arXiv subjects

Peter Duffy

Publications and source records attributed to Peter Duffy.

At least 19 recordsLinked to original sources

arXiv2025

Synchrotron-limited Particle Acceleration in Relativistic Shearing Flows

Fermi-type shear particle acceleration is a promising mechanism for sustaining ultra-relativistic particles along the kilo-parsec scale jets in Active Galactic Nuclei (AGNs). We explore the possibility of synchrotron-limited electron acceleration in mildly relativistic shearing flows and present numerical solutions to the corresponding particle transport equation. We compare our findings with analytical calculations to infer an effective electron cutoff energy, and discuss the relationship to a simplified box model treatment. The results show that mildly relativistic large-scale jets offer a suitable environment for distributed electron acceleration beyond Lorentz factors of $\gamma_e \sim 10^8$.

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arXiv2022

Particle Acceleration in Relativistic Shearing Flows: Energy Spectrum

We consider the acceleration of charged particles in relativistic shearing flows, with Lorentz factor up to $\Gamma_0 \sim 20$. We present numerical solutions to the particle transport equation and compare these with results from analytical calculations. We show that in the highly relativistic limit the particle energy spectrum that results from acceleration approaches a power law, $N(E)\propto E^{-\tilde{q}}$, with a universal value $\tilde{q}=(1+\alpha)$ for the slope of this power law, where $\alpha$ parameterizes the power-law momentum dependence of the particle mean free path. At mildly relativistic flow speeds, the energy spectrum becomes softer and sensitive to the underlying flow profile. We explore different flow examples, including Gaussian and power-law-type velocity profiles, showing that the latter yield comparatively harder spectra, producing $\tilde{q}\simeq 2$ for $\Gamma_0 \simeq 3$ and Kolmogorov turbulence. We provide a comparison with a simplified leaky-box approach and derive an approximate relation for estimating the spectral index as a function of the maximum shear flow speed. These results are of relevance for jetted, high-energy astrophysical sources such as active galactic nuclei, since shear acceleration is a promising mechanism for the acceleration of charged particles to relativistic energies and is likely to contribute to the high-energy radiation observed.

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arXiv2021

Turbulence and Particle Acceleration in Shearing Flows

We explore constraints imposed by shear-driven instabilities on the acceleration of energetic particles in relativistic shearing flows. We show that shearing layers in large-scale AGN jets are likely to encompass a sizeable fraction ($\geq 0.1$) of the jet radius, requiring seed injection of GeV electrons for efficient acceleration. While the diffusion process may depend on pre-developed turbulence if injection occurs at higher energies, electron acceleration to PeV and proton acceleration to EeV energies appears possible within the constraints imposed by jet stability.

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arXiv2019

Particle Acceleration in Shearing Flows: Efficiencies and Limits

We examine limits to the efficiency for particles acceleration in shearing flows, showing that relativistic flow speeds are required for efficient gradual shear acceleration. We estimate maximum achievable particle energies for parameters applicable to relativistic AGN jets. The implications of our estimates is that if large-scale jets are relativistic, then efficient electron acceleration up to several PeV, and proton acceleration up to several EeV energies appears feasible. This suggests that shear particle acceleration could lead to a continued energization of synchrotron X-ray emitting electrons, and be of relevance for the production of ultra-high-energy cosmic-ray particles.

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arXiv2019

Thermal emission from bow shocks I: 2D Hydrodynamic Models of the Bubble Nebula

The Bubble Nebula (or NGC 7635) is a parsec-scale seemingly spherical wind-blown bubble around the relatively unevolved O star BD+60$^\circ$2522. The small dynamical age of the nebula and significant space velocity of the star suggest that the Bubble Nebula might be a bow shock. We have run 2D hydrodynamic simulations to model the interaction of the central star's wind with the interstellar medium (ISM). The models cover a range of possible ISM number densities of $n=50-200 {\rm cm}^{-3}$ and stellar velocities of $v_{\star}=20-40$ km s$^{-1}$. Synthetic H$\alpha$ and 24 $\mu$m emission maps predict the same apparent spherical bubble shape with quantitative properties similar to observations. The synthetic maps also predict a maximum brightness similar to that from the observations and agree that the maximum brightness is at the apex of the bow shock. The best-matching simulation had $v_{\star}\approx20$ km s$^{-1}$ into an ISM with $n\sim100 {\rm cm}^{-3}$, at an angle of 60$^\circ$ with respect to the line of sight. Synthetic maps of soft ($0.3-2$ keV) and hard ($2-10$ keV) X-ray emission show that the brightest region is in the wake behind the star and not at the bow shock itself. The unabsorbed soft X-rays have luminosity $\sim10^{32}-10^{33}$ erg s$^{-1}$. The hard X-rays are fainter, luminosity $\sim 10^{30} - 10^{31}$ erg s$^{-1}$, and may be too faint for current X-ray instruments to successfully observe. Our results imply that the O star creates a bow shock as it moves through the ISM and in turn creates an asymmetric bubble visible at optical and infrared wavelengths, and predicted to be visible in X-rays. The Bubble Nebula does not appear to be unique, it could be just a favourably oriented very dense bow shock. The dense ISM surrounding BD+60$^\circ$2522 and its strong wind suggest that it could be a good candidate for detecting non-thermal emission.

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arXiv2016

Charge Exchange Losses and Stochastic Acceleration in the Solar Wind

Stochastic acceleration of particles under a pressure balance condition can accommodate the universal $p^{-5}$ spectra observed under many different conditions in the inner heliosphere. In this model, in order to avoid an infinite build up of particle pressure, a relationship between the momentum diffusion of particles and the adiabatic deceleration in the solar wind must exist. This constrains both the spatial and momentum diffusion coefficients and results in the $p^{-5}$ spectrum in the presence of adiabatic losses in the solar wind. However, this theory cannot explain the presence of such spectra beyond the termination shock, where adiabatic deceleration is negligible. To explain this apparent discrepancy, we include the effect of charge exchange losses, resulting in new forms of both the spatial and momentum diffusion coefficients that have not previously been considered. Assuming that the turbulence is of a large-scale compressible nature, we find that a balance between momentum diffusion and losses can still readily lead to the creation of $p^{-5}$ suprathermal tails, including those found in the outer heliosphere.

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arXiv2011

A New Time-Dependent Finite Difference Method for Relativistic Shock Acceleration

We present a new approach to calculate the particle distribution function about relativistic shocks including synchrotron losses using the method of lines with an explicit finite difference scheme. A steady, continuous, one dimensional plasma flow is considered to model thick (modified) shocks, leading to a calculation in three dimensions plus time, the former three being momentum, pitch angle and position. The method accurately reproduces the expected power law behaviour in momentum at the shock for upstream flow speeds ranging from 0.1c to 0.995c (1 < Γ< 10). It also reproduces approximate analytical results for the synchrotron cutoff shape for a non-relativistic shock, demonstrating that the loss process is accurately represented. The algorithm has been implemented as a hybrid OpenMP--MPI parallel algorithm to make efficient use of SMP cluster architectures and scales well up to many hundreds of CPUs.

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arXiv2011

The non-thermal emission of extended radio galaxy lobes with curved electron spectra

The existing theoretical framework for the energies stored in the synchrotron-emitting lobes of radio galaxies and quasars doesn't properly account for the curved spectral shape that many of them exhibit. We characterise these spectra using parameters that are straightforwardly observable in the era of high-resolution, low-frequency radio astronomy: the spectral curvature and the turnover in the frequency spectrum. This characterisation gives the Lorentz factor at the turnover in the energy distribution (we point out that this is distinctly different from the Lorentz factor corresponding to the turnover frequency in a way that depends on the amount of curvature in the spectrum) and readily gives the equipartition magnetic field strength and the total energy of the radiating plasma obviating the need for any assumed values of the cutoff frequencies to calculate these important physical quantities. This framework readily yields the form of the X-ray emission due to inverse-Compton (IC) scattering of Cosmic Microwave Background (CMB) photons by the electrons in the plasma having Lorentz factors of $\sim$1000. We also present the contribution to CMB anisotropies due to relativistic plasmas such as giant radio galaxy lobes, expressed in terms of the extent to which the lobes have their magnetic field and particle energies are in equipartition with one another.

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arXiv2008

Particle-acceleration timescales in TeV blazar flares

Observations of minute-scale flares in TeV Blazars place constraints on particle acceleration mechanisms in those objects. The implications for a variety of radiation mechanisms have been addressed in the literature; in this paper we compare four different acceleration mechanisms: diffusive shock acceleration, second-order Fermi, shear acceleration and the converter mechanism. When the acceleration timescales and radiative losses are taken into account, we can exclude shear acceleration and the neutron-based converted mechanism as possible acceleration processes in these systems. The first-order Fermi process and the converter mechanism working via SSC photons are still practically instantaneous, however, provided sufficient turbulence is generated on the timescale of seconds. We propose stochastic acceleration as a promising candidate for the energy-dependent time delays in recent gamma-ray flares of Markarian 501.

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arXiv2008

Properties of vertically self-gravitating accretion discs with a dissipative corona

The steady-state structure of a disc with a corona is analyzed when the vertical component of the gravitational force due to the self-gravity of the disc is considered. For the energy exchange between the disc and the corona, we assume a fraction f of the dissipated energy inside the accretion disc is transported to the corona via the magnetic tubes. Analytical solutions corresponding to a prescription for f (in which this parameter directly depends on the ratio of the gas pressure to the total pressure) or free f are presented and their physical properties are studied in detail. We show that the existence of the corona not only decreases the temperature of the disc, but also increases the surface density.The vertical component of the gravitational force due to the self-gravity of the disc decreases the self-gravitating radius and the mass of the fragments at this radius. However, as more energy is transported from the disc to the corona, the effect of the vertical component of the gravitational force due to the self-gravity of the disc on the self-gravitating radius becomes weaker, though the mass of the fragments is reduced irrespective of the amount of the energy exchange from the disc to the corona.

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arXiv2007

Particle Acceleration at Multiple Internal Relativistic Shocks

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch angle scattering. We use a well established eigenfunction method to calculate the resulting spectra for infinitely thin shocks. Implications for GRBs and relativistic jets are discussed.

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arXiv2007

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma ray burst sources and blazars, are discussed.

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arXiv2006

A microscopic analysis of shear acceleration

A microscopic analysis of the viscous energy gain of energetic particles in (gradual) non-relativistic 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 $τ(p) \propto p^α$ with $α\geq 0$. 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 $p_0$ power-law differential particle number density spectra $n(p) \propto p^{-(1+ α)}$ 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 (WATs) are addressed.

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arXiv2006

Fermi acceleration in astrophysical jets

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 AGNs, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.

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arXiv2005

Particle Acceleration in Gamma-Ray Burst Jets

Gradual shear acceleration of energetic particles in gamma-ray burst (GRB) jets is considered. Special emphasis is given to the analysis of universal structured jets, and characteristic acceleration timescales are determined for a power-law and a Gaussian evolution of the bulk flow Lorentz factor $γ_b$ with angle $ϕ$ from the jet axis. The results suggest that local power-law particle distributions may be generated and that higher energy particles are generally concentrated closer to the jet axis. Taking several constraints into account we show that efficient electron acceleration in gradual shear flows, with maximum particle energy successively decreasing with time, may be possible on scales larger than $r \sim 10^{15}$ cm, provided the jet magnetic field becomes sufficiently weak and/or decreases rapidly enough with distance, while efficient acceleration of protons to ultra-high energies $> 10^{20}$ eV may be possible under a wide range of conditions.

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arXiv2005

Particle acceleration timescales in relativistic shear flows

We review the acceleration of energetic particles in relativistic astrophysical jets characterized by a significant velocity shear. The possible formation of power-law momentum spectra is discussed and typical acceleration timescales are determined for a variety of different conditions such as parallel and azimuthal shear flows. Special attendance is given to the analysis of parallel shear flows with either a linear decreasing or a Gaussian-type velocity profile. It is shown that in the presence of a gradual shear flow and a particle mean free path scaling with the gyroradius, synchrotron radiation losses may no longer be able to stop the acceleration once it has started to work efficiently. Finally, the relevance of shear acceleration in small- and large-scale relativistic jets is addressed.

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arXiv2005

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 coordinate, (2) gradual velocity shear perpendicular to the jet axis, such as intrinsic jet rotation, and (3) non-gradual/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 the case of (2) the higher energy emission is expected to be concentrated closer to the jet axis, while in the case of (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.

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arXiv2005

Particle acceleration in astrophysical shear flows

We consider the acceleration of particles due to a velocity shear in relativistic astrophysical flows. The basic physical picture and the formation of power law momentum spectra is discussed for a non-relativistic velocity field using a microscopic approach. We identify possible sites for shear acceleration in relativistic astrophysical jets and analyze their associated acceleration timescales. It is shown in particular that for a mean scattering time $τ$ scaling with the gyro-radius, the acceleration timescale for gradual shear scales in the same manner as the synchrotron cooling timescale, so that losses may no longer be able to stop the acceleration once it has started to work efficiently. Finally, the possible role of shear acceleration is discussed with reference to the relativistic jet in the quasar 3C~273.

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