11institutetext: École Normale Supérieure Paris-Saclay, Université Paris-
Saclay, 4, avenue des Sciences, 91190, Gif-sur-Yvette, France22institutetext:
Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405,
Orsay, France33institutetext: IRFU/SAp Service D’Astrophysique, CEA, Orme des
Merisiers, Bât 709 91191, Gif-sur-Yvette, France44institutetext: I.
Physikalisches Institut, Universität zu Köln, Zülpicherstr. 77, 50937 Cologne,
Germany55institutetext: Laboratoire d’Astrophysique de Bordeaux, Université de
Bordeaux, CNRS, B16N, allée Geoffroy Saint-Hilaire, 33615, Pessac, France

# Radial distribution of the carbonaceous nano-grains in the protoplanetary
disk around HD 169142

Marie Devinat 11 Émilie Habart 22 Éric Pantin 33 Nathalie Ysard 22 Anthony
Jones 22 Lucas Labadie 44 Emmanuel Di Folco 55

(2021)

###### Abstract

Context. HD 169142 is part of the class of (pre-)transitional protoplanetary
disks showing multiple carbon nanodust spectroscopic signatures (aromatic,
aliphatic) dominating the infrared spectrum. Precise constraints on the
spatial distribution and properties of carbonaceous dust particles are
essential to understanding the physics, radiative transfer processes, and
chemistry of the disk. The HD 169142 disk is seen almost face-on and thus it
offers a unique opportunity to study the dust radial evolution in disks.

Aims. We investigate the spatial distribution of the carriers of several dust
aromatic emission features of the disk across a broad spatial range (10-200
au) as well as their properties.

Methods. We analysed imaging and spectroscopic observations in the 8–12 $\mu$m
range from the VLT Imager and Spectrometer for mid-Infrared (VISIR) at the
Very Large Telescope (VLT), as well as adaptive optics spectroscopic
observations in the 3–4 $\mu$m range from the Nasmyth Adaptive Optics System –
Near-Infrared Imager and Spectrograph (NACO) at VLT. The data probe the
spatial variation of the flux in the 3.3 $\mu$m, 8.6 $\mu$m, and 11.3 $\mu$m
aromatic bands. To constrain the radial distribution of carbonaceous nano-
grains, the observations were compared to model predictions using The
Heterogeneous dust Evolution Model for Interstellar Solids (THEMIS), which is
integrated into the POLARIS radiative transfer code by calculating the thermal
and stochastic heating of micro- and nanometer-sized dust grains for a given
disk structure.

Results. Our data show predominant nano-particle emission at all radii
(accessible with our resolution of about 0.1” or $\sim$ 12 AU at 3 $\mu$m and
$\sim$ 0.3”, 35 AU at 10 $\mu$m) in the HD 169142 disk. This unambiguously
shows that carbonaceous nano-grains dominate radiatively the infrared spectrum
in most of the disk, a finding that has been suggested in previous studies. In
order to account for both VISIR and NACO emission maps, we show the need for
aromatic particles distributed within the disk from the outermost regions to a
radius of 20 AU, corresponding to the outer limit of the inner cavity derived
from previous observations. In the inner cavity, these aromatic particles
might be present but their abundance would then be significantly decreased.

###### Key Words.:

¡Protoplanetary disks - Infrared: planetary systems¿

##  1 Introduction

The solid carbon content of protoplanetary disks is of primary importance for
improving the understanding of circumstellar disk evolution and planet
formation. Öberg et al. (2011) linked the initial carbon content of the region
of formation of planetesimals to the composition and chemistry of the
atmosphere of the evolved planet. Eistrup et al. (2018) showed that the
chemical composition of forming planets depends on the physical conditions and
the location of planetesimals in the disk, emphasising the necessity of taking
chemical evolution into account in planetary formation models. Hence, an
accurate and complete knowledge of the physical properties of primordial solid
carbon reservoirs through the disk is essential for describing the formation
and evolution paths and predicting the probability distribution of the
properties of evolved planets (e.g. Öberg et al. (2011)).

If the solid carbon in disks has been extensively studied at large
separations, it is only recently that investigations in planet-forming
regions, namely, those below $\sim$50 AU, were made possible through high-
resolution observations. In tracking down carbonaceous emission lines with the
MATISSE interferometer, Kokoulina et al. (2021) were able to probe the
distribution of solid carbon below 10 AU in the disk around HD 179218.
Recently, Boutéraon et al. (2019) investigated the spatial distribution of
carbon nano-grains down to 0.1” in protoplanetary disks around multiple stars,
including HD 100546 and HD 169142.

In this paper, we study HD 169142, a well-known Herbig Ae star (A5Ve; Keller
et al. (2008)), at a distance of 117 $\pm$ 4 pc (Manoj et al. 2006; Grady et
al. 2007; Gaia Collaboration 2016) (see stellar properties in Table 1). The
star is surrounded by an almost face-on (pre-)transitional disk, with an
inclination $\sim$ $None$ (Panić et al. 2008). The gas and dust spatial
distributions observed with SPHERE and ALMA hint at the presence of multiple
(giant) protoplanets shaping the disk structure via dynamical clearing (dust
cavity and gap) and dust trapping (double ring dust distribution). The
protoplanetary system shows an inner disk between 0.2 and 0.5 AU, two annular
gaps (from 1 to 20 AU and from 32 to 56 AU), and an outer disk extending to
250 AU (Quanz et al. 2013; Osorio et al. 2014; Ligi et al. 2018; Momose et al.
2015; Fedele et al. 2017; Bertrang et al. 2018; Honda et al. 2012; Gravity
Collaboration et al. 2019). The radial structure of the disk used in this work
is summarized in Fig. 1. It assumes the gap radial extension derived by Ligi
et al. (2018) from the results of Quanz et al. (2013), using the corrected
value of 117 pc for the distance to Earth.

HD 169142 is one of the few Herbig Ae/Be stars for which planet candidates
have been detected via direct imaging in the near-infrared (Biller et al.
2014; Reggiani et al. 2014; Osorio et al. 2014; Quanz et al. 2013). One of the
point sources detected around HD 169142 (Biller et al. 2014; Reggiani et al.
2014) was shown to be related to an inhomogeneous ring structure in the inner
region of the disk at 0.18” by Ligi et al. (2018). These authors also found
that an additional compact structure detected at about 0.1” projected
separation could possibly be related to an additional ring structure at the
given separation. Furthermore, the system shows near infrared flux decreasing
in the past decades (by 45%), which may have resulted from modifications of
the inner disk structure due to accretion or sculpting by planets undergoing
formation (Wagner et al. 2015).

The HD 169142 global spectrum presents very rich and intense infrared carbon
nano-dust spectroscopic features (aromatic, aliphatic) between 3 and 13 $\mu$m
(Meeus et al. 2001; Sloan et al. 2005; Acke et al. 2010; Boutéraon et al.
2019; Seok & Li 2017). The carriers of these bands can be attributed to carbon
nano-grains containing aromatic domains, for instance, astronomical polycyclic
aromatic hydrocarbons (PAH) or amorphous hydrocarbons a-C(:H) that are
undergoing stochastic heating. HD 169142 is one of the few disks with a very
large amount of aromatic species (Woitke et al. 2016) and very high normalised
aromatic infrared bands to UV luminosity ratio $L_{AIB}/L_{UV}$ (Acke & van
den Ancker 2004; Maaskant et al. 2014). In this study, we present spatially
resolved observations of the 3.3, 8.6, and 11.3 $\mu$m aromatic bands.

The disk of HD 169142 has been observed at different wavelengths, using ISO,
Spitzer, and ground-based spectroscopy. The detection of [OI] (Acke et al.
2005), H$\alpha$ (Dunkin et al. 1997), and Br$\gamma$ (Garcia Lopez et al.
2006) emission indicates the presence of gas in the inner parts of the disk.
The carbonaceous aromatic nano-particles are strongly coupled to the gas in
proto-planetary disks and are thus expected to follow the radial distribution
of gas in the disk. Given the detected distribution of gas, it is then natural
to wonder about the presence of aromatic carbonaceous nano-particles in the
inner regions of the disk.

Habart et al. (2006); Boutéraon et al. (2019) detected the 3-4 $\mu$m aromatic
features in the inner parts of the disk. These features are spatially
extended, with a FWHM of 0.3” or $\sim$30 AU. Both the spatial extension of
carbonaceous nano-grains in the HD 169142 disk and their presence in the
optically thin inner cavity have also been suggested by Maaskant et al. (2014)
and Seok & Li (2016). Furthermore, Seok & Li (2016) performed a comprehensive
modelling of the SED with a mixture of porous dust and astronomical-PAH and
found that three dust populations and relatively small PAH with an ionization
fraction of 0.6 can explain the entire SED. Backing up those observations,
Klarmann et al. (2017) compared the extended continuum flux measured at 1.3
$\mu$m with PIONIER (Lazareff et al. 2016) and the aromatic infrared bands to
UV luminosity ratio in multiple circumstellar objects and found an extended
hot emission in the cavity of the HD 169142 disk, which they linked to
stochastically heated carbonaceous particles. Finally, based on resolved Keck
NIRC2 data in the 3.4-4 $\mu$m region Birchall et al. (2019) suggested the
presence of a ring of emission at $\sim$ 0.06” (7 AU). They conclude that, in
contrast with the historical view of pre-transitional discs (e.g. Espaillat et
al. (2007)), the ‘gap’ region is radiatively dominated by emission from very
small grains and very small, likely carbonaceous, nano-particles.

In this paper, we use high angular-resolution data obtained with the NACO and
VISIR instruments to investigate the spatial distribution of the carriers of
the aromatic infrared bands at 3.3, 8.6, and 11.3 $\mu$m in the HD 169142
disk. We focus on the distribution of the carriers in the most evolved,
innermost regions of the disk (inner cavity and gap, below 60 AU). We model
the data using The Heterogeneous dust Evolution Model for Interstellar
Solids111https://www.ias.u-psud.fr/themis/ (THEMIS, Jones et al. (2017))
integrated in the radiative transfer code POLARIS (Reissl et al. 2016) to
constrain the spatial distribution of carbonaceous nano-particles and to
compare it with the distribution of micron- to millimeter-sized dust grains
derived in the literature. The data are presented in Sect. 2 and analysed in
Sect. 3. The radiative transfer modelling is described in Sect. 4. Section 5
compares it to the data and constrains the radial distribution of aromatic
carbon grains. We discuss and summarize our findings in Sect. 6.

Parameter | Value | Source
---|---|---
Mass ($\text{M}_{\astrosun}$) | 2; 1.65 | [1], [2]; [4], [5], [8]
Age (Myr) | 5.4; 3-12; 6; 12 | [1]; [4]; [5]; [8]
Distance (pc) | 145; 117; 151 | [1], [2], [4], [5], [6]; [7]; [8]
Radius $R_{*}$ ($\text{R}_{\astrosun}$) | 2.2; 1.6 | [1], [2]; [5],[8]
Temperature (K) | 8 100; 8 250; 8 400; 6 500; 7 800 | [1], [2]; [5]; [6]; [8]
Spectral type | Herbig Ae/Be : A5Ve; A7V; A7Vz | [1], [2], [5], [6]; [4]; [8]
Table 1: HD 169142 stellar properties. Values are taken from [1] Manoj et al.
(2006), [2] Monnier et al. (2017), [3] Quanz et al. (2013), [4] Biller et al.
(2014), [5] Seok & Li (2016), [6] Dunkin et al. (1997), [7] Ligi et al.
(2018), [8] Blondel & Djie (2006). The values chosen for the current study are
in bold font. Figure 1: Structure of the disk around HD 169142, taken from
Osorio et al. (2014); Monnier et al. (2017); Ligi et al. (2018).

##  2 Observations and data reduction

We analysed the distribution of the carriers of aromatic infrared bands in the
HD 169142, making use of VISIR imaging (Sect. 2.1) and spectroscopic
observations (Sect. 2.2), as well as NACO spectroscopic data (Sect. 2.3).

###  2.1 VISIR imaging data

HD 169142 was observed by the ESO mid-infrared instrument VISIR installed on
the VLT (Paranal, Chile) in the imaging mode in the PAH1 and PAH2 filters,
which probe the aromatic infrared bands at 8.6 and 11.3 $\mu$m. In addition,
the source was observed in the adjacent continuum (ArIII and SIV filters at 9
and 10.5 $\mu$m respectively). The observations were obtained in 2005 as part
of the VISIR GTO program on circumstellar disks, and partly from the VISIR
archive (ESO program 099.C-0794(A) on 07/21/2017). All observations were
obtained under fair conditions of seeing (less than 1” DIMM monitor) and
precipitable water content smaller than 5 mm (Tab. 2). Under good seeing
conditions, close to diffraction-limited imaging is obtained in the N band
(8-13 $\mu$m) with an angular resolution of about 0.3” around 10 $\mu$m. A
standard quadrangular (8” offsets) chopping-nodding technique was used to
remove the high thermal background. All observations except in the ArIII
filter used the burst mode, which allows for one image to be stored every
$\sim$ 15 ms. A dedicated pipeline was then used to perform lucky imaging (Law
et al. 2006) and image registration to minimize the effect of tip-tilt
smearing. Typical achieved Strehl ratios are of the order of 0.5. Standard
calibration stars were also observed in the same modes in order to perform the
photometric calibration and determine the instrument PSF (Table 2).

Data taken in PAH2, ArIII, and SIV filters have a pixel scale of 0.075”. They
are re-binned to the PAH1 pixel size of 0.046” which corresponds to the
upgraded VISIR instrument pixel scale after 2015. The emission maps probe the
disk from 0” to 3”. However, this study is limited to the range [0”, 2”] (see
Fig. 2) as the signal-to-noise ratio (S/N) drops at larger radii.

Filter | PAH1 | ArIII | PAH2 | SIV
---|---|---|---|---
Wavelength [ $\mu$m ] | 8.6 | 8.99 | 11.3 | 10.4
On source obs. time [min] | 10 | 10 | 20 | 20
Std star | HD167121 | HD151680 | HD151680 | HD151680
Table 2: Characteristics of the VISIR imaging observations.

Figure 2: Total emission map (band + continuum) in the 11.3 $\mu$m PAH2 and 8.6 $\mu$m PAH1 VISIR filter, compared to the PSF of the observation in the same filters in the inset (Left panel). The PAH1 and PAH2 emission in HD 169142 are spatially more extended than the filter PSF and show no Airy ring, which is also indicative of a spatially resolved emission. Azimuthally averaged emission profiles (centered on the brightest pixel) in the PAH1 and PAH2 VISIR filter, compared to the underlying continuum emission, shown as dashed lines (computed as described in Sect. 3.2), and the associated PSF profiles, shown as thin lines (Right panel). The error bars on the profiles, taking into account the absolute calibration error, are shown in grey. The location of micron- and millimeter-sized grain dust, taken from the literature (see Fig. 1), are indicated by the grey fill. Table 3: Full width at half maximum in arcseconds, measured with the use of gaussian fitting on the VISIR 2D maps in the PAH1 and PAH2 filters (1st column) and the PSF of the observations (second column). | Filter FWHM [arcsec] | PSF FWHM [arcsec]
---|---|---
PAH1 | 0.41 | 0.26
PAH2 | 0.47 | 0.30

###  2.2 VISIR spectroscopic data

The spectroscopic observations were performed on the night of 18-19June 2005
(ESO program 60.A-9234(A)). The observing conditions were fair at less than
0.8” optical seeing and relatively low humidity. The low-resolution
spectroscopic mode of VISIR was used ($R\simeq 220$). The 0.75” slit was
north-south aligned. The entire N band is split into four grating settings. In
this paper, we focus only on the ones centred on the aromatic features at 8.6
and 11.3 $\mu$m, with the other ones affected by rather strong telluric
transmission errors. The on-source observing time for each setting was about
ten minutes, which corresponds to a median sensitivity of about 50
mJy/arcsec2. Chopping and nodding were performed parallel to the slit for all
observations. The standard star used for photometric calibration and telluric
correction was HD 177716 (Cohen et al. 1999).

VISIR resolved spectra are measured from 0” to 1.5”, with a pixel size of
0.127”. However, only the data under 1” is used (see Fig. 3) because the S/N
drops below a value of two at higher radii.

Figure 3: HD 169142 integrated spectra measured by Spitzer (crosses), and
spectrum summed from all the VISIR resolved spectra (black line, see bottom
panels) are shown in the upper panel. The red curve is the sum of VISIR
spatially resolved spectra from 0.0” to 0.25”, corresponding to the inner 30
AU, and the blue curve is the sum from 0.38” to 1.02”, corresponding to the
outer disk. Correction for the flux outside of the slit is done by weighting
each spectrum by the surface of a ring of corresponding radius, and width,
0.127”. Panels 2-7 show the surface brightness is measured on spatially
resolved slit spectra at radii of 0”, 0.25”, …The spectra are not continuum
subtracted. They probe ring-like regions of a width 0.128” (1 pixel) and mean
radii of 0”, 0.25” …in the disk. The spectral region without data delimits the
telluric ozone absorption region. The over-plotted vertical lines show the
positions of the aromatic (blue) and crystalline forsterite (red) main
features. The typical $\pm$3$\sigma$ error derived from background noise (50
mJy.as-2) is shown in every panel. The grey full line shows the continuum
interpolation under each band by a 2-degree polynomial.

###  2.3 NACO data

Observations of the HD 169142 disk were performed between 3.2 and 3.76 $\mu$m
using a long slit with the adaptive optics system NACO at the VLT. The on-sky
projection of the slit is 28” long and 0.086” wide, which corresponds to the
diffraction limit in this wavelength range. The spectral resolution is
$R=\lambda/\Delta\lambda\sim 1\,000$. Nine slit positions were taken, one
centred on the star and the other slits shifted by half a slit width. Nine
slit positions allowed to extract a spectral cube on an area of
$2^{\prime\prime}\times 0.354^{\prime\prime}$ centred on the star. The dataset
ESO program ID is 075.C-0624(A). Observations properties and data reduction
are summarised in Boutéraon et al. (2019).

The aromatic and aliphatic emission features at 3.3 and 3.4 $\mu$m are
detected near the star, down to a distance of 0.1”, but with a low S/N at such
small separations (Boutéraon et al. 2019). We focus on regions were the
features are clearly detected, from 0.168” to 0.4” (20-47 AU) from the star.
This corresponds to the transition region between the inner ring and the gap
(Fig. 1). For each pixel, the continuum is interpolated by a first-degree
polynomial and substracted from the spectrum. To create the pure band emission
map and emission profiles at 3.3 $\mu$m shown in Fig. 4, the spectral region
associated to the telluric band between 3.309 and 3.322 $\mu$m is removed, and
the flux is spectrally integrated between 3.2 and 3.35 $\mu$m.

Figure 4:  Spatial distribution of the emission of HD 169142 observed with
NACO, integrated over the 3.3 $\mu$m feature (continuum-subtracted, see
details in Sect. 2.3), shown in the upper panel. The inner and outer edge of
the gap are shown in with dashed lines. The flux is not computed below 0.168”
and above 0.4”, due to low S/N. The associated azimuthally averaged emission
profile is shown in the lower panel. The black solid line is the radial
emission profile at 3.3 $\mu$m and the grey line is the associated PSF. The
grey fill indicates the location of micron- and millimeter-sized grain dust
that has been taken from the literature.

##  3 Analysis of the spatial distribution of the AIB and underlying continuum
emission

###  3.1 Spatial distribution of AIB carriers

Figure 3 shows the VISIR resolved spectra from 0” to 1.02” as well as the HD
169142 spectra integrated over the entire disk, measured by Spitzer, and
computed from the VISIR observations. All spectra include both aromatic band
emission and dust-continuum emission. The aromatic infrared bands at 8.6 and
11.3 $\mu$m are predominant in all VISIR resolved spectra and in the Spitzer
spectrum. This confirms that carbonaceous nano-particles dominate the infrared
emission in HD 169142, as pointed out by Seok & Li (2016). In particular, it
shows that the carbonaceous species dominate the infrared emission in the
inner regions from 0” to 1” ($\sim$100 AU). The detection of the features at
0”, corresponding to a region of a radius of $\sim$0.128” or 15 AU (1 pixel
size) centred onto the star, hints towards the presence of carbonaceous nano-
particles in the inner cavity. However, we cannot exclude that it is due to
the contribution of the inner radius of the ring, located at $\sim$0.17” (20
AU).

A secondary aromatic feature at 12 $\mu$m is also detected in the VISIR
resolved spectra and Spitzer integrated spectrum. It has already been reported
by Maaskant et al. (2013); Seok & Li (2016) in the ISO/SWS and Spitzer/IRS
integrated spectra. In the VISIR resolved spectra, this feature is strong in
the spectrum centered on the star until a distance of $\sim$0.25” (29 AU) from
the star, and decreases at higher radii.

Figure 2 (left) compares the total emission maps (continuum included) of HD
169142 in the VISIR PAH1 and PAH2 filters to the associated PSF. The full
widths at half maximum, computed by a 2D gaussian model fitting, are shown in
Table 3 for the PAH1 and PAH2 filters, along with the associated PSF. The
emission in the PAH1 and PAH2 filters is spatially more extended than the PSF.
Similar observations can be made based on the centro-symmetrically averaged
profiles (Fig. 2, right, neglecting the disk inclination of $\sim$ $None$).
This hints towards an intrinsically extended aromatic emission up to at least
2” (234 AU). The rather flat behaviour of the emission profiles towards the
star, and the absence of airy side-lobes in the emission maps and profiles
also suggest the need for an inner region (radii below 0.2”), producing
relatively low levels of emission in these two bands. A strongly peaked
emission towards the inner parts of the disk would indeed lead to noticeable
PSF modulations, as described in Sect. 5.1.

Figure 4 shows the spatial distribution of the emission of HD 169142 observed
with NACO, integrated over the 3.3 $\mu$m feature (continuum-subtracted). The
band emission is detected in the inner ring (0.17-0.27”, 20-32 AU) and the gap
(0.27-0.48”, 32-56 AU). Boutéraon et al. (2019) detected the emission feature
at 3.3 and 3.4 $\mu$m down to 0.1” with a low S/N. They suggest the presence
of a small amount of carbonaceous nano-grains in the inner regions.

###  3.2 Estimation of the underlying continuum emission

To gain more insight in the intrinsic distribution of the AIB carriers, we
aimed at disentangling the pure band emission at 8.6 and 11.3 $\mu$m and the
underlying continuum emission in the PAH1 and PAH2 filters maps. This requires
an accurate estimation of the continuum from the emission in the nearby ArIII
and SIV filters, centred at 9 and 10.4 $\mu$m. In Fig. 3, it can be noted that
the continuum emission below the aromatic features at 11.3 $\mu$m, and
especially at 8.6 $\mu$m, shows a spectral slope which vary with distance to
the star. Hence, the flux in the ArIII and SIV filters underestimate the
continuum emission under each aromatic band. We therefore apply a correcting
factor to the flux measured in the ArIII and SIV filters to account for the
spectral slopes observed and to derive an accurate continuum flux level at 8.6
and 11.3 $\mu$m. The corrected continuum profiles are shown in Fig. 2. We
derive the correcting factors as follows: (i) For each spatially resolved
spectrum shown in Fig. 3, at a radius of $r_{i}$ = {0”, 0.25”, 0.38”, 0.64”,
0.76”, 1.02”}, we fit the continuum emission by a second order polynomial, and
use it to accurately evaluate the continuum flux under each band,
$I^{s}_{cont,8.6}$ and $I^{s}_{cont,11.3}$; (ii) from the same spectra, at the
same radii, we measure the flux at the wavelength corresponding to the ArIII
and SIV filters, $I^{s}_{9}$, $I^{s}_{10.45}$; (iii) we compute the correcting
factors for radius, $r_{i},$ as
$f_{8.6}(r_{i})=\frac{I^{s}_{cont,8.6}}{I^{s}_{9}}$ and
$f_{11.3}(r_{i})=\frac{I^{s}_{cont,11.3}}{I^{s}_{10.45}}$; (iv) by
interpolating the sets {$f_{8.6}(r_{i})$}i and {$f_{11.3}(r_{i})$}i over the
range of [0”, 2”], we derive the correcting factors at all radii $f_{8.6}(r)$,
$f_{11.3}(r)$.

Those factors are then used to compute the underlying continuum maps in the
PAH1 and PAH2 filters shown in Fig. 2. These maps are estimated by multiplying
the ArIII and SIV filters flux by the correcting factors at each radius :
$I_{cont,PAH1}(r)=f_{8.6}(r)\,I_{ArIII}(r)$ and
$I_{cont,PAH2}(r)=f_{11.3}(r)\,I_{SIV}(r)$, where $I_{X}(r)$ is the flux in
the filter X at a radius r.

###  3.3 AIB emission versus the continuum

In this section, we make use of the derivation of the underlying continuum
emission in the PAH1 and PAH2 filters (described in Sect. 3.2) to compare the
spatial distributions of the infrared band emission and the continuum emission
at 8.6 and 11.3 $\mu$m. As can be seen in Fig. 2 (right) the total emission
(band+continuum) at 8.6 and 11.3 $\mu$m and the underlying continuum emission
have very similar spatial distributions. The discrepancy between the FWHM of
the observational PSF in the PAH1 and PAH2 filters and in the associated
continuum filters is smaller than 10%. Therefore, the comparison between the
profiles of the total emission in the PAH1 and PAH2 filters and the underlying
continuum can safely be interpreted in terms of the spatial distribution of
the emission of the disk. The similarity between the distribution of the total
flux and the underlying continuum suggests that the continuum emission at 8.6
and 11.3 $\mu$m is dominated by the aromatic infrared band carriers everywhere
in the disk. This is in agreement with the dominating aromatic infrared bands
in the spatially resolved spectra (Fig. 3).

Figure 5 shows the ratios between the total emission and the continuum
emission at 8.6 and 11.3 $\mu$m. At 11.3 $\mu$m, the variations of the ratios
are included in the error bars and are not significant. At 8.6 $\mu$m, the
ratio appears to drop at small radii and increases from 0.75” (0.88 AU), but
shows overall little change over 0”-1”. These globally flat behaviors of the
total emission/continuum ratios are different from what was observed by Habart
et al. (2021) in the HD 100546 disk. For HD 100546, the emission near the star
is dominated by micronic grains, resulting in an important increase of the
band-to-continuum ratios with distance to the star between 0” and 1”, and
constant ratios at larger distance. The low ratio values closer to the star
are mostly due to the increasing thermal emission of the micronic grains at
thermal equilibrium (contributing as continuum emission). On the contrary, the
flat band-to-continuum ratios in the HD 169142 disk indicate that carbonaceous
nano-grains strongly contribute to the infrared spectra at all radii.

Overall, our data provides evidence of the domination of carbonaceous nano-
grains in the infrared emission of the HD 169142 disk at all radii. This is to
be linked with the presence of an inner cavity in the disk below 0.17” (20
AU), resulting in a lack of hot micronic grains, which were observed to
dominate the continuum emission in, for instance, HD 100546 Habart et al.
(2021).

Figure 5: VISIR bands to continuum ratios at 8.6 $\mu$m and 11.3 $\mu$m. The
8.6 and 11.3 $\mu$m band fluxes are azimuthally averaged from the 2D images in
the PAH1 and PAH2 VISIR filter (see profiles in Fig. 2), and include the
continuum and the pure band emission. The derivation of the pure continuum
emission is described in Sect. 3.2. The grey fill indicates the ring and outer
disk regions with a continuous distribution of micron- and millimeter-sized
grain dust deduced from previous observations (see Fig. 1).

###  3.4 AIB carriers properties

Maaskant et al. (2014) interpreted the HD 169142 spectrum in the mid-infrared
(5-13 $\mu$m) using an interstellar-PAH model to account for the aromatic
infrared bands and showed that the spectrum is intermediate between fully
neutral, for which the 11.3 $\mu$m feature dominates over the 6.2, 8, and 8.6
$\mu$m features as well as the fully ionized interstellar PAH, showing
predominant 6.2, 8, and 8.6 $\mu$m features over the 11.3 $\mu$m band (Peeters
et al. 2002). Following their interpretation, we note that the VISIR spectra
show intermediate features between fully ionized and fully neutral at all
radii (Fig. 3). Nevertheless, as the radius increases, the slope at 8.6 $\mu$m
flattens, which might suggest a higher neutral fraction in the outer regions
of the disk. To highlight this effect, we spatially integrate the spectra
within 0.3” (35 AU) and outside of 0.3” separately (see Fig. 3, upper panel).
The spectrum of the inner regions shows a stronger slope at 8.6 $\mu$m than
that of the outer regions, hinting towards a higher ionization fraction in the
inner parts of the disk.

According to Maaskant et al. (2014), the spectrum corresponding to a fully
optically thin cavity should show completely ionised features. Nonetheless, it
is not the case for the spectrum at 0” (Fig. 3), which probes the inner cavity
up to 0.128” (15 AU). The observed neutral carriers emission could originate
from the optically thick inner rim of the ring, and be mixed with the emission
within 0.128” (15 AU) due to the PSF of the observation. However, it should be
noted that the evolution of the spectrum may reflect other effects linked to
the irradiation condition (spectral shape and intensity of the UV field) or
variations in the properties of the aromatic band carriers, such as their size
or their structure (see Sect. 5.2).

##  4 Radiative transfer modelling

In the following, we use the radiative transfer code POLARIS (Reissl et al.
2016), coupled to the grain model THEMIS (Jones et al. 2017) to derive the
emission of the disk from a given distribution of small dust grains in HD
169142. Our objectives are to draw better constraints on the distribution of
carbonaceous nano-particles in the disk, and to confirm the first preliminary
trends provided by the a priori analysis in Sect. 2. We mainly focus on the
comparison between the radial distribution of carbonaceous nano-grains and
that of bigger grains derived from the literature. In particular, we try to
constrain the presence of carbonaceous nano-particles in the inner cavity and
towards the outer disk.

###  4.1 THEMIS dust grain model

The grain optical properties are modelled using THEMIS, which is an
evolutionary core-mantle dust model designed to allow variations in the dust
structure, composition, and size according to the local density and radiation
field (Jones et al. 2013, 2017). The a-C(:H) nano-particles, are modelled as
hydrogenated aromatic-rich carbonaceous nano-particles with mixed aromatic,
aliphatic, and olefinic domains. It is applied, in particular, to the
modelling of dust in the diffuse and dense ISM (Ysard et al. 2015, 2016;
Saajasto et al. 2021), near-infrared to sub-millimeter observations of nearby
galaxies (Chastenet et al. 2017; Viaene et al. 2019), the near-infrared
observations of protoplanetary disks (Boutéraon et al. 2019; Habart et al.
2021), and in photon-dominated regions (Schirmer et al. 2020, 2021).

For the study of the HD 169142 disk, we assume the dust composition and size
distribution used by Habart et al. (2021) in their modelling of the HD 100546
disk. It corresponds to the THEMIS diffuse-ISM dust model developed by Jones
et al. (2013); Köhler et al. (2014). The dust is modelled as a-C nano-
particles populations with different size distributions (a-C1, a-C2, VSG),
amorphous carbon dust grains of radius $\sim$ 20 nm (amC), and silicates,
modelled as a balanced mix of amorphous pyroxene-type and olivine-type
silicate grains (Sil1, Sil2) (see Habart et al. (2021) for more details). The
properties of each dust population are given in Table 4. The Habart et al.
(2021) model corresponds to a weighted mix of the a-C1, a-C2, VSG, and Sil1.
It is used in the outer regions of the HD 169142 disk.

The Sil2 dust component is used to model the emission of the HD 169142 inner
disk. Similarly to Chen et al. (2018), we use large grains in the inner
structure, with sizes from $10^{-2}$ to $10^{3}$ $\mu$m, and a power-law
distribution with exponent -3.5 (see Table 4). The higher amount of large
grains has already been suggested in inner disk regions, for instance, in the
HD 100546 disk by Tatulli et al. (2011), who used 5 $\mu$m-sized dust grains,
as well as Miley et al. (2019), who suggested that grain populations could
reach millimeter to centimeter sizes in the inner hot regions of the disk. It
is thought to be due to the sublimation of smaller grains in such intense
radiation field and temperature conditions (Tatulli et al. 2011). This
assumption is physically supported by the fact that the smallest grains are
also the hottest ones and are thus more prone to destruction by sublimation.

Table 4: Dust grain populations. The optical properties of the dust populations are computed using the CM20, aPyM5 and aOlM5 components provided by POLARIS as part of the THEMIS model (Jones et al. 2013, 2017). Name | Composition | Density [kg.m-3] |  $a_{min}-a_{max}$ [$\mu$m] | Distribution law | (Power-law) exponent/
---|---|---|---|---|---
|  |  |  |  | (Log-normal) mean [$\mu$m]
a-C1 | CM20 | 1600 | 4 10-4 \- 7 10-4 | power-law | -3.5
a-C2 | CM20 | 1600 | 7 10-4 \- 1.5 10-3 | power-law | -3.5
VSG | CM20 | 1600 | 1.5 10-2 \- 2 10-2 | power-law | -3.5
amC | CM20 | 1570 | 5 10-4 \- 4.9 | log-normal | 7 10-3
Sil1 |  $\frac{1}{2}$ aPyM5 + $\frac{1}{2}$ aOlM5 | 2190 | 1 10-3 \- 4.9 10 | log-normal | 8 10-3
Sil2 |  $\frac{1}{2}$ aPyM5 + $\frac{1}{2}$ aOlM5 | 2190 | 1 10-2 \- 1 103 | power-law | -3.5
Table 5: Total mass in $M_{\astrosun}$ of each dust population depending on the region in the disk. | Inner disk | Inner | Ring+Gap
---|---|---|---
|  | cavity | +Outer disk
Limits [AU] | 0.2-0.5 |  $R_{cav}^{a-C}$-20 | 20-200
a-C1 | 0 | 0.59 $M_{cav}^{a-C}$ | 2.3 10-6
a-C2 | 0 | 0.41 $M_{cav}^{a-C}$ | 1.61 10-6
VSG | 0 | 0 | 1.38 10-6
amC | 0 | 0 | 1.84 10-6
Sil1 | 0 | 0 | 1.59 10-5
Sil2 | 5.13 10-13 | 0 | 0

###  4.2 POLARIS radiative transfer code

POLARIS is a three-dimensional radiative transfer code (Reissl et al. 2016)
which solves the radiative transfer problem self-consistently using the Monte
Carlo method. POLARIS has been developed to simulate polarised emission and
Zeeman splitting due to magnetic fields in dusty media. We used the recent
updates of the code, which allow for the modelling of the emission of
protoplanetary disks by considering complex structures and varying dust
populations in space, and take into account the stochastic heating of
nanometer-sized grains, including single as well as multi-photon absorption.
In particular, feeding POLARIS with optical properties of small carbon grains
from THEMIS allows us to build a detailed model of the infrared emission in
the HD 169142 disk.

The stellar parameters, R = 1.6 R☉ and T = 7 800 K, are taken from previous
works (Table 1). We use an axis-symmetrical, cylindrical grid. The gas density
distribution is computed assuming hydrostatic equilibrium in the disk (Hayashi
1981):

$n(r,z)=n_{0}\left(\frac{r_{0}}{r}\right)^{\alpha}exp\left(-\frac{1}{2}\left(\frac{z}{h(r)}\right)^{2}\right)\text{,
}h(r)=h_{0}\left(\frac{r}{r_{0}}\right)^{\beta}\text{, }$ (1)

where $\alpha$ = - 2.09, yielding decrease in the density with radius slightly
steeper than squared, and $\beta$ = 1.1, corresponding to a flared disk, are
taken from Monnier et al. (2017). We make the commonly used assumption of an
approximate $\frac{1}{10}$ ratio for the disk scale height, we set $r_{0}$= 1
AU, $h_{0}$ = 0.07 AU in the inner disk and we set $r_{0}$ = 100 AU, $h_{0}$ =
15 AU in the outer regions. The dust model does not include grains bigger than
5 $\mu$m, as large grains do not contribute substantially to the thermal
emission below 13 $\mu$m. The small inclination of the disk is neglected, and
the system is modelled face-on, as observed by Panić et al. (2008), for
instance.

Models featuring an empty gap (0.27-0.48”, 32-56 AU) or no gap (full disk from
0.17”, 20 AU) resulted in similar profiles after convolving them with the
VISIR PSF, showing that the VISIR data does not have a high enough angular
resolution to study the gap properties (see PSF in Table 3). Because of the
very narrow gap region probed by the NACO data, neither did it allow to
distinguish between both cases. For simplicity the gap from 30 to 55 AU is
therefore not taken into account in our simulations and the outer region from
20 to 250 AU is modelled as a full disk. Both Osorio et al. (2014) and Monnier
et al. (2017) place the inner disk between 0.2 AU and 0.5 AU, and we follow
this choice. The mass of the inner disk is chosen small enough to create an
optically thin structure which does not contribute significantly to the disk
emission (see Table 5), in agreement with the absence of silicate bump in the
HD 169142 spectrum.

The spatial distribution of each type of dust is given in Table 5. We modeled
the dust in the outer regions of the disk from 0.17” (20 AU), according to the
dust model used by Habart et al. (2021). It only features dust grains smaller
than 5 $\mu$m as a mix of a-C1, a-C2, VSG, and Sil1 dust populations (Table 5,
third column). The inner disk, below 0.5 AU is modelled as pure silicate dust,
with grain sizes up to 1 mm (Table 5, first column). The properties of the
dust populations are detailed and discussed in Sect. 4.1. Finally, the model
allows the addition of carbonaceous nano-particles below 0.17” (20 AU)
starting from an inner radius $R_{cav}^{a-C}$ and following the gas density
distribution given in Equation 1 with values for $\alpha$, $\beta$, $r_{0}$,
and $h_{0}$ identical to the outer disk. This new component is composed only
of carbonaceous nano-particles (a-C1, a-C2, Table 5, second column) with a
density depleted by a factor $f$ compared to the outer disk, resulting in a
total carbon nano-particles mass $M_{cav}^{a-C}$ between $R_{cav}^{a-C}$ and
20 AU. The numerical values used for the model parameters ($h_{0}$,
$R_{cav}^{a-C}$, $M_{cav}^{a-C}$) are given in Table 6 and will be discussed
in Sect. 5.1.

Table 6: Properties of the POLARIS models for the HD 169142 disk. $h_{0}$ is the disk height à 100 AU, $R_{cav}^{a-C}$ is the inner radius of the aromatic particles in the cavity, $M_{cav}^{a-C}$ is the total mass of aromatic particles below 0.17” (20 AU). Model | $h_{0}$ | $R_{cav}^{a-C}$ | $M_{cav}^{a-C}$
---|---|---|---
| [AU] | [AU] | [$M_{\astrosun}$]
M0 | 15 | 20 | 0
M1 | 5 | 20 | 0
M2 | 5 | 5 | 3.56 10-4
|  |  | (f=1)
M3 | 5 | 5 | 1.19 10-7
|  |  | (f=3000)

###  4.3 Predicted intensity profiles

POLARIS outputs are obtained as data cubes: 2D intensity maps computed at
regularly spaced wavelengths (150 values between 7 and 13 $\mu$m). To account
for the spectral width of VISIR PAH1 and PAH2 filters in our simulations, the
maps are spectrally averaged over the filter widths. The resulting images are
then convolved with the observed PSF (given in Fig. 2) and azimuthally
averaged to compute the profiles shown in Fig. 6. The continuum maps and
profiles are computed first by a two-degree polynomial interpolation of the
continuum around 8.6 and 11.3 $\mu$m on the initial POLARIS cube, resulting in
a continuum cube, from which the continuum profiles are then similarly
derived.

Similar work has been done to reproduce the NACO maps and profiles to account
for the spectral width of the aromatic band at 3.3 $\mu$m. The simulated
spectral cube (100 wavelengths between 3 and 4 $\mu$m) is first spectrally
integrated between 3.2 and 3.35 $\mu$m, ignoring the region between 3.309 and
3.322 $\mu$m, which corresponds to a telluric band. Ignoring the telluric band
results in a underestimation of the modelled integrated band flux by less than
0.5%. We then extract a 1D flux profile and convolve it with the PSF (1D, see
Fig. 4) of the observation, integrated in the same way around 3.3 $\mu$m. The
resulting profiles are compared with NACO data in Fig. 7.

##  5 Comparison between model and data

###  5.1 Constraining the nano-grain distribution in the disk

We first compared the data with the standard disk model described in Sect.
4.2, having no carbonaceous nano-particles below 0.17” (20 AU), as shown in
model M0 in Table 6 and Fig. 6. Figure 6 (top) compares the resulting profiles
with the VISIR imaging data in the 11.3 $\mu$m PAH2 filter. We focus mainly on
the model-data comparison in this filter, because it is less affected by the
state of charge of the carriers. The VISIR flux is overestimated at 11.3
$\mu$m in the entire disk by a factor of 1.8 to 2.2, both for the continuum
and the total emission, resulting in an overestimation of the band flux by a
factor of 1.9 over the full disk (Table 7).

Figure 6: VISIR radial profiles (black full line), compared to simulated
results (dotted, dashed, dash-dash-dotted, and dash-dot-dotted lines) for the
PAH2 filter and associated continuum on the top panels, and the PAH1 filter
and continuum on the bottom panels. For a description of the different models,
we refer to Table 6. The grey fill indicates the location of micron- and
millimeter-sized grain dust.

This overestimation at all radii can be linked to the presence of a spatially
unresolved component showing very strong emission from all dust populations in
the inner regions in our model. Such a component would indeed contribute as an
additional, almost unresolved flux at every radius in the disk. We lower the
value of the disk height in the whole disk by decreasing $h_{0}$ from 15 to 5
AU at $r_{0}$ = 100 AU. This allows to reduce the amount of hot dust close to
the star and recover the VISIR total flux level in the PAH2 filter also as the
associated continuum (model M1 in Table 6 and Fig. 6) and the integrated
continuum-subtracted emission in the band (Table 7). The slope of the modelled
profile agrees with the VISIR data in the PAH2 band for radii higher than 0.2”
(Fig. 6) and the absolute flux at 11.3 $\mu$m is well reproduced. However, the
modelled flux in the 11.3 $\mu$m feature drops by 20% (1.8 Jy.$as^{-2}$) below
the VISIR error bars at radii smaller than 0.2” (23 AU).

Adding a very small amount of carbonaceous nano-particles in the inner cavity
leads our model to match the entire observed profile within the error bars
(model M3 in Table 6 and Fig. 6). However, a degeneracy is observed between
the inner radius, $R_{cav}^{a-C}$, and the depletion factor, $f,$ of the
carbonaceous nano-grains in the cavity. This is because models using
($R_{cav}^{a-C}=0.128\text{" or }15\leavevmode\nobreak\ \text{AU};f=100$),
($R_{cav}^{a-C}=0.09\text{" or }10\leavevmode\nobreak\ \text{AU};f=1000$) and
($R_{cav}^{a-C}=0.04\text{" or }5\leavevmode\nobreak\ \text{AU};f=3000$)
account similarly well for the VISIR profiles at 11.3 $\mu$m, the ISO, and the
Spitzer spectra. A model having non-depleted carbonaceous nano-grains in the
cavity from 0.04 to 0.17” (5 AU to 20 AU) strongly overestimates the flux of
the aromatic infrared bands (model M2 in Table 7). The associated profile at
11.3 $\mu$m overestimates the band flux near the star, and shows Airy side-
lobes (Fig. 6). The much better agreement achieved between model M3 and the
data thus supports the need for depletion of carbonaceous nano-particles in
the cavity.

In summary, the comparison between our models and the VISIR data at 11.3
$\mu$m hints towards depleted carbonaceous nano-grains in the cavity below
0.17” (20 AU). It could be due to photo-destruction of the grains in the
strongly irradiated inner regions. The photo-destruction and depletion of
small dust grains has been observed, for instance, in the interstellar photon
dominated regions by Schirmer et al. (2020). However, this study faces strong
degeneracy due to the limited angular resolution of the data. A higher
angular-resolution is required to better quantify the level of depletion as
well as the spatial distribution of the band carriers in the cavity.

###  5.2 Carbonaceous nano-particles properties

####  5.2.1 Analysis of the 8.6 $\mu$m band

None of the models have satisfactorily reproduced the VISIR 8.6 $\mu$m band
profile (Fig. 6). Both the M1 and M3 models, which optimally reproduce the
data at 11.3 $\mu$m, underestimate the flux at 8.6 $\mu$m by a factor 2 in the
entire disk, as well as in the integrated spectra (Fig. 8).

This could be explained considering the charge state of the band carriers.
Using an interstellar-PAH description of the aromatic infrared band carriers,
the 8.6 $\mu$m feature is expected to be stronger for ionised PAH. The
underestimation of the emission at 8.6 $\mu$m would then suggest the need for
a higher ionisation fraction in the HD 169142 disk than what is considered in
our model. Indeed, THEMIS includes no charge dependence of the aromatic
particles, while Seok & Li (2016) derived an ionization fraction of 0.6 for
the PAH in HD 169142 from SED fitting.

In addition, all simulated VISIR profiles at 8.6 $\mu$m are too flat near the
star and show a strong slope between 0.2” and 0.5” (20-60 AU). In order to
better fit the data, the predicted emission of the 8.6 $\mu$m feature should
be stronger below 0.17” (20 AU) and quickly decrease when entering the disk.
It is in agreement with the evolution of the 8.6 $\mu$m slope observed in the
VISIR resolved spectra (see Fig. 3 and Sect. 3.4). In the interstellar-PAH
framework, as the 8.6 $\mu$m to 11.3 $\mu$m ratio is higher for ionised PAH,
it thus suggests the need for a greater amount of ionised emission near the
star in our disk models. As the POLARIS/THEMIS models assume no variations of
the ionisation fraction, the comparison to the data would then hint towards an
increasing ionisation fraction towards the irradiated inner regions. Maaskant
et al. (2014) associated the emission from ionized PAH to optically thin inner
disk regions where the UV field is high and the electron density is low;
whereas optically thick outer disk regions would be dominated by neutral PAH
emission with little variation with radius. This is in agreement with the
trend found in our observations.

However, the interpretation of the spectral signatures at 7.7, 8.6, and 11.3
$\mu$m is not unequivocal, and could be as well explained, for instance, by
varying size distribution of carbonaceous nano-grains. The underestimation of
the flux at 8.6 $\mu$m, and the need for a steeper radial slope near the star
would, within this framework, suggest the need for a higher abundance of
bigger carbonaceous dust grains in the inner regions. This is consistent with
stronger photo-destruction of smaller grains in optically thin, strongly
irradiated media and is supported by the work of Schirmer et al. (2020, 2021)
on dust evolution in photon dominated regions.

####  5.2.2 Analysis of the 3.3 $\mu$m band profile

The standard model M0 as well as models M1 and M3 are consistent with the NACO
absolute flux in the 3.3 $\mu$m band (Table 7). Yet, none of the simulated
flux distributions agree with the NACO radial profile shown in Fig. 7. The 3.3
$\mu$m is produced by very small carbon grains, with radii smaller than 0.7
nm. A stronger depletion of this population of grains in the innermost regions
could explain the discrepancy between the data and the model. Such a depletion
could originate from photo-destruction of the smaller grains in the irradiated
regions, as was observed in the interstellar photon dominated regions by
Schirmer et al. (2020).

Figure 7: NACO emission profiles (black line) and PSF (grey line) compared to POLARIS simulated results (dotted, dashed, dash-dash-dotted and dash-dot-dotted lines). For a description of the different models, see Table 6. The grey fill indicates the location of micron- and millimeter-sized grain dust. Table 7: Continuum-subtracted band fluxes in $10^{-14}\,W.m^{-2}$, integrated over the disk in the three aromatic bands, computed for the different the POLARIS models. The modelled values are compared to the fluxes computed on ISO data (Acke & van den Ancker 2004) and Spitzer data (Acke et al. 2010). Band | 3.3 $\mu$m | 8.6 $\mu$m | 11.3 $\mu$m
---|---|---|---
Data
Spitzer |  | 0.89 $\pm$ 0.01 | 2.08 $\pm$ 0.01
ISO | 1 $\pm$ 0.2 | 2.55 $\pm$ 0.5 | 2.3 $\pm$ 0.5
Model
M0 : $R_{cav}^{a-C}$=20, $h_{0}$=15 | 0.55 | 1.3 | 2.2
M1 : $R_{cav}^{a-C}$=20, $h_{0}$=5 | 0.26 | 0.64 | 1.1
M2 : $R_{cav}^{a-C}$=5, $h_{0}$=5, f=1 | 1.7 | 3.5 | 7.8
M3 : $R_{cav}^{a-C}$=5, $h_{0}$=5, f=3000 | 0.87 | 0.92 | 1.5
Figure 8: ISO and Spitzer spectra, compared to the simulated results. For a
description of the different models, we refer to Table 6.

##  6 Conclusion

We investigated the carbonaceous nano-grains emission in the HD 169142 disk by
comparing high angular observations with model predictions. We analysed the
imaging and spectroscopic data (VLT/VISIR, 8-12 $\mu$m, angular resolution
0.3”) as well as the adaptive optics spectroscopic data (VLT/NAOS-CONICA, 3-4
$\mu$m, angular resolution 0.1”). Our main results derived from both
observations and model predictions are summarised below.

  1. 1.

Probing the emission in the HD 169142 disk in the 3.3, 8.6, and 11.3 $\mu$m
aromatic infrared bands, we were able to provide new strong evidence of the
extended nature of the distribution of carbonaceous nano-particles populations
and their domination in the infrared emission of the disk at all radii, in
agreement with previous studies, for instance Seok & Li (2016).

  2. 2.

The flattening VISIR spatial emission profiles near the star, the absence of
Airy side-lobes in the VISIR imaging data and the faint aromatic feature
detection by NACO below 20 AU points towards a fairly large depletion of PAH
inside the 20 AU cavity.

  3. 3.

To gain more insight in the spatial distribution of carbonaceous nano-
particles in the disk, we modelled the distribution of small dust grains using
the POLARIS radiative transfer code coupled to the THEMIS model for the
emission of carbonaceous nano-grains. The VISIR radial profile at 11.3 $\mu$m
is reproduced within the error bars, assuming a continuous radial distribution
of micronic grains and carbonaceous nano-grains from 20 to 250 AU, as well as
carbonaceous nano-grains decreased in abundance in the inner cavity between
0.5 and 20 AU. The precise amount of carbon nano-grains needed in the cavity
and their inner radius are strongly degenerate and could not be derived from
our modelling. Nonetheless, the comparison between simulations and the
emission profile at 11.3 $\mu$m shows the need for strongly depleted
carbonaceous nano-grains below 20 AU. This result supports previous studies
from Maaskant et al. (2013) and Seok & Li (2016), which hinted at the presence
of interstellar PAH in the cavity and offers evidence of their depletion.

  4. 4.

The VISIR spectra clearly shows a spectral evolution from the inner regions
towards the outer regions. In the interpretation framework of interstellar
PAH, this evolution can be explained by a transition between dominating
ionized PAH in the optically thin internal regions to neutral PAH in the
optically thick outer disk media. The discrepancy between our models and the
VISIR profiles at 8.6 $\mu$m seems to support this interpretation. It first
suggests that the ionization which has be considered in the model is too small
(full neutrality was assumed). As the emission at 8.6 $\mu$m shows more radial
variations in the data than in the model, it also suggests the need for
ionization variations throughout the disk. However, the interpretation of the
spectral signatures at 8.6 and 11.3 $\mu$m as indicators of the ionization
fraction of the PAH is not unequivocal. The evolution of the spectrum may
reflect other effects linked to the irradiation condition (spectral shape and
intensity of the UV field) or the size or structure of the band carriers. The
evolution of the HD 169142 spectrum towards the center could also be
consistent with a higher abundance of larger grains in the inner cavity.

  5. 5.

Finally, the NACO radial slope is strongly overestimated. This could be linked
to a depletion in very small carbonaceous nano-particles towards the most
irradiated regions, caused by a stronger photo-dissociation of small particles
(Schirmer et al. 2020).

Our understanding of the evolution of carbonaceous nano-grains in disks is
expected to make significant progress thanks to upcoming spatially resolved
observations with the VLTI/MATISSE interferometer, the JWST integral-
spectrograph, and the ELT/METIS high-resolution spectrograph and high-contrast
imager. Interferometric measurements using MATISSE would provide valuable and
precise information on the distribution of carbon nano-grains in the innermost
regions, namely, the inner cavity and the inner disk (1 $<$ r $<$ 15 AU). On
the other hand, observations with the JWST covering a complete spectral domain
between 0.6 and 28 $\mu$m will mainly probe the dust content with a spectral
resolution of $\sim$3000-4000, a spatial resolution of 10-100 AU, and for
distances up to 500 AU. Spatially resolved spectroscopy of the aromatic and
aliphatics sub-features will be obtained and allow for a better identification
of the nature and properties of the bands carriers. Finally, ELT-METIS will
achieve a combination of high spatial resolution with a large field-of-view
and a spectral resolution allowing the detection of aromatic infrared bands,
thus providing an great opportunity to probe the dust content in the gap
region (0.27”-0.48” or 32-56 AU). Furthermore, combining dust models with new
high-resolution data could allow a more detailed analysis of the local
properties of the particles (charge, size, excitation). This would help to
break some of the degeneracies encountered in this work, differentiate between
the various proposed disk compositions, and study more precisely the
distribution of aromatic dust populations in the gaps.

###### Acknowledgements.

We thank the anonymous referee for enlightening comments. This work was based
on observations collected at the European Southern Observatory, Chile (ESO
proposal number: 075.C-0624(A)), and was supported by P2IO LabEx
(ANR-10-LABX-0038) in the framework of the “Investissements d’Avenir”
(ANR-11-IDEX-0003-01) managed by the Agence Nationale de la Recherche (ANR,
France), P2IO LabEx (A-JWST-01-02-01+LABEXP2IOPDO), and Programme National
“Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with INC/INP
co-funded by CEA and CNES.

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