set1-f5 - r from the central star b Now suppose the density...

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Astro 405/505, fall semester 2005 Homework, 1st set, return before Friday, September 16, 4pm. Don’t forget to give your name. Problem 1: equation of state Show that for anonrelativistic ( ~p = m~v ) isotropic distribution function f = f ( | ~p | ) the kinetic pressure tensor is indeed a scalar π ij = P δ ij Also show that the following relation between the scalar pressure and the thermal energy density, ² , is true: P = 2 3 ² Write down an equation of state that you know and explain under what condition it applies. Problem 2: Cygnus OB2 No.5 The Frst page of the research paper below describes radio ±ux measurements of a very massive hot star in the constellation Cygnus. The emission is variable. Here we are interested in the low state, during which the ±ux spectrum is proportional to the frequency as F ν ν 0 . 6 . a) Suppose the star blew o² a spherically symmetric wind of ionized gas with constant mass ±ux and ±ow velocity independent of position. How would the gas density scale with distance
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Unformatted text preview: r from the central star? b) Now suppose the density, emission coe³cient and absorption coe³cient show the following scalings: ρ = ρ r-2 j ν = j ρ 2 α n u = α ρ 2 ν-2 These radiation coe³cients are approximately those for thermal emission at hν ¿ kT . Calcu-late the intensity for an arbitrary line-of-sight, that means not only through the center. Hint: It is beneFcial to use the integration variable x = tan φ i the calculation of the optical depth. c) ´inally calculate the ±ux by integration over all possible lines-of-sight. Assume the distance D to the star is much larger than the size of the system, so you can replace the solid-angle integration by one over the apparent surface. We are interested only in the spectral form. Can you reproduce the quiet-phase spectrum of the star mentioned in the research paper? 1994A&A. ..282. .547M...
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set1-f5 - r from the central star b Now suppose the density...

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