Aragog

1-D two-phase interior dynamics solver with mixing-length convective closure.

Aragog integrates the spherically symmetric specific-entropy equation for a partially molten silicate mantle from the core-mantle boundary to the surface. Two design choices define Aragog's approach:

• Mixing-length theory (MLT) closes the convective heat flux locally at every radial node. The full radial entropy profile $S(r,t)$ is the prognostic variable, so solidification fronts, retained melt pockets, and EOS-resolved adiabats are recovered without an assumed reference state. See Mixing-length theory.
• Two-phase flow treats the mushy mantle as a coexisting solid + melt mixture at every node. This activates gravitational separation of melt and solid, chemical mixing of melt fraction across the rheological transition, and a continuous (lever-rule) treatment of latent heat through the partial-melt regime. See Two-phase flow in Aragog.

Together, MLT and two-phase flow let Aragog resolve the partial-melt window between first crystallisation and final solidification, where atmospheric outgassing, surface volatile budgets, and the timing of solidification are shaped by the coupled mantle-atmosphere evolution. Aragog is part of the PROTEUS coupled atmosphere-interior evolution framework and is its production interior-energetics backend.

• Documentation: https://proteus-framework.org/aragog
• Source code: https://github.com/FormingWorlds/aragog

Features

• Entropy-form, two-phase interior dynamics solver. Specific entropy $S(r,t)$ at staggered nodes is the only state variable; $T$, $\rho$, $\phi$, $c_p$, $\alpha$, $(\partial T/\partial P)_S$ are read from PALEOS or SPIDER-format pressure-entropy tables. Lever-rule blending, gravitational separation, and chemical mixing all enter the energy budget continuously across the solidus and liquidus.
• Mixing-length theory with smooth viscous-to-inviscid blend. Convective eddy diffusivity $\kappa_h$ is built per cell from the local entropy gradient, gravity, density, viscosity, and a mixing length $l(r)$, with a tanh blend at $\mathrm{Re}_\mathrm{crit} = 9/8$. Captures both the laminar and turbulent regimes inside one closure.
• Production-grade integrator. SUNDIALS CVODE via scikits.odes is the default (solver_method = "cvode"), paired with a JAX-derived analytic Jacobian (use_jax_jacobian = true) for production-tolerance coupled runs. scipy Radau and BDF are available as fall-backs (solver_method = "radau" / "bdf"); standalone installs without scikits.odes or JAX fall back automatically.
• SPIDER bit-parity boundary conditions. Default core_bc = "energy_balance" evolves $dS/dr|_\mathrm{cmb}$ as an extra ODE state, mirroring SPIDER's bc.c:76-131. Three other modes (quasi_steady, gradient, bower2018) are available for parity testing and quick exploration.
• Per-call mass-weighted $\Delta\Phi$ cap. SUNDIALS root function returns at the exact step where the global melt-fraction change first reaches the configured limit; required at the rheological transition where any rate estimate from $t = 0$ overshoots within the call window and stalls the adaptive $dt$.
• Coupling to Zalmoxis. External P-T tables, mesh, and per-node gravity profiles read from the structure solver are accepted via eos_method = 2 and mass_coordinates = true, so the interior dynamics solve and the structure solve share a single self-consistent mantle.
• Configurable radiogenic and tidal heating. Six radionuclides ($^{40}\mathrm{K}$, $^{232}\mathrm{Th}$, $^{235}\mathrm{U}$, $^{238}\mathrm{U}$ for present-day heating; $^{26}\mathrm{Al}$ and $^{60}\mathrm{Fe}$ for early-Solar-System studies) plus a per-staggered-node tidal-heating array.

Quick start

Install

git clone git@github.com:FormingWorlds/aragog.git
cd aragog
pip install -e ".[jax,test,docs]"

The optional extras are: jax (JAX, equinox, scikits-odes-sundials for the production CVODE+JAX path), test (pytest with xdist + cov), docs (Zensical + mkdocstrings for building the doc site). Plain pip install -e . works for an inspection-only install.

A PyPI release is available as fwl-aragog:

pip install fwl-aragog

Equation-of-state tables

Aragog requires SPIDER-format pressure-entropy lookup tables on disk. Inside a PROTEUS coupled run the tables are produced on the fly by Zalmoxis from PALEOS; for standalone use, point eos_dir at any directory containing the ten required files (see Reference: data for the schema and the canonical file list).

FWL_DATA is honoured as the default data root if it is set:

export FWL_DATA=/your/data/path

Run a smoke integration

from pathlib import Path

from aragog import aragog_file_logger
from aragog.solver import EntropySolver

aragog_file_logger(log_dir=str(Path.cwd()))

solver = EntropySolver.from_file(
    filename="src/aragog/cfg/abe_solid.toml",
    eos_dir="path/to/eos/tables",
)
solver.initialize()
solver.set_initial_entropy(2900.0)
solver.solve()

out = solver.get_state()
print(f"Status: {out.status}")
print(f"T_magma: {out.T_magma:.0f} K, T_core: {out.T_core:.0f} K, Phi: {out.Phi_global:.4f}")

EntropySolver.from_file builds Parameters from the TOML file and loads the EOS tables in one call. The bundled configs in src/aragog/cfg/ are short standalone smoke setups; for a full walkthrough including the SolverOutput dataclass fields, see the first-run tutorial. The production-tolerance defaults that PROTEUS uses (CVODE + JAX, core_bc = "energy_balance", mass_coordinates = true, phase_smoothing = "tanh", kappah_floor = 10 m$^2$/s, the six-isotope radionuclide cocktail) are set on the PROTEUS side, not in abe_solid.toml or abe_mixed.cfg.

Test suite

pytest -m unit                           # ~2 min on a workstation
pytest -m "unit or smoke or slow"        # full nightly suite, 10 min wall + EOS-table data

Coverage is enforced at 90% by [tool.coverage.report] in pyproject.toml. Both push CI (unit tier) and the nightly (full suite) upload to Codecov under separate flags so the dashboard distinguishes the two cadences.

PROTEUS integration

When PROTEUS drives Aragog, the configuration lives in PROTEUS's TOML schema, not in input/abe_mixed.cfg. The PROTEUS-side attrs class is proteus.config._interior.Aragog; the wrapper at src/proteus/interior_energetics/aragog.py translates PROTEUS settings into Aragog Parameters and registers the JAX CVODE factory.

Recommended PROTEUS-side knobs (in priority order):

1. interior_struct.module = "zalmoxis" + interior_energetics.module = "aragog" for new production runs.
2. interior_energetics.aragog.core_bc = "energy_balance" (default).
3. interior_energetics.aragog.backend = "jax" (default; the wrapper translates to use_jax_jacobian = true).
4. interior_energetics.aragog.solver_method = "cvode" (default).
5. interior_energetics.aragog.phi_step_cap = 0.05 for typical evolution; leave at 0.0 unless mushy-zone melt-fraction oscillations show up early.

Full theory and the prioritised-settings table live in docs/Explanations/.

Citation

If you use Aragog (or the original SPIDER code) please cite:

• Bower et al. (2018). Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets. Physics of the Earth and Planetary Interiors, 274, 49 to 62.

The PALEOS pressure-entropy tables used by the production path are described in Attia et al. (2026), PALEOS: Multiphase Equations of State and Mass-Radius Relations for Exoplanet Interiors (submitted to A&A; arXiv:2605.03741).