Earth analogue

This tutorial simulates the thermal and atmospheric evolution of an Earth-mass planet at 1 AU from a Sun-like star, reproducing the nominal Earth case from the CHILI intercomparison¹.

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 follows Table 2 of the CHILI protocol paper:

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 Spada² 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+4 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 at T\(_\mathrm{s}\) \(\approx\) 3300 K. The magma ocean radiates through a thick CO\(_2\)/steam atmosphere, with the net interior and atmospheric fluxes reaching ~10\(^5\) W m\(^{-2}\) initially (a). Radiogenic heating (purple) 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) decreases from ~3300 K to ~1870 K at the solidus over ~1.3 Myr. The decline slows around 10\(^5\) yr as the mantle enters the mushy zone and latent heat release buffers the cooling.

Atmospheric evolution (b, d)

The atmosphere evolves in composition as the mantle solidifies:

1. Early phase (t < 10\(^5\) yr): CO\(_2\) dominates the atmosphere at ~80-105 bar (b), while H\(_2\)O starts at only ~4 bar because nearly all water is dissolved in the silicate melt (≥99% interior, f). In mole fraction (d), CO\(_2\) dominates early.

2. Late phase (t > 10\(^5\) yr): As the melt fraction drops, H\(_2\)O exsolves from the crystallizing mantle and its partial pressure rises to ~364 bar at solidification. H\(_2\)O overtakes CO\(_2\) in mole fraction around 8 \(\times\) 10\(^5\) yr (d) and dominates the final atmosphere at ~84 mol%. The total surface pressure reaches ~434 bar.

CO and H\(_2\) remain minor species throughout (~1-10 bar), consistent with the oxidizing conditions (IW+4). CH\(_4\) is negligible.

Mantle evolution (e, f)

The Zalmoxis structure solver computes the hydrostatic profile at initialization: R\(_\mathrm{planet}\) = 6.91 Mm (1.08 R\(_\oplus\)), core radius = 3.38 Mm (0.53 R\(_\oplus\)), CMB pressure = 114 GPa, center pressure = 360 GPa.

In (e), the core-mantle boundary (dashed purple) sits at ~0.49 of the planet radius. The rheological front (orange), defined as the radius where \(\Phi\) = 0.4, propagates outward from the CMB as the mantle crystallizes from the base up. The global melt fraction (dotted black) 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 and drops to near 0% as the melt fraction approaches zero, releasing volatiles into the atmosphere. CO\(_2\) (orange) follows a similar trend but with a smaller interior fraction (~15% initially) because of its lower solubility in silicate melt at IW+4.

Next steps

• Venus analogue: Run the Venus tutorial (input/tutorials/tutorial_venus.toml) with planet.mass_tot = 0.815 and orbit.semimajoraxis = 0.723 to explore the effect of higher instellation on solidification.
• 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 simulate a reduced mantle producing H\(_2\)-rich instead of H\(_2\)O-rich atmospheres.

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