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The equation of hydrostatic equilibrium is dP dr GM, where M, is the mass interior to the radius r, and p is the density. Consider the atmosphere of a star which is isothermal. You may assume that the mass of the atmosphere does not contribute significantly to the total mass of the star, so that the surface gravity g = GM,/² is constant at all heights in the isothermal atmosphere. Assume an ideal gas law P = nkTkT, where is the mean molecular weight and my is the mass of a hydrogen atom. By solving the equation of hydrostatic equilibrium with these approximations, show that P(r) = P(0) exp[-917 r. . Briefly describe the meaning of the expression kT/gμm. Some white dwarfs have an atmosphere of mostly hydrogen plasma, whereas others have an at- mosphere dominated by helium plasma. For the simple model above, briefly discuss what major difference would be seen between these two cases. You can assume the same temperature and surface gravity for the two cases.

The equation of hydrostatic equilibrium is dP dr GM, where M, is the mass interior to the radius r, and p is the density. Consider the atmosphere of a star which is isothermal. You may assume that the mass of the atmosphere does not contribute significantly to the total mass of the star, so that the surface gravity g = GM,/² is constant at all heights in the isothermal atmosphere. Assume an ideal gas law P = nkTkT, where is the mean molecular weight and my is the mass of a hydrogen atom. By solving the equation of hydrostatic equilibrium with these approximations, show that P(r) = P(0) exp[-917 r. . Briefly describe the meaning of the expression kT/gμm. Some white dwarfs have an atmosphere of mostly hydrogen plasma, whereas others have an at- mosphere dominated by helium plasma. For the simple model above, briefly discuss what major difference would be seen between these two cases. You can assume the same temperature and surface gravity for the two cases.

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The equation of hydrostatic equilibrium is


dP/dr = ( −GMr / r2 ) ρ

where Mr is the mass interior to the radius r, and ρ is the density.
Consider the atmosphere of a star which is isothermal. You may assume that the mass of the
atmosphere does not contribute significantly to the total mass of the star, so that the surface
gravity g = GMr/r2 is constant at all heights in the isothermal atmosphere. Assume an ideal
gas law P = nkT = (ρ/µmH) kT, where µ is the mean molecular weight and mH is the mass of a
hydrogen atom.


By solving the equation of hydrostatic equilibrium with these approximations, show that


P(r) = P(0) exp ((−gµmH/kT)r)

Briefly describe the meaning of the expression kT/gµmH.


Some white dwarfs have an atmosphere of mostly hydrogen plasma, whereas others have an atmosphere dominated by helium plasma. For the simple model above, briefly discuss what major difference would be seen between these two cases. You can assume the same temperature and surface gravity for the two cases. 

The equation of hydrostatic equilibrium is dP dr GM, where M, is the mass interior to the radius r, and p is the density. Consider the atmosphere of a star which is isothermal. You may assume that the mass of the atmosphere does not contribute significantly to the total mass of the star, so that the surface gravity g = GM₁/² is constant at all heights in the isothermal atmosphere. Assume an ideal gas law P = nkTkT, where is the mean molecular weight and my is the mass of a hydrogen atom. By solving the equation of hydrostatic equilibrium with these approximations, show that P(r) = P(0) exp[-97TH] Briefly describe the meaning of the expression kT/gμm. Some white dwarfs have an atmosphere of mostly hydrogen plasma, whereas others have an at- mosphere dominated by helium plasma. For the simple model above, briefly discuss what major difference would be seen between these two cases. You can assume the same temperature and surface gravity for the two cases.
Transcribed Image Text:The equation of hydrostatic equilibrium is dP dr GM, where M, is the mass interior to the radius r, and p is the density. Consider the atmosphere of a star which is isothermal. You may assume that the mass of the atmosphere does not contribute significantly to the total mass of the star, so that the surface gravity g = GM₁/² is constant at all heights in the isothermal atmosphere. Assume an ideal gas law P = nkTkT, where is the mean molecular weight and my is the mass of a hydrogen atom. By solving the equation of hydrostatic equilibrium with these approximations, show that P(r) = P(0) exp[-97TH] Briefly describe the meaning of the expression kT/gμm. Some white dwarfs have an atmosphere of mostly hydrogen plasma, whereas others have an at- mosphere dominated by helium plasma. For the simple model above, briefly discuss what major difference would be seen between these two cases. You can assume the same temperature and surface gravity for the two cases.
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