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Hydrostatic Equilibrium

Hydrostatic Equilibrium. Physical Astronomy Professor Lee Carkner Lecture 9. Questions. 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 How far away could we still see Deneb? M=-7, m=6

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Hydrostatic Equilibrium

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  1. Hydrostatic Equilibrium Physical Astronomy Professor Lee Carkner Lecture 9

  2. Questions • 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 • How far away could we still see Deneb? • M=-7, m=6 • D = 10^((m-M+5)/5) = 3981 pc • 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: Fg = -(GMrdm)/r2 • Where r is the distance from the center of the star and Mr is the mass interior to r

  4. Pressure dP/dr = -GMrr/r2 = -rg • 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 = r/mmean m = mmean/mH • We can then write the ideal gas law as: P = rkT/mmH

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

  8. Mass Continuity • Mass is continuous dMr = r(4pr2 dr) dMr/dr = 4pr2r • Where r is the density for that shell • The total mass is just the integral over the whole star

  9. Particle Energy • Kinetic energy = thermal energy ½mv2 = (3/2)kT • Need high speeds to overcome Coulomb repulsion and fuse

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

  11. EnergyTransport 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

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