11institutetext: Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
11email<EMAIL_ADDRESS>22institutetext: LESIA,
Observatoire de Paris, CNRS, Université Paris Diderot, Université Pierre et
Marie Curie, 5 place Jules Janssen, 92190 Meudon, France 33institutetext:
SUPA, Institute for Astronomy, University of Edinburgh, Blackford Hill,
Edinburgh EH9 3HJ, UK 44institutetext: Centre for Exoplanet Science,
University of Edinburgh, Edinburgh, UK 55institutetext: Aix Marseille
Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326,
13388, Marseille, France 66institutetext: Unidad Mixta Internacional Franco-
Chilena de Astronomía, CNRS/INSU UMI 3386 and Departamento de Astronomía,
Universidad de Chile, Casilla 36-D, Santiago, Chile 77institutetext: INAF -
Osservatorio Astronomico di Padova, Vicolo della Osservatorio 5, 35122,
Padova, Italy 88institutetext: Steward Observatory, Department of Astronomy,
University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA
99institutetext: University of Exeter, School of Physics & Astronomy, Stocker
Road, Exeter, EX4 4QL, UK 1010institutetext: Dipartimento di Fisica a
Astronomia ”G. Galilei”, Universita di Padova, Via Marzolo, 8, 35121 Padova,
Italy 1111institutetext: Observatoire de l’Université de Genève, Chemin Pegasi
51, 1290 Versoix, Switzerland 1212institutetext: Department of Physics, and
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute
of Technology, Cambridge, MA02139, USA 1313institutetext: Physikalisches
Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
1414institutetext: Núcleo Milenio Formación Planetaria - NPF, Universidad de
Valparaíso, Av. Gran Bretaña 1111, Valparaíso, Chile 1515institutetext: School
of Physics and Astronomy, Monash University, Clayton, Vic 3800, Australia

# Narrow belt of debris around the Sco-Cen star HD 141011 ††thanks: Based on
observations made with ESO Telescopes at the Paranal Observatory under
programs ID 095.C-0607, 097.C-0060, 0101.C-0016, 098.C-0739, and 1101.C-0557.,
††thanks: This work has made use of the the SPHERE Data Centre, jointly
operated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CESAM (Marseille), OCA/Lagrange
(Nice), Observatoire de Paris/LESIA (Paris), and Observatoire de Lyon.

M. Bonnefoy 11 J. Milli 11 F. Menard 11 P. Delorme 11 A. Chomez 11 2 2 M.
Bonavita 33 4 4 A-M. Lagrange 11 2 2 A. Vigan 55 J.C. Augereau 11 J.L. Beuzit
33 B. Biller 33 4 4 A. Boccaletti 22 G. Chauvin 11 6 6 S. Desidera 77 V.
Faramaz 88 R. Galicher 22 R. Gratton 88 S. Hinkley 99 C. Lazzoni 77 10 10 E.
Matthews 1111 12 12 D. Mesa 77 C. Mordasini 1313 D. Mouillet 11 J. Olofsson
1414 C. Pinte 11 15 15

(Received 22/07/2021; accepted 22/10/2021)

###### Abstract

Context. We initiated a deep-imaging survey of Scorpius-Centaurus A-F stars in
2015. These stars are predicted to host warm inner and cold outer belts of
debris reminiscent of the architecture of emblematic systems such as HR 8799.

Aims. We present resolved images of a ring of debris around the F5-type star
HD 141011 that was observed as part of our survey. We aim to set constraints
on the properties of the disk, compare them to those of other resolved debris
disks in Sco-Cen, and detect companions.

Methods. We obtained high-contrast coronagraphic observations of HD 141011 in
2015, 2016, and 2019 with VLT/SPHERE. We removed the stellar halo using
angular differential imaging (ADI). We searched for scattered light emission
from a disk in the residuals and applied a forward-modeling approach to
retrieve its morphological and photometric properties. We combined our radial
velocity and imaging data to derive detection probabilities for companions co-
planar with the disk orientation.

Results. We resolve a narrow ring of debris that extends up to $\sim$1.1”
($\sim$141 au) from the star in the IRDIS and IFS data obtained in 2016 and
2019. The disk is not detected in the 2015 data which are of poorer quality.
The disks is best reproduced by models of a noneccentric ring centered on the
star with an inclination of $69.1\pm 0.9^{\circ}$, a position angle of
$-24.6\pm 1.7^{\circ}$, and a semimajor axis of $127.5\pm 3.8$ au. The
combination of radial velocity and imaging data excludes brown-dwarf (M¿13.6
MJup) companions coplanar with the disk from 0.1 to 0.9 au and from 20 au up
to 500 au (90% probability).

Conclusions. HD 141011 adds to the growing list of debris disks that are
resolved in Sco-Cen. It is one of the faintest disks that are resolved from
the ground and has a radial extent and fractional width ($\sim$12.5%)
reminiscent of Fomalhaut. Its moderate inclination and large semimajor axis
make it a good target for the James Webb Space Telescope and should allow a
deeper search for putative companions shaping the dust distribution.

###### Key Words.:

techniques: high contrast imaging- stars: planetary systems - stars:
individual: HD~141011 (HIP~77432)

##  1 Introduction

Table 1: Log of SPHERE observations

|  |  | IRDIS | IFS |  |  |  |  |
---|---|---|---|---|---|---|---|---|---
Date, UT start | Setup | Density | $\mathrm{DIT\times NDIT\times N_{EXP}}$ |  $\Delta$PA | $\epsilon$ | Airmass | $\tau_{0}$ | Remarks
|  |  | (s) | (s) | (∘) | (”) |  | (ms) |
25/07/2015, 23:28 | IRDIS-H23+IFS-YJ | ND_1.0 | 2$\times$5$\times$1 | 8$\times$3$\times$1 | 0.1 | 1.0 | 1.1 | 1.4 | Unsat. PSF
25/07/2015, 23:33 | IRDIS-H23+IFS-YJ | ND_0.0 | 64$\times$3$\times$16 | 64$\times$3$\times$15 | 35.7 | 1.1 | 1.1 | 1.2 | ADI seq.
09/04/2016, 06:53 | IRDIS-H23+IFS-YJ | ND_1.0 | 2$\times$2$\times$1 | 4$\times$1$\times$1 | 0.1 | 0.6 | 1.1 | 4.6 | Unsat. PSF
09/04/2016, 06:54 | IRDIS-H23+IFS-YJ | ND_0.0 | 32$\times$8$\times$16 | 64$\times$4$\times$16 | 49.2 | 0.6 | 1.1 | 4.5 | ADI seq.
09/04/2016, 08:05 | IRDIS-H23+IFS-YJ | ND_1.0 | 2$\times$2$\times$1 | 4$\times$1$\times$1 | 0.1 | 0.7 | 1.1 | 3.5 | Unsat. PSF
26/04/2019, 05:22 | IRDIS-BBH+IFS-YJ | ND_2.0 | 4$\times$8$\times$1 | 32$\times$1$\times$1 | 0.4 | 0.6 | 1.1 | 4.3 | Unsat. PSF
26/04/2019, 05:25 | IRDIS-BBH+IFS-YJ | ND_0.0 | 32$\times$14$\times$16 | 64$\times$7$\times$16 | 79.3 | 0.6 | 1.1 | 4.3 | ADI seq.
26/04/2019, 07:31 | IRDIS-BBH+IFS-YJ | ND_2.0 | 4$\times$8$\times$1 | 32$\times$1$\times$1 | 0.3 | 0.6 | 1.1 | 4.3 | Unsat. PSF

111DIT, NDIT, and $N_{EXP}$ correspond to the Detector Integration Time per
frame, the number of individual frames per exposure, and the number of
exposures, respectively. $\Delta$PA is the amplitude of the parallactic
rotation. $\epsilon$ and $\tau_{0}$ correspond to the seeing and coherence
time, respectively.

The proximity (d=90-200 pc), large number of intermediate-mass stars, and
young age ($\sim$11-17 Myr) of the Scorpius-Centaurus OB association (de Zeeuw
et al. 1999, and references therein) all contribute to make it a niche for the
direct-imaging search of young self-luminous planets and circumstellar disks.
The planet-finder instruments SPHERE (Spectro-Polarimetric High-contrast
Exoplanet REsearch, Beuzit et al. 2019) and GPI (Gemini Planet Imager,
Macintosh et al. 2008) are starting to probe the circumstellar environnements
in Sco-Cen at unprecedented contrasts ($10^{-6}$) down to 0.1” separations (10
au at 100 pc). They have already yielded images of 15 debris disks around
these stars in the past six years (see Appendix A and references therein).
ALMA resolved eight additional disks in the association (Lieman-Sifry et al.
2016; Su et al. 2017; Moór et al. 2017) at more moderate spatial resolutions
with no corresponding detection in scattered light so far (HD 112810, HD
113766, HD 121191, HD 121617, HD 131488, HD 138813, HD 142446, and HD 146181).
The morphology of each of these disks (wing-tilt, rings) inferred from
scattered-light images provides indications about the diversity of planetary
system architectures (Lee & Chiang 2016) beyond a separation of 10 au in a
narrow age bin ($\sim$10-17 Myr) immediately after the end of giant planet
formation.

We initiated a direct-imaging survey with SPHERE in 2015 to image new giant
planets and circumstellar disks around a sample of Sco-Cen F5-A0 stars with
high infrared excesses, modeled with two blackbody components, each
corresponding to a belt of debris (Chen et al. 2014, hereafter C14). This
architecture is reminiscent of the iconic systems previously identified by
direct imaging, such as HR 8799 (Marois et al. 2008, 2010), 51 Eridani
(Macintosh et al. 2015), the Sco-Cen member HD 95086 (Rameau et al. 2013), and
of the Solar System. Bonnefoy et al. (2017) presented the images of two belts
of debris around the F0 star HIP 67497 that we inferred from our survey (Paper
I).

We report in this work the discovery of a narrow ring of debris around the F5V
star HD~141011 (HIP~77432). This intermediate-mass star
($\mathrm{M=1.4\>M_{\odot}}$) is located at a distance of $128.37\pm 0.32$ pc
according to the Gaia-EDR3 (Gaia Collaboration 2020). The Gaia-EDR3 kinematics
and the Banyan $\Sigma$ tool222http://www.exoplanetes.umontreal.ca/banyan/
(Gagné et al. 2018) confirm the star’s membership in the 16 Myr old (Mamajek
et al. 2002) Upper Centaurus Lupus subgroup (de Zeeuw et al. 1999). C14
modeled the infrared excess of the star with two belts of debris: a warm
($499\pm 9$ K) belt at 0.8 au and a cold ($100\pm 11$ K) belt at 25.9 au.
Ballering et al. (2017) proposed their own analysis of the excess, confirming
a two-belt architecture with a warm belt at 0.5 au and a cold belt at a
temperature of 101.5 K with no given location. The authors also reported clear
silicate features in the best-fit model spectra, which is indicative of
exozodiacal dust. Jang-Condell et al. (2015) rather modeled the infrared
excess with only one warm belt located at $1.62\pm 0.63$ au. These previous
modelings of the excess all assumed a distance to HD 141011 of 96.34 pc, which
has considerably changed with Gaia. They relied mostly on the Spitzer IRS
spectrum that was available for that target, which covers a limited fraction
of the excess emission and can lead to spurious identification of two-belt
components (see section 4.3 of Kennedy & Wyatt 2014).

Previous adaptive optics observations revealed three candidate companions
(Janson et al. 2013) with separations between 1.77″and 4.25″ , but lacked the
sensitivity to resolve the circumstellar emission. Our high-contrast
observations allow us to constrain its morphology and to clarify the nature of
previously identified candidate companions. We use them as well as new radial
velocity observations to search for additional companions. We present the
observations and data in § 2 and an analysis of the disk, candidate companion
properties, and detection limits in § 3. We discuss our findings in § 4.

##  2 Observations

###  2.1 SPHERE imaging

We observed HD 141011 on July 25, 2015, April 9, 2016, and April 26, 2019,
with the VLT/SPHERE instrument (Beuzit et al. 2019) mounted on the VLT/UT3
(Table 1). The instrument was operated with the IRDIS (Dohlen et al. 2008) and
IFS (Claudi et al. 2008) subinstruments in parallel. The mode enabled pupil-
stabilized observations of the source placed behind the apodized Lyot
coronagraph N_ALC_YJH_S with a radius of 92.5 mas. IRDIS recorded $\sim
11.1\arcsec\times 12.4\arcsec$ images of the target in the H2
($\lambda_{c}$=1.593 $\mu$m, width=52 nm) and H3 ($\lambda_{c}$=1.667 $\mu$m,
width=54 nm) filters for the 2015 and 2016 epochs (Vigan et al. 2010). We
rather used the broad H-band filter ($\lambda_{c}$=1.625 $\mu$m,
$\Delta\lambda$=290 nm) in 2019 in both IRDIS channels to provide a deeper
image of the disk. The IFS yielded images with a $1.8\arcsec\times 1.8\arcsec$
field of view each in 39 spectral channels covering the 0.96-1.33 $\mu$m
spectral range at all epochs. We obtained additional coronagraphic
observations of the source with satellite spots created by a waffle pattern
introduced onto the deformable mirror of the instrument for registration
purposes. We recorded nonsaturated exposures of the star placed outside of the
coronagraphic mask with neutral density filters (ND_1.0 or ND_2.0) before
and/or after the deep-imaging sequence. The point spread function (PSF)
extracted from these images were used to estimate the flux and position of the
point sources detected in the field of view.

Figure 1: Images of the ring of debris around HD 141011 obtained in 2016 and
2019 with the IRDIS subinstrument and in 2016 with the IFS (convolved with a
Gaussian $\sigma$=2-pixel kernel). The IRDIS images obtained with the cADI and
TLOCI algorithms reveal different portions of the ring. The IFS field of view
is overlaid (dashed white circle) on the IRDIS/TLOCI panel.

The data were reduced by the SPHERE Data Center (Delorme et al. 2017) in in
the same way as for HIP 67497 (Paper I) to obtain a temporal sequence of
recentered coronagraphic frames for each of the 2 IRDIS channels and for the
39 IFS channels. We used true north values of $-1.769\pm 0.055^{\circ}$,
$-1.731\pm 0.070^{\circ}$, $-1.750\pm 0.030^{\circ}$ and plate scales of
$12.211\pm 0.021$, $12.243\pm 0.015$, and $12.249\pm 0.007$ mas/pixel for the
2015, 2016, and 2019 epochs (see Maire et al. 2016). We adopted a plate scale
of $7.46\pm 0.02$ mas/pixel for the IFS.

We then applied the classical ADI (cADI, Marois et al. 2006) and TLOCI
(Lafrenière et al. 2007) algorithms as implemented in the SPECAL pipeline of
the SPHERE Data Center (Galicher et al. 2018) and the principal component
analysis algorithm (PCA; Soummer et al. 2012) as implemented in the VIP HCI
package (Gomez Gonzalez et al. 2017) on the registered sequence of IRDIS
frames to supress the stellar halo. We averaged the H2 and H3 IRDIS images
(hereafter H2H3) at each epoch (2015 and 2016) in order to maximize our
sensitivity to faint extended structures. We also averaged the two independent
BB_H frames obtained from the 2019 observations and produced three averaged
IFS images from the 39 spectral channels (from Y to J) of the 2015, 2016, and
2019 epochs, respectively. The first five modes of the PCA contained most of
the extended structures in the IRDIS images. We also applied the PCA algorithm
relying on the angular and spectral diversity of the IFS data (Mesa et al.
2015, hereafter sPCA). The images are shown in Fig. 1. We extracted the
position and flux of each identified candidate in the TLOCI-reduced frames.

###  2.2 Radial velocity measurements on HIP 141011A

We obtained 13 optical spectra (378-691nm) between March 30, 2018, and March
12, 2020, with the HARPS high-resolution spectrograph (Mayor et al. 2003)
mounted on the ESO 3.6m telescope. The data were reduced using the Software
for the Analysis of the Fourier Interspectrum Radial velocities (SAFIR Galland
et al. 2005). We do not find evidence for spectroscopic binary signals. The
measurements are reported in Table 2 and are used in Section 3.3 to set
constraints on massive close-in companions in the system.

Table 2: HARPS radial velocity measurements of HD 141011 MJD - 2 450 000 | RV (km.s-1) | Error (km.s-1)
---|---|---
8207.78 | -0.087 | 0.062
8207.79 | -0.096 | 0.061
8207.81 | -0.066 | 0.062
8208.84 | -0.021 | 0.038
8208.85 | 0.017 | 0.039
8534.79 | 0.094 | 0.039
8534.80 | 0.061 | 0.040
8593.81 | 0.141 | 0.054
8593.82 | 0.092 | 0.052
8605.71 | -0.006 | 0.044
8605.72 | 0.113 | 0.043
8920.79 | 0.056 | 0.041
8920.81 | 0.098 | 0.042

##  3 Results

We resolve a ring of debris extending up to 1.1” from the star (141.2 au) into
the IRDIS field of view in the 2016 and 2019 images (Figure 1). The disk is
retrieved in the cADI, PCA, and TLOCI reductions. We also detect a similar
structure with the IFS data taken in 2016 (Figure 1 right) and 2019 (marginal
detection) when the cubes are collapsed in wavelength. The disk detection is
only marginal in the 2015 IRDIS data (no detection in the IFS) because the
observing conditions were poorer. We therefore did not use the 2015 images in
the remaining paper to characterize the disk.

###  3.1 Disk morphology

The various reductions enable us to capture different portions of the disk.
The cADI algorithm is the reduction with the least self-subtraction of the
disk flux. Therefore it provides deeper images of the faint emission zones far
from the star (ansae). The PCA and TLOCI algorithms are more efficient in
suppressing the residual halo at short separations. This residual halo is
mostly created by the servolag error of the adaptive optics system (also known
as wind-driven halo; Cantalloube et al. 2020).

To determine the best disk model that best reproduces the scattered-light
image of the disk, we used a python implementation333GraTeR was implemented in
python as part of the high-contrast pipeline VIP HCI (Gomez Gonzalez et al.
2017) of the GraTeR code (Augereau et al. 1999). The dust radial density is
described by a two-component power law of index $\alpha_{in}$ and
$\alpha_{out}$, inside and outside a reference radius $r_{0}$, respectively.
The vertical dust distribution is parameterized by a Gaussian profile, with a
reference scale height $\xi_{0}$ at the reference radius $r_{0}$ and a linear
dependence on the distance $r$ to the star (constant opening angle). The dust
density $\rho$ is therefore parameterized with

$\rho(r,z)=\rho_{0}\times\left[\left(\frac{r}{r_{0}}\right)^{-2\alpha_{in}}+\left(\frac{r}{r_{0}}\right)^{-2\alpha_{out}}\right]^{-1/2}\times\exp\left[-\left(\frac{z}{\xi_{0}(r/r_{0})}\right)^{2}\right]$
(1)

We modeled the scattering phase function (hereafter SPF) with a Henyey-
Greenstein phase function, which is a common and simple way to describe the
phase function of debris disks. It is parametrized by the anisotropic
scattering factor $g$ (between $-1$ and $1$),

$SPF(g,\varphi)=\frac{1}{4\pi}\frac{1-g^{2}}{\left(1-2g\cos{\varphi}+g^{2}\right)^{3/2}}$
(2)

where $\varphi$ is the scattering angle.

Figure 2: Left: IRDIS-reduced image used as a starting point for the forward-
modeling, and obtained by averaging the PCA reductions from the 2016 and 2019
epochs. Middle: Residuals after subtraction and forward-modeling of the best
model. Right: Best unconvolved model. North is up and east to the left.

We applied a forward-modelling approach to find the best disk parameters that
are compatible with the data. We first generated a synthetic scattered light
image from our model, convolved it with the PSF (here the unsaturated images
of the star), and we subtracted it from all individual frames of the IRDIS
2016 and 2019 data sets. We then reduced these disk-subtracted data sets with
a PCA algorithm, removing five principal components, to obtain four disk-
subtracted images (one for each epoch and IRDIS spectral channel), which we
averaged together to have a single disk-subtracted image. We iterated over the
disk model parameters until the level of residuals in this final image was
minimized. To estimate the goodness of fit, we computed the $\chi^{2}$ in an
elliptical ring encompassing the disk. The $\chi^{2}$ was estimated using the
following definition of the noise in the final image. We assumed that the
noise is purely radial without azimuthal dependence. The noise radial profile
was then estimated as the azimuthal root-mean square of the fluxes encircled
in apertures with a diameter of one resolution element ($\lambda/D$), taking
into account a correction factor from the small-sample statistics (Mawet et
al. 2014) and after masking the disk signal in the final image. The
uncertainties on the model parameters were derived following the method
described in Bonnefoy et al. (2017).

The initial disk image we started from is shown in Fig. 2 (left). Initial
trials showed that we were little sensitive to the scale height $\xi_{0}$ as
long as it was below 5 au (for $r_{0}$ between 125 and 130 au). We therefore
set its value to 3.5 au to save computational time. This value represents a
half-width at half maximum for the vertical density profile of $H=2.9$ au and
an aspect ratio $H/r_{0}$ of $2.3\%$ that is compatible with the minimum
natural aspect ratio of debris disks, which is predicted to be $4\%\pm 2\%$ by
Thébault (2009). Similarly, the forward-modeling approach favored models with
a very steep inner slope $\alpha_{in}>20$. However, we cannot constrain an
inner slope steeper than 20 because we are limited by the angular resolution
of our data. We therefore set the inner slope $\alpha_{in}$ to 20. We used as
free parameters the reference radius $r_{0}$, the inclination $i$, the
position angle $PA$, the outer slope of the radial dust density $\alpha_{out}$
and the anisotropic scattering factor $g$. We minimized the $\chi^{2}$ using
the Nelder & Mead (1965) algorithm. The best model is shown in Fig. 2 (right),
along with the residuals after subtraction of the best model (middle). The
reduced $\chi^{2}$ is 1.037, indicating that our model is compatible with the
data. The disk peak flux decreases by $\sim 30\%$ due to the convolution with
the IRDIS point-spread function, and then by another $\sim 65\%$ due to the
ADI reduction technique (Milli et al. 2012). The best parameters of the model
are indicated in Table 3. The model favors a narrow ring inclined by
$69.1^{\circ}\pm 0.9^{\circ}$, with a steep outer slope for the radial dust
density of $-13.9^{+3.4}_{-4.6}$ and a reference radius $127.5\pm 3.9$ au.
Because $|\alpha_{in}|>|\alpha_{out}|$, the location of the maximum dust
surface density is slightly greater than $r_{0}$ and equals 128.2 au, with a
ring FWHM of 16.1 au, corresponding to about three resolution elements in the
H band. This implies a fractional width for the ring of 12.6%.

Table 3: Best model parameters. The uncertainty is given at the $1\sigma$ level. Parameter | Best value
---|---
$r_{0}$ (au) | $127.5\pm 3.9$
$i$ (∘) | $69.1\pm 0.9$
$PA$ (∘) | $-24.6\pm 1.7$
$\alpha_{out}$ | $-13.9^{+3.4}_{-4.6}$
$g$ | $0.65\pm 0.11$

###  3.2 Excess emission

Figure 3: Spectral energy distribution of HD 141011 and the infrared
measurements from Spitzer (black line, gray shading for the uncertainty, and
triangle for the upper limit). We overplot in colors the four SED models that
are compatible with the mid-infrared excess, all with a minimum particle size
of $1\>\mu m$. The plain lines represent the stellar photosphere and disk
emission, while the dashed lines isolate the contribution of the disk alone.
The inset is a zoom in the $10-40\>\mu$m range, highlighting the model
mismatch between 15 and $25\>\mu$m.

The parameters of the disk that we detect are not compatible with the previous
models of the SED alone (C14; Jang-Condell et al. 2015; Ballering et al.
2017). The SED is indeed unconstrained beyond $36\>\mu m$, with only one upper
limit from Spitzer/MIPS at $70\>\mu m$ (see Fig. 3). The SED fitting can be
highly degenerate in these conditions. The absence of more constraining mid-
and far-infrared measurements prevents us from carrying out a detailed
modeling of the SED of the cold belt detected in the imaging. We do not know
either whether the infrared excess detected between $10\>\mu m$ and $37\>\mu
m$ comes from this cold belt or from a warm belt suggested by C14, Jang-
Condell et al. (2015), and Ballering et al. (2017).

We therefore modeled the SED anew using the following approach. We assumed
that the excess emission detected with Spitzer/IRS between $30\>\mu m$ and
$37\>\mu m$ is entirely due to the imaged cold belt. We also investigated
which families of dust particle property models are compatible with this
hypothesis.

To do this, we first re-estimated the star’s photospheric contribution,
normalizing a Kurucz synthetic spectrum with T${}_{e\\!f\\!f}$ =6500K, log
g=4.5, and M/H=0.0 onto a compilation of published photometry (GALEX NUV,
TYCHO B, Gaia EDR3, and 2MASS JHK) that is not affected by the excess emission
gathered through the VOSA tool (Bayo et al. 2008).

We then used the radiative transfer code MCFOST (Pinte et al. 2006, 2009) and
the disk morphological parameters described in section 3.1 to model the excess
emission.

|  |
---|---|---
|  |
Figure 4: Relative position of the candidate companions in 2015 (blue; epoch
1), 2016 (green; epoch 2), and 2019 (red; epoch 3) with respect to the
expected positions (dots) for background objects. Table 4: Photometry and
astrometry of the point sources inferred from the three observation epochs
(”Ep.”). All are background stars.

# |  Ep.a |  $\Delta$H2 or $\Delta$H |  $\Delta$H3 | PA | Sep.
---|---|---|---|---|---
|  | (mag) | (mag) |  (∘) | (mas)
1 | 1 | $12.54\pm 0.12$ | $12.33\pm 0.12$ | $196.98\pm 0.09$ | $1336\pm 4$
| 2 | $12.48\pm 0.07$ | $12.38\pm 0.03$ | $197.12\pm 0.09$ | $1314\pm 2$
| 3 | $12.59\pm 0.22$ | … | $196.28\pm 0.04$ | $1207\pm 2$
2 | 1 | $9.76\pm 0.11$ | $9.64\pm 0.11$ | $269.34\pm 1.47$ | $1702\pm 3$
| 2 | $9.60\pm 0.07$ | $9.50\pm 0.07$ | $270.1\pm 0.06$ | $1704\pm 3$
| 3 | $9.62\pm 0.22$ | … | $273.43\pm 0.47$ | $1670\pm 1$
3 | 1 | $11.42\pm 0.11$ | $11.32\pm 0.11$ | $132.25\pm 0.07$ | $2900\pm 6$
| 2 | $11.34\pm 0.07$ | $11.25\pm 0.07$ | $131.87\pm 0.08$ | $2899\pm 2$
| 3 | $11.56\pm 0.22$ | … | $129.78\pm 0.04$ | $2881\pm 2$
4 | 1 | $8.52\pm 0.11$ | $8.43\pm 0.11$ | $157.45\pm 0.06$ | $3358\pm 6$
| 2 | $8.33\pm 0.07$ | $8.26\pm 0.07$ | $157.26\pm 0.08$ | $3346\pm 2$
| 3 | $8.58\pm 0.22$ | … | $155.99\pm 0.03$ | $3281\pm 2$
5 | 1 | $9.70\pm 0.12$ | $9.68\pm 0.12$ | $68.77\pm 0.08$ | $4329\pm 7$
| 2 | $9.57\pm 0.07$ | $9.51\pm 0.07$ | $68.53\pm 0.08$ | $4348\pm 3$
| 3 | $9.73\pm 0.23$ | … | $67.65\pm 0.03$ | $4412\pm 2$
6 | 1 | $14.04\pm 0.16$ | $13.91\pm 0.15$ | $334.80\pm 0.06$ | $4659\pm 9$
| 2 | $13.48\pm 0.08$ | $13.50\pm 0.91$ | $334.95\pm 0.08$ | $4690\pm 4$
| 3 | $13.66\pm 0.23$ | … | $336.00\pm 0.04$ | $4752\pm 3$
7 | 1 | $14.42\pm 0.28$ | $14.57\pm 0.58$ | $141.52\pm 0.12$ | $4833\pm 12$
| 2 | $14.20\pm 0.12$ | $13.92\pm 0.09$ | $141.30\pm 0.10$ | $4827\pm 5$
| 3 | $14.53\pm 0.23$ | … | $140.30\pm 0.04$ | $4784\pm 3$
444a Epoch 1, 2, and 3 correspond to the 2015, 2016, and 2019 observations,
respectively.

We restrained our investigation to a population of dust particles in a size
distribution with a power-law index -3.5 (Dohnanyi 1969), with a minimum
particle size of 1, 2, 5 and $10\>\mu m$. A rough estimate of the blow-out
size $s_{bo}=0.8\frac{L/L_{\odot}}{M/M_{\odot}}\frac{2700}{\rho}$ (assuming
blackbody grains, Wyatt 2008) is $1.9\>\mu m$ for $L=3.39\>L_{\odot}$ ($\pm
0.03$) and compact astrosilicates of density $\rho=2700\>\text{kg/m}^{3}$, and
more porous particles would have a larger blow-out size (e.g., Arnold et al.
2019).

We explored four different compositions: pure astrosilicates (Draine & Lee
1984), pure amorphous carbon (Rouleau & Martin 1991), a mix of both in equal
amounts, or a mix of astronomical silicates, amorphous carbon, and water ice
(Li & Greenberg 1998) in equal amounts. We used the Mie theory, which is valid
for spherical particles and assumed either compact particles or 30% or 60%
porous particles. We therefore investigated 48 dust models.

We then started from a low initial mass for the belt and scaled it up until
the SED of the disk and star either matched the Spitzer/IRS measurements
between $30\>\mu m$ and $37\>\mu m$, or reached the Spitzer/MIPS $70\>\mu m$
upper limit, whichever occured first. For completeness, we provide in Appendix
B the SED of the 48 models we explored. The quality of the fit was assessed
using the reduced $\chi^{2}$ computed between the measured and predicted SED
at wavelengths between $30$ and $37\mu m$ (38 degrees of freedom).

Out of our 48 models, 11 are compatible with the $30-37\>\mu m$ IRS spectra
and $70\>\mu m$ Spitzer/MIPS upper limit with a reduced $\chi^{2}$ below 1.
These 11 models correspond to dust populations with a minimum particle size of
$1$ or $2\>\mu m$ because all larger minimum particle sizes cannot
simultaneously be compatible with the infrared excess and the Spitzer/MIPS
upper limit. Out of these 11 models, only 4 stay strictly below (but close to)
the $70\>\mu m$ Spitzer/MIPS upper limit (the other seven models have a
$70\>\mu m$ flux equal to the Spitzer/MIPS upper limit) and these 4 models all
have a minimum particle size of $1\>\mu m$ with the best reduced $\chi^{2}$
below $0.2$. The MIPS image shows a faint point-source at the target location,
but overlaid on a variable background so that it cannot be considered as a
detection but may indicate that the disk excess indeed falls close to the
tabulated upper limit. We highlight that these four models slightly
underpredict the SED between $15$ and $25\>\mu m$, as shown in the inset of
Fig. 3. We did not try to match the measured flux in this wavelength range
because the contribution of the cold belt imaged with SPHERE is negligible
compared to a potential warmer belt for which we have no observational
constraint from the high-contrast images presented in this paper. A warmer
belt at $\sim 500$ K, as proposed by C14, may therefore account for the
underestimated $15-25\>\mu m$ flux. We defer this discussion to a further
study when a far-infrared or (sub-)millimeter SED measurement of the resolved
cold belt will be secured to raise the degeneracy between the cold and warmer
components. The fractional luminosity of the four best disk models ranges
between $2.7\times 10^{-4}$ and $3.0\times 10^{-4}$, which is significantly
higher than the value reported in C14 ($9.2\times 10^{-5}$).

Figure 5: Scattering phase functions of the four dust population models that
are compatible with the SED (color lines). The black line shows the HG
analytical SPF favored by the scattered light forward-modelling, along with
the $1\sigma$ uncertainty in gray. All SPFs are normalized to $90^{\circ}$ for
comparison.

To confirm the compatibility of this family of models with our observations,
we verified that they could also reproduce the scattered light images of the
disk, especially the scattering phase function (hereafter SPF) of the dust,
for which our forward-modeling approach favored an HG with a parameter
$g=0.65\pm 0.11$. The comparison between the theoretical SPF and the HG model
is shown in Fig. 5. It shows that the theoretical SPF are compatible with the
fitted SPF, except for the more porous dust population including
astrosilicates, carbonaceous material, and water ice. Most models predict some
slight backward scattering beyond $140^{\circ}$. The back side of the disk is
unfortunately not detected in the image, and a single HG SPF cannot reproduce
this behavior, so that we cannot discuss the reality of this behavior in the
present data.

###  3.3 Searching for perturbers

Figure 6: Detection limits (5$\sigma$) for the IFS (spectral PCA) and IRDIS
(TLOCI) converted into mass assuming the Gaia-EDR3 distance of the system. The
vertical dot-dashed line corresponds to the projected separation of the disk
ansae.

We detect seven point sources in the IRDIS field of view. None of them falls
into the field of view of the IFS. Their astrometry is reported in Table 4 and
in Figure 4. It confirms that all point sources follow the expected apparent
on-sky motion of background objects. Point sources 2, 4, and 5 correspond to
those detected by Janson et al. (2013).

Detection limits for the three epochs of observations were estimated by
injecting fake companions with flat spectra into the datacubes for the IFS.
The IRDIS detection limits were estimated from the TLOCI coefficients and the
local level of the noise. We used the COND evolutionary tracks to convert the
derived contrasts into masses (Baraffe et al. 2003) along with the 2MASS
photometry of the host star (Cutri et al. 2003). We report these limits in
Fig. 6 for the 2016 and 2019 epochs. Any hot-start companion more massive than
2 $M_{Jup}$ would have been detected down to 40 au (projected separation). The
IFS data are less sensitive than the IRDIS data beyond 40 au. This is coherent
with the loose detection of the disk achieved in the data at J band. The
detection limits confirm that the 2019 data are less sensitive than the 2016
epoch in spite of the better seeing and coherence time.

We combined the detection limits obtained at the three epochs of SPHERE
observations together with the available HARPS radial velocity data (Section
2.2) on the star through the MESS2 tool (Lannier et al. 2017). The tool runs
Monte Carlo simulations and compares them against the observations at each
epoch to evaluate the detection probabilities down to 0.1 au semimajor axis.
We assumed a flat distribution of planet eccentricities from $e=0.0$ to 0.9
and report the results in Fig 7 for planets coplanar with the disk.

Figure 7: Planet detection probabilities inferred from the MESS2 tool relying
on the available SPHERE and HARPS data of the system. The blue shadings
indicate the probability of a detection of an exoplanet of a given mass and
semimajor axis. The vertical black lines indicate the inner and outer edge of
the disk. The red line labeled Wisdom criteria indicates the expected mass-to-
semimajor axis relation for a planet carving the inner or outer edge of the
disk through its chaotic zone.

We exclude (90% probability) brown dwarf (M$>$13.6 MJup) companions from 0.1
to 0.9 au, for instance, inside the warm belt component proposed by C14. The
imaging data rule out planets more massive than 4 MJup beyond 50 au and up to
the disk inner edge.

In an attempt to bring additional constraints from the known system
architecture, we investigated whether the very steep inner and outer edges of
the disk might be due to the presence of an undetected low-mass companion. A
possible mechanism to explain such a sharp ring is indeed the presence of a
gravitational perturber shaping the inner or the outer edge of the disk
because a planet is surrounded by a chaotic zone where the orbits of potential
particles are unstable (Wisdom 1980). The width $\delta a$ of this chaotic
zone created by the overlap of mean-motion resonances of a planet on a
circular orbit is given by

$\delta a/a=1.3\mu^{2/7}$ (3)

where $\mu$ is the ratio of the planetary to stellar mass, and a is the
semimajor axis of the planet. Mustill & Wyatt (2012a) extended this result
with numerical simulations to the case of a planet on an eccentric orbit,
showing that Eq. 3 still applies when the eccentricity is kept below the
critical value of $0.21\mu^{3/7}$. In our case, this means that Eq. 3 remains
valid for an eccentricity below $0.04$ for planets with masses lower than 30
MJup. We show in Fig. 7 with the red line the mass and semimajor axis of
planets with an outer (inner) edge of the chaotic zone corresponding to the
inner (outer) edge of the debris disks, overplotted with our detection limits.
We can exclude with a confidence level higher than 90% that planets more
massive than 3 MJup shape the inner or outer edge of the disk.

To conclude, we note that the analysis of the Gaia-eDR3 and HIPPARCOS data
(e.g, Kervella et al. 2021) do not reveal significant differences in proper
motion values that could be exploited to place further constraints on unseen
companions in the system.

##  4 Discussion and conclusions

HD 141011 is the 53th debris disk that has been resolved in scattered light.
It can be compared to the growing sample of related GPI and SPHERE disks that
are resolved around stars from the association (see the Appendix A for a
summary of the disk and host star properties based on the latest observational
inputs, e.g., the Gaia eDR3). We show in figure 8 the radial extent of these
disks (except for HD98363, for which no values are reported in the
literature). We overlaid the position of the cold classical Kuiper belt (42-47
au) whose objects are thought to have experienced the least interactions with
the migrating planets (Parker & Kavelaars 2010; Gomes 2021) and might provide
a representative comparison to the radial dust distribution of young debris
disks. The symbol sizes are proportional to the reported fractional
luminosities.

Figure 8: Radial extent of the debris disks in Sco-Cen inferred from
scattered-light images obtained with SPHERE and GPI. The systems are ranked by
stellar luminosities. The symbols are located at the peak of the brightness
distribution ($\mathrm{r_{peak}}$) or at the location of estimated
$\mathrm{r_{0}}$, and their sizes are proportional to the fractional
luminosity. The figure does not extend below 13 au, which corresponds to the
typical shortest physical separations accessible by SPHERE and GPI for Sco-Cen
targets. The extent of the cold Kuiper belt is reported for comparison (shaded
area). Figure 9: Fractional width and radius of debris rings with non-edge-on
geometries in Sco-Cen (circles). The circle sizes are proportional to the disk
fraction luminosity. HD 141011 (cross) falls in a void space close to the
outer belt of HD 120326. The morphology of Fomalhaut inferred from optical
(brown star, Kalas et al. 2005) or ALMA (yellow star, MacGregor et al. 2017)
data are similar to those of HD 141011.

HD141011 has the faintest fractional luminosity ($L_{IR}/L_{\star}$) and is
one of the largest rings of debris that have been imaged in Sco-Cen. Its
inclination and brightness enhancement on the forward-scattering side makes it
favorable for detection in scattered light, and our multi-epoch observations
have been critical in vetting the detection. The figure also shows no clear
correlation between the belt spatial location and the star’s luminosity (e.g.,
Pawellek et al. 2014; Matrà et al. 2018; Esposito et al. 2020). The sample in
Sco-Cen is still limited (in particular, the range of stellar luminosity),
however, and the figure rather reveals the unique diversity of architectures
encountered in the association.

The ring is found at a larger separation than predicted by the power-law
radius - stellar luminosity relation derived by Esposito et al. (2020) and
Matrà et al. (2018). When resolved debris disks are considered regardless of
their age, the reference radius $r_{0}$ and fractional luminosity of HD 141011
are relatively close to those of the ring of debris surrounding the F-type
star HD 160305 (Perrot et al. 2019). This young ($\sim 18-26$ Myr; e.g.,
Miret-Roig et al. 2020) disk has also been resolved with SPHERE, but shows a
clear asymmetry, and the outer edge is shallower than that of HD 141011.

The fractional width of the rings ($\Delta R/R$) can inform about the dust
confinement mechanisms (Mustill & Wyatt 2012b). The disks in Sco-Cen have all
been observed at commensurable spatial resolutions (SPHERE/GPI). However,
large uncertainties remain on the disk $R_{in}$ and $R_{out}$ values (Table 5)
because most of these values rely on the modeling of the flux distribution
(with sometime fixed $\alpha_{min}$ values) in a relatively low S/N regime,
which in turn depends on the disk orientation. A tentative analysis is shown
in Figure 9. Disks with radii smaller than 100 au have comparable fractional
widths below $\sim$40%. HD129590 appears as an outlier in this separation
range: it has the largest fractional width and highest fractional luminosity.
Matthews et al. (2017) noted however that the morphology of this disk might be
more complex than a simple ring. Moreover, we did not include several disks
whose morphology is less constrained (HD 156623, HD146897) and which might
populate this parameter space. Conversely, HD141011 falls close to the outer
belt of HD 120326, but the latter is a peculiar case, showing a strong
asymmetry that might be related to large-scale structures seen at optical
wavelengths (Bonnefoy et al. 2017). When all known debris disks resolved in
scattered light are considered (see Adam et al. 2021, for a complete sensus),
the spatial extent and fractional width of HD 141011 are in fact similar to
the ones of the emblematic older disk around Fomalhaut (Kalas et al. 2005,
2013; MacGregor et al. 2017). The fractional width and low (or null)
eccentricity of HD141011 is also similar to that of HR4796, whose age is more
similar to that of HD 141011 (e.g., TW Hydrae association; $\sim$10 Myr
Weinberger et al. 2013; Ducourant et al. 2014). Planets have been proposed to
explain the morphologies of both Fomalhaut and HR4796 (e.g., Lagrange et al.
2012; Pearce et al. 2021), and the detection limits (Section 3.3) for the
system must now be improved, in particular, along the semiminor axis with
deeper observations benefiting from improved AO and contrast performances
(SPHERE star-hopping mode, SPHERE+, see Boccaletti et al. 2020), the JWST, or
the E-ELT.

###### Acknowledgements.

We thank our anonymous referees for their constructive comments which helped
improving the manuscript. We thank the ESO staff for the help during the
preparation of the observations and their execution. We are grateful to the
SPHERE consortium for providing us with the most recent measurements of the
instrument platescale and True North. We thank Aurélia Leclerc from IPAG for
fruitful discussions about the robustness of the Gaia-eDR3 and HIPPARCOS
proper motion determination. We acknowledge support in France from the French
National Research Agency (ANR) through project grants ANR-14-CE33-0018 and
ANR-20-CE31-0012, the CNRS-D2P PICS grant, and the Programmes Nationaux de
Planetologie et de Physique Stellaire (PNP & PNPS). This project has received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (COBREX; grant agreement
885593). SDe, RGr, CLa, and Dme acknowledge financial support from the ASI-
INAF agreement n.2018-16-HH.0 and from PRIN-INAF 2019 ”Planetary systems at
young ages (PLATEA)”. C.P. acknowledges funding from the Australian Research
Council via FT170100040 and DP180104235. J. O. acknowledges support by ANID, –
Millennium Science Initiative Program – NCN19_171, from the Universidad de
Valparaíso, and from Fondecyt (grant 1180395). This work has made use of the
SPHERE Data Centre, jointly operated by OSUG/IPAG (Grenoble),
PYTHEAS/LAM/CeSAM (Marseille), OCA/Lagrange (Nice), Observatoire de
Paris/LESIA (Paris), and Observatoire de Lyon/CRAL, and supported by a grant
from Labex OSUG@2020 (Investissements d’avenir – ANR10 LABX56). This
publication makes use of VOSA, developed under the Spanish Virtual Observatory
project supported by the Spanish MINECO through grant AyA2017-84089. VOSA has
been partially updated by using funding from the European Union’s Horizon 2020
Research and Innovation Programme, under Grant Agreement nº 776403
(EXOPLANETS-A).

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##  Appendix A Disks in Sco-Cen

We report in this section a homogeneous set of properties of debris disks that
have been resolved in scattered light in Sco-Cen. The host star luminosities
were estimated with the VOSA tool (Bayo et al. 2008). The dust radial
distributions and the infrared luminosity are updated based on the Gaia-EDR3
parallaxes.

The parameters defining the disk radial distributions ($R_{in}$, $R_{out}$,
$r_{0}$) vary depending on the framework used to model the images (e.g.,
Wahhaj et al. 2016; Esposito et al. 2020; Lagrange et al. 2016), or are
directly extracted from the flux distribution in the images ($r_{peak}$;
Feldt, M. et al. 2017) numerically deprojected whenever the disks are not seen
edge-on. We re-estimated the minimum and maximum extent of the belts
($R_{in}$, $R_{out}$) from $r_{0}$, $\alpha_{in}$, and $\alpha_{out}$ whenever
the former was not given in the reference papers following the method
described in Adam et al. (2021).

In the sample of targets, HD 98363 has been reported to form a $\sim$7000 au
wide system with the K-type star Wray 15-788, bearing a circumstellar disk
(Bohn et al. 2019), making that system an exceptional case within the sample
of disks that are resolved in Sco-Cen. However, the Gaia-EDR3 increases the
distance difference between the two objects ($1.99\pm 0.44$ pc) with respect
to the DR2 ($1.08\pm 0.84$pc), as well as the significance of the deviation in
proper motion on the declination ($\mathrm{\Delta\>pm_{DEC}=0.598\pm
0.025\>mas/yr}$ for the EDR3 versus $\mathrm{\Delta\>pm_{DEC}=0.616\pm
0.064\>mas/yr}$ for the DR2). Conversely, the difference in proper motion in
right ascension ($\mathrm{\Delta\>pm_{RA}=0.050\pm 0.025\>mas/yr}$ for the
EDR3 versus $\mathrm{\Delta\>pm_{RA}=0.092\pm 0.068\>mas/yr}$ for the DR2) is
slightly reduced. The nature of this putative system should be reinvestigated
based on the improved astrometry and radial velocity measurement of both
objects, which are provided as part of the future releases of Gaia.

Table 5: Properties of debris disks in Sco-Cen inferred from scattered-light
images and ranked according to the host star luminosity.

# Name | Distance |  L/L⊙ | Sub-grp | # belts | $\mathrm{R_{in}}$ | $\mathrm{R_{out}}$ | $\alpha_{in}$ | $\alpha_{out}$ |  r0 | $\mathrm{r_{peak}}$ | $\mathrm{L_{IR}/L_{\star}}\>^{c}$ | Morphology | Refs
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (pc) |  |  |  | (au) | (au) |  |  | (au) | (au) |  |  |
HD 156623a | $108.33\pm 0.33$ | $11.73\pm 0.50$ | UCL | 1 |  $\leq$13.70 | 89.13 | … | … | … | … | $4.82\times 10^{-3}$ | ring | 2, 3
HD 98363 | $137.21\pm 0.35$ | $9.95\pm 0.10$ | LCC | 1 | … | … | … | … | … | … | $9.71\times 10^{-4}$ | asym. ring | 4, 3
HD 131835a | $129.74\pm 0.47$ | $9.37\pm 0.71$ | UCL | 1 | 59.68 | 75.24 | … | … | … | 70.06 | $3.43\times 10^{-3}$ | ring | 5, 3
|  |  |  | 2 | 89.52 | 127.14 | $8.2^{+1.1}_{-0.8}$ | $-2.3\pm 0.2$ | $95.24^{+1.3}_{-1.2}$ | 103.79 | $3.43\times 10^{-3}$ | ring | 5, 3
HD 110058a | $130.08\pm 0.53$ | $8.20\pm 0.10$ | LCC | 1 | $\leq 26$ | $\geq 78$ | … | … | … | 39.02 | $2.98\times 10^{-3}$ | asym. edge-on | 6, 3
HD 143675 | $135.70\pm 0.52$ | $7.98\pm 0.43$ | UCL | 1 | $42.9^{+3.4}_{-7.4}$ | $50.8^{+1.4}_{-1.0}$ | … | … | … | … | $6.76\times 10^{-4}$ | edge-on | 4, 3
HD 111161 | $109.37\pm 0.25$ | $7.81\pm 0.08$ | LCC | 1 | $71.4^{0.5}_{-1.0}$ | $217.9^{+15.5}_{-15.3}$ | … | … | … | … | $5.06\times 10^{-3}$ | ring | 4, 3
HD 106906d | $102.38\pm 0.19$ | $5.92\pm 0.36$ | LCC | 1 |  70.12b |  98.92b | 10.0 | $4.2\pm 0.5$ | $77.19^{+3.28}_{-2.33}$ | … | $5.01\times 10^{-3}$ | asym. ring | 7, 8, 3
HD 117214 | $107.35\pm 0.25$ | $5.11\pm 0.09$ | UCL | 1 |  43.48b |  56.04b | $24^{+18}_{-10}$ | $-4.2^{+0.3}_{-0.5}$ | $45.08\pm 1.08$ | … | $2.62\times 10^{-3}$ | asym. ring | 2, 9, 3
HD 115600 | $109.04\pm 0.25$ | $4.57\pm 0.07$ | LCC | 1 |  40.08b |  52.79b | 7.5 | -7.5 | $46\pm 2$ | … | $2.60\times 10^{-3}$ | ring | 10, 11, 3
HD 120326d | $113.27\pm 0.38$ | $4.15\pm 0.05$ | UCL | 1 |  55.99b |  75.66b | 10: | -5: | $61.8\pm 3.2$ | … | $1.53\times 10^{-3}$ | ring | 12, 3
|  |  |  | 2 |  123.75b |  155.97b | 10: | $-8^{+4}_{-8}$ |  137.1$\pm 8.5$ | … | $1.53\times 10^{-3}$ | asym. ring | 12, 3
HD 114082a | $95.06\pm 0.20$ | $3.50\pm 0.04$ | LCC | 1 |  30.43b |  41.25b | 10: | -4.98 | 30.08 | … | $4.92\times 10^{-3}$ | ring | 13, 3
HD 141011 | $128.38\pm 0.32$ | $3.39\pm 0.03$ | UCL | 1 |  121.17b |  137.31b | 20: | $-13.9^{+3.4}_{-4.6}$ | $127.5\pm 3.9$ | … | $2.90\times 10^{-4}$ | ring | 6, 3
HD 146897a | $132.19\pm 0.42$ | $3.27\pm 0.06$ | US | 1 |  64.40b |  117.52b | $5.0\pm 2.8$ | $-2.5\pm 1.4$ | $78\pm 18$ | … | $1.06\times 10^{-2}$ | edge-on | 14, 3
HD 145560a | $121.23\pm 0.29$ | $3.18\pm 0.14$ | UCL | 1 | $69.1^{+3.0}_{-1.3}$ | $225.7^{+27.4e}_{-10.9}$ | … | … | … | … | $1.38\times 10^{-3}$ | ring | 1, 3, 4
HD 129590a | $136.32\pm 0.44$ | $2.92\pm 0.56$ | UCL | 1 |  42.18b |  122.30b | $3.15\pm 0.03$ | $-1.31\pm 0.01$ | $57.3\pm 0.2$ | … | $7.97\times 10^{-3}$ | ring | 15, 3
HD 111520a,d | $108.05\pm 0.21$ | $2.51\pm 0.17$ | LCC | 1 |  $\leq$32 | $\geq 108$ | … | … | … | 62 | $1.10\times 10^{-3}$ | asym. edge-on | 16, 3

555References: 1 - this work, 2 - Esposito et al. (2020)

, 3 - Gaia Collaboration (2020), 4 - Hom et al. (2020), 5 - Feldt, M. et al.
(2017), 6 - Kasper et al. (2015), 7 - Kalas et al. (2015), 8 - Lagrange et al.
(2016), 9 - Engler et al. (2020), 10 - Currie et al. (2015), 11 - Gibbs et al.
(2019), 12 - Bonnefoy et al. (2017), 13 - Wahhaj et al. (2016), 14 - Engler et
al. (2017), 15 - Matthews et al. (2017), 16 - Draper et al. (2016).
Notes: a Also resolved at submillimeter wavelengths (Lieman-Sifry et al. 2016;
Kral et al. 2020). b Estimated from $R_{0}$, $\alpha_{in}$, and
$\alpha_{out}$. c Fractional luminosity of both belts, d Extended structures
at optical wavelengths (Kalas et al. 2015; Padgett & Stapelfeldt 2016;
Bonnefoy et al. 2017), e Esposito et al. (2020) presents a lower limit for
Rout of 196.2 au.

##  Appendix B Disk modeling

Fig. 10 shows the SED of the 48 disk models.

Figure 10: Spectral energy distribution of the 48 disk models (four different
compositions in columns, four different minimum particle sizes in rows, and
three different porosities in three colors). The infrared excess of each model
is indicated in the label.