11institutetext: Anton Pannekoek Institute for Astronomy, University of
Amsterdam, Science Park 904, 1098 XH, Amsterdam, the Netherlands
11email<EMAIL_ADDRESS>22institutetext: School of Earth and Planetary
Sciences (SEPS), National Institute of Science Education and Research (NISER),
Jatani, India 33institutetext: Astrophysics Reseach Center (ARCO), The Open
University of Israel, Ra’anana, 43107, Israel 44institutetext: Frontier
Research Institute for Interdisciplinary Sciences, Tohoku University, 6-3
Aramaki aza Aoba, Aoba-ku, Sendai, Miyagi 980-8578, Japan 55institutetext:
Department of Geophysics, Graduate School of Science, Tohoku University, 6-3
Aramaki aza Aoba, Aoba-ku, Sendai, Miyagi 980-8578, Japan 66institutetext:
Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan
77institutetext: Cluster for Pioneering Research, RIKEN, 2-1 Hirosawa, Wako,
Saitama 351-0198, Japan 88institutetext: Department of Astronomy &
Astrophysics, University of California, Santa Cruz, CA 95064, USA.
99institutetext: Department of Astronomy and Astrophysics, University of
Chicago, Chicago, IL, USA 1010institutetext: School of Earth and Space
Exploration, Arizona State University, Tempe, AZ 85287, USA 1111institutetext:
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
1212institutetext: Centre for Exoplanets and Habitability, University of
Warwick, Coventry CV4 7AL, UK. 1313institutetext: Lowell Observatory, 1400 W
Mars Hill Road, Flagstaff, AZ, 86001, USA 1414institutetext: Center for
Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA.
1515institutetext: Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588,
Japan. 1616institutetext: National Astronomical Observatory of Japan,2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan. 1717institutetext: Department of
Astronomy, Graduate University for Advanced Studies (SOKENDAI), Tokyo, 2-21-1
Osawa, Mitaka, Japan.

# First Comparative Exoplanetology Within a Transiting Multi-planet System:
Comparing the atmospheres of V1298 Tau b and c

Saugata Barat  11 Jean-Michel Désert  11 Jayesh M. Goyal 22 Allona Vazan 33
Yui Kawashima 44556677 Jonathan J. Fortney 88 Jacob L. Bean 99 Michael R. Line
1010 Vatsal Panwar 11111212 Bob Jacobs 11 Hinna Shivkumar 11 James Sikora
111313 Robin Baeyens 11 Antonija Oklopčić 11 Trevor J. David 1414 John H.
Livingston 151516161717

The V1298 Tau system (20-30Myr), is a benchmark young multi-planet system that
provides the opportunity to perform comparative exoplanetology between planets
orbiting the same star right after their formation. We present the first
atmospheric comparison between two planets in the same transiting system:
V1298 Tau b and V1298 Tau c. We derive constraints on the mass of planet b and
c (¡20M⊕ at 3$\sigma$ confidence level and $17_{-6}^{+13}M_{\oplus}$
respectively) and atmospheric metallicity (logZ/Z⊙=-2.04${}_{-0.59}^{0.69}$,
-0.16${}_{-0.94}^{1.15}$ respectively) from atmospheric retrievals. The V1298
Tau planets, are likely to be similar in terms of mass at the current age,
implying that both planets are potential sub-Neptune/super-Earth progenitors.
However, planet c is expected to lose a higher fraction of its mass compared
to planet b given its close proximity to the host star. Alternatively, the
observed spectrum of planet c can be explained by atmospheric hazes, which is
in contrast to planet b where efficient haze formation can be ruled out.
Higher haze formation efficiency in planet c could be due to differences in
atmospheric composition, temperature and higher UV flux incident compared to
planet b.

##  1 Introduction

Demographic studies on mature exoplanets (Fulton et al., 2017; Van Eylen et
al., 2018; Szabó & Kiss, 2011) suggest that early evolutionary processes like
photoevaporation (Owen & Wu, 2017) and core-powered mass loss (Ginzburg et
al., 2018; Gupta & Schlichting, 2019) significantly influence the structure
and composition of super-Earths and sub-Neptunes. Therefore, observing planets
in their early stages is key to understanding these processes.

V1298 Tau, a 20-30 Myr old weak-lined T-Tauri star in the foreground of the
Taurus-Auriga star forming region (Oh et al., 2017; Luhman, 2018), is
particularly valuable for such studies. It hosts four transiting planets,
making it one of the youngest known multi-planet systems. The inner three
planets (V1298 Tau c, d, and b) are in a near 3:2:1 mean-motion resonance
(Feinstein et al., 2022; Sikora et al., 2023; David et al., 2019b), suggesting
possible migration within a gas disk (Terquem & Papaloizou, 2018; Kajtazi et
al., 2023). The orbital period of the outermost planet, V1298 Tau e, remains
unconfirmed but is under investigation (Damasso et al., 2023).

In this paper, we compare the atmospheric composition and chemistry of two
planets in the V1298 Tau system: V1298 Tau b (0.9 RJ, 24.14 day period) and
V1298 Tau c (0.5 RJ, 8.24 day period). A comparison between the known physical
properties of both planets is shown in Table 1. V1298 Tau c receives four
times the stellar irradiation as V1298 Tau b due to their orbital distance
ratio of $\sim$1:2. Stellar XUV flux is believed to play an important role in
atmospheric chemistry (Kawashima & Ikoma, 2018; Tsai et al., 2023; Venot &
Agúndez, 2015; Shulyak et al., 2020) as well as early evolution (Owen & Wu,
2013, 2017), which we aim to test with two planets in the same young system.

Mass measurement for these young planets is challenging due to stellar
activity affecting radial velocity (RV) observations (Blunt et al., 2023).
Initial RV estimates (Suárez Mascareño et al., 2021), which reported Jovian
masses for the two outer V1298 Tau planets, has been challenged (Sikora et
al., 2023; Finociety et al., 2023). Barat et al. (2024) estimated V1298 Tau
b’s mass to be less than 23M⊕ at 3$\sigma$ level of confidence from HST/WFC3
transmission spectra, and ruled out earlier RV measurements at 5$\sigma$ level
of confidence. Ongoing Transit timing variations (TTVs) studies (private
communication) suggest that both V1298 Tau b and c are in the sub-
Neptune/super-Earth mass regime, indicating they are likely sub-Neptune/super-
Earth progenitors with similar masses.

We have observed a transmission spectrum of V1298 Tau c using the same
instrumental configuration as Barat et al. (2024) to allow for comparison. We
discuss the data reduction, light curve analysis and atmospheric modelling in
Section 2, followed by the main results in Section 3. We discuss and interpret
our findings in Section 4 and 5.

Parameter | V1298 Tau b | V1298 Tau c
---|---|---
Period [days] | 24.14 | 8.24
Semi-major axis [AU] | 0.17 | 0.08
Equilibrium temperature [K] | 685 | 979
Radius [R⊕] | 9.95 | 5.24
Known mass [M⊕] |  $<$23M⊕ | 20$\pm$10
Mass reference | Barat et al. (2024) | Sikora et al. (2023)

Table 1: Table comparing the physical properties of V1298 Tau b and c

##  2 Data analysis and modelling

###  2.1 Observations

We observed one primary transit of V1298 Tau c (18th October 2021) with 8 HST
orbits using the WFC3 instrument for Program GO 16462. The observations were
taken with the G141 grism in bidirectional spatial scanning mode covering a
range of 1.1-1.7 $\mu$m. We used the $256\times 256$ pixel subarray and
SPARS25, NSAMP=5 readout mode which resulted in 88.4 s exposures. We used a
0.23”/second scan rate resulting a 170 pixel long image in the spatial
direction.

###  2.2 Data reduction and light curve analysis

We use a custom data reduction pipeline for analyzing the raw HST spatially
scanned images (Arcangeli et al., 2018; Jacobs et al., 2022; Barat et al.,
2024) mirroring the approach for planet b in Barat et al. (2024).

The broadband integrated light curve is shown in Figure 4. It shows ‘hook’
like systematics, which are typical for similar HST observations (Wakeford et
al., 2016). Our observations covered only one pre-transit orbit and no
ingress/egress observations. Typically, the first orbit of a visit for HST is
known to exhibit large systematics, and it is common practice to not include
it in time series analysis (e.g see Kreidberg et al., 2014; Jacobs et al.,
2022; Barat et al., 2024). However, since we have only one pre-transit orbit,
we do not remove it in our light curve analysis. Further details of the light
curve fitting methods are provided in Appendix B.

We derive a transmission spectrum of V1298 Tau c following Appendix B and
Appendix C which has been shown in Figure 1.

###  2.3 Atmospheric modelling with ATMO and planet mass

We interpret the transmission spectra of V1298 Tau c and V1298 Tau b using a
chemically consistent ATMO retrieval framework (Tremblin et al., 2015;
Drummond et al., 2016; Goyal et al., 2018). ATMO has been previously used to
analyze various exoplanet atmospheres (see for e.g Evans et al., 2018; Goyal
et al., 2019; Carter et al., 2020). Details about the ATMO models are provided
in Appendix D.

Figure 1 shows the best-fit atmospheric models for both planets alongside the
observed spectra. The retrieved parameters are listed in Table 2, with
posterior distributions in Figures 12, 13. Following Barat et al. (2024), we
include planet mass as a free parameter. For planet b, the posterior
distribution peaks around 8M⊕ with a 3$\sigma$ upper limit of 20M$\oplus$,
consistent with Barat et al. (2024). For planet c, the posterior peaks around
17M⊕ with a 3$\sigma$ upper limit of $\sim$50M⊕, consistent with previous RV
upper limits (Finociety et al., 2023; Sikora et al., 2023). These results
suggest both planets are likely in the sub-Neptune/super-Earth mass range.

Our retrievals indicate low atmospheric metallicity for both planets, with
planet b having 0.1-0.01 solar and planet c consistent with solar. The
temperature of planet b peaks around 850-900K (See Appendix E for further
discussion on planet b’s temperature), while planet c’s temperature is
unconstrained. No constraints were found on the C/O ratio or clouds for either
planet.

We also performed retrievals with fixed masses to assess their impact on other
parameters. For V1298 Tau c, we used 10 and 50M$\oplus$, and for planet b, we
used 10 and 23M$\oplus$. The posterior distributions for these fixed mass
retrievals are shown in Figures 15, 14, with retrieved parameters in Table 2.
The overall conclusion of sub-solar/solar atmospheric metallicity for both
planets remains valid even with fixed masses.

##  3 Results

###  3.1 The transmission spectrum of V1298 Tau c

We compared the observed transmission spectrum of V1298 Tau c to a flat line
and found that models with atmospheric water absorption are slightly favored
(2.5$\sigma$). To confirm the presence of water, we conducted a free
atmospheric retrieval using the open-source code PetitRadtrans (Mollière et
al., 2019). We fixed the planet mass and temperature to the median of the ATMO
retrieval posteriors (Table 2) and included a grey cloud deck opacity. The
posterior distribution from this fit is shown in Figure 11. While we did not
find constraints on CH4, our models preferred the presence of water, with a
lower limit for the water volume mixing ratio ($>10^{-5}$) at 3$\sigma$
confidence level.

Comparing the spectrum of V1298 Tau c to its sibling planet, V1298 Tau b,
revealed that the transit depth uncertainties for V1298 Tau c are larger by a
factor of about 1.5. This higher uncertainty is likely due to including the
first orbit of the visit for V1298 Tau c, known to have larger wavelength-
dependent systematics. Consequently, we did not apply the common-mode
correction to the spectroscopic light curves of planet c, as we did for planet
b. The common-mode correction could correct for the curvature of the time-
series baseline, which then allowed us to fit a linear baseline to the
spectroscopic light curves of planet b.

###  3.2 Relative transmission spectroscopy between planet b and c

In Figure 1 (lower panel), we present the first relative transmission spectrum
between two planets within the same system. This relative spectrum is
independent of the star’s radius and limb darkening. Stellar inhomogeneities
are known to contaminate transmission spectra (Désert et al., 2011; Rackham et
al., 2019), which has also been highlighted in recent JWST observations(May et
al., 2023; Moran et al., 2023; Lim et al., 2023). A relative transmission
spectrum between planets theoretically bypasses stellar contamination issues,
assuming consistent stellar contamination across both transits. This enables a
better relative comparison of abundances between the planets without precise
information on the stellar properties, including metallicity, elemental
abundance ratios, and limb-darkening. However, in the case of V1298 Tau, an
active star, changes in the stellar surface between observation epochs may
still introduce contamination to the relative spectrum extracted at different
times.

Planet | Parameter | Free mass retrieval (ATMO) | Fixed mass (10M⊕) | Fixed mass (50M⊕)
---|---|---|---|---
| logZ [solar] | -0.16${}_{-0.94}^{1.15}$ | -0.02${}_{-1.2}^{1.3}$ | -0.001${}_{-1.08}^{1.05}$
| Rp [$R_{\oplus}$] | 0.48${}_{-0.01}^{0.01}$ | 0.48${}_{-0.01}^{0.03}$ | 0.48${}_{-0.01}^{0.01}$
V1298 Tau c | Teq [K] | 947${}_{-80}^{+104}$ | 921${}_{-79}^{+113}$ | 985${}_{-105}^{+95}$
| log${\kappa}_{cld}$ | 0.26${}_{-0.83}^{+1.03}$ | 0.73${}_{-0.94}^{+0.81}$ | -0.11${}_{-0.60}^{+0.97}$
| C/O | 0.06${}_{-0.05}^{+0.2}$ | 0.07${}_{-0.06}^{+0.26}$ | 0.06${}_{-0.04}^{+0.22}$
| Mass [M⊕] | 17${}_{-6}^{+13}$ | 10 (fixed) | 50 (fixed)
Planet | Parameter | Free mass retrieval (ATMO) | Fixed mass (10M⊕) | Fixed mass (23M⊕)
| logZ [solar] | -2.04${}_{-0.59}^{0.69}$ | -1.80${}_{-0.7}^{1.07}$ | -0.86${}_{-0.85}^{1.05}$
| Rp [$R_{\oplus}$] | 0.84${}_{-0.01}^{0.02}$ | 0.84${}_{-0.01}^{0.03}$ | 0.84${}_{-0.01}^{0.01}$
V1298 Tau b | Teq [K] | 889${}_{-180}^{+150}$ | 806${}_{-210}^{+196}$ | 824${}_{-125}^{+137}$
| log${\kappa}_{cld}$ | 1.03${}_{-0.75}^{+0.61}$ | 0.88${}_{-0.98}^{+0.68}$ | 0.25${}_{-0.62}^{+1.02}$
| C/O | 0.08${}_{-0.06}^{+0.18}$ | 0.05${}_{-0.03}^{+0.18}$ | 0.04${}_{-0.03}^{+0.15}$
| Mass [M⊕] | 7.58${}_{-1.5}^{+3.8}$ | 10 (fixed) | 23 (fixed)

Table 2: Table showing derived parameters from atmospheric retreivals run
using ATMO (See section 2.3) for planet c and planet b. We ran retrievals
keeping both planet mass fixed and as a free parameter in our retrievals. The
corresponding posterior distributions are shown in Figure 12, Figure 13,
Figure 14, Figure 15. A description of the models used for the retrievals is
given in Appendix D. The quoted values are median and 68% confidence intervals
from the retrieved posteriors.

###  3.3 Haze formation in the atmosphere of V1298 Tau planets

Hazes have been found to be ubiquitous in exoplanet atmospheres (Kempton et
al., 2023; Libby-Roberts et al., 2020a; Knutson et al., 2014). The temperature
of V1298 Tau b and c is expected to be between 600-1000K and the host star is
young and active, producing copious amounts of XUV radiation, which are
important ingredients for haze formation (Yu et al., 2021).

We simulated the transmission spectrum of V1298 Tau b and c, including
hazes.We assumed tholin like composition for the hazes (Khare et al., 1984).
The simulations were done following the approach in Kawashima & Ikoma (2019).
The details of the haze microphysics model are provided in Kawashima & Ikoma
(2018). We assumed 20M⊕ and 23M⊕ (Barat et al., 2024) for planet c and b
respectively. For further details see Appendix F. The simulated transmission
spectrum for V1298 Tau b and c, assuming a 1% haze formation efficiency is
shown in Figure 1. The effect of hazes in the HST bandpass is to damp the
water absorption feature. Given the large observable water feature in V1298
Tau b’s spectrum, efficient haze formation can be ruled out for this planet.
However, atmospheric models with hazes can explain the observed transmission
spectrum of planet c. If we assume a lower mass for planet c ($\sim$10M⊕),
which is consistent with current estimates from TTV analysis, we would require
even higher haze formation rates to explain the observed spectrum of V1298 Tau
c.

##  4 Discussion

###  4.1 Relative orbital distances and stellar density

In multi-planet systems, it is possible to fix one planet’s semi-major axis
based on another’s measured semi-major axis, since they are related to their
orbital periods ratio. However, due to known TTVs in this system, we refrain
from fixing the semi-major axis in this analysis. The semi-major axis ratio
from independent fits to the white light curves of V1298 Tau b and c is
2.08$\pm$0.1 and agrees with the expected value from their known orbital
periods. Assuming circular orbits, the semi-major axis can be used to estimate
stellar density (Sandford & Kipping, 2017). From the fits to our white light
curves, we estimate the stellar density from the planet b and planet c to be
0.70$\pm$0.01gm/cm3 and 0.67$\pm$0.1gm/cm3. These values align with the
published stellar density for V1298 Tau (0.68$\pm$0.1gm/cm3, David et al.
(2019b)). indicating that it is inflation compared to similar-mass main
sequence stars.

###  4.2 Limb darkening of V1298 Tau

Modeling stellar limb darkening is crucial for deriving transmission spectra.
Prior studies often employed fixed limb darkening for main-sequence stars
based on theoretical stellar structure models (e.g, see Deming et al., 2013;
Sing et al., 2016). Barat et al. (2024) fitted a linear limb darkening
coefficient for V1298 Tau, revealing significant differences compared to
theoretical models for a main-sequence star with a similar spectral type (K1).
Higher limb darkening compared to theoretical expectations for mature stars
has previously been noted for $\beta$-Pictoris (Landman et al., 2024). The
fitted limb darkening coefficients and a theoretical linear limb darkening
model is shown in Figure 9. This constitutes the first direct measurement of
limb darkening on a weak-lined T-Tauri star.

In Section 4.1, we highlighted that V1298 Tau’s density is lower than that of
similar-mass main-sequence stars. Furthermore, it has a relatively high
magnetic field strength of the order of 100-300 Gauss (Finociety et al.,
2023). High magnetic fields have been proposed as a potential cause for
discrepancies between observed and theoretical limb darkening models
(Kostogryz et al., 2024). Therefore, a combination of structural differences
and higher magnetic fields compared to main-sequence stars, could explain the
differences we find with the model.

While leveraging light curves from multiple planets in the same system could
potentially reduce limb darkening coefficient uncertainties, the absence of
ingress or egress coverage in the light curves of planet c led us to fix the
limb darkening coefficients to the values from Barat et al. (2024). A
comparison of the transmission spectrum of planet c derived using fixed and
free limb darkening is shown in Figure 8. The transit depth uncertainties are
higher by 5-10% for each spectroscopic bin in the latter case. Residuals in
both cases are approximately 1.2 times the expected photon noise, indicating
that stellar variability and instrumental systematics from the first orbit are
likely to be the dominant sources of noise in our case.

###  4.3 Comparative exoplanetology between V1298 Tau b and c

A comparison between the atmospheres of V1298 Tau b and c, measured relative
to atmospheric scale height (Figure 1, upper panel), shows that these two
planets could host similar atmospheres. Our retrievals show that these planets
are likely to have similar masses in the sub-Neptune/super-Earth regime (Table
2). Furthermore, we also find that the atmospheric metallicities of both the
planets are solar/sub-solar, which is relatively low compared to their mature
counterparts which have been found to have metal-rich/hazy (¿$100\times$solar)
atmospheres (Désert et al., 2011; Kempton et al., 2023; Madhusudhan et al.,
2023; Libby-Roberts et al., 2020b). In this scenario, both the V1298 Tau
planets are similar in terms of mass and composition, but their observable
atmospheres are distinct from their mature counterparts.

Atmospheric hazes can be ruled out for V1298 Tau b, given the large
atmospheric absorption feature, however for planet c atmospheric hazes can
explain the observed spectrum.. A comparison between the transmission spectra
of planet b and c shows that planet c could have a higher haze formation. Haze
formation has been linked to the UV flux of the host star; a higher UV flux
results in higher monomer production rates for organic hazes (Kawashima &
Ikoma, 2019). Higher atmospheric metallicity could also lead to higher haze
formation. The higher haze formation in planet c compared to its sibling
planet could be due to difference in metallicity, temperature and incident UV
flux of the two planets.

###  4.4 Comparing the early evolution of V1298 Tau b and c

We ran evolutionary models for the V1298 Tau planets. These models start from
the time of disk dispersal, and model the structural and thermal evolution of
the planet, including atmospheric mass loss due to photoevaporation (Owen &
Wu, 2013). We run models assuming both a core-envelope interior structure, as
well as with a gradually mixed interior. We have used the evolutionary models
presented in Vazan et al. (2022). A brief description of the models is
provided in Appendix G. Figure 2 shows a possible mass and radius evolution
tracks for these planets.

V1298 Tau c being closer to its host star compared to planet b, is more
susceptible to atmospheric mass loss driven by photoevaporation. While the
final mass and radius depend on photoevaporation efficiency and the star’s
activity level (Poppenhaeger et al., 2021), our models show that V1298 Tau c
is likely to lose a larger fraction of its current envelope compared to planet
b. Therefore, even if both planets have similar masses now, their early
evolution could lead them to different mass-radius regimes.

Our models assume solar metallicity for the envelope opacity. However, the
transmission spectrum of V1298 Tau c could also be explained using atmospheric
hazes, unlike V1298 Tau b (Figure 1. Young planets are expected to cool and
contract over time (Kubyshkina et al., 2020; Linder et al., 2019). The
presence of high altitude hazes can increasing the atmospheric opacity,
therefore increasing the cooling and contraction timescale (Lee & Chiang,
2015), leading to higher photoevaporative mass loss. Thus, a hazy atmosphere
of V1298 Tau c as opposed to a clear atmosphere of V1298 Tau b, could lead to
slower cooling and higher mass loss.

###  4.5 Comparing the composition of V1298 Tau planet with the exoplanet
population

Figure 3 shows V1298 Tau b and c on the mass-metallicity and metallicity-
orbital distance planes. The observed low atmospheric metallicity for these
planets deviates from the mass-metallicity trend predicted by core-accretion
models (Pollack et al., 1996; Bodenheimer & Pollack, 1986) and reported for
exoplanets (Welbanks et al., 2019; Thorngren & Fortney, 2019). This could
potentially be explained by ongoing evolutionary processes that transform
their current metal-poor atmospheres into the metal-rich atmospheres seen in
mature sub-Neptune/super-Earth planets (Désert et al., 2011; Kempton et al.,
2023; Libby-Roberts et al., 2020a; Madhusudhan et al., 2023).

We compare the V1298 Tau system with the $\sim$30 Myr old HR 8799 system
(Marois et al., 2010) with four directly imaged planets (HR8799 b, c , d and
e) with masses 7${}^{+4}_{-2}$, 10${}^{+3}_{-3}$, 10${}^{+3}_{-3}$,
10${}^{+7}_{-4}$ (Marois et al., 2010; GRAVITY Collaboration et al., 2019).
Nasedkin et al. (2024) using ground based spectra from the VLTI/GRAVITY
program, report super-stellar($\sim$100 times stellar) atmospheric metallicity
for these planets. Assuming a -0.65 dex metallicity for HR8799 (Swastik et
al., 2021) we convert the retrieved atmospheric metallicity to stellar unit.

The HR 8799 planets exhibit higher atmospheric metallicity compared to the
mass-metallicity trend (Thorngren & Fortney, 2019) predicted by core-accretion
formation, while V1298 Tau planets fall below this trend. HR 8799 is a system
of widely separated massive gas giants, whereas V1298 Tau likely consists of
compact, low-mass sub-Neptune/super-Earth progenitors. Both systems likely
host primordial atmospheres. The different mass regimes suggest HR 8799
planets underwent runaway gas accretion or gravitational collapse, unlike
V1298 Tau planets. Theories propose close-in sub-Neptunes and super-Earths
formed in situ within the water ice-line in dusty or depleting disks to
prevent runaway gas accretion (Lee et al., 2014; Lee & Chiang, 2016). Wide
orbit gas giants likely formed beyond the ice lines, allowing for runaway
accretion (Pollack et al., 1996) or gravitational instability (Boss, 1997;
Dodson-Robinson et al., 2009), but these mechanisms alone do not explain HR
8799’s high metallicity, necessitating the accretion of volatile-rich solids
(Nasedkin et al., 2024). Formation location relative to ice lines could lead
to differences in volatile enrichment, as beyond the ice-line, the disk
contains volatile-rich solids, enhancing the metal content of primordial
atmospheres (Öberg et al., 2011; Bitsch et al., 2019).

###  4.6 Formation and evolution of multi-planet systems

The mass of the V1298 Tau planets indicates they are likely sub-Neptune/super-
Earth progenitors, which are in a near mean-motion resonance (1:2:3).
Atmospheric retrievals suggest these planets could have low metallicity
atmospheres. Population synthesis studies (Mordasini, 2018; Benz et al., 2014)
show sub-Neptunes and super-Earths often form in multi-planet systems in mean
motion resonance (Lambrechts et al., 2019). Emsenhuber et al. (2023)
classified systems with multiple low-mass planets into two types: Class I:
inner dry/rocky planets formed in situ with outer icy sub-Neptunes migrating
inwards, and Class II: multiple sub-Neptunes forming beyond the water ice line
and migrating inwards. In the first scenario, inner planets have volatile-poor
atmospheres, whereas, in the second, all planets are volatile-rich.

The relatively low atmospheric metallicity of V1298 Tau b and c suggests a
formation similar to class I planets . However, these young planets’
atmospheric composition may evolve. In the pebble accretion scenario, a
metallicity gradient forms in the protoplanet’s envelope (Ormel et al., 2021;
Bodenheimer et al., 2018), with metal-rich layers hidden deep inside. Over
time, atmospheric mass loss can strip volatile-poor upper layers, enriching
atmospheric metallicity (Vazan et al., 2022), aligning them with mature sub-
Neptune/super-Earth population. In this case, the V1298 Tau system could also
have a formation similar to the class II systems.

If V1298 Tau c has a hazy atmosphere, it might be more metal-rich than the
outer planet b, which doesn’t fit either class I or class II systems. Class I
systems have inner volatile-poor planets, while class II systems have planets
with similar compositions. Due to its proximity to the star, V1298 Tau c is
likely to lose more of its primordial envelope compared to V1298 Tau b 2.
Thus, V1298 Tau b and c might have formed like class II systems, with
volatiles hidden deep inside, but atmospheric mass loss caused planet c’s
composition to evolve faster than planet b, explaining their difference in
their atmospheric composition.

Figure 1:  Transmission spectrum of V1298 Tau c (blue points) shown in
comparison with its sibling planet V1298 Tau b (green points). The spectra
have been derived by subtracting the median of the observed spectrum. The
upper panel shows the spectra in terms of atmospheric scale height and the
middle panel in terms of transit depth. We assumed Teq=968K and 17M⊕ for
planet c and 670K and 23M⊕ for planet b to calculate the scale height for each
planet. We assumed H/He dominated primordial atmospheres and assumed a mean
molecular weight of 2.33. The green and blue solid lines show the best fit
ATMO models from our retrievals for planet b and c respectively (Section 2.3).
The dashed lines show hazy atmospheric models for both planets simulated using
the formalism presented in Kawashima & Ikoma (2018) (See Section 3.3). The
lower panel shows the relative transmission spectrum between V1298 Tau b and
V1298 Tau c (See Section 3.2).  Figure 2: Potential mass and radius
evolutionary tracks for V1298 Tau c (black) and V1298 Tau b (red). M0 and R0
refers to the current mass and radius respectively. We assumed 9.85R⊕ and 23M⊕
and 5.59R⊕ and 20M⊕ for the radius and mass of V1298 Tau b and c (Table 2)
respectively at the current age (23 Myr). The left panels zoom in on the first
100Myr and the right panels show the evolutionary tracks for 1Gyr. The
evolutionary models described in Appendix G calculate the mass and radius
evolution due to cooling and atmospheric mass loss. We used evolutionary
models described in Vazan et al. (2022). For further discussion see Section
4.4. Figure 3: Comparing the retrieved atmospheric metallicity of V1298 Tau b
and c with those of mature exoplanets, with the solar system planets and with
young directly imaged planets orbiting HR 8799 (30Myr old). The left panel
shows these planets in the metallicity-orbital distance plane and in the right
panel we compare the mass-metallicity of these planets. The atmospheric
metallicity of the V1298 Tau planets have been derived from the ATMO
retrievals (Table 2). The stars show metallicities for retrievals performed
using 10M⊕ for both planets and the squares for retrievals using 23 and 50M⊕
for planet b and c respectively. The metallicities of the HR 8799 system (blue
circles) have been obtained from Nasedkin et al. (2024). The grey points show
metallicity constraints from pre-JWST observations (mostly driven by HST)
taken from Wakeford & Dalba (2020) and the magenta points show metallicities
derived from JWST observations. Table 3 shows the data for the planets shown
in magenta with corresponding references. For planets which appear both in the
sample of Wakeford & Dalba (2020) and Table 3, we plot the latter. A
comparison between the measured metallicties between he V1298 Tau and HR8799
systems show that these planets have very different atmospheric metal
enrichment, indicative of differences in their formation mechanism, disk
properties, and location. The red dashed line in the right panel shows a mass-
metallicity relation derived in Thorngren & Fortney (2019). The V1298 Tau
planets have metal-poor atmospheres by an order of magnitude compared to their
mature counterparts and observed mass-metallicity trend among exoplanets.

##  5 Conclusion

In this paper, we perform the first comparative study of atmospheres of
multiple planets in the same transiting system. Comparing the transmission
spectra of the young V1298 Tau b and c planets reveals that planet b has a
large, haze-free envelope, while the presence of hazes in planet c cannot be
ruled out. Atmospheric models suggest similar masses for both planets in the
sub-Neptune/super-Earth regime. These models also find relatively low
atmospheric metallicities for both these young planets compared to their
matured counterparts, indicating they are sub-Neptune/super-Earth progenitors.
Alternatively, if planet c has a hazy atmosphere, higher haze formation in
planet c compared to planet b could be due to differences in composition,
temperature, and incoming stellar UV flux. The higher envelope opacity of
planet c would affect its cooling rate and evolution differently than for
planet b.

##  6 Acknowledgements

J.M.D acknowledges support from the Amsterdam Academic Alliance (AAA) Program,
and the European Research Council (ERC) European Union’s Horizon 2020 research
and innovation program (grant agreement no. 679633; Exo-Atmos). This work is
part of the research program VIDI New Frontiers in Exoplanetary Climatology
with project number 614.001.601, which is (partly) financed by the Dutch
Research Council (NWO). Y.K. acknowledges the support from JSPS KAKENHI Grant
Numbers JP21K13984 and 22H05150.

##  7 Softwares used

numpy, scipy, matplotlib, emcee, lmfit, pandas, ATMO, PetitRadtrans

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##  Appendix A Description of raw data reduction

We start our analysis from the ‘ima.fits’ files downloaded from MAST archive.
During each exposure, the detector is read multiple times, without flushing
out the accumulated charge (non-destructive reads). We create sub-exposures by
subtracting consecutive non-destructive reads for each exposure which are
reduced separately. This technique has been widely applied in past
observations with HST (e.g, see Kreidberg et al. 2014; Arcangeli et al. 2018;
Jacobs et al. 2022). We apply a wavelength dependent flat-field correction and
flag bad pixels with data quality DQ=4, 32, or 512 by calwf3. We apply a local
median filter to identify cosmic rays and clip pixels which are more than five
median deviations from the median. To account for the dispersion direction
drift of the spectrum (Wakeford et al. 2016) we use the first exposure of a
visit as a template and shift the spectrum for an exposure along the
dispersion direction to match the template. The maximum shift that we require
is 0.1 pixels. We apply optimal extraction algorithm (Horne 1986) on each
subexposure to maximize signal-to-noise ratio.

##  Appendix B Light curve fitting

HST WFC3 light curves often exhibit strong systematics like charge-trapping
ramps and visit-long slopes (Kreidberg et al. 2014; Deming et al. 2013;
Tsiaras et al. 2016; Wakeford et al. 2016). Common practice involves
discarding the first orbit due to significantly larger systematics (See Figure
4) compared to the rest of the visit (e.g see, Wakeford et al. 2013; Arcangeli
et al. 2018; Jacobs et al. 2022; Barat et al. 2024). However, in this case, we
could not remove from the analysis because the transit occurred two hours
earlier than expected from the linear ephemeris (Feinstein et al. 2022) due to
large TTVs and we could only secure one orbit prior to ingress.

The first-orbit systematics are strongly wavelength dependent (Zhou et al.
2020, 2017) and cannot be corrected for using common-mode approaches, which
had been previously applied to similar observations of V1298 tau b (Barat et
al. 2024). Therefore, to handle these systematics, we used the physically
motivated RECTE charge-trapping model (Zhou et al. 2017), which fits the first
orbit ramp better than other methods (Berta et al. 2012; Kreidberg et al.
2014). We fixed the mid-transit time using simultaneous TESS observations
(Feinstein et al. 2022). V1298 Tau shows strong rotational variability, with
an average amplitude of 2$\%$ and a rotational period of 2.83 days (David et
al. 2019b). We modeled it with a second-order polynomial for the out-of-
transit baseline. See Appendix C for more discussion on the baseline
modelling. The planetary transit signal was modelled using batman (Kreidberg
2015).

For the white light curve (1.12-1.6 $\mu$m), we fit the RECTE parameters and
the baseline polynomial coefficients, along with the planet’s transit depth
and semi-major axis. Other orbital parameters were fixed to literature values
(Feinstein et al. 2022; Sikora et al. 2023; David et al. 2019a). The RECTE
parameters constitute 4 parameters: the number of initially filled fast/slow
charge traps and the number of fast/slow charge traps that are filled in
between orbits. Due to the lack of ingress and egress data, our limb darkening
precision was impaired. However, by using the limb darkening parameter
retrieved from the observations of planet b (Barat et al. 2024), we were able
to significantly reduce the uncertainties on the transit spectrum (Figure 8).
This highlights the advantage and uniqueness of studying multiple planets in
the same system. For a discussion on the limb darkening of V1298 Tau see
Appendix 4.2. We also independently measure the stellar density from the HST
white light curves which is discussed in Appendix 4.1.

The fit was performed using emcee (Foreman-Mackey et al. 2013). The posterior
distribution from these fits is shown in Supplementary Figure 5 and the best-
fit transit model and residuals, are shown in Supplementary Figure 4 (upper
panel).

Spectroscopic light curves were analyzed similarly by dividing the stellar
spectra into 7-pixel bins, resulting in 17 channels (identical to V1298 Tau
b). We fixed the semi-major axis from the white light curve fits and fit the
RECTE parameters and baseline for each bin, and the transit depth. We fix the
wavelength dependent limb-darkening coefficients to values derived in Barat et
al. (2024). The detrended spectroscopic light curves and residuals are shown
in Supplementary Figure 6.

##  Appendix C Modelling the baseline

Young stars exhibit quasi-periodic flux modulation due to rotational
variability (e.g see Feinstein et al. 2022; David et al. 2019b; Mann et al.
2016, 2022). The transit of planet c analyzed in this work occurred near an
inflection point of the stellar baseline, resulting in significant deviation
from a linear function. We modeled the baseline using linear, quadratic, and
cubic polynomial functions for all the spectroscopic channels. The transit
depths from all three fits were consistent within 1$\sigma$, but quadratic and
cubic polynomials were statistically favored over a linear baseline (See
Supplementary Figure 7).

Higher-order polynomials, however, introduce correlation between the transit
depth and baseline, increasing uncertainties and scatter in the transmission
spectrum. The Bayesian Information Criterion (BIC) did not improve
significantly with a cubic baseline compared to a quadratic one, and the cubic
polynomial coefficients strongly correlated with the transit depths, likely
adding noise. Therefore, we used a quadratic polynomial to model the baseline
for the final transmission spectrum.

##  Appendix D Atmospheric models with ATMO

ATMO’s python based retrieval framework was applied and bench-marked in Lewis
et al. (2020) and Rathcke et al. (2021) for HAT-P-41b and WASP-79b,
respectively . This same retrieval framework is applied to V1298 Tau b and c
in this work. This framework includes a Nested sampling Bayesian sampler
DYNESTY (Speagle 2020) coupled to ATMO. We perform chemical equilibrium
retrieval with isothermal $P$-$T$ profile. Chemical equilibrium abundances are
computed using Gibbs energy minimization as detailed in Drummond et al.
(2016). We include H2-H2, H2-He Collision Induced opacity (CIA), as well as
H2O, CH4 and CO high temperature molecular opacity in the retrieval. The
clouds are treated as grey cloud deck between 1 and 50 millibar pressure
levels, but with variable cloud opacity governed by the cloud factor used as
the variable in the retrieval, as detailed in Goyal et al. (2018).

##  Appendix E Comparing V1298 Tau b ATMO retrieval with Barat et al. (2024)

For this study, we performed atmospheric retrieval on V1298 Tau b using the
same setup as for planet c, assuming an isothermal atmosphere. Our results,
indicating sub-solar metallicity and a mass upper limit of 20M⊕, align with
Barat et al. (2024), who used PetitRadtrans. However, our retrieved
temperatures are higher (800-900K) compared to their 600-700K. The discrepancy
arises because Barat et al. (2024) used a non-isothermal temperature-pressure
(T-P) profile with high interior temperature and vertical mixing to explain
the non-detection of methane for this planet. Our isothermal model lacks this
flexibility, leading to higher temperatures beyond the CH4/CO transition
(Fortney et al. 2020) to eliminate methane from the upper atmosphere.

##  Appendix F Haze formation models

The haze microphysics models were simulated using the models described in
Kawashima & Ikoma (2018), following the approach of Kawashima & Ikoma (2019).
First, using a photochemical model the abundance of gaseous species was
calculated. The XUV spectrum of V1298 Tau was adopted from Duvvuri et al.
(2023). Haze production rates (or efficiency of haze formation) are uncertain,
therefore we assumed a certain fraction of precursor molecules to be
dissociated to form haze monomers. The haze precursor molecules are assumed to
be CH4, HCN and C2H2 in our model. We derived vertical density and radius
distributions of the haze particles following Kawashima & Ikoma (2018). We
assumed solar elemental abundance ratio and other parameters such as eddy
diffusion coefficient, monomer radius, internal density, and refractive index
of haze particles similar to Kreidberg et al. (2022). We simulated
transmission spectra, for V1298 Tau b and c assuming 23 and 20M⊕ respectively
with obtained profiles of gas and haze particles. In Figure 1 we show the
simulated transmission spectra assuming a 1$\%$ haze production efficiency.

##  Appendix G Theoretical evolutionary models

Our models start from the time of disk dispersal and calculate the thermal
evolution and structural evolution. We consider both core-envelope as well as
gradually mixed interior structures. We include atmospheric mas loss due to
photoevaporation from the topmost layer of the planets using the formalism of
Rogers & Owen (2021). The mass loss rates are estimated from an energy-limited
model (Erkaev et al. 2007), assuming a fixed photoevaporation efficiency. Our
models include core erosion and mixing with the envelope. The evolutionary
models are described in Vazan et al. (2022). We choose the initial conditions
(mass, radius) such that it matches the current mass and radius for the
planets. We assumed 23M⊕ and 20M⊕ for the current mass estimates of the V1298
Tau b and c respectively. We run simulations with both core-envelope and
gradually mixed interior models. Both interior structure models can explain
the current mass/radius of the planets. Mass and radius (normalized at current
value) evolution models for the V1298 Tau planets are shown in Figure 2.

##  Appendix H Effect of stellar activity on transmission spectrum

We estimate the effect of stellar activity on the transmission spectrum of
V1298 Tau c. We adopt the method outlined in Rackham et al. (2019), where we
estimate a correction factor based on the spot coverage fraction and spot
temperature contrast. We adopt a spot coverage fraction of 20% for V1298 Tau
(Feinstein et al. 2021). We adopt an extreme spot contrast of 1000K following
spot contrasts derived for a sample of T Tauri stars (Koen 2016). We show a
comparison between the observed and corrected transmission spectrum in
Supplementary Figure 10. The observed and contamination corrected normalized
spectra are consistent within 1$\sigma$ for all spectroscopic channels.

Since V1298 Tau is a K-type star, its contamination function does not show
molecular features like M-dwarfs (Barclay et al. 2021). Therefore, the effect
of the stellar correction is to change the level of the continuum in this
case. However, the atmospheric features, which are relative to the continuum
remain largely unaffected.

##  Appendix I Supplementary Figures

Figure 4:  Upper panel: Raw white (1.12-1.65$\mu$m band) light-curve. Blue and
green points show forward and reverse scanned exposures respectively. Black
solid lines show best fit transit model. We use a physically motivated charge
trapping model, RECTE (Zhou et al. 2017, 2020) to fit the exponential ramps.
The baseline is modelled using a quadratic function in time. See Appendix C
for further discussion. The transit has been modelled using batman (Kreidberg
2015). For details of light-curve fitting see Section B. Lower panel: The
residuals from the fit to the white light curve observations. Figure 5:
Posterior distribution from the white light curve fit (See Appendix B. We use
a charge trapping model (RECTE) to model the instrumental systematics (Zhou et
al. 2017) and a second order polynomial to model the out of transit baseline.
Figure 6: Systematics detrended spectroscopic light curves (left panel) and
residuals (right panel). The light-curves have been offset for visual clarity.
The light curve fitting methodology is described in Appendix B. Figure 7:
Upper panel: Comparison of transit depths for all spectroscopic channels for
linear, quadratic and cubic stellar baseline models. The transit depths are
normalized by their respective median values for the sake of visual
comparison. Lower panel: Comparison of Bayesian Information Criteria (BIC) for
linear, quadratic and cubic stellar baseline models. The transit depths agree
within 1$\sigma$ of each other for the different polynomial orders, except for
the last spectroscopic channel. The BIC clearly favours higher order
polynomial models compared to linear for modelling the stellar baseline. For
further discussion see Section C. Figure 8: Comparing the derived transmission
spectrum of V1298 Tau c for a fixed and free limb darkening fit to the light
curves. The fixed limb darkening points (red circles) have been derived using
linear limb darkening coefficients from Barat et al. (2024). For the free limb
darkening, we do not find any constraints on limb darkening from our
observations of planet c. A comparison between the transit depth uncertainty
for the two cases shows that fixing the limb darkening reduces the transit
depth uncertainty by 5-10% for each channel.  Figure 9: Comparison between the
fitted linear limb darkening coefficients for V1298 Tau (Barat et al. 2024)
and theoretical limb darkening model for a main sequence star of a similar
spectral type. The theoretical models have been derived using EXOCTK (Bourque
et al. 2021) for a star with similar spectral type as V1298 Tau (K1). This is
the first time we have measured the limb darkening of a weak-lined T-Tauri
star and the observed limb darkening appears significantly different compared
to a main sequence star. This discrepancy between with main-sequence models is
could be due to different interior structure and high magnetic field of this
young star (See Section 4.2. It highlights the importance of fitting for the
limb darkening when analyzing transit light curves around such young stars.
Figure 10: Comparison between observed (red circles) and stellar contamination
corrected (green circles) transmission spectrum of V1298 Tau c. The respective
spectra have been normalized for the sake of comparison. All the spectroscopic
bins are consistent within their 1$\sigma$ uncertainties. The contamination
spectra have been derived following the prescription outlined in Rackham et
al. (2019), with stellar spot coverage parameters adopted from Feinstein et
al. (2021). See Appendix H for further discussion. Figure 11: Posterior
distribution from free atmospheric chemistry retrieval using PetitRadtrans. We
include H2O and CH4 opacity in our forward model. The results from this free
retrieval are discussed in Section 3.1 Figure 12: Posterior distribution from
retrievals on V1298 Tau c transmission spectrum using ATMO where planet mass
has been included as a free parameter. The retrieved parameters are tabulated
in Table 2. Description of models used for this fit are given in Appendix D.
Figure 13: Posterior distribution from retrievals on V1298 Tau b transmission
spectrum using ATMO where planet mass has been included as a free parameter.
The retrieved parameters are tabulated in Table 2. Description of models used
for this fit are given in Appendix D. Figure 14:  Posterior distribution from
ATMO retrievals of the transmission spectrum of V1298 Tau c by assuming fixed
planet mass of 10M⊕ (blue) and 50M⊕ (red). The median values of the fitted
parameters are shown in Table 2. Description of models used for this fit are
given in Appendix D Figure 15:  Posterior distribution from ATMO retrievals of
the transmission spectrum of V1298 Tau b by assuming fixed planet mass of 10M⊕
(blue) and 23M⊕ (red). The median values of the fitted parameters are shown in
Table 2. Description of models used for this fit are given in Appendix D

Planet name | Mass [M⊕] | Atmospheric metallicity [solar] | Semi-major axis [AU] | Stellar metallicity [dex] | Reference
---|---|---|---|---|---
Wasp-18b | 10.20$\pm$0.35 | 1.03${}^{+1.1}_{-0.51}$ | 0.02 | 0.11$\pm$0.08 | Coulombe et al. (2023)
Wasp-39b | 0.280$\pm$0.03 | 10${}^{+21}_{-7}$ | 0.048 | -0.03$\pm$0.1 | Rustamkulov et al. (2023)
Wasp-77Ab | 1.66$\pm$0.06 | 0.12${}^{+0.1}_{-0.05}$ | 0.023 | -0.01$\pm$0.1 | August et al. (2023)
Wasp-96b | 0.48$\pm$0.03 | 7.5${}^{+2.5}_{-2.5}$ | 0.045 | 0.14$\pm$0.19 | Radica et al. (2023)
TOI-270d | 0.015$\pm$0.001 | 225${}^{+86}_{-98}$ | 0.07 | -0.2$\pm$0.1 | Benneke et al. (2024)
Wasp-107b | 0.1$\pm$0.005 | 10${}^{+11}_{-5}$ | 0.05 | 0.02$\pm$0.09 | Welbanks et al. (2024)
HD149026b | 0.358$\pm$0.01 | 20${}^{+11}_{-8}$ | 0.0436 | 0.33$\pm$0.1 | Gagnebin et al. (2024)
HD209458b | 0.5902904$\pm$0.01 | 3${}^{+4}_{-1}$ | 0.05 | -0.01$\pm$0.05 | Xue et al. (2024)
Wasp-80b | 0.53$\pm$0.03 | 6${}^{+4}_{3}$ | 0.03 | -0.1$\pm$0.1 | Bell et al. (2023)
Wasp-17b | 0.78$\pm$0.2 | 50${}^{+50}_{-20}$ | 0.051 | -0.07$\pm$0.1 | Grant et al. (2023)
GJ1214b | 0.026$\pm$0.001 |  $>$100 | 0.01 | 0.02$\pm$0.1 | Kempton et al. (2023)

Table 3: Table showing the mass and atmospheric metallicities of planets with
measured metallicity using JWST. In Figure 3 we show these planets in the
mass-metallicity and metallicity-distance diagram to compare with the V1298
Tau system. The stellar metallicity provided in this table has been used to
convert the derived atmospheric metallicity from atmospheric in solar units to
stellar units.