sol4 - Astro 405/505 fall semester 2004 Homework 4th set...

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Astro 405/505, fall semester 2004 Homework, 4th set, solutions. Problem 1: Supernova remnants and shock waves First calculate the sound speed. c s = γ kT m p 200 km / sec = 2 · 10 7 cm / sec Equate that with the velocity of the blast wave to find the endtime and final size of the supernova remnant using x 0 = 1 . U s ( t ) = dr s dt = 2 5 x 0 E ρ u t 3 1 5 r s ( t ) = x 0 E t 2 ρ u 1 5 U s ( t e ) = c s r s ( t e ) 2 2 E ρ u 5 2 c 2 s 1 3 so the volume filled by the remnant is V ( t e ) 4 π 3 r 3 s ( t e ) 0 . 65 E ρ u c 2 s 10 60 cm 3 3 . 7 · 10 4 pc 3 The repetition timescale for an arbitrary location to be overrun by a blast wave is the time between two supernovae time the ratio of total volume to the volume of one remnant. t rep = t SN V tot V ( t e ) 2 · 10 8 years The cooling time of gas at that temperature is t cool 1 . 6 · 10 6 years t rep So in our example the shock-heated gas would cool before the next blast waves arrives. Hence the shock waves wouldn’t keep gas of that density at the given temperature. Typically inter-
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