For example s2 would correspond to a steady presn

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Unformatted text preview: oints] Suppose that instead of exploding in a uniform medium, a supernova explodes in a medium that is spherically symmetric with density profile ρ( r) ∝ r− s . For example, s=2 would correspond to a steady pre ­SN stellar wind. Compute the power ­law exponents for how the radius of the blast wave R, € the shock velocity v1, and the post ­shock temperature T2 vary as a function of time t for each of the major supernova remnant phases discussed in class (free expansion; energy ­conserving/Sedov ­Taylor; cooling of shocked ISM gas; and cooling of the hot central bubble). 1 The answer you get here will be an overestimate because some of the energy is taken up by dissociation of O2. #3. Faraday Rotation. [10 points] (a) AGN jets are sometimes theorized to contain a pair plasma (i.e. equal numbers of e+ and e−). Show that (to linear order in the magnetic field) such a plasma does not lead to Faraday rotation. (b) The Earth’s daytime ionosphere has a typical free electron density of ~106 cm−3 and a thickness of ~100 km. The Earth’s magnetic field is ~0.3 G. Estimate the critical frequency above which radio polarization is significantly rotated (≥1 radian) by the ionosphere....
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This document was uploaded on 03/08/2014 for the course AY 102 at Caltech.

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