When a star goes supernova, it ejects its' outer layers. Alright, hopefully we've cemented that during the core collapse handouts, but we need to # Stage 1: Ejecta Stage 1: Ejecta-dominated stage (free expansion) We can find the time for this stage as a function: $\tau \approx [ \frac{3}{4\pi} \frac{M_{ej}}{\rho v^3_{sh}} ]^{\frac{1}{3} }$ Where: $M_{ej}$ is the mass of the ejecta created by the supernova $\rho$ is the density within the ejecta $v$ is the velocity of the ejecta shell, the material shorn off by the supernova. As supernovae are mostly different, the time spent at this stage varies wildly, ranging from 10-100 years. This means we keep sweeping up more mass from the initial supernova shock - this will slow down the expansion of the remnant. This will keep it from expanding. However, this is part of the second stage. # Stage 2: Adiabatic Expansion More commonly known as the **Sedov-Taylor Expansion**, this stage of stellar remnant evolution dictates a resumption in nebula expansion after initial "pull" of gravity. It revolves around the concept that thermal energy will begin to "push" particles away from each other, thanks to the Pauli exclusion principle and the thermal - kinetic energy equivalence equation. The time for this phase to pass can be given by: $E_{0} = E_{th} + \frac{1}{2}M_{shell}v^2_{sh} = const$ Where: - $const$ is an arbitrary constant - $E_0$ is the - $E_{th}$ is the thermal energy of the stellar remnant system - $M_{shell}$ is the mass of the ejecta shell surrounding the stellar remnant - $v$ is the velocity of the object $\xi = rt^{-\frac{2}{5}}\rho^{\frac{1}{5}}E^{\frac{1}{5}}$ $\tau_{sh} \propto t^{-\frac{2}{5}}$ $v_{sh} \propto t^{-\frac{3}{5}}$ This gives us a value of: $\tau \approx 20,000 \ years$ # Stage 3: Radiative Stage (Snow Plow!)