Model of Radio Emission from Spherically Symmetric Pulsar Wind Nebulae

We study spatially resolved radio emission from pulsar wind nebulae (PWNe). We model the evolution of the magnetic field and the particle energy distribution inside the spherically symmetric PWNe. We assume that a PWN has the pure toroidal magnetic field and has the power-law radial velocity profile. Our spherically symmetric model of PWNe do not consider the synchrotron cooling of particles but consider the adiabatic cooling, because we are mostly interested in the radio emission from PWNe. We apply the model to the Crab Nebula and succeed to reproduce the observed spatially integrated radio spectrum with a single power-law injection. This is in contrast to our previous works, where we found that a broken power-law injection of particles reproduces the observed spectrum from radio to gamma-ray in the one-zone spectral evolution model of young PWNe. However, the obtained radial velocity profile is very different from the model by Kennel & Coroniti and the spatially resolved radio emission in our model is inconsistent with that in observations. Further studies about the spherically symmetric PWNe are important to understand the origin of the radio emission from young PWNe.