ASTR 610 Theory of Galaxy Formation
Lecture 15: Heating & Cooling
Frank van den Bosch Yale University, Fall 2020 Heating & Cooling
In this lecture we address heating and cooling of gas inside dark matter haloes. After discussing shock heating & hydrostatic equilibrium, we introduce the concept of `virial temperature’, discuss radiative cooling processes and introduce the cooling function. We discuss the link between cooling and galaxy formation, and end with a discussion of photo-ionization heating.
Topics that will be covered include:
shock heating hydrostatic equilibrium virial temperature radiative cooling cooling function & cooling time ionization equilibrium photo-ionization heating
ASTR 610: Theory of Galaxy Formation © Frank van den Bosch, Yale University Shock Heating
Consider a gas cloud of mass M gas falling into a halo of mass M h with velocity vin At some point the gas is shocked; either close to center, where flow lines converge, or at the accretion shock, which is typically located close to the virial radius.
If we assume that the shock thermalizes all the kinetic energy of the gas cloud, so 2 kBTin that v gas 0 after it is shocked (a reasonable assumption), and that v in µmp (so that internal energy of infalling gas can be ignored) then the internal energy of the shocked gas is equal to the kinetic energy of the gas at infall:
3 1 2 Eint,sh = 2 NkB Tsh = 2 Mgasvin
where N = M gas / ( µm p ) is the number of gas particles, and we have assumed a mono-atomic gas, for which =5/3
µmp 2 Tsh = vin 3kB
If the gas falls in from large distance (where ( r ) 0 ), and has negligible, initial velocity, then v v (r )= 2 (r ) in esc sh | sh | ASTR 610: Theory of Galaxy Formation © Frank van den Bosch, Yale University Shock Heating
2 GMvir 2 If we assume that r sh = r vir (a common assumption), then vin = = Vvir rvir Here = (1) is a parameter that depends on the detailed density profile of the halo. O
The temperature of the shocked gas in a halo with virial velocity V vir is