# Planetary Equations of State¶

Configuring SWIFT with the --with-equation-of-state=planetary and --with-hydro=planetary options enables the use of multiple EoS. Every SPH particle then requires and carries the additional MaterialID flag from the initial conditions file. This flag indicates the particle’s material and which EoS it should use.

So far, we have implemented several Tillotson, SESAME, and Hubbard & MacFarlane (1980) materials, with more on their way. The material’s ID is set by a base type ID (multiplied by 100), plus a minor type:

• Tillotson (Melosh, 2007): Base type 1
• Iron: 100
• Granite: 101
• Water: 102
• Hubbard & MacFarlane (1980): Base type 2
• Hydrogen-helium atmosphere: 200
• Ice H20-CH4-NH3 mix: 201
• Rock SiO2-MgO-FeS-FeO mix: 202
• SESAME (and similar): Base type 3
• Iron (2140): 300
• Basalt (7530): 301
• Water (7154): 302
• Senft & Stewart (2008) water (in a SESAME-style table): 303

Unlike the EoS for an ideal or isothermal gas, these more complicated materials do not always include transformations between the internal energy, temperature, and entropy. At the moment, we have only implemented $$P(\rho, u)$$ and $$c_s(\rho, u)$$. This is sufficient for the simple Planetary (Density-Energy, Multi-Material) SPH hydrodynamics scheme, but makes these materials currently incompatible with entropy-based schemes.

The Tillotson sound speed was derived using $$c_s^2 = \left. \dfrac{\partial P}{\partial \rho} \right|_S$$ as described in Kegerreis et al. (2019). The table files for the HM80 and SESAME-style EoS can be downloaded using the swiftsim/examples/EoSTables/get_eos_tables.sh script.