Revisiting the non-thermal radiation from the Crab nebula: requiring two distinct electron components

We revisit the non-thermal radiation from the Crab nebula in the framework of a one-dimensional time-dependent model. In this model, two electron components are considered: a low-energy electron component, which has a power-law form, and a high-energy electron component, which has a power-law form or a relativistic Maxwellian plus a high-energy power-law tail. After fitting the observed multiband data of the Crab nebula using the Levenberg-Marquardt method of the χ²-minimization procedure, we show the following. (i) Electron injection with a relativistic Maxwellian plus a power-law tail (i.e. one electron population) cannot account for the observed multiband emission of the Crab nebula. (ii) Two distinct electron populations are required, although their origins are still under debate, and moreover there would be a low-energy electron component having a power-law form with a slope of ∼1.6 for the Crab nebula and Crab-like pulsar wind nebulae.