Ionization & the potential energy reservoir

Download the specific thermal energy tables here

Simulation codes for galaxy formation and evolution take on board as many physical processes as possible beyond the standard gravitational and hydrodynamical physics. Most of this extra physics takes place below the resolution level of the simulations and is added in a sub-grid fashion. However, these sub-grid processes affect the macroscopic hydrodynamical properties of the gas and thus couple to the on-grid physics that is explicitly integrated during the simulation.

We have focused on the link between partial ionization and the hydrodynamical equations. The energy stored in ions and free electrons constitutes a potential energy term which breaks the linear dependence of the internal energy on temperature. Correctly taking into account ionization hence requires modifying both the equation of state and the energy-temperature relation. The left panel accompanying figure shows the specific energy of a hydrogen-helium gas as a function of temperature with (black line) and without (grey line) the potential energy reservoir. Between 10,000 K and 20,000 K, hydrogen ionizes and the potential energy stored in free proton/electron pairs suddenly jumps up. This causes the adiabatic index of the gas to drop to almost 1. Therefore, between 10,000 K and 20,000 K, the gas behaves essentially isothermally. In Vandenbroucke et al. 2013 (arXiv:1305.2927), we have investigated the influence of this potential energy reservoir on the expansion of Sedov-Taylor blastwaves. Depending on the initial density and temperature of the gas, up to 50% of the blast energy is used to ionize the gas (and is therefore converted into potential energy) and, therefore, does not go into heating the gas. That means that, in galaxy evolution simulations, supernova feedback can be substantially reduced ...

Hydrodynamical codes already integrate the specific energy through time, including feedback, photo-heating, and radiative cooling terms in the energy equation. In order to derive the gas temperature from the specific energy, it is crucial to have easily interpolatable tables of temperature vs. specific energy. Here, we provide such tables.

If you are interested in using interpolating tables of specific thermal energy vs. temperature, go here.