PALEOS: Thermodynamic Equation of State Tables for Fe, MgSiO₃, and H₂O at Planetary Interior Conditions

PALEOS: Thermodynamic Equation of State Tables for Fe, MgSiO₃, and H₂O at Planetary Interior ConditionsPrecomputed thermodynamic property tables for three key planetary materials—iron (Fe), magnesium silicate (MgSiO₃), and water (H₂O)—generated with the open-source Python package PALEOS (Planetary Assemblage Layers: Equations Of State). These tables are designed for direct use in planetary interior structure and thermal evolution models, spanning the pressure–temperature conditions encountered from terrestrial to giant planets.Scope and motivationInterior modelling of rocky and water-rich exoplanets requires thermodynamic properties of core, mantle, and volatile-layer materials over many orders of magnitude in pressure and temperature. PALEOS provides a centralized, validated equation-of-state toolkit that consolidates published EoS for each material, implements full phase diagrams with automatic phase selection, and derives all seven thermodynamic quantities analytically from the underlying P(V,T) relations via Maxwell relations and fundamental thermodynamic identities. The tables released here are the primary data product of PALEOS: they encode the analytically computed properties on regular grids that can be loaded and interpolated with minimal effort.Tables includedFileMaterialP rangeT rangeResolutionpaleos_iron_tables_pt.datFe1 bar – 100 TPa300 – 10⁵ K150 ppdpaleos_mgsio3_tables_pt.datMgSiO₃1 bar – 100 TPa300 – 10⁵ K150 ppdpaleos_water_tables_pt.datH₂O1 μbar – 100 TPa100 – 10⁵ K150 ppdAll grids are log-uniform in both P and T at 150 points per decade (ppd), chosen so that bilinear interpolation in (log₁₀P, log₁₀T) space achieves a relative density error below 10⁻⁴ at the 99th percentile. The Jupyter notebooks used to generate these tables are available in the tables/ directory of the PALEOS repository.ColumnsEach table contains the same ten columns:P — Pressure [Pa]T — Temperature [K]rho — Density [kg/m³]u — Specific internal energy [J/kg]s — Specific entropy [J/(kg·K)]cp — Isobaric heat capacity [J/(kg·K)]cv — Isochoric heat capacity [J/(kg·K)]alpha — Thermal expansion coefficient [K⁻¹]nabla_ad — Adiabatic gradient (d ln T / d ln P)_S [dimensionless]phase — Stable phase identifier (string)FeThe iron table covers the complete planetary core phase diagram with five phases: α-bcc, δ-bcc, γ-fcc (Dorogokupets et al. 2017), ε-hcp (Miozzi et al. 2020 blended with Hakim et al. 2018 via a smoothstep transition for pressures above ~310 GPa), and liquid (Luo et al. 2024). Solid–solid phase boundaries follow Dorogokupets et al. (2017) and the melting curve follows Anzellini et al. (2013). Internal energy and entropy are referenced to the bcc–fcc–liquid triple point (5.2 GPa, 1991 K).MgSiO₃The MgSiO₃ table covers the complete planetary mantle phase diagram with six phases: three pyroxene polymorphs—low-pressure clinoenstatite, orthoenstatite, and high-pressure clinoenstatite from Sokolova et al. (2022)—bridgmanite (Wolf et al. 2015, pure Mg end-member), postperovskite (Sakai et al. 2016), and liquid (Wolf & Bower 2018 with parameters from Luo & Deng 2025). The pyroxene boundaries follow Sokolova et al. (2022), the bridgmanite–postperovskite boundary follows Ono & Oganov (2005), and the melting curve combines Belonoshko et al. (2005) below ~2.55 GPa with Fei et al. (2021) above. Internal energy and entropy are referenced to the pyroxene triple point (6.5 GPa, 1100 K). Grid points where the EoS failed to converge (primarily in the low-P, high-T liquid regime, reflecting vapor/supercritical phase uncaptured by PALEOS) are omitted; users should reconstruct the full rectangular grid with NaN fill before interpolation (see usage example below).H₂OThe water table is regridded from the AQUA equation of state (Haldemann et al. 2020), a composite description assembled from seven underlying EoS covering ice polymorphs (Ih through X), liquid, vapor, and supercritical/superionic water. A correction is applied to the entropy and internal energy to fix a sign error in the Mazevet et al. (2019) Helmholtz free energy parametrization used in the supercritical regime. Heat capacities and thermal expansion are derived from the tabulated AQUA quantities using standard thermodynamic relations.UsageTables are plain-text, whitespace-delimited files with comment headers (lines starting with #). Grid points where the EoS did not converge are omitted, so a table may contain fewer rows than the full rectangular grid (in this current implementation, only the MgSiO₃ table has an irregular structure). The following Python snippet reconstructs the full grid with NaN fill and builds an interpolator:import numpy as npfrom scipy.interpolate import RegularGridInterpolator# Grid parameters (adjust per table; see file headers)n_P, n_T = 1351, 380P_min, P_max = 1e5, 1e14 # PaT_min, T_max = 300.0, 1e5 # K# Load datacols = ['P','T','rho','u','s','cp','cv','alpha','nabla_ad','phase']data = np.genfromtxt('paleos_iron_tables_pt.dat', names=cols, dtype=None, encoding='utf-8')# Reconstruct full regular gridlog_P = np.linspace(np.log10(P_min), np.log10(P_max), n_P)log_T = np.linspace(np.log10(T_min), np.log10(T_max), n_T)rho = np.full((n_P, n_T), np.nan)for row in data: i = np.searchsorted(log_P, np.log10(row['P'])) j = np.searchsorted(log_T, np.log10(row['T'])) if i < n_P and j < n_T: rho[i, j] = row['rho']# Interpolate (NaN propagates near missing points)interp = RegularGridInterpolator((log_P, log_T), rho)rho_query = interp([[np.log10(100e9), np.log10(4000)]])[0]Alternatively, PALEOS can be used directly as a Python package for on-the-fly EoS evaluation with automatic phase selection:from paleos import iron_eos as feeos, phase = fe.get_iron_eos_for_PT(P=100e9, T=4000)rho = eos.density(100e9, 4000)Thermodynamic consistencyAll EoS implementations have been validated against the Maxwell-relation consistency parameter Δ ≡ 1 − ρ²(∂S/∂P)_T / (∂ρ/∂T)_P, which vanishes for a perfectly self-consistent equation of state. Across the iron phase diagram, 98.2% of the P–T domain satisfies |Δ| < 0.01 (median |Δ| ≈ 1.4 × 10⁻⁷). Across the MgSiO₃ phase diagram, 100% of the valid domain satisfies |Δ| < 0.01 (median |Δ| ≈ 3.5 × 10⁻⁸). See the PALEOS documentation and benchmark notebooks for detailed consistency reports.License and citationThese tables are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. If you use these tables, please cite the forthcoming PALEOS paper (Attia et al., in prep.).* * *Version log (1.1.0): added S₀ fix to Mazevet et al. (2019) correction and gated the entire correction analytically to Region 7 of Haldemann et al. (2020).