exc3 - Introduction to Astrophysics 0321.3108 Exercise 3 1...

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Introduction to Astrophysics 0321.3108 Exercise 3 1. In class we showed that in thermal equilibrium N ( H + ) N ( H ) = 1 N ( e ) 2 πm e k B T h 2 3 / 2 exp - 1 . 6 × 10 5 T , (1) where N ( H + ) is the proton number density, N ( H ) is the atomic hydrogen number density, N ( E ) is the electron number density and T is the gas temperature. For a typical density in a stellar photosphere: 5 × 10 14 cm - 3 , find the temperature such that N ( H + ) /N ( H ) = 1. Guidance: assume that the density of the electrons is the same as the density of the protons. The last equation must be solved numerically! 2. Find the frequencies of the spectral lines: Ly α , Ly β , Ly γ , H α , H β and H γ . Explain your derivations. 3. Suppose a star of total mass M and radius R has a density profile ρ = ρ c (1 - r/R ), where ρ c is the central density. a. Find M(r). b. Express the total mass M in terms of R and ρ c . c. Solve for the pressure profile, P(r), with the boundary condition P(R) = 0. 4. Consider a hypothetical star of radius R, with density ρ that is constant, i.e., independent of radius. The star is composed of a classical, non-relativistic, ideal gas of fully ionized hydrogen.

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