arXiv subjects

J. G. Kirk

Publications and source records attributed to J. G. Kirk.

At least 55 records · Page 3Linked to original sources

arXiv2001

Shock Acceleration of Cosmic Rays - a critical review

Motivated by recent unsuccessful efforts to detect the predicted flux of TeV gamma-rays from supernova remnants, we present a critical examination of the theory on which these predictions are based. Three crucial problems are identified: injection, maximum achievable particle energy and spectral index. In each case significant new advances in understanding have been achieved, which cast doubt on prevailing paradigms such as Bohm diffusion and single-fluid MHD. This indicates that more realistic analytical models, backed by more sophisticated numerical techniques should be employed to obtain reliable predictions. Preliminary work on incorporating the effects of anomalous transport suggest that the resulting spectrum should be significantly softer than that predicted by conventional theory.

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arXiv2000

Particle acceleration at ultrarelativistic shocks: an eigenfunction method

We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock fronts to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo simulations, we find the index of the power-law distribution of accelerated particles which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock is s=4.23 (where s=-d(ln f)/dp with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of a=0.62 (taking cooling into account a=1.12), where a=-d(ln F)/dn, F is the radiation flux and n the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the non-relativistic case the angular distribution is weighted more towards the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the ratio of Poynting to kinetic energy flux upstream is not small are less compressive and lead to larger values of $s$.

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arXiv2000

Reconnection in a striped pulsar wind

It is generally thought that most of the spin-down power of a pulsar is carried away in an MHD wind dominated by Poynting flux. In the case of an oblique rotator, a significant part of this energy can be considered to be in a low-frequency wave, consisting of stripes of toroidal magnetic field of alternating polarity, propagating in a region around the equatorial plane. Magnetic reconnection in such a structure has been proposed as a mechanism for transforming the Poynting flux into particle energy in the pulsar wind. We have re-examined this process and conclude that the wind accelerates significantly in the course of reconnection. This dilates the timescale over which the reconnection process operates, so that the wind requires a much larger distance than was previously thought in order to convert the Poynting flux to particle flux. In the case of the Crab, the wind is still Poynting-dominated at the radius at which a standing shock is inferred from observation. An estimate of the radius of the termination shock for other pulsars implies that all except the milli-second pulsars have Poynting-flux dominated winds all the way out to the shock front.

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arXiv2000

On the nonthermal X-ray emission in blazar jets

We consider particle acceleration to high energy via diffusive shock acceleration in a simple, self-consistent shock in jet model for blazars. Electrons are assumed to be accelerated at a shock front in relativistic jets and radiate synchrotron emission in a post-shock region. The full time, space and momentum dependence of the electron distribution function is used for a calculation of the nonthermal synchrotron spectra. We discuss the evolution of the spectral index by varying the rate at which particles enter the acceleration process. The results indicate that the synchrotron spectral index displays a characteristic looplike behaviour with intensity (as has been observed in several blazars), where the orientation of the loop depends on whether the acceleration time scale is comparable to the synchrotron cooling time scale or not. We show that our model provides a good fit to the observed evolution of the spectral index of Mkn 421 during a flare in 1994.

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arXiv1999

Probing Pulsar Winds Using Inverse Compton Scattering

We investigate the effects of inverse Compton scattering by electrons and positrons in the unshocked winds of rotationally-powered binary pulsars. This process can scatter low energy target photons to produce gamma rays with energies from MeV to TeV. The binary radio pulsars PSR B1259-63 and PSR J0045-73 are both in close eccentric orbits around bright main sequence stars which provide a huge density of low energy target photons. The inverse Compton scattering process transfers momentum from the pulsar wind to the scattered photons, and therefore provides a drag which tends to decelerate the pulsar wind. We present detailed calculations of the dynamics of a pulsar wind which is undergoing inverse Compton scattering, showing that the deceleration of the wind of PSR B1259-63 due to `inverse Compton drag' is small, but that this process may confine the wind of PSR J0045-73 before it attains pressure balance with the outflow of its companion star. We calculate the spectra and light curves of the resulting inverse Compton emission from PSR B1259-63 and show that if the size of the pulsar wind nebula is comparable to the binary separation, then the gamma-ray emission from the unshocked wind may be detectable by atmospheric Cerenkov detectors or by the new generation of satellite-borne gamma-ray detectors such as INTEGRAL and GLAST. This mechanism may therefore provide a direct probe of the freely-expanding regions of pulsar winds, previously thought to be invisible.

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arXiv1999

Monte-Carlo simulation of particle acceleration in braided magnetic fields

Supernova remnants are expected to contain braided (or stochastic) magnetic fields, which are in some regions directed mainly perpendicular to the shock normal. For particle acceleration due to repeated shock crossings, the transport in the direction of the shock normal is crucial. The mean squared deviation along the shock normal is then proportional to the square root of the time. This kind of anomalous transport is called sub-diffusion. We use a Monte-Carlo method to examine this non-Markovian transport and the acceleration. As a result of this simulation we are able to examine the propagator, density and pitch-angle distribution of accelerated particles, and especially the spectral properties. These are in broad agreement with analytic predictions for both the sub-diffusive and the diffusive regimes, but the steepening of the spectrum predicted when changing from diffusive to sub-diffusive transport is found to be even more pronounced than predicted.

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arXiv1999

Computation of diffusive shock acceleration using stochastic differential equations

The present work considers diffusive shock acceleration at non-relativistic shocks using a system of stochastic differential equations (SDE) equivalent to the Fokker-Planck equation. We compute approximate solutions of the transport of cosmic particles at shock fronts with a SDE numerical scheme. The momentum gain is given by implicit calculations of the fluid velocity gradients using a linear interpolation between two consecutive time steps. We validate our procedure in the case of single shock acceleration with different shock thickness, with or without synchrotron losses. A comparative discussion of implicit and explicit schemes for different shock thickness shows that implicit calculations extend the range of applicability of SDE schemes to infinitely thin 1D shocks. The method is then applied to multiple shock acceleration for a system of identical shocks which free parameters are the distance between two consecutive shocks, the synchrotron losses time and the escape time of the particles. The stationary distribution reproduces quite well the flat differential logarithm energy distribution produced by multiple shock effect, and also the piling-up effect due synchrotron losses at a momentum where they equilibrate the acceleration rate. At higher momenta particle losses dominate and the spectrum drops. The competition between acceleration and loss effects leads to a pile-up shaped distribution which appears to be effective only in a restrict range of inter-shock distances of 10-100 diffusion lengths. We finally compute the optically thin synchrotron spectrum produced such periodic pattern which can explain flat and/or inverted spectra observed in Flat Radio spectrum Quasars and in the galactic centre.

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arXiv1999

Particle acceleration and relativistic shocks

Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising the astrophysically interesting cases. This is followed by an overview of the theory of particle acceleration at such shocks. We summarise the applications to the astrophysics of relativistic jets and fireball models of gamma-ray-bursts.

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arXiv1999

Models of variability in blazar jets

We present the expected variability features in the context of the Synchro- Self-Compton (SSC) model of emission from Active Galactic Nuclei (AGNs) and show that the homogeneous SSC model describes well the observed multi- wavelength spectrum and variability of objects such as Mkn 421 and Mkn 501; however in order to explain the very fast flaring timescales occasionally observed from these objects one should use a laminar, rather than spherical, source geometry. This picture leads naturally to a shock-in- jet model which we approach as a site of diffusive particle acceleration. We show that this acceleration scheme can explain certain characteristic features of AGN X-ray spectra and provides us with further observational tests.

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arXiv1999

Particle acceleration at oblique shocks and discontinuities of the density profile

In the theory of diffusive acceleration at oblique shock fronts the question of the existence of a discontinuity of energetic particle density is contentious. The resolution of this problem is interesting from a theoretical point of view, and potentially for the interpretation of observations of particle densities at heliospheric shocks and of high-resolution radio observations of the rims of supernova remnants. It can be shown analytically that an isotropic particle distribution at a shock front implies continuity of the particle density -- whether or not the shock is oblique. However, if the obliquity of the shock induces an anisotropy, a jump is permitted. Both semi-analytic computations and Monte-Carlo simulations are used to show that, for interesting parameter ranges, a jump is indeed produced, with accelerated particles concentrated in a precursor ahead of the shock front.

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arXiv1998

Inverse Compton Emission of TeV Gamma Rays from PSR B1259-63

We derive light curves for the hard gamma-ray emission, at energies up to several TeV, expected from the unique pulsar/Be-star binary system PSR B1259-63. This is the only known system in our galaxy in which a radio pulsar is orbiting a main sequence star. We show that inverse Compton emission from the electrons and positrons in the shocked pulsar wind, scattering target photons from the Be star, produces a flux of hard gamma-rays that should be above the sensitivity threshold of present day atmospheric Cerenkov detectors. Furthermore, we predict that the flux of hard gamma-rays produced via this mechanism has a characteristic variation with orbital phase that should be observable, and which is not expected from any other mechanism.

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arXiv1998

Comment on: Diffusion through a slab

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick & Kuscer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalised to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.

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arXiv1998

Particle acceleration and synchrotron emission in blazar jets

We model the acceleration of electrons at a shock front in a relativistic blazar jet and compute the radiation they emit in a post-shock region which contains a homogeneous magnetic field. The full space, time and momentum dependence of the electron distribution is used in this calculation. It is shown that the "homogeneous" synchrotron model is recovered, provided the downstream speed of the plasma away from the shock front is nonrelativistic, and provided that the light travel times across the face of the shock front is unimportant. By varying the rate at which particles are picked up by the acceleration process, we calculate the time-dependence of the spectra. Since the magnetic field strength is assumed constant within the emission region, each frequency band can be identified with electrons of a particular energy. We find that for a band in which the electrons are accelerated rapidly compared to the rate at which they cool, the spectra typically harden during phases of rising flux, and soften during phases of falling flux, as has been observed in the objects PKS 2155-304 and Mkn 421. However, in a frequency band in which the timescales are comparable, the reverse behaviour is to be expected. We discuss the extent to which observations of both the stationary spectrum and the spectral variability of the synchrotron component of blazar emission can be used to constrain the model.

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arXiv1997

Particle acceleration at shocks in relativistic jets

The theory of particle acceleration at shock fronts is briefly reviewed, with special emphasis on the production of the particles responsible for the nonthermal emission from blazars. The flat radio/IR spectra of these sources cannot be produced by diffusive acceleration at a simple nonrelativistic shock front propagating in a homogeneous medium. It can, however, be produced by a single unmodified mildly relativistic shock, if the pressure in the shocked gas is provided by the leptonic component, or, independently of the equation of state, by a relativistic shock which is oblique to the magnetic field. The analytic theory of these shocks makes several simplifications, but Monte-Carlo simulations exist which extend the range of validity. Of particular interest is acceleration in a tangled magnetic field. Here, however, the Monte-Carlo simulations have not yet yielded unambiguous results. The "homogeneous" models of blazar emission are discussed, and is it shown that they imply a geometry of the emitting region which is laminar in form, with an aspect ratio of d/R< 3% in the case of Mkn~421. Identifying these with relativistic shock fronts, a model of acceleration is described, which displays characteristic variations in the synchrotron spectral index with intensity.

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arXiv1997

Anomalous transport of cosmic ray electrons

Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the required dependence on space and time and use these to find the spatial dependence of the synchrotron radiation emitted by a population of continuously injected electrons. As the electrons are transported away from the source they cool, and the synchrotron spectrum softens. Sub-diffusive transport -- corresponding to stochastic trapping, or restriction of the transport across the average direction of a stochastic magnetic field -- produces a much slower rate of change of spectral index than does supra-diffusion -- which occurs when particles move almost without scattering, in a field containing large ordered regions. Application to the diffuse emission of the outer parts of the Coma cluster favours an interpretation in terms of supra-diffusion.

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arXiv1996

An eigenfunction method for the comptonisation problem. Angular distribution and spectral index of radiation from a disk

We present a semi-analytic approach to solving the Boltzmann equation describing the comptonisation of low frequency input photons by a thermal distribution of electrons in the Thomson limit. Our work is based on the formulation of the problem by Titarchuk & Lyubarskij (ApJ 450 (1995) 876), but extends their treatment by accommodating an arbitrary anisotropy of the source function. To achieve this, we expand the eigenfunctions of the integro/differential eigenvalue problem defining the spectral index of comptonised radiation in terms of Legendre polynomials and Chebyshev polynomials. The resulting algebraic eigenvalue problem is then solved by numerical means, yielding the spectral index and the full angular and spatial dependence of the specific intensity of radiation. For a thin (τ_0 < 1) plasma disk, the radiation is strongly collimated along the disk surface - for an optical thickness of τ_0 = 0.05, the radiation intensity along the surface is roughly ten times that along the direction of the normal, and varies only slightly with the electron temperature. Our results for the spectral index confirm those of Titarchuk & Lyubarskij over a wide range of electron temperature and optical depth; the largest difference we find is roughly 10% and occurs at low optical depth.

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arXiv1996

Variability in the synchrotron self-Compton model of blazar emission

We present a model of the spectra of gamma-ray emitting blazars in which a single homogeneous emission region both emits synchrotron photons directly and scatters them to high (gamma-ray) energy before emission (a ``synchrotron self-Compton'' or SSC model). In contrast to previous work, we follow the full time dependent evolution of the electron and photon spectra, assuming a power-law form of the electron injection and examine the predictions of the model with regard to variability of the source. We apply these computations to the object Mkn 421, which displayed rapid variability in its X-ray and TeV emission during a multiwavelength campaign in 1994. This observation strongly implies that the same population of electrons produces the radiation in both energy bands. By fitting first the observed quiescent spectrum over all 18 orders of magnitude in frequency, we show that the time dependence of the keV/TeV flare could have been the result of a sudden increase in the maximum energy of the injected electrons. We show also that different types of flare may occur in this object and others, and that the energy band most sensitive to the properties of the acceleration mechanism is the X-ray band.

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arXiv1996

Stochastic particle acceleration at shocks in the presence of braided magnetic fields

The theory of diffusive acceleration of energetic particles at shock fronts assumes charged particles undergo spatial diffusion in a uniform magnetic field. If, however, the magnetic field is not uniform, but has a stochastic or braided structure, the transport of charged particles across the average direction of the field is more complicated. Assuming quasi-linear behaviour of the field lines, the particles undergo sub-diffusion on short time scales. We derive the propagator for such motion, which differs from the Gaussian form relevant for diffusion, and apply it to a configuration with a plane shock front whose normal is perpendicular to the average field direction. Expressions are given for the acceleration time as a function of the diffusion coefficient of the wandering magnetic field lines and the spatial diffusion coefficient of the charged particles parallel to the local field. In addition we calculate the spatial dependence of the particle density in both the upstream and downstream plasmas. In contrast to the diffusive case, the density of particles at the shock front is lower than it is far downstream. This is a consequence of the partial trapping of particles by structures in the magnetic field. As a result, the spectrum of accelerated particles is a power-law in momentum which is steeper than in the diffusive case. For a phase- space density $f\propto p^{-s}$, we find $s=\sdiff[1+1/(2\rcomp)]$, where $\rcomp$ is the compression ratio of the shock front and $\sdiff$ is the standard result of diffusive acceleration: $\sdiff=3\rcomp/(\rcomp-1)$. A strong shock in a monatomic ideal gas yields a spectrum of $s=4.5$. In the case of electrons, this corresponds to a radio synchrotron spectral index of $α=0.75$.

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