An Introduction to Modern Astrophysics · Problem 15.5
The Degenerate Remnants of Stars — Carroll & Ostlie
Physics — Astrophysics · core-collapse-supernova-remnant-radius
Problem
Assume that the core of a star collapses to produce a Type II supernova. Assume further that 100\% of the energy released by the collapsing core is converted to neutrinos and that 1\% of the neutrinos are absorbed by the overlying envelope to power the ejection of the supernova remnant. Estimate the final radius of the stellar remnant if sufficient energy is to be liberated to just barely eject the remaining to infinity. Be sure to state clearly any additional assumptions you make in determining your estimate of the final radius of the remnant.Intuitive explanation
The core of this problem is gravitational binding energy: when a massive core collapses, it releases enormous gravitational potential energy that gets carried away by neutrinos. You need to work backwards from the energy budget—figure out how much kinetic energy the envelope needs to escape to infinity, then use the neutrino energy fraction to find what final core radius makes that possible. The key insight is that the binding energy of the collapsing core scales as , so a smaller final radius means more energy available to power the explosion.
Intuitive explanation
The core of this problem is gravitational binding energy: when a massive core collapses, it releases enormous gravitational potential energy that gets carried away by neutrinos. You need to work backwards from the energy budget—figure out how much kinetic energy the envelope needs to escape to infinity, then use the neutrino energy fraction to find what final core radius makes that possible. The key insight is that the binding energy of the collapsing core scales as , so a smaller final radius means more energy available to power the explosion.