# Insight into the Formation of $\beta$ Pic b through the Composition of Its
Parent Protoplanetary Disk as Revealed by the $\beta$ Pic Moving Group Member
HD 181327

Henrique Reggiani Gemini Observatory/NSF’s NOIRLab, Casilla 603, La Serena,
Chile  The Observatories of the Carnegie Institution for Science, 813 Santa
Barbara St, Pasadena, CA 91101, USA  Jhon Yana Galarza Carnegie Fellow  The
Observatories of the Carnegie Institution for Science, 813 Santa Barbara St,
Pasadena, CA 91101, USA  Kevin C. Schlaufman William H. Miller III Department
of Physics and Astronomy, Johns Hopkins University, 3400 N Charles St,
Baltimore, MD 21218, USA  Tuve Fellow, Carnegie Institution for Science Earth
& Planets Laboratory, 5241 Broad Branch Road NW, Washington, DC 20015, USA
David K. Sing William H. Miller III Department of Physics and Astronomy, Johns
Hopkins University, 3400 N Charles St, Baltimore, MD 21218, USA  Department of
Earth and Planetary Sciences, Johns Hopkins University, 3400 N Charles St,
Baltimore, MD 21218, USA  Brian F. Healy School of Physics and Astronomy,
University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA  Andrew
McWilliam  The Observatories of the Carnegie Institution for Science, 813
Santa Barbara St, Pasadena, CA 91101, USA  Joshua D. Lothringer Department of
Physics, Utah Valley University, College of Science - MS 179, 800 W University
Pkwy, Orem, UT 84058, USA  Laurent Pueyo Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA

(Accepted 20 November 2023)

###### Abstract

It has been suggested that $\beta$ Pic b has a supersolar metallicity and
subsolar C/O ratio. Assuming solar carbon and oxygen abundances for the star
$\beta$ Pic and therefore the planet’s parent protoplanetary disk, $\beta$ Pic
b’s C/O ratio suggests that it formed via core accretion between its parent
protoplanteary disk’s H2O and CO2 ice lines. $\beta$ Pic b’s high metallicity
is difficult to reconcile with its mass
$M_{\text{p}}~{}=~{}11.7~{}M_{\text{Jup}}$ though. Massive stars can present
peculiar photospheric abundances that are unlikely to record the abundances of
their former protoplanetary disks. This issue can be overcome for early-type
stars in moving groups by infering the elemental abundances of the FGK stars
in the same moving group that formed in the same molecular cloud and
presumably share the same composition. We infer the photospheric abundances of
the F dwarf HD 181327, a $\beta$ Pic moving group member that is the best
available proxy for the composition of $\beta$ Pic b’s parent protoplanetary
disk. In parallel, we infer updated atmospheric abundances for $\beta$ Pic b.
As expected for a planet of its mass formed via core-accretion beyond its
parent protoplanetary disk’s H2O ice line, we find that $\beta$ Pic b’s
atmosphere is consistent with stellar metallicity and confirm that is has
superstellar carbon and oxygen abundances with a substellar C/O ratio. We
propose that the elemental abundances of FGK dwarfs in moving groups can be
used as proxies for the otherwise difficult-to-infer elemental abundances of
early-type and late-type members of the same moving groups.

Exoplanet astronomy(486) — Exoplanet atmospheric composition(2021) — Exoplanet
formation(492) — Exoplanet migration(2205) — Exoplanet systems(484) —
Exoplanets(498) — Planet hosting stars(1242) — Stellar abundances(1577)

††journal: AAS Journals††facilities:  LCO, CDS, Exoplanet Archive, Gaia, IRSA,
Skymapper, Sloan, TESS, ESO††software: astropy (Astropy Collaboration et al.,
2013, 2018), Carpy (Kelson et al., 2000; Kelson, 2003; Kelson et al., 2014),
colte (Casagrande et al., 2021), IRAF (Tody, 1986, 1993), isochrones (Morton,
2015), lightkurve (Lightkurve Collaboration et al., 2018), MOOG (Sneden,
1973), MultiNest (Feroz & Hobson, 2008; Feroz et al., 2009, 2019), numpy
(Harris et al., 2020), pandas (McKinney, 2010; pandas Development Team, 2020),
PyMultinest (Buchner et al., 2014), q2 (Ramírez et al., 2014), RadVel (Fulton
et al., 2017, 2018), scipy (Virtanen et al., 2020)

##  1 Introduction

It has been proposed that a giant planet’s formation location in its parent
protoplanetary disk can be discerned by studying the abundances of the
elements in the planet’s atmosphere. Öberg et al. (2011) suggested that
stellar C/O abundance ratios of giant planets can be used to infer which ice
line (H2O, CO, CO2) its formation was interior to. Sub-stellar or stellar C/O
abundance ratios combined with superstellar carbon abundance were argued to
result from the accretion of large amounts of icy planetesimals after envelope
accretion. Superstellar C/O abundance ratios and carbon abundances could be
attributed either to formation close to the CO2 or CO ice lines or by the
accretion of carbon-rich grains in the narrow range inside the H2O ice line
but outside the carbon-grain sublimation line. Superstellar C/O abundance
ratios and sub-stellar carbon and oxygen abundances were put forward as a
unique signature of formation beyond the H2O ice line.

This straightforward scenario outlined for the case of static disks (Öberg et
al., 2011) is significantly complicated in more realistic models that include
disk chemical and structural evolution, the radial migration of solids,
detailed models for planetesimal accretion, and/or post envelope-accretion
migration. It has also been argued that the abundances in giant planet
envelopes depend critically on the assumptions made regarding the refractory
composition of the inner disk. For a detailed discussion of the complications
we refer the readers to Section $1$ of Reggiani et al. (2022) and the papers
cited therein (Harsono et al., 2015; Piso et al., 2015; Ali-Dib et al., 2014;
Ali-Dib, 2017; Madhusudhan et al., 2014; Mordasini et al., 2016; Madhusudhan
et al., 2017; Booth et al., 2017; Cridland et al., 2016; Eistrup et al., 2018;
Cridland et al., 2019a, 2020; Notsu et al., 2020; Lothringer et al., 2021).

All of these analyses rely on two assumptions: (1) that the envelope of a
young giant planet stays well mixed during its formation even though most
metals are accreted before most gas and (2) that a mature giant planet’s
atmosphere has a similar composition to the average composition of its
envelope at the end of the planet formation process. Therefore, convection and
mixing within the planetary atmosphere and planetary runaway during the gas
accretion phase (e.g., Leconte & Chabrier, 2012; Thiabaud et al., 2015) can
also change the interpretation of these C/O ratios from the idealized view
first proposed by Öberg et al. (2011). Despite all of these complications, one
robust prediction of giant planet formation models in dynamically evolving
disks is that the metal abundances of giant planets with $M_{\text{p}}\lesssim
2~{}M_{\text{Jup}}$ are dominated by the accretion of planetesimals after
envelope accretion. On the other hand, the metal abundances of giant planets
with $M_{\text{p}}\gtrsim 2~{}M_{\text{Jup}}$ are dominated by envelope
accretion itself (Mordasini et al., 2014, 2016; Espinoza et al., 2017;
Cridland et al., 2019b).

The properties of the planet $\beta$ Pic b have been extensively studied in
the literature. Previous studies indicate it has an estimated effective
temperature of T$=1590\pm 20$ K, a surface gravity log$(g/g_{0})=4.0$, a
metallicity of [Fe/H]$=0.5$ dex with a C/O$=0.43\pm 0.05$ (GRAVITY
Collaboration et al., 2020), a mass of $\textrm{M}=11.7\pm 2.2\ M_{Jup}$ (Feng
et al., 2022), and an estimated radius of $\textrm{R}=1.46\pm 0.01\ R_{Jup}$
(Chilcote et al., 2017). The analysis by the GRAVITY Collaboration et al.
(2020) points to a slow formation via core-accretion, somewhere between the
H2O and CO2 icelines. A scenario that can potentially explain the subsolar C/O
ratio if the planet was enriched in oxygen by icy planetesimal accretion. For
more details on the planet’s formation, we refer the reader to GRAVITY
Collaboration et al. (2020).

However, the interpretation of giant planet formation is also dependent on its
atmospheric carbon, oxygen, and C/O abundances, and as outlined above it is
far from simple. Moreover, giant planet atmospheric abundance ratios can only
be meaningfully interpreted relative to the mean compositions of their parent
protoplanetary disk. Directly inferring the abundances from protoplanetary
disks is not straightforward even when the disk is still observable. However,
in most cases the protoplanetary disk has already dissipated by the time we
observe the planets. Therefore, the only way to reveal the mean compositions
of those disks is to use the photospheric abundances of their host stars.
During the era of giant planet formation, the star growing at the center of a
protoplanetary disk has already accreted 99% of the material that ever passed
through its disk. As a result, the photospheric abundances of planet-host
stars are an excellent proxy for mean protoplanetary disk abundances. The
implication is that accurate and precise host star elemental abundances for
the same elements observed in giant planet atmospheres are critically needed
to achieve the full potential of giant planet atmospheric abundance inferences
as planet formation constraints, as was shown in Reggiani et al. (2022).

However, it is not always possible to directly infer all elemental abundances
of a star. This is a notoriously difficult task for stars such as $\beta$ Pic
because of its high effective temperature, surface gravity, and fast rotation
($\textrm{T}_{eff}=8084\pm 130$ K, log$g=4.22\pm 0.13$,
$v_{\textrm{micro}}=3.31$ km.s-1, and vsin(i)$=113\pm 1.13$ km.s-1, Saffe et
al., 2021). Thus, it is not easy/possible to directly infer its entire
chemical pattern. With exquisite HARPS spectra (R$\sim 115000$, SNR$=1500$)
Saffe et al. (2021) was able to measure the abundances of C I, Mg I, Al I, Si
II, Ca I, Ca II, Ti II, Cr II, Mn I, Fe I, Fe II, Sr II, Y II, Zr II, and Ba
II. Its oxygen abundance is noticeably missing, an essential element to the
interpretation of planetary formation/migration scenarios, as described above.
For $\beta$ Pic, to the best of our knowledge, oxygen was not yet measured
(GRAVITY Collaboration et al., 2020).

There are extra complications to analyze $\beta$ Pic. It is a $\delta$ Scuti
star (e.g., Mékarnia et al., 2017), very close to the ZAMS (Crifo et al.,
1997), surrounded by a debris disk composed of dust and gas known to be
continuously replenished by evaporating exocomets and colliding planetesimals
(Ferlet et al., 1987; Lecavelier des Etangs et al., 1996; Beust & Morbidelli,
2000; Wilson et al., 2017). $\beta$ Pic has very low-amplitude periodic
variations in brightness, radial velocity, and line profiles (Koen, 2003; Koen
et al., 2003; Galland et al., 2006).

Like many other A-type stars, $\beta$ Pic has a peculiar abundance pattern.
Typical abundance peculiarities of A-type stars can be as extreme as the large
underabundances ($\sim 1-2$ dex) of iron-peak elements, with near-solar
abundances of C, N, O, and S seen in $\lambda$ Boötis stars (Kamp et al.,
2001; Andrievsky et al., 2002; Heiter, 2002). Up to 20% of A- B-type stars
have a wide range of chemical peculiarities, often associated with the
presence of magnetic fields (e.g., Folsom et al., 2012). Folsom et al. (2012)
also discusses the possibility that recently formed Hot Jupiters block the
accretion of heavier material onto the star.

Similar to other stars of its spectral type, $\beta$ Pic is also known to have
a peculiar abundance pattern: sub-solar (in [X/H]) abundances of C, Mg I, Al,
Si, Sc, Ti, Cr, Mn, Fe, and Sr, while showing solar abundance of Mg II, Y, and
Ba, and super-solar abundance of Ca (Saffe et al., 2021). $\beta$ Pic, formed
$\sim 30$ Myr ago in the thin disk of the Galaxy, does not follow the expected
abundance pattern (e.g., Buder et al., 2021). While the metallicity of $\beta$
Pic is [Fe/H]$=-0.28$ (Saffe et al., 2021), the metallicity distribution
function of the solar neighborhood peaks at [Fe/H]=0.0 (e.g., Kobayashi et
al., 2020). While it is not impossible for a young star to have the estimated
metallicity of $\beta$ Pic, it is unlikely.

Therefore, as the abundance pattern of $\beta$ Pic, a star of a spectral type
known to show chemical peculiarities (A-type), does not correspond to the
expected abundance distribution of the solar neighborhood, the analysis of its
photospheric abundances is unlikely to be a reliable tracer of the composition
of the molecular cloud from which it formed. Therefore, it is also not a
reliable tracer of the composition of the protoplanetary disk from which its
planets were formed. On the other hand, stars are not formed isolated. They
are formed in clusters, and stars that are co-natal share the same chemical
composition. This assumption has been thoroughly tested in the literature, in
studies testing the limits of chemical tagging (e.g. Ness et al., 2018;
Andrews et al., 2019), in analyzes of binary stars (e.g., Hawkins et al.,
2020; Nelson et al., 2021), and stars in open clusters (e.g. Ting et al.,
2012; García Pérez et al., 2016).

In light of the above we propose that, for systems such as $\beta$ Pic, the
stars that are part of their moving groups are a better probe of the
interstellar material from which they, and their exoplanets, formed. In
particular, the photospheric abundances of less massive, less evolved, stars
in $\beta$ Pic’s moving group are the best possible window into the
protoplanetary disk’s composition where $\beta$ Pic b formed.

In this article we infer the potospheric and fundamental parameters as well as
individual elemental abundances—including carbon and oxygen—for a star that is
part of $\beta$ Pic’s moving group. We also perform a new retrieval of $\beta$
Pic b. We discuss how our results compare to the results previously published
by GRAVITY Collaboration et al. (2020). Our combined interpretation of the
stellar abundances and planetary abundances corroborate the GRAVITY
Collaboration et al. (2020) conclusions, although our results of star and
planet are a better fit, especially for the planetary metallicity. We describe
in Section 2 the high-resolution optical spectrum we collected for our
programme stars. We then infer stellar parameters in Section 3. We derive the
individual elemental abundance in Section 4. We present our retrieval of
$\beta$ Pic b in Section 5. We review our results and their implications in
Section 6. We conclude in Section 7.

##  2 Data

In order to analyze stellar data that would ultimately allow us to discuss
$\beta$ Pic b’s formation, we wanted to study stars that are part of $\beta$
Pic’s moving group. In an effort to study the dynamical age of $\beta$ Pic’s
moving group, Miret-Roig et al. (2020) presented Gaia-based updated members of
the moving group (see their Table 3). Their methodology is currently the gold
standard for membership probability, i.e., they use the complete set of
kinematic information available, provided by Gaia (Gaia Collaboration et al.,
2016, 2018), to traceback the Galactic Orbit and associate individual stars
with $\beta$ Pic’s moving group. All the stars they identified as members of
the moving group have a traceback position within 7 pc, with an uncertainty
smaller than 2 pc at the time of minimum size. For reference, Miret-Roig et
al. (2020) shows that the $\beta$ Pic association size (at time of birth) to
be comparable to that of known starforming regions such as Ophiuchus (Cánovas
et al., 2019), Taurus (Galli et al., 2019), and Corona Australis (Galli et
al., 2020). For more details on the membership analysis we refer the reader to
Miret-Roig et al. (2020).

From their Table 3 (containing a total of 26 members of the $\beta$ Pic moving
group), there are only two F type stars and two K type stars. The first K star
is V* AO Men, an active eruptive variable. Its variability makes it so that
the analysis we aim to do is unreliable, as spectral lines can change based on
variability yielding different stellar abundances that are dependent on the
current level of stellar activity. Its temperature is also not ideal for the
measurement of atomic carbon lines ($\mathrm{T_{eff}}=4431$ K based on an
Infrared Flux Method estimative - Casagrande et al., 2021). The second K star
is CPD -72 2713. It is also active, and even cooler ($\mathrm{T_{eff}}=3992$
\- based on the same analysis method); therefore, it is also not suitable for
our methodology. Twenty-two out of the 26 members of the moving group are M
stars. M stars have much more crowded optical spectra, leading to blended
features. The spectra of M stars exhibit numerous molecular features, some of
which are still being identified (e.g. Crozet et al., 2023), and a more
complex atmospheric structure (for colder M dwarfs even clouds are an
important factor). While we have many Benchmark analysis of FG stars, we are
still benchmarking analysis methods of M dwarf (e.g., Souto et al., 2022;
Balmer et al., 2023), which involves comparing their abundances to those of
already benchmarked FGK dwarfs. In essence, all the M and K stars that are
part of $\beta$ Pic’s moving group are not amenable to accurate and precise
analysis of their chemistry, and in particular of the carbon and oxygen
abundances needed to interpret planetary formation and migration scenarios.
Moreover, our analysis methodology (e.g., Reggiani et al., 2022) has been
tested for FG and hot K stars. For these stars, we can obtain reliable stellar
fundamental and photospheric parameters using our linelist and
spectra+isochrones-based analysis.

Therefore, only two stars, HD 181327 and HD 191089, were suitable for our
analysis methodology. We collected their spectra with the Magellan Inamori
Kyocera Echelle (MIKE) spectrograph on the Magellan Clay Telescope at Las
Campanas Observatory (Bernstein et al., 2003; Shectman & Johns, 2003). We used
the 0$\farcs$7 slit with standard blue and red grating azimuths, yielding
spectra between 335 nm and 950 nm with resolution $R\approx 40,\\!000$ in the
blue and $R\approx 31,\\!000$ in the red arms.

We collected all calibration data (e.g., bias, quartz & “milky” flat field,
and ThAr lamp frames) in the afternoon before each night of observations. We
reduced the raw spectra and calibration frames using the
CarPy111http://code.obs.carnegiescience.edu/mike software package (Kelson et
al., 2000; Kelson, 2003; Kelson et al., 2014). Radial velocity correction and
spectra normalization were performed using the Spectroscopy made Harder (smhr;
Casey, 2014)222https://github.com/andycasey/smhr/tree/py38-mpl313 code.

Once our spectra were reduced and normalized we visually inspected them. After
our inspection we dropped star HD 191089 from subsequent analysis. Because of
the visibly high rotational velocity ($\approx 40$ km.s-1, Zúñiga-Fernández et
al., 2021), some lines of interest (mainly carbon and oxygen transitions) are
blended and cannot be reliably measured. In Figure 1 we show a region of the
spectra of HD 181327, $beta$ Pic, and HD 191089. The high rotation of HD
191089, and the extreme velocity of $\beta$ Pic are easily observable. The
$\beta$ Pic spectrum showed is an extremely high resolution (R$=115,000$), and
high signal-to-noise (SNR$=215$) spectrum. Data for $\beta$ Pic was collected
from the ESO archive, from observing program ID 0104.C-0418(C). After our data
collection, reduction, and initial assessment, we will focus our efforts in
studying HD 181327. This star is the only gold-standard confirmed $\beta$ Pic
moving group member amenable to a never-before-published accurate and precise
carbon and oxygen abundance inference, necessary for the interpretation of
planetary formation scenarios.

Figure 1: We show the $4500-4540\ \AA$ region of our spectra along with HARPS
archival data of $\beta$ Pic from observing program ID 0104.C-0418(C). The
high rotational velocities of HD 191089 ($\approx 40$ km.s-1, Zúñiga-Fernández
et al., 2021) and $\beta$ Pic are visible, and individual important atomic
features are not possible to distinguish.  Table 1: Log of Magellan/MIKE
Observations

ID | R.A. | Decl. | UT Date | Start | Slit | Exposure | $v_{r}$ | S/N | S/N | Spectral Type
---|---|---|---|---|---|---|---|---|---|---
Designation | (h:m:s) | (d:m:s) |  |  | Width | Time (s) | (km s-1) | $4500\ \rm{\AA}$ | $6500\ \rm{\AA}$ |
HD 181327 | 19:22:58.94 | -54:32:16.98 | 2022 Apr 26 | 09:37:05 | 0$\farcs$7 | $70$ | $-21.8$ | $220$ | $335$ | F$7$
HD 191089 | 20:09:05.22 | -26:13:26.52 | 2022 Apr 28 | 09:16:23 | 0$\farcs$7 | $120$ | $-33.6$ | $300$ | $380$ | F$5^{a}$

Note. — a: Spectral type from Miret-Roig et al. (2020)

##  3 Stellar Parameters

We derive photospheric and fundamental stellar parameters for our program star
using the algorithm described in Reggiani et al. (2022) that makes use of both
the classical spectroscopy-only approach333The classical spectroscopy-only
approach to photospheric stellar parameter estimation involves simultaneously
minimizing for individual line-based iron abundance inferences the difference
between Fe I & Fe II-based abundances as well as their dependencies on
transition excitation potential and measured reduced equivalent width. and
isochrones to infer accurate, precise, and self-consistent photospheric
(T${}_{\text{eff}}$, log$g$, and [Fe/H)] and fundamental (mass, luminosity,
and radius) stellar parameters.

For our isochrone fitting we use high-quality multiwavelength photometry from
the ultraviolet to the near-infrared: Tycho-2 BT and VT (Høg et al., 2000),
Gaia DR2 (Gaia Collaboration et al., 2016, 2018; Arenou et al., 2018; Evans et
al., 2018; Hambly et al., 2018; Riello et al., 2018; Gaia Collaboration et
al., 2021; Fabricius et al., 2021; Lindegren et al., 2021a, b; Torra et al.,
2021) G, J, H, and Ks bands from the Two Micron All Sky Survey (2MASS) All-Sky
Point Source Catalog (PSC, Skrutskie et al., 2006), and W1 and W2 bands from
the Wide-field Infrared Survey Explorer (WISE) AllWISE mid-infrared data
(Wright et al., 2010; Mainzer et al., 2011). We also include Gaia DR3 (Gaia
Collaboration et al., 2021) parallax-based distances (Bailer-Jones et al.,
2021) of our targets. We include the extinction $A_{V}$ inference based on
three-dimensional (3D) maps of extinction in the solar neighborhood from the
Structuring by Inversion the Local Interstellar Medium (Stilism) program
(Lallement et al., 2014, 2018; Capitanio et al., 2017).

For the spectroscopic-based inferences we use the equivalent widths (EWs) of
Fe I and Fe II atomic absorption lines. The EWs were measured from our MIKE
spectrum using Gaussian profiles with the splot task of IRAF444IRAF is
distributed by the National Optical Astronomy Observatory, which is operated
by the Association of the Universities for Research in Astronomy, Inc. (AURA)
under cooperative agreement with the Na- tional Science Foundation.. The
atomic absorption line data is an updated version from the lines described in
Yana Galarza et al. (2019). We assume Asplund et al. (2021) photospheric solar
abundances.

As described in detail in Reggiani et al. (2022), we use the isochrones
package555https://github.com/timothydmorton/isochrones (Morton, 2015) to fit
the MESA Isochrones and Stellar Tracks (MIST; Dotter, 2016; Choi et al., 2016;
Paxton et al., 2011, 2013, 2015, 2018, 2019) library to our photospheric
stellar parameters as well as our input multiwavelength photometry, parallax,
and extinction data using
MultiNest666https://ccpforge.cse.rl.ac.uk/gf/project/multinest/ (Feroz &
Hobson, 2008; Feroz et al., 2009, 2019) via PyMultinest (Buchner et al.,
2014).

We also analyzed the rotational period using TESS data and the technique of
Healy & McCullough (2020); Healy et al. (2021, 2023). We processed PCA-
detrended light curves from eleanor (Feinstein et al., 2019) by masking
transits, removing outliers, flattening the light curves using 1-D
polynomials, and binning the resulting points. We then generated a Lomb-
Scargle periodogram and an autocorrelation function for each light curve,
analyzing the peak positions and widths to determine periods and
uncertainties.

Our adopted stellar parameters ($\rm{T_{eff}}$ and surface gravity from the
isochrone analysis, and [Fe/H] and $\xi$ inferred from the atomic Fe I and Fe
II lines) are in Table 2. All of the uncertainties quoted in Table 2 include
random uncertainties only. That is, they are uncertainties derived under the
unlikely assumption that the MIST isochrone grid we use in our analyses
perfectly reproduces all stellar properties.

Table 2: Adopted Stellar Parameters for HD 181327 Property | Value | Unit
---|---|---
Tycho $B$ | $7.588\pm 0.016$ | Vega mag
Tycho $V$ | $7.091\pm 0.010$ | Vega mag
Gaia DR2 $G$ | $6.936\pm 0.002$ | Vega mag
2MASS $J$ | $6.200\pm 0.024$ | Vega mag
2MASS $H$ | $5.980\pm 0.044$ | Vega mag
2MASS $K_{\text{s}}$ | $5.910\pm 0.029$ | Vega mag
WISE W1 | $5.877\pm 0.053$ | Vega mag
WISE W2 | $5.792\pm 0.023$ | Vega mag
Gaia DR3 parallax | $20.931\pm 0.029$ | mas
Isochrone-inferred parameters
Effective temperature $T_{\text{eff}}$ | $6498^{+56}_{-53}$ | K
Surface gravity $\log{g}$ | $4.33\pm 0.01$ | cm s-2
Stellar mass $M_{\ast}$ | $1.36\pm 0.02$ | $M_{\odot}$
Stellar radius $R_{\ast}$ | $1.32\pm 0.01$ | $R_{\odot}$
Luminosity $L_{\ast}$ | $0.44\pm 0.02$ | $L_{\odot}$
Isochrone-based age $\tau_{\text{iso}}$ | $60\pm 30$ | Myr
Spectroscopically inferred parameters
Metallicity $[\text{Fe/H}]$ | $0.05\pm 0.06$ |
Microturbulent velocity $\xi$ | $1.63\pm 0.16$ | km s-1
Light-curve inferred parameters
Rotational period $P_{\text{rot}}$ | $1.542\pm 0.048$ | day

##  4 Elemental Abundances

To infer the elemental abundances of the $\alpha$, light odd-$Z$, iron-peak,
and neutron-capture elements we first measure the EWs of atomic absorption
lines of Li I, C I, N I, O I, Na I, Mg I, Al I, Si I, S I, K I, Ca I, Sc I, Sc
II, Ti I, Ti II, V I, Cr I, Cr II, Mn I, Fe I, Fe II, Ni I, Cu I, Zn I, Y II,
and Ba II in our continuum-normalized spectrum by fitting Gaussian profiles
with the splot task in IRAF. We use the deblend task to disentangle absorption
lines from adjacent spectral features whenever necessary. We measure an EW for
every absorption line in our line list that could be recognized, taking into
consideration the quality of the spectrum in the vicinity of a line and the
availability of alternative transitions of the same species. We assume Asplund
et al. (2021) solar abundances and local thermodynamic equilibrium (LTE) and
use the 1D plane-parallel solar-composition ATLAS9 (Castelli & Kurucz, 2003)
model atmospheres and the 2019 version of the LTE radiative transfer code MOOG
to infer elemental abundances based on our EWs.

We report in Table 3 our abundance inferences in three common systems:
$A(\text{X})$, $[\text{X/H}]$, and
$[\text{X/Fe}]$777$A(\text{X})=\log{N_{\text{X}}/N_{\text{H}}}+12$
$[\text{X/H}]=A(\text{X})-A(\text{X})_{\odot}$
$[\text{X/Fe}]=[\text{X/H}]-[\text{Fe/H}]$. We define the uncertainty in the
abundance ratio $\sigma_{[\text{X/H}]}$ as the square root of the sum of the
square as the standard deviation of the individual line-based abundance
inferences $\sigma_{[\text{X/H}]}^{\prime}$ divided by $\sqrt{n_{\text{X}}}$.
We define the uncertainty $\sigma_{[\text{X/Fe}]}$ as the square root of the
sum of squares of $\sigma_{[\text{X/H}]}$ and $\sigma_{[\text{Fe/H}]}$.

Table 3: Elemental Abundances HD 181327

Species | $A(\text{X})$ | [X/H] | $\sigma_{\text{[X/H]}}$ | [X/Fe] | $\sigma_{[\text{X/Fe}]}$ | $n$
---|---|---|---|---|---|---
LTE abundances |
Li I | $3.49$ | $2.53$ | $\cdots$ | $2.48$ | $0.04$ | $1$
C I | $8.39$ | $-0.07$ | $0.06$ | $-0.12$ | $0.04$ | $5$
N I | $\leq 7.81$ | $\leq-0.02$ | $\cdots$ | $\leq-0.07$ | $\cdots$ | $1$
O I | $8.92$ | $0.23$ | $0.09$ | $0.18$ | $0.08$ | $3$
Na I | $6.20$ | $-0.02$ | $0.12$ | $-0.07$ | $0.12$ | $2$
Mg I | $7.65$ | $0.10$ | $0.12$ | $0.04$ | $0.07$ | $5$
Al I | $6.21$ | $-0.22$ | $0.34$ | $-0.28$ | $0.24$ | $3$
Si I | $7.77$ | $0.26$ | $0.32$ | $0.20$ | $0.10$ | $12$
S I | $7.20$ | $0.08$ | $0.26$ | $0.02$ | $0.19$ | $3$
K I | $5.64$ | $0.57$ | $0.00$ | $0.52$ | $0.07$ | $1$
Ca I | $6.54$ | $0.24$ | $0.19$ | $0.18$ | $0.07$ | $11$
Sc I | $3.53$ | $0.39$ | $0.38$ | $0.33$ | $0.38$ | $2$
Sc II | $3.57$ | $0.43$ | $0.61$ | $0.38$ | $0.22$ | $9$
Ti I | $5.23$ | $0.26$ | $0.38$ | $0.21$ | $0.12$ | $12$
Ti II | $5.49$ | $0.52$ | $0.88$ | $0.47$ | $0.32$ | $9$
V I | $4.54$ | $0.64$ | $0.05$ | $0.59$ | $0.07$ | $2$
Cr I | $5.74$ | $0.12$ | $0.24$ | $0.07$ | $0.09$ | $11$
Cr II | $5.90$ | $0.28$ | $0.21$ | $0.23$ | $0.10$ | $7$
Mn I | $5.26$ | $-0.16$ | $0.30$ | $-0.22$ | $0.13$ | $7$
Fe I | $7.51$ | $0.05$ | $0.09$ | $\cdots$ | $\cdots$ | $37$
Fe II | $7.63$ | $0.17$ | $0.15$ | $\cdots$ | $\cdots$ | $15$
Ni I | $6.34$ | $0.14$ | $0.34$ | $0.09$ | $0.09$ | $17$
Cu I | $4.35$ | $0.17$ | $0.29$ | $0.11$ | $0.29$ | $2$
Zn I | $4.51$ | $-0.05$ | $0.08$ | $-0.11$ | $0.10$ | $2$
Y II | $2.70$ | $0.49$ | $0.62$ | $0.43$ | $0.36$ | $4$
Ba II | $2.79$ | $0.52$ | $0.22$ | $0.47$ | $0.15$ | $4$
1D non-LTE abundancesa
C I | $8.37$ | $-0.09$ | $0.06$ | $-0.19$ | $\cdots$ | $1$
O I | $8.56$ | $-0.13$ | $0.09$ | $-0.23$ | $\cdots$ | $1$
Al I | $6.10$ | $-0.33$ | $0.36$ | $-0.43$ | $\cdots$ | $2$
Si I | $7.74$ | $0.23$ | $0.30$ | $0.13$ | $\cdots$ | $12$
K I | $5.14$ | $0.07$ | $0.00$ | $-0.3$ | $\cdots$ | $1$
Ca I | $6.04$ | $-0.26$ | $0.06$ | $-0.36$ | $\cdots$ | $2$
Fe I | $7.56$ | $0.10$ | $0.09$ | $\cdots$ | $\cdots$ | $37$
Fe II | $7.68$ | $0.22$ | $0.16$ | $\cdots$ | $\cdots$ | $15$
3D non-LTE abundances
Li I | $3.27$ | $2.31$ | $\cdots$ | $2.18$ | $0.04$ | $1$
C I | $8.38$ | $-0.08$ | $0.06$ | $-0.18$ | $\cdots$ | $5$
O I | $8.59$ | $-0.10$ | $0.06$ | $-0.20$ | $\cdots$ | $3$
Additional abundance ratios of interestb
$[\text{Fe/H}]_{\text{1Dnon-LTE}}=+0.13\pm 0.10$
$[\text{(C+O)/H}]_{\text{1DLTE}}=+0.16\pm 0.11$
$[\text{(C+O)/H}]_{\text{1Dnon-LTE}}=-0.22\pm 0.11$
$[\text{(C+O)/H}]_{\text{3Dnon-LTE}}=-0.18\pm 0.08$
$[\text{C/O}]_{\text{1DLTE}}=-0.3\pm 0.11$
$[\text{C/O}]_{\text{1Dnon-LTE}}=+0.04\pm 0.11$
$[\text{C/O}]_{\text{3Dnon-LTE}}=+0.02\pm 0.08$
C/O${}_{\text{1DLTE}}=+0.30\pm 0.11$
C/O${}_{\text{1Dnon-LTE}}=+0.65\pm 0.11$
C/O${}_{\text{3Dnon-LTE}}=+0.62\pm 0.08$

aafootnotetext: [X/Fe] ratios calculated using the 1D non-LTE corrected Fe I a
bundances ([Fe I/H]$=+0.10$).

bbfootnotetext: C/O ratios are defined as C/O$=10^{(A(C)-A(O))}$.

When possible, we update our elemental abundances for departures from LTE
(i.e., non-LTE corrections) by linearly interpolating published grids of non-
LTE corrections using scipy (Virtanen et al., 2020). We use the publicly
available correction tables from Amarsi et al. (2020) for carbon, oxygen,
aluminium, and calcium. Silicon corrections are from Amarsi & Asplund (2017),
potassium corrections are from Reggiani et al. (2019), and iron corrections
are from Amarsi et al. (2016). There is one caveat for our carbon 1D non-LTE
corrected abundance. The Amarsi et al. (2020) non-LTE grid only includes one
carbon transition: the $6588\ \AA$ transition. This line is visible in our
spectrum, but blended with a telluric feature which we have not been able to
properly remove. Therefore, we used the mean 1D LTE abundance of all carbon
lines (Table 3) to estimate our correction. For oxygen, the grid has a mean
correction based on all three lines at the $777$ nm region. We, therefore, use
our mean 1D LTE oxygen abundance (Table 3) to estimate the correction. Our
reported 3D non-LTE abundances for carbon and oxygen are a nearest neighbor
extrapolation based on the Amarsi et al. (2019) grid. Our extrapolations are
to values extremely close to the edge of the correction grids, and therefore
reliable results. All our non-LTE estimated abundances are presented in Table
3.

We estimated possible systematics in our non-LTE corrections by interpolating
oxygen abundance corrections from Bergemann et al. (2021), through the online
tool Spectrum Tools888https://nlte.mpia.de/. Our interpolation resulted in a
mean 1D non-LTE correction of $\Delta\text{A(O)}=-0.18$, considerably
different than the 1D non-LTE correction we inferred
($\Delta\text{A(O)}=-0.36$) from Amarsi et al. (2020).

We confirmed our own estimates by interpolating the same corrections using the
online tool INSPECT999http://www.inspect-stars.com/, which is based on the
same oxygen model-atom used in Amarsi et al. (2020). For its interpolation
process Spectrum Tools does not request line abundances, therefore the
interpolated correction is not specific for a line/abundance measurement. It
does, however, show the curve of growth from which the result was
interpolated. From visual inspection of the curves of growth, the abundance
corrections appear higher than what we reported here
($\Delta\text{A(O)}=-0.18$). Nevertheless, because of the uncertainty
generated by not being able to directly interpolate our abundances, we chose
to adopt the Amarsi et al. (2020), Amarsi et al. (2019) 1D and 3D corrections,
respectively.

Even so, we caution the reader of a possible systematic in our oxygen
corrections of up to $\approx 0.18$ dex. It is outside the scope of this study
to understand the differences between the models that might be responsible for
this difference, but we point that if we were to adopt the 1D non-LTE
correction from Spectrum Tools, the C/O ratio would be C/O${}_{\text{1Dnon-
LTE}}=+0.43$. This different C/O ratio would not, however, change the
interpretations of our results (Section 6.2).

Table 4: Atomic data, Equivalent Widths and line Abundances. Full version
online.

Wavelength | Species | Excitation Potential | log($gf$) | EW | $\log_{\epsilon}(\rm{X})$
---|---|---|---|---|---
| (Å) |  | (eV) |  | (mÅ)
$6154.225$ | Na I | $2.102$ | $-1.547$ | $25.3$ | $6.318$
$6160.747$ | Na I | $2.104$ | $-1.246$ | $28.3$ | $6.081$
$4571.095$ | Mg I | $0.000$ | $-5.623$ | $87.5$ | $7.781$
$4730.040$ | Mg I | $4.340$ | $-2.389$ | $44.0$ | $7.610$

Note. — This table is published in its entirety in the machine-readable
format. A portion is shown here for guidance regarding its form and content.

##  5 $\beta$ Pic b Retrieval

###  5.1 Retrievals for $\beta$ Pic b

We performed spectral retrievals on $\beta$ Pic b, using the GRAVITY and GPI
data (GRAVITY Collaboration et al., 2020; Chilcote et al., 2017). Compared to
previous work, we re-calibrated the GPI data following the procedures in De
Rosa et al. (2020) which improves the photometric precision and reduces
systematic errors. We use ATMO, a 1D-2D radiative-convective equilibrium model
for planetary atmospheres to generate models of beta Pic b. More comprehensive
descriptions of the model can be found in Amundsen et al. (2014); Tremblin et
al. (2015, 2016, 2017); Drummond et al. (2016), Goyal et al. (2018), and Goyal
et al. (2018).

Table 5: ATMO Retrieval parameters. Parameter | Posterior
---|---
Fit parameters
$[Z/Z$${}_{\odot}]$ | 0.021${}_{-0.117}^{+0.243}$
$R$pl(RJup,1 mbar) | 1.2941${}_{-0.011}^{+0.015}$
cloud opacity ln($\delta$) | 3.26${}_{-0.48}^{+0.32}$
log cloud top (bar) | -0.982${}_{-0.162}^{+0.115}$
$\kappa_{IR}$ (cm2/g) | -1.29$\pm$-0.17
$\gamma_{1}$ | -3.57${}_{-1.52}^{+1.37}$
Internal Temp (K) | 1840${}_{-18}^{+12}$
$[\text{C/H}]$ | 0.255${}_{-0.150}^{+0.179}$
$[\text{O/H}]$ | 0.467${}_{-0.158}^{+0.159}$
$\text{A(C)}$ | $8.755_{-0.150}^{+0.179}$
$\text{A(O)}$ | $9.227_{-0.158}^{+0.159}$
Asplund et al. (2021) Scaled Abundances
$[\text{Fe/H}]$ | $0.081^{+0.246}_{-0.124}$
$[\text{C/H}]$ | $0.295_{-0.155}^{+0.183}$
$[\text{O/H}]$ | $0.537_{-0.163}^{+0.164}$
Inferred parameters
C/O | 0.35${}_{-0.03}^{+0.02}$
Mass ($M_{\rm Jup}$) | 7.2${}_{-2.5}^{+3.6}$
Figure 2: $\beta$ Pic b GPI and Gravity spectrum (black datapoints) along with
the posterior distribution of the spectral retrieval model.

For the model assuming chemical equilibrium, the elemental abundances for each
model were freely fit and calculated in equilibrium on the fly. Two elements
were selected to vary independently, as they are major species which are also
likely to be sensitive to spectral features in the data, while the rest were
varied by a metallicity parameter ([Z/Z⊙]). By varying the carbon and
oxygen,elemental abundances separately ([C/C$\odot$] & [O/O$\odot$]) we allow
for non-solar compositions but with chemical equilibrium imposed such that
each model fit has a chemically-plausible mix of molecules given the retrieved
temperatures, pressures and underlying elemental abundances. In addition, we
alleviate an important modeling assumption which can affect the retrieved C/O
value (see Drummond et al. 2019). The solar abundances of C, N, O, P, S, K, Fe
were defined from Caffau et al. (2011) while we used Asplund et al. (2009) for
the other species. As our stellar abundances are scaled to the Asplund et al.
(2021) photospheric solar abundances we also present, in Table 5, the
planetary metallicity, as traced by iron, carbon, and oxygen abundances re-
scaled to the Asplund et al. (2021) solar photospheric abundances. While the
solar abundance uncertainties were not included in our original retrieval, we
include the uncertainties of the Asplund et al. (2021) solar abundances in
Table 5. The updated uncertainties are the square root of the sum of squares
of the planetary uncertainties and the Asplund et al. (2021) uncertainties.
For the spectral synthesis, we included the spectroscopically active molecules
of H2, He, H2O, CO2, CO, CH4, NH3, H2S, HCN, C2H2, Na, K, TiO, VO, FeH, Fe,
and H-. To parameterize the T-P profile, we use the analytic radiative
equilibrium model as described Guillot (2010). We vary three parameters,
corresponding to one optical channel, one infrared channel and the internal
temperature. The suface gravity was also allowed to vary.

We also included a grey cloud parameterized by a uniform opacity and a cloud
top pressure level. Rainout of condensate species was also included. In total,
10 free parameters were used to fit the 337 datapoints. The results are shown
in Figs. 2 and 3 with the results also given in Table 5 including the best-
fitting model parameters and 1 $\sigma$ uncertainties. We retrieve a mass of
7.2${}_{-2.5}^{+3.6}$ $M_{Jup}$ which consistent with the latest estimates of
9 to 11 $M_{Jup}$ using radial velocity, astrometry, and direct imaging data
Feng et al. (2022); Lagrange et al. (2019).

Figure 3: Posterior distribution for the ATMO atmospheric retrieval model fit
to the $\beta$ Pic b spectrum.

##  6 Discussion

###  6.1 HD 181327 as a Tracer of the Composition of $\beta$ Pic b’s Proto-
Planetary Disk

The inferred metallicity of $\beta$ Pic is subsolar (Saffe et al., 2021).
Although technically not impossible, it is very unlikely for a solar
neighborhood, younger than 100 Myrs star, to be formed in a low metallicity
environment (e.g. Kobayashi et al., 2020). On the other hand, the chemical
abundances we inferred for HD 181327 are within the expected range of
abundances for a solar neighborhood, solar/mildly super-solar metallicity star
(both observationally and theoretically, Kobayashi et al., 2020), unlike
$\beta$ Pic itself. This difference is a result of $\beta$ Pic’s chemical
peculiarities, (see Section 1 and the brief discussion on A stars). This
provides initial, albeit indirect, evidence that HD 181327 might be a better
representation of the composition of the molecular cloud from which $\beta$
Pic, and $\beta$ Pic b formed.

Stars are formed in clusters, and moving groups are remnants of the clusters
where stars were formed. There is now ample evidence indicating that stars
formed together are chemically homogeneous. Previous studies of co-moving
pairs of stars show that their abundances are homogeneous at the $0.05$ dex
level (e.g., Hawkins et al., 2020; Nelson et al., 2021).

Studying open clusters homogeneity, Poovelil et al. (2020) recently found that
their chemistry is homogeneous at the $0.03$ dex level. They used APOGEE to
study a set of ten open clusters. Each open cluster has at least 13 members
(ranging from 13 to 381 members), with an average of 29 members per cluster,
excluding the one cluster with 381 studied members (the only cluster with more
than 60 members in their sample). This extremely good homogeneity has
previously been reported in other open clusters as well: IC 4756 has a star-
to-star variation smaller than [X/H]$<0.03$ dex (Ting et al., 2012, e.g.,);
The Hyades are homogeneous within $0.02$ dex (De Silva et al., 2006a, b; Liu
et al., 2016); M67, NGC 6819, and NGC 2420 also show homogeneity within $0.03$
dex (Bovy, 2016); Bertran de Lis et al. (2016) found homogeneity better than
$0.01$ dex for [O/Fe] in several clusters. In conclusion, it is safe to assume
that open clusters are homogeneous. Consequently, we can assume that stars in
the same moving group are chemically homogeneous at least to the $0.03$ dex
level.

Miret-Roig et al. (2020) found 26 members of $\beta$ Pic’s moving group, a
similar number of members as those of the Poovelil et al. (2020) open clusters
study. With a number of members similar to the previously studied clusters, we
assume the homogeneity of the $\beta$ Pic moving group to be similar
(dispersion $<0.03$ dex). Therefore, if one can measure the chemical
abundances of a reliable tracer of the moving group, its abundances should be
within the order of $\sim 0.03$ dex of the remaining moving group members.
Thus, the abundances inferred for HD 181327 should be a good reflection of the
abundances of the molecular cloud where the $\beta$ Pic moving group formed.

That is not the case for $\beta$ Pic itself. It is an A star with an unusual
chemical composition: sub-solar (in [X/H]) abundances of C, Mg, Al, Si, Sc,
Ti, Cr, Mn, Fe, and Sr, while showing solar abundance of Mg II, Y, and Ba, and
super-solar abundance of Ca (Saffe et al., 2021). $\beta$ Pic is also
classified as a $\delta$ Scuti star, with over 30 $\delta$ Scuti pulsation
frequencies identified (Mékarnia et al., 2017). The pulsation alone makes it
challenging for an abundance analysis, as spectroscopic line-profiles vary
with pulsation (Aerts et al., 2008). Moreover, its high rotational velocity
($>100\ \mathrm{km.s^{-1}}$, see Fig. 1) makes it challenging for an accurate
and precise determination of several species, such as oxygen (never directly
inferred from $\beta$ Pic). In fact, because of the difficulties, and
intrinsic characteristics of $\beta$ Pic, a comparison between its composition
and the composition we inferred for HD 181327 shows differences far exceeding
the $0.03$ dex homogeneity observed in stars formed within the same molecular
clouds. We show these differences in Figure 4. Because the inferred chemistry
of $\beta$ Pic cannot be reliably used as a proxy for its molecular cloud (due
to its pulsation, rotational velocity, and chemical peculiarities), we turned
ourselves to another proxy: Hd 181327.

Based on the information presented above, we argue that, for the specific case
of $\beta$ Pic b, the best way to interpret its planetary retrieved chemistry
is to analyze the chemical makeup of star HD 181327, the only slow rotator,
low activity, F star in $\beta$ Pic’s moving group amenable to the analysis we
perform in this study, and for which both carbon and oxygen (among other
elements) can be accurately inferred. When it comes to the remaining members
of $\beta$ Pic’s moving group, to the best of our knowledge, there are no non-
LTE, or 3D, carbon and oxygen abundance corrections available for M stars, and
any analysis are therefore not as accurate as that of F stars. Thus, not only
the analysis of HD 181327 is a better representation of $\beta$ Pic b’s
protoplanetary disk than $\beta$ Pic, but also the only analysis that allows
us to accurately and precisely infer the abundances of key species such as
carbon and oxygen in a well understood stellar context.

Figure 4: We show the abundance differences between HD 181327 and $\beta$ Pic.
The abundances from $\beta$ Pic are from Saffe et al. (2021).

GRAVITY Collaboration et al. (2020) made an extensive discussion of $\beta$
Pic b formation scenario based on the assumption that $\beta$ Pic’s C/O ratio
is solar (C/O$=0.59$, from Asplund et al., 2021), and according to them: A
subsolar C/O ratio (i.e., $\approx$ 0.4) would invalidate most of the
discussion regarding the formation of $\beta$ Pic b. In Figure 5 we show the
distribution of carbon and oxygen ratios in the solar neighborhood, using data
from the third data release of the Galactic Archaeology with HERMES (GALAH)
survey (Buder et al., 2021), and in white the abundances of HD 181327. It is
clear from Figure 5 that the abundances of HD 181327 are not located in the
bulk of the solar neighborhood distribution. From GALAH, the peak of the
distribution of C/O ratios at solar metallicity, in the solar neighborhood, is
$\sim 0.1$ dex below solar (C/O$=0.49^{+0.15}_{-0.12}$). Thus, for a solar
neighborhood, solar metallicity star, it is more likely to find subsolar than
solar abundance for the C/O ratio, and this fact must be taken into account
when analyzing planetary abundance information.

As one needs to interpret planetary formation and migration processes taking
into account the composition of the disk from which the planet formed (e.g.,
Reggiani et al., 2022), we propose that the interpretation of planetary
abundances should be done in light of:

  1. 1.

Preferably through the photospheric abundances of the host star.

  2. 2.

The photospheric abundance of a star formed within the same molecular cloud as
the host star/planet.

  3. 3.

The mean abundances observed in the Galactic substructure where we observe the
planet (solar neighborhood).

  4. 4.

If all other options are not possible, one should assume solar abundances.

For the photosphere of HD 181327, and therefore the protoplanetary disk from
which $\beta$ Pic b formed, we found (3D non-LTE corrected abundances)
[C/H]$=-0.08\pm 0.06$, [O/H]$=-0.10\pm 0.06$, [(C+O)/H]$=-0.18\pm 0.08$,
C/O]$=+0.02\pm 0.08$, and C/O$=+0.62\pm 0.08$. We will discuss $\beta$ Pic b’s
formation using the 3D non-LTE abundances calculations as the basis of our
discussions. We reinforce that our carbon 1D LTE, 1D non-LTE, and 3D non-LTE
abundances are all compatible, and the differences between them are smaller
than the uncertainties.

###  6.2 The Formation of $\beta$ Pic b

Our retrieval of $\beta$ Pic b yields different results than those reported by
the GRAVITY Collaboration et al. (2020). We attribute the differences mostly
to our updated methodology in the GPI data reduction. Compared to the GRAVITY
Collaboration et al. (2020) retrieval, our metallicities are in much better
agreement to the stellar results. The 1D non-LTE metallicity of the planetary
disk, as traced by HD 181327, is [Fe/H]${}_{\text{1DNLTE}}=+0.13\pm 0.10$, and
the planetary metallicity is [Fe/H]$=0.5$, and [Fe/H]$=+0.08^{+0.25}_{-0.12}$
from GRAVITY Collaboration et al. (2020) and our own retrieval, respectively.
Ours is a clear improvement as it is now fully reconciled to the metallicity
traced by the stellar information recorded in HD 181327. Not only that, but
the much lower metallicity we inferred is much more amenable to the core-
accretion formation scenario of $\beta$ Pic $b$, than the [Fe/H]$=0.5$ dex
previously inferred.

Our retrieved C/O abundance ratio is smaller than what was previously
reported, although there is agreement within the quoted uncertainties
(C/O$=+0.35^{+0.02}_{-0.03}$ from us and C/O$=0.43\pm 0.05$ from GRAVITY
Collaboration et al. (2020)). The GRAVITY Collaboration et al. (2020) team,
however, did not report the individual carbon and oxygen abundances, as carbon
in their retrieval was scaled to the planetary metallicity101010See the
petitRADTRANS documentation for details., and oxygen was freely varied to
recover the inferred C/O ratio. In our retrieval the abundances are estimated
on the fly and every element retrieved is treated as a free parameter.
Therefore, our carbon and oxygen abundances are not biased by the assumption
of solar scaled [C/H].

We present in Figure 6 the retrieved
$(\textrm{C/O})_{\textrm{Planet}}/(\textrm{C/O})_{\textrm{Star}}$ as a
function of $\textrm{A(C)}_{\textrm{Planet}}/\textrm{A(C)}_{\textrm{Star}}$
and as a function of
$\textrm{A(O)}_{\textrm{Planet}}/\textrm{A(O)}_{\textrm{Star}}$, for both ours
and GRAVITY Collaboration et al. (2020) retrievals. We present in both cases
the abundances assuming solar C/O and carbon and oxygen for the host star, and
our inference from HD 181327. In both panels we outline the different possible
formation scenarios as described in the model presented by Öberg et al.
(2011).

As already pointed by GRAVITY Collaboration et al. (2020) we have little
information about the relationship between the current orbit of $\beta$ Pic b
and its formation location, and about possible variations of the locations of
the ice lines in systems such as that of $\beta$ Pic (no direct observations
of the ice lines in $\beta$ Pic have been made to the best of our knowledge).
However, based on the formation model presented by Öberg et al. (2011), our
results indicate $\beta$ Pic b formed beyond the H2O ice line by accreting
large ammounts of icy planetesimals after envelope accretion.

Even though we obtained different results in our planetary retrieval (see the
metallicity difference), our stellar and planetary analysis corroborates the
discussion presented by the Gravity Team. GRAVITY Collaboration et al. (2020)
inferred $\beta$ Pic b’s atmospheric C/O ratio is indicative $\beta$ Pic b
slowly formed between the H2O and CO2 ice lines, via core-accretion. Its
substellar C/O can be explained if the planet was enriched in oxygen by icy
planetesimals. For more complete calculations we refer the reader to their
study. We would also like to point out that even with the possible maximum
systematic differences in the stellar non-LTE corrections from Bergemann et
al. (2021) (stellar C/O$=+0.43$) the conclusions drawn are the same. The
planet would be located in the same quadrant as is in Figure 6. We have,
therefore, strong evidence on the formation scenario of this planet, as all
results converge regardless of analysis (two different planetary atmospheric
retrievals, and different assumptions to the composition of its protoplanetary
disk pointing to the same conclusion).

Figure 5: We present, as blue points, the distribution of carbon and oxygen
abundances (in different scales) as a function of metallicity from the GALAH
DR3 survey. In white we show the abundance of HD 181327, as a proxy for
$\beta$ Pic’s molecular cloud. One can see that its abundance is outside of
the most populated region in all abundance spaces. This shows the importance
of individually determining the stellar abundances for the interpretation of
planetary retrievals.

Figure 6: On the left we present the planetary to stellar (protoplanetary disk
proxy) C/O ratios of $\beta$ Pic b as a function of planet to stellar carbon
abundances, and on the right we present the planetary to stellar C/O ratios as
a function of planetary to stellar oxygen abundance. In dark and light green
we present the planetary results of the GRAVITY Collaboration et al. (2020)
study, scaled to solar and stellar (HD 181327) abundances, respectively. In
dark and light blue we present the same, but for the carbon and oxygen
abundances retrieved for $\beta$ Pic b from our study. We see that regardless
of the retrieval there is a difference in using solar and stellar abundances,
portraying the importance of a dedicated stellar analysis. It is also clear
that our retrieval has considerably changed the results. While there are
visible differences, for $\beta$ Pic b our different analysis corroborate
previsous conclusions about the planetary formation. It formed beyond the H2O
ice-line, accreting large amounts of icy planetesimals after envelope
accretion.

##  7 Conclusion

We find that the chemical pattern of HD 181327, a member of the $\beta$ Pic
moving group, can be reliably used as a proxy to infer the chemical content of
the molecular cloud form which $\beta$ Pic was formed. As such, and
considering the abundances of $\beta$ Pic itself are not a reliable
representation of its parent molecular cloud because of its intrinsic
characteristics, we argue that the composition of the Hot Jupiter $\beta$ Pic
b should be interpreted in light of HD 181327 composition.

We enumerate what we argue to be the most reliable ways to infer the
composition of the protoplanetary disks from which exoplanets formed.

We also performed our own retrieval of the parameters and abundances of
$\beta$ Pic b. We retrieved a planetary metallicity that is fully in agreement
to the abundance of HD 181327. We present carbon and oxygen abundances for
both star and planet (stellar abundances are 3D non-LTE corrected). Our
stellar C/O ratio is close to solar, but we found an important discrepancy in
the abundances (in articular the metallicity) from our retrieval and the
retrieval by GRAVITY Collaboration et al. (2020). We attribute the differences
to the our updated (recalibrated) data reduction pipeline. The combination of
our stellar analysis and planetary retrieval indicate $\beta$ Pic. $b$ formed
beyond the H2O ice-line, and accreted large amounts of icy planetesimals after
envelope accretion. It is important to point that our updated retrieval along
with a new stellar analysis arrived at the same conclusion as previous
studies, corroborating their conclusions and strongly reinforcing the proposed
scenario for the formation of $\beta$ Pic $b$.

## Acknowledgments

We thank the referee for a careful read of our paper, and their comments that
helped us improve the quality of our paper. The work of Henrique Reggiani was
partially supported by NOIRLab, which is managed by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation, and partially supported by a Carnegie
Fellowship. Jhon Yana Galarza acknowledges support from their Carnegie
Fellowship. This work made use of data collected with the Clay 6.5 meters
Magellan Telescope. This work made use of ESO archival data, collected from
its science portal. This work has made use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This publication makes use
of data products from the Two Micron All Sky Survey, which is a joint project
of the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. This research
has made use of the NASA/IPAC Infrared Science Archive, which is funded by the
National Aeronautics and Space Administration and operated by the California
Institute of Technology. This research has made use of NASA’s Astrophysics
Data System Bibliographic Services. This research has made use of the SIMBAD
database, operated at CDS, Strasbourg, France (Wenger et al., 2000). This
research has made use of the VizieR catalogue access tool, CDS, Strasbourg,
France (DOI: 10.26093/cds/vizier). The original description of the VizieR
service was published in 2000, A&AS 143, 23 (Ochsenbein et al., 2000). This
research has made use of the NASA Exoplanet Archive, which is operated by the
California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.

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