Suppose a spherical shell identified as a supernova remnant is observed with radius r and(adsbygoogle = window.adsbygoogle || []).push({});

with outward expansion speed v. Assume the mass density of the ambient medium to have

the uniform value "ro_0". then the supernova remnant must have swept up mass M = ((ro_0)*4pi*r^3)/3.

Let the original mass M_0 be ejected at speed v_0. If we ignore communication between

different parts of the shell (via the thermal pressure of the hot interior), and suppose that

each piece of the shell preserves its outward linear momentum as it sweeps up more material initially at rest, we have the snowplow model.

a) Show that the snowplow model implies

(M +M_0)v = M_0*v_0.

b) The original kinetic energy E_0 of the ejected material equals (M_o*(v_0)^2)/2

0/2. The present

kinetic energy E of the shell equals ((M + M_0)v^2)/2. Show that the ratios E/E_0 and v/v_0 are given by:

E/E_0 = v/v_0 = M_0/(M +M_0).

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# Snowplow model of a supernova remnant

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