In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new longterm three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.

In recent years, it has become a well-established paradigm that many aspects of the physics of Pulsar Wind Nebulae (PWNe) can be fully accounted for within a relativistic MHD 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.

The Crab Nebula is one of the most efficient accelerators in the Galaxy and the only galactic source showing direct evidence of PeV particles. In spite of this, the physical process behind such effective acceleration is still a deep mystery. While particle acceleration, at least at the highest energies, is commonly thought to occur at the pulsar wind termination shock, the properties of the upstream flow are thought to be non-uniform along the shock surface, and important constraints on the mechanism at work come from exact knowledge of where along this surface particles are being accelerated. Here we use axisymmetric relativistic MHD simulations to obtain constraints on the acceleration site(s) of particles of different energies in the Crab Nebula. Various scenarios are considered for the injection of particles responsible for synchrotron radiation in the different frequency bands, radio, optical and X-rays. The resulting emission properties are compared with available data on the multi wavelength time variability of the inner nebula. Our main result is that the X-ray emitting particles are accelerated in the equatorial region of the pulsar wind. Possible implications on the nature of the acceleration mechanism are discussed.

Bow shock pulsar wind nebulae are a large class of non-thermal synchrotron sources associated to old pulsars, that have emerged from their parent supernova remnant and are directly interacting with the interstellar medium. Within this class a few objects show extended X-ray features, generally referred as "jets", that defies all the expectations from the canonical MHD models, being strongly misaligned respect to the pulsar direction of motion. It has been suggested that these jets might originate from high energy particles that escape from the system. Here we investigate this possibility, computing particle trajectories on top of a 3D relativistic MHD model of the flow and magnetic field structure, and we show not only that beamed escape is possible, but that it can easily be asymmetric and charge separated, which as we will discuss are important aspects to explain known objects.

Bow shock pulsar wind nebulae (BSPWNe) are know to show a large variety of shapes and morphologies, both when comparing different objects, and for the same object in different energy bands. It is unclear if such a variety is related to differences in the pulsar wind properties, or to differences in the conditions of the ambient medium. We present here a set of full three-dimensional, relativistic and magneto-hydrodynamic simulations of BSPWNe, with the intention of determining how differences in the injection conditions by the pulsar wind reflect in the nebular dynamics. To achieve a good coverage of the available parameter space we have run several simulations varying those parameters that are most representative of the wind properties: the latitudinal anisotropy of the wind energy flux with respect to the pulsar spin axis, the level of magnetization, the inclination of the pulsar spin axis with respect to the pulsar direction of motion. We have followed the dynamics in these systems, not just in the very head, but also in the tail, trying to assess if and how the system retains memory of the injection at large distances from the pulsar itself. In this paper we focus our attention on the characterization of the fluid structure and magnetic field properties. We have tried to evaluate the level of turbulence in the tail, and its relation to injection, the survival of current sheets, and the degree of mixing between the shocked ambient medium and the relativistic pulsar wind material.

Since the day of its explosion, SN 1987A (SN87A) was closely monitored with the aim to study its evolution and to detect its central compact relic. The detection of neutrinos from the supernova strongly supports the formation of a neutron star (NS). However, the constant and fruitless search for this object has led to different hypotheses on its nature. To date, the detection in the Atacama Large Millimeter/submillimeter Array data of a feature that is somehow compatible with the emission arising from a proto-pulsar wind nebula (PWN) is the only hint of the existence of such elusive compact object. Here we tackle this 33 yr old issue by analyzing archived observations of SN87A performed by Chandra and NuSTAR in different years. We firmly detect nonthermal emission in the 10–20 kev energy band, due to synchrotron radiation. The possible physical mechanism powering such emission is twofold: diffusive shock acceleration (DSA) or emission arising from an absorbed PWN. By relating a state-of-the-art magnetohydrodynamic simulation of SN87A to the actual data, we reconstruct the absorption pattern of the PWN embedded in the remnant and surrounded by cold ejecta. We found that, even though the DSA scenario cannot be firmly excluded, the most likely scenario that well explains the data is that of PWN emission.

The standard approach to the long term evolution of pulsar wind nebulae (PWNe) is based on one-zone models treating the nebula as a uniform system. In particular for the late phase of evolved systems, many of the generally used prescriptions are based on educated guesses for which a proper assessment lacks. Using an advanced radiative code we evaluate the systematic impact of various parameters, like the properties of the supernova ejecta, of the inner pulsar, as well of the ambient medium, upon the extent of the reverberation phase of PWNe. We investigate how different prescriptions shift the starting time of the reverberation phase, how this affects the amount of the compression, and how much of this can be ascribable to the radiation processes. Some critical aspects are the description of the reverse shock evolution, the efficiency by which at later times material from the ejecta accretes onto the swept-up shell around the PWN, and finally the density, velocity and pressure profiles in the surrounding supernova remnant. We have explicitly treated the cases of the Crab Nebula, and of J1834.9–0846, taken to be representatives of the more and the less energetic pulsars, respectively. Especially for the latter object the prediction of large compression factors is confirmed, even larger in the presence of radiative losses, also confirming our former prediction of periods of super-efficiency during the reverberation phase of some PWNe.

In this contribution we review the recent progress in the modeling of Pulsar Wind Nebulae (PWN). We start with a brief overview of the relevant physical processes in the magnetosphere, the wind-zone and the inflated nebula bubble. Radiative signatures and particle transport processes obtained from 3D simulations of PWN are discussed in the context of optical and X-ray observations. We then proceed to consider particle acceleration in PWN and elaborate on what can be learned about the particle acceleration from the dynamical structures called "wisps" observed in the Crab nebula. We also discuss recent observational and theoretical results of gamma-ray flares and the inner knot of the Crab nebula, which had been proposed as the emission site of the flares. We extend the discussion to GeV flares from binary systems in which the pulsar wind interacts with the stellar wind from a companion star. The chapter concludes with a discussion of solved and unsolved problems posed by PWN.Comment: To appear in "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release" of the Space Science Reviews series. The final publication is available at Springer via http://dx.doi.org/10.1007/s11214-017-0344-