Fermi Process Research Articles

PARTICLE ACCELERATION AND HEATING BY TURBULENT RECONNECTION

ABSTRACT Turbulent flows in the solar wind, large-scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains “turbulent reconnection.” We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (i.e., magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large-scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution, and their escape time distribution. We have developed a new method to estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the “magnetic clouds” with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker–Planck (FP) equation, we can recover the energy distribution of the particles only for the stochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is “anomalous,” in contrast to the case of the second-order Fermi process.

KINETIC SIMULATIONS OF THE LOWEST-ORDER UNSTABLE MODE OF RELATIVISTIC MAGNETOSTATIC EQUILIBRIA

ABSTRACT We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold–Beltrami–Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.

A corrugated termination shock in pulsar wind nebulae?

Successful phenomenological models of pulsar wind nebulae assume efficient dissipation of the Poynting flux of the magnetized electron–positron wind as well as efficient acceleration of the pairs in the vicinity of the termination shock, but how this is realized is not yet well understood. This paper suggests that the corrugation of the termination shock, at the onset of nonlinearity, may lead towards the desired phenomenology. Nonlinear corrugation of the termination shock would convert a fraction of order unity of the incoming ordered magnetic field into downstream turbulence, slowing down the flow to sub-relativistic velocities. The dissipation of turbulence would further preheat the pair population on short length scales, close to equipartition with the magnetic field, thereby reducing the initial high magnetization to values of order unity. Furthermore, it is speculated that the turbulence generated by the corrugation pattern may sustain a relativistic Fermi process, accelerating particles close to the radiation reaction limit, as observed in the Crab nebula. The required corrugation could be induced by the fast magnetosonic modes of downstream nebular turbulence; but it could also be produced by upstream turbulence, either carried by the wind or seeded in the precursor by the accelerated particles themselves.

Fixation times in evolutionary games with the Moran and Fermi processes

We combined the standard Moran and Fermi process into a mixed process with two strategies C (co-operation) and D (defection). In a well-mixed population of size N+M, N individuals have the same update mechanism as that of Moran process, while the other M individuals have the same update mechanism as that of Fermi process. We obtain the balance equations of the conditional fixation time and unconditional fixation time. What these equations are doing is to make numerical sense for all the figures. We find that the expectation values of conditional fixation times of a single co-operator are smaller than the average values of the standard Moran and Fermi process. In addition, the conditional fixation time of a single co-operator with update rule of Moran is larger than that of Fermi when the intensity of selection is sufficiently small. The simulation results show that the unconditional fixation time of a co-operator who obtains more information is smaller. In addition, the larger the difference of individuals׳ payoff, the smaller the unconditional fixation time.

Radio relics tracing the projected mass distribution in CIZA J2242.8+5301

Abstract We present a weak-lensing analysis for a merging galaxy cluster, CIZA J2242.8+5301, which hosts double radio relics, using three-band Subaru/Suprime-Cam imaging (Br′z′). Since the lifetime of dark matter halos colliding into clusters is longer than that of X-ray emitting gas halos, weak-lensing analysis is a powerful method to constrain merger dynamics. Two-dimensional shear fitting using a clean background catalog suggests that the cluster undergoes a merger with a mass ratio of about 2 : 1. The main halo is located around the gas core in the southern region, while no concentrated gas core is associated with the northern sub-halo. We find that the projected cluster mass distribution resulting from an unequal-mass merger is in excellent agreement with the curved shapes of the two radio relics and the overall X-ray morphology, except for the lack of the northern gas core. The lack of a prominent radio halo enables us to constrain an upper limit of the fractional energy of magnetohydrodynamic turbulence of $(\delta B/B)^2<\mathcal {O}(10^{-6})$ at a resonant wavenumber, by finding a balance between the acceleration time and the time after the core passage or the cooling time, with an assumption of resonant acceleration by a second-order Fermi process.

PARTICLE ACCELERATION AND PLASMA DYNAMICS DURING MAGNETIC RECONNECTION IN THE MAGNETICALLY DOMINATED REGIME

Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two- and three-dimensional kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron-positron plasmas starting with a magnetically dominated, force-free current sheet ($\sigma \equiv B^2/(4\pi n_e m_e c^2) \gg 1$). For this limit, we demonstrate that relativistic reconnection is highly efficient at accelerating particles through a first-order Fermi process accomplished by the curvature drift of particles along the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra $f \propto (\gamma-1)^{-p}$ and approaches $p = 1$ for sufficiently large $\sigma$ and system size. Eventually most of the available magnetic free energy is converted into nonthermal particle kinetic energy. An analytic model is presented to explain the key results and predict a general condition for the formation of power-law distributions. The development of reconnection in these regimes leads to relativistic inflow and outflow speeds and enhanced reconnection rates relative to non-relativistic regimes. In the three-dimensional simulation, the interplay between secondary kink and tearing instabilities leads to strong magnetic turbulence, but does not significantly change the energy conversion, reconnection rate, or particle acceleration. This study suggests that relativistic reconnection sites are strong sources of nonthermal particles, which may have important implications to a variety of high-energy astrophysical problems.

A magnetic reconnection model for explaining the multiwavelength emission of the microquasars Cyg X-1 and Cyg X-3

Recent studies have indicated that cosmic ray acceleration by a first-order Fermi process in magnetic reconnection current sheets can be efficient enough in the surrounds of compact sources. In this work, we discuss this acceleration mechanism operating in the core region of galactic black hole binaries (or microquasars) and show the conditions under which this can be more efficient than shock acceleration. In addition, we compare the corresponding acceleration rate with the relevant radiative loss rates obtaining the possible energy cut-off of the accelerated particles and also compute the expected spectral energy distribution (SED) for two sources of this class, namely Cygnus X-1 and Cygnus X-3, considering both leptonic and hadronic processes. The derived SEDs are comparable to the observed ones in the low and high energy ranges. Our results suggest that hadronic non-thermal emission due to photo-meson production may produce the very high energy gamma-rays in these microquasars.

Formation of hard power laws in the energetic particle spectra resulting from relativistic magnetic reconnection.

Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B(2)/(4πnm(e)c(2))>1 and when the system size is sufficiently large. In the limit σ ≫ 1, the spectral index approaches p = 1 and most of the available energy is converted into nonthermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.

NON-THERMAL ELECTRON ACCELERATION IN LOW MACH NUMBER COLLISIONLESS SHOCKS. I. PARTICLE ENERGY SPECTRA AND ACCELERATION MECHANISM

Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3 and a quasi-perpendicular pre-shock magnetic field. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

Fixation probabilities in evolutionary games with the Moran and Fermi processes

An evolutionary dynamic model of 2×2 games with finite population of size N+M was built. Among these individuals, N individuals have the same update mechanism as that of the Moran process, while the other M individuals have the same update mechanism as that of the Fermi process. We obtain the balance equations of the fixation probability and analyze some concrete cases. In contrast with the results of neutral evolution, the fixation probability of a single co-operator with the same update mechanism as that of the Fermi process is higher. Besides, more co-operators with the update mechanism of the Fermi process lead to higher fixation probabilities when co-operators׳ quantity is the same.

A MAGNETOHYDRODYNAMIC MODEL OF THE M87 JET. II. SELF-CONSISTENT QUAD-SHOCK JET MODEL FOR OPTICAL RELATIVISTIC MOTIONS AND PARTICLE ACCELERATION

We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the {\em Hubble Space Telescope} during 1994 -- 1998. The model concept consists of ejection of a {\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the {\em optical} observations of HST-1 with the same model we used previously to describe similar features in radio VLBI observations in 2005 -- 2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge of the HST-1 complex as observed from radio to optical wavelengths, with forward/reverse fast-mode MHD shocks then responsible for observed moving features. Moreover, we identify such intrinsic properties as the shock compression ratio, degree of magnetization, and magnetic obliquity and show that they are suitable to mediate diffusive shock acceleration of relativistic particles via the first-order Fermi process. We suggest that relativistic MHD shocks in Poynting-flux dominated helical jets may play a role in explaining observed emission and proper motions in many AGNs.

COLLISIONLESS RELATIVISTIC SHOCKS: CURRENT DRIVEN TURBULENCE AND PARTICLE ACCELERATION

The physics of collisionless relativistic shocks with a moderate magnetization is presented. Micro-physics is relevant to explain the most energetic radiative phenomena of Nature, namely that of the termination shock of Gamma Ray Bursts. A transition towards Fermi process occurs for decreasing magnetization around a critical value which turns out to be the condition for the scattering to break the mean field inhibition. Scattering is produced by magnetic micro-turbulence driven by the current carried by returning particles, which had not been considered till now, but turns out to be more intense than Weibel's one around the transition. The current is also responsible for a buffer effect on the motion of the incoming flow, on which the threshold for the onset of turbulence depends.

The spectra of jet bases in FR I radio galaxies: implications for particle acceleration

We present accurate, spatially resolved imaging of radio spectra at the bases of jets in eleven low-luminosity (Fanaroff-Riley I) radio galaxies, derived from Very Large Array (VLA) observations. We pay careful attention to calibration and to the effects of random and systematic errors, and we base the flux-density scale on recent measurements of VLA primary amplitude calibrators by Perley & Butler (2013). We show images and profiles of spectral index over the frequency range 1.4 - 8.5 GHz, together with values integrated over fiducial regions defined by our relativistic models of the jets. We find that the spectral index decreases (the spectrum flattens) with distance from the nucleus in all of the jets. The mean spectral indices are 0.66 +/- 0.01 where the jets first brighten abruptly and 0.59 +/- 0.01 after they recollimate. The mean change in spectral index between these locations, which is independent of calibration and flux-density scale errors and is therefore more accurately and robustly measured, is -0.067 +/- 0.006. Our jet models associate the decrease in spectral index with a bulk deceleration of the flow from 0.8c to <0.5c. We suggest that the decrease is the result of a change in the characteristics of ongoing particle acceleration. One possible acceleration mechanism is the first-order Fermi process in mildly relativistic shocks: in the Bohm limit, the index of the electron energy spectrum, p, is slightly larger than 2 and decreases with velocity upstream of the shock. This possibility is consistent with our measurements, but requires shocks throughout the jet volume rather than at a few discrete locations. A second possibility is that two acceleration mechanisms operate in these jets: one (with p = 2.32) dominant close to the galactic nucleus and associated with high flow speeds, another (with p = 2.18) taking over at larger distances and slower flow speeds.

Diffusive shock acceleration at laser-driven shocks: studying cosmic-ray accelerators in the laboratory

The non-thermal particle spectra responsible for the emission from many astrophysical systems are thought to originate from shocks via a first order Fermi process otherwise known as diffusive shock acceleration. The same mechanism is also widely believed to be responsible for the production of high energy cosmic rays. With the growing interest in collisionless shock physics in laser produced plasmas, the possibility of reproducing and detecting shock acceleration in controlled laboratory experiments should be considered. The various experimental constraints that must be satisfied are reviewed. It is demonstrated that several currently operating laser facilities may fulfil the necessary criteria to confirm the occurrence of diffusive shock acceleration of electrons at laser produced shocks. Successful reproduction of Fermi acceleration in the laboratory could open a range of possibilities, providing insight into the complex plasma processes that occur near astrophysical sources of cosmic rays.

Maximum synchrotron frequency for shock-accelerated particles

Abstract It is widely believed that the maximum energy of synchrotron photons when electrons are accelerated in shocks via the Fermi process is about 50 MeV (in plasma comoving frame). We show that under certain conditions, which are expected to be realized in relativistic shocks of gamma-ray bursts, synchrotron photons of energy much larger than 50 MeV (comoving frame) can be produced. The requirement is that magnetic field should decay downstream of the shock front on a length-scale that is small compared with the distance travelled by the highest energy electrons before they lose half their energy; photons of energy much larger than 50 MeV are produced close to the shock front, whereas the highest Lorentz factor that electrons can attain is controlled by the much weaker field that occupies most of the volume of the shocked plasma.

The “toothbrush-relic”: evidence for a coherent linear 2-Mpc scale shock wave in a massive merging galaxy cluster?

Some merging galaxy clusters host diffuse extended radio emission, so-called radio halos and relics. Here we present observations between 147 MHz and 4.9 GHz of a new radio-selected galaxy cluster 1RXS J0603.3+4214 (z=0.225). The cluster is also detected as an extended X-ray source in the RASS. It hosts a large bright 1.9 Mpc radio relic, an elongated ~2 Mpc radio halo, and two smaller radio relics. The large radio relic has a peculiar linear morphology. For this relic we observe a clear spectral index gradient, in the direction towards the cluster center. We performed Rotation Measure (RM) Synthesis between 1.2 and 1.7 GHz. The results suggest that for the west part of the large relic some of the Faraday rotation is caused by ICM and is not only due to galactic foregrounds. We also carried out a detailed spectral analysis of this radio relic and created radio color-color diagrams. We find (i) an injection spectral index of -0.6 to -0.7, (ii) steepening spectral index and increasing spectral curvature in the post-shock region, and (iii) an overall power-law spectrum between 74 MHz and 4.9 GHz with \alpha=-1.10 \pm 0.02. Mixing of emission in the beam from regions with different spectral ages is probably the dominant factor that determines the shape of the radio spectra. Changes in the magnetic field, total electron content, or adiabatic gains/losses do not play a major role. A model in which particles are (re)accelerated in a first order Fermi process at the front of the relic provides the best match to the observed spectra. We speculate that in the post-shock region particles are re-accelerated by merger induced turbulence to form the radio halo as the relic and halo are connected. The 1RXS J0603.3+4214 merger is probably more complex than the "simple'" binary merger events that are thought to give rise to symmetric double radio relics.

Particle Acceleration in Turbulence and Weakly Stochastic Reconnection

In this Letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in and demonstrated numerically in . When turbulence is included within the current sheet, the acceleration rate is highly enhanced, because reconnection becomes fast and independent of resistivity and allows the formation of a thick volume filled with multiple simultaneously reconnecting magnetic fluxes. Charged particles trapped within this volume suffer several head-on scatterings with the contracting magnetic fluctuations, which significantly increase the acceleration rate and results in a first-order Fermi process. For comparison, we also tested acceleration in MHD turbulence, where particles suffer collisions with approaching and receding magnetic irregularities, resulting in a reduced acceleration rate. We argue that the dominant acceleration mechanism approaches a second order Fermi process in this case.

Inertia in strategy switching transforms the strategy evolution

A recent experimental study [Traulsen et al., Proc. Natl. Acad. Sci. 107, 2962 (2010)] shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy, which is equivalent to inertia. However, it remains largely unclear how such a predisposed inertia affects 2 × 2 games in a well-mixed population of finite size. To address this issue, the "inertia bonus" (strategy switching cost) is added to the learner payoff in the Fermi process. We find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes, with each covering seven regions in the plane spanned by two inertia parameters. We also obtain the extended "1/3" rule with inertia and the speed criterion with inertia; these two findings hold for a population above two. We illustrate the above results in the framework of the Prisoner's Dilemma game. As inertia varies, two intriguing stationary distributions emerge: the probability of coexistence state is maximized, or those of two full states are simultaneously peaked. Our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and, in particular, the evolution of cooperation.

Pick-up ion transport under conservation of particle invariants: how important are velocity diffusion and cooling processes?

Context. The phase space transport of pick-up ions (PUIs) in the heliosphere has been studied for the cases that these particles are experiencing a second-order Fermi process, i.e. velocity diffusion, a convection with the solar wind, and adiabatic or “magnetic” cooling, i.e. cooling connected with the conservation of the magnetic moment.Aims. The study aims at a quantification of the process of “magnetic cooling” that has recently been introduced as a modification of adiabatic cooling in the presence of frozen-in magnetic fields.Methods. The isotropic PUI velocity distributions are obtained as numerical solutions of a Fokker-Planck phase space transport equation.Results. It is demonstrated that this newly discussed process is, like adiabatic energy changes, not limited to cooling but can also, depending on the shape of the distribution function, result in heating. For pure cooling with negligible velocity diffusion a v -5 velocity power law is found for magnetic cooling, thus confirming earlier analytical results. For non-negligible second-order Fermi acceleration, the tails of the distribution functions exhibit different shapes, which in special cases are also close to the prominent v -5 behaviour, which is often found in observations. Conclusions. The existence of an exact v -5 power law of PUI distribution functions can be confirmed for insignificant velocity diffusion and its approximate validity for specific choices of the velocity dependence of the diffusion coefficient.

MAGNETOHYDRODYNAMIC SIMULATIONS OF RECONNECTION AND PARTICLE ACCELERATION: THREE-DIMENSIONAL EFFECTS

Magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first-order Fermi process. In this work we study the properties of particle acceleration inserted in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in magnetohydrodynamic (MHD) domains of reconnection without including kinetic effects, such as pressure anisotropy, the Hall term, or anomalous effects, increases exponentially. Also, the acceleration of the perpendicular component is always possible in such models. We find that within contracting magnetic islands or current sheets the particles accelerate predominantly through the first-order Fermi process, as previously described, while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients. Considering two-dimensional MHD models without a guide field, we find that the parallel acceleration stops at some level. This saturation effect is, however, removed in the presence of an out-of-plane guide field or in three-dimensional models. Therefore, we stress the importance of the guide field and fully three-dimensional studies for a complete understanding of the process of particle acceleration in astrophysical reconnection environments.