Modeling the effect of small-scale magnetic turbulence on the X-ray properties of Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) constitute an ideal astrophysical environment to test our current understanding of relativistic plasma processes. It is well known that magnetic fields play a crucial role in their dynamics and emission properties. At present, one of the main issues concerns the level of magnetic turbulence present in these systems, which in the absence of space resolved X-ray polarization measures cannot be directly constrained. In this work, we investigate, for the first time using simulated synchrotron maps, the effect of a small-scale fluctuating component of the magnetic field on the emission properties in X-ray. We illustrate how to include the effects of a turbulent component in standard emission models for PWNe and which consequences are expected in terms of net emissivity and depolarization, showing that the X-ray surface brightness maps can provide already some rough constraints. We then apply our analysis to the Crab and Vela nebulae and by comparing our model with Chandra and Vela data, we found that the typical energies in the turbulent component of the magnetic field are about 1.5-3 times the one in the ordered field.