JuanCastillo29/space-mission-intelligence-data huggingface dataset:
Jontof-Hutter et al. (2021) used forward dynamical modelling of known Kepler TTV systems to identify 26 systems hosting at least one planet whose projected TTVs diverge by more than 90 minutes by BJD 2460900 (corresponding to approximately 2025 August 12, 12:00 UTC), which are therefore prime targets for follow-up transit photometry. From this set, two systems were excluded from our sample because their host stars are likely subgiants (Kepler-87 and Kepler-223), and a further nine systems because none of their planets were flagged as exhibiting TTVs in the NASA Exoplanet Archive (Kepler-149, Kepler-184, Kepler-254, Kepler-266, Kepler-372, Kepler-382, Kepler-662, Kepler-822, and Kepler-1802). The remaining 15 systems, hosting 42 transiting planets, were included in our simulations. These planets, with their periods, calculated PLATO transit SNRs, and projected TTV uncertainties at BJD 2460900, are shown in Table 1. Among the 42 planets in these 15 systems, we identify five planets (KOI-1783.01, KOI-1783.02, Kepler-36 c, Kepler-177 c, and Kepler-324 c) with expected transit SNRs sufficient for individual transit timing measurements (SNR ≥3.8). These planets are distributed across four systems hosting 10 transiting planets in total. In addition, we identify 27 planets in 13 systems with expected transit SNRs ≥ 1); these systems collectively host 38 transiting planets. Of the 15 systems considered, only KOI-1599 and KOI-3503 host no planets with expected SNR ≥1. The overlap between the systems identified by Jontof-Hutter et al. (2021) as promising TTV targets and those for which PLATO is expected to deliver useful timing information demonstrates that PLATO has the potential to meaningfully extend the temporal baseline for a subset of known Kepler TTV systems. Even modestly precise timing measurements, when separated by the long baseline between the
97 Kepler-307 b 10.42 2.06 10 Kepler-307 c 13.07 1.75 19 Kepler-324 b 4.39 0.61 152 Kepler-324 c 51.81
10.65
41 Kepler-324 d 34.17 0.84 218 Kepler-324 e 13.98 2.36 34 Kepler-342 b 15.17 2.14 19 Kepler-342 c 26.23 1.77 711 Kepler-342 d 39.46 3.08 28 Kepler-342 e 1.64 0.23 299 Kepler-359 b 25.56 0.71 >1 day Kepler-359 c 57.69 1.21 759 Kepler-359 d 77.10 1.10 >1 day
7.05
Kepler and PLATO missions, can provide valuable information on long-term dynamical evolution.
In this work, we have assessed the extent to which the PLATO mission can deliver useful transit timing measurements for known transiting exoplanets in the Kepler field. While PLATO will not achieve the per-transit photometric precision of Kepler for these targets, its longduration stare and temporal separation from the Kepler era provide an opportunity to extend transit timing baselines by almost two decades in favourable cases.

Using end-to-end simulated PLATO photometry, we investigated the relationship between target brightness and photometric precision, including for dim Kepler hosts considered out of scope for the prime PLATO mission. We found that for all but the most contaminated hosts, noise is mostly white and well modelled by the simple noisemagnitude relation of Cabrera et al. (2026). Moreover, we found that for our sample of Kepler hosts, PLATO data typically exhibits 2.68– 5.14 times the photometric noise of Kepler on one-hour timescales, with the ratio varying with the number of co-pointing cameras. We quantified the precision with which individual mid-transit times can be recovered as a function of transit signal-to-noise ratio. We introduced a posterior-based classification scheme to distinguish between prior-limited, low-significance, and well-constrained timing measurements, and demonstrated that the transition between these regimes occurs gradually over the range SNR ≃2.1–4.3. Additionally, we found that timing precision is only weakly dependent on observational cadence within the range of expected data products to be delivered by the PLATO mission. Together, we provide a framework for using catalogue-level quantities to predict photometric precision and, by extension, transit SNR. From these, the predicted mid-transit timing precision can be computed using the relation calibrated in this work. While most individual transits fall below the threshold for independent detection, a non-negligible fraction nonetheless yield statistically powerful timing constraints when prior knowledge of the ephemeris is available. When individual transits are weak, combining multiple transits using a river diagram or photodynamical approach can provide a plausible way to recover timing information, particularly for systems with large-amplitude TTVs. We find that PLATO is well-positioned to contribute additional timing constraints for a subset of known TTV systems, thereby strengthening dynamical inferences through an extended temporal baseline. PLATO can play a valuable complementary role in refining the long-term evolution of carefully selected systems identified from Kepler data.
This work presents results from the European Space Agency (ESA) space mission PLATO. The PLATO payload, the PLATO Ground Segment and PLATO data processing are joint developments of ESA and the PLATO Mission Consortium (PMC). Funding for the PMC is provided at national levels, in particular by countries participating in the PLATO Multilateral Agreement (Austria, Belgium, Czech Republic, Denmark, France, Germany, Italy, Netherlands, Portugal, Spain, Sweden, Switzerland, Norway, and United Kingdom) and institutions from Brazil. Members of the PLATO Consortium can be found at https://platomission.com/. The ESA PLATO mission website is https://www.cosmos.esa.int/plato. We thank the teams working for PLATO for all their work. 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. This research has made use of the SIMBAD database, CDS, Strasbourg Astronomical Observatory, France. MAM gratefully acknowledges the support of the Science and Technology Facilities Council (STFC) through the training grant ST/X508871/1, which made this research possible. The work of RS, DR and EG has benefited from financial support by Centre National
d’Etudes Spatiales (CNES) in the framework of its contribution to the PLATO mission. YNEE acknowledges support from a Science and Technology Facilities Council (STFC) studentship, grant number ST/Y509693/1. IA acknowledges the support of STFC under the CASE Industry scheme ST/W005077/1. ISL acknowledges support from UKRI grant EP/X027562/1.
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This paper has been typeset from a TEX/LATEX file prepared by the author.
Mariana Sastre1⋆, Tim Lichtenberg1, Laurent Soucasse2, 3, Dan J. Bower4, Harrison Nicholls5, Inga Kamp1 1 Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands 2 Netherlands eScience Center, Amsterdam, The Netherlands 3 Interuniversity Micro Electronics Centre, Leuven, Belgium 4 Institute of Geochemistry and Petrology, Department of Earth and Planetary Sciences, ETH Zürich, Zürich, Switzerland 5 Institute of Astronomy, University of Cambridge, Cambridge, United Kingdom
The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years, governing bulk density, surface conditions, and long-term geodynamics. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves ( fO2 ≤IW, where IW denotes the iron–wüstite buffer) promote earlier deep-mantle crystallisation relative to oxidised (IW+2.0) and Earth-like (IW+4.0) cases (range IW−4.0 to IW+4.0), favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H2-CO-rich atmospheres; oxidized mantles favour thinner H2O-CO2 envelopes. In volatile-rich systems, the
interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.
Key words. planets and satellites: interiors – planets and satellites: atmospheres – planets and satellites: composition – planets and satellites: terrestrial planets – planets and satellites: physical evolution
of accretion by impacts of planetesimals and the accretion of
pebbles within the protoplanetary disc (Johansen & Lambrechts
2017; Raymond et al. 2020; Batygin & Morbidelli 2023). The
timescales and initial heat budget at which this process occurs
imply a significant amount of energy, enough to induce multi-
ple episodes of large-scale mantle melting. This stage is known
as the magma ocean phase (Elkins-Tanton 2012). As the magma
ocean cools and crystallizes, some fraction of the volatile content
dissolved within the planet’s interior is outgassed to the exte-
rior, contributing to the growth and composition of a secondary
atmosphere and initiating long-term climate evolution (Elkins-
Tanton 2008; Lebrun et al. 2013; Hamano et al. 2013; Bower
et al. 2019, 2022; Salvador et al. 2023; Lichtenberg et al. 2023;
Nicholls et al. 2024; Boukaré et al. 2025). The outgassed at-
mosphere strongly influences the crystallisation of the magma
ocean. By producing a greenhouse blanketing effect, it retains
heat and can keep surface temperatures above the solidus tem-
perature, which is the threshold for melting under given ther-
modynamic and compositional conditions. This helps maintain
a molten surface and extends the lifetime of the magma ocean.
volatile exchange
Convective mixing

[Figure: Fig. 1. Schematic overview of the PROTEUS framework and its time-integration workflow. The interior, surface volatile exchange, and radiative– convective atmosphere are solved as independent modules that iteratively exchange boundary conditions at each timestep. In the time-flowchart, each timestep proceeds by iterating the coupled modules until the surface fluxes, volatile inventories, and atmospheric structure converge to a selfconsistent solution. If convergence is not achieved, the boundary conditions are iteratively updated until convergence of the coupled solution is reached. The colour-coding in the time-flowchart (left) corresponds to the module descriptions in the model diagram (right), where each coloured module in the flowchart solves the physical processes listed in its corresponding coloured box on the right.]
tempt to model the subsequent long-term solid-state or tectonic
evolution beyond this stage.
Figure 1 summarizes this workflow by showing how
PROTEUS cycles through its modular components until conver-
gence is achieved at each time step. In this study, we primar-
ily modified the interior module (SPIDER) to incorporate redox-
dependent melting relations, while the atmospheric, stellar evo-
lution and volatile exchange modules follow previous implemen-
tations and are therefore only briefly described below.
1-D evolution code designed to track the coupled thermal
and compositional history of rocky planets. PROTEUS is struc-
tured as a set of stand-alone but interdependent physical mod-
ules that simulates: interior, atmospheric energy transport, es-
cape to space, stellar evolution, and outgassing that communi-
cate through shared boundary conditions (Nicholls 2026). At
each interior timestep, energy, mass, and compositional fluxes
are iteratively exchanged between modules until convergence
of the coupled solution is achieved. The interior evolves for-
ward in time, while the atmosphere is solved in quasi-steady
state and responds instantaneously to evolving boundary con-
ditions. This enables the model to track planets from an ini-
tially molten state through crystallisation and volatile exchange
between mantle and atmosphere, resolving equilibrium states
at each timestep and the hysteresis that emerges from coupled
atmospheric–interior feedbacks (Lichtenberg et al. 2025, 2026;
Nicholls et al. 2025a).
Within the PROTEUS framework, the temporal evolution of stel-
lar irradiation is modelled using the MORS stellar evolution code,
originally developed by Johnstone et al. (2021). MORS mod-
els stars as coupled rotating shells surrounding a homogeneous
core, allowing it to self-consistently calculate angular momen-
tum transport and rotational spin-down over time. Since stel-
lar activity and high-energy emission are closely linked to ro-
tation, MORS then calculates the evolution of X-ray, extreme ul-
traviolet, and bolometric luminosities as a function of stellar
mass, age, and initial rotation rate (Johnstone et al. 2021). These
outputs are combined with empirical scaling relations to build
the star’s evolving emission spectrum (Nicholls et al. 2024).
The resulting time-dependent stellar fluxes are continuously up-
dated and coupled to the interior and atmospheric modules of
PROTEUS, enabling a self-consistent treatment of how changing
stellar irradiation influences planetary climate, chemistry, and in-
Earth oceans. Our nominal values are guided by estimates for
the early Earth (Wang et al. 2018), whereas oxygen fugacity is
varied across a range motivated by expected mineralogical di-
versity, which alone may generate differences of at least four log
duced Mercury-like conditions (Cartier & Wood 2019) to more
oxidized scenarios like the Earth’s mantle today (Stagno & Fei
2020). In all simulations, we adopted a fixed core radius fraction
to ensure that the initial adiabat lies above the liquidus through-
out the mantle. This approach allows us to assess the sensitiv-
ity of magma ocean evolution and volatile outgassing to poorly
constrained initial compositions. The complete simulation grid
comprises 600 models and is summarized in Table 1.

[Figure: Fig. 2. Solidus (solid lines) and liquidus (dashed lines) for mantle redox states relative to the iron–wüstite buffer (IW-4.0, IW-2.0, IW+0, IW+2.0, IW+4.0). Colours indicate increasing oxidation from dark blue (IW-4.0) to pink (IW+4.0). The reference melting curves correspond to IW+2.0, representing an oxidized, broadly Earth-like mantle state consistent with experimental constraints (Andrault et al. 2011; Hamano et al. 2013). Other curves are obtained by applying the redox-dependent parametrization of Lin et al. (2024). Curves are shown up to 30 GPa for visualisation, although the full melting curves extends to 400 GPa; the redox-dependent temperature offset remains constant across this pressure range.]
behaviour introduced in Section 2.6 affects the thermal evolu-
tion of the planetary interior during magma ocean evolution.
Fig 3 compares two representative simulations with an initial
tion equal to Earth’s present-day incident flux, which differ only
in their choice of melting curves: the unshifted experimentally
based curves from Andrault et al. (2011) and Hamano et al.
(2013), and the same curves shifted according to the redox-
dependent parametrization of Lin et al. (2024) assuming the
mantle is buffered at IW+2.0 relative to the iron–wüstite buffer.
As a result of the differing melting curves, the thermal evolution
is not a simple rescaling of temperature: shifts in the melting
region produce a markedly non-linear response in the coupled
interior–atmosphere system.
In the baseline case, a cooler set of melting curves allows
a substantial region of the mantle to remain partially molten
over an extended period. The melt is relatively well distributed
throughout the interior, and the planet cools through a long-lived
phase in which deep melt continues to supply heat to the sur-
face. In contrast, the shifted IW-2.0 melting curves favours ear-
lier and more extensive crystallisation at depth. As the rheologi-
cal front moves upward, melt becomes increasingly confined to
a thin shell near the surface, so that the late-time configuration
is dominated by a shallow surface magma ocean rather than a
deeply distributed molten layer.
In both simulations, we followed the evolution until they
reach a steady state, but the internal melt distribution and atmo-
spheric structure differ substantially. In both cases, the thermal
profile rapidly approaches the rheological transition, which sets
the bulk melt fraction and thereby regulates volatile partition-
ing between the interior and atmosphere. In our simulations, the
To test the effects of the varying redox states on the geophysical
and melting evolution of young rocky planets, we ran a grid of
simulations for the specific case of the super-Earth exoplanet GJ
1132 b, where we fixed the melting curve at different redox states
to study the possible implications on the subsequent formation
of the atmosphere and the evolution of mantle melt fraction. We
also explored the orbital distance of exoplanets as exerting sig-
nificant control over the stellar irradiation, which strongly affects
the total heat flux to space. We probed a temperate and highly ir-
radiated case. The orbital separation a was set by defining two
reference instellations at 4.5 Gyr for an Earth-like planet, such
that our simulated planets receive (i) the stellar irradiation as the
Earth today at an age of 4.5 Gyr, and (ii) the same as the real
exoplanet GJ 1132 b.
Primordial volatile inventories and bulk compositions of
close-in rocky exoplanets remain poorly constrained, motivat-
ing an exploration of a wide range of plausible initial conditions.
We therefore varied both the initial C/H ratio and the total hy-