Comparison between R Scl in 2014 and 2018 observed respectively with PIONIER and MATISSE. Left: MIRA image reconstruction at 3.51 $\mu$m using the 2018 MATISSE observations at $\phi$ = 0.96. Center: MIRA image reconstruction at 3.11 $\mu$m using the 2018 MATISSE observations at $\phi$ = 0.96. Right: IRBis image reconstruction made by Wittkowski et al. (2017) using PIONIER 2014 data at 1.76 $\mu$m and $\phi$ = 0.78. Table 2: Summary of key structures in the inner region of R Scl from our MATISSE observations. Structure | Composition | Distance from the stellar center | Spectral signature | Central Wavelength
---|---|---|---|---
Star | – |  $0-(5.3\pm 0.6)$,mas |  Continuum | All
Rosseland Radius | – |  $5.3\pm 0.6$ mas ($\sim$ 0–1 $R_{\star}$) | – | –
Central Component | C2H2 \+ HCN |  $0-5$ mas ($\sim$ 0–1 $R_{\star}$) | Absorption band | 3.05 $\mu$m
Inmost Layer | C2H2 \+ HCN |  $5-10$ mas ($\sim$ 1–2 $R_{\star}$) | Emission band | 3.05 and 3.9 $\mu$m
Distinct Layer | C2H2 \+ HCN + amC |  $12-18$ mas ($\sim$ 2.3–3.4 $R_{\star}$) | Not clear | –
Fuzzy emission | amC (and SiC?) |  $20-90$ mas ($\sim$ 3.8–17.0 $R_{\star}$) | Continuum | All

###  5.4 Comparison with PIONIER data

In Figure 7, we compare our VLTI/MATISSE images with those from VLTI/PIONIER
from Wittkowski et al. (2017) 111111IRBis and MIRA packages are based on the
same principle, which justifies the comparison..

The PIONIER 1.76 $\mu$m observations give us information mainly on the stellar
surface and its extended atmosphere, being outside of the 1.53 $\mu$m C2H2+HCN
molecular absorption band. We need to keep in mind that C2 bands are also
present in the observing bandwidth of PIONIER and could affect the images of
the continuum emission. The 1.76 $\mu$m VLTI/PIONER data were observed in
2014, corresponding to a pulsation phase of $\phi=0.78$, and the VLTI/MATISSE
data were observed in 2018 at a pulsation phase of $\phi=0.96$. The two epochs
at four years apart are expected to show an evolution: the long-term
variability of the star had time to completely reshape the region of the
envelope close to the inmost layers of the vicinity of the star. The
comparison shows similarities: the size of the central source (0–5 mas) with
PIONIER is akin to our central source at 3.51 $\mu$m (in the pseudo-
continuum).

It also exhibits some differences: asymmetries are not located at the same
place between the two epochs. Two hypotheses for this variation: a significant
evolution of the stellar and circumstellar environment shape or wavelength-
dependent opacities related to the presence of molecules and possibly dust in
front of the star. Then, this comparison has underlined the fact that it is
possible to observe stellar surface variability at a timescale of few years
for this kind of object. This means that in the case of a high observation
frequency with MATISSE or another imaging interferometer, we should be able to
estimate the characteristic timescale and sizes of patterns caused by
convection onto the stellar surface.

##  6 Conclusion

In this paper, for the first time, we present our processing of simultaneous
$L$-band and $N$-band observational data of the AGB star R Scl obtained with
the VLTI/MATISSE instrument. Thanks to the good (u,v)-plane coverage of the
MATISSE observations, we derived a consistent MIRA image and Hankel intensity
profile reconstruction. The use of both independent and complementary methods
allows us to locate the dust and molecules around R Scl. In the images (and
intensity profiles), we find the signature of a sporadic mass-loss event maybe
responsible for the formation of a distinct layer. Based on the MIRA images,
we also detected some asymmetric structures confirming the presence of clumps
in the envelope of R Scl. We did not find any clear signature of SiC forming
regions around the star. We present the main steps of our work as follows:

  1. 1.

Data obtained with the VLTI/MATISSE instrument during the seven-days of the
long commissioning session from 2018-12-03 to 2018-12-15 was used in this
work.

  2. 2.

Using the COMARCS stellar atmospheric model and the dust radiative transfer
code DUSTY, we confirm the previously published characteristics of a thin dust
shell, mainly composed of amorphous carbon with a small amount of silicon
carbide (10%), leading to the location of the inner boundary estimated by
DUSTY at about 4.6 $R_{\star}$ from the central star (i.e., 24.4 mas) and a
mass-loss rate of $1.2\pm 0.4\times 10^{-6}M_{\odot}\leavevmode\nobreak\
\rm{yr}^{-1}$.

  3. 3.

In order to locate the dust and molecule regions, we compared two different
methods: one based on the MIRA image reconstruction and an other one based on
a brand-new approach which consists of reconstructing the Hankel intensity
profile of the circumstellar environment using the code RHAPSODY121212Link to
RHAPSODY: https://github.com/jdrevon/RHAPSODY. This method allowed us to
simultaneously reproduce the spectral energy distribution and the MATISSE
visibilities.

  4. 4.

These complementary and independent approaches allow us to get a better view
of both the composition and the geometry of the close environment of R Scl. We
locate the dust emission region between 20 and 90 mas ($\sim$ 3.8–17.0
$R_{\star}$), as well as the presence of molecular shell around 5–10 mas
($\sim$ 1–2 $R_{\star}$) and a distinct one around 12–18 mas ($\sim$ 2.3–3.4
$R_{\star}$). This distinct layer could be made of both: dust and molecules.
To reconstruct the formation history of such layer would require a monitoring
of the source. Our results are in qualitative agreement with the predictions
of dynamic models (Paladini et al., 2009) and a detailed comparison with such
models is the subject of further study.

###### Acknowledgements.

MATISSE has been built by a consortium composed of French (INSU-CNRS in Paris
and OCA in Nice), German (MPIA, MPIfR and University of Kiel), Dutch (NOVA and
University of Leiden), and Austrian (University of Vienna) institutes. It was
defined, funded and built in close collaboration with ESO. The _Conseil
Départemental des Alpes-Maritimes_ in France, the Konkoly Observatory and
Cologne University have also provided resources to manufacture the instrument.
The results are based on public data released from the MATISSE commissioning
observations at the VLT Interferometer under Programme IDs 60.A-9257(E). We
have great remembrance of the contributions from our two deceased colleagues,
Olivier Chesneau and Michel Dugué to the MATISSE instrument. We acknowledge
with thanks the variable star observations from the AAVSO International
Database contributed by observers worldwide and used in this research. This
work was supported by the _Action Spécifique Haute Résolution Angulaire_
(ASHRA) of CNRS/INSU co-funded by CNES, as well as from the _Programme
National de Physique Stellaire_ (PNPS) from CNRS. It has also been supported
by the French government through the UCA-JEDI Investments in the Future
project managed by the National research Agency (ANR) with the reference
number ANR-15-IDEX-01 and the Hungarian governent through NKFIH grant K132406.
Vincent Hocdé is supported by the National Science Center, Poland, Sonata BIS
project 2018/30/E/ST9/00598. FM acknowledges support from the French National
Research Agency (ANR) funded project PEPPER (ANR-20-CE31-0002). The authors
made extensive use of the Jean-Marie Mariotti Center (JMMC) tools to prepare
this paper. We can cite among others ASPRO131313Link to ASPRO on www.jmmc.fr
used to prepare observations, and OIdb141414Link to OIdb: oidb.jmmc.fr to
publish the reduced data. The authors are very grateful to the anonymous
referee for his/her careful review of the manuscript, resulting in insightful
recommendations and constructive suggestions leading to the great improvement
of its content and presentation. We are also very grateful to Orlagh Creevey
for her precious information regarding the Gaia distances of R Scl, and
Bernhard Aringer for the fruitful discussions about the COMARCS models.

## References

  * Agúndez et al. (2020) Agúndez, M., Martínez, J. I., de Andres, P. L., Cernicharo, J., & Martín-Gago, J. A. 2020, A&A, 637, A59
  * Aringer et al. (2016) Aringer, B., Girardi, L., Nowotny, W., Marigo, P., & Bressan, A. 2016, MNRAS, 457, 3611
  * Aringer et al. (2009) Aringer, B., Girardi, L., Nowotny, W., Marigo, P., & Lederer, M. T. 2009, A&A, 503, 913
  * Aringer et al. (2019) Aringer, B., Marigo, P., Nowotny, W., et al. 2019, MNRAS, 487, 2133
  * Bagnulo et al. (1998) Bagnulo, S., Doyle, J. G., & Andretta, V. 1998, Monthly Notices of the Royal Astronomical Society, 296, 545
  * Barnbaum et al. (1996) Barnbaum, C., Stone, R. P. S., & Keenan, P. C. 1996, ApJS, 105, 419
  * Bourgés et al. (2014) Bourgés, L., Lafrasse, S., Mella, G., et al. 2014, in Astronomical Society of the Pacific Conference Series, Vol. 485, Astronomical Data Analysis Software and Systems XXIII, ed. N. Manset & P. Forshay, 223
  * Brunner et al. (2018) Brunner, M., Maercker, M., Mecina, M., Khouri, T., & Kerschbaum, F. 2018, A&A, 614, A17
  * Chandler et al. (2016) Chandler, C. O., McDonald, I., & Kane, S. R. 2016, AJ, 151, 59
  * Chubb et al. (2020) Chubb, K. L., Tennyson, J., & Yurchenko, S. N. 2020, MNRAS, 493, 1531
  * Cruzalèbes et al. (2019) Cruzalèbes, P., Petrov, R. G., Robbe-Dubois, S., et al. 2019, MNRAS, 490, 3158
  * Cruzalèbes et al. (2013) Cruzalèbes, P., Jorissen, A., Rabbia, Y., et al. 2013, Monthly Notices of the Royal Astronomical Society, 434, 437
  * De Beck et al. (2010) De Beck, E., Decin, L., de Koter, A., et al. 2010, A&A, 523, A18
  * Elitzur & Ivezić (2001) Elitzur, M. & Ivezić, Ž. 2001, MNRAS, 327, 403
  * Eriksson et al. (1984) Eriksson, K., Gustafsson, B., Jorgensen, U. G., & Nordlund, A. 1984, in Observational Tests of the Stellar Evolution Theory, ed. A. Maeder & A. Renzini, Vol. 105, 199
  * Fitzpatrick (1999a) Fitzpatrick, E. L. 1999a, PASP, 111, 63
  * Fitzpatrick (1999b) Fitzpatrick, E. L. 1999b, PASP, 111, 63
  * Gaia Collaboration (2018) Gaia Collaboration. 2018, VizieR Online Data Catalog, I/345
  * Gail & Sedlmayr (1999) Gail, H. P. & Sedlmayr, E. 1999, A&A, 347, 594
  * Gobrecht et al. (2017) Gobrecht, D., Cristallo, S., Piersanti, L., & Bromley, S. T. 2017, ApJ, 840, 117
  * Hanner (1988) Hanner, M. 1988, NASA Conf. Publ.
  * Höfner et al. (2005) Höfner, S., Gautschy-Loidl, R., Aringer, B., et al. 2005, in High Resolution Infrared Spectroscopy in Astronomy, 269–280
  * Hron et al. (1998) Hron, J., Loidl, R., Hoefner, S., et al. 1998, A&A, 335, L69
  * Huang et al. (2015) Huang, Y., Liu, X. W., Yuan, H. B., et al. 2015, MNRAS, 454, 2863
  * Ivezić & Elitzur (1996) Ivezić, Z. & Elitzur, M. 1996, MNRAS, 279, 1011
  * Ivezić & Elitzur (1997) Ivezić, Z. & Elitzur, M. 1997, Monthly Notices of the Royal Astronomical Society, 287, 799
  * Jofré et al. (2015) Jofré, E., Petrucci, R., Saffe, C., et al. 2015, A&A, 574, A50
  * Johnson et al. (1966) Johnson, H. L., Mitchell, R. I., Iriarte, B., & Wisniewski, W. Z. 1966, Communications of the Lunar and Planetary Laboratory, 4, 99
  * Keenan (1993) Keenan, P. C. 1993, PASP, 105, 905
  * Lopez et al. (2022) Lopez, B., Lagarde, S., Petrov, R. G., et al. 2022, A&A, accepted
  * Maercker et al. (2018) Maercker, M., Brunner, M., Mecina, M., & De Beck, E. 2018, A&A, 611, A102
  * Maercker et al. (2012) Maercker, M., Mohamed, S., Vlemmings, W. H. T., et al. 2012, Nature, 490, 232
  * Mathis et al. (1977) Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425
  * Men’shchikov et al. (2001) Men’shchikov, A. B., Balega, Y., Blöcker, T., Osterbart, R., & Weigelt, G. 2001, A&A, 368, 497
  * Millour et al. (2016) Millour, F., Berio, P., Heininger, M., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9907, Optical and Infrared Interferometry and Imaging V, ed. F. Malbet, M. J. Creech-Eakman, & P. G. Tuthill, 990723
  * Millour et al. (2012) Millour, F. A., Vannier, M., & Meilland, A. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8445, Optical and Infrared Interferometry III, ed. F. Delplancke, J. K. Rajagopal, & F. Malbet, 84451B
  * Monnier (2003) Monnier, J. D. 2003, Reports on Progress in Physics, 66, 789
  * Nowotny et al. (2010) Nowotny, W., Höfner, S., & Aringer, B. 2010, A&A, 514, A35
  * Olofsson et al. (1996) Olofsson, H., Bergman, P., Eriksson, K., & Gustafsson, B. 1996, A&A, 311, 587
  * Paladini et al. (2009) Paladini, C., Aringer, B., Hron, J., et al. 2009, A&A, 501, 1073
  * Paladini et al. (2017) Paladini, C., Klotz, D., Sacuto, S., et al. 2017, A&A, 600, A136
  * Paladini et al. (2012) Paladini, C., Sacuto, S., Klotz, D., et al. 2012, A&A, 544, L5
  * Pegourie (1988) Pegourie, B. 1988, A&A, 194, 335
  * Perrin (2003) Perrin, G. 2003, A&A, 400, 1173
  * Renard et al. (2011) Renard, S., Thiébaut, E., & Malbet, F. 2011, A&A, 533, A64
  * Rouleau & Martin (1991) Rouleau, F. & Martin, P. G. 1991, ApJ, 377, 526
  * Rutten (2000) Rutten, R. 2000, Radiative Transfer in Stellar Atmospheres (lecture notes Utrecht Univ., 7th edition)
  * Sacuto et al. (2011) Sacuto, S., Aringer, B., Hron, J., et al. 2011, A&A, 525, A42
  * Samus et al. (2009) Samus, N. N., Kazarovets, E. V., Durlevich, O. V., Kireeva, N. N., & Pastukhova, E. N. 2009, VizieR Online Data Catalog, B/gcvs
  * Schöier et al. (2005) Schöier, F. L., Lindqvist, M., & Olofsson, H. 2005, A&A, 436, 633
  * Soszyński et al. (2021) Soszyński, I., Olechowska, A., Ratajczak, M., et al. 2021, ApJ, 911, L22
  * Sousa et al. (2018) Sousa, S. G., Adibekyan, V., Delgado-Mena, E., et al. 2018, A&A, 620, A58
  * Stevens et al. (2017) Stevens, D. J., Stassun, K. G., & Gaudi, B. S. 2017, AJ, 154, 259
  * Tatulli et al. (2007) Tatulli, E., Millour, F., Chelli, A., et al. 2007, A&A, 464, 29
  * Thiébaut (2008) Thiébaut, E. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7013, Optical and Infrared Interferometry, ed. M. Schöller, W. C. Danchi, & F. Delplancke, 70131I
  * Thiebaut & Giovannelli (2010) Thiebaut, E. & Giovannelli, J. F. 2010, IEEE Signal Processing Magazine, 27, 97
  * V. Coudé du Foresto et al. (1997) V. Coudé du Foresto, Ridgway, S., & Mariotti, J.-M. 1997, Astron. Astrophys. Suppl. Ser., 121, 379
  * VanderPlas (2018) VanderPlas, J. T. 2018, ApJS, 236, 16
  * von Helden et al. (2000) von Helden, G., Tielens, A. G. G. M., van Heijnsbergen, D., et al. 2000, Science, 288, 313
  * Whitelock et al. (2006) Whitelock, P. A., Feast, M. W., Marang, F., & Groenewegen, M. A. T. 2006, MNRAS, 369, 751
  * Wittkowski et al. (2017) Wittkowski, M., Hofmann, K. H., Höfner, S., et al. 2017, A&A, 601, A3
  * Wood et al. (1999) Wood, P. R., Alcock, C., Allsman, R. A., et al. 1999, in Asymptotic Giant Branch Stars, ed. T. Le Bertre, A. Lebre, & C. Waelkens, Vol. 191, 151
  * Yang et al. (2004) Yang, X., Chen, P., & He, J. 2004, A&A, 414, 1049
  * Yasuda & Kozasa (2012) Yasuda, Y. & Kozasa, T. 2012, ApJ, 745, 159
  * Yudin & Evans (2002) Yudin, R. V. & Evans, A. 2002, A&A, 391, 625

##  Appendix A Observational Information

###  A.1 Log of the MATISSE observations

Table 3: Log of the MATISSE observations of R Scl.

Observing date | VLTI config. | $BLR$ | $N/N_{\star}$ | Seeing | $\tau_{0}$
---|---|---|---|---|---
2018-12-03 $\rightarrow$ 05 | A0–B2–C1–J2 | 10–129 | 9/14 | 0.94 | 0.6
2018-12-07 $\rightarrow$ 08 | A0–B2–C1–D0 | 9–34 | 6/7 | 0.94 | 2.3
2018-12-09 | B2–D0–J3–K0 | 29–137 | 5/5 | 0.73 | 4.1
2018-12-10 $\rightarrow$ 11 | D0–G2–J3–K0 | 34–104 | 10/10 | 0.82 | 4.0
2018-12-12 | A0–D0–G1–J3 | 25–131 | 4/4 | 0.80 | 4.6
2018-12-13 $\rightarrow$ 14 | A0–G1–J2–J3 | 39–132 | 9/9 | 0.67 | 5.0
2018-12-15 | A0–G1–J2–K0 | 48–123 | 2/2 | 0.53 | 4.7

  * •

Notes: $BLR$ stands for Baseline Length Range expressed in m covered with each
VLTI configuration. The ratio $N/N_{\star}$ is the ratio of the used files to
the pointings to the star, the seeing in arcseconds, and $\tau_{0}$ is the
coherence time in ms.

###  A.2 List of calibrators

Table 4: List of the calibrator targets used for R Scl sorted by their
decreasing effective temperature.

Name | Sp. Type |  $T_{\rm eff}$ (K) |  $\theta_{\rm UD}$ (mas) |  $F_{\rm L}$ (Jy) |  $F_{\rm N}$ (Jy)
---|---|---|---|---|---
HD 10144 | B6V |  $15\,216\pm 100$151515Chandler et al. (2016) | $1.8\pm 0.2$ | $120\pm 14$ | $18\pm 4$
HD 48915 | A1V |  $9\,711\pm 23$161616Huang et al. (2015) | $6.2\pm 0.5$ | $996\pm 55$ | $118\pm 14$
HD 6805 | K2-IIIb |  $4\,687\pm 85$171717Sousa et al. (2018) | $3.3\pm 0.3$ | $135\pm 3$ | $20\pm 2$
HD 39425 | K1III |  $4\,631\pm 120$181818Stevens et al. (2017) | $3.7\pm 0.4$ | $178\pm 24$ | $23\pm 4$
HD 32887 | K4III |  $4\,243\pm 25$191919Jofré et al. (2015) | $6.0\pm 0.6$ | $403\pm 42$ | $56\pm 7$
HD 23614 | M1III | $3\,841\pm 100^{a}$ | $5.3\pm 0.5$ | $199\pm 36$ | $28\pm 4$
HD 1038 | M1III | $3\,802\pm 100^{a}$ | $5.6\pm 0.6$ | $255\pm 45$ | $41\pm 10$
HD 51799 | M1III | $3\,780\pm 100^{a}$ | $4.7\pm 0.6$ | $183\pm 38$ | $29\pm 6$
HD 11695 | M4III | $3\,550\pm 50^{b}$ | $9.3\pm 1.2$ | $224\pm 198$ | $69\pm 19$

  * •

Notes: The values of the uniform-disk angular diameter are reported in the
II/346 VizieR catalog (Bourgés et al. 2014), those of the $L$\- and $N$-band
fluxes in the II/361 catalog (Cruzalèbes et al. 2019).

###  A.3 (u,v)-plane coverage

Figure 8: Final (u,v)-plane coverage on R Scl with VLTI/MATISSE. The U and V
coordinates are those of the projected baseline vectors.

###  A.4 Photometric data

Table 5: List of the photometric data used in this work (see text for
details).

Band | MJD | $\varphi$ | $A_{\lambda}$ | Magnitude | Flux (Jy)
---|---|---|---|---|---
V | 38 700 | 0.85 | 0.18 | $5.84\pm 0.02$ | $20.8\pm 1.0$
V | – | – | – | $5.76\pm 0.02$ | $22.6\pm 1.1$
V | – | – | – | $5.71\pm 0.02$ | $23.5\pm 1.2$
R | – | – | 0.13 | $3.76\pm 0.02$ | $105\pm 4.2$
R | – | – | – | $3.72\pm 0.02$ | $108\pm 4.3$
R | – | – | – | $3.68\pm 0.02$ | $112\pm 4.5$
I | – | – | 0.07 | $2.38\pm 0.03$ | $345\pm 10.4$
I | – | – | – | $2.35\pm 0.03$ | $318\pm 9.6$
I | – | – | – | $2.29\pm 0.03$ | $323\pm 9.7$
J | 52 888 | 0.98 | 0.05 | $1.64\pm 0.03$ | $371\pm 11$
H | – | – | 0.03 | $0.39\pm 0.03$ | $779\pm 23$
K | – | – | 0.02 | $-0.23\pm 0.03$ | $843\pm 25$
L | – | – | 0.01 | $-0.81\pm 0.05$ | $614\pm 18$
J | 50 274 | 0.95 | 0.05 | $1.69\pm 0.03$ | $354\pm 10$
H | – | – | 0.03 | $0.45\pm 0.03$ | $736\pm 22$
K | – | – | 0.02 | $-0.14\pm 0.03$ | $777\pm 23$
L | – | – | 0.01 | $-0.66\pm 0.05$ | $535\pm 16$

  * •

Notes: $\varphi$ is the pulsation phase and $A_{\lambda}$ is the extinction
value given with relative errors of 25%, computed thanks to the tabulated
extinction values E(B-V) from Fitzpatrick (1999b). Magnitude is the observed
magnitude provided by the catalog and the last column Flux is the dereddened
flux computed using the $A_{\lambda}$ values.

###  A.5 Closure phase

Figure 9: Comparison between the closure phase from the MIRA image
reconstruction using the MATISSE (u,v)-plane coverage (blue dots) and the
closure phase from MATISSE (orange dots).

###  A.6 Images convolved by the interferometer beam

Figure 10: Reconstructed Hankel distribution from radial profiles (upper
panels) and MIRA images (lower panels) convolved by a Gaussian beam of FWHM
the angular resolution of the interferometer.

###  A.7 Contour plots

Figure 11: Reconstructed Hankel distribution from radial profiles (upper
panels) and MIRA images (lower panels) with contours plot in white at 50%, 5%,
and 0.5% of the peak intensity level of the images.

##  Appendix B Hankel Profile Reconstructor (RHAPSODY)

Here, we describe the method used to reconstruct Hankel profiles in the
current work with our Hankel Profile Reconstructor, named RHAPSODY, which
stands for: Reconstructing Hankel rAdial Profiles in centro-Symmetric Objects
with Discrete rings for astrophYsics.

Instead of forcing the routine to describe a given component (e.g., the dust
envelope) with a particular geometrical model (e.g., a Gaussian disk), we use
a large number of concentric uniform narrow rings (of width given by the
angular resolution of the instrument) to reproduce the radial profile of the
stellar environment. With this method, thick rings are reproduced by
contiguous narrow rings. This Hankel profile is built thanks to a set of
$N_{\rm step}$ concentric circular rings with diameters
$\theta_{k}=k\theta_{0}$, where $\theta_{0}=0.5\lambda/B$ is selected as a
fraction of the angular resolution of the interferometer. Within that
assumption, we can write the normalized monochromatic radial profile as:

$\begin{aligned} \end{aligned}I_{\rm
Hankel}(\lambda)=\frac{4}{\pi}\sum_{k=0}^{N_{\rm
step}-1}h_{k}(\lambda)\leavevmode\nobreak\
\frac{\Pi(\theta_{k+1})-\Pi(\theta_{k})}{\theta_{k+1}^{2}-\theta_{k}^{2}},$
(1)

where $\Pi(\theta)$ is the rectangular function of width $\theta$. For
physical reasons, the height in intensity $h_{k}$ of each step fulfils the
condition $0\leq h_{k}\leq h_{0}$ whatever the wavelength.

Thus, the final expression of the global visibility is:

$\begin{aligned} \end{aligned}V_{\rm Hankel}(q,\lambda)=\sum_{k=0}^{N_{\rm
step}-1}a_{k}(\lambda)\leavevmode\nobreak\
\frac{\theta_{k+1}^{2}\leavevmode\nobreak\ V_{\rm
UD}(q;\theta_{k+1})-\theta_{k}^{2}\leavevmode\nobreak\ V_{\rm
UD}(q;\theta_{k})}{\theta_{k+1}^{2}-\theta_{k}^{2}},$ (2)

where the visibility coefficients $a_{k}$ estimated by our reconstruction
method are:

$\begin{aligned}
\end{aligned}a_{k}(\lambda)=\frac{h_{k}(\lambda)}{\sum_{k=0}^{N_{\rm
step}-1}h_{k}(\lambda)}.$ (3)

Adjusting $V_{\rm Hankel}$ to the measured visibilities $V_{\rm obs}$ (with
their uncertainties $\sigma_{\rm obs}$) is then a matter of minimizing the
distance between both through the $\chi^{2}$ minimization, varying the $a_{k}$
coefficients.

However, trying to adjust the visibility deduced from a lot of regular
intensity steps using a bare final $\chi^{2}$ value usually gives poor
results, because the number of parameters $a_{k}$ to fit outperforms rapidly
the number of available data, in a similar way as in an image reconstruction
problem. This is where the Bayesian method comes into the play by adding to
the simple $\chi^{2}$ an a priori bit of information. This additional
information to the problem-solving is called a regularization term, $f_{\rm
prior}$, calculated on the variable parameters themselves. Such a
regularization term must be designed so as to maximize the probability that
the reconstructed profile resembles the actual one. For more details on how to
deal with heavy inverse problems in a Bayesian framework, we refer to the
excellent introduction to image reconstruction for optical interferometry
Thiebaut & Giovannelli (2010).

Adjusting the Hankel profile to the visibility data is then a matter of adding
the $\chi^{2}$ and the regularization term $f_{\rm prior}$ multiplied with a
so-called hyperparameter __ $\mu$, which is arbitrarily set:

$f_{\rm tot}(\lambda)=\chi^{2}(\lambda)+\mu\leavevmode\nobreak\ f_{\rm
prior}(\lambda).$ (4)

In our case, we tested two different regularization terms for $f_{\rm prior}$:
(1) a smoothness term, $f_{\rm prior}=f_{\rm smooth}$, or (2) a total
variation term, $f_{\rm prior}=f_{\rm var}$. On the one hand, $f_{\rm
smooth}$, described by the intensity difference between adjacent rings, is
given by:

$\displaystyle f_{\rm smooth}(\lambda)=\sum_{k=0}^{N_{\rm
step}-1}\sqrt{\bigg{[}h_{k+1}(\lambda)-h_{k}(\lambda)\bigg{]}^{2}}.$ (5)

We note that $f_{\rm smooth}$ will tend to minimize the variations between
consecutive radii, resulting into a smooth radial profile. On the other hand,
$f_{\rm var}$ is defined as:

$\displaystyle f_{\rm var}(\lambda)=\sum_{k=0}^{N_{\rm
step}-1}\left[\frac{h_{k+1}(\lambda)-h_{k}(\lambda)}{\theta_{k+1}-\theta_{k}}\right]^{2},$
(6)

and will tend to reconstruct uniform intensities with sharp edges. Solving the
problem (i.e., finding the right radial profile) consists therefore of
minimizing the term in Eq. 4, by varying the parameters $a_{k}$ using standard
Cobyla minimization routines from the Lmfit 202020made freely available at
https://github.com/lmfit/lmfit-py/ library, found in Python.

##  Appendix C RHAPSODY dynamic range and detection limit

In this section, we describe how we tested the robustness of the RHAPSODY code
by determining its intrinsic dynamic range. To achieve such estimation, we
built a toy model mimicking R Scl environment. Such model is composed of:
DUSTY and a gaussian layer at 15 mas with an intensity ratio with respect to
the central source starting from 1/1000 and reaching up to 1/10 (Fig 12).
Using ASPRO2, we generated VLTI/MATISSE visibilities, added error noise to the
data, and used the same (u,v)-plane coverage as the one of our R Scl
observations (see Fig 8) for each of our different models and for both $LM$\-
and $N$-bands. The initial guess intensity profiles used by RHAPSODY for all
the simulations in both bands are similar to the one used in this paper (i.e.,
Gaussian profile with a $FWHM=7$ mas). The value of the hyperparameter used is
$\mu=1$. Figure. 12 shows the spectra of the intensity profile reconstruction
produced by RHAPSODY. We can notice that the lower limit of the dynamic range
in $L$-band is about 1/200 (0.5%). In $N$-band, the code does not reconstruct
(or does so very marginally) the inner Gaussian structure added at 15 mas,
whatever its intensity. We suspect this non-detection in the $N$-band is due
to an unfortunate combination of instrumental angular resolution and dynamical
range.

(a) Without the gaussian layer at 15 mas

(b) Additional gaussian layer at 15 mas with an intensity ratio with respect
to the star of 1/1000

Figure 12: continued.

(c) Additional gaussian layer at 15 mas with an intensity ratio with respect
to the star of 1/200

(d) Additional gaussian layer at 15 mas with an intensity ratio with respect
to the star of 1/100

Figure 12: continued. (e) Additional gaussian layer at 15 mas with an
intensity ratio with respect to the star of 1/10 Figure 12: Modeled intensity
spectra from DUSTY panels 1 and 3 and its associated RHAPSODY intensity
profiles reconstruction spectra 2 and 4 in the $L$-Band and $N$-band,
respectively (from left to right). A gaussian layer has been also added at 15
mas with an intensity ratio compared to the star of 1/1000, 1/200, 1/100,
1/50, 1/20, and 1/10.