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sol5-f5 - Astro 405/505 fall semester 2005 Homework 5th set...

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Astro 405/505, fall semester 2005 Homework, 5th set, solutions Problem 9: collisionless shocks I first calculate the sound speed and the Alfv´ en velocity. c s 11 . 7 km / s v A 6 . 5 km / s The shock velocity is about 3 orders of magnitude higher than these two, so we have a strong shock. The shock thickness should be of the order of the mean free path for scattering on magnetic turbulence. δ r g B 0 δB 2 = V Ω g B 0 δB 2 = m e,p c V B 0 e ( δB ) 2 where V ( V s ) is the velocity of SN particle that run into the ambient medium. The pro- tons and other ions apparently determine the shock thickness. The typical size of supernova remnants is about 10 pc in radius, as given by the charateristic sizes at which the blast wave turns in and out of the Sedov phase. The shock thickness should be a small fraction of that, e.g. down by a factor 0.001. Then 3 · 10 16 cm = m p c V B 0 e ( δB ) 2 δB 0 . 003 μ G The magnetic fluctuations are at a level of one per mille of the homogeneous field and thus small, at least at the wavenumbers or wavelengths in resonance with the particles.
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