initialization.md

Initialization

Temperature initialization follows Hayne et al. (2017), Appendix A2.3 (Eqs. A34--A36).

Initial Temperature Profile

The temperature profile is initialized to the equilibrium mean temperature, which approximates the expected time-averaged temperature for a rapidly rotating body:

$$ T_{eq}(\phi) = \frac{T_{rad}(\phi)}{\sqrt{2}} $$

where $T_{rad}$ is the radiative equilibrium temperature at local noon:

$$ T_{rad}(\phi) = \left[ \frac{(1 - A) S_0 \cos\phi}{\varepsilon \sigma} \right]^{1/4} $$

and $\phi$ is the latitude.

This initialization provides a reasonable starting point that speeds up convergence to the periodic steady state. All layers are initially set to the same temperature.

Property Initialization

After the temperature profile is set, the heat capacity and thermal conductivity profiles are computed from the initial temperatures:

1. Heat capacity: $c_p(T)$ via the polynomial fit
2. Thermal conductivity: $K(z, T)$ combining depth-dependent contact conductivity and temperature-dependent radiative conductivity