Fermi Acceleration Research Articles

From GPGPU to Many-Core: Nvidia Fermi and Intel Many Integrated Core Architecture

Comparing the architectures and performance levels of an Nvidia Fermi accelerator with an Intel MIC Architecture coprocessor demonstrates the benefit of the coprocessor for bringing highly parallel applications into, or even beyond, GPGPU performance regions.

Molecular and Atomic Gas toward HESS J1745−303 in the Galactic Center: Further Support for the Hadronic Scenario

Abstract We compared TeV $\gamma$-rays with new $^{12}$CO $J$$=$ 2–1 data toward HESS J1745$-$303 in the Galactic center, and confirmed that the molecular cloud MG358.9$-$0.5 toward ($l$, $b$) $=$ (358$^\circ\!\!\!.$9, $-$0$^\circ\!\!\!.$5) at $V_\mathrm{LSR}$$=$$-$100–0 km s$^{-1}$ shows a reasonable positional agreement with the primary peak (northern part) of the $\gamma$-ray source. For the southern part of HESS J1745$-$303, we have seen no CO counterpart, whereas H I gas in the SGPS H I dataset shows a possible counterpart to the $\gamma$-ray source. This H I gas may be optically thick, as supported by the H I line shape similar to the optically thick $^{12}$CO. We estimate the total mass of interstellar protons including both the molecular and atomic gas to be 2 $\times$ 10$^{6}M\odot$ and the cosmic-ray proton energy to be 6 $\times$ 10$^{48}\ $erg in the hadronic scenario. We discuss possible origins of the cosmic-ray protons including the nearby SNR G359.1$-$0.5. The SNR may be able to explain the northern $\gamma$-ray source, but the southern source seems to be too far to be energized by the SNR. As an alternative, we argue that the second-order Fermi acceleration in the inter-clump space surrounded by randomly moving high-velocity clumps may offer a possible mechanism to accelerate protons across the entire HESS source. The large turbulent motion with a velocity dispersion of $\sim\ $15 km s$^{-1}$ has an energy density two orders of magnitude higher than in the solar vicinity, and is viable as the energy source.

Fermi acceleration as a possible mechanism of rapid diffusion of gold clusters on graphite

Diffusion of gold nanoclusters on a graphite substrate is discussed. We propose a solution to the contradiction between the extremely high value of the diffusion coefficient and its Arrhenius-type temperature dependence. The possibility of applying the Fermi acceleration model to this problem is shown.

ACCELERATION AND PARTICLE FIELD INTERACTIONS OF COSMIC RAYS: FORMALISM

The acceleration of ultra high energy cosmic rays is conjectured to occur through various interactions with the electromagnetic fields in different astrophysical objects, like magnetic matter clumps, besides the well-known shock and stochastic Fermi mechanisms. It is apparent that the latter are not depending on the particle's charge, quantitatively. Based on this model, a considerable portion of the dynamics, that derives a charged particle parallel to a magnetic field $\mathbf{B}$ and under the influence of a force $\mathbf{F}$, is assumed to be composed of an acceleration by a non-magnetic force $\mathbf{F}_{\parallel}$ and a gyromotion along $\mathbf{B}$ direction, plus drifts in the direction of $\mathbf{F}_{\perp}$. The model and its formalism are introduced. Various examples for drift motions and accelerating forces are suggested. The formalism is given in a non-relativistic version. Obviously, the translation into the relativistic version is standard. In a forthcoming work, a quantitative estimation of the energy gained by charged cosmic rays in various astrophysical objects will be evaluated.

Strong evidence for hadron acceleration in Tycho’s supernova remnant

Very recent gamma-ray observations of G120.1+1.4 (Tycho's) supernova remnant (SNR) by Fermi-LAT and VERITAS provided new fundamental pieces of information for understanding particle acceleration and non-thermal emission in SNRs. We want to outline a coherent description of Tycho's properties in terms of SNR evolution, shock hydrodynamics and multi-wavelength emission by accounting for particle acceleration at the forward shock via first order Fermi mechanism. We adopt here a quick and reliable semi-analytical approach to non-linear diffusive shock acceleration which includes magnetic field amplification due to resonant streaming instability and the dynamical backreaction on the shock of both cosmic rays (CRs) and self-generated magnetic turbulence. We find that Tycho's forward shock is accelerating protons up to at least 500 TeV, channelling into CRs about the 10 per cent of its kinetic energy. Moreover, the CR-induced streaming instability is consistent with all the observational evidences indicating a very efficient magnetic field amplification (up to ~300 micro Gauss). In such a strong magnetic field the velocity of the Alfv\'en waves scattering CRs in the upstream is expected to be enhanced and to make accelerated particles feel an effective compression factor lower than 4, in turn leading to an energy spectrum steeper than the standard prediction {\propto} E^-2. This latter effect is crucial to explain the GeV-to-TeV gamma-ray spectrum as due to the decay of neutral pions produced in nuclear collisions between accelerated nuclei and the background gas. The self-consistency of such an hadronic scenario, along with the fact that the concurrent leptonic mechanism cannot reproduce both the shape and the normalization of the detected the gamma-ray emission, represents the first clear and direct radiative evidence that hadron acceleration occurs efficiently in young Galactic SNRs.

THE FERMI BUBBLE AS A SOURCE OF COSMIC RAYS IN THE ENERGY RANGE >1015eV

The {\it Fermi} Large Area Telescope has recently discovered two giant gamma-ray bubbles which extend north and south of the Galactic center with diameters and heights of the order of $H\sim 10$ kpc. We suggest that the periodic star capture processes by the Galactic supermassive black hole Sgr A$^*$, with a capture rate of $\tau_{\rm cap}^{-1}\sim 3\times 10^{-5}$ yr$^{-1}$ and an energy release of $W\sim 3\times 10^{52}$ erg per capture, can result in hot plasma injecting into the Galactic halo at a wind velocity of $u\sim 10^8$ cm s$^{-1}$. The periodic injection of hot plasma can produce a series of shocks. Energetic protons in the bubble are re-accelerated when they interact with these shocks. We show that for energy larger than $E> 10^{15}$ eV, the acceleration process can be better described by the stochastic second-order Fermi acceleration. We propose that hadronic cosmic rays (CRs) within the ``knee'' of the observed CR spectrum are produced by Galactic supernova remnants distributed in the Galactic disk. Re-acceleration of these particles in the Fermi Bubble produces CRs beyond the knee. With a mean CR diffusion coefficient in this energy range in the bubble $D_B\sim 3\times 10^{30}$ cm$^2$ s$^{-1}$, we can reproduce the spectral index of the spectrum beyond the knee and within. The conversion efficiency from shock energy of the bubble into CR energy is about 10\%. This model provides a natural explanation of the observed CR flux, spectral indices, and matching of spectra at the knee.

A FOCUSED TRANSPORT APPROACH TO THE TIME-DEPENDENT SHOCK ACCELERATION OF SOLAR ENERGETIC PARTICLES AT A FAST TRAVELING SHOCK

Some of the most sophisticated models for solar energetic particle (SEP) acceleration at coronal mass ejection driven shocks are based on standard diffusive shock acceleration theory. However, this theory, which only applies when SEP pitch-angle anisotropies are small, might have difficulty in describing first-order Fermi acceleration or the shock pre-heating and injection of SEPs into first-order Fermi acceleration accurately at lower SEP speeds where SEP pitch-angle anisotropies upstream near the shock can be large. To avoid this problem, we use a time-dependent focused transport model to reinvestigate first-order Fermi acceleration at planar parallel and quasi-parallel spherical traveling shocks between the Sun and Earth with high shock speeds associated with rare extreme gradual SEP events. The focused transport model is also used to investigate and compare three different shock pre-heating mechanisms associated with different aspects of the nonuniform cross-shock solar wind flow, namely, the convergence of the flow (adiabatic compression), the shear tensor of the flow, and the acceleration of the flow, and a fourth shock pre-heating mechanism associated with the cross-shock electric field, to determine which pre-heating mechanism contributes the most to injecting shock pre-heated source particles into the first-order Fermi acceleration process. The effects of variations in traveling shock conditions, such as increasing shock obliquity and shock slowdown, and variations in the SEP source with increasing shock distance from the Sun on the coupled processes of shock pre-heating, injection, and first-order Fermi acceleration are analyzed. Besides the finding that the cross-shock acceleration of the solar wind flow yields the dominant shock pre-heating mechanism at high shock speeds, we find that first-order Fermi acceleration at fast traveling shocks differs in a number of respects from the predictions and assumptions of standard steady-state diffusive shock acceleration theory as is discussed below.

Second-order Fermi acceleration as the origin of the Fermi bubbles

Gamma-ray data from Fermi-LAT show a bi-lobular structure extending up to 50° above and below the Galactic centre, coincident with a possibly related structure in the ROSAT X-ray map which presumably originated in some energy release close to the centre a few million years ago. It has been argued that the gamma-rays arise due to inverse Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons undergo stochastic second-order Fermi acceleration in the entire volume of the bubbles by plasma wave turbulence. This turbulence is generated behind the outer shock and propagates into the bubble volume, leading to a non-trivial spatial variation of the electron spectral index. Rather than a constant volume emissivity as predicted in other models we find an almost constant surface brightness in gamma-rays and also reproduce the observed sharp edges of the bubbles. We comment on possible cross-checks in other channels.

Twinkling pulsar wind nebulae in the synchrotron cut-off regime and the γ-ray flares in the Crab Nebula

ABSTRACT Synchrotron radiation of ultrarelativistic particles accelerated in a pulsar wind nebula may dominate its spectrum up to γ-ray energies. Because of the short cooling time of the γ-ray-emitting electrons and positrons, the γ-ray-emission zone is in the immediate vicinity of the acceleration site. Particle acceleration likely occurs at the termination shock of a relativistic striped wind, where multiple forced magnetic field reconnections provide strong magnetic fluctuations facilitating Fermi acceleration processes. The acceleration mechanisms imply the presence of stochastic magnetic fields in the particle acceleration region, which cause stochastic variability of the synchrotron emission. This variability is particularly strong in the steep γ-ray tail of the spectrum, where modest fluctuations of the magnetic field lead to strong flares of spectral flux. In particular, stochastic variations of magnetic field, which may lead to quasi-cyclic γ-ray flares, can be produced by the relativistic cyclotron ion instability at the termination shock. Our model calculations of the spectral and temporal evolution of synchrotron emission in the spectral cut-off regime demonstrate that the intermittent magnetic field concentrations dominate the γ-ray emission from highest energy electrons and provide fast, strong variability even for a quasi-steady distribution of radiating particles. The simulated light curves and spectra can explain the very strong γ-ray flares observed in the Crab Nebula and lack of strong variations at other wavelengths. The model predicts high polarization in the flare phase, which can be tested with future polarimetry observations.

Relation of astrophysical turbulence and magnetic reconnection

Astrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHD turbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink et al. [Astrophys. J. 743, 51 (2011)] to show that the expressions of fast magnetic reconnection in A. Lazarian and E. T. Vishniac [Astrophys. J. 517, 700 (1999)] can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of flux-freezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnection diffusion as it based on reconnection of magnetic field lines. The reconnection diffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.

NEUTRINO ANALYSIS OF THE 2010 SEPTEMBER CRAB NEBULA FLARE AND TIME-INTEGRATED CONSTRAINTS ON NEUTRINO EMISSION FROM THE CRAB USING ICECUBE

We present the results for a search of high-energy muon neutrinos with the IceCube detector in coincidence with the Crab nebula flare reported on September 2010 by various experiments. Due to the unusual flaring state of the otherwise steady source we performed a prompt analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed gamma-rays. We performed two different and complementary data selections of neutrino events in the time window of 10 days around the flare. One event selection is optimized for discovery of E^-2 neutrino spectrum typical of 1st order Fermi acceleration. A similar event selection has also been applied to the 40-string data to derive the time-integrated limits to the neutrino emission from the Crab. The other event selection was optimized for discovery of neutrino spectra with softer spectral index and TeV energy cut-offs as observed for various galactic sources in gamma-rays. The 90% CL best upper limits on the Crab flux during the 10 day flare are 4.73 x 10^-11 cm-2 s-1 TeV-1 for an E^-2 neutrino spectrum and 2.50 x 10^-10 cm-2 s-1 TeV-1 for a softer neutrino spectra of E-2.7, as indicated by Fermi measurements during the flare. IceCube has also set a time-integrated limit on the neutrino emission of the Crab using 375.5 days of livetime of the 40-string configuration data. This limit is compared to existing models of neutrino production from the Crab and its impact on astrophysical parameters is discussed. The most optimistic predictions of some models are already rejected by the IceCube neutrino telescope with more than 90% CL.

A new analytic solution for 2nd-order Fermi acceleration

A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.

Gamma-ray bursts afterglows in magnetized stellar winds

ABSTRACT Recent analytical and numerical work argue that successful relativistic Fermi acceleration requires a weak magnetization of the unshocked plasma, all the more so at high Lorentz factors. The present Letter tests this conclusion by computing the afterglow of a gamma-ray burst outflow propagating in a magnetized stellar wind using ‘ab initio’ principles regarding the microphysics of relativistic Fermi acceleration. It is shown that in magnetized environments, one expects a drop-out in the X-ray band on subday scales as the synchrotron emission of the shock-heated electrons exits the frequency band. At later times, Fermi acceleration becomes operative when the blast Lorentz factor drops below a certain critical value, leading to the recovery of the standard afterglow light curve. Interestingly, the observed drop-out bears resemblance with the fast decay found in gamma-ray bursts early X-ray afterglows.

DIFFUSIVE PARTICLE ACCELERATION IN SHOCKED, VISCOUS ACCRETION DISKS: GREEN'S FUNCTION ENERGY DISTRIBUTION

The acceleration of relativistic particles in a viscous accretion disk containing a standing shock is investigated as a possible explanation for the energetic outflows observed around radio-loud black holes. The energy/space distribution of the accelerated particles is computed by solving a transport equation that includes the effects of first-order Fermi acceleration, bulk advection, spatial diffusion, and particle escape. The velocity profile of the accreting gas is described using a model for shocked viscous disks recently developed by the authors, and the corresponding Green's function distribution for the accelerated particles in the disk and the outflow is obtained using a classical method based on eigenfunction analysis. The accretion-driven, diffusive shock acceleration scenario explored here is conceptually similar to the standard model for the acceleration of cosmic rays at supernova-driven shocks. However, in the disk application, the distribution of the accelerated particles is much harder than would be expected for a plane-parallel shock with the same compression ratio. Hence the disk environment plays a key role in enhancing the efficiency of the shock acceleration process. The presence of the shock helps to stabilize the disk by reducing the Bernoulli parameter, while channeling the excess binding energy into the escaping relativistic particles. Inmore » applications to M87 and Sgr A*, we find that the kinetic power in the jet is {approx}0.01 M-dot c{sup 2}, and the outflowing relativistic particles have a mean energy {approx}300 times larger than that of the thermal gas in the disk at the shock radius. Our results suggest that a standing shock may be an essential ingredient in accretion onto underfed black holes, helping to resolve the long-standing problem of the stability of advection-dominated accretion disks.« less

Escape and transport for an open bouncer: Stretched exponential decays

We consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decays depending on the choice of the lead or “hole”, raising the question of whether this feature is due to special properties of the stadium. The system considered here is much more general, having a generic mixed phase space structure, time-dependence of the dynamics, and Fermi acceleration (trajectories with unbounded velocity). We propose an efficient numerical scheme for this model, observe escape and transport effects including similar asymmetry, and also clear stretched exponential decays.

In situ observations of particle acceleration in shock-shock interaction

[1] We use detailed multispacecraft observations to study the interaction of an interplanetary (IP) shock with the bow shock of the Earth on August 9–10, 1998. We can distinguish four different phases of particle acceleration in the shock-shock interaction: (1) formation of magnetic contact with IP shock and the seed population of energetic particles accelerated by it, (2) reacceleration of this population by the bow shock, (3) first order Fermi acceleration as the two shocks approach each other, and (4) particle acceleration and release as the shocks collide. Such a detailed analysis was made possible by the particularly advantageous quasi-radial interplanetary magnetic field configuration. To our knowledge this is the first time the last phase of acceleration at a shock-shock collision has been reported using in situ space plasma observations.

Variable synchrotron emission from BL Lacertae objects. I. Shock-in-jet scenario

This paper presents a modeling of the variable synchrotron emission in the BL Lacertae sources (BLLs). Flux variability is assumed to be a result of the interaction between a relativistic shock wave with a magnetized jet material. Long-term flares (of months to years durations) are modeled via the propagation of a plane relativistic shock wave though the emission zone of a cylindrical form with the radius R and length H. As for short-term bursts (lasting from days to weeks), they may result from shock passage through the jet inhomogeneities such as a shell of enhanced density downstream to a Mach disc, originated due to pressure imbalance between the jet and its ambient medium. Emitting particles (electrons) gain the energies, sufficient to produce synchrotron photons at optical—X-ray frequencies, via the first-order Fermi mechanism. Observation’s frequency is the main parameter determining a rate of the increase/ decay of the emission via the characteristic decay time of emitting electrons. The magnetic field, assumed to be turbulent with an average field constant throughout the entire emission zone, is another key parameter determining the slope of a lightcurve corresponding to the flare—the higher strength the magnetic field has, the steeper the lightcurve is. The rest input parameters (shock speed, jet viewing angle, maximum/minimum energies of the electrons, particles’ density etc.), as well the strength of average magnetic field, influence the energy output from a flare.

A long-wavelength instability involving the stress tensor

Cosmic ray acceleration through first-order Fermi acceleration in a collisionless plasma relies on efficient scattering off magnetic field fluctuations. Scattering is most efficient for magnetic field fluctuations with wavelengths on the order of the gyroradius of the particles. In order to determine the highest energy to which cosmic rays can be accelerated, it is important to understand the growth of the magnetic field on these large scales. We derive the growth rate of the long-wavelength fluctuations in the linear regime, using the kinetic equation coupled to Maxwell's equations for the background plasma. The instability, driven by the cosmic ray current, acts on large scales due to the stress tensor and efficient scattering on small scales, and operates for both left- and right circular polarisations. This long-wavelength instability is potentially important in determining the acceleration efficiency and maximum energy of cosmic rays around shock waves such as in supernova remnants.

Simulations reveal fast mode shocks in magnetic reconnection outflows

Magnetic reconnection is commonly perceived to drive flow and particle acceleration in flares of solar, stellar, and astrophysical disk coronae but the relative roles of different acceleration mechanisms in a given reconnection environment are not well understood. While outflow fast mode shocks have been predicted analytically, we show for the first time via direct numerical simulations that such shocks do indeed occur in the outflows of fast reconnection when an obstacle is present. These shocks are distinct from the slow mode Petschek inflow shocks. If Fermi acceleration of electrons operates in the weak fast shocks, the associated compression ratios will induce a Fermi acceleration particle spectrum that is significantly steeper than strong fast shocks commonly studied, but consistent with the demands of solar flares. While this is not the only acceleration mechanism operating in a reconnection environment, it is plausibly a ubiquitous one.

Phase space interpretation of exponential Fermi acceleration

Recently, the occurrence of exponential Fermi acceleration (FA) has been reported in a rectangular billiard with an oscillating bar inside (Shah et al 2010 Phys. Rev. E 81 056205). In this paper, we analyze the underlying physical mechanism and show that the phenomenon can be understood as a sequence of highly correlated motions, consisting of alternating phases of free propagation and motion along the invariant spanning curves of the well-known one-dimensional Fermi–Ulam model. The key mechanism for the occurrence of exponential FA can be captured in a random walk model in velocity space with step width proportional to the velocity itself. The model reproduces the occurrence of exponential FA and provides a good ab initio prediction of the value of the growth rate, including its full parameter dependence. Our analysis clearly points out the requirements for exponential FA, thereby opening the prospect of finding other systems exhibiting this unusual behavior.