Evolution of the Crab nebula in a low energy supernova

The nature of the supernova leading to the Crab Nebula has long been controversial because of the low energy that is present in the observed nebula. One possibility is that there is significant energy in extended fast material around the Crab but searches for such material have not led to detections. An electron capture supernova model can plausibly account for the low energy and the observed abundances in the Crab. Here, we examine the evolution of the Crab pulsar wind nebula inside a freely expanding supernova and find that the observed properties are most consistent with a low energy event. Both the velocity and radius of the shell material, and the amount of gas swept up by the pulsar wind point to a low explosion energy ($\sim 10^{50}$ ergs). We do not favor a model in which circumstellar interaction powers the supernova luminosity near maximum light because the required mass would limit the freely expanding ejecta.