## A Remnant Problem

I haven’t posted any physics problems for a while so here’s  a quickie involving dimensional analysis. You have to assume that the supernova remnant mentioned in the question is roughly spherical, like the one shown above (SNR 0500-67.5):

Click on the `continue reading’ thing if you would like to see my worked solution:

This is known as the Sedov solution for a spherical blast wave.

### 5 Responses to “A Remnant Problem”

1. Probably made a mistake, but I get R propto E^0.2 p^-0.2 and t^0.4

2. Anton Garrett Says:

Typo in your equation for powers of mass! You typed \alpha + \gamma = 0 but you mean \alpha + \beta = 0.

3. The assumption here seems to be that there’s no dependence on the initial mass of the star or mass of the ejecta…is that because it’s assumed that the mass of the star has a one-one correlation (approximately) with the energy of the explosion, and so there’s no need for a separate variable?

4. I reached the same result in a rather quick and simple manner:
assume that all the energy (E) of the explosion is turned into kinetic
energy (KE) of the swept-up material.

mass M = (4/3) pi R^3 rho

avg velocity v = (R/t)

KE = (1/2) M * v^2 ~ R^3 rho (R^2 / t^2) ~ R^5 rho t^(-2)

So

E ~ R^5 rho t^(-2)

Re-arrange to solve for R

R ~ E^(1/5) rho^(-1/5) t^(2/5)