# Equations of state available in Phantom

The following is a list of equations of state currently implemented in phantom. For full details have a look in the source code

ieos |
Description |
---|---|

1 |
\(P = c_s^2 \rho\) where \(c_s^2 \equiv K\) is a constant stored in the dump file header |

2 |
\(P = (\gamma - 1) \rho u\) if the code is compiled with ISOTHERMAL=yes, ieos=2 gives a polytropic eos: \(P = K \rho^\gamma\) where K is a global constant specified in the dump header |

3 |
\(P = c_s^2 (r) \rho\) sound speed (temperature) is prescribed as a function of radius using: \(c_s = c_{s,0} r^{-q}\) where \(r = \sqrt{x^2 + y^2 + z^2}\) |

4 |
Warning this is experimental: use with caution |

6 |
As in ieos=3 but in this version radius is taken with respect to a designated sink particle (by default the first sink particle in the simulation) |

7 |
sound speed is prescribed as a function of (cylindrical) radius R and height z above the x-y plane Warning should not be used for misaligned discs |

8 |
\(P = K \rho^\gamma\) where the value of gamma (and K) are a prescribed function of density |

9 |
\(P = K \rho^\gamma\) where the value of gamma (and K) are a prescribed function of density. Similar to ieos=8 but with different defaults and slightly different functional form |

10 |
a tabulated equation of state including gas, radiation pressure and ionisation/dissociation. MESA is a stellar evolution code, so this equation of state is designed for matter inside stars |

11 |
\(P = 0\) useful for simulating test particle dynamics using SPH particles |

12 |
\(P = (\gamma - 1) \rho u\) but solved by first solving the quartic equation: \(u = \frac32 \frac{k_b T}{\mu m_H} + \frac{a T^4}{\rho}\) for temperature (given u), then solving for pressure using \(P = \frac{k_b T}{\mu m_H} + \frac13 a T^4\) hence in this equation of state gamma (and temperature) are an output |

13 |
Assuming all sink particles are stars. Generalisation of Farris et al. (2014; for binaries) to N stars. For two sink particles this is identical to ieos=14 |

14 |
uses the locations of the first two sink particles |

15 |
Warning not widely tested in phantom, better to use ieos=10 |

16 |
this equation of state requires evolving temperature as the energy variable Warning not tested: use with caution |

20 |
from HORMONE, Hirai+2020, as used in Lau+2022b |