11institutetext: STAR Institute, Université de Liège, 19c Allée du Six Août,
4000 Liège, Belgium 22institutetext: Large Binocular Telescope Observatory,
933 North Cherry Avenue, Tucson, AZ 85721, USA 33institutetext: Steward
Observatory, Department of Astronomy, University of Arizona, 993 N. Cherry
Ave, Tucson, AZ, 85721, USA 44institutetext: Institute of Astronomy, KU
Leuven, Celestijnlaan 200D, 3001 Leuven, Belgium 55institutetext: Department
of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK
66institutetext: Nicolaus Copernicus Astronomical Center, Polish Academy of
Sciences, Bartycka 18, 00-716, Warsaw, Poland 77institutetext: Univ. Grenoble
Alpes, CNRS, IPAG, 38000 Grenoble, France 88institutetext: School of Physics
and Astronomy, Monash University, Clayton, Vic 3800, Australia
99institutetext: Institute of Astronomy, University of Cambridge, Madingley
Road, Cambridge CB3 0HA, UK 1010institutetext: Instituto de Física y
Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña
1111, Playa Ancha, Valparaíso, Chile 1111institutetext: Núcleo Milenio
Formación Planetaria - NPF, Universidad de Valparaíso, Av. Gran Bretaña 1111,
Valparaíso, Chile

# A near-infrared interferometric survey of debris-disk stars

VII. The hot/warm dust connection††thanks: Based on observations made with ESO
Telescopes at the La Silla Paranal Observatory under program IDs 093.C-0712
and 094.C-0325.

O. Absil, F.R.S.-FNRS Research Associate11 L. Marion 11 S. Ertel 2233 D.
Defrère 44 G. M. Kennedy 55 A. Romagnolo 66 J.-B. Le Bouquin 77 V. Christiaens
88 J. Milli 77 A. Bonsor 99 J. Olofsson 10101111 K. Y. L. Su 33 J.-C. Augereau
77

(Received 6 June 2017; accepted 21 April 2021)

###### Abstract

Context. Hot exozodiacal dust has been shown to be present in the innermost
regions of an increasing number of main sequence stars over the past fifteen
years. The origin of hot exozodiacal dust and its connection with outer dust
reservoirs remains however unclear.

Aims. We aim to explore the possible connection between hot exozodiacal dust
and warm dust reservoirs ($\geq 100$ K) in asteroid belts.

Methods. We use precision near-infrared interferometry with VLTI/PIONIER to
search for resolved emission at H band around a selected sample of 62 nearby
stars showing possible signposts of warm dust populations.

Results. Our observations reveal the presence of resolved near-infrared
emission around 17 out of 52 stars with sufficient data quality, four of which
are shown to be due to a previously unknown stellar companion. The 13 other
H-band excesses are thought to originate from the thermal emission of hot dust
grains, close to their sublimation temperature. Taking into account earlier
PIONIER observations, where some stars with warm dust were also observed, and
after re-evaluating the warm dust content of all our PIONIER targets through
spectral energy distribution modeling, we find a detection rate of
$17.1^{+8.1}_{-4.6}\%$ for H-band excess around main sequence stars hosting
warm dust belts, which is statistically compatible with the occurrence rate of
$14.6^{+4.3}_{-2.8}\%$ found around stars showing no signs of warm dust. After
correcting for the sensitivity loss due to partly unresolved hot disks, under
the assumption that they are arranged in a thin ring around their sublimation
radius, we however find tentative evidence at the $3\sigma$ level that H-band
excesses around stars with outer dust reservoirs (warm or cold) could be
statistically larger than H-band excesses around stars with no detectable
outer dust.

Conclusions. Our observations do not suggest a direct connection between warm
and hot dust populations, at the sensitivity level of the considered
instruments, although they bring to light a possible correlation between the
level of H-band excesses and the presence of outer dust reservoirs in general.

###### Key Words.:

stars: circumstellar matter – binaries: close – techniques: interferometric

##  1 Introduction

Studying the formation and evolution of potentially habitable Earth-like
planets requires a good knowledge of the environment close to the habitable
zone, and thus of the _exozodiacal_ dust residing in this region (similar to
our zodiacal dust). The presence of exozodiacal dust around other stars may
represent a major obstacle for future terrestrial planet-finding missions
(Defrère et al., 2010, 2012; Roberge et al., 2012; Stark et al., 2014a).
Indeed, exozodiacal dust disks (“exozodis”) not only add a significant amount
of photon noise to the observations, but may also result in confusion, where
the structures of the exozodis mimic the expected signal of an Earth-like
planet as seen by future coronagraphic or interferometric space-based
observatories. Usually, when referring to exozodiacal dust, one considers
primarily the dust in the habitable zone (e.g. Defrère et al., 2010; Roberge
et al., 2012; Stark & Kuchner, 2008). However, in our Solar system, zodiacal
dust is much more extended than the habitable zone, and actually shows an
increasing density down to the F-corona, with a possible dust-free zone within
0.1–0.2 au from the Sun (e.g. Dikarev & Schwarz, 2015; Howard et al., 2019).
Likewise, it is expected that exozodiacal dust can extend over a broad range
of separations from its host star, much larger than just the habitable zone.

The capability of near-infrared interferometry to probe the presence of hot
dust in the innermost regions around nearby stars was first demonstrated by
Ciardi et al. (2001) and by Absil et al. (2006). The study of Absil et al.
(2006) was then followed by a series of papers, which have extended the search
to about 150 nearby stars, mostly using the CHARA/FLUOR and VLTI/PIONIER
instruments (Absil et al., 2006; di Folco et al., 2007; Absil et al., 2008,
2013; Ertel et al., 2014; Nuñez et al., 2017). These studies have shown that
near-infrared excesses can be resolved around about 10% to 30% of nearby main
sequence stars depending on the observing wavelength. Ertel et al. (2016) have
also demonstrated the repeatability of the detections, showing that near-
infrared excesses are not spurious and caused by poorly understood
instrumental or astrophysical errors. Our current understanding is that near-
infrared excesses around main sequence stars are related to the thermal
emission from hot dust grains close to their sublimation temperature
($\sim$1500 K for silicate dust grains). The contribution of scattered light
cannot be excluded in some cases (di Folco et al., 2007; Mennesson et al.,
2011; Defrère et al., 2012; Ertel et al., 2014), although recent polarimetric,
interferometric, and theoretical studies argue against scattered light as a
prominent contributor to the detected excesses (Kennedy & Piette, 2015;
Kennedy et al., 2015; Marshall et al., 2016; Kirchschlager et al., 2017,
2020). These previous studies have highlighted a tentative correlation between
spectral type and near-infrared excess detection rate, but could not formally
identify any correlation between the presence of hot dust and of cold, distant
dust reservoirs detected by far-infrared and submillimeter photometry. The
factors influencing the presence of hot exozodiacal dust around nearby main
sequence stars are therefore still unclear, which calls for more observational
constraints.

Figure 1: Illustration of the typical orbital distances and temperatures for
the hot, warm, cold dust belts considered in this work, and of the
corresponding wavelength ranges in terms of spectral energy distribution.
Adapted from Kirchschlager et al. (2017).

Here, we study the possible correlation of the hot dust phenomenon with the
presence of warm asteroid belts around nearby main sequence stars. We define
warm dust as dust producing a detectable excess in the mid-infrared but not in
near-infrared (typical temperatures in the range 100–500 K), while hot dust is
defined as dust producing an excess in the near-infrared (see Fig. 1). Our
main goal is to determine whether the presence of hot exozodiacal dust could
be directly related to the presence of a large reservoir of planetesimals in
an asteroid belt, in an attempt to improve our understanding of the origin,
architecture, and evolution of bright exozodiacal dust disks, as well as of
the factors influencing their detection rate. To this aim, we build a sample
of stars known to have a mid-infrared excess attributed to debris disks based
on infrared space missions such as Spitzer and WISE (Sect. 2). After detailing
the PIONIER observations and data reduction in Sect. 3, we present in Sect. 4
the search for unknown companions in this sample – a necessary step to remove
possible contamination in our sample. In Sect. 5, we present the search for
hot exozodis in this sample, detailing the search method and the results.
Finally, in Sect. 6, we discuss the connection between hot and warm dust. We
also challenge the standard hypothesis of fully resolved exozodis in
interferometric observations, and explore the consequences of partly resolved
disks on the measured detection rates.

##  2 Stellar sample

Figure 2: Histograms of excess significance for PACS70 (left) and PACS100
(right) measurements. The purple dotted curve shows the noise distribution
derived by Yelverton et al. (2019) for their PACS70 (left) and PACS100 (right)
data sets, while the red dashed curve shows the same noise distribution
derived from our PACS100 data set—our PACS70 data set was not large enough to
robustly fit the noise distribution. The values noted as $\mu_{\rm Fit}$ and
$\sigma_{\rm Fit}$ are respectively the mean and standard deviation of the
significance in our PACS100 distribution, while $\mu_{\rm Yel}$ and
$\sigma_{\rm Yel}$ are the ones from Yelverton et al. (2019).

Searching for correlations between hot and warm dust populations first
requires to build a large enough sample of nearby stars hosting warm dust.
Three main space-based missions have been used to search for warm dust around
nearby stars: Spitzer, AKARI, and WISE. We searched the literature for warm
excesses around nearby stars, focusing mostly on these three missions
(Carpenter et al., 2009; Chen et al., 2006; Hillenbrand et al., 2008; Ishihara
et al., 2010; Morales et al., 2012; Ballering et al., 2013; Fujiwara et al.,
2013; Chen et al., 2014; Vican & Schneider, 2014; Patel et al., 2014). To
identify warm dust, these missions rely on spectrophotometric observations at
wavelengths shorter than 25 $\mu$m. Showing a mid-infrared excess is however
not a sufficient condition to infer the presence of warm dust, as excesses in
this wavelength range can sometimes correspond to the short-wavelength end of
a bright but cold circumstellar emission. We originally built our sample based
on the dust temperature estimated in the literature, using a threshold of 130
K111This temperature threshold of 130 K was only used to select our target
stars, based on the available literature in 2013. We will discuss later that a
temperature of 100 K was finally chosen to classify between warm and cold dust
populations. A significant fraction of the selected targets actually turned
out not to show the presence of any warm dust after re-evaluation of their
mid- to far-infrared excess, as described in Sect. 2.1. as a criterion to
distinguish warm from cold populations, following Ballering et al. (2013). In
several cases, the warm excesses could only be detected at a single
wavelength, making an accurate temperature determination impossible. In these
cases, the authors generally quote the highest possible temperature compatible
with their data set. Lacking more precise information, we decided to use these
upper limits as a criterion to select stars with possible warm dust
populations, where applicable. While our previous near-infrared
interferometric surveys were targeting stars brighter than $H=5$, here to
build a sufficiently large sample we include stars up to $H=7$, which remains
comfortably within the magnitude limit of VLTI/PIONIER. Stars with visual
companions within the interferometric field of view of PIONIER on the VLTI
Auxiliary Telescopes ($\sim$400 mas full width at half maximum in H band) are
not appropriate for detecting weak, extended circumstellar emission. Even
light from companions outside the field of view may enter the optical path in
case of bad seeing. Thus, as in Ertel et al. (2014), all known binary systems
with angular separation $<5\arcsec$ are removed from our sample. We identified
a total of 62 stars meeting our criteria, which had not been observed yet with
precision near-infrared interferometry. The main properties of these 62
targets to be observed with PIONIER are summarized in Table LABEL:tab:allsurv.
We collected PIONIER data of sufficient quality for only 52 of them, as
described in Sect. 3. Furthermore, four of these 52 stars turned out to be
binaries, based on our PIONIER observations (see Sect. 4). These binary stars
are not amenable to a search for exozodiacal dust, and are therefore removed
from our sample, so that we are left with 48 new stars to study the
correlation between warm and hot dust.

To assess a possible correlation between the presence of hot and warm dust, we
also need to build a control sample. Our control sample is based on the
VLTI/PIONIER survey for hot exozodiacal dust carried out by Ertel et al.
(2014). The reader is referred to that paper for a detailed description of the
stellar parameters of this sample. Among the 85 single and non-evolved stars
included in that sample, we expected from the literature that a large majority
does not host any warm dust population, based on the absence of mid-infrared
excesses. We however noted that the warm vs. cold dust classification derived
from the dust temperatures described in the literature was inconsistent,
because of the various assumptions made in the publications of these mid-
infrared surveys. We therefore decided to re-assess the presence of warm dust
around the 133 stars included in both the Ertel et al. (2014) sample (85
stars) and our new sample (48 stars).

###  2.1 Reassessing the presence of warm and cold dust

Figure 3: Histograms of excess significance for WISE12 (top left), WISE22 (top
right), MIPS24 (bottom left), and MIPS70 (bottom right), together with their
best-fit Gaussian noise distribution (red dashed curve). The mean ($\mu$) and
standard deviation ($\sigma$) of the noise distributions are also plotted
respectively as red vertical and horizontal lines. Significance values lower
than $-4$ and higher than $8$ are not displayed for the sake of clarity.

In order to reassess the presence of warm and/or cold dust around our combined
sample of 133 stars, we collected photometry at all available optical, mid-,
and far-infrared wavelengths for all targets. In most cases these are
available in literature catalogues, for example for optical $UVB$ and $ubvy$
data (Mermilliod, 1987; Paunzen, 2015), and 2MASS and WISE IR data (Cutri et
al., 2003; Wright et al., 2010). However, far-IR photometry for our targets is
either unpublished or spread across many different analyses. To maximize
consistency, Spitzer/MIPS photometry at 24 and 70 $\mu$m uses our own updated
PSF fitting for all targets, as described in Sierchio et al. (2014) and
Yelverton et al. (2019), except four bright targets, which use 70 $\mu$m
photometry from Chen et al. (2014). Herschel/PACS photometry at 70, 100, and
160 $\mu$m, and SPIRE photometry at 250, 350, and 500 $\mu$m, also uses our
PSF fitting, as described in Sibthorpe et al. (2018). We also use Spitzer/IRS
spectra from the CASSIS archive (Lebouteiller et al., 2011), where available.

The data for each star are initially fit with a star + disk model using the
sdf code, as described by Yelverton et al. (2019). The star is a BT-Settl
photosphere model (Allard et al., 2012) and the disk is a modified blackbody
(a Planck function that is multiplied by $\lambda_{0}^{-\beta}$ at wavelengths
longer than $\lambda_{0}$), and the fitting is done using the multinest code
(Feroz et al., 2009). The fitting serves two purposes, firstly to provide an
estimate of the stellar flux at all wavelengths to allow the presence of any
IR excess to be quantified, and secondly to estimate the temperature and
luminosity of any disk if the excess is deemed significant as described below
(if no excess is present the disk component has negligible flux by definition,
and is not used). In some cases the single-component disk provides a poor fit
to the IR excess, in which case a second disk component is added. Whether a
second component is needed is somewhat subjective, since the true dust
spectrum is unknown and might mimic a two-component disk (Kennedy & Wyatt,
2014). Our assessment primarily considers whether two disk components are
needed to fit all photometry and the IRS spectrum, but also considers whether
the dust temperatures of a two-component fit are sufficiently different
(Kennedy & Wyatt, 2014).

To assess whether IR excesses are significant, we use the empirical method
used by many previous studies (e.g. Su et al., 2006; Ertel et al., 2014;
Yelverton et al., 2020), and which we also use below for the PIONIER
observations. Essentially, we assume that most stars do not have a significant
excess, and therefore that the distribution of excess significance in a given
band $i$

$\chi_{i}=\frac{F_{obs}-F_{\star}}{\sqrt{\sigma_{obs}^{2}+\sigma_{\star}^{2}}}$

should be approximately Gaussian with zero mean and unity standard deviation.
Any positive outliers with $\chi_{i}>3$ would therefore be considered to have
a significant excess. If the standard deviation is greater or smaller than
unity, as is commonly the case, the uncertainties for that band are considered
to be under- or overestimated respectively, and the threshold for an excess
adjusted accordingly. For example, Yelverton et al. (2020) found the standard
deviation for PACS 100 $\mu$m to be 1.68, and therefore set the threshold for
an excess to be $3\times 1.68$. In general the IRS spectra were used as
important input for deriving disk temperatures, but in a few cases (HD 40307,
HD 90874, HD 91324) were also used to confirm an excess that was not
significant photometrically (due to low signal-to-noise ratio and/or poor
wavelength coverage).

We decided to classify as dusty any stellar system whose excess significance
was beyond four standard deviations from the average ($\chi>\mu+4\sigma$) in
at least one band. In order to keep an average excess significance around zero
in our noise distributions, the Gaussian fitting of the noise distribution was
done without any star with $\chi>3$. In the case of PACS70, there were not
enough data points to fit a decent Gaussian distribution. We therefore
explored the possibility to use the noise distributions from Yelverton et al.
(2019) for that filter. In Fig. 2, we compare our Gaussian fit to the PACS100
significance with the ones obtained by Yelverton et al. (2019) for their
PACS70 and PACS100 data sets. The difference, in terms of outliers, was found
to be marginal: only the excesses of two additional stars (namely HD 7570 for
PACS100, and HD 174474 for PACS70) were significant with the use of Yelverton
et al. (2019) parameters but not with ours. We therefore decided to adopt the
Gaussian noise distributions fitted by Yelverton et al. (2019) for our PACS70
and PACS100 data sets. The $\chi$ histograms for the remaining four WISE and
MIPS filters are plotted in Fig. 3 with their respective noise distributions.

Figure 4: (Left). Equivalent black body radius of the dust disks around the 66
stars in our combined sample showing a significant mid- to far-infrared
excess, for which a dust temperature could be derived. Disks classified as
warm ($>100$ K) and as cold ($<100$ K) are respectively colored red and blue.
(Right). Same as left, for the corrected black body radius, using the 50%
astrosilicate + 50% ice composition of Pawellek & Krivov (2015). A purple
dashed line at 50 au shows a rough separation between warm and cold dust
populations. The vertical green dotted lines link the warm and the cold dusts
that were found in the same stellar system.

Among the 133 stars in our combined sample, 68 show the presence of
circumstellar dust in their mid- to far-infrared SED based on our analysis
(see Appendix A for an illustration of all 133 SEDs). In order to separate
these 68 stars into two categories (warm and cold dust), we set an arbitrary
limit of 100 K to distinguish between the two populations. The new warm/cold
dust classification for these 68 stars is given in Table LABEL:tab:class. We
note that two stars (HD 36187 and HD 89886) do not have sufficient mid- to
far-infrared data to conclude on the temperature of the detected excess. These
two stars are therefore removed from our warm/cold dust samples, leaving us
with a total of 131 stars, among which 66 show the presence of circumstellar
dust.

###  2.2 Statistics of our combined sample

Based on our SED modeling, our final sample of 131 stars contains a total of
35 stars that show the presence of warm dust populations ($>100$ K), among
which 11 also show the presence of a cold dust reservoir ($<100$ K). Another
31 stars show the presence of cold dust only, while 65 stars show no sign of
circumstellar dust, at a sensitivity level that depends on the stellar
brightness and spectral type, and on the quality of the mid- to far-infrared
observations available for each star. For the 66 stars that show the presence
of circumstellar dust, we plot in Fig. 4 the equivalent black-body radius of
the dust disk, as well as the corrected black-body radius following Pawellek &
Krivov (2015), using a 50% astrosilicate + 50% ice composition. The correction
takes into account the blow-out of the smallest dust grains, and is meant to
provide a more representative estimate of the true radius of a spatially
unresolved dust disk. The right-hand side plot in Fig. 4 shows that our 100 K
criterion corresponds more or less to a 50 au limit in terms of corrected
black body radius between the warm and cold dust disks, although some A-type
stars show warm dust up to about 60 au, while late-type stars show cold dust
down to about 40 au. This relatively good agreement between our temperature
classification and a classification based on the corrected black body distance
to the host star provides an independent justification to our classification
strategy. While a 50 au limit between warm and cold dust populations may seem
large, it ensures that the two populations are balanced in size, and we argue
in Sect. 6.1 that choosing a higher temperature threshold would not change the
conclusions of our study.

While the dusty and non-dusty samples are relatively equally spread between
A-type, F-type and G/K-type stars, with $33\%\pm 8\%$ of stars in each of the
three spectral type categories, it must be noted that the warm dust sample is
largely biased towards A-type stars (with 18 A-type stars out 35), while the
cold dust sample is biased towards G/K-type stars (14 G/K-type stars out of
31). This imbalance likely arises because disks tend to be warmer around
earlier type stars (e.g. Kennedy & Wyatt, 2014). This could also be partly due
to the fact that warm dust appears up to larger orbital distances around
A-type stars, even after taking into account the black body correction of
Pawellek & Krivov (2015).

Table 1: Summary of the new VLTI/PIONIER observations. Run | Night | # stars | Seeing (″) |  $\tau_{0}$ (ms) | Notes
---|---|---|---|---|---
093.C-0712(A) | 07-04-2014 | 7 | 1.6 (0.8 - 2.5) | 1.4 (1.1 - 1.7) | Strong seeing at the end of the night
093.C-0712(A) | 08-04-2014 | 9 | 1.7 (0.6 - 2.9) | 2.2 (0.8 - 3.7) | Strong seeing in the middle of the night
093.C-0712(A) | 09-04-2014 | 9 | 1.3 (0.6 - 2.0) | 2.5 (1.3 - 3.8) | Some clouds
093.C-0712(B) | 30-08-2014 | 8 | 1.2 (0.6 - 1.9) | 1.7 (1.1 - 2.3) | Good conditions
093.C-0712(B) | 31-08-2014 | 9 | 1.2 (0.6 - 1.9) | 2.1 (1.0 - 3.2) | Some clouds
093.C-0712(B) | 01-09-2014 | 4 | 1.1 (0.7 - 1.6) | 3.2 (1.9 - 4.5) | Thin clouds, dome closed for a part of the night
094.C-0325(A) | 22-12-2014 | 7 | 1.0 (0.5 - 1.5) | 2.3 (1.4 - 3.2) | Good conditions
094.C-0325(A) | 23-12-2014 | 11 | 1.4 (0.5 - 2.4) | 2.3 (1.1 - 3.6) | Strong seeing at the beginning of the night
094.C-0325(A) | 24-12-2014 | 8 | 1.5 (0.4 - 2.5) | 3.1 (0.9 - 5.3) | Strong seeing at the beginning of the night

Our target stars mostly consist of old, main sequence field stars, generally
not younger than a few hundreds of million years. A handful of stars in our
sample are somewhat younger: HD 141943 (field star, 30 Myr, Chen et al.,
2014); HD 203, HD 39060, HD 172555, HD 181327 and HD 191089 (part of the
$\beta$ Pic moving group, 21 Myr, Binks & Jeffries, 2014); HD 192758 (part of
IC 2391, 40 Myr, Wahhaj et al., 2013); HD 109573 (part of the TW Hya
association, 10 Myr, Mittal et al., 2015); HD 106906 (part of the Lower
Centaurus Crux association, 15 Myr, Pecaut & Mamajek, 2016); and HD 188228
(part of the Argus association, 38 Myr, Booth et al., 2013). We note that the
average stellar age of the warm dust sample (0.83 Gyr) is significantly lower
than for the control sample (2.7 Gyr), which is not unexpected as the presence
of warm dust is known to be correlated with the system age (e.g., Su et al.,
2006; Vican & Schneider, 2014). Any correlation between hot and warm dust will
therefore also be tested for a possible age bias, although previous studies
(e.g. Absil et al., 2013; Ertel et al., 2014) do not suggest a significant age
dependence in the hot exozodi phenomenon.

##  3 Observations and data reduction

Observations were carried out with VLTI/PIONIER (Le Bouquin et al., 2011) at H
band in April, August and December 2014, each run consisting of three
consecutive observing nights. An observing log of all nights can be found in
Table 1. We used the four 1.8-m ATs to obtain six visibility measurements
simultaneously. We used for all observing runs an array configuration
(D0-H0-G1-I1) with baselines ranging between 41 m and 82 m. This configuration
is larger than the one used for the Ertel et al. (2014) survey, because the
stars in the present sample are more distant in average and therefore require
a higher angular resolution to resolve their sublimation radius (see Sect. 6.3
for more details). After the August run, the detector of PIONIER was changed,
which implied a change in the read-out mode. The read-out mode was set to
FOWLER with SMALL dispersion (three spectral channels) for the observations of
April and August 2014, and to HIGH SENS with a GRISM dispersion (six spectral
channels) for the observations of December 2014. Four calibrator stars were
selected from Mérand et al. (2005) for each science target, typically within
10 ° on sky to minimize the effects of pupil rotation or instrumental
polarization (see Le Bouquin et al., 2012). Additional selection criteria were
an H-band magnitude similar to the science target, and a small angular
diameter. Most of the targets were observed in a CAL1-SCI-CAL2-SCI-CAL3-SCI-
CAL4 sequence, where two non-consecutive calibrators can be the same.

Out of the 62 stars in our observing list, a total of ten stars had to be
removed from our final sample for various reasons. Four could not be
appropriately observed: HD 141378 and HD 43879 due to incomplete observing
sequences (not enough data), HD 59967 because of inappropriate calibrators,
and HD 93453 because two out of the three SCI observations were obtained
during a burst of bad seeing ($>2\arcsec$). The other six stars were removed
after the data reduction and calibration procedure, as detailed below. The
data reduction consists of the conversion of raw observations into calibrated
interferometric observables. We use the exact same method as in Ertel et al.
(2014). The first step of the calibration is to calibrate the instrumental
visibility within the CAL-SCI-$\dots$-CAL sequence. To do so, we calibrate
each SCI individually by pairing it with either the preceding or the following
CAL. During this process, we also make sure to discard all calibrators with
low S/N or with a clear closure phase signal (see Ertel et al., 2014, for
details). After calibration, six stars had to be rejected from our sample (HD
4247, HD 10008, HD 31392, HD 142139, HD 178606, and HD 184932), because of
large discontinuities in the interferometric transfer function222The
interferometric transfer function monitors the instrumental visibility, or
instrumental closure phase, as a function of time. due to poor seeing
conditions, low coherence time, or clouds. The actual number of new stars
added through this observing program therefore amounts to 52.

The last step in the data analysis procedure is to assess the systematic
polarization effects of PIONIER. This part is automatically corrected by a
dedicated option in the standard PIONIER pipeline (pndrs, Le Bouquin et al.,
2011) used for the reduction. A detailed explanation of the polarization
effects can be found in Ertel et al. (2014).

##  4 Searching for companions

Before searching for hot exozodiacal disks based on our interferometric
observations, we first need to identify possible unknown (sub-)stellar
companions that could also produce an infrared excess. This will ensure that
all our target stars are single.

###  4.1 Principle of the search

Following the same lines as in Absil et al. (2011) and Marion et al. (2014),
we use the full information delivered by PIONIER (squared visibilities,
$V^{2}$, and closure phases, CP) to systematically search for companions
around all the stars. Doing so, we are able to discriminate whether the small
near-infrared excess detected around some of the target stars is due to an
extended, mostly symmetric source, or to a point-like companion. The method
used to detect companions is fully described in Marion et al. (2014). We
provide here a brief summary.

First, we define the search region, taking into account three main factors.
The first one is the Gaussian profile of the single-mode fiber used in PIONIER
(FWHM $\approx$ 400 mas). The second one is the finite scan length of the
optical path delay. With the medium configuration used here and for a typical
scan length of 100 $\mu$m, the maximum separation that can be probed is
$\Delta\theta_{\rm max}\simeq 200$ mas, although we recognize that companions
with separations larger than 70 mas may not be simultaneously visible on all
baselines. The third one is the sufficient sampling of the closure phase
signal as a function of wavelength, which depends on the baseline and on the
spectral resolution. Following Absil et al. (2011), the well-sampled field-of-
view is about 50 mas in radius. Taking all of this into account, we consider a
search region 50 mas in radius in this study. We note however that our search
is actually sensitive to companions out to about 200 mas, with point-like
sources between 50 and 200 mas creating aliasing within our 50 mas search
region. As explained in Sect. 2, companions beyond 200 mas may bias our
observations, but we expect that such companions (with contrasts of 1% or
more) would have already been identified in the literature.

Table 2: Summary of the stars showing a significance level higher than $5\sigma$ based on the analysis of the combined $\chi^{2}$ (CP+$V^{2}$). The significance of the detection based on the separate analysis of the CP and the $V^{2}$ is also given. The nature of the detection is either a disk or a point-like source, in which case its main properties are given in the last three columns. |  |  |  |  | Point-like source
---|---|---|---|---|---
Name | Significance | Nature | Separation | P.A. | Contrast
| (CP+$V^{2}$) | (CP) | ($V^{2}$) |  | (mas) | (deg) | (%)
HD 203 | 5.4 | 3.7 | 7.3 | disk | – | – | –
HD 31203 | 14.5 | 20.2 | 25.6 | point-like | $64.6\pm 1.3$ | $-50.2\pm 0.4$ | $4.3\pm 0.6$
HD 36187 | 9.3 | 2.2 | 23.4 | disk | – | – | –
HD 61005 | 6.7 | 2.5 | 7.7 | disk | – | – | –
HD 76143 | 6.4 | 5.3 | 4.9 | disk | – | – | –
HD 80133 | 4642.7 | 318.5 | 14616.4 | point-like | $6.0\pm 0.2$ | $13.2\pm 0.7$ | $85.2\pm 2.6$
HD 106906 | 145.0 | 12.0 | 509.1 | point-like | $1.4\pm 0.1$ | $95.2\pm 5.1$ | $95.0\pm 7.4$
HD 175073 | 64.7 | 59.6 | 391.3 | point-like | $31.2\pm 0.6$ | $-84.7\pm 0.4$ | $13.0\pm 0.9$

To detect the presence of a companion, we use the closure phases and the
squared visibilities in a combined way. As in Marion et al. (2014), we compute
a binary model considering the primary star at the center of the search region
with an off-axis companion of various contrast $c$ at each point $(x,y)$ of
the search region. In the present case, we can safely assume that both the
primary and the secondary stars are unresolved, since all of our targets have
an angular diameter $\lesssim 0.5$ mas. Then, we compute the $V^{2}$ and CP
for each model and derive a combined goodness of fit that we normalize and
collapse along the contrast axis to keep only the best-fitting companion
contrast (i.e., minimum $\chi^{2}$ value) at each position in the search
region. The resulting $\chi^{2}$ map can then be used to derive the
probability for the single-star model to adequately represent the data, based
on the $\chi^{2}$ distribution under a Gaussian noise assumption. If this
probability is below a predefined threshold, the single-star model can be
rejected and the best-fit binary solution is then considered as statistically
significant. The detection criterion is defined as a threshold on the
significance of the detection, which can be translated into a confidence level
if the underlying probability distribution function is known.

Figure 5: Statistics of the (signed) significance level for the 52 stars based
on the combined $\chi^{2}$, taking into account the CP and $V^{2}$. Four stars
with a significance level higher than $10\sigma$ are not represented here for
the sake of clarity.

To determine the significance level to use as a detection threshold, we study
the noise properties of the data set by including negative contrasts in our
model for the off-axis companions. While non-physical, negative companions can
be used to represent positive fluctuations in the $V^{2}$ (i.e., situations
where the measured $V^{2}$ is higher than the expected $V^{2}$ from the
photosphere). Negative companions can also be attributed to noise fluctuations
in the CP, which can take both positive and negative values. In the following,
we associate negative significance levels to negative companions. The
histogram of the significance levels for our complete sample is illustrated in
Fig. 5, where the range of the plot has been limited to $[-10,10]$ for the
sake of clarity. The negative significance levels in the histogram are purely
due to noise fluctuations, and can therefore be used as a reference to study
the noise properties of our sample. The absence of significance levels close
to 0 in the histogram can be explained by the fact that, in presence of noise
and due to the limited number of observations, it is generally possible to
obtain a better fit to our data sets by inserting a companion somewhere in the
field-of-view than by using a single-star model. Out of the 52 stars in our
observed sample, ten show a negative significance level, but none are below
$-5\sigma$. We therefore decide to use $5\sigma$ as our empirical companion
detection threshold based on the combined analysis of $V^{2}$ and CP. We note
that a $4\sigma$ threshold would also have been appropriate for this analysis,
owing to the distribution of the negative excesses. However, after a more
detailed inspection of the closure phases, all the stars with a significance
level between $4\sigma$ and $5\sigma$ actually turned out to be surrounded by
extended emission, and not by point-like sources (see below for details on how
this inspection was performed).

###  4.2 Results of the search

Figure 6: Normalized $\chi^{2}$ maps related to the combined CP+$V^{2}$
analysis for the four stars showing clear signs of an off-axis companion: HD
31203, HD 80133, HD 106906, and HD 175073 (from left to right and top to
bottom). The black circles indicate the positions of the minima in the maps.

Table 2 lists the stars that have a significance level higher than $5\sigma$
for the combined $\chi^{2}$ analysis. HD 31203, HD 80133, HD 106906, and HD
175073 have strong detections, not only in the combined analysis but also in
the individual analysis of $V^{2}$ and CP. They are therefore identified as
bona fide binary stars. The $\chi^{2}$ maps illustrating the detection of a
point-like source in these four data sets are illustrated in Fig. 6. HD 36187
and HD 61005 have a low significance for the CP-only analysis, so that the
detected excess is identified as being due to extended emission (no evidence
for the presence of a point source). For HD 203 and HD 76143, the situation is
not as clear, as the detection is at best marginal in the combined and
individual analyses. This requires more careful data inspection to decide on
the nature of the excess. For HD 203, we note that the detection in the
$V^{2}$ is about twice as significant as in the closure phases. This is a sign
that the excess identified in the combined analysis is most probably due to
the presence of a disk, which creates a strong signal in the $V^{2}$ but not
in the CP. For HD 76143, looking at the closure phases signal reveals a global
offset from 0, which is the sign of a poor calibration. This poor calibration
of the CP is suspected to be at the origin of the (marginal) detection of an
excess emission in the CP, and we propose that the most likely explanation is
rather the presence of a circumstellar disk (although more observations would
be needed to firmly confirm this statement). This leaves four stars in our
sample with previously unknown companions, which will be removed from our
search for hot exozodiacal disks. The four new binary stars are described in
more details the following paragraphs.

###  4.3 Notes on newly identified companions

#### HD 31203 (iot Pic A).

This F0V-type star is located at 37.1 pc, and known to be a member of a
multiple star system (Tokovinin et al., 2015). The first companion (HD 31204,
F4V) is located at $12\aas@@fstack{\prime\prime}3$, and the second one (HD
31261, K2V) at $289\arcsec$. These companions are well outside the PIONIER
field-of-view, and even outside the AT field-of-view, so that they do not
affect our observations. Besides being a visual multiple system, iot Pic A is
known to have variable radial velocities (Nordstrom & Andersen, 1985), with a
variability larger than 30 km s-1 on a timescale of a few days, based on four
measurements. The nature and orbital parameters of the potential close
companion are however not constrained, although the amplitude of the radial
velocity (RV) variation point toward a solar-type companion.

Based on the measured contrast $c=0.04$ and the distance, we estimate the
companion found by our interferometric observations to have an absolute
magnitude $M_{H}=5.49$, which corresponds roughly to a K7V spectral type
according to Cox (2000). Assuming a face-on, circular orbit with a semi-major
axis of 2.39 au, and a mass of 1.52 $M_{\odot}$ for iot Pic A (David &
Hillenbrand, 2015), the orbital period would be around 3 years. Determining
whether this companion corresponds (at least partly) to the source of the RV
variability found by Nordstrom & Andersen (1985) would require more RV and
interferometric observations.

#### HD 80133.

This K1V-type star is located at 32.8 pc. Based on the measured contrast
$c=0.85$ and the distance, we estimate the companion to have an absolute
magnitude $M_{H}=4.16$, which corresponds roughly to a G8V spectral type
according to Cox (2000). In practice, the measured contrast would rather point
to a pair of K1-2V stars, or to a slightly evolved K1IV-V primary with a less
evolved G8V secondary, owing to their estimated age of about 13 Gyr (Takeda et
al., 2007). Assuming a face-on, circular orbit with a semi-major axis of 0.19
au, and a mass of about $1M_{\odot}$ for HD 80133 (Takeda et al., 2007), the
period would be around 1 month. Surprisingly, this star has not been
identified as a binary star based on RV measurements, while it was included in
the California/Carnegie Planet Search programs (Valenti & Fischer, 2005;
Takeda et al., 2007). This might be explained either by a (very) poor time
coverage in the RV survey, or by a quasi-perfectly face-on orbit. We note that
the warm dust disk detected around HD 80133 by Vican & Schneider (2014) is
located well outside the estimated semi-major axis of the companion (beyond 1
au), and should therefore be in a stable circumbinary configuration.

#### HD 106906.

This F5V-type star is located at 92.1 pc, and is identified as a short-period
binary in Lagrange et al. (2021) based on RV measurements. The interferometric
observations presented here confirm the binary nature of the star, which turns
out to be a quasi-equal flux binary. Our interferometric observations have
been included in the analysis of Lagrange et al. (2021) to better constrain
the orbital parameters of the system. We refer to that paper for a full
discussion of this system.

#### HD 175073.

This K1V-type star is located at 24 pc. Based on the measured contrast
$c=0.13$ and the distance, we estimate the companion to have an absolute
magnitude $M_{H}=6.36$, which corresponds roughly to an M2V spectral type
according to Cox (2000). Assuming a face-on, circular orbit with a semi-major
axis of 0.76 au, and a mass of 0.8 $M_{\odot}$ for HD 175073 (Casagrande et
al., 2011), the period would be around 9 months. Surprisingly, this star has
not been identified as a binary star based on RV measurements, while it was
included in previous RV planet surveys according to Grether & Lineweaver
(2006). This might be explained either by a (very) poor time coverage in the
RV survey, or by a quasi-perfectly face-on orbit. We note that this newly
discovered companion cannot be at the origin of the W4 WISE excess detected by
Patel et al. (2014) as their analysis was purely based on mid-infrared colors,
which are similar for the host star and its companion. We also note that the
warm dust disk detected around HD 175073 by Patel et al. (2014) is located
well outside the estimated semi-major axis of the companion (beyond 2 au), and
should therefore be in a stable circumbinary configuration.

###  4.4 On the PIONIER sensitivity to faint companions

In the cases where no companion, nor hot exozodiacal disk, is detected around
the target stars (35 stars out of the 52 in our sample, see Sect. 5 for a
discussion of the hot exozodi detections), we can compute an upper limit on
the contrast of faint companions around the target stars, as a function of the
position in the field-of-view. These sensitivity maps are derived from the
$\chi^{2}$ analysis, as explained in Absil et al. (2011), with the difference
that here we use both the $V^{2}$ and the CP in our $\chi^{2}$ analysis. From
the sensitivity maps, we can derive the median sensitivity at a given radial
distance by computing the median upper limit along an annulus. The result is
illustrated in Fig. 7, where the median sensitivity is plotted as a function
of the angular separation for the 35 stars. The typical $5\sigma$ sensitivity
of PIONIER in “survey mode” (3 OBs per target), illustrated by the red curve
in Fig. 7, is a flux ratio of 0.7% (i.e., $\Delta H=5.4$) for angular
separations larger than 2 mas in the medium-sized AT configuration. This
sensitivity corresponds typically to companions with spectral types ranging
from M1V to M6V around main sequence stars with spectral types ranging from
A0V to K0V.

Figure 7: Sensitivity of PIONIER to point-like companions as a function of the
radial distance to the central star for the 35 stars showing no H-band excess
in our observations. The sensitivity is expressed as the azimuthal median of
the $5\sigma$ upper limit, based on an analysis of the combined $\chi^{2}$ for
the CP and $V^{2}$. The red curve is the median sensitivity on the 35 stars.

##  5 Search for exozodis

After removing the four stars identified as binaries in Sect. 4, we are left
with a combined sample of 133 stars, as already described in Sect. 2. Of these
133 stars, 48 are new observations from the observing program described in
this paper. In this section, we briefly summarize the principle of the search
for hot exozodis, and detail the new exozodis found around our 48 new targets.

When it comes to the detection of faint, circumstellar excess emission, the
strength of infrared interferometry is the ability to spatially resolve this
emission and thus spatially disentangle it from the much brighter stellar
emission. When observing at small baselines of up to a few tens of meters, the
host star is nearly unresolved (minimizing the effects of its uncertain
diameter on the prediction of the system’s $V^{2}$), while an extended
circumstellar emission is ideally fully resolved (see di Folco et al., 2007).
This results in a drop in $V^{2}$ compared to the purely stellar $V^{2}$,
because it adds incoherent flux. This represents the core of our detection
strategy.

###  5.1 Fitting strategy

As shown by previous studies (Absil et al., 2009; Defrère et al., 2011), the
$V^{2}$ drop induced by a circumstellar disk does not depend significantly on
the assumed geometry of the disk, provided that the disk is resolved at the
considered baselines. As in previous studies, we therefore consider a model
consisting of a limb-darkened photosphere surrounded by a uniform
circumstellar emission filling the entire field of view of PIONIER ($\sim 400$
mas). The visibility expected from a limb-darkened photosphere is estimated
according to Hanbury Brown et al. (1974) using the linear H-band limb-
darkening coefficients of Claret et al. (1995). We estimate the visibility for
the whole bandwidth of each spectral channel, considering the actual spectrum
of the star using tabulated H-band spectra from Pickles (1998) and the
spectral transmission of the PIONIER instrument. The estimated $V^{2}$ are
then compared with the measurements, and the flux ratio for each data set is
derived. The computation is performed by a set of IDL routines initially
developed for CHARA observations by Absil et al. (2006), and later adapted to
other interferometers by Defrère et al. (2011). To derive the value and
uncertainty of the flux ratio for each target, we use a bootstrapping
algorithm, where each individual fit to the data is performed using a
Levenberg-Marquardt least-squares minimization (Markwardt, 2009). This means
that the individual uncertainties on the data points are not considered
directly in the estimate of the uncertainty of the flux ratio, but rather
their scatter. In addition, a systematic uncertainty of $5\times 10^{-4}$ due
to chromaticism is added to the estimated flux ratio (Ertel et al., 2014). For
the bootstrapping, we consider that simultaneous spectral channels are fully
correlated while the six baselines are fully uncorrelated.

###  5.2 Results of the search

Table 3: Summary of the results for the 48 stars used for our new hot
exozodiacal disk survey (excluding all binaries, and the data sets removed in
Sect. 3). Stars showing a significant level of excess emission (significance
higher than 3$\sigma$) are highlighted in gray. The reduced $\chi^{2}$ of the
star+disk model fit to the data is given in the last column.

Star | Contrast | Signif. | $\chi^{2}_{r}$
---|---|---|---
| (%) | ($\sigma$) |
HD 203 | $0.96\pm 0.23$ | 4.25 | 0.84
HD 2834 | $2.29\pm 0.85$ | 2.69 | 5.69
HD 3126 | $-0.01\pm 0.24$ | $-0.04$ | 0.63
HD 4113 | $0.75\pm 0.20$ | 3.82 | 0.63
HD 9672 | $0.30\pm 0.31$ | 0.96 | 1.85
HD 10269 | $-0.16\pm 0.14$ | $-1.15$ | 0.31
HD 10939 | $0.35\pm 0.33$ | 1.05 | 1.11
HD 15427 | $0.05\pm 0.18$ | 0.28 | 0.46
HD 17848 | $1.21\pm 0.14$ | 8.69 | 0.37
HD 23484 | $0.69\pm 0.25$ | 2.71 | 0.74
HD 24649 | $1.14\pm 0.23$ | 5.05 | 0.80
HD 28287 | $0.06\pm 0.32$ | 0.19 | 1.36
HD 29137 | $0.23\pm 0.16$ | 1.45 | 0.66
HD 36187$^a$ | $1.95\pm 0.13$ | 15.00 | 0.40
HD 37306 | $0.26\pm 0.15$ | 1.75 | 0.49
HD 37484 | $0.28\pm 0.21$ | 1.36 | 0.84
HD 38949 | $-0.09\pm 0.18$ | $-0.51$ | 0.71
HD 41278 | $0.40\pm 0.22$ | 1.85 | 0.68
HD 44524 | $0.01\pm 0.20$ | 0.05 | 0.66
HD 60491 | $0.44\pm 0.16$ | 2.78 | 0.61
HD 61005 | $0.81\pm 0.12$ | 6.70 | 0.36
HD 71722 | $0.37\pm 0.17$ | 2.21 | 0.57
HD 76143 | $0.60\pm 0.18$ | 3.33 | 0.47
HD 80883 | $1.43\pm 0.18$ | 8.07 | 0.65
HD 89886$^a$ | $0.92\pm 0.26$ | 3.47 | 1.02
HD 90781 | $0.63\pm 0.16$ | 3.98 | 0.41
HD 90874 | $0.34\pm 0.13$ | 2.62 | 0.36
HD 92945 | $0.00\pm 0.18$ | 0.00 | 0.51
HD 105850 | $-0.06\pm 0.18$ | $-0.34$ | 0.56
HD 105912 | $0.31\pm 0.15$ | 2.08 | 0.45
HD 109573 | $0.35\pm 0.15$ | 2.35 | 0.39
HD 109704 | $0.85\pm 0.12$ | 7.03 | 0.34
HD 112603 | $0.41\pm 0.25$ | 1.61 | 0.84
HD 117716 | $0.40\pm 0.18$ | 2.26 | 0.44
HD 118972 | $0.16\pm 0.09$ | 1.70 | 0.16
HD 136544 | $1.43\pm 0.35$ | 4.04 | 1.16
HD 141943 | $-0.15\pm 0.19$ | $-0.76$ | 0.51
HD 161612 | $-0.30\pm 0.12$ | $-2.48$ | 0.30
HD 174474 | $-0.12\pm 0.20$ | $-0.61$ | 0.75
HD 179520 | $0.44\pm 0.24$ | 1.79 | 0.76
HD 181327 | $0.48\pm 0.16$ | 3.03 | 0.45
HD 185615 | $-0.61\pm 0.31$ | $-1.94$ | 0.92
HD 191089 | $0.33\pm 0.48$ | 0.68 | 2.29
HD 192758 | $0.12\pm 0.28$ | 0.42 | 0.89
HD 196141 | $0.39\pm 0.20$ | 1.99 | 0.58
HD 205674 | $0.43\pm 0.50$ | 0.86 | 2.52
HD 220476 | $0.04\pm 0.18$ | 0.23 | 0.49
HD 224228 | $0.27\pm 0.39$ | 0.69 | 0.98
333(a) not used in the statistical analysis due to insufficient mid- to far-
infrared data.

Figure 8: Distribution of the excess significance level (left) and of the
uncertainties on the disk-to-star flux ratio (right) for the observed sample.
The Gaussian fit to the negative part of the significance distribution is
represented by a dotted line.

Table 3 presents the results of the fit in terms of disk/star flux ratio, for
the 48 new targets observed here. The measured flux ratio is averaged over the
three or six spectral channels in our PIONIER observations. To define an
appropriate detection threshold, we study the distribution of the significance
level $\chi_{f}$, defined as the ratio between the measured disk/star flux
ratio and the uncertainty on this quantity. Figure 8 shows the histogram of
the significance level for our sample of 48 stars. We decided to use a
threshold of $3\leavevmode\nobreak\ \sigma$ for the detection as in the study
of Ertel et al. (2014). Since we used the same methods for observation and
data reduction on the same instrument, we can assume that the distribution of
the uncertainties will also be comparable. As an additional argument, we study
the negative part of the distribution of the significance level. The standard
deviation of the negative part, after mirroring it on the positive side is
found to be equal to 1.2. In Fig. 8, a Gaussian distribution with this
standard deviation is over-plotted on the data to guide the eye. The good
match in shape, and the width of the distribution, confirm that a 3$\sigma$
criterion is appropriate, which corresponds to a false alarm probability of
0.27%, and should therefore avoid spurious detections in our sample.

The 13 stars highlighted in gray in Table 3 have a significance level above
$3\sigma$, and are therefore classified as having a near-infrared
circumstellar excess associated with the presence of circumstellar emission.
In Fig. 9, we show the wavelength dependence of the measured flux ratio for
the 13 stars showing a significant near-infrared excess. The large number of
stars with significance levels in the 1$\sigma$-3$\sigma$ range suggests that
there may be a population of excesses just below the detection threshold,
which remain undetected in our study. Comparing the negative and positive
parts of the histogram, we estimate that an additional dozen stars could have
an undetected H-band excess in the 1$\sigma$-3$\sigma$ range.

Figure 9: Disk/star flux ratio as a function of wavelength for the 13 targets
showing a significant H-band excess in our observations, as well as for HD
109573 (HR 4796), which shows a significant excess only in the reddest
spectral channel. The blue, red, and green curves show the best fit to these
measured flux ratios using blackbodies at 1000 K, 2000 K, and at the star’s
temperature (constant flux ratio), respectively.

###  5.3 Notes on specific hot-exozodi targets

#### HD 4113.

This old G5V star is known to have a planetary companion, discovered by RV
measurements (Tamuz et al., 2008), as well as a directly imaged brown dwarf
companion at a projected separation of 22 au (Cheetham et al., 2018). The
properties of the inner, planetary companion were revisited by Cheetham et al.
(2018): $M\sin i=1.602$ MJup, $a=1.298$ au, $e=0.8999$. While this star was
originally classified as surrounded by a warm dust disk by Vican & Schneider
(2014), this classification was based on a single WISE photometric data point
at 22 $\mu$m. Our revised SED analysis does not show the presence of any
significant dust population around this star, based on WISE and AKARI
photometry. The presence of a hot dust population therefore does not seem to
be connected to a massive outer reservoir of larger bodies. It is interesting
to assess whether its inner, eccentric giant planet may have a direct
influence on the architecture of the hot dust population. We assume that most
of the hot dust is located at the sublimation distance of silicate grains
(sublimation temperature of 1500 K), i.e., a distance of 0.04 au. Based on the
orbital elements of the planets, the periastron is at 0.12 au, while the
apastron is at 2.42 au. This orbital configuration suggests that the planet
could have a direct influence on the architecture of the dust disk. To our
knowledge, this is only the second hot dust system with a well-characterized
inner giant planet (the first one being $\beta$ Pictoris). This configuration
could be used to constrain the origin of the hot dust. Due to the presence of
the planet, Poynting-Robertson (P-R) drag acting on dust grains from a
hypothetical (warm or cold) outer dust belt that would remain below the
detection threshold is unlikely to efficiently replenish the hot disk, as
already suggested in a more general case by van Lieshout et al. (2014) and by
Bonsor et al. (2018) based on numerical simulations. A scenario where
planetesimals belonging to an outer reservoir would be destabilized by the RV
planet and sent towards the inner, hot regions where they would sublimate
seems like a more plausible hot dust production scenario in this case, in a
process somewhat akin to the falling evaporating bodies scenario proposed for
the $\beta$ Pictoris system (Beust et al., 1990) – although such a massive
planet would be better at ejecting planetesimals than scattering them inwards
(e.g., Wyatt et al., 2017).

#### HD 20794.

The near-infrared excess detected around this nearby Solar-type star was
already reported in Ertel et al. (2014). This star is known to be the host of
at least three (maybe four) super-Earth planets, orbiting between 0.1 and 1 au
from the star (Feng et al., 2017), and may also host a massive giant planet at
a separation between 2 and 10 au based on Gaia proper motion analysis
(Kervella et al., 2019). Based on our SED analysis, and on the detailed model
described in Kennedy et al. (2015), we do not confirm the presence of a warm
dust population as suggested by Cotten & Song (2016), and classify this target
as a cold disk system with a temperature of 80 K. It is another case where a
planetary system is located between the hot, inner disk and the outer debris
disk, as discussed in detail by Kennedy et al. (2015). Even only considering
the RV planets orbiting around HD 20794, which are much less massive than the
Jupiter-sized companion of HD 4113, the planetary system is still expected to
largely prevent dust from replenishing the inner disk through P-R drag. This
is another indication that P-R drag is probably not at the origin of – or at
least not the only contributor to – the detected near-infrared excess.

#### HD 61005 and HD 181327.

These two stars are known to be surrounded by copious amounts of dust, and
show asymmetries in their outer debris disk, which might be due to collision
of Pluto-like objects. HD 61005 is also found by our SED analysis to include a
warm dust population, at a black-body temperature of $\sim$120 K. Based on
near-infrared scattered light observations, Olofsson et al. (2016) and
Esposito et al. (2016) show that the eastern side of HD 61005 disk is brighter
than the western side. Olofsson et al. (2016) argue that an observed peak of
density at the pericenter of the disk may be the signpost of a recent impact,
since the material released by the impact would pass again through the initial
collision point, creating more collision and thus enhancing the density. HD
181327, a member of the $\beta$ Pic moving group ($\sim$20 Myr), also shows an
asymmetry in its outer disk, which may be caused by a recent massive
collisional event or by interactions with the interstellar medium (Stark et
al., 2014b). The possible collisional activity in the outer part of these two
debris disks could be related to a major dynamical instability akin to the
Large Heavy Bombardment in our Solar system. In such an event, we would expect
planetesimals to be injected in the inner parts of the planetary system, where
they may create the hot dust detected in our observations.

#### HD 109573 (HR 4796).

This A0-type member of the TW Hya association ($\sim$10 Myr) does not show a
significant H-band excess when considering the three PIONIER spectral channels
together. However, looking at the spectral channels separately shows a strong
slope of the excess emission, increasing with wavelength to a level such that
the longest channel has an excess of $0.51\%\pm 0.17\%$, significant at the
$3\sigma$ level (see Fig. 9). This may correspond to the onset of thermal
emission of a hot exozodiacal disk at a temperature around 1000 K. Although
tentative, this possible H-band excess is interesting to put in perspective
with the global debris disk architecture. According to Chen et al. (2014), the
debris disk can be best represented by a two-temperature black body model,
with the innermost ring at a temperature of 231 K (i.e., at about 5.7 au from
the star). We note however that the presence of warm dust in this system is
disputed. Indeed, Wahhaj et al. (2005) found evidence of warm dust based on
mid-infrared imaging, but Kennedy & Wyatt (2014) proposed that the emission of
HR 4796 is compatible with a single black body. A single black body is also
suggested by our SED analysis, with a temperature of 97 K, which results in a
cold dust classification in our statistical sample. More recently, Lisse et
al. (2017) suggested the presence of a tenuous thermal emission component from
close-in, $\sim$850 K circumstellar material based on near- to mid-infrared
spectroscopy, which might be directly connected to the small H-band excess
detected in our PIONIER data.

Near-infrared high-contrast imaging shows that the outer belt around HR 4796
consists of a sharp, offset ring of dust (e.g., Milli et al., 2017; Chen et
al., 2020), with an angular separation from the star as small as $\sim 200$
mas along the semi-minor axis due to projection effects. The detected H-band
excess may therefore also be (partly) due to the contribution of scattered
light from the outer debris disk. Based on the surface brightness of the disk
extracted by Milli et al. (2017), and considering the off-axis transmission of
the PIONIER single-mode fibers, we estimate that the outer disk could
contribute up to 0.1% in terms of integrated H-band excess. The outer disk
alone would therefore most probably not explain the measured excess of $\sim
0.5\%$. Another piece of evidence for that is the tentative slope in the
measured excess, which would not be consistent with scattered light.

The morphology of the HR 4796 outer disk can be best explained through the
influence of an eccentric planetary companion that would clear the interior
region of the cold dust belt (Lagrange et al., 2012). Both Perrin et al.
(2015) and Milli et al. (2017) suggest that the main contribution to scattered
light in the outer dust ring comes from rather large, porous grains. This
points towards a low dynamical excitation in the outer disk (Lisse et al.,
2017), which seems at odds with the main scenarios proposed to explain the
presence of a hot exozodiacal disk. Once again, the hot dust population seems
disconnected from the cold dust reservoir, but before further investigating
the global disk architecture, follow-up observations with near-infrared
interferometry will be needed to confirm the tentative H-band excess.

##  6 Discussion

Table 4: Hot exozodiacal disk statistics from the combined PIONIER surveys of
Ertel et al. (2014) and this work. Columns “#S” and “#E” represent the number
of target stars and of hot exozodi detections, respectively.

| A-type stars | F-type stars | G/K-type stars | Total
---|---|---|---|---
| #S | #E | detect. rate | #S | #E | detect. rate | #S | #E | detect. rate | #S | #E | detect. rate
Alla | 40 | 7 | $17.5^{+7.5}_{-4.4}\%$ | 51 | 10 | $19.6^{+6.7}_{-4.4}\%$ | 42 | 5 | $11.9^{+6.8}_{-3.3}\%$ | 133 | 22 | $16.5^{+3.7}_{-2.7}\%$
Warm dust | 18 | 3 | $16.7^{+12.1}_{-5.3}\%$ | 11 | 2 | $18.2^{+16.3}_{-6.4}\%$ | 6 | 1 | $16.7^{+23.2}_{-6.3}\%$ | 35 | 6 | $17.1^{+8.1}_{-4.6}\%$
Warm dust only | 12 | 2 | $16.7^{+15.5}_{-5.8}\%$ | 7 | 2 | $28.6^{+20.3}_{-10.6}\%$ | 5 | 0 | $0.0^{+26.3}_{-0.0}\%$ | 24 | 4 | $16.7^{+10.1}_{-5.0}\%$
Cold dust only | 5 | 2 | $40.0^{+21.4}_{-15.6}\%$ | 12 | 2 | $16.6^{+15.5}_{-5.8}\%$ | 14 | 1 | $7.1^{+13.2}_{-2.3}\%$ | 31 | 5 | $16.1^{+8.6}_{-4.5}\%$
No warm dust | 21 | 3 | $14.3^{+10.8}_{-4.6}\%$ | 39 | 7 | $17.9^{+7.7}_{-4.5}\%$ | 36 | 4 | $11.1^{+7.4}_{-3.2}\%$ | 96 | 14 | $14.6^{+4.3}_{-2.8}\%$
No dust | 16 | 1 | $6.3^{+11.8}_{-2.0}\%$ | 27 | 5 | $18.5^{+9.6}_{-5.2}\%$ | 22 | 3 | $13.6^{+10.4}_{-4.3}\%$ | 65 | 9 | $13.8^{+5.4}_{-3.2}\%$

444(a) also includes two dusty stars that have no warm/cold classification: HD
36187 (A0V) and HD 89886 (F7V).

In Table 4, we summarize the results of the PIONIER surveys for hot exozodis
presented here and in Ertel et al. (2014), in terms of number of detections
and detection rates. The results are separated as a function of spectral type,
and as a function of the presence of detectable amounts of warm and/or cold
dust populations. A graphical representation of the most important information
of this table is shown in Fig. 10, and forms the basis of the discussion in
the next paragraphs.

###  6.1 Correlation between hot and warm dust

Figure 10: Detection rate of hot exozodiacal dust as a function of spectral
type, and as a function of the presence of a known warm dust reservoir. No
significant difference in detection rate is found between the various
populations.

In our warm dust sample, we measure a detection rate of $17.1^{+8.1}_{-4.6}$%
for H-band excesses, while the control sample with no warm dust shows a
detection rate of $14.6^{+4.3}_{-2.8}\%$. These two occurrence rates are well
within the error bars of each other, and we note that choosing any temperature
threshold in the 100–200 K range to classify warm against cold dust
populations would not change this conclusion. In order to confirm that this
result is compatible with the two samples being drawn from the same
population, we perform a two-sample Anderson-Darling test, which tests the
null hypothesis that two samples are drawn from the same population, without
having to specify the distribution function of that population. Here, the two
samples are defined as the collection of the H-band excess levels in the warm
dust and control samples, regardless of their spectral type. The two-sample
test returns a p-value of 0.13, which confirms that the null hypothesis cannot
be rejected. Performing the Anderson-Darling test on the significance of the
H-band excess instead of the excess level itself, to account for the specific
sensitivity level reached on each star, does not change the conclusion, with a
p-value of 0.22. This is consistent with the study of Mennesson et al. (2014),
who used the mid-infrared Keck Interferometer Nuller (KIN) to search for warm
dust around 11 stars already known to host hot excesses from near-infrared
interferometric observations (among a total KIN sample of 40 stars), and did
not find a significant correlation between the presence of hot and warm dust.
The same conclusion was reached by the recent analysis of the Large Binocular
Telescope Interferometer (LBTI) HOSTS survey (Ertel et al., 2018, 2020), based
on a sample of 38 stars. This lack of correlation is understood as the
telltale sign of a disconnection between hot and warm dust populations, which
would then not be created by the same parent bodies. Here, with our much
larger sample (131 stars), we confirm that the detection rate of hot dust is
not significantly enhanced by the presence of a warm asteroid belt. While it
cannot be excluded that warm asteroid belts act as prominent suppliers of
material to replenish the short-lived hot dust population, the presence of
large amounts of warm dust does not seem to be a pre-requisite to the presence
of hot exozodiacal dust, and we confirm that hot dust should not be considered
as the bright, near-infrared counterpart of warm belts (or at least not in a
directly connected way). This conclusion is of course only valid at the
sensitivity level of the instruments used in this study (both regarding near-
infrared interferometry and mid- to far-infrared spectrophotometry), and may
be challenged by future, more sensitive observations.

Figure 11: Occurrence rate of H-band excesses for the 66 stars hosting a known
dust reservoir, as a function of the estimated temperature of the dust.

To refine our analysis, we also investigate the possible correlation between
the temperature of the outer dust reservoirs and the detection of an H-band
excess. If there is a direct connection between inner and outer dust disks, we
may expect that the warmer the outer disk, the higher the chances will be to
detect an H-band excess. However, Fig. 11 indicates a lack of correlation
between the temperature of the outer dust reservoir and the occurrence rate of
H-band excesses – the apparent drop in occurrence rate for the warmest dust
reservoirs being non-significant. A more relevant way of making this analysis
may be to use the expected warm belt location rather than its temperature.
Since the dust temperature is a good proxy for its location, when taking into
account the black-body correction of Pawellek & Krivov (2015) as discussed in
Sect. 2.1, this does not change the conclusion. A last possible correlation
that we investigated is between the luminosity of the warm debris disk (as a
proxy for its mass) and the H-band excess. The inward flux of dust due to P-R
drag is indeed expected to scale (albeit weakly) with the mass of the warm
dust disk (Kennedy & Piette, 2015). No correlation was found here either,
which seems to concur with the conclusions of Sezestre et al. (2019) that P-R
drag is unlikely to be at the origin of the hot exozodi phenomenon, although
we recognize that fractional luminosities may not be directly proportional to
the dust mass. Finally, our new results also make it possible to revisit the
conclusion of Ertel et al. (2014) that the presence of hot dust does not
correlate with the presence of cold dust. We confirm this conclusion by
comparing the detection rate of H-band excesses around the “cold dust only”
(no warm dust) and “no dust” samples (see Table 4), and find them to be fully
compatible within the statistical uncertainties.

###  6.2 Occurrence rate vs. stellar parameters

Previous studies suggested that hot exozodiacal dust is more frequent around
early-type stars than solar-type stars, although no firm conclusion could be
drawn due to the limited sample (Absil et al., 2013; Ertel et al., 2014).
Here, this correlation does not appear as obvious any more, with A-type stars
showing a similar detection rate ($17.5^{+7.5}_{-4.4}\%$) as FGK-type stars
($16.1^{+4.5}_{-3.1}\%$) in the combined sample. This result may seem to
contradict the prediction of the magnetic trapping model, which is shown by
Rieke et al. (2016) to be more efficient around rapidly rotating stars.
Although a measurement of $v\sin i$ is not available for all of the stars of
our sample, we consider that stars with spectral type earlier than F5 have a
much higher chance of showing high rotational velocities, due to the absence
of a strong convective layer to brake their initial rotation. A two-sample
Anderson-Darling test comparing the H-band excess levels of hot exozodis
around stars earlier and later than F5 shows a 2.5% probability for them to be
drawn from the same population, which suggests, at a $2.2\sigma$ level, that
the two samples are drawn from different populations. The same Anderson-
Darling test, performed on the excess significance instead of the excess
levels, shows a 5.3% probability for them to be drawn from the same
population, a marginal evidence at best.

We found in the previous section that there is a lack of correlation between
the presence of inner (hot) dust and outer (warm/cold) dust in our combined
sample of 133 stars. It is interesting to investigate whether this lack of
correlation holds when looking separately at different spectral types. To do
so, we perform the same two-sample Anderson-Darling test as before,
considering separately early-type stars and solar-type stars. We choose to set
the boundary between early-type and solar-type stars at F5, which corresponds
to the spectral type where strong convective envelopes start to appear. The
probability of the null hypothesis turns out to above 0.3 in both cases, which
suggests once again that the distribution of H-band excesses does not have a
different behavior around stars with and without warm dust.

Figure 12: Occurrence rate of H-band excesses as a function of stellar age in
the combined sample of 133 stars.

Based on 85 single stars in their PIONIER survey, Ertel et al. (2014)
investigated the possible relation between stellar age and hot exozodi
detection rate, showing the absence of correlation, although a possible trend
was observed that FGK stars could have more frequent hot exozodis at old ages.
We revisit their analysis including the 48 new single stars observed here (see
Fig. 12). Based on this larger sample of young main sequence stars, we note an
increase in detection rate at very young ages, with in particular three stars
out of five within the $\beta$ Pic moving group ($\sim$20 Myr) showing a hot
exozodi in the combined sample. Actually, among the two stars from the $\beta$
Pic moving group showing no hot exozodi, HD 172555 was identified as a
marginal H-band detection by Ertel et al. (2014) based on the longest
wavelength channel, and this detection was later confirmed to be significant
through follow-up observations (Ertel et al., 2016). This leads to an actual
detection rate of $80^{+8}_{-25}\%$ for hot exozodis at 20 Myr of age. To
determine whether the population of young stars is significantly different
from the older stars, we perform an Anderson-Darling test on two samples: the
first one composed of young stars (younger than 30 Myr) and the second one
composed of the other stars. We find a probability that the two samples are
drawn from the same population of 6.8%, i.e., a marginal evidence for them to
be issued from different populations, at a $1.8\sigma$ level. Although this
trend is based on a very small sample, it fits well within the picture that
young main sequence stars might still be in the process of forming terrestrial
planets, which may lead to strong dust production rate even in the innermost
parts of the planetary systems. It is somewhat puzzling, though, that the
youngest star in our sample (HD 109573 aka HR 4796, part of the TW Hya
association), only shows a marginal H-band excess ($0.35\pm 0.15\%$).

###  6.3 Influence of partly resolved exozodis

An important aspect of the hot exozodi detection statistics, which was not
explored in previous works, is the influence of the location of the dust on
its detectability with infrared interferometry. The most critical case in
terms of angular resolution is for the most compact disks, which corresponds
to the case where the circumstellar emission comes mostly from a region close
to the sublimation distance of the dust grains. This situation actually
corresponds to our current picture of hot exozodi detected with near-infrared
interferometry, for which the measured excesses are understood to originate
from the thermal emission of hot grains at a temperature close to sublimation
(e.g., Mennesson et al., 2011; Lebreton et al., 2013). The emission could be
even more confined by physical mechanisms such as grain pile-up (Kobayashi et
al., 2009), magnetic trapping (Rieke et al., 2016), or gas drag (Pearce et
al., 2020). In this case, the circumstellar emission might only be partly
resolved by the interferometer, which would decrease the strength of the
visibility drop, especially at the shortest baselines. Partly resolving the
hot exozodiacal disk would therefore lead to a decreased sensitivity, as only
part of the disk emission would affect the measured $V^{2}$. Here, we explore
how the uneven sensitivity to compact hot exozodis around our target stars
could bias the results of our survey.

So far, our working hypothesis has always been that circumstellar disks are
fully resolved, and we have modeled them as a uniform emission filling the
whole field of view. To test the impact of this working hypothesis on the
measured detection rates, we computed the sublimation radius of the grains for
each of the 133 stars in our combined sample, assuming silicates with a
sublimation temperature of 1500 K. Our estimation of the sublimation radius is
based on a simple black-body assumption, which we validated by running
specific simulations with the GRaTeR radiative transfer package (Augereau et
al., 1999; Lebreton et al., 2012) to explore the dependency of the sublimation
radius as a function of the grain size and composition. The resulting
sublimation radii are given in Table LABEL:tab:subdiam.

Table 5: Hot exozodiacal disk statistics from the combined PIONIER surveys
(Ertel et al., 2014, and this work), after removing all stars showing an
effective sensitivity larger than $0.5\%$, taking into account partial
resolution effects. Columns “#S” and “#E” represent the number of target stars
and of hot exozodi detections, respectively.

| A-type stars | F-type stars | G/K-type stars | Total
---|---|---|---|---
| #S | #E | detect. rate | #S | #E | detect. rate | #S | #E | detect. rate | #S | #E | detect. rate
Alla | 34 | 7 | $20.6^{+8.5}_{-5.2}\%$ | 28 | 7 | $25.0^{+9.7}_{-6.3}\%$ | 6 | 1 | $16.7^{+23.2}_{-6.3}\%$ | 68 | 15 | $22.1^{+5.8}_{-4.2}\%$
Warm disk | 16 | 3 | $18.8^{+13.1}_{-6.1}\%$ | 8 | 2 | $25.0^{+19.3}_{-9.1}\%$ | 1 | 1 | $100^{+0.0}_{-60.0}\%$ | 25 | 6 | $24.0^{+10.3}_{-6.4}\%$
Warm disk only | 11 | 2 | $18.2^{+16.3}_{-6.4}\%$ | 6 | 2 | $33.3^{+21.1}_{-12.7}\%$ | 0 | 0 | N.A. | 17 | 4 | $23.5^{+12.7}_{-7.1}\%$
Cold disk only | 4 | 2 | $50.0^{+20.2}_{-20.2}\%$ | 6 | 2 | $33.3^{+21.1}_{-12.7}\%$ | 2 | 0 | $0.0^{+45.7}_{-0.0}\%$ | 12 | 4 | $33.3^{+15.1}_{-10.3}\%$
No warm disk | 17 | 3 | $17.6^{+12.6}_{-5.7}\%$ | 20 | 5 | $25.0^{+11.7}_{-7.1}\%$ | 5 | 0 | $0.0^{+26.3}_{-0.0}\%$ | 42 | 8 | $19.0^{+7.4}_{-4.6}\%$
No disk | 13 | 1 | $7.7^{+14.0}_{-2.6}\%$ | 14 | 3 | $21.4^{+14.2}_{-7.0}\%$ | 3 | 0 | $0.0^{+36.8}_{-0.0}\%$ | 30 | 4 | $13.3^{+8.6}_{-4.0}\%$

555(a) also includes one dusty star with no warm/cold classification: HD 36187
(A0V).

The estimated sublimation radii must then be compared with the angular
resolution of the interferometric array to determine whether the disks are
fully or only partly resolved. To do so, we considered infinitesimally thin
rings with diameters ranging between 1.2 and 8.5 mas, corresponding to twice
the minimum and maximum sublimation distance for the newly observed stars on
the medium-sized AT configuration (see Table LABEL:tab:subdiam). We injected
these thin rings around a typical star of our survey to produce the expected
$V^{2}$ for the star-disk system, using the medium-sized AT configuration at
the VLTI (D0-H0-G1-I1) and a typical observing setup in terms of target
elevation and hour angle coverage. This expected $V^{2}$ was then passed to
our exozodi detection routine, which is based on the assumption of a fully
resolved circumstellar disk filling the entire field-of-view, and we extracted
the measured disk/star flux ratio using our standard fitting method. This
measured flux ratio was then compared to the actual flux ratio injected in the
model (chosen to be $3\%$ in this case), to produce a “sensitivity reduction
factor” ($\phi$), defined as the ratio of measured to injected disk/star flux
ratio. The result of this exercise is illustrated in Fig. 13, where we plot
the sensitivity reduction factor for thin annular disks of increasing
diameters. As expected, smaller disk diameters lead to a bigger hit in
sensitivity, with only about 15% of the flux detected for the most compact
disks. Half of the flux is missed for a disk diameter of about 2.5 mas (i.e.,
disk radius of 1.25 mas). The same exercise was carried out on the compact AT
configuration (A1-B2-C1-D0) for the sample observed by Ertel et al. (2014).
The resulting sensitivity reduction factor $\phi$ is given for all of the
stars in our combined sample in Table LABEL:tab:subdiam, where asterisks
denote the stars observed on the medium-sized AT configuration within the
observing program presented in this paper.

Figure 13: Sensitivity reduction factor (i.e., ratio between the measured and
injected flux ratio) as a function of the diameter of the circumstellar ring,
for the medium-sized AT configuration (D0-H0-G1-I1).

Knowing the sensitivity reduction factor for all the stars in the PIONIER
surveys, we can compute the effective sensitivity ($\sigma_{\rm eff}$) of our
observations under the new working hypothesis that all the disks are confined
to the sublimation radius of silicates. The effective sensitivity, defined as
the $1\sigma$ error bar on the disk/star flux ratio divided by the sensitivity
reduction factor, is given in Table LABEL:tab:subdiam. Based on these revised
sensitivities, we define a homogeneous sample in terms of effective
sensitivity, by rejecting all the stars that have an effective sensitivity
larger than $0.5\%$ (for which the chances to detect a hot exozodi are much
lower, owing to the typical brightness of hot exozodis). This gives us a new
sample of 68 stars, among which 25 show the presence of warm dust. The hot
exozodi detection rate can then be recomputed on this new, more homogeneous
sample, which is however strongly biased towards early-type stars because of
the larger star/disk angular separation in those systems. The new detection
rates are summarized in Table 5. They are still compatible with each other
within error bars, although the occurrence rate for the “no-dust” sample
($13.3^{+8.6}_{-4.0}\%$) seems to be systematically lower than for the rest of
the sample (stars hosting warm and/or cold dust), which shows an occurrence
rate of $28.9^{+8.2}_{-6.1}\%$ (11 out of 38 stars666this includes one dusty
star for which the dust temperature could not be determined, so that it does
not show up in either of the “warm” and “cold” dust categories in Table 5). To
further explore this possible correlation, we used a two-sample Anderson-
Darling test to compare the H-band excess distribution within the dusty and
non-dusty samples, containing respectively 38 and 30 stars. The Anderson-
Darling test on the H-band excess levels shows that the null hypothesis that
the two samples are drawn from the same population can be rejected at
significance level $p=0.0028$, which corresponds to a $3.0\sigma$ level. Using
the excess significance instead of the excess levels in the Anderson-Darling
test would increase the significance level to $3.4\sigma$ that the two samples
are drawn different populations. Since the $1\sigma$ sensitivity threshold of
0.5% used to define our sensitivity-corrected sample is somewhat arbitrary, we
also examine a case where the threshold is set to 0.33%. This new threshold
boosts the significance that a common underlying population can be rejected to
a $3.7\sigma$ level, for a sample of 40 stars. A tentative evidence for a
correlation between the presence of hot dust and an outer reservoir was
already found based on K-band observations at the CHARA array, but only for
solar-type stars (FGK types), and based on a smaller sample (Absil et al.,
2013; Nuñez et al., 2017). This tentative correlation was not confirmed at H
band on a larger sample of stars in the study of Ertel et al. (2014). The
analysis presented here seems to finally reconcile the trends observed at H
and K bands. It provides the first evidence at a $>3\sigma$ level that the
presence of an outer dust reservoir may have a significant influence on the
appearance of a near-infrared excess across all spectral types, although we
underline the facts that this conclusion is based on the assumption that the
dust is arranged in a thin ring close to its sublimation radius, and that the
samples are still relatively small. It must also be kept in mind that the
absence of observable amounts of warm/cold dust populations does not mean the
complete absence of outer dust reservoirs, which could artificially increase
or decrease the significance of this tentative correlation.

Figure 14: Measured and modeled squared visibilities for HD 80883 using a
limb-darkened star surrounded by uniform circumstellar emission (left) or by a
ring of dust at the sublimation radius (right). The different colors of the
data points represent the different spectral channels (one color per channel).
The solid blue line shows the expected visibility for the stellar photosphere
alone, and the dotted blue line the best fit for the star+disk model. Both
disk models provide a reasonable fit to the measured visibilities, with
$\chi_{r}^{2}\leq 1$.

###  6.4 Location and temperature of the hot dust

In order to further investigate the robustness of the tentative conclusion
from the previous section, an interesting question is whether we could
discriminate between a fully resolved (uniform) circumstellar emission, and a
thin annulus model. This type of morphological study has already been
attempted on Fomalhaut by Absil et al. (2009) using VLTI/VINCI, and on $\beta$
Pictoris by Defrère et al. (2012) using VLTI/PIONIER. In both cases, a very
large number of observations were available, but no constraint could be
derived on the disk morphology. We do not expect this situation to change in
the present case, where we only collected three OBs on each of our targets.
Nevertheless, we search for possible signs of partly resolved disks in our
whole sample of detected hot exozodis, by looking for a slope in the $V^{2}$
drop as a function of baseline. Indeed, partly resolved disks should lead to
smaller $V^{2}$ drop at shorter baselines, as they become less and less
resolved. This exercise is illustrated in Fig. 14 for the case of HD 80883,
for which the expected sublimation radius is particularly small. The data set
shows no significant slope, suggesting that the excess is more probably caused
by an extended disk than by a thin ring at the sublimation radius, although
both models are consistent with the available data set.

Another possible way to constrain the location of the dust grains would be to
infer their temperature. This can potentially be done by exploring the
wavelength dependence of the measured disk/star flux ratio. To test this, we
have fitted blackbodies of various temperatures, including the host star
temperature (flat contrast) to simulate the effect of scattered light, to the
measured disk/star flux ratio as a function of wavelength (Fig. 9). Blackbody
models with temperatures between 1500 K and the host star temperature fit the
data almost equally well, with a reduced $\chi^{2}$ around 1. Using a
blackbody temperature of 1000 K increases the median reduced $\chi^{2}$ to
about 2 for our sample of 13 hot exozodis. The accuracy that can currently be
reached with precision infrared interferometers such as VLTI/PIONIER is
therefore not high enough to conclude on the dust temperature. At best, we
could reject the hypothesis that the detected excess are due to the thermal
emission of grains at temperature below 1000 K, which is not expected as such
grains would not produce a significant H-band emission anyway. A possible way
to circumvent this limitation would be to follow up our detections at other
wavelengths, for instance using the second generation interferometric
instruments of the VLTI (GRAVITY in the near-infrared and MATISSE in the mid-
infrared, see e.g., Kirchschlager et al., 2020).

###  6.5 Origin of the hot dust

The lack of a strong correlation between the hot exozodi phenomenon and the
amount of warm and/or cold dust in outer reservoirs remains puzzling. Our
understanding is that the hot dust is likely supplied from an outer reservoir
for most stars, because parent bodies cannot survive on Myr timescales close
to the dust sublimation radius due to collisional activity (e.g., Absil et
al., 2006). However, the determining factor of whether detectable amounts of
hot dust are present seems not to be the mass or location of this reservoir,
but rather a different condition triggering the phenomenon. Trapping
mechanisms have been proposed to sustain the observed, high dust masses that
would otherwise require extreme replenishment rates due to the efficient
removal of the hot dust (e.g., Pearce et al., 2020). These mechanisms include
the pile-up of sublimating dust (Kobayashi et al., 2009), the effect of the
stellar magnetic field (Czechowski & Mann, 2010; Rieke et al., 2016), or the
effect of gas (Lebreton et al., 2013; Pearce et al., 2020), possibly
originating in the sublimation of the dust grains themselves. Trapping
mechanisms could explain why even faint, undetected outer belts can supply
sufficient material to produce detectable hot dust. Alternatively, or in
addition, a specific configuration of the dust reservoir and a planetary
system could be required to supply sufficient material to the inner regions
(Bonsor & Wyatt, 2012; Bonsor et al., 2012, 2014; Faramaz et al., 2017). Such
a mechanism could also be sufficiently efficient to act indistinguishably by
us on systems with detectable and undetectable cold reservoirs.

Irrespective of the delivery mechanism and of the presence or absence of a
trapping mechanism, a larger reservoir of cold material provides more material
to be delivered to the inner region. Thus, naively one would still expect a
correlation between the presence of massive debris disks and near-infrared
excesses, at least statistically if not for individual targets. There is only
a weak evidence for this to be the case in our sample, with a tentative
correlation appearing only after correcting the sample for sensitivity under
the assumption that all the hot dust is located close to the sublimation
distance of silicates (Sect. 6.3). The lack of a more prominent correlation
between hot dust and outer reservoirs might imply that there is an upper limit
on the amount of hot dust that may be present or be supplied, and that this is
reached in systems where the conditions for delivery and trapping are met,
even for relatively small outer reservoirs. In the case of P-R drag, the
amount that reaches the innermost regions is limited by collisions between the
migrating dust grains (Wyatt, 2005): while massive, collision-dominated outer
belts produce more dust that can be dragged inward, most of this dust is
destroyed before it reaches the inner regions. In contrast, most of the dust
created in more tenuous, transport-dominated outer belts may reach the inner
regions. This naturally decouples to some degree the amount of dust supplied
to the hot exozodi region from the mass of the outer reservoir. For other
scenarios, like comet delivery of the hot dust, an upper limit on the amount
of hot dust could be set by the collisional evolution of the dust, which
happens at a shorter time scale for more massive disks so that an equilibrium
between dust influx and removal could typically be reached around similar dust
levels. It is also possible that the amount of material transported inwards is
dominated by the efficiency of the transport process (e.g., scattering) rather
than the supply of material, which would also result in a (partial) decoupling
of the hot dust quantity from the brightness of the cold reservoir. Finally,
some trapping mechanisms may have intrinsic upper limits on the amount of dust
they can trap. An alternative explanation for the similar flux ratios observed
around all stars with near-infrared excess would be that the hot dust is
optically thick. In that case, the observed flux would be driven by the
surface area of the disk, and would be independent of the dust mass to the
first order. This scenario would then require the surface area of the hot disk
to increase for earlier spectral types, which could at least partly be
explained by the larger dust sublimation radius around earlier spectral types.

Among the potential origins for the hot dust population, the possibility that
hot dust is primordial (i.e., a remnant of the initial protoplanetary disk)
cannot be completely ruled out without a detailed analysis of the possible
trapping mechanisms. This would however require the trapping mechanism at play
to be efficient enough on Gyr timescales, and to be on-going since the late
stages of the primordial disk dispersal, which seems rather unlikely. This
scenario would also be expected to show a more prominent age dependence in the
hot exozodi phenomenon.

The apparent lack of correlation between hot and warm dust populations could
be both an asset and a drawback in the preparation of space-based missions
dedicated to Earth-like planet imaging. On one hand, the lack of correlation
means that stars hosting hot dust populations should not necessarily be
removed from the potential target lists of such missions, because they are not
necessarily associated with large amounts of warm dust in the habitable zone.
The influence on the mission performance of hot dust populations located at
much smaller angular separation from the star than the habitable zone is
however still to be investigated – a task that we defer to a future, dedicated
work. On the other hand, the lack of correlation also means that the detection
of significant near-infrared emission with precision interferometry is not a
prime criterion to build the target lists, which means that more mid-infrared
interferometric observations with existing (LBTI/NOMIC, Ertel et al., 2020) or
upcoming (VLTI/Hi-5, Defrère et al., 2018) instruments will be needed.

##  7 Conclusions

In this paper, we used the VLTI/PIONIER interferometric instrument to search
for resolved near-infrared circumstellar emission around a sample of main
sequence stars known to harbor a warm dust disk from previous mid-infrared
spectrophotometric observations, in an attempt to identify a possible
connection between warm and hot dust populations. For that, we built a target
list of 62 stars that showed signs of warm dust in the literature. Among the
52 stars for which we obtained data of sufficient quality, we identified 17
new H-band excesses, among which four are shown to be due to the presence of a
previously unknown close stellar companion. The remaining 13 excess are
thought to originate from hot dust populations, adding to the nine hot exozodi
systems already detected with PIONIER by Ertel et al. (2014). Combining these
two samples, resulting in a total of 133 stars, we find an overall detection
rate of $16.5^{+3.7}_{-2.7}\%$ for H-band excesses around nearby main sequence
stars, with a possible hint for a larger underlying population of excesses
below our sensitivity limit. Taking into account the fact that some of the hot
exozodiacal disks may only be partly resolved by our interferometric baseline
lengths, we estimate that the true occurrence rate could actually be as high
as $22.1^{+5.8}_{-4.2}\%$, if we only include stars that have a corrected
$1\sigma$ sensitivity of 0.5% or better on the disk/star flux ratio. Our data
sets do however not allow us to discriminate between a fully resolved disk and
a thin annulus at the sublimation radius as the most appropriate model to
reproduce our observations, so that the true occurrence rate at our
sensitivity level could be anywhere between 16.5% and 22.1%.

We then searched for a possible correlation between the presence of a known
warm dust population around the target stars and the detection of a near-
infrared excess in our interferometric observations. For that, we re-evaluated
the presence of warm and/or cold dust around all of the 133 stars in our
combined sample through SED modeling, and defined two samples containing
respectively the stars showing warm dust emission or not. We found that the
distribution of near-infrared excesses around the warm dust sample is fully
compatible with that of the control sample, suggesting the absence of direct
connection between warm and hot dust populations. This conclusion does not
depend on the considered spectral type. No correlation was found either
between the detection rate of near-infrared excess and the stellar age,
although there is a marginal trend for young stars ($\leq 30$ Myr) to have
more frequent H-band excesses. After correcting the sensitivity of our
observations for the fact that the hot dust could be arranged in a thin ring
around its sublimation radius, and subsequently limiting our sample to the
stars for which the corrected $1\sigma$ error bar is smaller than 0.5%, we
find tentative evidence at the $3\sigma$ level that the distribution of near-
infrared excesses around stars showing any kind of outer dust reservoir (warm
or cold) is statistically different from the distribution of near-infrared
excesses around stars showing no outer dust reservoir, with larger near-
infrared excesses around the dusty stars. This conclusion pertains mostly to
early-type (A and F) stars, which make up the most of our sensitivity-
corrected sample, and only holds if the dust is arranged in a thin annulus
close to its sublimation radius, a hypothesis that we cannot confirm nor
infirm based on our PIONIER data. A possible caveat to these conclusions is
that some of the near-infrared excesses might be variable, as suggested by
Ertel et al. (2016) and Nuñez et al. (2017), so that a non-detection does not
necessarily mean that there is never any detectable excess around a particular
star. It must also be kept in mind that we can only probe correlations down to
the sensitivity level of both the near-infrared interferometric observations
and the mid- to far-infrared photometry used in this study, and that
underlying correlations may exist at lower sensitivity levels.

Although the present work puts in light a tentative, previously unknown
correlation between hot and warm/cold dust populations, it does not settle the
question of the origin of hot exozodiacal dust. Our current understanding is
that at least one transport mechanism is at play to inject material in the
innermost parts of planetary systems, and that the material additionally needs
to be confined close to its sublimation radius by a trapping mechanism. The
nature of these transport and trapping mechanisms is however still unclear,
and will probably require new diagnostic tools to be properly constrained,
although it is worth noting that some specific hot-dust systems in our sample
look incompatible with P-R drag dust production. High-contrast interferometric
observations in the thermal infrared (L, M, and N bands) would be a powerful
way to derive useful new constraints on these dust populations.

###### Acknowledgements.

The authors thank the French National Research Agency (ANR, contract ANR-2010
BLAN-0505-01, EXOZODI) for financial support. L. M. acknowledges the
F.R.S.-FNRS for financial support through a FRIA PhD fellowship. G. M. K. is
supported by the Royal Society as a Royal Society University Research Fellow.
J. O. acknowledges support by ANID, – Millennium Science Initiative Program –
NCN19_171, from the Universidad de Valparaíso, and from Fondecyt (grant
1180395). We thank the Belgian GTO on VISA for the generous allocation of
observing time. This work made use of the Smithsonian/NASA Astrophysics Data
System (ADS) and of the Centre de Données astronomiques de Strasbourg (CDS).

## References

  * Absil et al. (2013) Absil, O., Defrère, D., Coudé du Foresto, V., et al. 2013, A&A, 555, A104
  * Absil et al. (2006) Absil, O., di Folco, E., Mérand, A., et al. 2006, A&A, 452, 237
  * Absil et al. (2008) Absil, O., di Folco, E., Mérand, A., et al. 2008, A&A, 487, 1041
  * Absil et al. (2011) Absil, O., Le Bouquin, J.-B., Berger, J.-P., et al. 2011, A&A, 535, A68
  * Absil et al. (2009) Absil, O., Mennesson, B., Le Bouquin, J.-B., et al. 2009, ApJ, 704, 150
  * Allard et al. (2012) Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765
  * Augereau et al. (1999) Augereau, J. C., Lagrange, A. M., Mouillet, D., Papaloizou, J. C. B., & Grorod, P. A. 1999, A&A, 348, 557
  * Ballering et al. (2013) Ballering, N. P., Rieke, G. H., Su, K. Y. L., & Montiel, E. 2013, ApJ, 775, 55
  * Beust et al. (1990) Beust, H., Lagrange-Henri, A. M., Madjar, A. V., & Ferlet, R. 1990, A&A, 236, 202
  * Binks & Jeffries (2014) Binks, A. S. & Jeffries, R. D. 2014, MNRAS, 438, L11
  * Bonfanti et al. (2016) Bonfanti, A., Ortolani, S., & Nascimbeni, V. 2016, A&A, 585, A5
  * Bonsor et al. (2012) Bonsor, A., Augereau, J. C., & Thébault, P. 2012, A&A, 548, A104
  * Bonsor et al. (2014) Bonsor, A., Raymond, S. N., Augereau, J.-C., & Ormel, C. W. 2014, MNRAS, 441, 2380
  * Bonsor & Wyatt (2012) Bonsor, A. & Wyatt, M. C. 2012, MNRAS, 420, 2990
  * Bonsor et al. (2018) Bonsor, A., Wyatt, M. C., Kral, Q., et al. 2018, MNRAS, 480, 5560
  * Booth et al. (2013) Booth, M., Kennedy, G., Sibthorpe, B., et al. 2013, MNRAS, 428, 1263
  * Carpenter et al. (2009) Carpenter, J. M., Bouwman, J., Mamajek, E. E., et al. 2009, ApJS, 181, 197
  * Casagrande et al. (2011) Casagrande, L., Schönrich, R., Asplund, M., et al. 2011, A&A, 530, A138
  * Chauvin et al. (2010) Chauvin, G., Lagrange, A.-M., Bonavita, M., et al. 2010, A&A, 509, A52
  * Cheetham et al. (2018) Cheetham, A., Ségransan, D., Peretti, S., et al. 2018, A&A, 614, A16
  * Chen et al. (2020) Chen, C., Mazoyer, J., Poteet, C. A., et al. 2020, ApJ, 898, 55
  * Chen et al. (2014) Chen, C. H., Mittal, T., Kuchner, M., et al. 2014, ApJS, 211, 25
  * Chen et al. (2006) Chen, C. H., Sargent, B. A., Bohac, C., et al. 2006, ApJS, 166, 351
  * Ciardi et al. (2001) Ciardi, D., van Belle, G. T., Akeson, R. L., & Thompson, R. R. 2001, in Bulletin of the American Astronomical Society, Vol. 33, American Astronomical Society Meeting Abstracts, 1508
  * Claret et al. (1995) Claret, A., Diaz-Cordoves, J., & Gimenez, A. 1995, A&AS, 114, 247
  * Cotten & Song (2016) Cotten, T. H. & Song, I. 2016, ApJS, 225, 15
  * Cox (2000) Cox, A. N., ed. 2000, Allen’s astrophysical quantities (Springer)
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, 2MASS All Sky Catalog of point sources.
  * Czechowski & Mann (2010) Czechowski, A. & Mann, I. 2010, ApJ, 714, 89
  * David & Hillenbrand (2015) David, T. J. & Hillenbrand, L. A. 2015, ApJ, 804, 146
  * De Rosa et al. (2014) De Rosa, R. J., Patience, J., Wilson, P. A., et al. 2014, MNRAS, 437, 1216
  * Defrère et al. (2011) Defrère, D., Absil, O., Augereau, J.-C., et al. 2011, A&A, 534, A5
  * Defrère et al. (2018) Defrère, D., Absil, O., Berger, J. P., et al. 2018, Experimental Astronomy, 46, 475
  * Defrère et al. (2010) Defrère, D., Absil, O., den Hartog, R., Hanot, C., & Stark, C. 2010, A&A, 509, A9
  * Defrère et al. (2012) Defrère, D., Stark, C., Cahoy, K., & Beerer, I. 2012, in Proc. SPIE, Vol. 8442, Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, 84420M
  * Delgado Mena et al. (2015) Delgado Mena, E., Bertrán de Lis, S., Adibekyan, V. Z., et al. 2015, A&A, 576, A69
  * Delgado Mena et al. (2014) Delgado Mena, E., Israelian, G., González Hernández, J. I., et al. 2014, A&A, 562, A92
  * Desidera et al. (2015) Desidera, S., Covino, E., Messina, S., et al. 2015, A&A, 573, A126
  * di Folco et al. (2007) di Folco, E., Absil, O., Augereau, J.-C., et al. 2007, A&A, 475, 243
  * Dikarev & Schwarz (2015) Dikarev, V. V. & Schwarz, D. J. 2015, A&A, 584, A9
  * Durkan et al. (2016) Durkan, S., Janson, M., & Carson, J. C. 2016, ApJ, 824, 58
  * Eiroa et al. (2013) Eiroa, C., Marshall, J. P., Mora, A., et al. 2013, A&A, 555, A11
  * Ertel et al. (2014) Ertel, S., Absil, O., Defrère, D., et al. 2014, A&A, 570, A128
  * Ertel et al. (2016) Ertel, S., Defrère, D., Absil, O., et al. 2016, A&A, 595, A44
  * Ertel et al. (2020) Ertel, S., Defrère, D., Hinz, P., et al. 2020, AJ, 159, 177
  * Ertel et al. (2018) Ertel, S., Defrère, D., Hinz, P., et al. 2018, AJ, 155, 194
  * Esposito et al. (2016) Esposito, T. M., Fitzgerald, M. P., Graham, J. R., et al. 2016, AJ, 152, 85
  * Faramaz et al. (2017) Faramaz, V., Ertel, S., Booth, M., Cuadra, J., & Simmonds, C. 2017, MNRAS, 465, 2352
  * Feltzing et al. (2001) Feltzing, S., Holmberg, J., & Hurley, J. R. 2001, A&A, 377, 911
  * Feng et al. (2017) Feng, F., Tuomi, M., & Jones, H. R. A. 2017, A&A, 605, A103
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601
  * Fujiwara et al. (2013) Fujiwara, H., Ishihara, D., Onaka, T., et al. 2013, A&A, 550, A45
  * Grether & Lineweaver (2006) Grether, D. & Lineweaver, C. H. 2006, ApJ, 640, 1051
  * Hanbury Brown et al. (1974) Hanbury Brown, R., Davis, J., Lake, R. J. W., & Thompson, R. J. 1974, MNRAS, 167, 475
  * Hillenbrand et al. (2008) Hillenbrand, L. A., Carpenter, J. M., Kim, J. S., et al. 2008, ApJ, 677, 630
  * Holmberg et al. (2009) Holmberg, J., Nordström, B., & Andersen, J. 2009, A&A, 501, 941
  * Howard et al. (2019) Howard, R. A., Vourlidas, A., Bothmer, V., et al. 2019, Nature, 576, 232
  * Huensch et al. (1998) Huensch, M., Schmitt, J. H. M. M., & Voges, W. 1998, A&AS, 132, 155
  * Ishihara et al. (2010) Ishihara, D., Onaka, T., Kataza, H., et al. 2010, A&A, 514, A1
  * Kennedy et al. (2015) Kennedy, G. M., Matrà, L., Marmier, M., et al. 2015, MNRAS, 449, 3121
  * Kennedy & Piette (2015) Kennedy, G. M. & Piette, A. 2015, MNRAS, 449, 2304
  * Kennedy & Wyatt (2014) Kennedy, G. M. & Wyatt, M. C. 2014, MNRAS, 444, 3164
  * Kervella et al. (2019) Kervella, P., Arenou, F., Mignard, F., & Thévenin, F. 2019, A&A, 623, A72
  * Kervella et al. (2004) Kervella, P., Thévenin, F., Di Folco, E., & Ségransan, D. 2004, A&A, 426, 297
  * Kharchenko & Roeser (2009) Kharchenko, N. V. & Roeser, S. 2009, VizieR Online Data Catalog, 1280
  * Kirchschlager et al. (2020) Kirchschlager, F., Ertel, S., Wolf, S., Matter, A., & Krivov, A. V. 2020, MNRAS, 499, L47
  * Kirchschlager et al. (2017) Kirchschlager, F., Wolf, S., Krivov, A. V., Mutschke, H., & Brunngräber, R. 2017, MNRAS, 467, 1614
  * Kobayashi et al. (2009) Kobayashi, H., Watanabe, S.-i., Kimura, H., & Yamamoto, T. 2009, Icarus, 201, 395
  * Lagrange et al. (2021) Lagrange, A.-M., Kepler, M., Kiefer, F., et al. 2021, A&A, submitted
  * Lagrange et al. (2012) Lagrange, A.-M., Milli, J., Boccaletti, A., et al. 2012, A&A, 546, A38
  * Le Bouquin et al. (2011) Le Bouquin, J.-B., Berger, J.-P., Lazareff, B., et al. 2011, A&A, 535, A67
  * Le Bouquin et al. (2012) Le Bouquin, J.-B., Berger, J.-P., Zins, G., et al. 2012, in Proc. SPIE, Vol. 8445, Optical and Infrared Interferometry III, 84450I
  * Lebouteiller et al. (2011) Lebouteiller, V., Barry, D. J., Spoon, H. W. W., et al. 2011, ApJS, 196, 8
  * Lebreton et al. (2012) Lebreton, J., Augereau, J.-C., Thi, W.-F., et al. 2012, A&A, 539, A17
  * Lebreton et al. (2013) Lebreton, J., van Lieshout, R., Augereau, J.-C., et al. 2013, A&A, 555, A146
  * Lisse et al. (2017) Lisse, C. M., Sitko, M. L., Marengo, M., et al. 2017, AJ, 154, 182
  * Maire et al. (2014) Maire, A.-L., Boccaletti, A., Rameau, J., et al. 2014, A&A, 566, A126
  * Maldonado et al. (2012) Maldonado, J., Eiroa, C., Villaver, E., Montesinos, B., & Mora, A. 2012, A&A, 541, A40
  * Mamajek & Hillenbrand (2008) Mamajek, E. E. & Hillenbrand, L. A. 2008, ApJ, 687, 1264
  * Marion et al. (2014) Marion, L., Absil, O., Ertel, S., et al. 2014, A&A, 570, A127
  * Markwardt (2009) Markwardt, C. B. 2009, in Astronomical Society of the Pacific Conference Series, Vol. 411, Astronomical Data Analysis Software and Systems XVIII, ed. D. A. Bohlender, D. Durand, & P. Dowler, 251
  * Marshall et al. (2016) Marshall, J. P., Cotton, D. V., Bott, K., et al. 2016, ApJ, 825, 124
  * McDonald et al. (2012) McDonald, I., Zijlstra, A. A., & Boyer, M. L. 2012, MNRAS, 427, 343
  * Mennesson et al. (2014) Mennesson, B., Millan-Gabet, R., Serabyn, E., et al. 2014, ApJ, 797, 119
  * Mennesson et al. (2011) Mennesson, B., Serabyn, E., Hanot, C., et al. 2011, ApJ, 736, 14
  * Mérand et al. (2005) Mérand, A., Bordé, P., & Coudé du Foresto, V. 2005, A&A, 433, 1155
  * Mermilliod (1987) Mermilliod, J.-C. 1987, A&AS, 71, 413
  * Milli et al. (2017) Milli, J., Vigan, A., Mouillet, D., et al. 2017, A&A, 599, A108
  * Mittal et al. (2015) Mittal, T., Chen, C. H., Jang-Condell, H., et al. 2015, ApJ, 798, 87
  * Morales et al. (2012) Morales, F. Y., Padgett, D. L., Bryden, G., Werner, M. W., & Furlan, E. 2012, ApJ, 757, 7
  * Nordstrom & Andersen (1985) Nordstrom, B. & Andersen, J. 1985, A&AS, 61, 53
  * Nuñez et al. (2017) Nuñez, P. D., Scott, N. J., Mennesson, B., et al. 2017, A&A, 608, A113
  * Olofsson et al. (2016) Olofsson, J., Samland, M., Avenhaus, H., et al. 2016, A&A, 591, A108
  * Pace (2013) Pace, G. 2013, A&A, 551, L8
  * Patel et al. (2014) Patel, R. I., Metchev, S. A., & Heinze, A. 2014, ApJS, 212, 10
  * Paunzen (2015) Paunzen, E. 2015, A&A, 580, A23
  * Pawellek & Krivov (2015) Pawellek, N. & Krivov, A. V. 2015, MNRAS, 454, 3207
  * Pawellek et al. (2014) Pawellek, N., Krivov, A. V., Marshall, J. P., et al. 2014, ApJ, 792, 65
  * Pearce et al. (2020) Pearce, T. D., Krivov, A. V., & Booth, M. 2020, MNRAS, 498, 2798
  * Pecaut & Mamajek (2016) Pecaut, M. J. & Mamajek, E. E. 2016, MNRAS, 461, 794
  * Perrin et al. (2015) Perrin, M. D., Duchene, G., Millar-Blanchaer, M., et al. 2015, ApJ, 799, 182
  * Pickles (1998) Pickles, A. J. 1998, PASP, 110, 863
  * Rieke et al. (2016) Rieke, G. H., Gáspár, A., & Ballering, N. P. 2016, ApJ, 816, 50
  * Roberge et al. (2012) Roberge, A., Chen, C. H., Millan-Gabet, R., et al. 2012, PASP, 124, 799
  * Sezestre et al. (2019) Sezestre, É., Augereau, J. C., & Thébault, P. 2019, A&A, 626, A2
  * Sibthorpe et al. (2018) Sibthorpe, B., Kennedy, G. M., Wyatt, M. C., et al. 2018, MNRAS, 475, 3046
  * Sierchio et al. (2014) Sierchio, J. M., Rieke, G. H., Su, K. Y. L., & Gáspár, A. 2014, ApJ, 785, 33
  * Stark & Kuchner (2008) Stark, C. C. & Kuchner, M. J. 2008, ApJ, 686, 637
  * Stark et al. (2014a) Stark, C. C., Roberge, A., Mandell, A., & Robinson, T. D. 2014a, ApJ, 795, 122
  * Stark et al. (2014b) Stark, C. C., Schneider, G., Weinberger, A. J., et al. 2014b, ApJ, 789, 58
  * Su et al. (2006) Su, K. Y. L., Rieke, G. H., Stansberry, J. A., et al. 2006, ApJ, 653, 675
  * Takeda et al. (2007) Takeda, G., Ford, E. B., Sills, A., et al. 2007, ApJS, 168, 297
  * Tamuz et al. (2008) Tamuz, O., Ségransan, D., Udry, S., et al. 2008, A&A, 480, L33
  * Tokovinin et al. (2015) Tokovinin, A., Pribulla, T., & Fischer, D. 2015, AJ, 149, 8
  * Tsantaki et al. (2013) Tsantaki, M., Sousa, S. G., Adibekyan, V. Z., et al. 2013, A&A, 555, A150
  * Tucci Maia et al. (2016) Tucci Maia, M., Ramírez, I., Meléndez, J., et al. 2016, A&A, 590, A32
  * Valenti & Fischer (2005) Valenti, J. A. & Fischer, D. A. 2005, ApJS, 159, 141
  * van Lieshout et al. (2014) van Lieshout, R., Dominik, C., Kama, M., & Min, M. 2014, A&A, 571, A51
  * Vican & Schneider (2014) Vican, L. & Schneider, A. 2014, ApJ, 780, 154
  * Wahhaj et al. (2005) Wahhaj, Z., Koerner, D. W., Backman, D. E., et al. 2005, ApJ, 618, 385
  * Wahhaj et al. (2013) Wahhaj, Z., Liu, M. C., Nielsen, E. L., et al. 2013, ApJ, 773, 179
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Wu et al. (2013) Wu, C.-J., Wu, H., Lam, M.-I., et al. 2013, ApJS, 208, 29
  * Wyatt (2005) Wyatt, M. C. 2005, A&A, 433, 1007
  * Wyatt et al. (2017) Wyatt, M. C., Bonsor, A., Jackson, A. P., Marino, S., & Shannon, A. 2017, MNRAS, 464, 3385
  * Yelverton et al. (2020) Yelverton, B., Kennedy, G. M., & Su, K. Y. L. 2020, MNRAS, 495, 1943
  * Yelverton et al. (2019) Yelverton, B., Kennedy, G. M., Su, K. Y. L., & Wyatt, M. C. 2019, MNRAS, 488, 3588
  * Zuckerman et al. (2004) Zuckerman, B., Song, I., & Bessell, M. S. 2004, ApJ, 613, L65

##  Appendix A Spectral energy distributions

Figures 15 to 19 show observations and model spectral energy distribution for
each target in our combined sample of 133 stars.

Figure 15: Observations and models for the targets in our survey. Each sub-
panel shows photometry as dots, upper limits as triangles, and IRS spectra as
black lines. Models are shown as solid lines, with blue for the star, green
for the disc, and orange for the total model. Where two are fitted, individual
disc components are shown as dotted lines. Figure 16: Observations and models
for the targets in our survey. Each sub-panel shows photometry as dots, upper
limits as triangles, and IRS spectra as black lines. Models are shown as solid
lines, with blue for the star, green for the disc, and orange for the total
model. Where two are fitted, individual disc components are shown as dotted
lines. Figure 17: Observations and models for the targets in our survey. Each
sub-panel shows photometry as dots, upper limits as triangles, and IRS spectra
as black lines. Models are shown as solid lines, with blue for the star, green
for the disc, and orange for the total model. Where two are fitted, individual
disc components are shown as dotted lines. Figure 18: Observations and models
for the targets in our survey. Each sub-panel shows photometry as dots, upper
limits as triangles, and IRS spectra as black lines. Models are shown as solid
lines, with blue for the star, green for the disc, and orange for the total
model. Where two are fitted, individual disc components are shown as dotted
lines. Figure 19: Observations and models for the targets in our survey. Each
sub-panel shows photometry as dots, upper limits as triangles, and IRS spectra
as black lines. Models are shown as solid lines, with blue for the star, green
for the disc, and orange for the total model. Where two are fitted, individual
disc components are shown as dotted lines.