We show that a purely kinetic approach to the excitation of waves by cosmic rays in the vicinity of a shock front leads to predict the appearance of a non-Alfvénic fast-growing mode which has the ...same dispersion relation as that previously found by Bell in 2004 by treating the plasma in the magnetohydrodynamic approximation. The kinetic approach allows us to investigate the dependence of the dispersion relation of these waves on the microphysics of the current which compensates the cosmic ray flow. We also show that a resonant and a non-resonant mode may appear at the same time and one of the two may become dominant on the other depending on the conditions in the acceleration region. We discuss the role of the unstable modes for magnetic field amplification and particle acceleration in supernova remnants at different stages of the remnant evolution.
Supernova remnants (SNRs) are thought to be the primary sources of Galactic cosmic rays (CRs). In the last few years, the wealth of γ-ray data collected by GeV and TeV instruments has provided ...important information about particle energization in these astrophysical sources, allowing us to make progress in assessing their role as CR accelerators. In particular, the spectrum of the γ-ray emission detected by AGILE and Fermi-LAT from the two middle-aged SNRs W44 and IC 443, has been proposed as a proof of CR acceleration in SNRs. Here we discuss the possibility that the radio and γ-ray spectra from W44 may be explained in terms of reacceleration and compression of Galactic CRs. The recent measurement of the interstellar CR flux by Voyager 1 has been instrumental for our work, in that the result of the reprocessing of CRs by the shock in W44 depends on the CR spectrum at energies that are precluded from terrestrial measurement owing to solar modulation. We introduce both CR protons and helium nuclei in our calculations, and secondary electrons produced in situ are compared with the flux of Galactic CR electrons reprocessed by the slow shock of this SNR. We find that the multiwavelength spectrum of W44 can be explained by reaccelerated particles with no need of imposing any break on their distribution, but just a high-energy cutoff at the maximum energy the accelerator can provide. We also find that a model including both reacceleration and a very small fraction of freshly accelerated particles may be more satisfactory on physical grounds.
We present a new model for the spectral evolution of pulsar wind nebulae (PWNe) inside supernova remnants (SNRs). The model couples the long-term dynamics of these systems, as derived in the 1D ...approximation, with a one-zone description (all quantities are assumed uniform in the nebula) of the spectral evolution of the emitting plasma. Our goal is to provide a simplified theoretical description that can be used as a tool to put constraints on unknown properties of PWN-SNR systems: a piece of work that is preliminary to any more accurate and sophisticated modelling. In this paper, we apply the newly developed model to a few objects of different ages and luminosities. We find that an injection spectrum in the form of a broken power law gives a satisfactory description of the emission for all the systems we consider. More surprisingly, we also find that the intrinsic spectral break turns out to be at a similar energy for all sources, in spite of the differences mentioned above. We discuss the implications of our findings on the workings of pulsar magnetospheres, pair multiplicity and on the particle acceleration mechanism(s) that might be at work at the pulsar wind termination shock.
Abstract
The propagation of particles accelerated at supernova remnant shocks and escaping the parent remnants is likely to proceed in a strongly non-linear regime, due to the efficient ...self-generation of Alfvén waves excited through streaming instability near the sources. Depending on the amount of neutral hydrogen present in the regions around the sites of supernova explosions, cosmic rays may accumulate an appreciable grammage in the same regions and get self-confined for non-negligible times, which in turn results in an enhanced rate of production of secondaries. Here we calculate the contribution to the diffuse gamma-ray background due to the overlap along lines of sight of several of these extended haloes as due to pion production induced by self-confined cosmic rays. We find that if the density of neutrals is low, the haloes can account for a substantial fraction of the diffuse emission observed by Fermi-Large Area Telescope (LAT), depending on the orientation of the line of sight with respect to the direction of the Galactic Centre.
Pulsars with high spin-down power produce relativistic winds radiating a non-negligible fraction of this power over the whole electromagnetic range from radio to gamma-rays in the pulsar wind nebulae ...(PWNe). The rest of the power is dissipated in the interactions of the PWNe with the ambient interstellar medium (ISM). Some of the PWNe are moving relative to the ambient ISM with supersonic speeds producing bow shocks. In this case, the ultrarelativistic particles accelerated at the termination surface of the pulsar wind may undergo reacceleration in the converging flow system formed by the plasma outflowing from the wind termination shock and the plasma inflowing from the bow shock. The presence of magnetic perturbations in the flow, produced by instabilities induced by the accelerated particles themselves, is essential for the process to work. A generic outcome of this type of reacceleration is the creation of particle distributions with very hard spectra, such as are indeed required to explain the observed spectra of synchrotron radiation with photon indices
Γ
≲
1.5
. The presence of this hard spectral component is specific to PWNe with bow shocks (BSPWNe). The accelerated particles, mainly electrons and positrons, may end up containing a substantial fraction of the shock ram pressure. In addition, for typical ISM and pulsar parameters, the
e
+
released by these systems in the Galaxy are numerous enough to contribute a substantial fraction of the positrons detected as cosmic ray (CR) particles above few tens of GeV and up to several hundred GeV. The escape of ultrarelativistic particles from a BSPWN—and hence, its appearance in the far-UV and X-ray bands—is determined by the relative directions of the interstellar magnetic field, the velocity of the astrosphere and the pulsar rotation axis. In this respect we review the observed appearance and multiwavelength spectra of three different types of BSPWNe: PSR J0437-4715, the Guitar and Lighthouse nebulae, and Vela-like objects. We argue that high resolution imaging of such objects provides unique information both on pulsar winds and on the ISM. We discuss the interpretation of imaging observations in the context of the model outlined above and estimate the BSPWN contribution to the positron flux observed at the Earth.
ABSTRACT
The ratio between secondary and primary cosmic ray (CR) particles is the main source of information about CR propagation in the Galaxy. Primary CRs are thought to be accelerated mainly in ...supernova remnant shocks and then released in the interstellar medium. Here, they produce secondary particles by occasional collisions with interstellar matter. As a result, the ratio between the fluxes of secondary and primary particles carries information about the amount of matter CRs have encountered during their journey from their sources to the Earth. Recent measurements by AMS-02 revealed an unexpected behaviour of two main secondary-to-primary ratios, the Boron-to-Carbon ratio and the antiproton-to-proton ratio. In this work, we discuss how such anomalies may reflect the action of two phenomena that are usually overlooked, namely the fact that some fraction of secondary particles can be produced within the acceleration region, and the non-negligible probability that secondary particles encounter an accelerator (and are re-accelerated) during propagation. Both effects must be taken into account in order to correctly extract information about CR transport from secondary-to-primary ratios.
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This non-linear process adds to the non-linear modification of the ...shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients, we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time; charged particles are accelerated in the background of Alfvén waves that they generate due to the streaming instability, and modify the dynamics of the plasma in the shock vicinity.
The supernova paradigm for the origin of galactic cosmic rays has been deeply affected by the development of the non-linear theory of particle acceleration at shock waves. Here we discuss the ...implications of applying such theory to the calculation of the spectrum of cosmic rays at Earth as accelerated in supernova remnants and propagating in the Galaxy. The spectrum is calculated taking into account the dynamical reaction of the accelerated particles on the shock, the generation of magnetic turbulence which enhances the scattering near the shock, and the dynamical reaction of the amplified field on the plasma. Most important, the spectrum of cosmic rays at Earth is calculated taking into account the flux of particles escaping from upstream during the Sedov–Taylor phase and the adiabatically decompressed particles confined in the expanding shell and escaping at later times. We show how the spectrum obtained in this way is well described by a power law in momentum with spectral index close to −4, despite the concave shape of the instantaneous spectra of accelerated particles. On the other hand we also show how the shape of the spectrum is sensible to details of the acceleration process and environment which are and will probably remain very poorly known.
ABSTRACT
Pulsar wind nebulae (PWNe) represent the largest class of sources that upcoming γ-ray surveys will detect. Therefore, accurate modelling of their global emission properties is one of the ...most urgent problems in high-energy astrophysics. Correctly characterizing these dominant objects is a needed step to allow γ-ray surveys to detect fainter sources, investigate the signatures of cosmic ray propagation, and estimate the diffuse emission in the Galaxy. In this paper, we present an observationally motivated construction of the Galactic PWNe population. We made use of a modified one-zone model to evolve for a long period of time the entire population. The model provides, for every source, at any age, a simplified description of the dynamical and spectral evolution. The long-term effects of the reverberation phase on the spectral evolution are described, for the first time, based on physically motivated prescriptions for the evolution of the nebular radius supported by numerical studies. This effort tries to solve one of the most critical aspects of one-zone modelling, namely the typical overcompression of the nebula during the reverberation phase, resulting in a strong modification of its spectral properties at all frequencies. We compare the emission properties of our synthetic PWNe population with the most updated catalogues of TeV Galactic sources. We find that the firmly identified and candidate PWNe sum up to about 50 per cent of the expected objects in this class above threshold for detection. Finally, we estimate that Cherenkov Telescope Array will increase the number of TeV-detected PWNe by a factor of ≳3.
Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are ...known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles, pmax, decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t, particles with momenta larger than pmax(t) leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.
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