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set5-f7 - Problem 10 Stellar cores Do you think convection...

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Astro 405/505, fall semester 2007 Homework, 5th set, return before Friday, October 12, 4pm. Don’t forget to give your name. Problem 9: Time-dependent line profles Let us as in class consider the optically thin line proFle resulting from material that is expelled in a supernova explosion. In contrast to the time-independent treatment that we used in class, we now want to know the temporal evolution of the line proFle, P ( E obs , t obs ) . Assume all particles have the same velocity P ( v ) = δ ( v - v 0 ) , have been expelled isotropically at the same location and time ( t = 0 ). a) Derive relations that link t and t obs as well as E obs and E 0 . b) Assuming the particles decay exponentially after instantaneous injection as would beFt a radioactive particle ( P ( t ) = exp( - t/t 0 ) Θ( t ) ), calculate the time-dependent line proFle. Explain the evolution of the derived proFle qualitatively.
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Unformatted text preview: Problem 10: Stellar cores Do you think convection would signiFcantly contribute to the stability of stars via turbulent ram pressure ( ∼ ρ V 2 )? Hint: recall typical values of the convection velocity and consult the momentum conservation equation. Do you think it is justiFed to assume adiabatic stratiFcation of temperature and density of the material inside stars as a reasonable approximation? Assuming adiabatic stratiFcation with adiabatic index γ = 1 . 4 , can you estimate the mass density in the core of the sun, if you know the core temperature to be 15 million degrees, the surface temperature as 6.000 degrees, and the surface mass density ρ s = 3 · 10-7 gr cm-3 ?...
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