Tim Lichtenberg

We present a Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) G141 phase-curve observation of the ultrashort-period rocky planet TOI-2431 b and detect its secondary eclipse in the near-infrared. Combined with the TESS optical eclipse, these measurements constrain the planet’s dayside brightness temperature, reflected light contribution, albedo, and heat redistribution. We detect the eclipse in the optical and near-infrared wavelengths of TESS and HST/WFC3 G141, with a planet-to-star flux ratio of 37 ± 10 ppm and 6 9 − 13 + 14 ppm , respectively. Assuming negligible reflected light, the joint TESS+HST fit yields a brightness temperature T b , joint = 252 4 − 84 + 77 K and a brightness temperature ratio of R joint = T b , joint / T p , max = 0.98 0 − 0.034 + 0.032 consistent with the zero-albedo, no-redistribution limit T p , max = 257 4 − 35 + 36 K . The HST phase curve is consistent with zero nightside emission and no measurable hotspot offset, consistent with inefficient day-night heat distribution. Under this thermal-dominated interpretation, TOI-2431 b lies at the zero-albedo, no-redistribution limit and contrasts with previously observed lava worlds. At optical and near-infrared wavelengths, however, thermal emission is degenerate with reflected light. For a geometric albedo of A _g = 0.1, reflected light would contribute approximately 11 ppm in each bandpass, reducing the temperature to T b , joint ( A g = 0.1 ) = 240 7 − 102 + 91 K . Longer-wavelength observations are required to isolate the thermal component. Planned JWST/MIRI LRS observations are expected to substantially reduce this degeneracy and provide more direct constraints on heat redistribution and possible silicate-atmosphere spectral features. This marks the first secondary eclipse detection of a rocky exoplanet using HST and establishes TOI-2431 b as a benchmark target for studying properties of lava worlds.

Context. The earliest rocky planet atmospheres were shaped by the competition between initial volatile inventories and atmospheric escape driven by stellar irradiation. On young magma ocean planets, volatile exchange between the atmosphere and the interior through in- and outgassing competes with atmospheric escape, controlling volatile retention and atmospheric evolution. Aims. We investigate how atmospheric escape and replenishment via outgassing during magma ocean crystallization shape rocky exoplanet atmospheres. Methods. We extended a coupled interior-atmosphere model to simulate rocky planet evolution during the magma ocean era by incorporating an energy-limited atmospheric escape module. Comparing self-consistent radiative-convective and prescribed-convective atmospheres, we quantified how atmospheric energy transport affects escape. We explored a wide range of orbital separations, escape efficiencies, oxidation states, and initial volatile inventories to identify regimes where sustained magma-ocean outgassing or escape dominates. We estimated atmospheric mass loss and compositions for young rocky planets around Sun-like and M dwarf stars over geologic timescales. Results. Atmospheric escape shortens magma ocean lifetimes by weakening greenhouse insulation and accelerating cooling, with radiative-convective atmospheres reducing solidification timescales compared to purely convective cases. Volatile dissolution into the magma ocean interacts with the escape of atmospheric species to chemically fractionate the planetary volatile budget over time by retaining more soluble species. For Earth-mass planets, atmospheres survive if mass-loss rates remain moderate ( Ṁ _EL ≈ 10 ¹⁰ g s ⁻¹ ). When atmospheric escape is included, the mantle redox state remains a key control on atmospheric composition: high oxygen fugacity ( f O ₂ ) yields heavier H ₂ O- and CO ₂ -rich atmospheres, while low f O ₂ produces light H ₂ - or CO-dominated atmospheres, consistent with previous studies. Orbital separation, initial volatile inventory, and stellar type produce diverse evolutionary pathways, from bare rocky planets to magma oceans with thick atmospheres, spanning compositions from H ₂ - to SO ₂ -dominated atmospheres.

Ultrashort period (USP) rocky planets are expected to be depleted of any substantial gaseous envelope due to the intense irradiation they receive from their host star, making the recent detection of an atmosphere around TOI-561 b particularly surprising. That finding was based on the planet’s bulk density and dayside emission spectrum, but full-orbit phase-curve observations offer a more comprehensive way to constrain the presence and characteristics of a planet’s atmosphere. In this paper, we map TOI-561 b’s 3–5 μ m emission using JWST/NIRSpec multiorbit spectroscopic phase curves, explicitly accounting for the curvature of the out-of-eclipse baseline and possible hotspot offsets. From a simple energy balance argument as well as comparing to general circulation models, we find the phase-curve observations are best explained with high Bond albedo and moderate global heat transfer. Our 37 hr continuous observation provides a long baseline that allows us to model stellar granulation, the planetary phase curve, and dayside emission simultaneously, effectively disentangling these signals and yielding a dayside emission spectrum that is more robust against stellar variability and consistent with previous eclipse-only fits. Using general circulation model outputs, we constrain where clouds can plausibly form and test candidate compositions, finding that silicate clouds, such as SiO ₂ and MgSiO ₃ , can form on the dayside near the terminator and explain the observed albedo. Our findings confirm that TOI-561 b appears to have a global reflective atmosphere, suggesting exchange of volatiles with the interior to maintain it.

Modeling the interior of a rocky or water-rich exoplanet is fundamentally a thermodynamic closure problem. Every layer’s density, temperature gradient, and phase state must follow from an equation of state (EoS) that stays self-consistent across the many orders of magnitude in pressure and temperature spanned between the surface and the core, but existing EoSs are scattered across disciplines, employ different formalisms, and rarely provide the full set of thermodynamic quantities needed for such a model. This presents fundamental hurdles for evolutionary models that rely on a self-consistent thermodynamic treatment of interior phase transitions. We present PALEOS (Planetary Assemblage Layers: Equations of State), an open-source and extensible Python toolkit that consolidates published EoSs for iron and magnesium silicate (MgSiO ₃ ) with the composite AQUA EoS for water (H ₂ O), which we further correct at high pressure and temperature, into a unified phase-aware and thermally responsive framework covering 17 thermodynamic phases. Vapor and supercritical silicate phases lie outside the current scope of the toolkit. For each material, PALEOS analytically derives the density, specific internal energy, entropy, heat capacities, thermal expansion, and adiabatic gradient from the underlying pressure–volume–temperature relations via Maxwell relations. The resulting EoSs are validated for thermodynamic consistency and compiled into lookup tables on regular pressure–temperature grids, which are publicly released. We validate the framework against the preliminary reference Earth model, recovering Earth’s radius to 0.3% and lower-mantle densities to 3%. Using PALEOS , we computed a grid of 17 900 mass–radius relations spanning 0.1–100 M _⊕ for rocky (Fe + MgSiO ₃ ) and water-rich (Earth-like core plus H ₂ O envelope) compositions at surface temperatures from 300 to 4000 K. Because these EoSs treat solid and molten states continuously, thermal expansion remains active from fully solid interiors into the magma-ocean regime. For low-mass silicate planets, thermal expansion inflates the radius by more than 1% above 1500 K and by up to 16% at 4000 K, a change as large as both the radius spread from bulk composition (the iron–rock–water degeneracy) and the typical transit radius measurement uncertainty. We demonstrate the resulting degeneracy on two ultrashort-period super-Earths, WASP-47 e and TOI-1807 b, showing that each admits two purely rocky interior solutions indistinguishable in mass and radius but occupying radically different geophysical states: one fully solid and the other hosting a deep magma ocean above a liquid iron core. Phase-aware thermally resolved EoSs are thus essential for translating astronomical observations into exoplanetary geophysics.

The chemical compositions of planets and their host stars are intrinsically linked, having formed from the same protostellar material. Characterizing this relationship provides key constraints on the processes governing planetary formation and evolution. Focusing on host stars with near-solar chemical abundances limits our understanding of how planetary composition varies across a broader chemical parameter space. Expanding the sample to include stars with compositions markedly different from the Sun is therefore essential for building a complete picture of star–planet compositional connections. Here, we focus specifically on iron-poor hosts since they are more likely to be alpha-enhanced and represent some of the most chemically distinct stars relative to the Sun (i.e. thick disc stars). We present a sample of 45 stars hosting 64 planets across the super-Earth and sub-Neptune regimes, for which we homogeneously obtain new stellar parameters including abundances, re-derive planetary mass and radius, and model the bulk interior compositions of their planetary companions. No statistically significant evidence for a correlation between stellar and planetary composition was found in our sample. We suggest that this null result is primarily driven by the large uncertainties inherent to both compositional proxies, which may obscure an underlying relationship. Quantifying these uncertainties is therefore a critical step that previous studies have not fully addressed. Furthermore, even with improved precision, uncovering such a relation may require a higher-dimensional treatment that accounts for additional parameters such as planetary equilibrium temperature.

The geochemical evolution of long-lived magma oceans is strongly regulated by the 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 the 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, and applied 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 ( f O ₂ ≤ IW, where IW denotes the iron–wüstite buffer) promote earlier deep-mantle crystallization relative to oxidized (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 H ₂ –CO-rich atmospheres; oxidized mantles favour thinner H ₂ O–CO ₂ 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.

We demonstrate that the redox-sensitivity of mantle outgassing can trigger transient episodes of atmospheric reinflation in highly irradiated and geochemically reduced super-Earths, a mechanism we term “reflation.” Mantle redox governs the outgassing and speciation of CHONS volatiles, setting the background secondary atmospheric composition during extended photoevaporation at highly irradiated conditions. Using simulations of the coupled atmosphere–interior evolution of irradiated super-Earths, we illustrate that reduced mantles close to the iron–wüstite buffer initially produce CO-dominated atmospheres. Hydrodynamic escape continuously removes volatiles while outgassing from the melt replenishes the atmosphere with H ₂ , converted from H ₂ O dissolved in the underlying magma ocean. This leads to a late-stage transition from C- to H-dominated gas that transiently reinflates super-Earth atmospheres and decreases their bulk densities by up to ∼60% between several hundreds of megayears to a gigayear after their formation, prior to complete atmospheric erosion by photoevaporation. In contrast, oxidized mantles, closer to Earth-like geochemistry, strongly buffer their atmospheric composition while exposed to hydrodynamic escape, producing monotonic radius deflation. Reflation events are triggered by geochemically reduced mantles, intermediate escape efficiencies, high irradiation, and initial water inventories ≳ 5 Earth oceans. This redox-dependent evolutionary divergence hinges on the sensitive feedback between interior and atmospheric evolution serving as a potential tracer of historical geochemical state. Population-level reflation signatures of close-in super-Earths may thus serve as tracers of interior geochemistry and formation conditions.