Fermi Acceleration Research Articles

TIME-DEPENDENT MODELS FOR BLAZAR EMISSION WITH THE SECOND-ORDER FERMI ACCELERATION

The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations. The hard electron spectrum predicted by the Fermi-II process agrees with the hard photon spectrum of 1ES 1101-232. For other blazars that show softer spectra, the Fermi-II model requires radial evolution of the electron injection rate and/or diffusion coefficient in the outflow. Such evolutions can yield a curved electron spectrum, which can reproduce the synchrotron spectrum of Mrk 421 from the radio to the X-ray regime.The photon spectrum in the GeV energy range of Mrk 421 is hard to fit with a synchrotron self-Compton model. However, if we introduce an external radio photon field with a luminosity of $4.9 \times 10^{38}~\mbox{erg}~\mbox{s}^{-1}$, GeV photons are successfully produced via inverse Compton scattering. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.

Dynamics of the spatial distribution of electrons and their gyrosynchrotron emission characteristics in a collapsing magnetic trap

The dynamics of the distribution of nonthermal electrons, injected into a collapsing magnetic trap, has been considered. The electron energy and pitch angle nonstationary spatial distributions in an extensive magnetic trap have been obtained for the first time for different laws of inhomogeneous magnetic field evolution in this trap by numerically solving the Fokker-Planck kinetic equation. The gyrosynchrotron emission intensity has been calculated for the obtained electron spatial distributions. It has been indicated that energetic electrons are effectively accumulated and accelerated at the top of a collapsing trap due to the first-order Fermi and betatron acceleration mechanisms at certain rates of variations in the magnetic field and background plasma density.

Hamiltonian Mechanics of Stochastic Acceleration

We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

Acceleration Modes in Fermi Accelerator

We explain Fermi acceleration of particles bouncing in a gravitational field and experiencing a force due to a modulated evanescent laser field. The acceleration strongly depends upon the initial conditions in the phase space and certain modulation amplitude. We study the accelerated modes by the Poincare surface of sections and Lyapunov exponents. Furthermore, we identify the initial areas of the phase space that support accelerated dynamics and write a mapping for accelerated dynamics. We show that a distinction between accelerated and chaotic evolutions can be made with the help of the aspect ratio. The Lyapunov exponent shows that the accelerated mode supports ordered evolution.

FROM LÉVY WALKS TO SUPERDIFFUSIVE SHOCK ACCELERATION

In this paper, we present a general scenario for nondiffusive transport and we investigate the influence of anomalous, superdiffusive transport on Fermi acceleration processes at shocks. We explain why energetic particle superdiffusion can be described within the Levy walk framework, which is based on a power-law distribution of free path lengths and on a coupling between free path length and free path duration. A self-contained derivation of the particle mean square displacement, which grows as (Δx {sup 2}) = 2D {sub α} t {sup α} with α > 1, and the particle propagator, is presented for Levy walks, making use of a generalized version of the Montroll-Weiss equation. We also derive for the first time an explicit expression for the anomalous diffusion coefficient D {sub α} and we discuss how to obtain these quantities from energetic particle observations in space. The results are applied to the case of particle acceleration at an infinite planar shock front. Using the scaling properties of the Levy walk propagator, the energy spectral indices are found to have values smaller than the ones predicted by the diffusive shock acceleration theory. Furthermore, when applying the results to ions with energies of a few MeV accelerated atmore » the solar wind termination shock, the estimation of the anomalous diffusion coefficient associated with the superdiffusive motion gives acceleration times much smaller than the ones related to normal diffusion.« less

Particle Acceleration and Emission Processes in Mrk 421

We investigated the X-ray and γ-ray flares of Mrk 421 on 2008 June 6–15 using the synchrotron self-Compton- (SSC) model with electron acceleration, in which an evident correlation between the X-ray and γ-ray bands appears, while no significant correlation between the optical and X-ray band was observed. We argue that the emission from Mrk 421 may originate from two different components. One is a steady component from the outer region, which is mainly attributed to the optical band, in which the electrons are accelerated by first-order Fermi acceleration mechanism. We used a steady electron spectrum to produce the SSC emission. The other is a variable component from the inner region, in which the electrons are accelerated by a stochastic acceleration process. We used the timedependent SSC model to produce the emission from the variable component. We suggest that the flares are due to a hardening of the electron spectrum under the process of stochastic acceleration, which leads to a hardening of the observed spectrum in the X-ray and γ-ray bands. Furthermore, we find that the energy densities of electrons and magnetic fields are at near equipartition in both jet regions.

Magnetic diffusion effects on the ultra-high energy cosmic ray spectrum and composition

We discuss the effects of diffusion of high energy cosmic rays in turbulent extra-galactic magnetic fields. We find an approximate expression for the low energy suppression of the spectrum of the different mass components (with charge Z) in the case in which this suppression happens at energies below ∼ Z EeV, so that energy losses are dominated by the adiabatic ones. The low energy suppression appears when cosmic rays from the closest sources take a time comparable to the age of the Universe to reach the Earth. This occurs for energies E < Z EeV (B/nG)√(lc/Mpc)(ds/70Mpc) in terms of the magnetic field RMS strength B, its coherence length lc and the typical separation between sources ds. We apply this to scenarios in which the sources produce a mixed composition and have a relatively low maximum rigidity (Emax ∼ (2–10)Z EeV), finding that diffusion has a significant effect on the resulting spectrum, the average mass and on its spread, in particular reducing this last one. For reasonable values of B and lc these effects can help to reproduce the composition trends observed by the Auger Collaboration for source spectra compatible with Fermi acceleration.

Origin of nonthermal emission from the Fermi bubbles and mechanisms of particle acceleration there

The discovery of the two giant γ-ray lobes (Fermi bubbles) in the Galactic center (see Dobler et al. 2010 and Su et al. 2010) was one of the most impressive events of the last few years in astrophysics. However, some indications on giant structures in the Galactic center (GC) were observed several years before by WMAP in the radio frequency range between 23 and 33 MHz (Finkbeiner 2004), and by ROSAT in hard X-rays (Bland-Hawthorn &amp; Cohen 2003). Recent observations performed by the Planck Collaboration (Ade et al. 2012) found also lobes in the microwave range which spatially coincided the Fermi bubbles that indicated on the common origin of these phenomena.

Searching for the high-energy neutrino counterpart signals: The case of the Fermi bubbles signal and of dark matter annihilation in the inner Galaxy

The recent uncovering of the \textit{Fermi} Bubbles/haze in the \textit{Fermi} gamma-ray data has generated theoretical work to explain such a signal of hard $\gamma$-rays in combination with the \textit{WMAP} haze signal. Many of these theoretical models can have distinctively different implications with regards to the production of high energy neutrinos. We discuss the neutrino signals from different models proposed for the explanation of the \textit{Fermi} Bubbles/haze, more explicitly, from Dark Matter annihilation in the galactic halo with conditions of preferential CR diffusion, from recent AGN jet activity, from periodic diffusive shock acceleration, from stochastic 2nd order Fermi acceleration and from long time-scale star formation in the galactic center in combination with strong galactic winds. We find that some of these models will be probed by the IceCube DeepCore detector. Moreover, with a km$^3$ telescope located at the north hemisphere, we will be able to discriminate between the hadronic, leptonic and the DM models. Additionally using the reconstructed neutrino spectra we will probe annihilation of TeV scale dark matter towards the galactic center.

Large-amplitude oscillations in the rectangular Fermi accelerator

Exponential energy growth in a rectangular billiard with an oscillating bar has been clearly demonstrated earlier. Using the log-normal approximation, analytical estimates for the energy growth rate have also been provided. However, these analytical estimates are valid only when the amplitude of oscillation of the bar is small. In this paper, for larger oscillation amplitude, the log-normal approximation is numerically shown to be invalid and analytical estimates are obtained for the true energy growth rate in the case of very large particle velocities or small bar length. It is also shown that when everything else remains constant, the length of the bar which gives rise to maximum energy growth rate decreases as the oscillation amplitude increases and the true value of this maximizing length is also smaller than what is predicted by the log-normal approximation. Thus, the rectangular Fermi accelerator forms a very good example of a contemporary research problem where the limitations of the log-normal approximation can be easily appreciated.

A statistical study of electron acceleration behind the dipolarization fronts in the magnetotail

AbstractWe investigate the electron acceleration behind dipolarization fronts (DFs) in the magnetotail from −25 RE to −10 RE through the examination of the energetic electron energy flux (&gt;30 keV) with the observations from Time History of Events and Macroscale Interactions during Substorms (THEMIS). Statistical results of 133 DF events are presented based on the data set from January to April of the years 2008 and 2009. As the DFs propagate earthward, the acceleration of energetic electrons behind the DFs is found to take place over several RE along the tail. The increase in energetic electron energy flux can reach 2–4 orders of magnitude. The dominant acceleration mechanisms are different in the midtail (XGSM ≤ −15 RE) and the near‐Earth region (−15 &lt; XGSM ≤ −10 RE). In the midtail, the majority of DF events show that the dominant electron acceleration mechanism is betatron acceleration. In the near‐Earth region, betatron acceleration is dominant in ~46% DF events while Fermi acceleration is dominant in ~39% DF events.

Periodic compression of an adiabatic gas: Intermittency-enhanced Fermi acceleration

A gas of non-interacting particles diffuses in a lattice of pulsating scatterers. In the finite-horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described by a master equation, leading to an asymptotic universal non-Maxwellian velocity distribution scaling as . The infinite-horizon case has intermittent dynamics which enhances the acceleration, leading to and a non-universal distribution.

Direct auroral precipitation from the magnetotail during substorms

AbstractIn this study, we examine the causes of electron precipitation during a substorm on 15 February 2008 that lead to auroral brightening. We use global kinetic simulations along with spacecraft and ground‐based data. We find ~keV electrons in the region modeled in the simulation precipitate into the premidnight sector at latitudes between 71° and 75° due to two distinct physical processes: (1) higher latitude precipitation due to electrons that undergo relatively rapid non‐adiabatic pitch angle scattering into the loss cone just earthward of a reconnection region, and (2) lower latitude precipitation due to electrons that are more gradually accelerated primarily parallel to the geomagnetic field by Fermi acceleration. These latter electrons enter the loss cone much closer to Earth at ~−15 to −10 RE. The electron precipitation due to the combination of these two mechanisms coincides spatially with observed auroral brightening during the disturbed event.

THEMIS observations of electron acceleration associated with the evolution of substorm dipolarization in the near‐Earth tail

AbstractWe present the evolution of dipolarizations in the near‐Earth tail during a substorm on 15 March 2009, based on the two‐point measurements in the nightside plasma sheet at X ~ −8.0 RE. The earthward‐moving dipolarization, the magnetic flux pileup, and the tailward‐moving dipolarization were observed. For the 30–200 keV electrons, betatron acceleration was the dominant process, which was caused by the much larger gradient of the magnetic field there during the earthward‐moving dipolarization or by a local compression of the magnetic field during the magnetic flux pileup and tailward‐moving dipolarization. These near‐perpendicular distributions for the 30–200 keV electrons are interpreted as produced by a two‐step acceleration: Electrons were first accelerated in the dipolarization fronts in the midtail or the near‐Earth tail and then were further accelerated near the tail current disruption region. For the more than 200 keV electrons, Fermi acceleration was the dominant process, which was caused by the shrinking length of magnetic field line during the tailward‐moving dipolarization. The source region of the more than 200 keV electrons may be near the tail current disruption region, but these electrons were accelerated locally. These field‐aligned electrons can precipitate into the ionosphere and form the discrete auroral arcs. Two parallel arcs were clearly observed around the substorm onset: one propagated equatorward, another propagated poleward. We suggest that the earthward‐moving dipolarization, the magnetic flux pileup, and the tailward‐moving dipolarization near the tail current disruption region can well explain the auroral evolution around the substorm onset.

Fermi Acceleration in Anti-Integrable Limits of the Standard Map

We consider a dynamical system on the semi-infinite cylinder which models the high energy dynamics of a family of mechanical models. We provide conditions under which we ensure that the set of orbits undergoing Fermi acceleration has measure zero.

Dynamical properties for a mixed Fermi accelerator model

The behavior of the decay of velocity in a semi-dissipative one-dimensional Fermi accelerator model is considered. Two different kinds of dissipative forces were considered: (i) F∝−v and; (ii) F∝−v2. We prove the decay of velocity is linear for (i) and exponential for (ii). During the decay, the particles move along specific corridors which are constructed by the borders of the stable manifolds of saddle points. These corridors organize themselves in a very complicated way in the phase space leading the basin of attraction of the sinks to be seemingly of fractal type.

Particle acceleration in dipolarization events

Using the electromagnetic fields of a recent MHD simulation of magnetotail reconnection, flow bursts and dipolarization, we investigate the acceleration of test particles (protons and electrons) to suprathermal energies, confirming and extending earlier results on acceleration mechanisms and sources. (Part of the new results have been reviewed recently in Birn et al., Space Science Reviews, 167, doi:10.1007/ s11214‐012‐9874‐4.) The test particle simulations reproduce major features of energetic particle events (injections) associated with substorms or other dipolarization events, particularly a rapid rise of energetic particle fluxes over limited ranges of energy. The major acceleration mechanisms for electrons are betatron acceleration and Fermi acceleration in the collapsing magnetic field. Ions, although non‐adiabatic, undergo similar acceleration. Two major entry mechanisms into the acceleration site are identified: cross‐tail drift from the inner tail plasma sheet and reconnection entry from field lines extending to the more distant plasma sheet. The former dominates early in an event and at higher energies (hundreds of keV) while the latter constitutes the main source later and at lower energies (tens of keV). Despite the fact that the injection front moves earthward in the tail, the peak of energetic particle fluxes moves to higher latitude when mapped from the near‐Earth boundary to Earth in a static magnetic field model.

THE FIRM REDSHIFT LOWER LIMIT OF THE MOST DISTANT TeV-DETECTED BLAZAR PKS 1424+240

We present the redshift lower limit of z>0.6035 for the very-high-energy (VHE; E>100 GeV) emitting blazar PKS 1424+240 (PG 1424+240). This limit is inferred from Lyman beta and gamma absorption observed in the far-ultraviolet spectra from the Hubble Space Telescope/Cosmic Origins Spectrograph. No VHE-detected blazar has shown solid spectroscopic evidence of being more distant. At this distance, VHE observations by VERITAS are shown to sample historically large gamma-ray opacity values at 500 GeV, extending beyond tau=4 for low-level models of the extragalactic background light (EBL) and beyond tau=5 for high-levels. The majority of the z=0.6035 absorption-corrected VHE spectrum appears to exhibit a lower flux than an extrapolation of the contemporaneous LAT power-law fit beyond 100 GeV. However, the highest energy VERITAS point is the only point showing agreement with this extrapolation, possibly implying the overestimation of the gamma-ray opacity or the onset of an unexpected VHE spectral feature. A curved log parabola is favored when fitting the full range of gamma-ray data (0.5 to 500 GeV). While fitting the absorption-corrected VHE data alone results in a harder differential power law than that from the full range, the indices derived using three EBL models are consistent with the physically motivated limit set by Fermi acceleration processes.

On the supernova remnants with flat radio spectra

A considerable fraction of Galactic supernova remnants (SNRs) characterize flat spectral indices ($\alpha<0.5$). There are several explanations of the flat radio spectra of SNRs in the present literature. The most of models involve a significant contribution of the second-order Fermi mechanism but some of them also discuss high compressions (>4), contribution of secondary electrons left over from the decay of charged pions, as well as the possibility of thermal contamination. In the case of expansion in high density environment, intrinsic thermal bremsstrahlung could theoretically shape the radio spectrum of an SNR and also account for observable curved -- "concave up" radio spectra of some Galactic SNRs. This model could also shed a light on the question of flat spectral indices determined in some Galactic SNRs. On the other hand, present knowledge of the radio continuum spectra (integrated flux densities at different frequencies) of SNRs prevent definite conclusions about the significance of proposed models so the question on flat spectral indices still remains open. New observations, especially at high radio continuum frequencies, are expected to solve these questions in the near future. Finally, as there is a significant connection between the majority of Galactic SNRs with flat integrated radio spectrum and their detection in $\gamma$-rays as well as detection of radiative recombination continua in their X-ray spectra, the analysis of high energy properties of these SNRs is very important.

Stochastic acceleration by multi-island contraction during turbulent magnetic reconnection.

The acceleration of charged particles in magnetized plasmas is considered during turbulent multi-island magnetic reconnection. The particle acceleration model is constructed for an ensemble of islands which produce adiabatic compression of the particles. The model takes into account the statistical fluctuations in the compression rate experienced by the particles during their transport in the acceleration region. The evolution of the particle distribution function is described as a simultaneous first- and second-order Fermi acceleration process. While the efficiency of the first-order process is controlled by the average rate of compression, the second-order process involves the variance in the compression rate. Moreover, the acceleration efficiency associated with the second-order process involves both the Eulerian properties of the compression field and the Lagrangian properties of the particles. The stochastic contribution to the acceleration is nonresonant and can dominate the systematic part in the case of a large variance in the compression rate. The model addresses the role of the second-order process, how the latter can be related to the large-scale turbulent transport of particles, and explains some features of the numerical simulations of particle acceleration by multi-island contraction during magnetic reconnection.