Peter Duffy

Fermi acceleration in astrophysical jets

Abstract We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given to recent progress in the field of viscous shear acceleration. We analyze the associated acceleration timescales and the resulting particle distributions, and discuss the relevance of these processes for the acceleration of charged particles in the jets of AGN, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.

The transport of Cosmic Rays in Self‐Excited Magnetic Turbulence

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic ray driven instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic-ray transport and acceleration in supernova remnants.

Time-sequenced multi-radio-frequency observations of Cygnus X-3 in flare

Multifrequency observations from the Very Large Array, Very Long Baseline Array (VLBA), and Owens Valley Radio Observatory Millimeter Array of a major radio outburst of Cygnus X-3 in 2001 September are presented, measuring the evolution of the spectrum of the source over 3 decades in frequency, over a period of 6 days. Following the peak of the flare, as the intensity declines the high-frequency spectrum at frequency ν steepens from ν-0.4 to ν-0.6, after which the spectral index remains at this latter terminal value, a trend previously observed but hitherto not satisfactorily explained. VLBA observations, for the first time, track over several days the expansion of a sequence of knots whose initial diameters are ~8 mas. The light-crossing time within these plasmons is of the same order as the timescale over which the spectrum is observed to evolve. We contend that properly accounting for light-travel time effects in and between plasmons that are initially optically thick but that after expansion become optically thin explains the key features of the spectral evolution, for example, the observed timescale. Using the VLBA images, we have directly measured for the first time the proper motions of individual knots, analysis of which shows a two-sided jet whose axis is precessing. The best-fit jet speed is β ~ 0.63, and the precession period is ~5 days, significantly lower than that fitted for a previous flare. Extrapolation of the positions of the knots measured by the VLBA back to zero separation shows this to occur approximately 2.5 days after the detection of the rise in flux density of Cyg X-3.

Shear Acceleration in Relativistic Astrophysical Jets

We consider the acceleration of energetic particles by a velocity shear in the relativistic background flow containing scattering centers. Three possible acceleration sites for astrophysical jets are identified: (1) gradual velocity shear parallel to the jet axis, such as a velocity profile decreasing linearly outward with radial coordinates, (2) gradual velocity shear perpendicular to the jet axis, such as intrinsic jet rotation, and (3) nongradual and/or discontinuous longitudinal velocity shear at the jet-side boundary. We determine the characteristic acceleration timescales, specify the conditions for efficient acceleration, and discuss observational features with respect to each process. In particular, it is shown that in case 2 the higher energy emission is expected to be concentrated closer to the jet axis, while in cases 1 and 3 the higher energy particles are likely to be located near the edges of the jet, thus possibly leading to some form of limb brightening.

Steady-State Solutions in Nonlinear Diffusive Shock Acceleration

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space—particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off—a diagnostic that is in principle accessible to observation.

A current-driven instability in parallel, relativistic shocks

Recently, Bell (2004 Mon. Not. R. Astron. Soc. 353 550) has reanalysed the problem of wave excitation by cosmic rays propagating in the pre-cursor region of a supernova remnant shock front. He pointed out a strong, non-resonant, current-driven instability that had been overlooked in the kinetic treatments by Achterberg (1983 Astron. Astrophys. 119 274) and McKenzie and Volk (1982 Astron. Astrophys. 116 191), and suggested that it is responsible for substantial amplification of the ambient magnetic field. Magnetic field amplification is also an important issue in the problem of the formation and structure of relativistic shock fronts, particularly in relation to models of gamma-ray bursts. We have therefore generalized the linear analysis to apply to this case, assuming a relativistic background plasma and a monoenergetic, unidirectional incoming proton beam. We find essentially the same non-resonant instability observed by Bell and show that also, under GRB conditions, it grows much faster than the resonant waves. We quantify the extent to which thermal effects in the background plasma limit the maximum growth rate.

A cosmic ray current-driven instability in partially ionised media

Context. We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. Aims. It is known that transverse waves propagating parallel to the mean magnetic field are unstable to anisotropies in the cosmic ray distribution, and may provide a mechanism to substantially amplify the ambient magnetic field. We quantify the extent to which temperature and ionisation fractions modify this picture. Methods. Using a kinetic description of the plasma we derive the dispersion relation for a collisionless thermal plasma with a streaming cosmic ray current. Fluid equations are then used to discuss the effects of neutral-ion collisions. Results. We calculate the extent to which the environment into which the cosmic rays propagate influences the growth of the magnetic field, and determines the range of possible growth rates. Conclusions. If the cosmic ray acceleration is efficient, we find that very large neutral fractions are required to stabilise the growth of the non-resonant mode. For typical supernova parameters in our Galaxy, thermal effects do not significantly alter the growth rates. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions. In the case of a supernova shock interacting with a molecular clouds, such as in RX J1713.7-3946, with high density and low ionisation, the modes can be rapidly damped.

A Microscopic Analysis of Shear Acceleration

A microscopic analysis of the viscous energy gain of energetic particles in (gradual) nonrelativistic shear flows is presented. We extend previous work and derive the Fokker-Planck coefficients for the average rate of momentum change and dispersion in the general case of a momentum-dependent scattering time τ(p) ∝ pα with α ≥ 0. We show that in contrast to diffusive shock acceleration, the characteristic shear acceleration timescale depends inversely on the particle mean free path, which makes the mechanism particularly attractive for high-energy seed particles. Based on an analysis of the associated Fokker-Planck equation we show that above the injection momentum p0, power-law differential particle number density spectra n(p) ∝ p-(1+α) are generated for α > 0 if radiative energy losses are negligible. We discuss the modifications introduced by synchrotron losses and determine the contribution of the accelerated particles to the viscosity of the background flow. Possible implications for the plasma composition in mildly relativistic extragalactic jet sources are addressed.

Multiwavelength study of Cygnus A – II. X‐ray inverse‐Compton emission from a relic counterjet and implications for jet duty cycles

The duty cycles of powerful radio galaxies and quasars such as the prototype Cygnus A are poorly understood. X-ray observations of inverse-Compton-scattered cosmic microwave background (ICCMB) photons probe lower Lorentz-factor particles than radio observations of synchrotron emission, and thus potentially reveal a more aged population. Comparative studies of the nearer and farther lobes, separated by many tens of kiloparsecs and thus by tens of thousands of years in light-travel time, yield additional temporal resolution in studies of the life-cycles of such objects. We have co-added all archival Chandra ACIS-I data and present a deep 200-ks image of Cygnus A. This deep image reveals the presence of X-ray emission from a counterjet, i.e. a jet receding from Earth. The outer part of this counterjet does not overlie the current counterjet detected in radio emission, excluding the possibility that we are detecting the current counterjet in X-rays. This non-thermal X-ray emission has a power-law photon index of 1.7, and we interpret this emission as ICCMB radiation. There is an absence of any discernible X-ray emission associated with a jet flowing towards Earth. We make the following conclusions. (1) This emission is from a relic jet, indicating a previous episode of jet activity that took place prior to the current jet activity appearing as synchrotron radio emission. (2) The presence of X-ray emission from a relic counterjet of Cygnus A and the absence of X-ray emission associated with any relic approaching jet constrain the time-scale between successive episodes of jet activity to ∼10 6 yr. (3) Transverse expansion of the jet causes expansion losses, which shift the energy distribution to lower energies. Particles with initially high Lorentz factors, which originally gave detectable synchrotron radiation, attain Lorentz factors ∼10 3 and scatter CMB photons, to give X-ray emission. (4) Assuming that the electrons cooled as a result of adiabatic expansion, the required magnetic field strength is substantially smaller than the equipartition magnetic field strength. (5) A high minimum Lorentz factor for the distribution of relativistic particles in the current jet, of a few 10 3 , seems to emerge from the central nucleus of this active galaxy.

A Model for the Radio Emission from SNR 1987A

The observations of radio emission from SNR~1987A can be accounted for on the basis of diffusive shock acceleration of electrons by the supernova blast wave. However, with this interpretation the observed spectral index implies that the compression ratio of the gas subshock is roughly