1. The Boltzmann and Jeans equations.
ASTC22. Lecture L11
The Boltzmann and Jeans equations.
The collisionless Boltzmann equation
and the Jeans equations

3. Ludwig Boltzmann ( )
(Sir) James H. Jeans ( )

5. The phase-space: space made of configuration space (x,y,z)
and velocity space (vx,vy,vz)

6. Boltzmann equation.
It is essentially a conservation equation in phase-space:
Df(x,v,t)/Dt = 0

7. Df(x,v,t)/Dt = 0

8. This leads immediately to the usual continuity equation
of fluids.
The next step:

9. The Jeans equation: velocity dispersion as “pressure” in stellar systems
Dv/Dt = -grad (potential) - (1/n) grad (pressure)
(this is a typical Lagrangian way to write the equations of motion for a
fluid with pressure).

10. 2 V

11. ~0
Integrate once

12. (read chapter 3 about the results...)
Stars and gas
Just gas
Just stars

13. Isothermal spheres all have energy E in the Boltzmann factor & velocity dispersion sigma=const.