# Molecules with ALMA at Planet-forming Scales (MAPS). VII. Sub-stellar O/H
and C/H and super-stellar C/O in planet feeding gas

Arthur D. Bosman Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Felipe Alarcón Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Edwin A. Bergin Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Ke Zhang NASA Hubble Fellow  Department of Astronomy, University of Wisconsin-Madison, 475 N Charter St, Madison, WI 53706  Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Merel L.R. van ’t Hoff Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Karin I. Öberg Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Viviana V. Guzmán Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile  Catherine Walsh School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK  Yuri Aikawa Department of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan  Sean M. Andrews Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Jennifer B. Bergner NASA Hubble Fellowship Program Sagan Fellow  University of Chicago Department of the Geophysical Sciences, Chicago, IL 60637, USA  Alice S. Booth Leiden Observatory, Leiden University, 2300 RA Leiden, the Netherlands  School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT UK  Gianni Cataldi National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan  Department of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan  L. Ilsedore Cleeves University of Virginia, 530 McCormick Rd, Charlottesville, VA 22904, USA  Ian Czekala NASA Hubble Fellowship Program Sagan Fellow  Department of Astronomy and Astrophysics, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA  Center for Exoplanets and Habitable Worlds, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA  Center for Astrostatistics, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA  Institute for Computational & Data Sciences, The Pennsylvania State University, University Park, PA 16802, USA  Department of Astronomy, 501 Campbell Hall, University of California, Berkeley, CA 94720-3411, USA  Kenji Furuya National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan  Jane Huang NASA Hubble Fellowship Program Sagan Fellow  Department of Astronomy, University of Michigan, 323 West Hall, 1085 S. University Avenue, Ann Arbor, MI 48109, USA  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  John D. Ilee School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK  Charles J. Law Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Romane Le Gal Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  IRAP, Université de Toulouse, CNRS, CNES, UT3, 31400 Toulouse, France  Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France  IRAM, 300 rue de la piscine, F-38406 Saint-Martin d’Hères, France  Yao Liu Purple Mountain Observatory & Key Laboratory for Radio Astronomy, Chinese Academy of Sciences, Nanjing 210023, China  Feng Long Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Ryan A. Loomis National Radio Astronomy Observatory, Charlottesville, VA 22903, USA  François Ménard Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France  Hideko Nomura National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan  Chunhua Qi Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Kamber R. Schwarz NASA Hubble Fellowship Program Sagan Fellow  Lunar and Planetary Laboratory, University of Arizona, 1629 East University Boulevard, Tucson, AZ 85721, USA  Richard Teague Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Takashi Tsukagoshi National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan  Yoshihide Yamato Department of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan  David J. Wilner Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA

(Received XX; Revised YY; Accepted ZZ)

###### Abstract

The elemental composition of the gas and dust in a protoplanetary disk
influences the compositions of the planets that form in it. We use the
Molecules with ALMA at Planet-forming Scales (MAPS) data to constrain the
elemental composition of the gas at the locations of potentially forming
planets. The elemental abundances are inferred by comparing source-specific
gas-grain thermochemical models, with variable C/O ratios and small-grain
abundances, from the DALI code with CO and C2H column densities derived from
the high-resolution observations of the disks of AS 209, HD 163296, and MWC
480. Elevated C/O ratios ($\sim 2.0$), even within the CO ice line, are
necessary to match the inferred C2H column densities, over most of the pebble
disk. Combined with constraints on the CO abundances in these systems, this
implies that both the O/H and C/H ratios in the gas are substellar by a factor
of 4–10, with the O/H depleted by a factor of 20–50, resulting in the high C/O
ratios. This necessitates that even within the CO ice line, most of the
volatile carbon and oxygen is still trapped on grains in the midplane. Planets
accreting gas in the gaps of the AS 209, HD 163296, and MWC 480 disks will
thus acquire very little carbon and oxygen after reaching the pebble isolation
mass. In the absence of atmosphere-enriching events, these planets would thus
have a strongly substellar O/H and C/H and superstellar C/O atmospheric
composition. This paper is part of the MAPS special issue of the Astrophysical
Journal Supplement.

Astrochemistry – Protoplanetary disks – Abundance ratios

††journal: ApJ††software: SciPy (Virtanen et al., 2020), NumPy (Van Der Walt
et al., 2011), Matplotlib (Hunter, 2007).

##  1 Introduction

More than 10% of stars are thought to host a Jupiter-sized planet (Johnson et
al., 2010; Winn & Fabrycky, 2015). Current observational campaigns are probing
the atmospheric composition of these gas giants, with future instruments
promising better characterization of more gas giants (e.g. Madhusudhan et al.,
2014; Sing et al., 2016; Greene et al., 2016). These composition measurements
place constraints on the process of planet formation and evolution by
comparison of the composition of protoplanetary disks and the planets that
formed within them (e.g. Madhusudhan et al., 2016). Achieving that goal will
require measurements of the elemental composition of disks, particularly
around substructures (e.g., gaps) in the millimeter disk, that are likely
opened by young planets (e.g. Paardekooper & Mellema, 2006; Rosotti et al.,
2016; Zhang et al., 2018).

The composition of a planet is predicted to depend on the location of
formation (e.g. Öberg et al., 2011; Cridland et al., 2017; Öberg & Bergin,
2020), particularly relative to the ice/gas transitions (ice lines) of major
volatile carriers such as CO, CO2, H2O, N2, and NH3. Further studies have
shown that the transport of ices via sedimentation and inward drift of pebbles
also has a significant impact on the composition of the gas and ice that can
be accreted by planets (Ciesla & Cuzzi, 2006; Piso et al., 2015; Booth et al.,
2017; Booth & Ilee, 2019; Krijt et al., 2020). All of these studies assume
that the disk material has a volatile interstellar-medium (ISM) elemental
composition with various additional assumptions regarding chemistry and disk
dynamics. The model-to-model variations create significant uncertainties for
predicting planetary composition (e.g. Eistrup et al., 2016; Booth et al.,
2017).

A more direct link between the composition and formation location of a giant
planet could be made by comparing the elemental composition of the material at
the specific radial locations or sites of planet formation with present-day
gas giant exoplanet atmospheric composition. On top of this, a measurement of
the elemental composition of the disk during planet formation can act as an
intermediary calibration point to improve the accuracy of population synthesis
models (e.g., Mordasini et al., 2009).

Accurately measuring the elemental composition of the disk requires an
observational data set that covers many different molecular species, as well
as a physical understanding of the regions being probed by the observations
(e.g. Bergin et al., 2016; Trapman et al., 2017; Cleeves et al., 2018; Bosman
et al., 2019). This limits the derivation of elemental composition to disks
with a broad range of observations and with a good physical model available.
With the Molecules with ALMA at Planet-forming Scales (MAPS) data and
ancillary modeling efforts (Oberg et al., 2021; Zhang et al.,
2021)111http://www.alma-maps.info, the disks in the MAPS sample are perfect
objects for an elemental composition study, especially as the high-resolution
of the data allows for a radially resolved measurement of the elemental
composition.

In this paper, we will focus on the carbon and oxygen abundances, which are
derived by comparison of models directly to the high-resolution MAPS data that
resolve putative sites of incipient giant planet formation. The carbon and
oxygen abundances in the disk will be derived using constraints on the CO
column from Zhang et al. (2021) and the C2H column from Guzmán et al. (2021).
CO is used to constrain the available total C or O column (e.g., C/H and O/H),
and we use the known dependency of C2H on the carbon-to-oxygen (C/O) ratio to
determine the C/O ratio in the disk gas (e.g. Bergin et al., 2016; Miotello et
al., 2019; Bosman et al., 2021a). A focus on the C/O ratio in the disk gas is
well matched to the available volatile abundance measurements of exoplanetary
atmospheres (Madhusudhan et al., 2014; Greene et al., 2016; Madhusudhan,
2019).222We note that nitrogen abundance can also be indicative of a planet’s
origin (Cridland et al., 2017), and that it is possible to constrain the
nitrogen abundance within protoplanetary disks (Cleeves et al., 2018), which
will be the subject of future work.

##  2 Methods

###  2.1 Source selection

We will focus on three of the five disks targeted by MAPS: the disks around AS
209, HD 163296, and MWC 480. All three of these disks have deep gaps in the
millimeter emission indicative of ongoing planet formation (see Fig. 1;
Andrews et al., 2018; Huang et al., 2018; Zhang et al., 2018; Guzmán et al.,
2018; Long et al., 2018; Liu et al., 2019), as well as gas velocity structures
thought to be perturbations induced by unseen planets in these gaps (Pinte et
al., 2018; Teague et al., 2018, 2019, 2021). We leave out the disks around IM
Lup and GM Aur. The composition of the IM Lup disk has already been discussed
in detail in Cleeves et al. (2018). The GM Aur disk is accreting new material,
influencing the chemical composition of the disk (Huang et al., 2021; Schwarz
et al., 2021), complicating modeling of the disk.

Furthermore, in these disks, we will focus on the gas on the scale of the
millimeter disk, that is, the size of the disk in the millimeter continuum,
using these large grains as a signpost of active planet formation. Fig. 1
shows millimeter continuum radial profiles, rich in structure, for the three
disks that are studied together with the planet masses that are inferred to
cause these structures (Zhang et al., 2018; Liu et al., 2019; Sierra et al.,
2021)333All planet masses assume a viscous $\alpha$ (Shakura & Sunyaev, 1973)
of 10-3. All three disks show potentially planet-induced dust structure that
is clearly seen at with the resolution of the MAPS continuum data
($\sim$0$\farcs$1 $\times$ 0$\farcs$1 Sierra et al., 2021). The MAPS data are
thus able to distinguish the gap region from the surrounding disk material.

Our focus is understanding the chemical composition of localized regions
associated with incipient planet formation. In the AS 209 disk, the structures
of interest are the gaps at 61 and 105 au, straddling a bright ring at 74 au
(Guzmán et al., 2018). These are all well outside of the CO ice line, which is
located around 15 au (Zhang et al., 2021; Alarcón et al., 2021). In the HD
163296 disk, we will focus on the dust gaps at 48 and 86 au, with one gap
inside and one gap outside the ice line at 70 au (Isella et al., 2018; Zhang
et al., 2020a, 2021; Calahan et al., 2021). Finally, for the MWC 480 disk we
focus on the 74 au gap, which is inside the CO ice line at 100 au (Liu et al.,
2019; Zhang et al., 2021). We disregard the inner $\sim$10 au, as an accurate
CO column density has not been derived for this region (Zhang et al., 2021).

To constrain the oxygen and carbon elemental abundances in the three selected
disks we base ourselves on results and models developed within the MAPS ALMA
large program (Oberg et al., 2021). For C2H the column density derived in
Guzmán et al. (2021) is used. These column densities are derived from the
imagecube by fitting the different C2H hyperfine components. The C2H column
density derived from the images is uncertain within 30 au. As such we derive a
separate constraint on the C2H column within 30 au using the kinematic
information in the line profile. This is discussed in Appendix A. The shown
upper limits in Fig. 1 assume a column of C2H that is constant in the inner 20
(AS 209) or 30 (HD 163296 and MWC 480) au.

We adopt the CO depletion factor Zhang et al. (2021) derived from the observed
CO isotopologues radial profiles (Law et al., 2021a). Zhang et al. (2021)
build disk-specific models based on high-resolution continuum and CO
isotopologue (13CO and C18O) line data. A total gas-to-dust mass ratio of 100
is assumed, with the gas disk size set by the extent of CO isotopologue
emission. Gas and small dust (0.005 $\mu$m - 1$\mu$m) are well coupled and
have the standard tapered-power law surface density distribution and a
vertical Gaussian density distribution (see Zhang et al., 2021, for the disk
parameters). The large dust is settled, at 0.2 times the gas scale height and
is structured to match the observed millimeter structure (see, Zhang et al.,
2021, Tables 1 and 2 and Fig. 5). The CO abundance in the disk is then varied
until the model CO isotopologue line emission matches the observed line
emission for ^13CO and C^18O for both the $J=$2-1 and $J=$1-0 transitions. The
ratio between the abundance necessary to reproduce that data and the ISM CO
abundance is called the CO depletion factor. The model CO columns are
consistent with the CO column derived from the hyperfine lines of C^17O in the
regions the latter is detected. Both the C2H column and the CO depletion
factor are shown in Fig. 1.

Figure 1: Top: Comparison of the CO depletion (blue, left axis) from Zhang et
al. (2021), with the C2H column (red, right axis) derived in Guzmán et al.
(2021), for, (from left to right) the AS 209, MWC 480 and HD 163296 disks. The
solid line shows where the C2H column density derivation is assumed to be
robust. In the inner 30 au the imagecube based fitting technique is less
robust and the column density derived values for these radii are shown with a
dotted line. For each disk the upper limit to the C2H abundance in the inner
disk as derived from the line profiles is also shown (See Appendix A)). The
grey vertical line shows the location of the CO ice line. Bottom: Continuum
azimuthal average radial intensity profile from Sierra et al. (2021) at 220
GHz. The green vertical lines show the locations of planets inferred from the
millimeter dust structure, together with their inferred mass (all planet
masses assume a viscous alpha of 10-3, Zhang et al., 2018; Liu et al., 2019).

###  2.2 C2H chemistry

The chemistry of C2H and its use as a tracer of the elemental C/O ratio in
protoplanetary disks has been discussed for a variety of sources and
conditions (e.g. Jansen et al., 1995; Nagy et al., 2015; Bergin et al., 2016;
Cleeves et al., 2018; Bosman et al., 2021a). As a radical it is most abundant
in regions with an active photo-chemistry, where it is continuously produced
and destroyed. The chemistry of C2H is tightly linked to that of CH4 and C2H2,
which is the main reservoir of carbon that is not locked in CO. C2H can be
directly formed by photo-dissociation of C2H2 or it is formed by dissociative
recombination of the C2H2+ and C2H3+ ions, which are part of a gas-phase
hydrocarbon radical and ion cycle (see, for example, Fig. 1 of Bosman et al.,
2021a).

The C2H abundance is very dependent on the C/O ratio in the gas, with
reactions as C2H + O -¿ CO + CH and CH + O -¿ CO + H, directly driving down
the C2H abundance as well as removing carbon from the hydrocarbon reservoir.
Reactions generally result in the formation of CO, which is stable against
photo-dissociation (van Dishoeck & Black, 1988). As such this carbon is no
longer available for hydrocarbon chemistry. Depending on the physical
structure of the disk and the stellar radiation field, the C2H column density
in a disk model can vary by four orders of magnitude, just by variations of
the C/O ratio between $\sim$0.5 and 2.0 (Bergin et al., 2016; Cleeves et al.,
2018). This makes C2H a very good tracer of the C/O ratio.

As a radical C2H traces the photo-dissociation region (PDR) layers of the
disk. At low C/O ratios, all carbon for C2H comes from the dissociation of CO,
which happens only in the top layer of the disk PDR, where CO self-shielding
is not yet active. The mass in this thin layer is relatively constant in a
disk, as well as disk-to-disk as it depends on a fundamental property of the
CO molecule, which starts to self-shield at a column of $10^{15}$ cm-2 (van
Dishoeck & Black, 1988). At C/O ratios above 1 the carbon for the formation of
C2H can be extracted from hydrocarbons as CH4 and C2H2. The thickness of the
layer in which these hydrocarbons can be dissociated depends on UV attenuation
by dust. The small dust content of the disk atmosphere thus has an effect on
the measured C2H column. Initial calculations in Bosman et al. (2021a) predict
that the small dust content will impact the C2H abundance, but is relatively
weak. An order of magnitude drop in small dust abundance should only lead to
an increase in the C2H abundance by a factor two.

###  2.3 Modeling setup

In our modeling we start with the model structure and CO depletion factor as
derived by Zhang et al. (2021). We vary the C/O ratio and the amount of small
dust in the surface layers as these parameters have the most impact of the C2H
abundance. The small dust content of the disks is varied by multiplying the
small dust abundances by a constant factor of 0.001, 0.01, 0.1 or 1 from the
base models of Zhang et al. (2021). The last of these are the fiducial dust
structures and are identical to those used in Zhang et al. (2021).444For
models with lower small-grain abundances the model SED no longer fits the
observational SED. Each model has a constant C/O ratio of either 0.47, 1.0, or
2.0. These correspond to the volatile ISM level (0.47), CO dominated gas (1.0)
and a high C/O value (2.0). Increasing the C/O ratio above 2.0 no longer has
an impact of the C2H abundance (e.g., Cleeves et al., 2018). Combining the
four different small dust abundances and 3 different C/O ratios this results
in twelve models per disk studied.

The model calculation is done in two steps. In the first step the dust and gas
temperatures are calculated. We start from the best fit structure and CO
depletion factors from Zhang et al. (2021). The structures are here modified
to vary the small dust content. The abundances of H2O and CH4 in initial
conditions of the chemical network are also modified at this point so the gas
temperature calculation includes the changes in composition driven by the
different C/O ratios. The dust and gas temperatures are then calculated using
DALI with the standard reduced chemical network, which correctly calculates
the abundances of the major gas coolants. (Bruderer et al., 2012; Bruderer,
2013). In the second step, a full gas-grain network was used to calculate the
2D-chemical composition based on the physical conditions determined in the
first step.

This two step approach was chosen to balance consistency with feasibility. To
calculate the gas temperature, the chemical solver has to run multiple times
per cell, which is prohibitively expensive to do with the gas-grain chemical
network. As mentioned, this approach does capture the effects of the C/O ratio
on the gas temperature, and the effect of these changes on the resulting
chemistry, while being computationally tractable.

###  2.4 Gas-grain chemical network

The gas-grain chemical network used for the second step of our calculations is
based on the network of Walsh et al. (2015), which is a combination of the
UMIST12555http://udfa.ajmarkwick.net/ (McElroy et al., 2013) for the gas-phase
reactions and the Ohio State University (OSU) network (Garrod et al., 2008)
for the grain surface reactions. Molecular binding energies are from McElroy
et al. (2013) and Penteado et al. (2017), with small adjustments for NH_x and
CH_x radicals (Bosman et al., 2018). These binding energies are tabulated in
Bosman et al. (2018), Table B.2. The freeze-out of H2 is also treated as in
Bosman et al. (2018), using the higher (430 K) binding energy for H2 when
there are less than two layers of H2 ice, but lowering the binding energy to
100 K when H2 covers the ice completely.

Photo-desorption yields are taken from experiments where available (Öberg et
al., 2009a, b, c), and assumed to be $10^{-3}$ otherwise. All photodesorption
is assumed to yield intact molecules in the gas-phase.666Many molecules are
expected to fragment on absorption of a UV photon, with some of the fragments
released from the ice, instead of photo-desorbing intact as assumed.
Fragmentation has been shown for methanol (Bertin et al., 2016) and is
expected for other, larger molecules. This is not expected to impact the
chemistry of the species studied here. The grain surface chemistry assumes a
diffusion-to-binding energy ratio of 0.3 and a tunneling barrier of 1 Å (as in
Bosman et al., 2018). For photo-dissociation, the wavelength dependent cross-
sections of Heays et al. (2017) are used in combination with the wavelength
dependent UV field that DALI calculates. For the few cases in which Heays et
al. (2017) do not have a compilation the wavelength dependent cross sections,
the rate parameterization of McElroy et al. (2013) is used. Self-shielding and
mutual shielding is included for C, CO, N2 and H2 (Draine & Bertoldi, 1996;
Kamp & Bertoldi, 2000; Visser et al., 2009, 2018).

The initial abundances used in the models with different C/O ratios are
tabulated in Table 1. Any molecule, atom, or ion not listed in the table has
zero abundance at the beginning of the chemical calculation. The abundances of
H2O, CO, and CH4, that is, the initial carbon and oxygen carriers, are scaled
with the CO depletion factors derived in Zhang et al. (2021) (see Fig. 1).
Further the elemental abundances have been choses such that the maximum amount
of CO that can be form, that is the lowest of the carbon and oxygen elemental
abundances, is the same for all three of the C/O ratio. CH4 was chosen as the
carrier for the excess carbon (instead of elemental C) in the models. The
exact initial abundances do not matter greatly for this calculation, as
abundances in the C2H layer will be set by photon-dominated steady-state
chemistry (Bosman et al., 2021a). The only exceptions to this rule are the
large (more than seven carbon atoms) carbon chains, which act as refractories
in the intermediate PDR layers. These large carbon chains are only formed in
the models when a significant fraction ($>$10%) of the carbon is in elemental
or ionized form. To prevent this, elemental or ionized form should not be
chosen for the initial carbon carrier. In other cases, the exact carrier of
the excess carbon does not substantially alter the resulting C2H abundance
(Bosman et al., 2021a).

A low cosmic-ray ionization rate of $10^{-18}$ s-1 is used for the chemical
models, similar to the models in Zhang et al. (2021) (see, e.g. Cleeves et
al., 2013, for a discussion of cosmic ray propagation in disks.). A higher
cosmic-ray ionization rate, coupled with the already low CO abundances
currently assumed, would quickly convert the remaining CO into other species
like CH4, CO2 and CH3OH (e.g. Furuya & Aikawa, 2014; Schwarz et al., 2016;
Bosman et al., 2018) in the 1 Myr chemical timescale that is assumed. This
would create a disagreement between the CO column in the models and the
intended, observationally motivated CO column density. This cosmic-ray
ionization rate is thus not the rate necessary to lower the CO abundance from
the ISM level to the observed levels, but it is the cosmic-ray ionization rate
that has to be used to prevent the CO abundance from dropping further. We note
that the cosmic-ray ionization rate used does not impact the C2H abundance in
chemical models (Cleeves et al., 2018) and that the cosmic-ray ionization rate
used here is consistent with modeling of MAPS sources by Aikawa et al. (2021).

Appendix B shows the CO columns for difference C/O ratios for the three disks
compared to the CO columns derived from the data. The difference C/O ratios do
not impact the CO column in the model. Furthermore, the agreement between our
model CO columns and the results from (Zhang et al., 2021) indicates that the
amount of volatiles in the surface layer is representative for the disks
studied.

Table 1: Initial abundances for the chemical models Species | C/O = 0.47 | C/O = 1.0 | C/O = 2.0
---|---|---|---
H2 | 0.495 | 0.495 | 0.495
H | 0.01 | 0.01 | 0.01
H2O∗ | $1.53\times 10^{-4}$ | $10^{-10}$ | $10^{-10}$
CO∗ | $1.35\times 10^{-4}$ | $1.35\times 10^{-4}$ | $1.35\times 10^{-4}$
CH4∗ | $10^{-10}$ | $10^{-10}$ | $1.35\times 10^{-4}$
N2 | $1.07\times 10^{-5}$ | $1.07\times 10^{-5}$ | $1.07\times 10^{-5}$
S | $1.91\times 10^{-8}$ | $1.91\times 10^{-8}$ | $1.91\times 10^{-8}$
Si | $7.94\times 10^{-8}$ | $7.94\times 10^{-8}$ | $7.94\times 10^{-8}$
Fe | $4.27\times 10^{-9}$ | $4.27\times 10^{-9}$ | $4.27\times 10^{-9}$
Mg | $1.00\times 10^{-11}$ | $1.00\times 10^{-11}$ | $1.00\times 10^{-11}$

##  3 Composition of the disk gas

Figure 2: C2H column densities as function of radius for AS 209 (top), HD
163296 (middle) and MWC 480 (bottom). From left to right the figures show
models with C/O ratios of 0.47, 1.0 and 2.0, with the colors showing the
depletion of the small dust grains, from the fiducial value (yellow) to
1000$\times$ depleted (dark red). The black line with the grey error region
shows the column densities extracted from the data (Guzmán et al., 2021), the
black line transitions into a dotted line in the harder to probe inner 30 au.
The blue bars and arrows show the inner disk C2H column density upper limits
derived from the line profiles (see Appendix A). The vertical grey line shows
the location of the CO ice line in the models. The model C2H column densities
are integrated over both sides of the disk. High C/O ratios are necessary to
reproduce the observed C2H column densities.

Figure 2 shows the model and observed C2H column densities for the AS 209, HD
163296, and MWC 480 disks for C/O ratios of 0.47, 1.0, and 2.0, and the
different depletion factors for the small dust grains. Two dimensional C2H
abundances structures can be found in Appendix C, together with a discussion
on the chemical behavior of the C2H. As expected, the C/O ratio has a large
effect on the C2H column density, especially the jump from C/O = 1.0 to C/O =
2.0.

Figure 2 clearly shows that C/O ratios $\geq$ 2.0 are necessary to match the
high, $>10^{13}$ cm-2, C2H column densities observed in the inner 100–150 au
of the AS 209, MWC 480 and HD 163296 disks. In all sources, the peak in the
C2H column density distribution require the signficant small-grain depletion,
with the AS 209 model requiring a depletion in small-grains of 1000 over our
baseline model to reproduce the C2H column density. Maxima in the derived C2H
column have some co-locality with the first deep gap in the millimeter disk
and region of low CO abundance (Fig. 1 Law et al., 2021a; Zhang et al., 2021;
Guzmán et al., 2021). However, peaks in C2H emission (and column) are much
broader than the gaps seen in the millimeter disk. Interestingly the secondary
peak around $\sim$110 au in the HD 163296 C2H abundance structure does not
line up with the second strong dust gap around $\sim 85$ au. This is further
explored in Sec. 4.2.

The C2H column density drops sharply towards large radii ($>100$ au, $>150$ au
and $>125$ au for AS 209, HD 163296 and MWC 480, respectively). A constant C/O
ratio model does not share this abundance drop at this radius, implying that
the C/O ratio drops around these radii in these disks.

All three disks show a decrease in the C2H column density inwards of 50 au.
The AS 209 disk models show a dip in C2H column in this region, driven by the
decreasing CO, and thus available carbon abundance in the models. In HD 163296
and MWC 480, the C2H column density decreases in the region where the CO
abundance and thus available carbon content increases. This implies a drop in
C/O ratio in the inner regions of these disks. While this drop is expected to
happen at the CO ice line, it appears to happen at a smaller radius for both
the HD 163296 and MWC 480 disks. This is discussed in more detail in Sec. 4.3.

In summary, a high C/O ratio, together with a strong depletion of small dust
is necessary to match maxima in the derived C2H column. A model with a
constant C/O ratio and small-grain depletion is not able to match the full
behavior of the C2H column density radial profiles. A radial variation in C/O
ratio and small dust content of the disk atmosphere are necessary to reproduce
this behavior. Implications of this inference are discussed in Sec. 4.2 and
4.3 and for the AS 209 disk, this is studied in more detail in Alarcón et al.
(2021).

##  4 Discussion

###  4.1 C/O ratios from C2H in the literature

The inferred C/O ratio associated with C2H emission locations in these disks
are 2.0 or higher above most of the milli-meter disk. This is higher than
previously derived for other disks. Miotello et al. (2019) found that a global
C/O ratio of 1.5 reproduced the flux for the sample of Lupus disks studied,
significantly lower than the C/O ratios found for these disks. This
discrepancy is caused by the fact that the MAPS data resolve the disk emission
and reveal existing emission structure. In the gas with strong C2H emission, a
C/O ratio $\geq 2.0$ is necessary. However, the C2H column density is not
elevated ($>10^{14}$ cm-2) over the entire disk. Thus in models using disk-
integrated flux a lower, global C/O ratio, will be estimated. This would be
especially prominent for the three disks studied here as the C2H column
densities drop below $10^{12}$ cm-2 around 150 au (see, Guzmán et al., 2021),
which imply C/O ratios $<1$ for the majority of the disk area.

In the IM Lup disk, the C/O ratio was determined by Cleeves et al. (2018) to
be around 0.8, even lower than the C/O ratios found for most of the disk in
Miotello et al. (2019). When comparing the C2H radial profiles in Law et al.
(2021a) and C2H column densities in Guzmán et al. (2021) between the IM Lup
disk and the AS 209, MWC 480 and HD 163296 disks, it is clear that the IM Lup
disk has less C2H than the other disks by more than an order of magnitude. The
observationally derived C2H column density for the IM Lup disk is $\sim
10^{13}$ cm-2 between 70 and 230 au, which is of the same order as the AS 209
disk model column densities for a C/O of 0.47 and 1.0. The elemental
composition of the IM Lup disk is thus clearly different from the three disks
studied here.

The difference between the composition of the IM Lup disk and the other disks
studied here could be due to the young age of the IM Lup disk (Mawet et al.,
2012). The process responsible for turning the volatile rich and oxygen
dominated ISM composition gas into the volatile poor and carbon rich gas seen
in many other disks could then still be underway (Zhang et al., 2020b; Bergner
et al., 2020). This composition transition can either be the result more
efficient trapping of oxygen carrying species, e.g. water, CO, and CO2, as
ices coating mm-sized dust particles that are confined to the mid-plane (Krijt
et al., 2020), or the release of carbon from a refractory source in a
uniformly depleted surface layer (Bosman et al., 2021a). Alternatively, the IM
Lup disk has less pronounced substructures in the millimeter disk. This could
simply be a result from the young age, but it can also imply that these
substructures are, at least partly, responsible for the high C/O ratios
(Bergin et al., 2016; Bosman et al., 2021a).

###  4.2 Structure in the C2H column density

While it is clear that to match the high ($>10^{13}$ cm-2) column densities of
C2H in the AS 209, MWC 480, and HD 163296 disks a C/O $\geq 2$ is necessary,
it is not obvious what causes the radial structures in the C2H column density.
These can be caused by either a variation of C/O ratio when the C/O ratio is
below 2.0, a variation in small dust content when the C/O ratio is larger than
unity or a combination of both. The effect on the C2H column density due to
changes in the C/O ratio are generally larger than those due to changes in the
small dust content (Fig. 2).

The regions in which a depletion of small-grains must be invoked to match the
C2H column density is wider than the millimeter dust gaps seen in these three
disks. As the chemical timescales are short, $<$ 1000 yr (Bosman et al.,
2021a), diffusive spreading of C2H from the millimeter gap, which happens on
time-scales $>10^{4}$ yr, can be ruled out. This is thus suggestive of a wider
small-grain gap, around the millimeter dust gap, possibly due to the
millimeter dust rings acting as a small-grain sink in a manner similar to that
predicted from the midplane (Krijt & Ciesla, 2016).

In the HD 163296 disk, the C2H column density outside 70 au is consistent with
an elevated C/O ratio of 2.0 and factor $\sim 10$ of small dust depletion. At
50 au, the radius of a prominent gap in the millimeter continuum, the C2H
column density is more comparable to the model with a factor 100 depletion is
small-grains. This indicates that the UV penetrates deeper into the disk
around the millimeter dust gap. This is not seen in the second dust gap at 90
au, where there is a local minimum in the C2H abundance. A possible
explanation for the difference in C2H column density can be found in the
scattered light image. There is a bright ring in scattered light associated
with the 66 au sub-millimeter dust ring (e.g. Garufi et al., 2014; Monnier et
al., 2017; Muro-Arena et al., 2018). This ring of abundant small dust could
shadow the region of the second dust gap lowering the available UV flux in the
gap and thus lowering the C2H column density.

The C2H column density in the MWC 480 disk peaks around 70 au, the location of
the millimeter continuum dust gap (Long et al., 2019; Liu et al., 2019; Law et
al., 2021a). Similar to the gap at 50 au in the HD 163296 disk, high UV
penetration at the gap location – again suggestive of small-grain depletion –
is necessary.

The need for additional small dust depletion on top of the fiducial dust
models that already have a degree of dust depletion in the surface layers
implies gas-to-dust ratios in the surface layers of at least 10000 and up to
$10^{6}$ at the location of the C2H emission peak in AS 209 (Zhang et al.,
2021). It is thus possible that other processes are increasing the C2H
abundance above the levels, predicted by the chemical models. One intriguing
possibility is that strong vertical or radial mixing is operating, which could
cycle C2H2 and other larger carbon species from more shielded regions into the
25-75 au region. This would lead to an out of equilibrium chemistry with a
higher C2H abundance. This could be consistent with a large scale meridional
flow into the gaps and would be an interesting subject of further study.

###  4.3 A link between CO abundance and C/O

It has been suggested that a low CO abundance and a high C/O ratio have a
common dynamical or chemical origin, which should cause a correlation between
CO abundance and C/O ratio (Bergin et al., 2016). However, a relation between
C2H flux and CO abundances, as traced by ^13CO over millimeter dust flux has
not been found (Miotello et al., 2019). The relation has not been studied as a
function of radius in a disk, where, for example, the release of CO at the CO
ice line is expected to have a strong impact on the gas-phase C/O ratio (Öberg
et al., 2011).

For the MWC 480 and HD 163296 disks, the regions within and outside of the CO
ice line are resolved by the observations. The emission maps of C18O (and the
derived CO column) do not exhibit a strong response at the CO ice line
location predicted by the detailed disk physical models. Most directly, the CO
abundance at the CO ice line does not return to the ISM level (e.g. 10-4
relative to H2; Zhang et al., 2021, Fig. 1). This is consistent with a lack of
the expected C2H column density drop at the CO ice line. Without the return of
CO, the C/O ratio does not drop towards unity, but stays high. Closer to the
star, there is an increase in the CO abundance, the CO abundance reaching
greater than ISM levels at 50 au in MWC 480 and at 30 au in HD 163296.

The increase in CO abundance at these radii is accompanied by a drop C2H
column density see Fig. 1, consistent with a drop in C/O ratio (Fig. 2) due to
the return of the oxygen carried by CO into the gas. As mentioned the location
that the CO abundance rises is not where the CO ice line is expected, based on
the thermal structure in the models (Zhang et al., 2021; Calahan et al.,
2021). Temperatures in the region where the CO abundance rises are between 25
and 30 K in the standard MAPS models (Zhang et al., 2021). These temperatures
are in line with modeling by Calahan et al. (2021) for HD 163296 and empirical
temperature measurements from the CO isotopologue emission (Law et al.,
2021b). Furthermore the location where the C2H column drops below the C/O=2
models is at smaller radii than the rise in CO abundance. This implies that
when the CO abundance rises to close to the ISM value, then the C/O ratio
drops.

If the rise of CO abundance is due to CO coming off the grains, this would
imply a higher binding energy than the 850 K ($\sim$ 22 K iceline temperature,
e.g. Harsono et al., 2015) assumed in the models, or be due to a different
physical effect such as large grains drifting, and only fully releasing their
icy CO mantle further in. Exact effects are going to be very disk dependent. A
higher CO desorption temperature was also inferred for CO in TW Hya (Zhang et
al., 2017). This could be indicative for CO as desorbed on H2O or CO2 mixture
(Noble et al., 2012; He & Vidali, 2014). In the case of HD 163296 and MWC 480,
in which the CO content of the grains is expected to be high, this would
indicate that the vast majority of the $\sim$ 100 monolayers of CO are all in
high binding energy sites. To move the ice line by $\sim$40 au due to fast
radial drift grains between 1 and 10 cm are necessary to reach the right drift
speeds and desorption speed (Piso et al., 2015). This is larger than the 3 mm
grains that Sierra et al. (2021) need at these radii to fit multiband
continuum data.

Similar relation between CO and C2H abundance is seen in the outer disk of AS
209, where outside 100 au the CO abundance increases, and the C2H column
density drops, again implying a low C/O ratio when the CO abundance is high.
HD 163296 and MWC 480 also show a drop in C2H column density and inferred C/O
ratio outside $\sim$120 and $\sim$150 au respectively. This is not paired with
an increase in CO abundance, however. This implies that a high C/O ratio
happens only in the regions with low CO abundance. However, something in
addition to low CO abundance is needed to explain a high C/O ratio. This could
be related to the presence of an additional carbon source, such as the photo-
ablation of carbonaceous grains (Bosman et al., 2021a).

###  4.4 Composition of planet building material

To properly predict the composition of a planet forming at a certain location,
it is necessary to know the elemental composition of the building materials.
For any planet forming outside of 30 au in the AS 209, HD 163296, and MWC 480
disks, such as those inferred in the various gaps in these systems, it is now
possible to make some inferences on the composition of the gas and solids that
will go into these putative planets. For this discussion we will assume that
the bulk of the gas mass is accreted late in the disk lifetime such that the
composition of the disk gas inferred here is representative of the gas
accreted onto the planet. If planets accrete their gas mass early in the disk
lifetime, when accretion onto the disk still delivers significant pristine
material, planetary composition would be very similar to that of the host
star.

The C2H emission in these three disks is strong, but an emission surface
height cannot be derived unambiguously over the entire disk (Law et al.,
2021b). This either implies that the line is optically thin, and thus too weak
to measure a height or that it comes from below the ^13CO surface, which
results in a measured height that is consistent with the disk midplane. The
hyperfine ratios, from which the C2H column densities have been derived, show
that the lines are optically thick. This means that the C2H lines come from
deeper than the ^13CO emission. This is consistent with the disk regions where
the C2H height can be derived (Law et al., 2021b) and is in agreement with the
models, that have most of the column density between 1 and 2 scale-heights
(see Appendix C, the scale-heights in these disks at 10-200 au vary between
z/r of 0.06 and 0.1 depending on the disk, Zhang et al., 2021). At this
height, mixing with the midplane is efficient and happens on 10 kyr time-
scales for turbulent viscosity coefficients of $\alpha\approx 10^{-3}$
(Ciesla, 2010). As such, it is unlikely that strong vertical elemental
abundance gradients exist, so the high C/O abundances and low O/H abundances
necessary to explain the C2H emission likely hold for the disk midplane as
well. Furthermore, if accretion onto a planet happens through meridional
flows, the gas accretion onto the planet will actually sample the vertical
height from where the C2H emission originates (Tanigawa et al., 2012;
Morbidelli et al., 2014); such flows have been observed in the higher layers
of the disk with ^12CO in the HD 163296 disk by Teague et al. (2019). As these
are the flows that feed the planet, gas from the C2H layer emitting layer is
expected to contribute significantly to the planetary accretion after gap
opening (Morbidelli et al., 2014; Cridland et al., 2020).

The amount of small-grains in the disk atmosphere, that can accrete with the
gas onto the planet, is strongly reduced from the ISM level of 1% of the total
mass. This happens both globally in the disk surface due to grain growth and
settling, and locally, as the inferred C2H column densities necessitate more
UV penetration in certain disk locations. The combined low CO abundance, and
depleted small dust thus imply that most of the ISM carbon and oxygen, both
volatile and refractory, is not present in gas accreting onto planets that
have reached pebble isolation mass.

Gas giants that accrete most of their atmospheres after reaching the pebble
isolation mass thus obtain envelopes, with substellar C/H and O/H, and high
($\gg 1.0$) C/O ratio compositions, unless efficient release of volatiles from
the core or late enrichment by planetesimals takes place. These potential
planets are formed at large radii, where CO can be depleted efficiently ($>$
50 au radii for HD 163296 and MWC 480). If these planets do not migrate from
their formation location, they are prime targets for composition analysis by
direct imaging with the James Webb Space Telescope, the most notable example
being the planets in the HR 8799 system. Substellar carbon and oxygen
abundances and a high C/O composition would distinguish planets formed through
pebble or core accretion from planets formed as a result of a gravitational
instability. The latter are expected to have a stellar or superstellar C/H and
O/H ratios with a stellar or substellar C/O ratio (e.g. Ilee et al., 2017).

Compositions of planets at large radii so far do not show the signature
predicted from the disk observations. $\beta$ Pic b has a low derived C/O
ratio, which is expected to be close or below the stellar C/O ratio (Gravity
Collaboration et al., 2020). This rules out a formation scenario in which one
of the $>40$ au putative planets in the disks studied here migrates inward to
9 au (Lagrange et al., 2020), unless this planet accreted $>$40 M⊕ of oxygen-
rich ice, or mixed a similar amount of ice from the core into the atmosphere
(Gravity Collaboration et al., 2020). Three other large radii ($>50$ au)
planets have their water abundance measured ($\kappa$ And b, HR8799 b and
HR8799 c Todorov et al., 2016; Lavie et al., 2017; Madhusudhan, 2019). The
water abundances are higher than the disk atmosphere gas, ice and refractory
oxygen abundances combined, by a factor 2 to 100, for the three disks studied
here. If these planets are the successors of the putative planets in these
disks, a significant amount of disk water ice needs to make it into the
atmosphere, at least 30 $M_{\oplus}$ for $\kappa$ And b and HR 8799 b, and
around 100 $M_{\oplus}$ for HR 8799 c (Madhusudhan, 2019). This would imply
very massive cores (60 - 200 $M_{\oplus}$) and very efficient core mixing,
6-20 $M_{\oplus}$ Myr-1 planetesimal accretion rates for a 10 Myr disk age, or
a gravitational instability origin from moderately (factor 1-3) water ice
enhanced core. The low water abundance measured for many transiting exoplanets
is comparable to the low total oxygen abundance in the gas at large ($>50$ au)
radii in the AS 209, HD 163296 and MWC 480 disks (Madhusudhan, 2019; Welbanks
et al., 2019). This could point at an outer disk origin for these hot
Jupiters, however without constraints on the C/O ratio this remains
speculation. A high C/O $\gtrsim 1.0$ would strengthen the case for an outer
disk origin for hot Jupiters.

##  5 Conclusions

We have studied the behavior of the C2H column densities above the millimeter
pebble disks orbiting AS 209, MWC 480, and HD 163296, and compared these to
C2H column densities to source specific thermochemical models calculated using
DALI (Bruderer et al., 2012; Bruderer, 2013) with an extended gas-grain
chemical network. We find that high ($\sim 2.0$) C/O ratios are necessary to
explain the strong C2H emission. The high column densities ($>10^{15}$ cm-2)
imply that there is an additional effect at play. One option is more efficient
UV penetration, leading to even higher C2H column densities. The high, but
localized, C2H column densities explain why these resolved observations need
locally higher C/O ratios than global models, like those from Miotello et al.
(2019).

Furthermore, a relation between the C/O ratio and CO abundance appears to
exist, with a higher CO abundance leading to a lower C/O ratio. This is
especially the case when looking at the inner 100 au of the HD 163296 and MWC
480 disks. The transition to an enhanced CO abundance and diminished C/O
ratios seems not to happen at the CO ice line, but further in.

The C/O ratio and the gas-to-dust ratio are elevated above stellar and ISM-
levels (respectively) along the radial extent of the pebbled disk, except in
the regions where the CO abundance is high (inner $\sim$30 au for HD 163296
and MWC 480). This includes the regions that most of the dust gaps are
located. The gas accreting onto the possibly forming planets is thus strongly
depleted of volatile and refractory carbon and oxygen, with a strongly super-
stellar C/O ratio. In the absence of core-envelope mixing and envelope
enrichment by planetesimal collisions, this would lead to a high C/O but
generally volatile depleted giant planets. Comparing this prediction to the
composition of gas giants at large orbits, such as will be inferred by the
James Webb Space Telescope, will be able to point at the origin of these large
orbit planets.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2018.1.01055.L.
ALMA is a partnership of ESO (representing its member states), NSF (USA) and
NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. A.D.B.,
E.A.B., F.A., and K.I.Ö. acknowledge support from NSF AAG grant No. 1907653.
K.Z. acknowledges the support of the Office of the Vice Chancellor for
Research and Graduate Education at the University of Wisconsin – Madison with
funding from the Wisconsin Alumni Research Foundation. K.Z., J.B.B., I.C.,
J.H. & K.R.S. acknowledge support from NASA through the NASA Hubble Fellowship
grants, HST-HF2-51401.001, #HST-HF2-51429.001-A, HST-HF2-51405.001-A, #HST-
HF2-51460.001-A & #HST-HF2-51419.001 awarded by the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., for NASA, under contract NAS5-26555. M.L.R.H. acknowledges
support from the Michigan Society of Fellows K.I.Ö. acknowledges support from
the Simons Foundation (SCOL No. 321183). V.V.G. acknowledges support from
FONDECYT Iniciación 11180904 and ANID project Basal AFB-170002. C.W.
acknowledges financial support from the University of Leeds, STFC and UKRI
(grant numbers ST/R000549/1, ST/T000287/1, MR/T040726/1). Y.A. acknowledges
support by NAOJ ALMA Scientific Research Grant Code 2019-13B, and Grant-in-Aid
for Scientific Research 18H05222 and 20H05847. S. M. A. and J. H. acknowledge
funding support from the National Aeronautics and Space Administration under
Grant No. 17-XRP17 2-0012 issued through the Exoplanets Research Program.
A.S.B acknowledges the studentship funded by the Science and Technology
Facilities Council of the United Kingdom (STFC). G.C. is supported by NAOJ
ALMA Scientific Research grant Code 2019-13B. L.I.C. gratefully acknowledges
support from the David and Lucille Packard Foundation and Johnson & Johnson’s
WiSTEM2D Program. J.D.I. acknowledges support from the Science and Technology
Facilities Council of the United Kingdom (STFC) under ST/T000287/1. C.J.L.
acknowledges funding from the National Science Foundation Graduate Research
Fellowship under Grant No. DGE1745303. R.L.G. acknowledges support from a CNES
fellowship grant. Y.L. acknowledges the financial support by the Natural
Science Foundation of China (Grant No. 11973090). F.L. & R.T. acknowledge
support from the Smithsonian Institution as a Submillimeter Array (SMA)
Fellow. F. M. acknowledges support from ANR of France under contract
ANR-16-CE31-0013 (Planet-Forming-Disks) and ANR-15-IDEX-02 (through CDP
”Origins of Life”). H.N. acknowledges support by NAOJ ALMA Scientific Research
Grant Code 2018-10B and Grant-in-Aid for Scientific Research 18H05441. T.T. is
supported by JSPS KAKENHI Grant Numbers JP17K14244 and JP20K04017. Y.Y. is
supported by IGPEES, WINGS Program, the University of Tokyo.

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##  Appendix A C2H column in the inner 30 au

To set limits on the C2H column from the inner regions of the disk, we use the
kinematic information in the C2H line profile to determine the flux that is
actually coming from the inner disk. First we filter out flux that seems to be
emitted from small radii in the image, but is instead flux from larger radii,
smeared to the inner regions by the beam. To accomplish this we use the method
outlined in Bosman et al. (2021b) to extract spectra from the image cube and
then transform these inner disk spectra into radial profiles using the
kinematical information assuming the disk is in Keplerian rotation. Instead of
using both the red and blue-shifted line wings as done for CO, we only use the
uncontaminated line wing for C2H. Radial profiles are created for the four
strong components of the C2H $N$=3–2 transition ($J$=7/2–5/2, $F$=4–3;
$J$=7/2–5/2, $F$=3–2; $J$=5/2–3/2, $F$=3–2 and $J$=5/2–3/2, $F$=2–1). The
weaker $N$=3–2, $J$=5/2–3/2, $F$=2–2 line does not contaminate the spectrum of
the nearest strong line. Figure 3 shows the redshifted wing of the $N$=3–2;
$J=$7/2-5/2, $F=$4–3 transition together with the extracted radial profile and
inner region upper limit for AS 209.

Figure 3: Left:

Redshifted line wing of the C2H $N$=3–2; $J=$7/2-5/2, $F=$4–3 transition in AS
209 (black). The red line shows a model fit to the flux at $>$2.6 km s-1 from
source velocity, corresponding to $<$55 au for AS 209 and the blue line shows
the profile of the flux upper limit in the inner region. Right: The fitted
radial profile (red) and flux upper limit (blue) derived from the data. The
grey line shows relation between the extend of an emitting area and the
minimal, constant flux that would be detectable from that area given the noise
in the data. This is our sensitivity limit estimate. The point where the
fitted radial profile dips under this sensitivity limits is where we set the
flux upper limit for the inner most region.

To account for the loss of sensitivity by only having one line-wing per fit,
we increase the radial grid spacing in the radial profile fitting to 10 au.
The emission is weak and within 30 au we are mostly constrained to estimating
upper limits. Only for the AS 209 disk can some flux be ascribed to the 20-30
au region. The radial extend as well as the flux upper limit derived are taken
from the radial profiles and these are converted into a column upper limit for
the inner disk. To convert flux into column densities we follow Bergner et al.
(2021) taking the quantum values for C2H from the JPL database (see Guzmán et
al. (2021)). To convert flux to column, gas temperature and continuum emission
temperature are necessary. For the gas temperature we assume the temperature
from Law et al. (2021b) for ^12CO $J$= 2–1 at 30 au and for the continuum we
take the brightness temperature at 30 au from Sierra et al. (2021), using disk
center values changes derived columns less than a factor 2. Values are given
in Table. 2. We also assume LTE and that the line width is fully thermal. Fig.
4 compares the derived limits from the line profiles to the columns derived
from the images.

Table 2: Temperatures used for the C2H column derivation Source | Gas temperature (K) | Dust emission temperature (K)
---|---|---
AS 209 | 30.2 | 12.4
HD 163296 | 53.8 | 22.7
MWC 480 | 69.1 | 25.5
Figure 4: Comparison of the image derived C2H column (black, Guzmán et al.,
2021) and the column density derived from the line profiles (blue) in the
inner 30 au for the AS 209, HD 163296 and MWC 480 disk. The analysis in the
image plane is overestimating the C2H column in the inner disk.

##  Appendix B Tracing the gaseous volatile content with CO

Figure 5:  CO column densities for the fiducial dust models for different C/O
ratios (blue) compared to the derived CO column densities from the data
(black, Zhang et al., 2021). Vertical grey lines show the CO ice line location
extracted from the RAC2D models (Zhang et al., 2021; Calahan et al., 2021).

Figure 5 compares the CO column densities derived by Zhang et al. (2021) and
the CO column densities extracted from the gas-grain network for the three
different C/O ratios tested here for the thermochemical models with undepleted
small dust. The CO column densities in the DALI models match well for models
of the MWC 480 and HD 163296 disks, but the AS 209 DALI models produce higher
CO column densities than in the AS 209 RAC2D model.

The AS 209 RAC2D model has a significant amount of carbon in CO2 ice, while in
the DALI models CO2 is barely formed, leaving more carbon in gas-phase CO near
the midplane. This is due to the more simplified implementation of the grain
surface chemistry in RAC2D (Du & Bergin, 2014). This difference is only seen
in the AS 209 model due to the larger X-ray luminosity and lower UV luminosity
in the AS 209 model compared to the HD 163296 and MWC 480 models. In the
latter two models, the low X-ray flux and higher UV flux suppresses the
formation of CO2 in the RAC2D models, putting them in line with the DALI
models.

Lowering the carbon and oxygen abundances in the DALI AS 209 models by a
factor of 2-3 within 120 au would lead to a better match of the DALI CO column
to the CO column that is used to reproduce the observed emission in the RAC2D
models. This drop in carbon and oxygen abundance would only very slightly
lower the C2H abundance and would not impact our conclusions on the C/O ratios
of these disks. Therefore we will continue to use the CO depletion factors as
derived for AS 209 in Zhang et al. (2021).

The small variation between the DALI models with different C/O ratios
showcases the chemical stability of CO. In both oxygen and carbon-rich
environments CO incorporates either the vast majority of the carbon, or of the
oxygen, whatever is in short supply. CO remains the most abundant observable
molecular carrier of elemental C and O. The CO column is thus a good tracer
for the gaseous volatile content at a large range of C/O ratios.

##  Appendix C C2H abundance structures

Figures 6, 7 and 8 show the C2H abundance structures for some of the AS 209,
HD 163296 and MWC 480 models that feed into the column densities shown in Fig.
2. There is a clear difference between the AS 209 disk and the MWC 480 and HD
163296 disks at low C/O ratios, with a higher C2H abundance in the AS 209
disk. This is driven by different levels of UV and X-ray flux in these
sources. The high X-ray flux of AS 209 allows for more efficient destruction
of CO, followed by CH4 and H2O formation. The lower gas-to-small-dust ratio in
the surface layer produces less UV penetration, so CH4 and H2O are not quickly
reverted back to CO: this allows for higher C2H abundances at low C/O ratios.
This also explains why the C2H column density strongly drops in AS 209 for a
C/O ratio of 0.47 when the small dust is depleted, the deeper penetrating UV
destroys the CH4 and H2O created by X-rays, increasing the amount of atomic
oxygen in the gas and lowering the amount of carbon not in CO. The low X-ray
flux and larger gas-to-dust ratios in the fiducial HD 163296 and MWC 480 disk
models more efficiently force the carbon into CO. Only when carbon is more
abundant than oxygen, does the C2H production take off.

Changes in the predicted C2H column densities due to modifications of the
small dust distribution are smaller than the effect of varying the C/O ratio
in all three disk models. For C/O $\leq$ 1.0, the C2H column density is not
strongly dependent on the small-grain column and no uniform change with a
varying small-grain content is seen. At C/O = 2, the models with different
small-grain abundances in the surface layers clearly follow the small-grain
abundance.

This nonlinear interplay between the small dust abundance and C/O ratios is
linked to the carbon source for the C2H. At C/O $\leq$ 1.0, the carbon for C2H
needs to be released from CO. As CO efficiently self-shields, the amount of CO
that is dissociated does not strongly depend on the continuum UV penetration,
and is thus not strongly dependent on the small-grain abundance. At high C/O,
the carbon comes from CH4 and other hydrocarbons deeper into the disk.
Increasing UV penetration will make it easier to extract carbon from these
species, and thus increases the C2H abundance (see Bosman et al., 2021a, for a
more complete discussion).

Figure 6: AS 209 C2H abundance structure for the fiducial small dust (top) and
factor 100 depleted small dust (bottom) for C/O ratios of 0.47, 1.0 and 2.0
(left to right).  Figure 7: As Fig. 6, but for HD 163296.  Figure 8: As Fig.
6, but for MWC 480.