Cooling and heating curves

Download the cooling & heating tables here

We have calculated new tables of radiative cooling and heating rates for different gas temperatures, densities, compositions, and redshifts. These tables are primarily intended for use in cosmological and galaxy formation/evolutions simulations. They include cooling contributed by inverse Compton cooling off the cosmic microwave background and by radiative free-free, free-bound, and bound-bound reactions between electrons and ions. We include ionization and heating by the cosmic UV background from Claude-André Faucher-Giguère and by the interstellar radiation field of Mathis et al. (1983) in a modified version of ChiantiPy, a python wrapper around the Chianty atomic data base. ChiantiPy provides electron collision ionization and recombination rates. On top of that, we equipped it with hydrogen and proton collision ionization rates, photo-ionization rates, charge-exchange reactions, and a new solver for the ionization equilibrium. We adopt an approximate scheme for HI self-shielding against UV radiation: the intensity of the radiation field at energies above 1 Ry is suppressed exponentially as Jν = Jν,0 e -nHI/n0 with n0=0.007 cm-3.

As to the composition of the gas, we employ a simple chemical enrichment scheme. Each gas parcel is enriched by elements from two contributions:

  • "fast": SNII and massive intermediate-mass stars,
  • "slow": SNIa and light-weight intermediate-mass stars.
  • We opted for Fe (a typical "slow" element) and Mg (a typical "fast" element) as tracers of both contributions. I.e. by specifying the Fe and Mg abundance in a gas parcel, it is possible to predict the abundances of all other elements. In the figure below, we predicted the elemental abundances for a few well studied standard stars. We adopted their measured Fe and Mg abundances and from those calculated the abundances of the other elements (red dots). The black dots are the measured data points. Clearly, our simply two-contribution chemical enrichment model works adequately.

    Thus, we can determine the ionization state of the interstellar gas for temperatures in the range 10 K < T < 109 K, hydrogen densities between 10-9 cm-3 < nH < 102 cm-3, and metallicities in the interval -∞ < [Fe/H] < 0.5 using only five parameters:

  • T, temperature, in K
  • nH, the hydrogen density, in cm-3
  • [Fe/H], iron abundance
  • [Mg/Fe], magnesium to iron abundance ratio
  • z, redshift

  • In a gas dynamical simulation, redshift, temperature, and density are usually followed explicitly anyway. This means that only two extra quantities, the Fe and Mg abundances, need to be evolved to be able to interpolate the cooling and heating curve tables.

    To the left is an example of our cooling curves for solar [Fe/H] and at different redshifts (as indicated in the panels) and for densities between 10-9 cm-3 (bottom curve in each panel) and 102 cm-3 (top curve in each panel). The color scale indicates the [Mg/Fe] ratio. It is clearly quite important to take into account the possible variation of the cooling contributed by α-elements from SNII: it can make an orde of magnitude difference to the cooling rate in some temperature ranges! If the density is low and self-shielding negligible, the UV background keeps hydrogen ionized. This eliminates the strong cooling peak between 10,000 and 20,000 K. The interstellar radiation field always keeps carbon in its CII state, allowing the gas to cool below 104 K mostly through the CII 157.7 micron finestructure emission line. At low densities and high redshifts, cooling is dominated by inverse Compton cooling, i.e. electrons scattering off the CMB photons.

    To the right is a plot of the net cooling rate (i.e. the absolute value of the cooling minus the heating rate) for solar abundance ratios and at different redshifts (as indicated in the panels) and for densities between 10-9 cm-3 (bottom curve in each panel) and 102 cm-3 (top curve in each panel). The color scale indicates the density. Full curves were calculated with self-shielding "on"; dotted curves with self-shielding "off". Allowing the UVB to flood even the densest gas parces clearly has a dramatic effect on the equilibrium temperature (marked by the sharp dip of the net cooling rate).