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We model the morphology and spectrum of a pulsar wind nebula using a leptonic emission code. This code is a time-dependent, multi-zone model that investigates the changes in the particle spectrum as they traverse the nebula. We calculate the synchrotron and inverse Compton emissivities at different positions in the nebula, obtaining the surface brightness versus the radius, and also the size of the nebula as a function of energy. We incorporate a time and spatially-dependent $B$-field, spatially-dependent bulk particle speed implying convection and adiabatic losses, diffusion, as well as radiative losses. We calibrate our new model using two independent models. We then apply the model to PWN G0.9+0.1 and show that simultaneously fitting the spectral energy distribution and the energy-dependent source size may lead to constraints on several model parameters pertaining to the spatial properties of the PWN.
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In the last decade, ground-based Imaging Atmospheric Cherenkov Telescopes have discovered about 175 very-high-energy (VHE; $E >$ 100 GeV) gamma-ray sources, with more to follow with the development of H.E.S.S. II and CTA. Nearly 40 of these are confirmed pulsar wind nebulae (PWNe). We present results from a leptonic emission code that models the spectral energy density of a PWN by solving a Fokker-Planck-type transport equation and calculating inverse Compton and synchrotron emissivities. Although models such as these have been developed before, most of them model the geometry of a PWN as that of a single sphere. We have created a time-dependent, multi-zone model to investigate changes in the particle spectrum as the particles traverse through the PWN, by considering a time and spatially-dependent magnetic field, spatially-dependent bulk particle motion causing convection, diffusion, and energy losses (SR, IC and adiabatic). Our code predicts the radiation spectrum at different positions in the nebula, yielding novel results, e.g., the surface brightness versus the radius and the PWN size as function of energy. We calibrated our new model against more basic models using the observed spectrum of PWN G0.9+0.1, incorporating data from H.E.S.S. as well as radio and X-ray experiments. We fit our predicted radiation spectra to data from G21.5$-$0.9, G54.1+0.3, and HESS J1356$-$645 and found that our model yields reasonable results for young PWNe. We next performed a parameter study which gave significant insight into the behaviour of the PWN for different scenarios. Our model is now ready to be applied to a population of PWNe to probe possible trends such as the surface brightness as a function of spin-down of the pulsar.
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.
We discuss the role of particle-in-cell (PIC) simulations in unveiling the origin of the emitting particles in PWNe. After describing the basics of the PIC technique, we summarize its implications for the quiescent and the flaring emission of the Crab Nebula, as a prototype of PWNe. A consensus seems to be emerging that, in addition to the standard scenario of particle acceleration via the Fermi process at the termination shock of the pulsar wind, magnetic reconnection in the wind, at the termination shock and in the Nebula plays a major role in powering the multi-wavelength signatures of PWNe.
In the last decade ground-based Imaging Atmospheric Cherenkov Telescopes have discovered roughly 30 pulsar wind nebulae at energies above 100 GeV. We present first results from a leptonic emission code that models the spectral energy density of a pulsar wind nebula by solving the Fokker-Planck transport equation and calculating inverse Compton and synchrotron emissivities. Although models such as these have been developed before, most of them model the geometry of a pulsar wind nebula as that of a single sphere. We have created a time-dependent, multi-zone model to investigate changes in the particle spectrum as the particles diffuse through the pulsar wind nebula, as well as predict the radiation spectrum at different positions in the nebula. We calibrate our new model against a more basic previous model and fit the observed spectrum of G0.9+0.1, incorporating data from the High Energy Stereoscopic System as well as radio and X-ray experiments.
The main goal of our present work is to provide, for the first time, a simple computational tool that can be used to compute the brightness, the spectral index, the polarization, the time variability and the spectrum of the non-thermal light (both synchrotron and inverse Compton, IC) associated with the plasma dynamics resulting from given relativistic magnetohydrodynamics (RMHD) simulations. The proposed method is quite general, and can be applied to any scheme for RMHD and to all non-thermal emitting sources, e.g. pulsar wind nebulae (PWNe), and in particular to the Crab Nebula (CN) as in the present proceeding. Here only the linear optical and X-ray polarization that characterizes the PWNe synchrotron emission is analyzed in order to infer information on the inner bulk flow structure, to provide a direct investigation of the magnetic field configuration, in particular the presence and the strength of a poloidal component, and to understand the origin of some emitting features, such as the knot, whose origins are still uncertain. The inverse Compton radiation is examined to disentangle the different contributions to radiation from the magnetic field and the particle energy distribution function, and to search for a possible hadronic component in the emitting PWN, and thus for the presence of ions in the wind. If hadronic radiation was found in a PWN, young supernova remnants would provide a natural birth-place of the cosmic-rays (CRs) up to the so-called knee in the CR spectrum.
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