Many stars possess powerful stellar winds that drive strong spherical shockwaves into the surrounding interstellar medium. If the strength of the wind remains constant, the kinetic and internal energy of the swept-up interstellar medium will increase linearly with time.

(a) Modify the text’s analysis of a point explosion to show that in this case the speed of the shock wave at time t is 3/5R(t)/t, where R is the associated shock radius. What is the speed of the post-shock gas?

(b) Now suppose that the star explodes as a supernova, and the blast wave expands into the relatively slowly moving stellar wind. Suppose that before the explosion the rate at which mass left the star and the speed of the wind were constant for a long time. How do you expect the density of gas in the wind to vary with radius? Modify the Sedov-Taylor analysis again to show that the expected speed of the shock wave at time t is now 2/3R(t)/t .