exam1-f5-sol

# exam1-f5-sol - only pressure supported Integrate the...

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Astro 405/505, fall semester 2005 Midterm Exam, solutions Problem 1: radiation transport (29P) Ray A carries the intensity B ν ( T c ) when leaving the central object, and that is essentially the observed intensity at the frequencies ν 1 . At frequency ν 0 we observe B ν ( T s ) which is smaller than B ν ( T c ) for T s < T c , so we see an absorption line, vice versa an emission line. Ray B starts with zero intensity and we always observe an emission line. At ν 1 the intensity is essentially zero, whereas at the line frequency ν 0 the intensity reaches B ν ( T s ) . At ν 0 the intensity along A and B is thus the same. At ν 1 we only see the central object, i.e. ray A. Problem 2: the mass of the galaxy (35P) The potential and its derivatives are V = - G M r 2 + z 2 ∂V ∂r = G M r ( r 2 + z 2 ) 3 / 2 ∂V ∂z = G M z ( r 2 + z 2 ) 3 / 2 G M z r 3 s for z r s because the thickness of the gas distribution is much smaller than
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Unformatted text preview: only pressure supported. Integrate the pressure-support equation along z at r s to obtain P ( z )-P (0) ’ -G M ρ r 3 s Z z ds s exp ±-s z c ² ’ P (0) ’ G M ρ z 2 c r 3 s for z c ¿ z ¿ r s which is the mid-plane pressure. There is little radial density structure, so ∂P ∂r . ∂P ∂z but ∂V ∂z ¿ ∂V ∂r so the pressure term in the radial stability equation must be very much smaller than the other two terms and may be neglected. Then the equation is trivial and yields M ’ r s v 2 φ G ’ 1 . 2 · 10 44 g ’ 6 · 10 10 M ¯ b) T = m p P (0) ρ k ’ G M m p z 2 c k r 3 s ’ v 2 φ m p z 2 c k r 2 s ’ 10 7 K c) Support arises from turbulent motion with < v z > of a few km/s....
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