The model is solving:

\[\frac{d T}{d t}=-2 H T+\frac{2 T}{3 \Delta} \frac{d \Delta}{d t} - \frac{T}{\sum_i X_i }\frac{d \sum_i X_i}{dt} +\frac{2}{3 k_{B} n_{t o t}} \frac{d Q}{d t}\]

The code for the solver is here: https://github.com/bvillasen/thermal_IGM

The Cooling mechanisms for Bruno’s model

  • Collisional Excitation Cooling:
  • HI + e: Hui & Gnedin 97

  • HeII + e: Hui & Gnedin 97

  • Collisional Ionization Cooling:
  • HI + e: Katz et al 95
  • HeI + e: Katz et al 95

  • HeII + e: Katz et al 95

  • Collisional Ionization Rates:
  • HI + e: Hui & Gnedin 97
  • HeI + e: Abel et al. 97
  • HeII + e: Abel et al. 97
  • HI + HI: Lenzuni et at. 91
  • HII + HI: Lenzuni et at. 91

  • HeI + HI: Lenzuni et at. 91

  • Recombination Cooling:
  • HII: Hui & Gnedin 97
  • HeII: Hui & Gnedin 97
  • HeII dielectronic: Hui & Gnedin 97

  • HeIII: Hui & Gnedin 97

  • Recombination Rates:
  • HII: Hui & Gnedin 97
  • HeII: Hui & Gnedin 97
  • HeII dielectronic: Hui & Gnedin 97

  • HeIII: Katz et al 95

  • Bremsstrahlung Cooling: Katz et al 95

  • CMB Compton Cooling: Milles & Ostriker 2001

Below is the evolution of the Density-Temperature distribution