Initial thermal conditions

A PROTEUS run starts the planet as a hot magma ocean and follows it as it cools. The initial thermal conditions fix the mantle's starting temperature and entropy profile, which is the state the interior solver evolves forward in time. This page explains what that starting state controls, how to set it through the [planet] section of the configuration file, and which option to favour.

The parameters described here are listed with their types and defaults in the planet and volatiles reference. For the physics of the interior modules that consume this state, see the model description.

What the initial conditions do

PROTEUS does not model planet formation. Instead it begins from a chosen thermal state and integrates the coupled interior-atmosphere system forward. The initial conditions therefore set:

The starting melt fraction. A hot enough profile starts the mantle fully molten; a cooler profile starts it partially crystallised. The magma-ocean stage only exists while melt is present, so a fully molten start is the usual intent.
The thermal energy budget. The hotter the initial mantle, the more energy has to be radiated away before the planet solidifies, and the longer the cooling track.
The initial atmosphere. A hotter mantle outgasses more vigorously, so the starting surface pressure and composition depend on the initial temperature.

The chosen mode is converted into an initial entropy (or temperature) profile that the interior solver (Aragog or SPIDER) carries forward. What the initial conditions do not do is move the long-term endpoint: the planet still cools toward its solidus or toward radiative balance regardless of where it started. The initial state sets the transient and the total cooling time, not the destination.

How to set the initial state

The initial profile is selected by planet.temperature_mode. Each mode anchors the profile at a different reference point and reads a different companion parameter:

Mode	Anchored at	Companion parameter(s)
`liquidus_super` (default)	core-mantle boundary, above the liquidus	`delta_T_super`
`adiabatic_from_cmb`	core-mantle boundary, fixed temperature	`tcmb_init`
`adiabatic`	surface	`tsurf_init`
`isothermal`	uniform	`tsurf_init`
`linear`	surface and centre	`tsurf_init`, `tcenter_init`
`accretion`	accretion energetics	`f_accretion`, `f_differentiation`
`isentropic`	entropy directly	`ini_entropy`, `ini_dsdr`

The two core-mantle-boundary (CMB) modes anchor the adiabat at the base of the mantle and integrate it upward to the surface. The surface modes do the opposite, anchoring at the surface and integrating downward. The remaining modes set the profile from accretion energetics (White & Li, 2025) or from the specific entropy itself.

The default needs nothing beyond the mode name, because delta_T_super already defaults to 500 K:

[planet]
    temperature_mode = "liquidus_super"   # the default; shown here for clarity
    delta_T_super    = 500.0              # [K] above the liquidus at the core-mantle boundary

What to favour

Use the default liquidus_super for most runs. It anchors the CMB temperature a fixed margin above the silicate liquidus:

\[T_\mathrm{cmb} = T_\mathrm{liq}(P_\mathrm{cmb}) + \Delta T_\mathrm{super}\]

where \(T_\mathrm{liq}\) is the Fei et al. (2021) MgSiO\(_3\) melting curve and \(\Delta T_\mathrm{super}\) is the superliquidus offset (delta_T_super, in K). Anchoring at the core-mantle boundary, where the pressure and therefore the melting temperature are highest, and integrating the adiabat upward guarantees that the whole mantle column starts molten. Because the anchor is set by a third-party melting curve rather than by a fixed temperature, the mode is EOS-agnostic: it does not bake in a particular entropy convention. That makes it robust both for cross-code comparisons and for larger super-Earths, where a fixed CMB temperature may not clear the elevated high-pressure liquidus.

The default delta_T_super = 500 K is a heuristic margin that places the CMB anchor above the liquidus for Earth-mass to few-Earth-mass mantles. Setting delta_T_super = 0 anchors the initial adiabat exactly on the liquidus, the coolest fully molten start.

Requires the silicate liquidus

liquidus_super evaluates the Fei et al. (2021) liquidus through the interior structure module (Zalmoxis), which is part of the standard installation. For a run built only from placeholder modules, use adiabatic_from_cmb instead, which needs no melting-curve lookup.

Large super-Earths

The Fei et al. (2021) liquidus is calibrated to about 500 GPa. For large super-Earths whose core-mantle-boundary pressure exceeds that, the anchor relies on extrapolation and PROTEUS logs a warning; treat the initial condition as approximate in that regime.

Use adiabatic_from_cmb for a fixed CMB temperature. This mode is identical to liquidus_super except that the anchor is the user-set tcmb_init rather than a liquidus-relative value:

[planet]
    temperature_mode = "adiabatic_from_cmb"
    tcmb_init        = 6000.0   # [K] adiabat anchor at the core-mantle boundary

It needs no melting curve, so it is also the mode used by the all-dummy quick-start configuration, which runs without any external structure solver.

Avoid the surface-anchored modes unless you have a specific reason. Under the current equation of state, an adiabat pinned at the surface (adiabatic, isothermal) can drop the deep mantle below its liquidus at t = 0, leaving a partially solid base that is not a clean magma-ocean start. The CMB-anchored modes avoid this by construction. The linear mode is likewise intended for controlled tests where you set the surface and centre temperatures directly.

Matching a published interior protocol

The isentropic mode sets the initial specific entropy directly through ini_entropy and ini_dsdr, bypassing the melting-curve lookup. Use it when reproducing a reference protocol that specifies the entropy IC, such as the Solar System CHILI intercomparison.