1. Hydrostatic Equilibrium Physical Astronomy Professor Lee Carkner Lecture 9

2. Questions 1)Suppose we can only see stars with our eyes with m<6. How far away could we still see Barnard’s star?  M=13, m=6  D = 10^((m-M+5)/5) = 0.4 pc 2)How far away could we still see Deneb?  M=-7, m=6  D = 10^((m-M+5)/5) = 3981 pc 3)Would you expect M dwarfs to be visible to the naked eye?  No, they would have to be very close (within about 1 pc)

3. Equilibrium  A star is just a big ball of gas   Pressure pushes out   Force of gravity on small mass dm is: F g = -(GM r dm)/r 2  Where r is the distance from the center of the star and M r is the mass interior to r

4. Pressure  dP/dr = -GM r  /r 2 = -  g  Equation of hydrostatic equilibrium   Pressure decreases as we move towards the surface

5. Equation of State   Related to density and temperature  PV = NkT P = nkT   Remember ideal gas law is gets less accurate as the density increases

6. Mean Weight  n =  /m mean   = m mean /m H  We can then write the ideal gas law as: P =  kT/  m H

7. Gas Composition  If a star is all neutral hydrogen,  If there are heavier elements,  increases  For example, stars are mostly hydrogen with significant helium and very small amounts of heavier elements   If the gas is ionized,  decreases   Ionized gas,  ~ 0.62

8. Mass Continuity   Mass is continuous  dM r =  (4  r 2 dr) dM r /dr = 4  r 2   Where  is the density for that shell   The total mass is just the integral over the whole star

9. Particle Energy   Kinetic energy = thermal energy ½mv 2 = (3/2)kT   Need high speeds to overcome Coulomb repulsion and fuse

10. Energy Transport   Convection dominates when: 1.  Radiation can’t get through 2.  Even with low opacity a lot of photons get absorbed

11. Energy Transport in Stars  Ionization decreases opacity:   Near the cores of medium mass stars there is high ionization and thus low opacity (rad then conv) 

12. Next Time  Read 10.3, 10.6, 11.1  Homework: 10.22, 10.23a, 11.1, 11.2a