set8-f7 - Compare with the cooling rate given in the notes...

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Astro 405/505, fall semester 2007 Homework, 8th set, return before Friday, November 2, 4pm. Don’t forget to give your name. Problem 15: Heating by photoelectric absorption In class we studied heating of the interstellar medium by supernova remnant shocks. Here we will derive the heating rate by absorption of UV radiation. UV radiation with photon energy higher than 13 . 6 eV can ionize a hydrogen atom by so-called photoelectric absorption. If the Galaxy was transparent for radiation below 13 . 6 eV, what would be the energy that is available for heating, if the atom is ionized by a photon of energy E γ ? The cross section for photoelectric absorption is (consult the textbook, pp 104-105) σ a (10 - 17 cm 2 ) ± E γ 13 . 6 eV ² - 3 = (10 - 17 cm 2 ) ± ν 3 . 25 · 10 15 Hz ² - 3 Assume the UV energy density to be u ν (10 - 5 eV cm - 3 ) (3 . 25 · 10 15 Hz) - 1 and calculate the heating rate ˙ T assuming only atomic hydrogen that behaves as ideal gas.
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Unformatted text preview: Compare with the cooling rate given in the notes for section 13. What would be the equilibrium temperature for atomic hydrogen at a density of 10 atoms per cubic centimeter? At what temperature would you expect hydrogen gas with density 10-3 cm-3 ? Think carefully before you answer. Problem 16: Structure formation Consider a cluster of galaxies in the process of formation, assuming M = 10 15 M ¯ and n H = 10-4 cm-3 . If the inner parts of the cluster have already stopped collapsing, e.g. on account rotation, argue in detail whether or not a continued infall at larger radii may lead to shocks. Hint: What is the maximum infall velocity? Also, what is the maximum temperature of the gas, so that the material may Fow in?...
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