# Modelling predicts a molecule-rich disk around the AGB star L2 Puppis

M. Van de Sande,1,2 C. Walsh,1 T. Danilovich,3,4,5 F. De Ceuster,5 and T.
Ceulemans5
1School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
2Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The
Netherlands
3School of Physics & Astronomy, Monash University, Wellington Road, Clayton
3800, Victoria, Australia
4ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Clayton 3800, Victoria, Australia
5Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The nearby oxygen-rich AGB star L2 Pup hosts a well-studied nearly edge-on
disk. To date, disks around AGB stars have not been chemically studied in
detail. By combining a parameterisation commonly used for protoplanetary disks
and archival ALMA observations, we retrieved an updated density and
temperature structure of this disk. This physical model was then used as input
to the first chemical model of an AGB disk. The model shows that the physical
structure of the disk has a large impact on its chemistry, with certain
species showing large changes in column density relative to a radial outflow,
indicating that chemistry could be used as a tracer of disks that cannot be
directly imaged. Despite its oxygen-rich nature, the daughter species formed
within the disk are surprisingly carbon-rich. Two chemical regimes can be
distinguished: cosmic-ray induced chemistry in the midplane and photochemistry
induced by the interstellar radiation field in the outer regions. Certain
complex organic molecules are formed in the midplane. This occurs via gas-
phase chemistry only, as the disk is too warm for dust-gas chemistry. The
photochemistry in the outer regions leads to the efficient formation of (long)
carbon-chains. The predictions of the model allow us to tentatively put the
disk’s age $\lesssim 10^{5}$ yr. Additional observations are necessary to
better constrain the physical structure of L2 Pup’s disk and are essential to
test the predictions made by the chemical model. Our exploratory work paves
the way for a more general study of the chemistry of AGB disks.

###### keywords:

stars: individual: HD 56096, L2 Puppis – stars: AGB and post-AGB –
circumstellar matter – astrochemistry – molecular processes – radiative
transfer

††pubyear: 2015††pagerange: Modelling predicts a molecule-rich disk around the
AGB star L2 Puppis–C

##  1 Introduction

The asymptotic giant branch (AGB) phase near the end of the lives of stars
with an initial mass up to 8 M⊙ is characterised by vigorous mass loss. AGB
stars lose their outer layers via a stellar wind or outflow at a rate between
$10^{-8}$ and $10^{-4}$ M⊙ yr-1, creating an expanding circumstellar envelope
(CSE, Habing & Olofsson 2003; Höfner & Olofsson 2018). CSEs are rich
astrochemical environments, with close to 100 different molecules and some 15
types of newly formed dust grains detected so far (Decin, 2021). Spherically
symmetric outflows appear to be the exception rather than the rule.
Asymmetrical structures are ubiquitously observed, ranging from small-scale
asymmetries, such as density-enhanced clumps (e.g., Leão et al., 2006; Khouri
et al., 2016; Velilla-Prieto et al., 2023), to large-scale structures, such as
spirals (e.g., Mauron & Huggins, 2006; Maercker et al., 2012) and disks (e.g.,
Kervella et al., 2016). These large-scale structures are thought to be caused
by binary interaction with (sub)stellar companions. Circumbinary disks are
expected around younger, lower mass-loss rate AGB stars, evolving into spirals
as the mass-loss rate increases and the companion’s orbit widens during the
AGB phase (Decin et al., 2020).

The classic spherically symmetric one-dimensional chemical kinetics model of
the CSE is hence applicable to only a minority of outflows. The effects of the
UV field of a stellar companion and a clumpy substructure on the chemistry
throughout the outflow have been included in chemical models of the CSE (Van
de Sande et al., 2018; Van de Sande & Millar, 2022; Van de Sande et al.,
2023). These models show that chemistry can be used to unveil a hidden stellar
companion (Siebert et al., 2022) and retrieve its orbital properties
(Danilovich et al., 2024). The influence of large-scale density structures on
the CSE’s chemistry requires specialised chemical models. So far, models have
been developed for the density-enhanced shells in the outflow of IRC+10216
(Brown & Millar, 2003; Cordiner & Millar, 2009; Agúndez et al., 2017), but no
general models applicable to a larger set of AGB stars exist. The chemistry of
disks around AGB stars has not been studied in detail.

The best-studied AGB disk is that around the oxygen-rich AGB star L2 Pup, the
second-closest AGB star at a distance of 64 pc (van Leeuwen, 2007). Optical
and infrared observations have shown the clear presence of an almost edge-on
compact dusty disk with an inner dust rim at 6 au, spanning to around 15 au.
Loops and plumes extending above the disk have also been identified (Ireland
et al., 2004; Kervella et al., 2014; Lykou et al., 2015; Ohnaka et al., 2015;
Kervella et al., 2015). ALMA observations probed the gaseous disk, which has
an inner rim at 2 au, and revealed a tentative planetary companion with a mass
of $12\pm 16$ MJ. This planet is probably not formed within the disk, but is
instead rather part of L2 Pup’s (first generation) planetary system (Chen et
al., 2016; Kervella et al., 2016). The physical structure of the disk has been
proposed to be similar to that of protoplanetary disks (PPDs), albeit with a
higher temperature in the midplane as it is assembled from warm stellar
outflow material (Homan et al., 2017).

In this paper, we develop a two-dimensional chemical model of L2 Pup’s disk:
the first such model of a disk around an AGB star. This exploratory work
probes the unique astrochemical regime of a hot and dense disk, irradiated by
the interstellar radiation field. By determining the effects of the physical
disk structure on the chemistry around L2 Pup, we can identify the chemical
differences with a spherically symmetric O-rich outflow and establish whether
the parent species are redistributed into different carriers. Such differences
can be used as chemical tracers of disks that are not as easily resolved as
the close-by L2 Pup. Additionally, the evolution of the disk’s chemical
structure over time can be used to determine the age of the disk.

In Sect. 2, we use archival ALMA data to retrieve the disk’s density and
temperature structure using a parametric model commonly used for PPDs. This
physical structure is then used as input to the chemical model in Sect. 3,
where we also show the chemical modelling results. The physical and chemical
modelling results are discussed in Sect. 4, followed by our conclusions in
Sect. 5.

##  2 Physical model

L2 Pup was observed by ALMA during Cycle 3 for project 2015.1.00141.S (PI
Pierre Kervella) in November 2015. The reduction of the Band 7 observations is
described in Kervella et al. (2016), and we use that dataset in the present
work. The resulting data have an angular resolution better than 15 mas and a
maximum resolvable scale of 200 mas. The $J=3-2$ lines of ^12CO and ^13CO from
the dataset are presented in Homan et al. (2017). The data cubes have a
spectral resolution of 0.22 km s-1 and an rms noise level of 2.5 and 2.6 mJy
beam-1, respectively. The channel maps of the lines are presented here in
Appendix A, now with beam information.

Homan et al. (2017) derived a physical model of L2 Pup’s disk from the ^12CO
and ^13CO $J=3-2$ lines. The model from that work, although provided by the
first author, was unable to be reproduced. Given the similarity of the disk to
PPDs, we opted to remodel the data using a parametric model commonly used for
PPDs.

The parametric model is described in Sect. 2.1. Sect. 2.2 describes the 3D
line radiative transfer code used, Magritte. The parameter space explored is
laid out in Sect. 2.3, the retrieved physical structure of the disk is
presented in Sect. 2.4.

###  2.1 Parametric model of a protoplanetary disk

We use the parametrisation of Williams & Best (2014), which assumes a disk
surface density profile based on the solution for an axisymmetric, steady-
state viscous accretion disk in hydrostatic equilibrium (e.g., Lynden-Bell &
Pringle, 1974; Hartmann et al., 1998). The surface density of the disk is
described by

$\Sigma(r)=\Sigma_{0}\left(\frac{r}{r_{0}}\right)^{-\gamma}\
\exp\left(-\left(\frac{r}{r_{0}}\right)^{2-\gamma}\right),$ (1)

where $r_{0}$ is a disk reference radius and $\gamma$ describes the radial
dependence. $\Sigma_{0}$ gives the global normalisation to the gas mass at
$r_{0}$, written as

$\Sigma_{0}=(2-\gamma)\ \frac{M_{\mathrm{gas}}}{2\pi r_{0}^{2}}\
\exp\left(\frac{r_{\mathrm{in}}}{r_{0}}\right)^{2-\gamma},$ (2)

with $M_{\mathrm{gas}}$ the disk’s total gas mass and $r_{\mathrm{in}}$ its
inner radius. Assuming hydrostatic vertical balance in the disk, the density
structure of the disk is described by

$\rho(r,z)=\frac{\Sigma(r)}{H_{p}(r)\
\sqrt{2\pi}}\exp\left(-\frac{z^{2}}{2H_{p}(r)^{2}}\right),$ (3)

with $H_{p}$ the pressure scale height derived from the midplane temperature.
This scale height is given by the ratio between the speed of sound, $c_{s}$,
and the Keplerian angular frequency $\Omega_{K}$, or,

$H_{p}=\frac{c_{s}}{\Omega_{K}}=\sqrt{\frac{k_{B}\ T_{\mathrm{mid}}(r)\
r^{3}}{G\ M_{*}\ \mu m_{H}}}.$ (4)

Here, $M_{*}$ is the stellar mass, $k_{B}$ is the Boltzmann constant, $G$ the
gravitational constant, $m_{H}$ the mass of the hydrogen atom, and $\mu$ the
mean molecular mass.

The midplane temperature profile is parametrised by a power law,

$T_{\mathrm{mid}}(r)=T_{\mathrm{mid,1}}\left(\frac{r}{1\mathrm{au}}\right)^{-q},$
(5)

with $T_{\mathrm{mid,1}}$ the temperature at 1 au and $q$ the power-law
exponent. Similarly, the atmospheric temperature surrounding the disk is
parametrised by

$T_{\mathrm{atm}}(r)=T_{*}\left(\frac{r}{1\mathrm{au}}\right)^{-\epsilon},$
(6)

with $T_{*}$ the stellar temperature and $\epsilon$ the power-law exponent.
The vertical temperature profile connects Eqs (5) and (6) by a sine function:

$T(r,z)=\begin{cases}T_{\rm mid}+(T_{\rm atm}-T_{\rm
mid})\left[\sin\left(\frac{\pi z}{2z_{q}}\right)\right]^{2\delta}&\mbox{if
}z<z_{q}\\\ T_{\rm atm}&\mbox{if }z\geq z_{q}\end{cases},$ (7)

where $\delta$ describes the steepness of the temperature profile and $z_{q}$
describes the height at which the disk reaches the atmospheric value.
Following Williams & Best (2014), we fix $\delta=2$ and $z_{q}=4H_{p}(r)$.

For a given stellar mass, the physical structure of the disk is described by
eight parameters: four for the density profile,
$\\{\gamma,r_{\mathrm{in}},r_{0},M_{\mathrm{gas}}\\}$, and four for the
temperature profile, $\\{T_{\mathrm{mid,1}},T_{\mathrm{atm,1}},q,\epsilon\\}$.

###  2.2 Magritte: 3D line radiative transfer

Magritte111Available at https://github.com/Magritte-code/Magritte, we used
version 0.3.2. is an open-source 3D non-LTE line radiative transfer code,
mainly used for creating synthetic spectral line observations (De Ceuster et
al., 2020a; De Ceuster et al., 2020b, 2022). We initialise the Magritte model
by defining the model on a uniform $60\times 60\times 30$ au grid. For each
point, we define the temperature, velocity, turbulent velocity, H2 density and
CO density. The grid is then resampled to speed up computation by limiting the
allowed variation of the density, which we evaluated at the uniform grid
positions (Ceulemans et al., in prep.). After model setup, the radiation field
is computed assuming non-LTE by taking into account the first seven rotational
CO lines. In this way, the energetic state of the CO gas is determined self-
consistently. Afterwards, we create spectral line images for the 12CO and 13CO
$J=3-2$ lines.

###  2.3 Parameter space of the physical model

Table 1 shows the parameters of the physical model along with the values which
best reproduce the integrated emission profiles. Based on previous
observations, we fixed the inner radius of the disk, velocity profile,
temperature profile of the disk’s atmosphere, the fractional abundance of
^12CO, and the stellar and disk mass. These parameters are listed in the top
rows of Table 1. The stellar radius is fixed at 1 au. The inner radius of the
disk, $r_{\mathrm{in}}$, is fixed at 2 au (Kervella et al., 2016). The
velocity profile is assumed to be Keplerian from the inner radius out to the
inner rim of the dusty disk at 6 au. Beyond 6 au, the velocity profile is sub-
Keplerian with a power-law exponent of 0.853 (Kervella et al., 2016). The
turbulent velocity is fixed to 0.5 km s-1 (Homan et al., 2017). The
temperature profile of the atmosphere is fixed at $T_{\mathrm{atm,1}}=2800$ K
with a power-law exponent of 0.65 (Danilovich et al., 2015). The fractional
abundance of ^12CO was taken to be $1\times 10^{-4}$ with respect to H2 (Homan
et al., 2017). The total gas mass of the disk, $M_{\mathrm{gas}}$, is fixed at
$2.5\times 10^{-4}$ M⊙ following Kervella et al. (2015) and assuming a dust-
to-gas mass ratio of 0.01. The stellar mass, $M_{*}$, is fixed to $0.659\
\times$ M⊙, as derived by Kervella et al. (2016).

The other parameters were allowed to vary and are listed in the bottom rows of
Table 1. Their starting points were based on the model of Homan et al. (2017).
The midplane temperature, $T_{\mathrm{mid,1}}$, was varied in increments of
100 K, the power-law of the midplane temperature, $q$, in increments of 0.05,
the characteristic disk radius, $r_{0}$, in increments of 1 au, the parameter
determining the surface density (Eq. 1), $\gamma$, in increments of 0.5, and
the ^13CO abundance in increments of $1\times 10^{-5}$ w.r.t. H2.

###  2.4 Physical structure of the disk

The model calculation was constrained by comparing slices along the disk
midplane through the moment 0 (integrated intensity) maps of the observed
lines. The moment 0 maps are presented in Kervella et al. (2016) (their Figs.
A1 and B1). The slices were chosen so that they go through the emission peaks
in the East and West sides of the disk as the disk’s position angle is not
zero. We choose to use this metric as a radial slice along the major axis of
the disk will capture well the radial behaviour of the emission without any
complication that may arise from deprojection of the emission from this highly
inclined disk. The slice through the moment 0 map of ^12CO is centred on
(07h13m32$\aas@@fstack{s}$477,
-44∘38$\arcmin$17$\aas@@fstack{\prime\prime}$845) at an angle of
$9.53^{\circ}$, that through the ^13CO moment 0 map is centred on
(07h13m32$\aas@@fstack{s}$475,
-44∘38$\arcmin$17$\aas@@fstack{\prime\prime}$843) at an angle of
$16.0^{\circ}$. The slices are different as the ^12CO and ^13CO probe
different layers within the disk.

We first modelled the ^12CO line by reproducing the slice through its moment 0
map. Good models were determined by minimising the chi-squared value of the
fit to the slice. For these models, we then calculated the corresponding ^13CO
model, varying the ^13CO abundance as an additional parameter while keeping
the others fixed and calculated the chi-squared value of the fit to the slice
through the ^13CO moment 0 map. The ^12CO/^13CO ratio is fixed throughout the
disk.

Our best-fitting model provides the best reproduction of the ^12CO moment 0
slice, with a chi-squared value of 3.92. A ^13CO abundance of $2\times
10^{-5}$ results in the fourth-best fit in our sampled parameter space to the
^13CO moment 0 slice, with $\chi^{2}=1.76$. A larger ^13CO abundance of
$3\times 10^{-5}$ results in the third-best model, with $\chi^{2}=1.74$.
However, this would yield a ^12CO/^13CO ratio of 3.33. Since this ratio is
lower than expected from observations (Ramstedt et al., 2014) and the
improvement to reproducing the observations is marginal, we chose the model
with a ^13CO abundance of $2\times 10^{-5}$ as our best model. Note that the
model that best reproduces the ^13CO moment 0 slice, with the lowest chi-
squared value of 1.65, corresponds to the fourth-best model to the ^12CO
moment 0 slice, with $\chi^{2}=4.19$.

Together with a visual inspection of the moment 0 maps, channel maps, and line
profiles, we chose the best-fitting model to the ^12CO moment 0 slice with a
^13CO abundance of $2\times 10^{-5}$ as our final model. Its parameters are
listed in Table 1. Figure 1 shows the slices through the moment 0 maps of the
^12CO and ^13CO $J=3-2$ lines along with the Magritte model results. The
negative flux in at the centre of the observed lines is due to line absorption
by the molecular gas located in front of the star. The Magritte model’s moment
0 and channel maps are shown in Appendix B.

Fig. 2 shows the density and temperature profile of the best-fitting model. We
find that L2 Pup’s disk has a surface density profile $\Sigma(r)\sim r^{-1}$
and an $r_{0}$ of 6 au. This radius corresponds to the radius where the disk’s
velocity profile changes from Keplerian to sub-Keplerian (Kervella et al.,
2016) and where the surface density steepens significantly from a power law
(Williams & Cieza, 2011). Its midplane is warm with $T_{\mathrm{mid,1}}=900$
K, and has a shallow temperature profile characterised by $q=0.2$. The ^13CO
abundance w.r.t. H2 is $2\times 10^{-5}$, yielding a ^12CO/^13CO ratio of 5.

Table 1: The physical disk model for L2 Pup that best reproduces the data
following the parametrisation of Williams & Best (2014). The top parameters
were fixed based on previous observations. The bottom parameters were obtained
from modelling the 12CO and 13CO $J=3-2$ data. Their ranges are described in
Sect. 2.3.

Atmospheric temperature, $T_{\mathrm{atm,1}}$ | 2800 K | (1)
---|---|---
Exponent power law $T_{\mathrm{atm}}(r)$, $\epsilon$ | 0.65 | (2)
Inner radius of the disk, $r_{\mathrm{in}}$ | 2 au | (2)
Velocity profile up to 6 au | Keplerian | (2)
Velocity profile beyond 6 au | sub Keplerian, $\propto r^{0.853}$ | (2)
Turbulent velocity | 0.5 km s-1 | (3)
^12CO abundance |  $1\times 10^{-4}$ w.r.t. H2 | (3)
Total gas mass of the disk, $M_{\mathrm{gas}}$ |  $2.5\times 10^{-4}$ M⊙ | (4)
Stellar mass, $M_{*}$ |  $0.659\ \times$ M⊙ | (2)
Midplane temperature, $T_{\mathrm{mid,1}}$ | 900 K |
Power-law exponent $T_{\mathrm{mid}}(r)$, $q$ | 0.2 |
Characteristic disk radius, $r_{0}$ | 6 au |
Power-law exponent surface density $\Sigma(r)$, $\gamma$ | -1.0 |
^13CO abundance |  $2\times 10^{-5}$ w.r.t. H2 |

References. (1) Danilovich et al. (2015); (2) Kervella et al. (2016);
(3) Homan et al. (2017); (4) Kervella et al. (2015).

Figure 1: Slice through the moment 0 map of 12CO (left) 13CO $J=3-2$ (right)
and along the major axis of the disk (blue) together with the Magritte
modelling results (black). The range marked in blue corresponds to the rms
error of the moment 0 map of the data. Model parameters are listed in Table 1.
Figure 2: Density (upper panel) and temperature (lower panel) of the Magritte
model that best reproduces the observations of L2 Pup’s disk. The parameters
of the physical model are listed in Table 1.  Figure 3: Fractional abundance
of CO (top panels) and SO (bottom panels) throughout the disk as predicted by
the chemical model. The colour map shows the logarithm of the abundance w.r.t.
H2. The different columns show the abundance maps after different times,
increasing from left to right.

##  3 Chemical model

The disk chemical model used is the PPD chemical model of Walsh et al. (2015),
which includes the full gas-phase chemical network of the UMIST Database for
Astrochemistry (UDfA) Rate12 (McElroy et al., 2013) supplemented with a
comprehensive dust-gas and grain-surface chemistry. The Rate12 gas-phase
network includes ion-molecule and neutral-neutral reactions, photoionisation
and photodissociation (parametrised to the interstellar radiation field),
cosmic-ray-ionisation, and cosmic-ray-induced photoreactions. We include all
these processes by default. To this base network, Walsh et al. (2015) added a
suite of three-body association reactions and hot neutral-neutral reactions
(those with a large activation barrier) from compilations used in combustion
chemistry (e.g., Baulch et al., 2005). Also added were a set of collisional
dissociation reactions for all species expected to be abundant at the high
densities and temperatures expected in inner disks (i.e., mostly saturated
molecules and associated radicals).

The protoplanetary disk chemical code also includes a treatment for self- and
mutual-shielding of H2, CO, and N2 (see e.g., Heays et al., 2017). To compute
the shielding functions for photodissociation of H2, CO, and N2, we estimate
the visual extinction, $A_{V}$ (mag), at each point in the disk by vertically
integrating the H2 column from the disk surface downwards, then scaling the H2
column to $A_{V}$ using the standard ISM scaling ($0.5\times(1.59\times
10^{21})\times A_{V}$; Bohlin et al. 1978). This is appropriate because the
AGB star is very cool ($T_{\mathrm{eff}}=2800-3500$ K, Kervella et al. 2014;
Danilovich et al. 2015), and the only source of UV radiation is the ISM. We
then interpolate the shielding functions provided by Heays et al. (2017) over
$A_{V}$ and column density, assuming conservative fractional abundances for CO
and N2 of $10^{-5}$ w.r.t. H2. This shielding factor is then added as a pre-
factor to the photodissociation rate which is calculated in the usual manner.
The chemical model of Walsh et al. (2015) also includes a suite of X-ray
reactions and grain surface processes. However, because there is no source of
X-rays in this system, X-ray chemistry is effectively inactive and is
therefore not included.

The physical model retrieved in Sect. 2 was used as input to the static
chemical model. As there are no observational constraints, we assumed that the
dust temperature is equal to the gas temperature. The assumption of thermally
coupled dust and gas is reasonable considering the high densities. The dust
extinction at each point in the disk was calculated by combining the H2 column
densities of the disk and that in the surrounding tenuous outflow in the
vertical direction for each point, assuming the ISM relation between $A_{V}$
and H2 column density. The chemistry is evolved for $10^{6}$ yr, roughly the
entire AGB lifetime.

We also calculate a 1D outflow chemical model to compare the predicted disk
chemistry with the chemistry in a low-density outflow. The smooth outflow
model is the publicly available CSE model of the UDfA Rate22 release (Millar
et al., 2024)222https://github.com/MarieVdS/rate22_cse_code. It describes a
spherically symmetric outflow with a constant mass-loss rate and outflow
velocity, with a power-law temperature profile. Following Danilovich et al.
(2015), we adopt a mass-loss rate of $\dot{M}=1.4\times 10^{-8}$ M⊙ yr-1, an
expansion velocity of $v_{\infty}=2$ km s-1, and a stellar temperature of
$T_{*}=2800$ K. We use the same exponent for the temperature power law as in
the disk physical model, $\epsilon=0.65$. The density and temperature
throughout the outflow is shown in Fig. 15.

Table 2 lists the O-rich parent species and their initial abundances as
derived from a range of observations by Agúndez et al. (2020) and augmented by
metal abundances (Van de Sande et al., 2021). Note that Kervella et al. (2016)
found a sub-solar metallicity of $Z=0.008$, which could reduce some of our
assumed abundances by a factor $\sim 2$ (Karakas & Lugaro, 2016). The parent
species are used as input to both chemical models. Therefore, we assume that
the material captured during the disk generation phase has the same
composition as the inner wind as an approximation of the disk’s initial
composition. We evolve the chemistry for an initial $10^{3}$ yr as our first
snapshot to allow the physical conditions to imprint on the chemistry.

The results of the chemical model are presented in the next Sections. We first
show the results for the parent species in Sect. 3.1, followed by the
daughters in Sect. 3.2. The formation of complex organic molecules (COMs) and
a C-rich reservoir in the outer regions is shown in Sects. 3.3 and 3.4,
respectively. All abundances are fractional abundances relative to H2.

###  3.1 Behaviour of the parent species

Fig. 3 shows the abundance of the parents CO and SO throughout the disk at
different time intervals. Their abundance distribution changes over time. The
CO abundance decreases in the outer, more tenuous layers due to
photodissociation by the interstellar UV radiation field (note that self- and
mutual CO self-shielding is included, Sect. 3). The abundance of SO decreases
in the midplane up to a radius of 10 au after $5\times 10^{5}$ yr, shifting
its peak abundance to the outer edge of the disk. This is not due to depletion
onto dust as the dust is too warm, but it is caused by reactions with C
(liberated predominantly from CO by cosmic rays), which reacts with SO to form
CS. SO2 shows similar behaviour (Fig. 16 in Appendix 3), where reactions with
C lead to the formation of SO. The large C/S abundance ratio of $\sim 12$
makes these efficient SO and SO2 destruction pathways. The observed emission
of SO and SO2 (Kervella et al., 2016) suggests that the disk is likely not
older than $\sim 10^{5}$ yr; this is further discussed in Sect. 4.3. The
abundance profiles of all parents at $10^{5}$ yr are shown in Fig. 17.

The radial extent measured at the midplane of the parents at different times
within the disk is shown in Fig. 4, together with the size of their molecular
envelopes in the outflow model. These are the radii where the initial
abundance has decreased by a factor of $e$, corresponding to the $e$-folding
radius in the outflow. All parents have a radial extent of $\sim$ 10 au, which
is consistent with the disk’s density distribution (Fig. 2). This is smaller
than the size of their molecular envelope in the outflow, which is larger by a
factor of a few (e.g., for H2S or NH3) to two orders of magnitude (for CO and
PN). In the disk, the radial extent of most parent species does not change
significantly over time. That of the parents SiS, SO2, SO and CO2 decreases by
a factor of $\sim 4-5$ over time; that of PO decreases by a factor of $\sim
2$. For SO2, SO and CO2, this is due to the abundance decreasing in the
midplane followed by photodissociation in the outer layers of the disk. The
decrease in radial extent for SiS and PO is purely due to photodissociation,
these species do not show a gap in the inner midplane (Fig. 17).

Figure 4: Radial extent of the parent species predicted by the disk and
outflow chemical models in au. Their radial extent in the disk measured at the
midplane is shown at different times, characterised by different markers and
colours. The grey cross shows their extent in a smooth outflow model.  Figure
5: Fractional bundance of the daughters OH, SiC2, CH3CN, and HCOOH throughout
the disk as predicted by the chemical model at $10^{5}$ yr. The colour map
shows the logarithm of the abundance w.r.t. H2. Note that each colourmap has a
different dynamic range.

###  3.2 Behaviour of daughter species

Fig. 5 shows the abundance of the daughters OH, SiC2, CH3CN and HCOOH
throughout the disk at $10^{5}$ yr. The abundance of OH peaks in the outer
regions of the disk, with abundances up to $\sim 3\times 10^{-6}$. This
distribution is due to its formation from the photodissociation of the parent
H2O and is similar to its behaviour in an outflow, where it forms a molecular
shell.

SiC2 is also present in the outer regions of the disk, but its abundance is
largest in the inner disk edge where it reaches $\sim 3\times 10^{-6}$. This
is caused by the unique combination of high density, high temperature, and
strong UV radiation field in this region. SiC2 is formed by the reaction Si +
C2H2, where Si is produced by the photodissociation of the parent SiO. The
higher abundance in the inner disk edge is inherited from that of the reactant
C2H2 (Fig. 18) and is caused by the temperature dependencies in its formation
pathway, which are elaborated on in Sect. 4.4.2.

CH3CN (methyl cyanide) is not located in the outer edge of the disk, but in
the inner disk midplane. Its peak abundance is $\sim 3\times 10^{-9}$, which
is two orders of magnitude larger than its predicted peak abundance in an
outflow. This C-bearing molecule is formed via CH3+ and the parent HCN
producing CH3CNH+, which then dissociatively recombines by collisions with
negatively charged dust grains into CH3CN. CH3+ plays a crucial role in the
chemistry of the inner midplane. It is formed via CH4 + He+, where both
reactants have a cosmic ray origin, as CH4 is formed by the successive
addition of hydrogen to C (liberated by cosmic rays from CO). Sect. 4.4.1
elaborates on the cosmic-ray induced midplane chemistry.

The abundance of HCOOH (formic acid) is also largest in the midplane. Its peak
abundance is $\sim 5\times 10^{-9}$, three orders of magnitude larger than its
peak abundance in an outflow. Its formation is also initiated by cosmic rays:
H3+ (a product of cosmic-ray reactions) reacts with the parent CO to form
HCO+. Reaction with the parent H2O produces HCOOCH2+ and HCOOH. Unlike CH3CN,
its peak abundance is not in the inner regions of the disk but between 5 and 9
au. This is due to the difference in destruction mechanisms: unlike CH3CN,
HCOOH is efficiently destroyed by collisional dissociation. The rate of this
destruction mechanism increases with density, destroying HCOOH in the dense
inner midplane.

###  3.3 Formation of complex organic molecules

The COMs CH3OH (methanol), CH3CN (vinyl cyanide), CH3NH2 (methylamide), C2H5CN
(ethyl cyanide), CH2CHCN (acrylonitrile), HCOOH (formic acid), and HCOOCH3
(methyl formate) are abundantly present in the inner disk and are formed by
cosmic-ray induced chemistry in the midplane (Sect. 4.4.1). Their abundance
distribution at $10^{5}$ yr is shown in Fig. 6.

Figure 6: Fractional abundances of complex organic molecules (COMs) formed
within the disk as predicted by the chemical model after $10^{5}$ yr. The
colour map shows the logarithm of the abundance w.r.t. H2. Note that each
colour map has a different dynamic range. The additional COMs CH3CN and HCOOH
are shown in Fig. 5.

Fig. 7 shows their column density at different times in the disk model,
together with their column density in the outflow model. The column density of
species in the disk is a disk-averaged column density, calculated via

$\bar{N}=\frac{2}{\pi r_{D}^{2}}\times\sum_{i=0}^{D}2\pi r_{i}\Delta
r_{i}N_{i},$ (8)

where $N_{i}$ is the vertical column density within $\Delta r_{i}$ and the
factor 2 accounts for the symmetry of the model across the midplane. At
$10^{5}$ yr, all COMs listed above have a disk-averaged column density larger
than $10^{10}$ cm-2. CH3CN has the largest column density of $1.80\times
10^{15}$ cm-2, followed by CH3OH with $3.37\times 10^{14}$ cm-2 and HCOOH with
$1.19\times 10^{14}$ cm-2. The column densities are at least five orders of
magnitude larger than those predicted by the outflow model. The largest
differences are seen for CH3NH2, C2H5CN, CH2CHCN, and HCOOCH3, with a
difference of at least 8 orders of magnitude, showing that the chemistry in
the disk is favouring the formation of larger saturated complex molecules.

Figure 7: Disk-averaged column densities of COMs produced in the chemical
model of the disk at different times, characterised by different markers and
colours. The grey cross shows the results from a smooth outflow model.

###  3.4 Carbon-rich reservoir in the outer regions

Carbon-bearing molecules are abundantly formed in the outer regions of the
disk. CO and other C-bearing parents are photodissociated by interstellar UV
photons, liberating the reactive C atom. Carbon-chains, e.g., C2H2 and HC3N,
are abundantly formed in this region (Fig. 18). Longer highly-unsaturated
carbon-chains, such as C10H2, C8H, and HC9N, are also produced. However, the
chemical reaction network is geared towards interstellar chemistry and does
not include full saturation of these carbon-chains. Hence, the predicted
abundances of these longer chains are likely over-estimated.

We therefore grouped all species with 6 or more C atoms into a “carbon sink”
reservoir. Fig. 8 shows the abundance of this sink particle throughout the
disk at different times in its evolution. The total abundance of carbon-
bearing species is large in the outer disk, with a maximum abundance of $\sim
3\times 10^{-5}$. This is remarkably large considering the disk is O-rich.
Unlike in the outer regions of an AGB outflow, newly liberated C can readily
react and form (long) carbon chains thanks to the higher densities in the
disk’s outer region.

Figure 8: Total fractional abundance of all species with 6 or more C atoms
(called carbon sinks, Sect. 3.4) in the disk as predicted by the chemical
model. The colour map shows the logarithm of the abundance w.r.t. H2. The
different columns show the abundance maps after different times, increasing
from left to right.

##  4 Discussion

The physical structure of the disk has a large influence on the chemistry
around L2 Pup. In Sect. 4.1, we compare our newly derived physical structure
to PPDs and disks around post-AGB stars. We then compare our results to those
of Homan et al. (2017) and suggest future observations to better constrain the
density and temperature within the disk. This is important, as the predicted
chemistry depends on the physical structure. In Sect. 4.2, we qualitatively
compare our predicted abundance profiles to the previous observations of
Kervella et al. (2016) as a first-order test of the model. We elaborate on
using the predicted SO and SO2 abundance profiles to age the disk at $\sim
10^{5}$ yr in Sect. 4.3. Finally, the chemistry within the disk is discussed
in Sect. 4.4, where we examine the surprisingly rich C-rich chemistry in the
O-rich disk and suggest molecular tracers of the disk structure.

###  4.1 Physical structure of the disk

We compare our retrieved physical structure of the disk around L2 Pup to PPDs
and post-AGB disks in Sect. 4.1.1. A comparison to the previous model of Homan
et al. (2017) is made in Sect. 4.1.2. Since our physical model was retrieved
using just two molecular emission lines, we describe the observations needed
for a further refinement of the model in Sect. 4.1.3.

####  4.1.1 Comparison to PPDs and post-AGB disks

We retrieved that the disk around L2 Pup has a surface density profile
$\Sigma(r)\sim r^{-1}$ and is warm, with a midplane temperature of 900 K and
$T_{\mathrm{mid}}(r)\sim r^{-0.2}$. The exponent of the surface density
distribution, $\gamma$, is on the shallower end of those found for PPDs, for
which $\gamma\lesssim-1$ (Andrews, 2020). Disks around post-AGB stars have
$-3\leq\gamma\leq-1$, although it is difficult to constrain this value with
infrared interferometry alone (Hillen et al., 2014; Hillen et al., 2015;
Corporaal et al., 2023). Our value of $\gamma=-1$ hence also agrees with post-
AGB disks and appears to suggest that the density profile of this disk around
an AGB star lies between that of a PPD and post-AGB disk.

The midplane temperature of L2 Pup’s disk is much warmer than in PPDs:
$T_{\mathrm{mid,1}}=900$ K compared to $100-300$ K for PPDs. The power-law is
also flatter, with $q=0.2$ rather than $q=0.5-0.7$ for PPDs (e.g., Andrews et
al., 2009; Williams & Best, 2014). The temperatures of post-AGB disks lie
within $1400-3600$ K, which are single blackbody temperatures for the disk as
it is, again, difficult to constrain their midplane temperatures using
infrared interferometry alone (Kluska et al., 2018; Corporaal et al., 2023).
The disk around L2 Pup again lies between these two ranges: warmer than PPDs,
colder than post-AGB disks. This is expected as the gas ejected by the AGB
star is warm and its high luminosity can provide a lot of dust heating. In
post-AGB stars, the stripped star is much warmer, leading to larger
temperatures.

####  4.1.2 Comparison to Homan et al. (2017)

We used a parametric model commonly used for PPDs to model the same
observations used by Homan et al. (2017) as we were unable to reproduce their
model from the information provided in that work. We did use the same velocity
profile of Kervella et al. (2016) and also adopted certain observational
parameters of Homan et al. (2017), as described in Sect. 2.3.

We find three main differences between our model and theirs:

  1. 1.

Homan et al. (2017) assumed a three-staged radial temperature profile, which
includes an exponential and arctan. This profile includes a feature the
authors attribute to the heating of the gas by the dust disk. The parameter
space explored to achieve this fit is not explained. We find that a power-law
expression (Eq. 6) is sufficient to reproduce the observations, indicating
that their analytical expression could be overfitted and may have been more
complex than needed.

  2. 2.

Homan et al. (2017) retrieved a steep radial density profile at the midplane
of $\rho(r,z=0)\sim r^{-3.1}$, which is much steeper than our $\rho(r,z=0)\sim
r^{-0.4}$ (Eqs 1, 3, 4). The steepness of their density profile does not agree
with observations of either PPDs or post-AGB disks. The large difference in
density profile could be due to the differences in temperature structures.

  3. 3.

The ^13CO abundance retrieved by Homan et al. (2017) is $1\times 10^{-5}$, we
find a value of $2\times 10^{-5}$ w.r.t. H2. We used the same ^12CO abundance
of $1\times 10^{-4}$ w.r.t. H2. This leads to different ^12CO/^13CO ratios: 10
by Homan et al. (2017), 5 in this work. While both values lie within the range
found by Ramstedt et al. (2014), our value of 5 is on the low side. Optical
depth effects might cause such a low ^12CO/^13CO ratio. Note that
photodissociation effects due to differences in self-shielding between the
isotopologues would increase the ratio (Saberi et al., 2019). Additionally, a
factor of 2 difference is reasonable within the uncertainties of modelling
(Ramstedt et al., 2008).

####  4.1.3 Refining the physical structure: further observations

Besides CO and ^13CO, the available ALMA data includes rotational transitions
of H2O, ^29SiO, ^30SiO, SiS, SO, and SO2. The isotopologues of SiO were used
to constrain the velocity structure of the disk by Kervella et al. (2016).
While the other lines shed some light on the chemical structure of the disk
(Sects. 4.2 and 4.3), further observations are necessary to better constrain
the disk’s physical structure, given the differences with Homan et al. (2017)
(Sect. 4.1.2). A better constraint of the physical structure of L2 Pup’s disk
will address the differences with the Homan et al. (2017) model and is a
crucial input to the chemical model and its predictions.

Spatially resolved emission of abundant optically thin CO isotopologues, such
as C^18O, C^17O, and ^13CO (Danilovich et al., 2017; De Nutte et al., 2017),
can help determine the disk gas mass and its density distribution more
accurately as they probe different layers within the disk. Similarly, H2CO
(e.g., Qi et al., 2013; Pegues et al., 2020), HCN (e.g., Long et al., 2021),
HC3N, CH3CN, and C3H2 (e.g., Bergner et al., 2018; Ilee et al., 2021), are
well-known temperature probes in PPDs. Our chemical model predicts column
densities of $3.72\times 10^{14}$, $8.54\times 10^{17}$, $4.21\times 10^{13}$,
$2.80\times 10^{15}$, and $3.65\times 10^{12}$ cm-2, respectively, for these
molecules.

CH3CN and C3H2 have yet not been detected towards O-rich AGB stars: their
detection would put strong constraints on our chemical model. HC3N has only
been detected around OH 231.8+4.2, which has a bipolar outflow with velocities
up to $\sim 400$ km s-1 (Velilla Prieto et al., 2015). So far, H2CO has only
been detected around the moderate mass-loss rate O-rich AGB star IK Tau with a
column density of $2.8\times 10^{14}$ cm-2, which is close to our predicted
column density (Velilla Prieto et al., 2017). IK Tau likely has a stellar
companion shaping its outflow (Coenegrachts et al., 2023). H2CO has also been
detected in the Rotten Egg Nebula, an AGB star with an A-type companion
(Lindqvist et al., 1992), and the Helix Nebula, which might host an unseen
dwarf M star (Gruendl et al., 2001; Tenenbaum et al., 2009; Zack & Ziurys,
2013). It seems that detections of H2CO around evolved stars appear to suggest
deviations from spherical symmetry.

###  4.2 Comparison of the chemical model to observations

We qualitatively compare our chemical modelling results with the observations
of Kervella et al. (2016). The observed ^12CO emission (Appendix A in Kervella
et al. 2016) has a radial extent of $\sim$ 9 au and a vertical extent of
$\sim$ 3 au. The peak CO abundance predicted by our chemical model lies within
$\sim$ 11 au radially and about 2.5 au vertically (Fig. 3). Keeping in mind
that we are comparing abundances with observations, the CO abundance predicted
by the chemical model is consistent with the observed ^12CO emission. A
standard set of parent species and their abundances was used as input when
running the chemical model. The initial CO abundance in the chemical model is
a factor 3 larger than that assumed in the physical model, following Homan et
al. (2017) ($3\times 10^{-4}$ versus $1\times 10^{-4}$ w.r.t. H2, Sect. 3). As
we did not a priori know how the chemical abundances would change over time,
nor which abundance (profile) to assume when retrieving the physical structure
from the observations, we kept these values when calculating the physical and
chemical structures. We find that the results of the chemical model are
consistent with its independently derived physical structure. The disk
averaged CO abundance at $10^{5}$ yr decreased to $2.86\times 10^{-4}$ w.r.t.
H2.

Besides the ^12CO and ^13CO $J=3-2$ lines, Kervella et al. (2016) also
presented the SO2 ($v=0,J_{K_{a},K_{c}}=34_{3,31}-34_{2,32}$), SO
($\nu=0,N_{J}=8_{8}-7_{7}$), and SiS ($\nu=1,{J}=19-18$) lines (their
Appendices C - E). The SO2 and SO emission is more extended vertically (about
6 au and $\sim$ 3 au, respectively) compared to the vertically compact SiS
emission (up to 2 au). The SO abundance of the chemical model is shown in Fig.
3, that of SO2 and SiS in Fig. 16. At $10^{5}$ yr, the region of highest SO2
abundance has a vertical extent of $\sim$ 6.5 au, that of SO about $\sim$ 5.5
au and of SiS about $\sim$ 1.5 au. The chemical model hence also qualitatively
reproduces the relative vertical extents of SO, SO2, and SiS, though a full
radiative transfer model is required to check.

Methanol has been detected towards the post-AGB star HD 101584 (Olofsson et
al., 2017) and OH 231.8+4.2, a bipolar nebula around an AGB star (Sánchez
Contreras et al., 2018). It is detected in the high-velocity outflows of these
objects and is thought to originate from post-shock chemistry, where shocks in
the outflow desorb the molecule from an icy grain mantle. The retrieved column
densities of CH3OH are $\sim 10^{16}$ and $1-8\times 10^{14}$ cm-2,
corresponding to fractional abundances of $\sim 3\times 10^{-6}$ and
$10^{-8}-10^{-7}$ w.r.t. H2, respectively. Our chemical model predicts a
column density of $\sim 10^{14}$ cm-2 around $10^{5}$ yr, with a peak
fractional abundance around $3\times 10^{-9}$ w.r.t. H2. The strongest CH3OH
line detected in HD 101584, the $8_{-1}$ \- $7_{0}$ line at 229.759 GHz, is
covered by the 2016.1.00207.S. dataset (PI P. Kervella), with a peak flux
around 80 mJy. It is not clearly detected in the archival L2 Pup data, with an
upper limit for the peak flux of around $2-3$ mJy. From running a simplified
radiative transfer calculation, using the accelerated lambda iteration method
code (ALI, e.g., Danilovich et al. 2021, with molecular data from Rabli &
Flower 2010), based on the spherically symmetric model of Danilovich et al.
(2015) and assuming a Gaussian abundance profile with an $e$-folding radius of
$10^{15}$ cm, we determine that for a methanol abundance of $3\times 10^{-9}$
w.r.t. H2 (the maximum abundance predicted by the chemical model) the $8_{-1}$
\- $7_{0}$ line would not be detected above the noise for L2 Pup. The non-
detection of CH3OH in L2 Pup could be due to its lower abundance or due to a
different excitation mechanism, as methanol is formed in the warm inner
midplane of the disk via gas-phase reactions rather than via shock chemistry
in a high-velocity outflow, as in the two other objects. Further observations
are necessary to confirm the (non)detection of methanol in L2 Pup’s disk.

A radiative transfer analysis of the chemical model predictions lies outside
the scope of this paper. Moreover, it is important to note that the predicted
chemistry depends on the input physical structure. A parameter study to
quantify the impact of different physical structures on the chemistry is
computationally intensive and will be addressed in future work. As stated in
Sect. 4.1.3, further observations are necessary to constrain the retrieved
physical model of L2 Pup’s disk.

Figure 9: Ratio of the disk column density relative to CO over the outflow
column density relative to CO (Eq. 9) for species that show a decrease (left
panel) and increase in column density relative to the outflow (right panel) of
more than an order of magnitude at any time in the disk chemical model.
Different markers and colours show the ratio at different times for the disk
model. The shaded regions group species originating from different types of
chemistry. Blue: midplane (cosmic ray) chemistry, orange: outer edge (photo)
chemistry, dark orange: hot inner edge. Boldfaced labels denote species that
are formed via cosmic ray and photochemistry. These species can be regarded as
chemical tracers of the disk.

###  4.3 Age of the disk

After $5\times 10^{5}$ yr, the chemical model predicts a gap in the inner
midplane for SO and SO2 (Figs. 3 and 16), which is about 1 au in height and 9
au radially for both molecules. Such a gap is not seen in the emission maps of
SO2 ($v=0,J_{K_{a},K_{c}}=34_{3,31}-34_{2,32}$) and SO
($\nu=0,N_{J}=8_{8}-7_{7}$, Appendices C and D in Kervella et al. 2016). The
beam size of the observations is $17.7\times 14.5$ mas $\approx 1.1\times 0.9$
au. The gap predicted by the chemical models should hence be observable,
especially as the upper energy level of the SO2 transition is 582 K.
Therefore, under the assumptions of our chemical model of a disk that is
formed at a specific time and then evolves in isolation of the outflow, we
expect it to be not older than $10^{5}$ yr. Hydrodynamical simulations suggest
that while the disk is formed on a timescale of a few 100 yr, some outflowing
gas will still be captured by and incorporated into the disk (Chen et al.,
2016). If the disk is continually refreshed with new material, its age could
be older.

L2 Pup is currently in the thermally pulsing-AGB (TP-AGB) phase (Kervella et
al., 2016), which is a short-lived phase of about $0.5\times 10^{5}$ yr
(Rosenfield et al., 2014). Assuming a static model, the disk could therefore
both be a remnant from the early-AGB phase or have originated in the TP-AGB
phase. The timeframe of $10^{5}$ yr is too short for the massive planet to
have been formed within this disk (which would take $\sim$10 Myr if formed via
core accretion, Pollack et al. 1996), and is likely to be a first-generation
planet present before the AGB phase.

###  4.4 Chemistry within the AGB disk

The chemistry within the disk around L2 Pup is different to that in a low-
density O-rich outflow both in distribution and composition. The only
similarity is the lack of dust-gas chemistry, although this is due to
different factors. In the outflow, the density is too low for gas-phase
species to efficiently accrete onto the dust. The density in the disk midplane
is at least four orders of magnitude larger, but the dust temperature is too
high for accreted ices to remain on the dust surface. The dust temperature was
taken to be that of the gas, a reasonable assumption given the density of the
disk. However, a lower dust temperature could result in the depletion of gas-
phase species and the formation of ices.

To compare the chemical composition of the disk to that of the outflow, we use
the ratio of their column densities. This column density ratio is weighted by
their respective CO column densities,

$\mathrm{Ratio}=\frac{\bar{N}_{X}}{\bar{N}_{\mathrm{CO}}}\times\frac{N_{\mathrm{CO}}}{N_{X}},$
(9)

with $\bar{N}_{X}$ the disk-averaged column density of species X (Eq. 8) and
$N_{X}$ the column density of species $X$ in the outflow. This normalises the
ratio to the most abundant molecule (after H2), allowing for a better
comparison between the chemistries of these different density distributions.
The CO column density ratio, $\bar{N}_{\mathrm{CO}}/N_{\mathrm{CO}}$, is $\sim
100$ for all times in the disk model, decreasing from 126 at $10^{3}$ yr to 98
at 106 yr.

The chemical composition of the disk is different from that of the outflow:
the disk does not simply inherit the initial composition, but also
significantly modifies the abundances of parent and daughter species. Unlike
in the outflow and despite its O-rich composition, numerous C-bearing
molecules are abundantly formed throughout the disk, including COMs. Two main
chemical regions can be distinguished: (i) the dense midplane, where chemistry
is initiated by cosmic rays, and (ii) the outer edge, where it is initiated by
interstellar UV photons. Within the outer region, the hot inner edge displays
a different chemistry than the cooler outer regions. The chemistry in the
dense midplane differs from that in a PPD because of the higher temperatures
in the disk, while the chemistry of the outer regions is different to an AGB
outflow due to the higher densities in this region.

Fig. 9 shows the column density ratio for a set of species which have a column
density larger than $10^{10}$ cm-2 at some time in the disk and which show a
difference of at least an order of magnitude at some time in the disk chemical
model. Their abundance profiles are shown in Fig. 18 and the absolute values
of their column densities are shown in Fig. 19. These species can be regarded
as chemical tracers of the presence of a disk structure. The left panel shows
species which have a smaller column density in the disk model compared to the
outflow model, the right panel shows those which have a larger column density.
The shaded regions group species originating from different types of
chemistry: midplane (cosmic ray) chemistry is highlighted in blue, outer edge
(photo) chemistry in orange, with species present in the hot inner edge
highlighted in dark orange. Species formed via both cosmic ray and
photochemistry are placed in the blue region with a boldface label. Sects.
4.4.1 and 4.4.2 elaborate on the cosmic-ray induced chemistry in the midplane
and in the photochemistry in outer regions, respectively.

####  4.4.1 Cosmic-ray induced chemistry

Cosmic rays dissociate parent species in the midplane, liberating atoms which
participate in a rich chemistry thanks to the high densities in this region. A
large role is played by the reactive C, produced mostly by the destruction of
the parent CO. Species whose column density is significantly impacted by this
chemistry are shown in the blue shaded regions of Fig. 9.

##### Decrease in column density relative to the outflow

Reactions between C and the parents SO and SO2 form CS, leading to a gap in
abundance in the dense midplane and a lower column density relative to the
outflow. At $10^{5}$ yr, their column densities are $\sim 5$ and $\sim 9$
times smaller than in the outflow, increasing to 100 times and $\sim 7\times
10^{3}$, respectively. CO2 shows a similar gap in the midplane, which is
caused by reactions with Si forming SiO. Its column density is more than 5
orders of magnitude smaller than in the outflow at $10^{5}$ yr. At longer
timescales, this difference is reduced to roughly 3 orders of magnitude thanks
to its reformation by collisional dissociation of HCOOH (see below).

The decrease in column density of SiS, reaching about an order of magnitude
after $5\times 10^{5}$ yr, is caused by reactions with H3+, a product of
cosmic-ray interactions. The resulting HSiS+ reacts with the parent H2O,
producing SiOH+ which goes on to react with the parent NH3, funnelling Si away
from SiS into SiO.

##### Increase in column density relative to the outflow

Hydrogen is efficiently added to carbon at the high densities and temperatures
in the midplane, forming CH4. Its column density is about 3 orders of
magnitude larger in the disk. CH4 reacts with N+, formed via cosmic rays,
producing HCNH+. This molecule then reacts with H2S and NH3 to form HCN and
HNC, with column densities more than 1 and 3 orders of magnitude larger than
in the outflow, respectively. The CS abundance increases thanks to the
reactions of C with SO2 and SO, increasing its column density by about 1 order
of magnitude.

HCO+ is produced by cosmic ray chemistry via H3+ + CO. Radiative association
of HCO+ with H2O yields HCOOH2+, which reacts with H2O and NH3 to form HCOOH
(increase in column density $\gtrsim$ 4 orders of magnitude compared to the
outflow).

The CH3+ cation plays a crucial role in the chemistry of the midplane. It is
formed via CH4 + He+, both products of cosmic rays, forming CH2+ which reacts
with H2 to CH3+. The formation of all detected COMs (and HC3N) is linked to
this cation. The high densities of the midplane allow for the slow radiative
association reactions, dissociative recombination with dust, and collisional
dissociation reactions in these pathways to be efficient. The main formation
pathways of COMs via reactions with CH3+ are:

  * •

Radiative association between the parent HCN and CH3+ yields CH3CNH+, which
dissociatively recombines with negatively charged dust grains to form CH3CN
(increase in column density of $\gtrsim$ 3 orders of magnitude at $10^{5}$ yr
compared to the outflow).

  * •

NH3 can radiatively associate with CH3+ forming CH3NH3+, which dissociatively
recombines with dust to CH3NH2 (column density $\gtrsim$ 6 orders of
magnitude). The association with CH3+ also forms C2H5CNH+, which
dissociatively recombines with dust to C2H5CN ($\gtrsim$ 6 orders of
magnitude). A sequence of collisional dissociations and reactions with C lead
to the formation of CH2CCH, which reacts with N to form HC3N ($\gtrsim$ 7
orders of magnitude).

  * •

Reactions of CH3+ with the parent H2O gives CH3OH2+, which produces CH3OH by
reacting with the parent NH3 ($\gtrsim$ 3 orders of magnitude). Subsequent
reaction with H2CO results in H5C2O2+, which dissociatively recombines with
dust to HCOOCH3 ($\gtrsim$ 8 orders of magnitude).

  * •

The formation of methanol initiates the production of H2CO, increasing its
column density by almost 3 orders of magnitude at $10^{5}$ yr, which is formed
by collisional dissociation of CH2OH and CH3O. Both have their origin in the
CH3+ + H2O reaction, which forms both CH3OH and CH3OH2+. CH2OH is formed via
CH3OH + H, CH3O is formed after CH3OH2+ reacting with CH3OH followed by
dissociative recombination with dust and collisional dissociation.

Other species formed by the successive addition of hydrogen to carbon also
play an active role in the cosmic-ray induced midplane chemistry. The column
density of H2CS increases by more than 3 orders of magnitude at $10^{5}$ yr.
It is formed via CH4 + S+ (both with a cosmic-ray origin) producing H3CS+,
which then dissociatively recombines with dust. HNCO is formed by CH2 + NO and
C2H5CN + OH, with a increased column density of about 3 orders of magnitude at
$10^{5}$ yr. The formation of HC3N is kickstarted by CH4 + CH3+, forming
C2H5+, which yields C2H4 after reaction with the parents H2O and H2S.
Subsequent reactions with C and N finally produce HC3N.

####  4.4.2 Interstellar UV photochemistry

The chemistry in the more tenuous outer regions of the disk is a rich
photochemistry initiated by interstellar UV photons. However, because of the
higher densities and temperatures of the disk, the products of this
photochemistry are different to those of the photochemistry taking place in
the outer regions of the outflow. C2H2 plays an important role in the
chemistry of the outer regions of the disk. It is formed by the successive
addition of hydrogen to C (produced by photodissociation of mainly the parent
CO) into CH, which then reacts with C again to form C2. These reactions lead
to the formation of C2H and finally C2H2. Species whose column density is
significantly impacted by this chemistry are shown in the orange shaded
regions of Fig. 9.

##### Decrease in column density relative to the outflow

The daughters OH, CN, HS, NH, and NH2 are all first-generation daughters
formed by photodissociation of the parents H2O, HCN, H2S, and NH3. They are
present in a shell in the outer disk. Their main destruction mechanisms are
photodissociation and reaction with H2 to reform the parent species in a
photodissociation - hydrogen addition loop, depending on the density. The
significant decreases in their column densities relative to the outflow is
caused by reactions funnelling them away from their parents.

Reactions with C-bearing species remove OH and CN from their photodissociation
- hydrogen addition loops, reducing their column densities by $\sim 5\times
10^{3}$ and 2 orders of magnitude, respectively. OH mainly reacts with C to
reform CO and with CH2 to produce H2CO, which is also formed by O + CH3. CN is
involved in reactions with C2H2 and C2H4, producing cyanopolyynes and CN-
bearing C-chains.

The column densities of HS, NH and NH2 decrease between one and two orders of
magnitude relative to the outflow. S is removed from the photodissociation -
hydrogen addition loop by the formation of CS via HS + C and S + CH2, and by
the formation of H2CS via S + CH3. NH reacts with O to produce NO, which is
then efficiently destroyed by Si forming SiO and NH forming N2O, which
photodissociates into N2. Subsequently, the column density of NO is about two
orders lower in the disk after $10^{5}$ yr. NH also efficiently reacts with S
to produce NS, which then reacts with O to form NO and SO.

The column density of the cation HCO+ is almost 4 orders of magnitude smaller
in the disk. Its main formation mechanism is C+ + H2O. However, unlike in the
outflow, C+ is also involved in the C-chain chemistry in this region, which
reduces the HCO+ abundance.

##### Increase in column density relative to the outflow

The column density of C2H2 increases by about 3 orders of magnitude due to
photochemistry in the outer regions of the disk. As stated earlier, C2H2 plays
an important role in the chemistry in this region. Reactions with SO+, formed
by photoionisation of SO and by OH + S+, produce C2S, the column density of
which increases by two to three orders of magnitude. Reactions with Si,
liberated by photodissociation of the parent SiO, produce SiC2, whose column
density increases by some 5 orders of magnitude at $10^{5}$ yr. SiC is a
product of SiC2 + O, with the latter produced mostly via the photodissociation
of the parents H2O and SiO.

These four species (C2H2, C2S, SiC2, and SiC) show large abundances at the
inner edge of the disk, within the first few au (marked by the dark orange
region in Fig. 9). This is caused by the strong temperature dependence of the
H2 + C2H reaction: its reaction rate depends on temperature as $T^{2.57}$
(Laufer & Fahr, 2004). This has a significant effect at the large temperatures
in this region (between 1100 and 1750 K). Even though the Si + C2H2 reaction
has a negative temperature dependence ($T^{-0.71}$, Canosa et al. 2001), the
large increase in C2H2 abundance leads to a larger SiC2 and SiC abundance in
this region.

The formation of SiN and SiH4 is linked to Si. The SiN column density is about
an order of magnitude larger than in the outflow at $10^{5}$ yr. Its
production is started by NH3 + Si+, with the latter produced by the
photoionisation of Si or charge exchange with S+. This reaction forms SiNH2+
which dissociatively recombines with electrons to SiN or recombines to HNSi,
which is then photodissociated into SiN. Closer to the midplane, the cation
dissociatively recombines with negatively charged dust grains. The SiH4 column
density is more than 5 orders of magnitude larger at $10^{5}$ yr. It is formed
by the successive addition of hydrogen to SiH+ into SiH5+, which then reacts
with H2O or dissociatively recombines with electrons to SiH4. SiH+ is formed
by Si + H3O+, with the latter formed by the addition of H to H2O+, a product
of the photoionisation of H2O.

##  5 Conclusions

We presented an updated model of the density and temperature of the disk
around L2 Pup by fitting archival ALMA ^12CO and ^13CO $J=3-2$ lines. The disk
has a surface density profile $\Sigma(r)\sim r^{-1}$ and is warm, with a
midplane temperature of 900 K and $T_{\mathrm{mid}}(r)\sim r^{-0.2}$. Unlike
Homan et al. (2017), we do not require a three-staged radial temperature
profile or an extremely steep vertical density profile (our $\rho(r)\sim
r^{-0.4}$ vs their $\sim r^{-3.1}$. A more simple parametrisation used
commonly for PPDs is able to reproduce the observations.

The chemical model presented in this paper is the first chemical model of a
disk around an AGB star, specifically of L2 Pup’s disk. The physical structure
of the disk has a large impact on its chemistry. All species are constrained
to the disk, within $\sim 15$ au radially and $\sim 10$ au vertically. This is
much smaller than the extent of the parents’ envelope in the outflow, which
ranges from $30-3000$ au radially from the star and is also where the peak
abundances of the daughter species are located.

The chemistry within the disk leads to large abundances of C-bearing
molecules, a surprising result given its O-rich composition. Certain COMs are
abundantly formed in the midplane. Unlike in PPDs, these are formed purely via
gas-phase chemistry as dust-gas chemistry does not play a role at the high
temperatures of L2 Pup’s disk. C-chains are readily formed in the outer
regions, though caution is needed as the chemical network does not include
fully saturated long (more than three C atoms) carbon-chain species. Two
chemical regimes can be distinguished: cosmic-ray induced chemistry in the
midplane and photoinduced chemistry in the outer regions. The abundances of
species are significantly increased or decreased with respect to an O-rich
outflow chemical model, allowing us to identify potential and unique tracers
of the disk such as H2CO, CH3CN, and HC3N. Moreover, the chemical model can be
used to constrain the age of the disk. The appearance of a gap in abundance in
the midplane of SO and SO2 after $5\times 10^{5}$ yr appears to suggest that
the disk around L2 Pup is about $10^{5}$ yr old, as these features were not
observed in the data presented by Kervella et al. (2016).

Further observations are necessary to further constrain the physical structure
of the disk. In particular, optically thin CO isotopologues are needed to
better pin down the disk mass and density structure, while species such as
H2CO, HC3N, CH3CN, and C3H2 can be used as empirical temperature probes.
Targeting the tracers of the midplane and outer region chemistries will
provide an essential test of the chemical model predictions.

Our unique chemical model clearly shows the impact that large-scale structures
within an AGB outflow can have on its chemistry. This exploratory work paves
the way for a more general study of AGB disks, ranging in density and
temperature structures. However, note that the 2D model used in this work
predicts the chemistry assuming a fixed density structure; coupling chemistry
to a hydrodynamical model is necessary to take the effect of dynamical
evolution of the chemistry into account.

## Acknowledgements

We thank Anita Richards for providing us with the reduced ALMA observations,
John D. Ilee for help with data analysis, Akke Corporaal for conversations
about post-AGB disks, and Wouter Vlemmings for discussions on methanol. MVdS
thanks Felix Sainsbury-Martinez for advice when scripting. This article makes
use of the following ALMA data: ADS/JAO.ALMA#2015.1.00141.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), NSC 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. MVdS acknowledges support
from the European Union’s Horizon 2020 research and innovation programme under
the Marie Skłodowska-Curie grant agreement No 882991 and the Oort Fellowship
at Leiden Observatory. TD is supported by the Australian Research Council
through a Discovery Early Career Researcher Award (DE230100183) and by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), through project number CE170100013. C.W. acknowledges
financial support from the Science and Technology Facilities Council and UK
Research and Innovation (grant numbers ST/X001016/1 and MR/T040726/1). FDC is
a Postdoctoral Research Fellow of the Research Foundation - Flanders (FWO),
grant number 1253223N. TC is a PhD fellow of FWO, grant number 1166722N.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A ALMA observations

Moment 0 maps of the ^12CO and ^13CO $J=3-2$ lines are presented in Kervella
et al. (2016) (their Figs A.1 and B.1). Here, we present channel maps of these
lines with beam information.

Figure 10: Channel maps of 12CO $J=3-2$ emission toward L2 Pup. The grey
contours show flux levels at 3 and 5 times the rms noise. The beam is shown in
white in the bottom left hand corners.

Figure 11: Channel maps of 13CO $J=3-2$ emission toward L2 Pup. The grey
contours show flux levels at 3 and 5 times the rms noise. The beam is shown in
white in the bottom left hand corners.

##  Appendix B Magritte modelling results

Figure 12: Modelled channel maps of 12CO $J=3-2$ emission toward L2 Pup. The
grey contours show flux levels at 3 and 5 times the rms noise. The beam is
shown in white in the bottom left hand corners. Model parameters are listed in
Table 1.  Figure 13: Modelled channel maps of 13CO $J=3-2$ emission toward L2
Pup. The grey contours show flux levels at 3 and 5 times the rms noise. The
beam is shown in white in the bottom left hand corners. Model parameters are
listed in Table 1.

Figure 14: Modelled moment 0 map of 12CO (left) 13CO $J=3-2$ (right). The grey
contours show flux levels at 3, 5, 10, 20, and 30 times the rms noise. The
beam is shown in white in the bottom left hand corners. Model parameters are
listed in Table 1.

##  Appendix C Chemical model results

Figure 15: The H2 number density (left) and temperature (right) assumed throughout the outflow chemical model (Sect. 3).  Table 2: Parent species and their initial abundances relative to H2 for the disk and outflow chemical kinetics models. Abundances are derived from observations, as compiled by Agúndez et al. (2020).  Species | Initial abundance
---|---
He | 0.17
CO | $3.00\times 10^{-4}$
H2O | $2.15\times 10^{-4}$
N2 | $4.00\times 10^{-5}$
SiO | $2.71\times 10^{-5}$
H2S | $1.75\times 10^{-5}$
SO2 | $3.72\times 10^{-6}$
SO | $3.06\times 10^{-6}$
SiS | $9.53\times 10^{-7}$
NH3 | $6.25\times 10^{-7}$
CO2 | $3.00\times 10^{-7}$
HCN | $2.59\times 10^{-7}$
PO | $7.75\times 10^{-8}$
CS | $5.57\times 10^{-8}$
PN | $1.50\times 10^{-8}$
HCl | $1.00\times 10^{-8}$
HF | $1.00\times 10^{-8}$
Cl | $1.00\times 10^{-8}$
Mg | $1.00\times 10^{-8}$
Fe | $1.00\times 10^{-8}$
Figure 16: Fractional abundance of SO2 (top row) and SiS (bottom row)
throughout the disk as predicted by the chemical model. The colour map shows
the logarithm of the abundance w.r.t. H2. The different columns show the
results after different times, increasing from left to right.  Figure 17:
Fractional abundances of the parent species throughout the disk as predicted
by the chemical model of the parent species after $10^{5}$ yr. The colour map
shows the logarithm of the abundance w.r.t. H2. Note that each colour map has
a different dynamic range.  Figure 18: Fractional abundances of some daughter
species shown in Fig. 9 throughout the disk as predicted by the chemical model
of the parent species after $10^{5}$ yr. The colour map shows the logarithm of
the abundance w.r.t. H2. Note that each colour map has a different dynamic
range.  Figure 19: Disk column density for species that show a decrease (left
panel) and increase in column density relative to the outflow (right panel) of
more than an order of magnitude at any time in the disk chemical model.
Different markers and colours show the ratio at different times for the disk
model. The shaded regions group species originating from different types of
chemistry. Blue: midplane (cosmic ray) chemistry, orange: outer edge (photo)
chemistry, dark orange: hot inner edge. Boldfaced labels denote species that
are formed via cosmic ray and photochemistry.