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Interior structure and energetics

PROTEUS separates the interior into two coupled subsystems: structure (hydrostatic equilibrium, density profile, planet radius) and energetics (thermal evolution, melt fraction, heat flux). Each has its own module selection and parameters.

Submodule documentation: Aragog | SPIDER | Zalmoxis. See also Model description.

Interior structure [interior_struct]

The structure module computes the planet's density profile, radius, and core-mantle boundary position by solving the hydrostatic equilibrium equation with an equation of state (EOS).

Parameter Type Default Description
core_frac float 0.325 Core fraction of the planet, by mass or by radius (see core_frac_mode). With module = 'zalmoxis' the core mass is this fraction of the planet mass without the volatile inventories that the outgassing takes as inputs (H, C, N, S, noble gases; O when it is an input), or without their atmosphere part with zalmoxis.dry_mantle = false. It is set when the init stage ends and then kept. Must be > 0 and < 1.
core_frac_mode str "mass" How core_frac is interpreted. 'radius': fraction of planet radius. 'mass': mass fraction, of planet.mass_tot with module = 'dummy' and of the mass that core_frac names with module = 'zalmoxis'. Only 'radius' is supported when module = 'spider'. The zalmoxis module always interprets core_frac as a mass fraction and ignores this flag (a warning is emitted at runtime if 'radius' is set with module = 'zalmoxis'). Choices: "radius", "mass".
module str or none "zalmoxis" Module for solving the planet's interior structure. Choices: none, "dummy", "spider", "zalmoxis".
core_density float or str "self" Density of the planet's core [kg m-3]. Set to 'self' for self-consistent calculation by Zalmoxis (requires module = 'zalmoxis').
core_heatcap float or str "self" Specific heat capacity of the planet's core [J kg-1 K-1]. Set to 'self' for self-consistent calculation by Zalmoxis (requires module = 'zalmoxis').
melting_dir str or none none Melting curve name in FWL_DATA. Required for the SPIDER structure module and for any run without a PALEOS table set; not read with module = 'zalmoxis' and a single PALEOS mantle EOS. With module = 'dummy' and a PALEOS mantle EOS, Aragog requires it but the solve uses the PALEOS set.
eos_dir str or none none EOS folder name in FWL_DATA, for the SPIDER structure module.

Zalmoxis [interior_struct.zalmoxis]

Zalmoxis solves the full hydrostatic structure with tabulated EOS (PALEOS, Chabrier, or Seager 2007). It supports 2-layer (core + mantle) and 3-layer (core + mantle + ice/water) models. The newton_* parameters apply when outer_solver = "newton"; the update_* and mesh_* parameters control the structure update triggers (Zalmoxis structure updates are expensive and decoupled from the main coupling loop); the miscibility_* parameters belong to the experimental binodal-aware mode.

Equation of state

Parameter Type Default Description
core_eos str "PALEOS:iron" EOS for the core layer. Format: ":". Tabulated: "PALEOS:iron" (default), "Seager2007:iron". Analytic: "Analytic:iron", "Analytic:MgFeSiO3", etc.
mantle_eos str "PALEOS:MgSiO3" EOS for the mantle layer. Format: ":". Tabulated: "PALEOS:MgSiO3" (default), "PALEOS-2phase:MgSiO3", "Seager2007:MgSiO3", "WolfBower2018:MgSiO3". Analytic: "Analytic:MgSiO3", "Analytic:MgFeSiO3", etc.
ice_layer_eos str or none none EOS for the ice/water layer (3-layer model). 'none' for 2-layer model (core + mantle only). Tabulated: "PALEOS:H2O", "Seager2007:H2O". Analytic: "Analytic:H2O".
mushy_zone_factor float 0.8 Cryoscopic depression factor controlling the width of the mushy zone (partially molten region) in the PALEOS EOS family. Defines the solidus as T_sol = T_liq * mushy_zone_factor. 1.0 = sharp phase boundary (no mushy zone). 0.8 = solidus at 80% of the liquidus temperature, the constant solidus-to-liquidus ratio of Stixrude+2014 for MgSiO3, applied here to the PALEOS liquidus. Must be in [0.7, 1.0]. Applies to the PALEOS EOS family (PALEOS, PALEOS-2phase, PALEOS-API, PALEOS-API-2phase); ignored for WolfBower2018 and RTPress100TPa (which use explicit melting curve files) and for Seager2007/Analytic (no derived solidus). Must be >= 0.7 and <= 1.0.
lowt_extension bool false Extend the solid P-S entropy tables below the 300 K edge of the PALEOS solid table, with the PALEOS phase potentials evaluated down to about 50 K on the rows below 12 GPa (file paleos_mgsio3_tables_pt_proteus_solid_lowT.dat next to the solid table). PALEOS values are used wherever the solid table has them. Applies to the P-S tables of the PALEOS MgSiO3 mantle and needs interior_energetics.module = 'aragog' and interior_struct.module 'zalmoxis' or 'dummy'; a mantle whose MgSiO3 (energetics) EOS is PALEOS-API or -highres is refused when the config loads, and a mantle without PALEOS tables ignores the switch with a warning. A resumed run keeps the tables it started with, so the switch acts on a fresh table build. The standard data set does not hold the extension file: write it with Zalmoxis's tools/converters/paleos_lowt_extension.py (--paleos-src, --table, and --out with the file name above in the folder of the solid table; see the Zalmoxis coupling page). A missing extension file, or a Zalmoxis whose table generator has no solid_lowt_file, stops the run at start-up (with the dummy structure, at the first table build). The Zalmoxis coupling page gives the range of the extended tables, the accuracy of their lowest entropy interval per planet mass and the entropy zero of each PALEOS phase. Aragog's entropy solver reads its thermodynamic properties from the P-S tables only; the phase P-T tables written for it are not read, so they need no extension. With the switch on, Aragog logs its minimum heat capacity warning at each coupling iteration.
mantle_mass_fraction float 0 Fraction of the planet's interior mass corresponding to the mantle. Required for 3-layer models (with ice layer) and for T-dependent 2-layer models (WolfBower2018, RTPress100TPa) where it partitions mass between core and mantle layers. Must be >= 0 and < 1.
dry_mantle bool true Structure EOS assumes a dry mantle. Set False for melt-fraction-aware dissolved-volatile mixing in the mantle density (per-shell volatile profile); the dissolved mass then stays inside the interior mass target and inside the mass that core_frac refers to.

Grid and solver

Parameter Type Default Description
num_levels int 150 Number of Zalmoxis radius layers.
outer_solver str "newton" Outer mass-radius solver: 'newton' (recommended) or 'picard'. Choices: "picard", "newton".
use_jax bool true Use the JAX backend for the structure solver.
use_anderson bool true Anderson Type-II Picard acceleration on the density loop.
solver_tol_outer float 0.003 Relative tolerance for mass convergence (outer loop). Must be > 0.
solver_tol_inner float 0.0001 Relative tolerance for density convergence (inner loop). Must be > 0.
solver_max_iter_outer int 100 Max iterations for mass convergence (outer loop). Must be >= 10.
solver_max_iter_inner int 100 Max iterations for density convergence (inner loop). Must be >= 10.

Newton solver tuning (used when outer_solver = "newton")

Parameter Type Default Description
newton_max_iter int 30 Maximum Newton iterations (outer_solver = 'newton'). Must be >= 5.
newton_tol float 0.0001 Newton convergence tolerance (outer_solver = 'newton'). Must be > 0.
newton_relative_tolerance float 1e-09 Integrator relative tolerance for the Newton path. Must be > 0.
newton_absolute_tolerance float 1e-10 Integrator absolute tolerance for the Newton path. Must be > 0.

Structure update triggers

Parameter Type Default Description
update_dphi_abs float 0.05 Re-solve the structure when the global melt fraction changes by this absolute amount since the last solve. Must be > 0 and < 1.
update_dtmagma_frac float 0.05 Re-solve the structure when T_magma changes by this fraction. Must be > 0 and < 1.
update_dw_comp_abs float 0.05 Re-solve when the relative dissolved-volatile (H2O or H2) mantle mass fraction changes by this amount. Must be > 0 and < 1.
update_interval float 1000000000.0 Maximum time between structure updates [yr]; effectively disabled at the default. Must be >= 0.
update_min_interval float 0 Minimum time between structure updates [yr]; prevents thrashing. Must be >= 0.
update_stale_ceiling float 25000.0 Time since the last successful re-solve after which a trigger refires [yr]; 0 disables. Must be >= 0.
mesh_max_shift float 0.05 Maximum fractional radius shift per structure update. Must be > 0 and < 1.
mesh_convergence_interval float 10.0 Convergence relaxation time after a mesh update [yr]. Must be > 0.

Initialisation

Parameter Type Default Description
equilibrate_init bool true Equilibrate structure and composition before the main loop.
equilibrate_max_iter int 15 Maximum equilibration iterations. Must be >= 1.
equilibrate_tol float 0.01 Equilibration convergence tolerance. Must be > 0.

P-S entropy lookup tables

Parameter Type Default Description
lookup_nP int 1350 Number of pressure points in SPIDER P-S tables generated from PALEOS. Must be >= 100.
lookup_nS int 280 Number of entropy points in SPIDER P-S tables generated from PALEOS. Must be >= 50.

Miscibility (experimental, not production-ready)

Parameter Type Default Description
global_miscibility bool false Enable the H2-silicate binodal-aware radial structure. True is rejected at config load: it requires the binodal handoff on the Zalmoxis side, which is not yet implemented.
miscibility_max_iter int 10 Maximum miscibility iterations. Must be >= 1.
miscibility_tol float 0.01 Miscibility convergence tolerance. Must be > 0.

How the core mass is set

Zalmoxis solves the structure for a target mass and a core mass. The target is the planet mass (planet.mass_tot plus the M_volatile_change ledger of delivered, stripped, escaped and desiccated volatiles) without the volatile mass that the structure does not hold: every element inventory with dry_mantle = true, and the atmosphere part of each inventory with dry_mantle = false. The core mass is core_frac of the planet without its kept volatiles, the inventories that the outgassing takes as inputs: H, C, N, S and the noble gases, and oxygen only when it is an input too (planet.fO2_source = "from_O_budget", or outgas.module = "dummy"). With dry_mantle = false only the atmosphere part of the kept inventories is taken off. With the default planet.fO2_source = "user_constant", CALLIOPE and atmodeller derive the oxygen inventory from the fO\(_2\) buffer at each call. That oxygen takes none of the core, like rock vapour: it is mantle mass, and with an ice layer zalmoxis.mantle_mass_fraction of it is mantle mass and the rest is mass of the ice layer. Each structure solve at Time = 0 computes the core mass from the inventories of its row, and the core mass is set when the init stage ends, from the inventories of that row. From then on the core mass is kept, and the mantle is the rest of the target: mass that escapes, that an impact strips, that desiccation removes or that leaves the mantle moves nothing across the core-mantle boundary. A giant impact adds core_frac of the impactor rock to the core mass: the impactor is taken to have the core fraction core_frac, and its core to merge with the core of the planet in full. With an ice layer the mantle is zalmoxis.mantle_mass_fraction of the target and the ice layer is the rest; the run stops with an error when the core and mantle fractions leave no ice layer.

The helpfile column M_core_target holds this mass. Zalmoxis puts the core-mantle boundary of its output at the first grid node at or above the core fraction of the mass it converged to, and M_core is the mass inside that node. M_core is therefore between the target less the mass tolerance of the solve (zalmoxis.solver_tol_outer) and the target plus that tolerance and one mantle shell at the boundary. For a planet of 1 Earth mass with core_frac = 0.325 and the default zalmoxis.num_levels = 150 that shell holds about 1.6 % of the core mass, and the measured range of M_core in runs of that planet is 0.1 to 1.5 % above the target. The structure takes a changed core mass at its next solve, so a run with no structure update after the init stage keeps the core of its last solve. When the target leaves no mantle (a core mass at or above the target mass, which a large buffered oxygen inventory over a hot magma ocean can cause), the run stops with an error that names the masses. A run that resumes from a helpfile without the column takes core_frac of the structure target of the row of its first structure solve, logs a warning, and keeps that core mass from there. This core mass depends on the oxygen inventory of that row, so it differs with the row at which the run resumes, and it is not the core mass of a run that starts with the column.

How the PALEOS mantle EOS is applied

The MgSiO\(_3\) mantle EOS resolves through two distinct paths depending on the <source> prefix of mantle_eos.

With mantle_eos = "PALEOS:MgSiO3" (the default), the hydrostatic structure solve uses the PALEOS unified MgSiO\(_3\) table for the density profile. The phase-specific property surfaces used by Aragog (density, heat capacity, thermal expansion, adiabatic gradient) and the pressure-entropy lookup tables are built from the PALEOS two-phase solid and liquid tables, which keeps the properties well resolved across the melting-curve discontinuity that a single unified table interpolates through. The liquidus is the analytic PALEOS curve (Belonoshko et al. 2005 below 2.55 GPa, Fei et al. 2021 above, in Simon-Glatzel form), and the solidus is derived as \(T_\mathrm{sol}(P) = f\,T_\mathrm{liq}(P)\) with \(f\) the mushy_zone_factor (default 0.8). The default is the constant solidus-to-liquidus ratio (\(\approx 0.809\)) of the Stixrude (2014)3 MgSiO\(_3\) melting parametrization, applied to the PALEOS liquidus instead of the Stixrude liquidus. The derived solidus is therefore a constant depression of the PALEOS liquidus, not the Stixrude solidus curve: its absolute value lies well above the Stixrude solidus at low to moderate pressure (about 2900 K against 1700 K at 20 GPa, and about 10% higher at 140 GPa) and below it above roughly 200 GPa. The melt fraction then follows from the lever rule between this solidus and liquidus.

With mantle_eos = "PALEOS-2phase:MgSiO3", the SPIDER/Aragog entropy tables use the separate solid and liquid PALEOS tables, which supply the latent-heat entropy gap across the melting curve directly rather than through a single interpolated unified table. Their phase boundaries follow the same construction as the unified case: the liquidus is the analytic PALEOS curve, and the solidus is derived as \(T_\mathrm{sol}(P) = f\,T_\mathrm{liq}(P)\) with \(f\) the mushy_zone_factor.

A run with a PALEOS EOS requires the table of each PALEOS layer, with the MgSiO\(_3\) unified table only when a layer is PALEOS:MgSiO3. A mantle with a PALEOS component also requires the MgSiO\(_3\) two-phase solid and liquid pair: the high-resolution pair for PALEOS-2phase:MgSiO3-highres, and the PALEOS-API cache for the PALEOS-API family. When one is missing, the run stops before the first solve with an error that names each missing file and the command that fetches them, proteus get interiordata --config-path <config.toml>; it does not fall back to another table set. With dry_mantle = false it also requires the tables of the dissolved volatiles (PALEOS:H2O and Chabrier:H). A resumed SPIDER run that keeps its pressure-entropy tables needs only the tables of its layers. With temperature_mode = "liquidus_super" it also needs the two-phase pair that its anchor reads. An Aragog resume always needs the two-phase pair, which it reads when the mesh changes. A mixture mantle (a + in mantle_eos) takes its melting curves, in the structure and in the energetics, and its SPIDER or Aragog tables from its MgSiO\(_3\) component: with PALEOS:MgSiO3 it gets exactly the curves and tables of a PALEOS:MgSiO3 mantle, and with WolfBower2018:MgSiO3 the eos_dir P-S tables (by default Wolf and Bower 2018) and the melting_dir curves. The other components enter only the structure density. A PALEOS mantle with no MgSiO\(_3\) component (for example mantle_eos = "PALEOS:H2O", "PALEOS:iron", or a mixture of the two) uses the density of its own material in the structure, while the PALEOS MgSiO\(_3\) melting curves and the two-phase MgSiO\(_3\) tables of its PALEOS family stand in for the energetics. With SPIDER or Aragog, the energetics must follow a PALEOS, WolfBower2018 or RTPress100TPa EOS; a mantle whose energetics would follow a Seager2007, Chabrier or analytic EOS is rejected when the configuration loads. temperature_mode = "liquidus_super" solves the initial adiabat on the MgSiO\(_3\) two-phase tables for every mantle, so those tables are required at the start of the run. The run logs one warning that names the cases that apply at the start of each run segment, so a resumed run logs it again.

mushy_zone_factor and the two-phase structure solve

In a PROTEUS-coupled run, load_zalmoxis_solidus_liquidus_functions builds the mushy_zone_factor * liquidus solidus described above and passes it into the Zalmoxis structure solve. The same curve pair sets the SPIDER/Aragog table boundaries, the adiabatic gradient in the mushy zone, and the two-phase density (PALEOS-2phase, PALEOS-API-2phase), so mushy_zone_factor acts consistently in the tables and in the structure. A standalone Zalmoxis run uses its own rock_solidus and rock_liquidus keys (Stixrude 2014 by default). With those defaults a two-phase mantle does not depend on mushy_zone_factor; with no unified PALEOS layer elsewhere (for example a Seager2007:iron core), a value below 1.0 is rejected at validation. A unified PALEOS layer such as a PALEOS:iron core does honor the factor in its own density, so validation accepts it, but it does not change the two-phase mantle. Setting rock_liquidus = "PALEOS-liquidus" selects the PALEOS liquidus and derives the solidus as mushy_zone_factor * liquidus, as in the coupled case. For a 1 \(M_\oplus\) planet with a Seager2007:iron core and a PALEOS-2phase:MgSiO3 mantle in a standalone Zalmoxis run with a linear temperature profile, the default Stixrude (2014) curves give a radius that does not depend on mushy_zone_factor, whereas rock_liquidus = "PALEOS-liquidus" makes the resolved radius respond to mushy_zone_factor, so mushy_zone_factor = 0.8 and 1.0 give different radii. Run this standalone case to quantify the shift for a given planet and table set.

Two-phase table versions

Two versions of the PALEOS two-phase MgSiO\(_3\) tables are in circulation: the set shipped in the Zalmoxis data directory, and the finer-grid set on Zenodo that the reference-data manifest fetches. They are generated from the same PALEOS EOS but on different grids, so for exact reproducibility record which set a run used (the shipped tables resolve through the Zalmoxis material registry; the fetched tables land under FWL_DATA).

The wet mantle carries dissolved water only

With dry_mantle = false and the production outgassing module (CALLIOPE), the only species blended into the mantle density is H2O. This is the intersection of the two sides of the coupling, not an arbitrary restriction: a species needs both a dissolved mass from the outgassing chemistry and an EOS table in the structure solver, and under CALLIOPE H2O is the only species with both. CALLIOPE also dissolves CO2, CO, CH4, N2, and S2, but these have no structure-side EOS mapping. Their dissolved mass stays inside the interior mass target, and because the silicate blend fraction is defined as the remainder 1 - w_H2O, those kilograms are packed at silicate density: the mass budget stays exact while the compressibility of these species is misrepresented. The radius error scales as the species' dissolved mass fraction times its density contrast against silicate, negligible at typical inventories. If a composition ever pushes an unmapped species to percent-level dissolved mass fractions, the fix is an EOS mapping for it, not a bookkeeping change. H2 has an EOS mapping (Chabrier:H) but no solubility law in CALLIOPE; a dissolved H2 mass can arise from the atmodeller outgassing module (its H2 solubility law), from the H2-silicate binodal partitioning (outgas.h2_binodal), or from the radial miscibility solve (interior_struct.zalmoxis.global_miscibility). The last two are rejected at config load until that physics is production ready, and the atmodeller wet combination has not been through the wet-path conservation verification. Every verified configuration therefore exercises the wet path with water alone, which is exactly the case covered by the dissolved-water conservation verification. Whoever lifts either gate or runs atmodeller wet must extend the wet-path verification to H2 first: the per-shell binodal suppression removes dissolved H2 from the structure without returning it to the atmosphere, so water-grade mass closure does not carry over.

P-S entropy lookup tables

The lookup_nP/lookup_nS tables are derived from PALEOS EOS data at runtime and cached. They provide the entropy-to-temperature mapping used by Aragog and SPIDER. By default each run derives its own copy of these tables under its output data/ directory. Set the PROTEUS_PS_CACHE_DIR environment variable to an absolute path to instead share one derived copy across runs: tables are stored in a subdirectory keyed by pressure ceiling, resolution, mushy zone factor, table layout, the resolved mantle-EOS identity, and the Zalmoxis table generator, so a run reuses the cache only when every one of those matches and different equations of state never collide. The generator identity is the Zalmoxis version plus a digest of two source files, zalmoxis/eos_export.py and zalmoxis/melting_curves.py; a new version or an edit to either file starts a new subdirectory. The digest does not cover other Zalmoxis modules (for example the PALEOS-API cache modules) or the contents of the EOS data files, which enter the key only through their resolved paths. A resumed run (proteus start -r) keeps the energetics P-S tables it already uses, in its own data/ directory or in the shared cache, whatever differs from the current settings, including a changed mantle EOS or a new table generator, unless they were built for another planet mass (another P_max, after an impact or on a walk-back past one); those are replaced by the tables of the current mass. The first time a process reads them, it logs one warning that names the difference, or the reason the current key is not checked (for example a PALEOS-API mantle EOS, which is not resolved on resume, or a mantle EOS that is no longer PALEOS). The structure solve uses the current melting curves. A resumed run with no kept tables (no completion marker with both phase-boundary files) logs a warning and continues on the tables of the current key, which it builds if they are absent. Sharing tables is the mitigation for the per-run disk duplication that a grid or batch of same-EOS runs would otherwise incur, since all such runs then read one shared copy. The cache directory is not size-limited or auto-pruned; it grows with the number of distinct pressure, resolution, and EOS combinations run against it, so point it at storage sized for the campaign.

Interior energetics [interior_energetics]

The energetics module evolves the mantle thermal state (temperature, entropy, melt fraction) and computes the interior heat flux that drives atmospheric evolution. The section carries the shared transport, heating, rheology, coupling-limit, and material-property parameters used by the solver modules; the const_* parameters enable a constant-properties mode that bypasses the EOS tables with an analytical \(T(S) = T_\mathrm{ref} \exp((S - S_\mathrm{ref}) / C_p)\) relationship for controlled parity tests.

Parameter Type Default Description
module str "aragog" Module for simulating the magma ocean. Choices: "spider", "aragog", "dummy", "boundary".
num_levels int 80 Number of radial grid levels for the energetics domain. Must be >= 40.
rtol float -1.0 Relative numerical tolerance for the interior ODE solver. SPIDER: -ts_sundials_rtol (used internally via atol_sf scaling). Aragog: scipy solve_ivp rtol. The deprecated aliases num_tolerance and [interior_energetics.spider].tolerance_rel copy into this field. Resolves to 1e-8 for Aragog and 1e-10 for SPIDER when left unset. With interior_struct.module = 'spider' it also sets the relative tolerance of the secant solve for the interior radius.
num_tolerance float -1.0 Deprecated alias for rtol; emits a DeprecationWarning when set.
atol float 1e-10 Absolute numerical tolerance for the interior ODE solver. SPIDER: -ts_sundials_atol (scaled by atol_sf at runtime). Aragog uses [interior_energetics.aragog].atol_temperature_equivalent instead because its state variable is entropy, not temperature, and a direct entropy-scale atol would be unintuitive to tune. Must be > 0.
flux_guess float -1 Initial heat flux guess [W m-2]. When < 0 (default), computed automatically as sigma * T_magma^4. Set to a positive value to prescribe a specific initial flux. Set to 0 for zero initial flux.
surface_bc_mode str "flux" Surface boundary condition mode for SPIDER and Aragog: 'flux' or 'grey_body'. 'flux' consumes prescribed F_atm from the atmosphere module as the upper boundary flux. 'grey_body' evaluates radiative surface cooling sigma * (T_surf^4 - T_eqm^4) inside the interior solver per substep from current top-cell T (SPIDER uses -SURFACE_BC 1 -emissivity0 1.0; Aragog uses outer_boundary_condition=1 with emissivity=1). The atmosphere module still runs to populate diagnostic helpfile fields (F_olr, F_sct, R_obs), but its F_atm output is not used by the interior. Incompatible with interior_energetics.aragog.top_cell_dt_limit = true. Choices: "flux", "grey_body".

Transport physics

Parameter Type Default Description
trans_conduction bool true Include conductive heat transfer.
trans_convection bool true Include convective heat transfer (mixing length theory).
trans_grav_sep bool true Include gravitational separation (Stokes settling).
trans_mixing bool true Include the chemical mixing flux.

Heating

Parameter Type Default Description
heat_tidal bool false Include tidal heating?.
heat_radiogenic bool true Include radiogenic heat production?.
radio_tref float 4.567 Reference age for setting radioactive decay [Gyr]. Must be >= 0.
radio_Al float 0.0 Concentration (ppmw) of aluminium-26 at reference age t=radio_tref; 1.23 is the canonical early solar system value. Must be >= 0.
radio_Fe float 0.0 Concentration (ppmw) of iron-60 at reference age t=radio_tref. Must be >= 0.
radio_K float 310.0 Concentration (ppmw) of potassium-40 at reference age t=radio_tref. Must be >= 0.
radio_U float 0.031 Concentration (ppmw) of uranium at reference age t=radio_tref. Must be >= 0.
radio_Th float 0.124 Concentration (ppmw) of thorium-232 at reference age t=radio_tref. Must be >= 0.

Rheology and convection

Parameter Type Default Description
rfront_loc float 0.4 Centre of rheological transition in terms of melt fraction. SPIDER receives it as -phi_critical. Aragog centres its viscosity blend, its reported rheological front and the melt-fraction ramp of kappah_floor on it; the boundary module uses it as the transition point of its viscosity models. SPIDER and Aragog use melt mass fraction (0.4 by volume is about 0.375 by mass at a 10 percent melt-solid density contrast); the boundary module takes its melt fraction linearly in temperature between solidus and liquidus and its rheological transition width from phase_transition_width, not rfront_wid. Must be > 0 and < 1.
rfront_wid float 0.2 Width of rheological transition in terms of melt fraction. Must be > 0 and < 1.
grain_size float 0.001 Crystal settling grain size [m]. Must be > 0.
mixing_length str "nearest" Mixing-length scale: 'nearest' (distance to nearest boundary) or 'constant' (a quarter of the mantle depth). Choices: "nearest", "constant".
kappah_floor float 10.0 Eddy diffusivity floor [m2 s-1]; prevents mixing-length transport from freezing out. Must be >= 0.

Coupling limits

Parameter Type Default Description
tmagma_atol float 20.0 Maximum increase in T_magma and T_surf per PROTEUS step (maximum increase atol + rtol * T_magma_prev) [K]; disabled on Aragog steps where interior_energetics.aragog.top_cell_dt_limit is true, tau_drain is finite, and the step does not exceed tau_drain. Must be >= 0.
tmagma_rtol float 0.02 Maximum relative increase in T_magma and T_surf per PROTEUS step (maximum increase atol + rtol * T_magma_prev); disabled on Aragog steps where interior_energetics.aragog.top_cell_dt_limit is true, tau_drain is finite, and the step does not exceed tau_drain. Must be >= 0.
tmagma_tides_step float 10.0 Maximum change in T_magma allowed when tides are active [K]. Must be >= 0.

Ultra-thin boundary layer

Parameter Type Default Description
param_utbl bool false Enable the ultra-thin boundary layer parameterisation.
param_utbl_const float 1e-07 Ultra-thin boundary layer scaling constant [K-1]. Must be > 0.

Hydrostatic EOS (Adams-Williamson)

Parameter Type Default Description
adams_williamson_rhos float 4078.95095544 Adams-Williamson surface density [kg/m^3]. Matches SPIDER -adams_williamson_rhos and Aragog _MeshParameters.surface_density. Must be > 0.
adams_williamson_beta float 1.1115348931000002e-07 Adams-Williamson density gradient [1/m]. Matches SPIDER -adams_williamson_beta. Aragog derives its own via bulk modulus, so this value applies to SPIDER only. Must be > 0.
adiabatic_bulk_modulus float 260000000000.0 Adiabatic bulk modulus [Pa] used by Aragog's Adams-Williamson EOS (_MeshParameters.adiabatic_bulk_modulus). SPIDER derives its own. Must be > 0.

Phase material properties

Parameter Type Default Description
melt_log10visc float 2.0 log10 viscosity of molten silicate [Pa s]. Matches SPIDER -melt_log10visc (2.0 = 1e2 Pa s).
solid_log10visc float 22.0 log10 viscosity of solid silicate [Pa s]. Matches SPIDER -solid_log10visc (22.0 = 1e22 Pa s). Shared by SPIDER and Aragog so both apply the same solid-phase rheology; a mis-set value diverges both solvers' solid-phase rheology by the same factor.
melt_cond float 4.0 Thermal conductivity of molten silicate [W/m/K]. Matches SPIDER -melt_cond. Must be > 0.
solid_cond float 4.0 Thermal conductivity of solid silicate [W/m/K]. Matches SPIDER -solid_cond. Must be > 0.
eddy_diffusivity_thermal float 1.0 Multiplier on the internally-computed thermal eddy diffusivity. SPIDER: -eddy_diffusivity_thermal (1.0 default).
eddy_diffusivity_chemical float 1.0 Multiplier on the internally-computed chemical eddy diffusivity. SPIDER: -eddy_diffusivity_chemical (1.0 default).
latent_heat_of_fusion float 4000000.0 Latent heat of fusion of silicate [J/kg]. Aragog uses this as a scalar in _PhaseMixedParameters. SPIDER derives it per-(P,S) from dS * T_fus via the EOS tables; the SPIDER derivation is more physically correct but this scalar is good to ~10% at Earth-mantle conditions. TODO: switch Aragog to SPIDER's derivation once the EntropyEOS exposes a dS_fus(P) method. Must be > 0.
phase_transition_width float 0.1 Width [fraction] of the mushy-zone transition in Aragog's _PhaseMixedParameters. Sets the width of the phase boundary in Aragog's mixed-phase blending (viscosity, thermal conductivity etc.). Distinct from [interior_energetics.spider].matprop_smooth_width which is SPIDER's analogous knob for its own solver. Must be > 0 and < 1.

Core thermal model

Parameter Type Default Description
core_tfac_avg float 1.147 Core T_avg / T_cmb ratio from adiabatic gradient (Bower+2018 Table 2). Used by Aragog's _BoundaryConditionsParameters.tfac_core_avg. SPIDER derives its own internally. Must be > 0.

Diagnostics

Parameter Type Default Description
write_flux_diagnostics bool false When True, Aragog's NetCDF output includes per-component flux decomposition (Jcond_b, Jconv_b, Jgrav_b, Jmix_b) and basic-node state variables (dSdr_b, eddy_diff_b, phi_basic_b, T/cp/rho_basic_b). Adds ~10 fields per snapshot; default False keeps output compact. Useful for diagnosing T_core and CMB-closure behaviour near phi=0. SPIDER path ignores this flag (uses SPIDER's own JSON output which already includes Jcond_b, Jconv_b, Jgrav_b, Jmix_b).

Constant-properties mode

Parameter Type Default Description
const_properties bool false Enable constant-properties mode: bypass the EOS tables and use the analytical T(S) = T_ref * exp((S - S_ref) / Cp) relationship, for controlled parity tests.
const_rho float 4000.0 Constant density [kg/m3]. Must be > 0.
const_Cp float 1000.0 Constant heat capacity [J/kg/K]. Must be > 0.
const_alpha float 1e-05 Constant thermal expansivity [1/K]. Must be > 0.
const_cond float 4.0 Constant thermal conductivity [W/m/K]. Must be > 0.
const_log10visc float 2.0 Constant log10 dynamic viscosity [Pa.s].
const_T_ref float 3500.0 Reference temperature for T(S) = T_ref * exp((S-S_ref)/Cp) [K]. Must be > 0.
const_S_ref float 3000.0 Reference entropy for T(S) [J/kg/K]. No positivity constraint since entropy reference states can be zero or negative.

Aragog [interior_energetics.aragog]

Aragog is the default interior thermal evolution module. It solves the mantle energy equation with CVODE (SUNDIALS) using JAX-derived analytic Jacobians for robust convergence.

Parameter Type Default Description
mass_coordinates bool true Whether to use mass coordinates in the model. Default is True. Uses uniform spacing in mass coordinate space, giving larger cells at the surface where density is lower, matching SPIDER's mesh.
backend str "jax" ODE backend selector. Default 'jax'. - 'jax' : CVODE with JAX-derived RHS and JAX analytic Jacobian (jax.jacrev). Recommended for production. - 'numpy' : CVODE with numpy RHS and CVODE finite-difference Jacobian. Available for development and SPIDER-parity comparisons; less robust than 'jax' at production resolution because the FD-Jacobian noise can trip Aragog's T_core-jump retry guard at tight tolerances. The diffrax direct-JAX integration path is research-only and gated on a code-level flag in proteus.interior_energetics.aragog. Choices: "numpy", "jax".
atol_temperature_equivalent float 1e-08 Effective temperature-scale absolute tolerance [K] for Aragog's ODE integrator. Default 1e-8 matches SPIDER's atol=rtol=1e-8 setting; this tight tolerance avoids a marginal-stability bifurcation at the first dt jump after equilibration. Must be > 0.
core_bc str "energy_balance" Core-mantle boundary condition mode. Default 'energy_balance'. Valid values: - 'quasi_steady': alpha-factor heat-flux partition; gives about -19% T_core offset vs SPIDER. - 'energy_balance': SPIDER bit-parity BC with dSdr_cmb as a new state variable (mirrors SPIDER bc.c:76-131). - 'gradient': gradient-based state with two boundary entropies as state variables. - 'bower2018': experimental, do not use for production. - 'core_module': full core evolution module with nucleation, crystallisation regimes, and dynamo energetics (aragog.core), coupled through a boundary-layer CMB flux in the core-mantle temperature contrast. Choices: "quasi_steady", "energy_balance", "gradient", "bower2018", "core_module".
phase_smoothing str "tanh" Phase-boundary smoothing for Jgrav and Jmix: 'tanh' (SPIDER parity) or 'cubic_hermite'. Choices: "tanh", "cubic_hermite".
separation_viscosity str "mixture" Drag viscosity for the gravitational-separation velocity v_rel = |dRho| g F(phi) / eta. 'melt' (fixed single-phase liquid viscosity, SPIDER parity) keeps separation active below the rheological transition in coupled caps-off runs, which collapses the CMB temperature; 'mixture' (rheological-transition-blended bulk viscosity) ties the drag viscosity to the same solid-fraction rise that stiffens the bulk rheology, so separation locks up at the same melt fraction instead, which is why the default here is 'mixture' while Aragog's own default stays 'melt' for SPIDER parity. The regime boundaries are the porosities where adjacent permeability laws cross (Bower et al. 2018, section 2.1, Eqs. 13a to 13c). The melt drainage of front trapping (outgas.trap_mode 'front') takes the melt viscosity whatever this setting. Choices: "melt", "mixture".
separation_buoyancy str "mixture" Buoyancy of the gravitational-separation velocity. 'mixture' takes it against the mixture, (1 - phi) (rho_s - rho_l) g (McKenzie 1984, Eq. 3.7), on the Blake-Kozeny-Carman and Rumpf-Gupte regimes, while the Stokes regime of a grain settling alone keeps (rho_s - rho_l) g; 'solid' takes (rho_s - rho_l) g on every regime (Abe 1995, Eq. 40), as SPIDER does, so 'solid' with separation_viscosity 'melt' is the SPIDER setting. The melt drainage of front trapping (outgas.trap_mode 'front') takes the same buoyancy. Up to a porosity of 0.4 'mixture' equals (1 - phi) times 'solid' within 1e-5; from a porosity of 0.91 up both modes take the plain-contrast Stokes rate within 1e-2. Choices: "mixture", "solid".
allow_resume_law_change bool false Let a resume change separation_viscosity or separation_buoyancy from the values in the run's init_coupler.toml, with one warning per switched law in the log. False stops such a resume, because the changed law would act from the resume row on. A law the record does not hold must be set in the config file either way; a record that names the Aragog module and lacks separation_viscosity counts as 'melt', and a record of another interior module holds neither law. init_coupler.toml records false.
solver_method str "cvode" ODE solver: 'cvode' (SUNDIALS, SPIDER parity; needs scikits-odes-sundials and stops the run at setup without it), 'radau' (scipy), 'bdf' (scipy). Choices: "cvode", "radau", "bdf".
scalar_gravity_override bool false Scalar-gravity comparison knob. When True, the external mesh file that Zalmoxis writes has its gravity column overwritten with a uniform scalar (the surface value from hf_row['gravity']) before Aragog reads it, so Aragog's per-node gravity path interpolates to that scalar everywhere. False by default; set True only when running a paired scalar-gravity comparison.
phi_step_cap float 0.0 Per-call melt-fraction step cap. When > 0 and any staggered cell is in or near the two-phase window at solve() entry, a CVODE root function (and the equivalent scipy event) returns control at the exact time the larger of the global mass-weighted |ΔΦ| and the maximum single-cell |Δφ| reaches this cap. Off by default: the schema default 0.0 resolves to no cap, because on a benign freezing-front crossing the root function slices the coupled step into many small ones and drives the reported CMB heat flux briefly negative where the uncapped run stays positive, so the cap is a debugging control, not a production setting. Set a positive value to enable it; -1.0 is the explicit off spelling. An explicit 0.0 is rejected at load, since it cannot be told apart from the unset default; any other negative, NaN, or infinity is rejected too.
temperature_step_cap float 0.0 Per-call per-cell temperature step cap [K]. Shares the same root function as phi_step_cap and fires on the maximum single-cell |ΔT| since solve() entry. When enabled it bounds the per-cell temperature change on the solid adiabat just below the solidus, where the melt-fraction cap cannot act because a fully solid cell's melt fraction no longer moves. Off by default (schema default 0.0 resolves to no cap); on a benign freezing-front crossing the caps slice the coupled step into many small ones and drive the reported CMB heat flux briefly negative, so they are a debugging control, not a production setting. Set a positive value to enable it; -1.0 is the explicit off spelling. An explicit 0.0 is rejected at load, since it cannot be told apart from the unset default; any other negative, NaN, or infinity is rejected too.
entropy_step_cap float 0.0 Per-call per-cell entropy step cap [J/kg/K], in the native solver variable; same role as temperature_step_cap without an EOS lookup in the root function. Off by default (schema default 0.0 resolves to no cap); on a benign freezing-front crossing the caps slice the coupled step into many small ones and drive the reported CMB heat flux briefly negative, so they are a debugging control, not a production setting. Set a positive value to enable it; -1.0 is the explicit off spelling. An explicit 0.0 is rejected at load, since it cannot be told apart from the unset default; any other negative, NaN, or infinity is rejected too.
phase_boundary_entropy_margin float 200.0 Phase-boundary proximity band [J/kg/K] within which a staggered cell counts as near a solidus or liquidus crossing, tightening the integrator max_step so CVODE resolves the stiff two-phase RHS across the boundary. This is a solver-accuracy control, not a cosmetic step-size setting: at the default it reproduces the fixed band and the converged trajectory is unchanged, but lowering it below the default can under-resolve a real phase crossing and shift the converged state, because CVODE's local error control can accept an over-large step across the near-discontinuous RHS. Keeping the default reproduces current behaviour, and modestly widening the band does not move a converged result because tighter steps only refine an adaptive integrator; but a value orders of magnitude above the default makes every cell count as near a boundary at all times, so every call runs under the phase-boundary step control: with phase_boundary_cap = 'fixed' that clamps the integrator to 1 yr steps (versus 100 yr otherwise) and stalls the run, and with 'rate' every call runs as CVODE segments with max_step between 1 and 100 yr. Keep the band of order a few hundred J/kg/K. Default 200.0, matching Aragog's own default; a positive value is required (0 or negative is not a valid disabled state for a proximity band). Must be > 0.
phase_boundary_cap str "rate" Phase-boundary step-size policy: 'fixed' tightens max_step to 1 yr whenever any cell is near or inside the two-phase band; 'rate' (default) uses event-driven CVODE segments with max_step scaled by approach time to the nearest phase boundary, clipped to [1, 100] yr. 'rate' needs the CVODE solver and a core_bc other than 'gradient'; otherwise Aragog logs it and uses 1 yr. Its accuracy is verified at rtol 1e-8; Aragog warns once per solver at an rtol above 1e-7. Choices: "fixed", "rate".
tolerance_struct float 100.0 Absolute mass tolerance [kg] for the secant solver in determine_interior_radius. Default 100 kg; pairs with Spider's matching field so both backends drive the same outer-loop convergence criterion. Must be > 0.
top_cell_dt_limit bool false Limit the coupling time step by the top-cell radiative drain time tau_drain (down to params.dt.minimum * escape.step_dt_floor_frac, below params.dt.minimum) and keep hf_row['T_magma'], hf_row['T_surf'], and hf_row['Phi_global'] on the Aragog solver state by skipping the tmagma_atol/tmagma_rtol post-step clip on steps where tau_drain is finite and the step does not exceed tau_drain (staying active when the escape step floor or an impact-landing snap-forward places the step above tau_drain); planet.prevent_warming still clamps T_magma, T_surf, Phi_global, and F_int when active. Incompatible with interior_energetics.surface_bc_mode = 'grey_body'; the rule is checked when the config is loaded (a grid case fails when its written TOML is read back). A 1-point EOS temperature lookahead probes S_trial = max(S_top - cp_eff * dT_allow / T_top, S_min + 300) and replaces the step-start heat capacity cp_eff with the chord heat capacity cp_chord = min(cp_eff, T_top * (S_top - S_trial) / (T_top - T_trial)) in the T_top form whenever T(P_top, S_trial) falls more than dT_allow below T_top (T_top - T_trial > dT_allow and S_top > S_trial), bounding the linearized unresupplied top-cell drop under the step's linearization dS = q / T_top with q = cp_chord * dT_allow. A lookahead trial that reaches or spans the flat part of the PALEOS solid table (T held at T_sol from the last node below S_sol) can give a step that exceeds dT_allow; this is shown on constructed slice states, and no step of the coupled runs exceeded dT_allow. On an energy basis (integral of T dS = q at constant P_top) the drop also exceeds dT_allow in the liquid, because the exact entropy step is larger than q / T_top: the PALEOS slice scans give at most 1.106 dT_allow at top_cell_dt_rel_dT = 0.08 and 1.204 at 0.15 for T_surf / T_top <= 1.02, and up to 1.110 and 1.211 at 1.05. Using T_mean = 0.5 * (T_top + T_trial) in the chord numerator would reduce cp_chord by the fraction (T_top - T_trial) / (2 * T_top). See docs/Explanations/coupling_loop.md for the measured run results and EOS evaluations.
top_cell_dt_rel_dT float 0.08 Relative surface-temperature change allowance eta_T at a top-cell melt fraction >= 0.40 (mush and liquid) for the top-cell drain-time step limit; must lie in (0, 0.15]. A value below 0.08 also needs top_cell_dt_rel_dT_solid set at or below it; the pair is checked when the config is loaded. Sets the allowed temperature scale dT_allow = eta_eff * T_surf for the step energy q = cp_chord * dT_allow, bounding the linearized unresupplied top-cell temperature drop T_top - T(P_top, S_top - q / T_top) <= dT_allow under the step's linearization dS = q / T_top with the chord heat capacity cp_chord in the T_top form. A lookahead trial that reaches or spans the flat part of the PALEOS solid table (T held at T_sol from the last node below S_sol) can give a step that exceeds dT_allow; this is shown on constructed slice states, and no step of the coupled runs exceeded dT_allow. On an energy basis (integral of T dS = q at constant P_top) the drop also exceeds dT_allow in the liquid: at most 1.106 dT_allow at 0.08 and 1.204 at 0.15 for T_surf / T_top <= 1.02, and up to 1.110 and 1.211 at 1.05. See docs/Explanations/coupling_loop.md for the measured run results and EOS evaluations. Must be > 0.0 and <= 0.15.
top_cell_dt_rel_dT_solid float 0.08 Relative surface-temperature change allowance eta_T_solid at a fully solid top cell (top-cell melt fraction 0), ramped linearly to top_cell_dt_rel_dT at a top-cell melt fraction of 0.40; must lie in (0, top_cell_dt_rel_dT] (up to 0.15), with the pair checked when the config is loaded. See docs/Explanations/coupling_loop.md for the measured run results and EOS evaluations. Must be > 0.0 and <= 0.15.

Core evolution [interior_energetics.aragog.core_module]

Active when core_bc = "core_module". The core carries its own state: an energy budget with inner-core nucleation, latent heat, and light-element gravitational energy, integrated as an extra ODE state inside Aragog, so the reported core temperature (T_cmb) is that solver state, not the temperature of the lowermost mantle node. The CMB radius and pressure always come from the running mesh.

Parameter Type Default Description
alpha float 1.35e-05 Core thermal expansion coefficient [K-1]. Must be > 0.
c_p float 840.0 Core specific heat capacity [J kg-1 K-1]. Must be > 0.
melting_curve str "iron" 'iron' (Anzellini et al. 2013 via PALEOS, with light-element depression) or 'quadratic' (Nimmo 2015 Eq. 6 parameterisation). Choices: "iron", "quadratic".
light_element_fraction float 0.0 Mole fraction of light elements depressing the iron melting curve. Must be >= 0 and < 1.
depression float 0.0 Melting-point depression per unit mole fraction, as a fraction of the melting temperature [1]; its product with light_element_fraction must stay below 1. Must be >= 0.
t_m0 float 2677.0 Quadratic-curve prefactor [K] (melting_curve = 'quadratic'). Must be > 0.
t_m1 float 2.95e-12 Quadratic-curve linear coefficient [Pa-1].
t_m2 float 8.37e-25 Quadratic-curve quadratic coefficient [Pa-2].
ds_fusion float 172.8 Entropy of fusion at the inner-core boundary [J kg-1 K-1]. Must be > 0.
alpha_c float 0.0 Compositional expansivity of the outer-core alloy. Must be >= 0.
c_light float 0.0 Light-element mass fraction of the outer core (complete rejection). Must be >= 0 and < 1.
q_radio float 0.0 Core radiogenic power [W], constant over a run. Must be >= 0.
stratification bool false When true, the outer core above layer_base_fraction of the CMB radius is a resolved shell whose temperatures are part of the solver state: heat moves through it by conduction and, where its gradient is superadiabatic, by convective mixing, so a stable layer forms below the CMB when the CMB heat flow is subadiabatic and erodes when it is not. The CMB heat flow sees the temperature of the top of the shell. Experimental: erosion of a layer does not run on CVODE at the default tolerances. Not available with accretion.
k_core float 130.0 Core thermal conductivity [W m-1 K-1] for conduction in the stratified shell and the entropy and dynamo diagnostics; the default is the Nimmo (2015) Table 2 value. Must be > 0.
layer_base_fraction float 0.4 Base of the stratified shell as a fraction of the CMB radius, in (0, 1); the inner core must stay below it. Used with the experimental stratification. Must be > 0 and < 1.
layer_k_mix float 10000000.0 Eddy diffusivity [m2 s-1] of convective mixing in the stratified shell at the reference superadiabatic gradient. Used with the experimental stratification. Must be > 0.
layer_g_mix float 0.001 Reference superadiabatic gradient of the shell mixing, as a fraction of the adiabatic gradient at the CMB. Used with the experimental stratification. Must be > 0.
f_ohm float 1.0 Ohmic fraction of the dissipation in the field-strength scaling, in (0, 1]; Christensen et al. (2009) adopt 1 for planets. Must be > 0 and <= 1.
ra_crit_cmb float 450.0 Critical Rayleigh number of the mantle-side boundary layer that sets the CMB heat flux from the core-mantle temperature contrast; the default is the theoretical value of Thiriet et al. (2019, Table 2). Must be > 0 and < inf.
flux_geometry str "const_flux" Which printed Earth-core efficiency factor converts the superadiabatic flux into the field-strength scaling's F: 'const_flux' or 'zero_outer'. Choices: "const_flux", "zero_outer".

When this mode is active, per-step diagnostics are written to the helpfile columns core_r_icb, core_C_eff, core_dynamo_margin, core_B_rms, core_regime, core_strat_depth and core_T_top, driven by the step-averaged CMB heat flow. With stratification = true, core_strat_depth is the depth of the stable layer in the resolved shell below the CMB and core_T_top the temperature of its top cell; the shell temperatures are stored in each interior snapshot, so a resume restarts the layer. Every other core_bc mode leaves them at zero; note that zero is also a reachable physical value for most of them while the mode is active (no inner core yet, no stratified layer, subadiabatic field estimate), so key any analysis on the configured core_bc, not on the column values. core_regime encodes the way the core freezes as 0 = fully liquid, 1 = from the centre outwards, 4 = fully frozen; the codes 2 (from the top) and 3 (snow) of aragog.core.regime do not appear, because Aragog ends the run at such a state. core_B_rms uses only the superadiabatic part of the heat flow as its reference flux, so a compositionally driven dynamo under a subadiabatic CMB reports a positive core_dynamo_margin with core_B_rms = 0; that pairing is the documented conservative floor of the field estimate, not an inconsistency.

SPIDER [interior_energetics.spider]

SPIDER is the C interior module. It requires PETSc and produces results consistent with Bower et al. (2018) 1.

Parameter Type Default Description
solver_type str "bdf" SUNDIALS integrator choice. Choices: "adams", "bdf".
tolerance_rel float -1.0 Deprecated alias for Interior.rtol. Set interior_energetics.rtol at the top level instead.
matprop_smooth_width float 0.01 Melt-fraction window width for smoothing material properties across the solidus/liquidus. Passed to SPIDER as -matprop_smooth_width and to Aragog via _PhaseMixedParameters. Must be > 0 and < 1.
tolerance_struct float 100.0 Absolute mass tolerance [kg] for the interior-radius secant solver. Must be > 0.
log_output bool true Write SPIDER solver log output.

Dummy [interior_energetics.dummy]

A parameterised cooling model with prescribed solidus and liquidus.

Parameter Type Default Description
mantle_tliq float 2700.0 Mantle liquidus temperature [K]. Must be >= 0.
mantle_tsol float 1700.0 Mantle solidus temperature [K]. Must be >= 0.
mantle_rho float 4550.0 Mantle density [kg m-3] for the dummy density profile and the fallback mantle-mass estimate. When the interior structure provides the masses, the mantle mass is taken as M_int - M_core instead. Must be > 0.
mantle_cp float 1792.0 Mantle specific heat capacity [J kg-1 K-1]. Must be >= 0.
heat_internal float 0.0 Fixed internal heating rate (e.g. radiogenic) [W kg-1]. Tidal heating is handled separately via heat_tidal and is added on top of this value. Must be >= 0.

Boundary [interior_energetics.boundary]

A 0-D box model for the mantle thermal evolution based on Schaefer et al. (2016) 2, with prescribed solidus and liquidus and parameterised convective heat transport.

Parameter Type Default Description
T_solidus float 1420.0 Mantle solidus temperature [K]. Must be >= 0.
T_liquidus float 2020.0 Mantle liquidus temperature [K]. Must be > 0.
critical_rayleigh_number float 1100.0 Critical Rayleigh number for onset of convection [-]. Must be > 0.
nusselt_exponent float 0.33 Nusselt-Rayleigh scaling exponent [-]. Must be > 0.
silicate_heat_capacity float 1200.0 Silicate heat capacity [J/kg/K]. Must be > 0.
core_density float 10738.0 Core density [kg/m^3]. Must be > 0.
core_shear float 0.1 Core shear modulus [Pa]. Must be > 0.
core_bulk float 500000000000.0 Core bulk modulus [Pa]. Must be > 0.
atm_heat_capacity_const bool true Always use fallback atmosphere heat capacity?.
atm_heat_capacity float 17000.0 Used as fallback for atmosphere heat capacity when layer-specific value is not available [J/kg/K]. Must be > 0.
silicate_density float 4103.0 Silicate density [kg/m^3]. Default taken from Fei et. al. 2021 (https://ui.adsabs.harvard.edu/abs/2021NatCo..12..876F). Must be > 0.
thermal_conductivity float 4.2 Thermal conductivity [W/m/K]. Must be > 0.
thermal_diffusivity float 1e-06 Thermal diffusivity [m^2/s]. Must be > 0.
thermal_expansivity float 2e-05 Thermal expansivity [1/K]. Must be > 0.
viscosity_model int 2 Viscosity parameterisation model. Choices: 1, 2, 3.
dynamic_viscosity float 3800000000.0 Reference dynamic viscosity [Pa s] for Arrhenius solid mantle model. Must be > 0.
activation_energy float 350000.0 Activation energy [J/mol] for Arrhenius solid mantle model. Must be > 0.
creep_parameter float 26.0 Creep parameter [-] for Arrhenius solid mantle model. Must be > 0.
viscosity_prefactor float 0.00024 Viscosity prefactor [Pa s] for Vogel-Fulcher-Tammann magma ocean model. Must be > 0.
viscosity_activation_temp float 4600 Activation temperature [K] for Vogel-Fulcher-Tammann magma ocean model. Must be > 0.
logging bool false Whether to create diagnostic CSV data files from boundary interior module.

Constraints

Cross-field constraints enforced when the config file loads:

  • Reject Aragog top_cell_dt_limit with grey_body surface boundary conditions.
  • Require top_cell_dt_rel_dT_solid <= top_cell_dt_rel_dT.
  • Require interior_struct.melting_dir for Aragog without a PALEOS table set.
  • Boundary backend assumes a fixed surface state coupling.
  • Check the mantle EOS that the dummy structure hands to SPIDER or Aragog.
  • Require a PALEOS or temperature-dependent energetics key for SPIDER or Aragog.
  • The low-temperature solid extension is run only with the Aragog interior.
  • The low-temperature solid extension acts on the P-S tables that the zalmoxis and dummy structures build from the standard PALEOS solid table.
  • Interior tidal heating requires an tides module to be enabled.
  • Aragog requires at least one energy transport term to be enabled.
  • Validate Boundary backend's solidus/liquidus ordering.
  • Dummy interior requires the liquidus to sit above the solidus.
  • SPIDER requires at least one energy transport term to be enabled.
  • Validate Zalmoxis EOS format strings and reject unsupported miscibility options.

See also: Interior modules | Structure module | Melting curves

  1. Bower, D.J., Sanan, P. & Wolf, A.S., 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, 49-62, 2018. SciX. ↩

  2. Schaefer, L., Wordsworth, R.D., Berta-Thompson, Z. & Sasselov, D., Predictions of the atmospheric composition of GJ 1132b, The Astrophysical Journal, 829, 63, 2016. SciX. ↩

  3. Stixrude, L., Melting in super-earths, Philosophical Transactions of the Royal Society A, 372, 20130076, 2014. SciX. ↩