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Table A.2
Model variables and their relationships.
| Variable name | Symbol | Equation | |
|---|---|---|---|
| Temperature floor | T0 | = 104 K | |
| Initial speed of sound | c1 |  |
|
| Incoming Mach number |  |
= vvir∕c1 | |
| Density of the halo gas at rvir | ρH |  |
|
| Temperature of the halo gas | TH |  |
|
| Pressure of the halo gas at rvir | PH | = kBTHρH∕μmp | |
| Density of the post-sock gasa | ρps |  |
|
| Pressure of the post-shock gasa | Pps |  |
|
| Post-shock speed of sound | cps | = γPps∕ρps | |
| Temperature of the warm phase | Tw | = T0 | |
| Density of the warm phase | ρw | = ρHTH∕Tw | |
| Density of the hot phase (post-expansion) | ρh |  |
|
| Temperature of the hot phase (post-expansion) | Th | = ρHTH∕ρh | |
| Volume-averaged density of the warm phase |  |
= ϕv,wρw | |
| Volume-averaged density | ρ2 | = ϕv,wρw + (1 − ϕv,wρh) | |
| Expansion factor of the post-shock streamb | S |  |
|
| Velocity dispersion of the warm clouds | σturb |  |
|
| Halo dynamical time | tdyn,halo | = rvir∕vvir | |
Cooling time of the phase  |
tcool,Φ |  |
|
| Expansion time of the post-shock gas | texpand | = 2γrstream∕cps | |
| Disruption time of the turbulent warm phase | tdisrupt | = rstream∕σturb | |
Isobaric cooling length  |
λcooling | = cΦtcool,Φ | |
Notes. A graphical representation of many of these variables is shown in Fig. 1. (a) Standard normal shock equation from the Rankine-Hugoniot jump conditions. (b) The equation assumes 
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