Evolutionary tracks for Steam Worlds

Evolutionary tracks from the Steam Worlds Evolution (SWE) model (Aguichine et al. 2025, in prep).

Link to manuscript: https://arxiv.org/abs/2412.17945

Model summary:
Earth-like core (32.5% iron-sulfur alloy, 67.5% mantle with Earth-like Fe/Si ratio)
Pure H2O envelope and pure H2O atmosphere connected at P_b = 1000 bar

Parameters:
ST: Stellar Type (M or G), for radiative transfer in the atmosphere
WMF: Water Mass Fraction, between 0.001 and 1
T_eq: Equilibrium temperature (K), between 500 K and 700 K
M_p: Planet mass (M_e), between 0.2 M_E and 20.0 M_E
Age: Host star age (Gyr), between 0.01 Gyr and 20 Gyr, assuming the planet formed at t_0 = 10 Myr (can be adjusted)

Model outputs:
R_b: Planet radius (R_E) at 1000 bar
R_b: Planet radius (R_E) at 20 mbar, pressure level where pure steam is opaque at 1 micron
R_b: Planet radius (R_E) at 1 µbar, pressure level of aerosols/haze formation
T_b: Temperature (K) at 1000 bar)
T_int: Intrinsic temperature (K), nominal values are between 10 K and 400 K
s_env: Specific entropy of H2O in the envelope (in J/K/kg)
I/MR^2: Moment of inertia factor

Sources of energy for the cooling, expressed as luminosities (in W):
L_env: energy from the H2O envelope (thermal + gravitational)
L_rad: radiogenic heat produced in the core
L_core: thermal energy of the core
L_grav: gravitational energy of the core
u_tot: total energy of the planet (J), obtained by fully integrating thermal (cp*T*dm) and gravitational energy


By construction:
L_env + L_rad + L_core + L_grav = (4 * Pi * R_p**2) * (sigma_SB * T_int**4)
d u_tot / d t = -L_int + L_rad 

NB: The last line of each track represents an estimate of the time until "full exhaustion" (see paper for details).