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	Sets the profile by	Companion parameter(s)
`liquidus_super` (default)	a fully molten adiabat, superheated above the liquidus	`delta_T_super`
`adiabatic_from_cmb`	an adiabat anchored at a fixed CMB temperature	`tcmb_init`
`adiabatic`	an adiabat anchored at the surface	`tsurf_init`
`isothermal`	a uniform temperature	`tsurf_init`
`linear`	a surface-to-centre gradient	`tsurf_init`, `tcenter_init`
`accretion`	accretion energetics	`f_accretion`, `f_differentiation`
`isentropic`	the specific entropy directly	`ini_entropy`, `ini_dsdr`

The default liquidus_super solves for the single adiabat that is fully molten throughout the mantle with a controlled superheat margin (see below). The adiabatic_from_cmb mode anchors an adiabat at the base of the mantle and integrates it upward to the surface; the surface modes anchor at the surface and integrate 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 starts the mantle on the coolest single adiabat that is fully molten everywhere, with at least \(\Delta T_\mathrm{super}\) (delta_T_super, in K) of superheat above the silicate liquidus:

\[\min_{P}\,\bigl[\,T_\mathrm{ad}(P) - T_\mathrm{liq}(P)\,\bigr] = \Delta T_\mathrm{super}\]

where \(T_\mathrm{ad}\) is the (isentropic) initial adiabat and \(T_\mathrm{liq}\) is the configured silicate liquidus. PROTEUS solves for the surface temperature, and hence the uniform initial entropy, that satisfies this at the most-constraining depth, checking the superheat against the liquidus actually in use. This guarantees a fully molten initial state with a known margin for any planet mass and any melting-curve parameterisation, without you choosing a surface temperature or entropy by hand. Because the binding depth is shallow, the solved entropy is essentially independent of planet mass, so a mass grid starts on a common adiabat.

The default delta_T_super = 500 K gives a comfortably molten start across the Earth-mass to ten-Earth-mass range. Setting delta_T_super = 0 makes the mantle marginally molten, just touching the liquidus at the binding depth.

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.

Very deep mantles

A sufficiently deep mantle cannot be made molten with an arbitrarily large superheat: past a point the deep adiabat would exceed the equation-of-state table. If the requested delta_T_super cannot be reached, PROTEUS raises with the largest achievable superheat rather than using an unphysical initial condition; lower delta_T_super (or the planet mass) in that case.

Use adiabatic_from_cmb for a fixed CMB temperature. This mode anchors the adiabat at a user-set core-mantle-boundary temperature tcmb_init and integrates it upward to the surface:

[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 default liquidus_super avoids this by solving for full melt directly, and adiabatic_from_cmb avoids it when you supply a hot enough tcmb_init. The linear mode is 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.