11institutetext: Faculty of Aerospace Engineering, Delft University of
Technology, Delft, The Netherlands
11email<EMAIL_ADDRESS>22institutetext: Kapteyn Astronomical Institute,
University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
33institutetext: University of Leiden, P.O. Box 9513, 2300 RA, Leiden, The
Netherlands 44institutetext: Universitäts-Sternwarte, Fakultät für Physik,
Ludwig-Maximilians-Universität München,
Scheinerstr. 1, 81679 München, Germany 55institutetext: Max-Planck-Institut
für extraterrestrische Physik, Gießenbachstraße 1, 85748 Garching, Germany
66institutetext: Institut für Astrophysik, Universität Wien,
Türkenschanzstraße 17, 1180 Wien, Austria

# Observing Circumplanetary Disks with METIS

N. Oberg 1122 I. Kamp 22 S. Cazaux 1133 Ch. Rab 4455 O. Czoske 66

(Received — accepted —)

###### Abstract

Context. A full understanding of the planet and moon formation process
requires observations that probe the circumplanetary environment of accreting
giant planets. The mid-infrared ELT imager and spectrograph (METIS) will
provide a unique capability to detect warm-gas emission lines from
circumplanetary disks.

Aims. We aim to demonstrate the capability of the METIS instrument on the
Extremely Large Telescope (ELT) to detect circumplanetary disks (CPDs) with
fundamental v=1-0 transitions of 12CO from 4.5-5 µm.

Methods. We consider the case of the well-studied HD 100546 pre-transitional
disk to inform our disk modeling approach. We use the radiation-thermochemical
disk modeling code ProDiMo to produce synthetic spectral channel maps. The
observational simulator SimMETIS is employed to produce realistic data
products with the integral field spectroscopic (IFU) mode.

Results. The detectability of the CPD depends strongly on the level of
external irradiation and the physical extent of the disk, favoring massive
($\sim 10$ MJ) planets and spatially extended disks with radii approaching the
planetary Hill radius. The majority of 12CO line emission originates from the
outer disk surface, and thus the CO line profiles are centrally peaked. The
planetary luminosity does not contribute significantly to exciting disk gas
line emission. If CPDs are dust-depleted, the 12CO line emission is enhanced
as external radiation can penetrate deeper into the line emitting region.

Conclusions. UV-bright star systems with pre-transitional disks are ideal
candidates to search for CO-emitting CPDs with ELT/METIS. METIS will be able
to detect a variety of circumplanetary disks via their fundamental 12CO ro-
vibrational line emission in only 60 s of total detector integration time.

###### Key Words.:

Planets and satellites: formation – Planets and satellites: individual: HD
100546 c – Infrared: planetary systems – methods: numerical – accretion,
accretion disks – protoplanetary disks

##  1 Introduction

Observations of circumstellar dust have revealed a zoo of intriguing
substructures in planet-forming disks (Andrews, 2020), including arms (e.g.
Pérez et al. (2016); Muto et al. (2012); Huang et al. (2018)), arcs (e.g.
Casassus et al. (2013); van der Marel et al. (2013); Isella et al. (2013)),
rings, gaps, and cavities (e.g. Calvet et al. (2002); Piétu et al. (2006);
Quanz et al. (2013b); ALMA Partnership et al. (2015); Andrews et al. (2018);
Long et al. (2018)). Several of these features are interpreted to be the
result of planet-disk interactions (Kley & Nelson, 2012; van der Marel et al.,
2016; Zhang et al., 2018; Andrews, 2020). Disks with large inner cavities or
gaps are known as (pre-)transition disks (Espaillat et al., 2014), and are
promising targets to search for giant planets embedded within (Strom et al.,
1989; Dodson-Robinson & Salyk, 2011; Zhu et al., 2011). Massive planets in
gaps are expected to continually accrete gas and dust from the surrounding
circumstellar disk (Kley, 1999; Lubow & D’Angelo, 2006; Morbidelli et al.,
2014; Teague et al., 2019) into a moon-forming circumplanetary disk (CPD)
(Canup & Ward, 2002; Mosqueira & Estrada, 2003; Szulágyi et al., 2016).

As of July 2022, direct detection of extrasolar circumplanetary dust
associated with an accreting planet has only been confirmed in the PDS 70
system. The PDS 70 circumstellar disk features a gap with a radial width of 70
au (Hashimoto et al., 2012) containing two planets. The first planet PDS 70 b
was detected in the NIR (Keppler et al., 2018; Müller et al., 2018) and in
H-$\alpha$ (Wagner et al., 2018; Haffert et al., 2019). A second planet PDS 70
c was discovered also in H-$\alpha$ (Haffert et al., 2019). Unresolved sub-mm
dust thermal emission is co-located with this planet, interpreted as
originating from a dusty CPD (Isella et al., 2019; Benisty et al., 2021).
Self-consistent radiative transfer modeling of the system suggests the CPD is
optically thick with an upper limit on the dust mass of 0.7 M⊕ (Portilla-
Revelo et al., 2022), but it is noted that high spatial and spectral
resolution observations of the gas component are needed to break degeneracies
between the planet and disk properties.

No other (pre-)transitional disk gap has been found to contain circumplanetary
dust. Francis & van der Marel (2020) suggest that PDS 70 is anomalous in that
the gap may only recently have been opened, with correspondingly high rates of
accretion onto the planets within the gap. Alternatively, episodic accretion
may limit the visibility of planets to brief periods, with the relatively
inviscid CPD acting as an accretion “bottleneck” (Lubow & Martin, 2012;
Brittain et al., 2020). The rapid depletion of dust due to fast inwards
aerodynamic drift in CPDs may also hinder attempts to detect them in continuum
emission (Zhu et al., 2018; Rab et al., 2019).

An additional candidate CPD has been detected in the AS 209 disk by 13CO
$J$=2-1 gas line emission (Bae et al., 2022). The CPD candidate candidate is
embedded within an annular gap seen in the 12CO emission at a radial distance
of 200 au. The gap region is still optically thick in 12CO and hence there is
no corresponding detection in 12CO. However, a perturbation in the velocity
field of the 12CO gas and evidence of localized heating further supports the
interpretation of a planet+CPD. Assuming a standard 13CO abundance, the gas
mass of the CPD is estimated to be 30 M⊕. Given the nondetection of associated
continuum emission the dust mass of the CPD must be $<0.027$ M⊕, suggesting a
dust-to-gas ratio $<9\times 10^{-4}$, in line with prediction of rapid dust
depletion of wide-separation CPDs (Zhu et al., 2018; Rab et al., 2019). Gas
line observations thus provide a way to detect CPDs even if they are strongly
dust depleted.

###  1.1 HD 100546

One of the best studied pre-transitional disks surrounds the Herbig star HD
100546 (van den Ancker et al., 1997; Vioque et al., 2018). The system lies at
a distance 108.1 $\pm$ 0.5 pc, right ascension 11h 33m 25.3s, declination -70∘
11’ 41.2′′ (Gaia Collaboration et al., 2021). The age is estimated to be 7.02
$\pm$ 1.49 Myr (Fairlamb et al., 2015) or 5.5${}^{+1.4}_{-0.8}$ Myr (Vioque et
al., 2018). The system is comprised of a clearly divided inner and outer disk,
with a gap depleted in gas and dust radially spanning $\sim$1-20 au (Bouwman
et al., 2003; Grady et al., 2005; Brittain et al., 2009; Avenhaus et al.,
2014; Fedele et al., 2015; Jamialahmadi et al., 2018; Pineda et al., 2019).

The HD 100546 system hosts several potential planet candidates, either claimed
via direct detection or indirectly via their influence on the circumstellar
disk structure and dynamics. The first candidate companion ”b” was identified
by direct imaging at 3.8 µm at a separation 0.48$\arcsec\pm$0.04 (projected
separation $\sim$70 au) (Quanz et al., 2013a; Currie et al., 2014; Quanz et
al., 2015). However the existence of this object has been called into question
as potentially being an artifact of data reduction (Rameau et al., 2017; Cugno
et al., 2019).

A second closer-in companion ”c” has been tentatively detected inside the
cavity during multi-epoch monitoring of spatially unresolved CO (v=1-0) line
profile asymmetries potentially originating from the gas component of a CPD
inside the cavity (Brittain et al., 2013, 2014). This claim has also been
disputed, with the line asymmetry being attributed to e.g. a slit misalignment
(Fedele et al., 2015). However Brittain et al. (2019) rebuts this claim,
arguing that a slit misalignment is not plausible given that the CO (v=1-0)
and hot band lines were observed simultaneously yet displayed differing
spectro-astrometric signals and profiles from 2006 to 2013. Furthermore the
signal attributed to the CPD appears to vanish when the predicted position of
the planet moves behind the cavity inner edge (Brittain et al., 2019).
Evidence for the “c” companion within the gap at 10-15 au has been further
strengthened by modeling efforts that reproduce the observed mm-dust disk
substructure with planet-disk interaction (Pinilla et al., 2015; Pyerin et
al., 2021; Fedele et al., 2021). In this work we focus on the direct detection
of the CPD of this potential planet candidate ”c” by 12CO (v=1-0) line
emission.

###  1.2 CO line observations with ELT/METIS

The Extremely Large Telescope (ELT) is a next generation observatory under
construction at the peak of Cerro Armazones in the Atacama desert of Chile.
With a segmented primary mirror diameter of 39.3 meters the sensitivity and
angular resolution of the ELT promises to significantly bolster the
capabilities of ground-based IR astronomy (Ramsay et al., 2018). The Mid-
infrared ELT Imager and Spectrograph (METIS) is a planned instrument designed
for the observation of exoplanets and protoplanetary disks (Brandl et al.,
2021). The single-conjugate adaptive optics system allows METIS to perform
high-contrast diffraction-limited integral field unit (IFU) spectroscopy at a
spectral resolution $R\sim 10^{5}$ in the L and M bands. This offers the
capability to observe the fundamental transitions of 12CO (v=1-0) from 4.5-5
µm. This CO emission primarily traces warm gas such as at the inner rim of the
disk gap above the midplane, and has been used to deduce the presence of
cavities or gaps (Brittain et al., 2009; Banzatti & Pontoppidan, 2015; Hein
Bertelsen et al., 2016; Antonellini et al., 2020). A CPD inside a disk gap may
be exposed to significant scattered stellar radiation (Turner et al., 2012;
Oberg et al., 2020), heating gas in the CO line emitting region of the CPD and
increasing emission.

Analysis of the emission allows for the kinematic derivation of a planet’s
mass (Rab et al., 2019). Limits on the CPD gas temperature, composition,
physical extent, and total mass may also be determined. High spectral
resolution observations in the Mid- and NIR can thus provide clues to
determine the properties of the planet, the process of gas giant accretion,
and the formation of regular satellite systems around massive planets. If CPDs
are strongly dust-depleted and accretion onto the planet is only episodic, gas
line observations may offer the most promising avenue to probe the
circumplanetary environment.

We performed simulations to demonstrate the METIS instrument capabilities will
enable the detection of a planet+CPD located in the gap of (pre-)transitional
disks, and that high spectral resolution IFU spectroscopy of CO ro-vibrational
emission will enable an unprecedented insight into the nature of these
objects. The outline of this work is as follows: in Sect. 2 we describe the
capabilities of the disk modeling code, the properties of the disk model, and
capabilities of the telescope observing simulation tools. In Sect. 3 we
describe our results, and discuss implications and conclusions in sections 4
and 5, respectively.

Figure 1: Continuum SED of the HD 100546 circumstellar disk (blue line) and of
the CPD for three cases of differing background radiation (orange, green, and
red lines) and in the case of no CPD (purple line) for a planet with $T_{\rm
eff}=1000$ K. The HD 100546 stellar spectrum is also included (thin blue
line). The METIS LMS wavelength range is indicated by the light blue filled
region. Figure 2: Geometry and intensity of the UV field strength $\chi_{\rm
RT}$ at each position in the CSD and CPD derived from the results of the 2D
radiative transfer. The CPD model UV field map is overlaid for illustrative
purposes. The black contours trace the surface of minimum optical extinction
AV=1 in the vertical or radial direction.

##  2 Methods

To model the disk physics and chemistry and to produce synthetic line emission
data cubes of the HD 100546 circumstellar disk (CSD) and candidate CPD we used
the radiation thermochemical disk modeling code ProDiMo (Protoplanetary Disk
Model) 111https://prodimo.iwf.oeaw.ac.at/ (Woitke et al., 2016; Kamp et al.,
2017; Woitke et al., 2019; Thi et al., 2020). The CO abundance in the disks is
self-consistently calculated with a rate-based approach using the ’large’
chemical network including 235 species and 13 elements described in Kamp et
al. (2017). The adopted elemental abundances of C and O are 1.38$\times
10^{-4}$ and 3.02$\times 10^{-4}$ relative to H, respectively (Savage &
Sembach, 1996). ProDiMo has been used previously to model observations of CO
line emission from CPDs around wide-orbit companions in the sub-mm (Rab et
al., 2019). To model CO emission from Herbig disks ProDiMo utilizes a CO
molecule model that includes up to 50 rotational levels and 9 vibrational
levels for the electronic ground state X${}^{1}\Sigma^{+}$ and the first
excited electronic state A${}^{1}\Pi$. Collisions between CO molecules and
hydrogen molecules (H2), hydrogen atoms (H), helium (He), and electrons are
taken into account (Thi et al., 2013; Song et al., 2015). Order-of-magnitude
uncertainties in rate coefficients result in model CO line flux variations of
up to 20$\%$.

###  2.1 System model properties

In this section we describe the properties of the circumstellar and
circumplanetary disk models. We assumed that the CSD and CPD are coplanar
($i_{\rm CSD}$ = $i_{\rm CPD}$), that the CPD lies within the midplane of the
CSD on a zero-inclination orbit, and that the CPD and CSD are co-rotating
(rotating in the same direction). The CPD is assumed to lie on a circular
orbit ($e_{\rm CPD}=0$) at a distance of 15 au from the star. For the
production of combined CPD+CSD data cubes the position angle of the CPD is
varied from 0-180∘ in steps of 45∘ relative to the total system position angle
of $\sim 140^{\circ}$. The continuum SED of the CSD and CPD for several of the
models can be found in Fig. 1.

####  2.1.1 Properties of the HD 100546 Circumstellar Disk

The properties of the HD 100546 disk have previously been derived by spectral
energy distribution (SED) fitting by means of a genetic algorithm (Woitke et
al., 2019). A multi-wavelength set of publicly available photometric fluxes,
low- and high resolution spectra, and interferometric data have been collated
to produce a global SED (Dionatos et al., 2019). Sixteen free parameters
describing the disk physical and chemical parameters have been fit to the SED
by iteratively performing MCFOST radiative transfer simulations. Details of
the disk modeling procedure, SED fitting, and limitations of the SED fitting
process can be found in Woitke et al. (2016), Kamp et al. (2017),Woitke et al.
(2019) and Dionatos et al. (2019). The disk gap is parameterized to span
4-19.3 au. A detailed description of the model parameters can be found in
Petit dit de la Roche et al. (2021) 222The model parameters and output can
also be accessed directly at http://www-star.st-
and.ac.uk/~pw31/DIANA/SEDfit/HD100546_model_index.html. Inside the gap the
vertical gas column density does not exceed $N_{\langle\rm H\rangle}=10^{17}$
cm-2. However in the following section we considered also the implications of
additional gas and dust being present in the gap.

Figure 3: Illustration of the circumstellar disk geometry and the components
contributing to the channel maps. In case 1 the CPD phase angle $\theta$ is ¡
90∘ (CPD as foreground object relative to the CSD). The CPD absorption map
(ii) is used to extinct the CSD emission map (i). The CPD emission (iii) is
then added to produce the final image (iv). When $\theta$ ¿ 90° the CSD gap
edge becomes the foreground object, and the process follows case 2. At
$\theta$ = 90∘ the extinction caused by either object on the other is
negligible and the two channel maps are simply co-added.

####  2.1.2 Properties of the planet and CPD

We considered two cases for the physical size of the CPD. The first reference
case is one in which the outer radius $R_{\rm out}$ of the CPD is equal to the
planetary Hill radius RH. In the second case we assume that the CPD is
truncated to one third of the Hill radius due to tidal interaction or
photoevaporative effects ($R_{\rm out}$ = 1/3 RH) (Martin & Lubow, 2011;
Mitchell & Stewart, 2011; Oberg et al., 2020). For the reference model we
assume a planetary mass of 10 MJ, but consider also the case of a 5, 3 and 1
MJ planet with correspondingly smaller Hill radii. An exponential decline in
the surface density profile of the CPD is parameterized to begin at one third
of the outer radius in either case. The planetary luminosity is set to be
$10^{-5}$ L⊙ to be consistent with the predicted post-runaway accretion phase
of giant planet evolution (Marley et al., 2007). The planetary spectrum is
adopted from the DRIFT-PHOENIX library for an object with $T_{\rm eff}=1000$ K
(Helling et al., 2008).

Given the short timescales of dust depletion in the CPD (Zhu et al., 2018; Rab
et al., 2019) and the possibility that pressure bumps at the gap edge prevent
significant transport of dust towards the CPD (Rice et al., 2006; Zhu et al.,
2012) we adopt a relatively dust depleted CPD with a dust-to-gas ratio
$d/g=10^{-3}$, but find that adopting a canonical value of 10-2 has a
negligible impact on the ro-vibrational CO line emission characteristics of
the CPD. We consider also more extreme cases of dust depletion with
$d/g=10^{-4}$, $10^{-5}$ and $10^{-6}$. A summary of the various CPD
variations of parameters can be found in Table 1. The parameters which remain
fixed and are shared between all models are found in Table 2.

The CPD is externally irradiated by the star located at the center of the
circumstellar disk. The strength of the attenuated UV field $\chi_{\rm RT}$
was calculated throughout the circumstellar disk as part of the full 2D
radiative transfer. The value of $\chi_{\rm RT}$ represents the strength of
the local UV radiation field with respect to the standard interstellar
radiation field (Röllig et al., 2007). We extracted the intensity of this
attenuated stellar radiation at the position of the CPD. This extracted
radiation field was then applied as a background to the CPD. In practice the
external radiation field is represented in the radiative transfer by a diluted
20000 K blackbody component which is isotropically incident on the CPD.

The geometry of the UV radiation field intensity derived from the 2D radiative
transfer in the CSD is depicted in Fig. 2. For illustrative purposes the
corresponding radiation field in and around the reference CPD has been scaled
and positioned at the stellocentric radius corresponding to its physical
separation and extent. The shadowing effect of the inner disk is apparent, and
the CPD sits entirely within this shadow. In the midplane the $\chi_{\rm RT}$
field strength at 15 au is 1.8$\times 10^{6}$. When applied as a background UV
field to the CPD model the irradiation is assumed to be isotropically
incident. Given the geometry and alignment of the CPD relative to the star and
corresponding potential for self-shadowing we test also significantly reduced
external UV field strengths of $\chi=10^{4}$, $10^{5},$ and $10^{6}$. We do
not consider the possibility of a warped or inclined inner disk, which might
periodically vary the magnitude of the inner-disk’s shadowing.

We assessed the contribution of back-scattered light by performing a separate
radiative transfer simulation where the outer disk component of the HD 100546
CSD model is removed to prevent back-scattering from the gap wall at 19.3 au.
If the outer disk is removed entirely the $\chi_{\rm RT}$ value at the
position of the CPD reduces by a factor 20 to $10^{5}$, hence 95$\%$ of the
incident emission is scattered radiation originating from the outer gap wall.
The question of how much external radiation is effectively incident on the CPD
is discussed further in Sect. D.

The distribution of gaseous CO in the reference CPD is shown in Fig.8(a). The
2D gas temperature and density structure of the CPD are shown in Fig. 8(c) and
Fig. 8(b), respectively. For the calculation of the line Doppler shift we
adopt for the stellar rest frame a radial velocity of 9.25 km s-1 (Gaia
Collaboration et al., 2021). The planetary radial velocity at maximum
elongation is 8.15 km s-1 for $a=15$ au, $i=42^{\circ}$.

###  2.2 Radiative transfer post-processing

The ProDiMo line radiative transfer implementation precludes a full 3D
treatment of the combined CPD and CSD system. Instead, two independent disk
models are combined in a post-processing step. First a 2D axisymmetric
radiative transfer is performed independently in the CSD model (see section
2.1.1). We extract the properties of the radiation field in the gap midplane
of the CSD model. These properties were used to inform the plausible magnitude
of external UV irradiation of the CPD. The CPD disk model was then initialized
with these background conditions.

Table 1: CPD model variations. Variations on the reference model are
highlighted in bold.

model id | $\chi_{\rm gap}$ |  $R_{\rm out}$ [au] |  $M_{\rm p}$ [MJ] |  $M_{\rm CPD}$ [MP] | $d/g$
---|---|---|---|---|---
reference | 2$\times 10^{6}$ | 1.62 | 10 | 10-2 | 10-3
chi1E6 | $\bm{1\times 10^{6}}$ | 1.62 | 10 | 10-2 | 10-3
chi5E5 | $\bm{5\times 10^{5}}$ | 1.62 | 10 | 10-2 | 10-3
chi1E5 | $\bm{1\times 10^{5}}$ | 1.62 | 10 | 10-2 | 10-3
chi2E6-s | $\bm{2\times 10^{6}}$ | 0.54 | 10 | 10-2 | 10-3
chi1E6-s | $\bm{1\times 10^{6}}$ | 0.54 | 10 | 10-2 | 10-3
chi5E5-s | $\bm{5\times 10^{5}}$ | 0.54 | 10 | 10-2 | 10-3
chi1E5-s | $\bm{1\times 10^{5}}$ | 0.54 | 10 | 10-2 | 10-3
chi2E6-5mj | 2$\times 10^{6}$ | 1.29 | 5 | 10-2 | 10-3
chi2E6-3mj | 2$\times 10^{6}$ | 1.08 | 3 | 10-2 | 10-3
chi2E6-1mj | 2$\times 10^{6}$ | 0.75 | 1 | 10-2 | 10-3
mcpd3 | 2$\times 10^{6}$ | 1.62 | 10 | 10-3 | 10-3
mcpd4 | 2$\times 10^{6}$ | 1.62 | 10 | 10-4 | 10-3
mcpd5 | 2$\times 10^{6}$ | 1.62 | 10 | 10-5 | 10-3
chi2E6-dg4 | 2$\times 10^{6}$ | 1.62 | 10 | 10-2 | 10-4
chi2E6-dg5 | 2$\times 10^{6}$ | 1.62 | 10 | 10-2 | 10-5
chi2E6-dg6 | 2$\times 10^{6}$ | 1.62 | 10 | 10-2 | 10-6

Table 2: Common parameters shared between all CPD models listed in Table 1. Parameter | Symbol | Value | Unit
---|---|---|---
Planetary Luminosity | $L_{\rm p}$ | $10^{-4}$ | L⊙
Effective Temperature | $T_{\rm eff,p}$ | 1000 | K
UV Luminosity | $L_{\rm UV,p}$ | 0.01 | Lp
Disk Inner Radius | $R_{\rm in}$ | 0.01 | au
Column Density Power Ind. | $\epsilon$ | 1.0 | -
Flaring Index | $\beta$ | 1.15 | -
Reference Scale Height | $H_{\rm 0.1au}$ | 0.01 | au
Minimum dust size | $a_{\rm max}$ | 0.05 | µm
Maximum dust size | $a_{\rm max}$ | 3000 | µm
Dust size power law index | $a_{\rm pow}$ | 3.5 | -
Dust composition: |  |  |
Mg0.7Fe0.3SiO3 |  | $60\%$ |
Amorphous carbon |  | $15\%$ |
Vacuum |  | $25\%$ |

Line radiative transfer was performed independently for the CSD and CPD,
producing data cubes for selected CO ro-vibrational lines in the METIS LMS-
mode wavelength range. In both cases a map of the line-of-sight optical depth
($\tau$ map) through the disks was also produced at each wavelength. The line
data cubes of the CSD and CPD were then combined. The details of the
combination process are dependent on the phase angle $\theta$ of the CPD along
its orbit (where $\theta=0$° corresponds to the northern minor axis of the
disk). For a given $\theta$ the line-of-sight velocity of the CPD is
calculated to determine the wavelength shift $\delta\lambda$ of the line
center. At values of $\theta<$ 90° (where 90° corresponds to maximum
elongation) the CPD partially occludes CSD emission originating from the near-
side cavity wall. The $\tau$ map was used to calculate the extinction of the
background CSD emission due to the CPD dust and gas. At each pixel $i,j$ in
the CSD cube the flux $S$ was extincted at the wavelength $\lambda$ according
to

$S_{i,j}(\lambda)=S^{\rm
CSD}_{i,j}(\lambda)\,e^{-\tau^{CPD}_{i,j}(\lambda+\delta\lambda)}+S^{\rm
CPD}_{i,j}(\lambda+\delta\lambda).$ (1)

The CPD channel map was then co-added with the partially extincted CSD channel
map. The data products that contribute to this overall process are illustrated
as Case 1 in Fig. 3. In the event that the CPD phase angle $\theta$ was
$>90$°, the roles are reversed and the CPD was partially extincted by
foreground dust and gas in the CSD cavity wall (Case 2 in Fig. 3) . In this
case the $\tau$ map of the CSD was used to extinct the CPD.

###  2.3 SimMETIS

To simulate the capabilities of the METIS instrument we used the SimMetis
software package 333https://github.com/astronomyk/SimMETIS release v0.2
(retrieved 19 Feb 2019) based on SimCADO. The telescope altitude is set to
3060 m at latitude -24.59° and longitude -70.19°. The telescope temperature is
282.15 K. The detector pixel scale is 8.2 mas444In reality the LMS mode FOV is
0.58 × 0.93” cut into 28 slices of 0.021 x 0.93”. The slices are projected
onto a detector with plate scale 0.0082” per pixel. Hence as the PSF is
undersampled in the across-slice direction an observation will require a
series of exposures with dithers/offsets or rotations, from which a spatially
fully sampled data cube will be reconstructed. The SimMetis pixel scale thus
represents an ideal data reduction scenario., corresponding to $\sim 1.1$ au
at 108 pc (Gaia Collaboration et al., 2021). The exposure time and number of
exposures has been varied. We consider a detector integration time (DIT) of 10
s and a number of DITs (NDIT) for total exposure times totalling 10s, 60s, 1h,
and 4h. A longer DIT is not adopted to prevent saturation of the detector.
From the maximum possible elevation of HD 100546 and altitude of the ELT we
adopt for observing parameters an airmass of 1.5. The atmospheric conditions
are ”median”.

##  3 Results

(a) $\chi_{\rm RT}=2\times 10^{6}$, $\theta=45$°, $R_{\rm out}=$ RHill

(b) $\chi_{\rm RT}=10^{5}$, $\theta=45$°, $R_{\rm out}=$ RHill

Figure 4: Synthetic channel maps of the v(1-0)P08 line (4.73587 µm) of the HD
100546 CSD + CPD model for the high external irradiation case (a) and for the
low external irradiation case (b). In both cases the CPD outer radius $R_{\rm
out}=$ RHill (1.62 au). The ProDiMo model used as input for SimMetis is in the
top row of each subfigure. The ellipses in the upper-leftmost panel indicate
the inner and outer edges of the gap at 4 and 19 au, and the companion orbit
at 15 au (dotted line). The corresponding simulated METIS observation panels
represent 6 detector integrations of 10 s each in the bottom row of every
subfigure. The white contour lines represent signal-to-noise ratios of 3, 5,
and 10. The velocity offset is relative to the stellar reference frame. Figure
5: Synthetic channel maps of v(1-0)P08 line (4.73587 µm) from the CPDs of
varying physical extent and background irradiation. The CPD is placed at
maximum elongation ($\theta=90$°) The leftmost column contains the input model
at the extracted velocity (+6.8 km s-1 relative to the stellar reference
frame). The asymmetry in the moment 0 map in column 2 is due to telluric
contamination. The third to sixth columns include the synthetic channel maps
for an increasing series of total detector integration times indicated at the
top of each column. The black contours indicate a count value excess relative
to the background of $25\%$, $50\%$, and $100\%$. The color range of each
image has been logarithmically scaled with boundaries corresponding to the
minimum and maximum values found outside of the central half of the stellar
PSF. Where it is not apparent by eye the position of the CPD is indicated with
a white vertical arrow. The six-fold symmetry apparent in longer integration
times is a result of the ELT point spread function acting on the central star.
The colormap normalization has been configured to maximize the visibility of
the CPD.

(a) Position Angle + 0°

(b) Position Angle + 45°

(c) Position Angle + 90°

(d) Position Angle + 135°

Figure 6: 12CO line profiles represented as the signal-to-noise ratio (SNR) of
the aperture centered on the CPD (top row of each subfigure) compared to the
case of no CPD (black line) for the CPDs with varying levels of background UV
irradiation $\chi$. Excess or deficit in flux $\Delta S$ in the aperture
relative to a no-CPD model (bottom row of each subfigure). Results are shown
for a companion position angle relative to the disk semiminor axes of (a) 0∘,
(b) 45∘, (c) 90∘, and (d) 135∘. The signal present in the case of no CPD is
indicated by the black lines, and arises purely from circumstellar disk
emission. The rest frame of the star is indicated by the vertical dashed gray
lines. A negative $\Delta S$ indicates that the CPD is seen in absorption.
Note that the vertical axis scaling can differ significantly between the left
and right sides of each subfigure.

At the CO line centers we find the CPD flux is 102-104 greater than the
planet+CPD continuum emission at 4.6-4.9 µm depending on the magnitude of
external irradiation. Over this wavelength range the CPD dust contributes at
most 10$\%$ of the combined planet+CPD emission. For the reference case we
find the peak CO line flux near 4.83 µm is of the same order as the entire CSD
disk-integrated continuum flux. This is evident in Fig. 9.

The flux of the CPD is extracted by placing a circular aperture at the
position of its centroid and summing across all pixels in the aperture. The
aperture has a radius of 3 pixels and is sized to include $>99.5\%$ of the
emission originating from the CPD. Expressing the statistical significance of
the CPD emission is complicated by contamination (blending) of CSD emission
within the aperture. Despite the Doppler shifting of the CPD line emission we
find that some contamination from circumstellar disk emission occurs in every
case for a CPD radial separation of 15 au. Fluxes are extracted from the
spectral channel with the maximum contrast with the CSD. A value of 100$\%$
would indicate a doubling of the emission within the aperture relative to a
no-CPD model. With real data a similar analysis would require the subtraction
of modeled CSD emission.

A lower dust-to-gas ratio allows UV radiation to penetrate more deeply into
the CPD and heat the gas, increasing the CO line emission by up to a factor
$\sim 2.5$. A CPD for a planet mass as low as 1 MJ is still present as a
localized excess emission of 10-60$\%$. If either the CPD gas mass is reduced
by a factor 1000 (to 10-4 MJ), the UV background is reduced by a factor 20, or
the CPD gas component radius is reduced to R${}_{\rm H}/3$, the signal of the
CPD is not present as an excess of more than 10$\%$ and becomes more
challenging to detect. A phase angle of 90° (maximum elongation) increases the
contrast with circumstellar disk emission by a factor 2 relative to
$\theta=45^{\circ}$. Conversely the CPD is not detectable at
$\theta=180^{\circ}$, where the CPD is spatially coincident with the optically
thick line-emitting region of the CSD ($\tau>1300$).

The CPD 12CO line strength is found to be coupled only weakly to the planetary
luminosity. Although the inner rim of the CPD is heated by the planet, the
corresponding effective emitting area is negligible. The majority of the line
emission originates instead from the disk surface. Background UV irradiation
of the CPD efficiently increases gas temperatures in a thin surface layer up
to 4000 K. This can be seen in Fig. 8(c). The resulting emission region is
comparable to the total disk surface area. The main emission region is
highlighted in Fig. 8(a). The line luminosity is thus closely proportional to
the physical extent of the circumplanetary gas and the intensity of the UV
background. In the “best case” scenario for detection, a Hill sphere-filling
CPD with background $\chi=2\times 10^{6}$ produces spatially resolved emission
with peak signal-to-noise ratio SNR = 5 in 60 s of total exposure. If the
external irradiation is reduced by a factor 20 the CPD becomes difficult to
distinguish from background circumstellar disk emission. Likewise if the CPD
outer radius is truncated to R${}_{\rm Hill}/3$, detection of the CPD gas
requires the most extreme case of background irradiation to ensure the CPD
emission can be distinguished from the background CSD gap wall at a level
greater than 10$\%$ localized excess.

We have produced a series of synthetic channel maps for each combined CSD+CPD
model representing plausible observational parameters. Synthetic channel maps
of the combined CSD+CPD for the high- and low-levels of background radiation
can be found in Fig. 4(a) and 4(b) respectively. The CPD is both spatially and
spectrally resolved in Fig. 4(a) owing to the line-of-sight velocity offset
with the gap wall emission surface. Interestingly the presence of the CPD can
be inferred in Fig. 4(b) even in the absence of detectable line emission. The
CPD dust continuum absorption produces a silhouette on the background of the
CSD gap wall line emitting region if the external irradiation is sufficiently
low. This effect is clearly demonstrated in Fig. 4(b) at +2.26 km s-1 and
+3.77 km s-1 where the position of the CPD is apparent in absorption.

The greatest contrast between the CPD and CSD is found at maximum elongation
($\theta=90^{\circ}$) when the relative Doppler shifting between the planet
and star are maximal. Synthetic channel maps for the high- and low-levels of
background radiation for both small ($R_{\rm out}=$ R${}_{\rm H}/3$) and large
($R_{\rm out}=$ RH) CPD models at maximum elongation can be found in Fig. 5.
In all cases where $R_{\rm out}=$ RH the CPD emission can be easily
distinguished from the circumstellar disk by eye.

The detectability of the CPD represented both in terms of the aperture SNR and
as an excess or deficit in emission relative to a no-CPD model for different
phase angles can be found in in Fig. 6. The CPD continuum absorption
silhouette effect is also clear in Fig. 6 (a) and (b) for $\theta=0^{\circ}$
and $45^{\circ}$, respectively, with a localized reduction in flux relative to
a smooth axisymmetric of $\sim 10\%$. We summarize our parameter exploration
in terms of the significance of the CPD emission as an excess or deficit in
the flux relative to a no-CPD model in Fig. 7 for all model configurations.

Given the instantaneous spectral coverage of the METIS instrument as many as
eight 12CO v=1-0 lines may be present in a single observation. Depending on
the magnitude of telluric contamination the eventual signal-to-noise of a CPD
detection may thus be increased by a factor $\sim 2.5-3$ over what we
demonstrate in e.g. Fig. 6.

As the C/O ratio of material accreting from the outer circumstellar disk onto
the CPD may differ substantially from abundances corresponding to the ISM
(e.g. Ansdell et al. (2016); Zhang et al. (2019)), we considered also the case
of a carbon depletion by a factor 10. Given that the 12CO v=1-0 lines are
highly optically thick, we find that a 10$\times$ depletion of C results in
peak line fluxes being reduced by $\sim 20\%$ relative to the value
corresponding to standard ISM abundances.

##  4 Discussion

We have found that a sufficiently large and externally irradiated CPD can
produce a signal which could be detected even when the entire gap region of
the CSD would be spatially unresolved. Although without a priori knowledge of
the line-of-sight velocity offset of the CPD signal w.r.t. the circumstellar
disk emission, multi-epoch observations would be required to deduce Keplerian
motion of the signal originating from the CPD. In the most extreme case we
find the CPD peak line luminosity approaches $\sim 40\%$ of the disk-
integrated circumstellar emission at the same wavelength (see Fig. 9). This is
comparable with the magnitude of the candidate CPD signal observed in 12CO P26
line emission discussed in Brittain et al. (2013). The centrally peaked CO
line morphology arises as a result of the emission originating from across the
entire disk surface at relatively low Keplerian velocities.

Dust depletion of CPDs due to grain drift is predicted to occur on relatively
short timescales (Zhu et al., 2018; Rab et al., 2019), frustrating attempts to
detect CPDs by continuum emission. This is consistent with the non-detection
of CPD-like dust emission in several pre-transitional disk cavities. However
we find that a CPD with severely depleted dust ($d/g\sim 10^{-6}$) can still
be readily detected in CO emission, while being simultaneously impossible to
detect in continuum emission with e.g. ALMA. Other pre-transitional disks
around UV-bright Herbig Ae/Be stars e.g. UX Tau A , HD34282, HD97048 ,CQ Tau,
MWC 758 (Andrews et al., 2011; van der Plas et al., 2017a, b; Ubeira Gabellini
et al., 2019; Calcino et al., 2020) offer similar opportunities to search for
CO emission from externally irradiated CPDs.

The possibility to detect the CPD in absorption against the CSD gap wall
represents an unique observational scenario allowing the dust properties of
the CPD to be revealed. In this sense the CPD is comparable to an externally
irradiated proplyd such as Orion 121-1925 (McCaughrean & O’dell, 1996). In the
event that the magnitude of the external radiation is as low or lower than the
minimum we have considered, this possibility will allow for the physical
extent, dust properties, and minimum dust mass of the CPD to be estimated.
However, even in the most optimistic case the spatially localized reduction in
flux relative to a no-CPD model ($\sim 10\%$) is minor, and spatial
inhomogeneity of background circumstellar disk CO emission could easily
obscure such a signal. Thus in practice it may be very difficult to achieve
lest the position of the planet and CPD were known a priori.

Figure 7: CPD induced excess/deficit flux in aperture for all CPD model
configurations and phase angles $\theta$. Fluxes are extracted from the
spectral channel with the maximum contrast with circumstellar disk emission. A
value below 0 indicates the CPD is seen in absorption. A value larger than 100
indicates that the aperture flux is more than double that of a no-CPD model.
The variation of parameters are relative to the reference CPD with planet mass
$M_{\rm P}=10$MJ, M${}_{\rm CPD}=0.01M_{\rm P}$, $\chi_{\rm RT}$ = $2\times
10^{6}$, $d/g$ = $10^{-3}$. A label ”small” indicates that the CPD outer
radius has been truncated to one third of the planet Hill radius. The angle of
the triangle markers indicates the phase angle of the CPD relative to the
circumstellar disk northern minor axes.

##  5 Conclusions

We have used thermochemical disk models to produce synthetic channel maps that
represent 12CO line observations of the HD 100546 system in an effort to
determine the plausibility of detecting CPDs in transition disk gaps with
METIS. We list our key findings:

  1. 1.

Fundamental 12CO ro-vibrational line emission from the gas component of a
circumplanetary disk can potentially be detected in only 60 s of detector
integration time with ELT/METIS

  2. 2.

Visibility of the CPD depends strongly on the level of external irradiation
and the physical extent of the disk, favoring massive ($\sim 10$ MJ) planets
and spatially extended disks with radii approaching the planetary Hill radius.

  3. 3.

The majority of 12CO line emission originates from across the entire disk
surface, and thus the CO line profiles are centrally peaked. The planetary
luminosity does not play a significant role in exciting the 12CO line
emission.

  4. 4.

Massive, UV-bright star systems with pre-transitional disks are ideal
candidates to search for CO-emitting CPDs with ELT/METIS.

The capabilities of METIS represent a critical component of the multi-pronged
effort to unveil the processes of giant planet and moon formation. If CPDs
prove to be strongly dust-depleted, gas line observations will play a critical
role in this endeavour.

###### Acknowledgements.

The research of N.O. and I.K. is supported by grants from the Netherlands
Organization for Scientific Research (NWO, grant number 614.001.552) and the
Netherlands Research School for Astronomy (NOVA). CHR acknowledges the support
of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
Research Unit “Transition discs” - 325594231. Ch.R is grateful for support
from the Max Planck Society. N.O. would like to thank B.R. Brandl and R. van
Boekel for helpful discussions. This research has made use of NASA’s
Astrophysics Data System Bibliographic Services. This research made use of
Astropy 3 a community-developed core Python package for Astronomy (Astropy
Collaboration et al., 2013; Price-Whelan et al., 2018)) This research has also
used Numpy (Harris et al., 2020), Matplotlib (Hunter, 2007), Scipy (Virtanen
et al., 2020), and Prodimopy https://gitlab.astro.rug.nl/prodimo/prodimopy. .

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##  Appendix A Properties of the reference CPD model

The 12CO abundance and v=1-0 line emitting region of the reference CPD can be
found in Fig. 8(a). The gas temperature and density structure can be found in
Fig. 8(c) and 8(b). Small dust grains in the upper layers of the CPD absorb
external UV photons but cool efficiently to radiative equilibrium. This heats
the surrounding gas which in turn cools predominantly by the relatively
inefficient H2O and CO rotational and vibrational emission. Hence the gas and
dust temperature are not closely coupled in this hot surface layer. The
parameters of the CPD models which are common to all models described in Table
1 are listed in Table 2.

(a) CPD CO abundance and line emitting region.

(b) CPD gas density.

(c) CPD gas temperature.

(d) CPD dust temperature.

(e) CPD and CSD gas temperature.

(f) CPD and CSD dust temperature.

Figure 8: Properties of the reference CPD with $\chi=2\times 10^{6}$ and
$R_{\rm out}=R_{\rm Hill}$ (a,b,c,d). The majority of the 12CO v=1-0 line
emission originates from within the green “box” region in panels a-d. The
dotted contour lines in panels (a,b,c,d) represent minimum optical extinction
AV surfaces of 1 (dotted line), 10 (dashed line) in the radial or vertical
direction. The gas and dust temperature structure of the CPD is contrasted for
illustrative purposes with that of the circumstellar disk in panels (e) and
(f).

##  Appendix B CPD line emission strength relative to the continuum

The estimated peak emission strength of each of the modeled 12CO lines is
shown in Fig. 9 for the circumstellar disk, three cases of varying background
radiation incident on the CPD, and the case of a planet without CPD.

Figure 9: Comparison of the estimated CPD and CSD 12CO line fluxes (dots) for
varying intensities of background UV radiation with the continuum SED of the
CSD and CPDs (solid lines). Only 12CO lines are plotted.

##  Appendix C Spatially unresolved CPD emission

We find that the CPD CO line emission can in certain cases be sufficient to be
detectable even when spatially unresolved. In Fig. 10 we demonstrate a
synthetic P26 line profile in the event that the disk would be spatially
unresolved. The spectral resolution and noise level of the combined CSD (blue
line) + CPD (red line) line profile has been degraded to correspond to the
excess CO emission observed with CRIRES and discussed in Brittain et al.
(2014, 2019) (black line). The corresponding line profile in the absence of a
CPD is indicated by the gray line. While the CPD-induced excess is notable,
without a priori knowledge of the properties and orbital phase of the CPD,
spectral decomposition would be implausible without long-term monitoring of
the signal.

Figure 10: Synthetic 12CO v(1-0)P26 (4.9204 µm) line profiles of the
circumstellar disk (blue) and circumplanetary disk (red) from the ProDiMo
radiative transfer. The combined and degraded signal corresponds to the
spectral resolution of the CRIRES observations performed by Brittain et al.
(2014, 2019) during multi-epoch monitoring of the HD 100546 system. The light
shaded red region indicates the contribution of the CPD.

##  Appendix D How much stellar radiation reaches the CPD?

In our reference model we have assumed the gap to be effectively empty with a
correspondingly negligible optical depth. As a verification step we perform a
series of radiative transfer simulations in which we populate the gap with
additional dust and gas to explore the potential for extinction of stellar UV
towards the CPD and of CPD emission towards the observer. Several cases of
increased gap dust mass are displayed in Fig. 11. Non-neglible extinction of
the stellar UV begins to occur if the gap is populated by 10$\times$ the dust
mass inferred to be present in the inner disk. With a gap dust mass of
$10\times m_{\rm dust,inner}$ the midplane FUV intensity $\chi_{\rm RT}$ falls
to $30\%$ of the reference value at the position of the CPD. The SED of the
CSD in this case is still consistent with observations, increasing the flux at
4 µm by no more than $\sim 4\%$. If the gap dust mass is increased to
100$\times$ the inner disk dust mass, the SED begins to diverge significantly
from WISE, ISO-SWS, and VISIR observations at 2-11 µm and is ruled out by
observations. Hence we consider it plausible that additional dust in the gap
may reduce the CPD-incident FUV flux by at least $\sim 70\%$ without becoming
inconsistent with observations.

We found in Sect. 2.1.2 that upwards of 95$\%$ of the UV radiation incident on
the CPD originates from back-scattering off of dust in the gap outer wall.
While radiative transfer in ProDiMo is calculated only using isotropic
scattering of photons, at wavelengths $\sim 0.1$ µm molecular gas can act as
an effective Rayleigh-scatterer. Furthermore, stellar Ly-$\alpha$ photons may
be resonantly scattered downwards into a gap by atomic hydrogen in the upper
layers of the circumstellar disk, although this phenomenon is also not
included in the 2D radiative transfer (Bethell & Bergin 2011). This leads us
to believe that isotropic incidence of external UV is a reasonable
approximation in this case. Nevertheless we consider the case where the
external radiation has been decreased by a factor 20 under the assumption that
scattering of UV photons would be particularly inefficient or that significant
quantities of undetected dust fills the gap.

Figure 11: Midplane $\chi_{\rm RT}$ extracted from the 2D radiative transfer
of the ProDiMo HD 100546 disk model for the reference case, and in the case of
the dust mass in the gap being equal to 1, 10, and 100$\times$ the amount of
dust in the inner disk. The case of no outer disk is included as the gray
dashed line to highlight the role of back-scattering off the gap outer wall.