EOS_Polytrope

Ian Hawke

22/4/2002

Abstract

EOS_Polytrope

1 The equations

This equation provides a polytropic equation of state to thorns using the CactusEOS interface found in EOS_Base. As such it’s a fake, as EOS_Base assumes that, e.g., the pressure is a function of both density and specific internal energy. Here the pressure is just a function of the density, and is set appropriately (the specific internal energy is always ignored).

The two fluid constants are K (eos_k) and Γ (eos_gamma), which default to 100 and 2 respectively. The formulas that are applied under the appropriate EOS_Base function calls are

P = KρΓ (1) 𝜖 = KρΓ1 Γ 1 (2) ρ = P (Γ 1)𝜖 (3) P ρ = KΓρΓ1 (4) P 𝜖 = 0. (5)

To calculate the units of the Cactus quantities and back, remember that G = c = M = 1 in Cactus.
Here is one example how to calculate densities:

ρCactus = G3M 2 c6 ρ 1.6167 1021m3 kg ρ = 1.6167 1018cm3 g ρ (6)

and one example for calculating K (for Γ = 2):