PALEOS MgSiO₃ EoS Lookup Table for PROTEUS

PALEOS MgSiO₃ Lookup Tables for PROTEUS

Precomputed MgSiO₃ equation of state lookup tables generated with PALEOS, designed for the PROTEUS planetary interior model. The tables cover pressures up to 100 TPa, extending the EoS coverage to the regime relevant for super-Earth and sub-Neptune interiors.

Contents

Two table files are provided:

Both tables share a common pressure grid: P = 0 Pa plus a log-uniform grid from 1 bar to 100 TPa at 150 or 600 points per decade. The temperature grids are also log-uniform at 150 or 600 points per decade. The temperature bounds are derived from the PROTEUS solidus and liquidus files: specifically min(T_solidus) and max(T_liquidus) as global bounds.

The grids are designed to be rectangular. Some points are missing where the EoS solver failed to converge; when reconstructing the full grid for interpolation, these entries should be filled with NaN. The nonconverging regions should not affect the physically relevant domain (beyond liquidus for the solid table, vapor/supercritical phase for the liquid table). 

Columns

Each row contains 10 columns, all in SI units:

1. P — Pressure [Pa]
2. T — Temperature [K]
3. rho — Density [kg/m³]
4. u — Specific internal energy [J/kg]
5. s — Specific entropy [J/(kg·K)]
6. cp — Isobaric heat capacity [J/(kg·K)]
7. cv — Isochoric heat capacity [J/(kg·K)]
8. alpha — Thermal expansion coefficient [K⁻¹]
9. nabla_ad — Adiabatic gradient (d ln T / d ln P)_S [dimensionless]
10. phase — Phase identifier

Phase selection

For the solid table, phase selection at each (P, T) point follows the full PALEOS MgSiO₃ phase diagram. At temperatures above the PALEOS melting curve (which can occur since the solid table extends to the PROTEUS liquidus), the code falls back to the solid phase stable just below the melting curve and evaluates that EoS at the requested temperature. The liquid table uses Wolf+Bower18 everywhere.

Generating the tables

The notebook to regenerate these tables is available in the PALEOS repository at utils/mgsio3_tables_proteus.ipynb. It contains a single clearly marked User Input cell where all parameters (file paths, P/T ranges, resolution, output filenames) can be adjusted.

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Version log (1.1.0): covered all PROTEUS solidi/liquidi, implemented consistent U₀/S₀ per-phase shifts to ensure dS/dT > 0 everywhere and Gibbs-energy continuity at triple points, and generated high-resolution (600 ppd) tables.