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In recent years, it has become a well-established paradigm that many aspects of the physics of Pulsar Wind Nebulae can be fully accounted for within a relativistic magnetohydrodynamic description. Numerical simulations have proven extremely successful in reproducing the X-ray morphology of the Crab nebula, down to very fine detail. Radio emission, instead, is currently one of the most obscure aspects of the physics of these objects, and one that holds important information about pulsar properties and their role as antimatter factories. Here, we address the question of radio emission morphology and integrated spectrum from the Crab nebula, by using for the first time an axisymmetric dynamical model with parameters chosen to best reproduce its X-ray morphology. Based on our findings we discuss constraints on the origin of the radio emitting particles. [ABSTRACT FROM AUTHOR]

Context. Observation of Balmer lines from the region around the forward shock of supernova remnants may provide precious information on the shock dynamics and on the efficiency of particle acceleration at the shock. Aims. We calculate the Balmer line emission and the shape of the broad Balmer line for parameter values suitable for SNR 0509-67.5, as a function of the cosmic ray acceleration efficiency and of the level of thermal equilibrium between electrons and protons behind the shock. This calculation aims to use the width of the broad Balmer line emission to infer the cosmic ray acceleration efficiency in this remnant. Methods. We use the recently developed nonlinear theory of diffusive shock acceleration in the presence of neutrals. The semianalytical approach that we developed includes a description of magnetic field amplification as due to resonant streaming instability, the dynamical reaction of both accelerated particles and turbulent magnetic field on the shock, and all channels of interaction between neutral atoms and background plasma that change the shock dynamics. Results. We achieve a quantitative assessment of the CR acceleration efficiency in SNR 0509-67.5 as a function of the shock velocity and different levels of electron-proton thermalization in the shock region. If the shock moves faster than ~4500 km s-1, one can conclude that particle acceleration must be taking place with an efficiency of several tens of percent. For lower shock velocity the evidence of particle acceleration becomes less clear because of the uncertainty in the electron-ion equilibrium downstream. We also discuss the role of future measurements of the narrow Balmer line. [ABSTRACT FROM AUTHOR]