Earth analogue¶

This tutorial simulates the thermal and atmospheric evolution of an Earth-mass planet at 1 AU from a Sun-like star. It follows the nominal Earth case from the CHILI intercomparison ¹, with a more reduced mantle (oxygen fugacity IW+2 instead of IW+4).

It uses the production-quality module combination: Aragog (interior energetics), Zalmoxis (interior structure), CALLIOPE (outgassing), and AGNI (atmosphere climate).

Prerequisites¶

• Full PROTEUS installation with AGNI and SOCRATES compiled
• FWL_DATA and RAD_DIR environment variables set
• Spectral files downloaded (proteus get spectral -n Dayspring -b 48)
• Solar spectrum downloaded (proteus get stellar)
• Interior data downloaded, including the PALEOS EOS tables for the structure solver (proteus get interiordata --config-path input/tutorials/tutorial_earth.toml)

Reference data is also fetched automatically when proteus start runs without the --offline flag, so the download commands above are only required for offline use.

Physical setup¶

This case takes its orbit, albedo, volatile inventories and initial thermal state from Table 2 of the CHILI protocol paper. It departs from the protocol in the following points. The oxygen fugacity is IW+2. Zalmoxis solves the interior structure from a core mass fraction instead of the fixed planet radius and core radius fraction of the protocol, with the MgSiO\(_3\) equation of state of PALEOS for the mantle, where the protocol names a bulk silicate Earth (BSE) composition. The star follows the Spada tracks with the solar spectrum, where the protocol asks for the Baraffe et al. (2015) track with a blackbody spectrum for models that evolve the stellar luminosity. The instellation is ~1005 W m\(^{-2}\) at the start; the 920 W m\(^{-2}\) of Table 2 is the value of the protocol for models with a constant luminosity. Radiogenic heating is on (~0.2 W m\(^{-2}\)), while the baseline cases of the protocol have none:

The planet starts fully molten and cools through a magma ocean stage. Volatiles partition between the atmosphere and silicate melt as the mantle solidifies. The atmosphere is solved at each timestep using correlated-k radiative transfer (AGNI). Atmospheric escape is energy-limited (ZEPHYRUS, 30% efficiency).

Running the simulation¶

conda activate proteus
mkdir -p output/tutorial_earth
nohup proteus start -c input/tutorials/tutorial_earth.toml \
    > /tmp/proteus_earth_launch.log 2>&1 & disown

Add --offline to skip the reference-data check on later runs; the first run must be able to download any missing data (or download it beforehand, see the prerequisites above).

Monitor progress with tail -f output/tutorial_earth/proteus_00.log (the log appears once PROTEUS has initialized).

Configuration¶

The config at input/tutorials/tutorial_earth.toml sets:

• Star: Sun on Spada ² tracks starting at 50 Myr. The solar spectrum is used for radiative transfer. Stellar luminosity, radius, and XUV flux evolve with age.
• Interior: Aragog solves the mantle energy equation on an 80-node radial grid using SUNDIALS CVODE with JAX Jacobian. Zalmoxis computes the hydrostatic structure using PALEOS EOS tables.
• Outgassing: CALLIOPE partitions H\(_2\)O, CO\(_2\), H\(_2\), CH\(_4\), and CO between atmosphere and melt at the fO\(_2\) = IW+2 buffer.
• Atmosphere: AGNI solves the radiative-convective equilibrium with Dayspring 48-band correlated-k opacities, a conductive skin layer at the surface, and real-gas corrections.
• Escape: ZEPHYRUS computes energy-limited mass loss at 30% efficiency, distributing the bulk escape rate across elements proportionally.

Results¶

After the run completes, generate plots:

proteus plot -c input/tutorials/tutorial_earth.toml all

Thermal evolution (a, c)¶

The planet starts fully molten, with a surface temperature T\(_\mathrm{s}\) \(\approx\) 3300 K and a magma temperature near 4300 K. The magma ocean radiates through a thick atmosphere, with the net interior and atmospheric fluxes reaching ~5 \(\times\) 10\(^5\) W m\(^{-2}\) initially (a). Radiogenic heating (magenta) provides a constant ~0.2 W m\(^{-2}\) baseline, negligible compared to the interior cooling flux. The absorbed stellar flux (ASF, dashed blue) is ~226 W m\(^{-2}\) at 1 AU (instellation F\(_\mathrm{ins}\) \(\approx\) 1005 W m\(^{-2}\) at 50 Myr, reduced by the geometry factor, Bond albedo, and zenith angle).

The surface temperature (c, solid) decreases from ~3300 K to ~1760 K at termination over ~3.8 Myr; the magma temperature (dashed orange) tracks above it, starting near 4300 K. The decline slows after ~10\(^5\) yr, when the melt fraction has dropped to ~0.75 and latent heat release buffers the cooling. At termination the net interior and atmospheric fluxes have fallen to ~138 W m\(^{-2}\) (OLR ~365 W m\(^{-2}\), absorbed stellar flux ~227 W m\(^{-2}\)).

Atmospheric evolution (b, d)¶

The atmosphere passes through three compositional stages as the mantle solidifies:

1. Superheated initial state (t \(\lesssim\) 4 \(\times\) 10\(^3\) yr): at the fully molten, superheated initial condition the atmosphere holds ~300 bar and O\(_2\) is its largest species (~72 mol%, ~210 bar), next to CO\(_2\) (~50 bar) and CO (~31 bar). This O\(_2\) collapses as the surface cools towards ~3000 K, falling below 10 bar within the first ~8 \(\times\) 10\(^3\) yr and to a negligible partial pressure by ~10\(^5\) yr.

2. CO\(_2\)-dominated phase (~4 \(\times\) 10\(^3\) to ~1.2 \(\times\) 10\(^6\) yr): as O\(_2\) collapses, CO\(_2\) becomes the dominant species. Its mole fraction peaks near 61% around 5 \(\times\) 10\(^4\) yr, where the partial pressure is ~59 bar and CO holds another ~33%; the partial pressure then rises to a broad maximum of ~61 bar near 3 \(\times\) 10\(^5\) yr (b, d). H\(_2\)O begins at only ~4 bar, with nearly all water dissolved in the silicate melt (~99.6% interior at the start, f), and rises through this phase as the crystallizing mantle exsolves it.

3. H\(_2\)O-dominated phase (t > ~1.2 \(\times\) 10\(^6\) yr): H\(_2\)O overtakes CO\(_2\) in mole fraction around 1.2 \(\times\) 10\(^6\) yr (d) and keeps rising as the melt crystallizes. It dominates the final atmosphere at ~76 mol% (~280 bar), with CO\(_2\) at ~9.7 mol% (~36 bar) and H\(_2\) at ~9.6 mol% (~35 bar). The total surface pressure at termination is ~370 bar.

The reduced species CO and H\(_2\) are not negligible at IW+2: CO falls from ~33 bar to ~16 bar (~4 mol% at the end), while H\(_2\) climbs from ~0.2 bar to ~35 bar as the mantle solidifies. CH\(_4\) is negligible.

Mantle evolution (e, f)¶

The Zalmoxis structure solver computes the hydrostatic profile at initialization: R\(_\mathrm{planet}\) = 7.16 Mm (1.12 R\(_\oplus\)), core radius = 3.46 Mm (0.54 R\(_\oplus\), 0.48 of the planet radius), surface gravity = 7.77 m s\(^{-2}\), CMB pressure = 102 GPa, center pressure = 347 GPa.

In (e), the dashed purple line is drawn at the core mass fraction (0.325). The rheological front (orange), defined as the radius where \(\Phi\) = 0.4, starts at the core-mantle boundary in radius (~0.48 of the planet radius, above the mass-fraction reference) and propagates outward as the mantle crystallizes from the base up. The global melt fraction (dotted) decreases from 1.0 to 0.05, at which point the run terminates.

In (f), H\(_2\)O (blue) starts with nearly all of its mass dissolved in the interior melt (~99.6%) and falls to ~45% at the \(\Phi\) = 5% termination. Because water is highly incompatible, the shrinking melt stays water-rich even at low melt fraction; the remaining water is released to the atmosphere only as crystallization completes. CO\(_2\) (orange) is far less soluble in silicate melt, starting at ~15% interior and dropping to ~0.5%.

Next steps¶

• Venus analogue: Run the Venus tutorial (input/tutorials/tutorial_venus.toml), which sets planet.mass_tot = 0.815 and orbit.semimajoraxis = 0.723, to explore the effect of higher instellation on solidification. The config stops that run at 3 Myr, where its mantle is still ~15% molten.
• CHILI comparison: See the CHILI intercomparison tutorial for multi-model comparison plots.
• Volatile sensitivity: Vary H_budget between 1.6\(\times\)10\(^{20}\) and 1.6\(\times\)10\(^{21}\) kg to explore the effect of hydrogen inventory on cooling time.
• Reduced mantle: Set outgas.fO2_shift_IW = -2 to explore a more reduced mantle.

See also: Model description | Coupling loop | Configuration reference | Output format