arXiv subjects

John G. Kirk

Publications and source records attributed to John G. Kirk.

At least 19 recordsLinked to original sources

arXiv2025

Spectral curvature and breaks from Fermi acceleration at oblique shocks

A major attraction of diffusive shock acceleration is the prediction of power-law spectra for energetic particle distributions. However, this property is not fundamental to the theory. We demonstrate that for planar shocks with an oblique magnetic field the generation of power-law spectra critically requires the particles' scattering rate to be both directly proportional to their gyro radius (Bohm scaling) and spatially uniform. Non-Bohm scaling results in curved spectra at oblique shocks, while abrupt changes in the spatial profile of the scattering upstream introduces spectral breaks. Using the publicly available code Sapphire++, we numerically explore the magnitude of these effects, which are particularly pronounced at fast shocks, as expected in active galactic nuclei and microquasar jets, or young supernova remnants.

astro-ph.HE↗

arXiv2023

Prospects for ultra-high-energy particle acceleration at relativistic shocks

We study the acceleration of charged particles by ultra-relativistic shocks using test-particle Monte-Carlo simulations. Two field configurations are considered: (i) shocks with uniform upstream magnetic field in the plane of the shock, and (ii) shocks in which the upstream magnetic field has a cylindrical geometry. Particles are assumed to diffuse in angle due to frequent non-resonant scattering on small-scale fields. The steady-state distribution of particles' Lorentz factors is shown to approximately satisfy $dN/dγ\propto γ^{-2.2}$ provided the particle motion is scattering dominated on at least one side of the shock. For scattering dominated transport, the acceleration rate scales as $t_{\rm acc}\propto t^{1/2}$, though recovers Bohm scaling $t_{\rm acc}\propto t$ if particles become magnetised on one side of the shock. For uniform field configurations, a limiting energy is reached when particles are magnetised on both sides of the shock. For the cylindrical field configuration, this limit does not apply, and particles of one sign of charge will experience a curvature drift that redirects particles upstream. For the non-resonant scattering model considered, these particles preferentially escape only when they reach the confinement limit determined by the finite system size, and the distribution approaches the escapeless limit $dN/dγ\propto γ^{-1}$. The cylindrical field configuration resembles that expected for jets launched by the Blandford $\&$ Znajek mechanism, the luminous jets of AGN and GRBs thus provide favourable sites for the production of ultra-high energy cosmic rays.

astro-ph.HE↗

arXiv2022

Particle acceleration at ultrarelativistic, perpendicular shock fronts

Using an eigenfunction expansion to solve the transport equation, complemented by Monte-Carlo simulations, we show that ultrarelativistic shocks can be effective particle accelerators even when they fail to produce large amplitude turbulence in the downstream plasma. This finding contradicts the widely held belief that a uniform downstream magnetic field perpendicular to the shock normal inhibits acceleration by the first order Fermi process. In the ultrarelativistic limit, we find a stationary power-law particle spectrum of index s=4.17 for these shocks, close to that predicted for a strictly parallel shock.

physics.plasm-ph↗

arXiv2019

Electron Acceleration in the Crab Nebula

We study electron and positron acceleration at the termination shock of a striped pulsar wind. Drift motion along the shock surface keeps either electrons or positrons -but not both, close to the equatorial plane of the pulsar, where they are accelerated by the first-order Fermi process. Their energy spectrum is a power law, and both the X-ray flux and photon index of the Crab Nebula, as measured by NuSTAR, can be reproduced for sufficiently large downstream turbulence levels. The implication that one sign of charge is preferentially accelerated in pulsar wind nebulae is potentially important for the interpretation of the positron fraction in cosmic-rays.

astro-ph.HE↗

arXiv2019

Inductive acceleration of ions in Poynting-flux dominated outflows

Two-fluid (electron-positron) plasma modelling has shown that inductive acceleration can convert Poynting flux directly into bulk kinetic energy in the relativistic flows driven by rotating magnetized neutron stars and black holes. Here, we generalize this approach by adding an ion fluid. Solutions are presented in which all particles are accelerated as the flow expands, with comparable power channeled into each of the plasma components. In an ion-dominated flow, each species reaches the limiting rigidity, according to Hillas' criterion, in a distance significantly shorter than in a lepton-dominated flow. These solutions support the hypothesis that newly born magnetars and pulsars are potential sources of ultra-high energy cosmic rays. The competing process of Poynting flux dissipation by magnetic reconnection is shown to be ineffective in low-density flows in which the conventionally defined electron multiplicity satisfies $κ_{\rm e}\lesssim 10^5\left(4πL_{38}/Ω\right)^{1/4} /\textrm{Max}\left(η_{\rm ion}^{1/2},1\right)$, where $L_{38}\times 10^{38}\textrm{erg s}^{-1}$ is the power carried by the flow in a solid angle $Ω$, and $η_{\rm ion}$ is the ratio of the ion to lepton power at launch.

astro-ph.HE↗

arXiv2018

TeV-PeV Cosmic-Ray Anisotropy and Local Interstellar Turbulence

We calculate the shape of the large-scale anisotropy of TeV-PeV cosmic-rays (CR) in different models of the interstellar turbulence. In general, the large-scale CR anisotropy (CRA) is not a dipole, and its shape can be used as a new probe of the turbulence. The 400 TeV and 2 PeV data sets of IceTop can be fitted with Goldreich-Sridhar turbulence and a broad resonance function, but other possibilities are not excluded. We then present our first numerical calculations of the CRA down to 3 TeV energies in 3D isotropic Kolmogorov turbulence. At these low energies, the large-scale CRA aligns well with the direction of local magnetic field lines around the observer. In this type of turbulence, the CR intensity is flat in a broad region perpendicular to field lines. Even though the CRA is quite gyrotropic, we show that the local configuration of the turbulence around the observer does result in the appearance of weak, "non-gyrotropic" small-scale anisotropies, which contain information on the local turbulence level.

astro-ph.HE↗

arXiv2018

Acceleration of X-ray Emitting Electrons in the Crab Nebula

We study particle acceleration at the termination shock of a striped pulsar wind by integrating trajectories in a prescribed model of the magnetic field and flow pattern. Drift motion on the shock surface maintains either electrons or positrons on "Speiser" orbits in a ring-shaped region close to the equatorial plane of the pulsar, enabling them to be accelerated to very high energy by the first-order Fermi mechanism. A power-law spectrum results: $dN_{\rm e}/dγ\proptoγ^{α_{\rm e}}$, where $α_{\rm e}$ lies in the range $-1.8$ to $-2.4$ and depends on the downstream turbulence level. For sufficiently strong turbulence, we find $α_{\rm e} \simeq -2.2$, and both the photon index and the flux of $1-100$ keV X-rays from the Crab Nebula, as measured by NuSTAR, can be reproduced. The particle spectrum hardens to $α_{\rm e} \simeq -1.8$ at lower turbulence levels, which may explain the hard photon index observed by the Chandra X-ray Observatory in the central regions of the Nebula.

astro-ph.HE↗

arXiv2017

Inductive spikes and gamma-ray flares from the Crab Nebula

The ~400 MeV flaring emission from the Crab Nebula is naturally explained as the result of an abrupt reduction in the mass-loading of the pulsar wind. Very few particles are then available to carry the current required to maintain wave activity, causing them to achieve high Lorentz factors. When they penetrate the Nebula, a tightly beamed, high luminosity burst of hard gamma-rays results, with characteristics similar to the observed flares. This mechanism may operate in other powerful pulsars, such as J0537-6910 (PWN N 157B), B0540-69, B1957+20 and J0205+6449 (3C 58).

astro-ph.HE↗

arXiv2017

Inductive spikes in the Crab Nebula - a theory of gamma-ray flares

We show that the mysterious, rapidly variable emission at ~400 MeV observed from the Crab Nebula by the AGILE and Fermi experiments could be the result of a sudden drop in the mass-loading of the pulsar wind. The current required to maintain wave activity in the wind is then carried by very few particles of high Lorentz factor. On impacting the Nebula, these particles produce a tightly beamed, high luminosity burst of hard gamma-rays, similar to those observed. This implies (i) the emission is synchrotron radiation in the toroidal field of the Nebula, and, therefore, linearly polarized and (ii) this mechanism potentially contributes to the gamma-ray emission from other powerful pulsars, such as the Magellanic Cloud objects J0537-6910 and B0540-69.

astro-ph.HE↗

arXiv2017

Large-Scale Cosmic-Ray Anisotropy as a Probe of Interstellar Turbulence

We calculate the large-scale cosmic-ray (CR) anisotropies predicted for a range of Goldreich-Sridhar (GS) and isotropic models of interstellar turbulence, and compare them with IceTop data. In general, the predicted CR anisotropy is not a pure dipole; the cold spots reported at 400 TeV and 2 PeV are consistent with a GS model that contains a smooth deficit of parallel-propagating waves and a broad resonance function, though some other possibilities cannot, as yet, be ruled out. In particular, isotropic fast magnetosonic wave turbulence can match the observations at high energy, but cannot accommodate an energy dependence in the shape of the CR anisotropy. Our findings suggest that improved data on the large-scale CR anisotropy could provide a valuable probe of the properties - notably the power-spectrum - of the interstellar turbulence within a few tens of parsecs from Earth.

astro-ph.HE↗

arXiv2017

Cosmic-Ray Anisotropy and the Local Interstellar Turbulence

We study the role of local interstellar turbulence in shaping the large-scale anisotropy in the arrival directions of TeV-PeV cosmic-rays (CRs) on the sky. Assuming pitch-angle diffusion of CRs in a magnetic flux tube containing the Earth, we compute the CR anisotropy for Goldreich-Sridhar turbulence, and for isotropic fast modes. The narrow deficits in the 400 TeV and 2 PeV data sets of IceTop can be fitted for some parameters of the turbulence. The data also rule out a part of the parameter space. The shape of the CR anisotropy may be used as a local probe of the still poorly known properties of the interstellar turbulence and of CR transport.

astro-ph.HE↗

arXiv2016

Electron acceleration at pulsar wind termination shocks

We study the acceleration of electrons and positrons at an electromagnetically modified, ultra-relativistic shock in the context of pulsar wind nebulae (PWNe). We simulate the outflow produced by an obliquely rotating pulsar in proximity of its termination shock with a two-fluid code which uses a magnetic shear wave to mimic the properties of the wind. We integrate electron trajectories in the test-particle limit in the resulting background electromagnetic fields to analyse the injection mechanism. We find that the shock-precursor structure energizes and reflects a sizeable fraction of particles, which becomes available for further acceleration. We investigate the subsequent first-order Fermi process sustained by small-scale magnetic fluctuations with a Monte Carlo code. We find that the acceleration proceeds in two distinct regimes: when the gyro-radius $r_{\textrm{g}}$ exceeds the wavelength of the shear $λ$, the process is remarkably similar to first-order Fermi acceleration at relativistic, parallel shocks. This regime corresponds to a low density wind which allows the propagation of superluminal waves. When $r_{\textrm{g}}<λ$, which corresponds to the scenario of driven reconnection, the spectrum is softer.

astro-ph.HE↗

arXiv2015

Rapid cosmic-ray acceleration at perpendicular shocks in supernova remnants

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio $u_{\rm s}$ of the shock speed to the particle speed roughly equals the ratio $1/η$ of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy generated at these shocks, and find, for $ηu_{\rm s}\approx1$, that the spectral index softens by unity and the acceleration time increases by a factor of two compared to the standard result of diffusive shock acceleration theory. These results provide a theoretical basis for the thirty-year-old conjecture that a supernova exploding into the wind of a Wolf-Rayet star may accelerate protons to an energy exceeding $10^{15}\,$eV.

astro-ph.HE↗

arXiv2013

The stability of strong waves and its implications for pulsar wind shocks

Strong waves can mediate a shock transition between a pulsar wind and its surroundings, playing the role of an extended precursor, in which the energy is effectively transferred from fields to non-thermal particles. The damping of such precursors results in an essentially unmagnetized shock near the equator. In this context, we discuss the stability of strong waves and its implications for the properties of shocks. Those with stable precursors can exist in the winds of most of isolated pulsars, but the precursors may be unstable if the external pressure in the nebula is high, as in Vela-like pulsars. Pulsar wind shocks in eccentric binary systems, such as B1259-63, can acquire precursors only at certain orbital phases, and this process should be accompanied by enhanced synchro-Compton and inverse Compton emission from the precursor. The same scenario may be at work in the binary HESS J0632+057.

astro-ph.HE↗

arXiv2013

Radiative damping and emission signatures of strong superluminal waves in pulsar winds

We analyse the damping by radiation reaction and by Compton drag of strong, superluminal electromagnetic waves in the context of pulsar winds. The associated radiation signature is found by estimating the efficiency and the characteristic radiation frequencies. Applying these estimates to the gamma-ray binary containing PSR B1259-63, we show that the GeV flare observed by Fermi-LAT can be understood as inverse Compton emission by particles scattering photons from the companion star, if the pulsar wind termination shock acquires a precursor of superluminal waves roughly 30 days after periastron. This constrains the mass-loading factor of the wind $μ=L/\dot{N}mc^2$ (where $L$ is the luminosity and $\dot{N}$ the rate of loss of electrons and positrons) to be roughly $6\times 10^4$.

astro-ph.HE↗

arXiv2013

Propagation and stability of superluminal waves in pulsar winds

Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system of equations that govern their evolution in spherical geometry. A confined mode is identified that stagnates to finite pressure at large radius and can form a precursor to the termination shock. Using a simplified criterion, we find this mode is stable for most isolated pulsars, but may be unstable if the external pressure is high, such as in the pulsar wind nebulae in starburst galaxies and in W44. Pulsar winds in eccentric binary systems, such as PSR 1259-63, may go through phases with stable and unstable electromagnetic precursors, as well as phases in which the density is too high for these modes to propagate.

astro-ph.HE↗

arXiv2013

The Role of Superluminal Electromagnetic Waves in Pulsar Wind Termination Shocks

The dynamics of a standing shock front in a Poynting-flux dominated relativistic flow is investigated by using a one-dimensional, relativistic, two-fluid simulation. An upstream flow containing a circularly polarized, sinusoidal magnetic shear wave is considered, mimicking a wave driven by an obliquely rotating pulsar. It is demonstrated that this wave is converted into large amplitude electromagnetic waves with superluminal phase speeds by interacting with the shock when the shock-frame frequency of the wave exceeds the proper plasma frequency. The superluminal waves propagate in the upstream, modify the shock structure substantially, and form a well-developed precursor region ahead of a subshock. Dissipation of Poynting flux occurs in the precursor as well as in the downstream region through a parametric instability driven by the superluminal waves. The Poynting flux remaining in the downstream region is carried entirely by the superluminal waves. The downstream plasma is therefore an essentially unmagnetized, relativistically hot plasma with a non-relativistic flow speed, as suggested by observations of pulsar wind nebulae.

astro-ph.HE↗

arXiv2013

Superluminal Waves and the Structure of Pulsar Wind Termination Shocks

The termination shock of a pulsar wind is located roughly where the ram pressure matches that of the surrounding medium. Downstream of the shock, MHD models of the diffuse nebular emission suggest the plasma is weakly magnetized. However, the transition from a Poynting-dominated MHD wind to a particle-dominated flow is not well understood. We discuss a solution of this "sigma problem" in which a striped wind converts into a strong, superluminal electromagnetic wave. This mode slows down as it propagates radially, and its ram pressure tends to a constant value at large radius, a property we use to match the solution to the surrounding nebula. The wave thus forms a pre-cursor to the termination shock, which occurs at the point where the wave dissipates. Possible damping and dissipation mechanisms are discussed qualitatively.

astro-ph.HE↗