Stochastic Acceleration Mechanism Research Articles

Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

ABSTRACT This work investigates the evolution of the distribution of charged particles (cosmic rays) due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasi-linear approximation, and by assuming turbulent spectra with power being available only in the sub-gyroscale range, we find that the Fokker–Planck diffusion coefficients Dγγ and Dμμ scale with the Lorentz factor γ as Dγγ ∝ γ−2/3 and Dμμ ∝ γ−8/3. We consider Alfvèn and fast waves in our calculations, and find a universal trend for the momentum diffusion coefficient irrespective of the properties of the small-scale turbulence. Such universality has already been reported regarding the spatial diffusion of the cosmic rays, and, here too, we observe a universality in the momentum diffusion coefficient. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion-type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss, and particle escape on the particle distribution by systematically varying the parameters of the problem. We observe that the effect of the small-scale turbulence is more impactful for the high-energy protons as compared to the electrons and such turbulence is capable of sustaining the energy of the protons from catastrophic radiative loss processes. Such a finding is novel and helps us to enhance our understanding about the hadronic emission processes that are typically considered as a competitor for the leptonic emission for certain astrophysical systems.

Curvature of the Spectral Energy Distribution, Compton Dominance, and Synchrotron Peak Frequency in Jetted Active Galactic Nuclei

We collect a large sample with a reliable redshift detected by the Fermi satellite after 10 yr of data (4FGL-DR2), including blazars, gamma-ray narrow-line Seyfert 1 galaxies (γNLS1s), and radio galaxies. The spectral energy distributions of these Fermi sources are fitted by using a second-degree polynomial, and some important parameters including spectral curvature, synchrotron peak frequency, and peak luminosity are obtained. Based on those parameters, we discuss the Fermi blazar sequence and the particle acceleration mechanism. Our main results are as follows: (i) By studying the relationship between the synchrotron peak frequency and the synchrotron peak frequency luminosity, jet kinetic power, and gamma-ray luminosity for jetted active galactic nuclei (AGNs), we find an “L” shape in the Fermi blazar sequence. (ii) There is a significant anticorrelation between the Compton dominance, the black hole spin, and the synchrotron peak frequency for jetted AGNs, respectively. These results support that the γNLS1s and radio galaxies belong to the Fermi blazar sequence. (iii) On the basis of previous work, statistical or stochastic acceleration mechanisms can be used to explain the relationship between the synchrotron peak frequency and synchrotron curvature. For different subclasses, the correlation slopes are different, which implies that the Fermi sources of different subclasses have different acceleration mechanisms. (iv) Flat-spectrum radio quasars and γNLS1s have a higher median spin of a black hole than BL Lac objects and radio galaxies.

Instabilities, anomalous heating, and stochastic acceleration of electrons in colliding plasmas

The collision of two expanding plasma clouds is investigated, emphasizing instabilities and electron energization in the plasma mixing layer. This work is not only directly relevant to laboratory experiments with explosively created laser or z-pinch plasmas but may also elucidate naturally occurring plasma collisions in astrophysical or space physics contexts. In the previous publications [Malkov and Sotnikov, Phys. Plasmas 25, 102108 (2018) and Sotnikov et al., Phys. Plasmas 27, 122113 (2020)], we have studied, analytically and numerically, the flow emerging from interpenetrating coronas launched by two parallel wires vaporized in a vacuum chamber. The main foci of the studies have been on the general flow pattern and lower-hybrid and thin-shell instabilities that under certain conditions develop in the collision layer. The present paper centers around the initial phase of the interpenetration of the two plasmas. Two-stream ion–ion instability, efficient electron heating, and stochastic acceleration dominate plasma mixing at this phase. Both the adiabatic (reversible) electron heating and stochastic (irreversible) acceleration and heating mechanisms, powered by unstably driven electric fields, are considered. The irreversibility results from a combination of electron runaway acceleration in the wave electric fields and pitch-angle scattering on ions and neutrals.

Particle acceleration in space: a universal mechanism?

AbstractExperimental evidence in favor of or against the existence of a universal mechanism for the acceleration of charged particles in the Universe is analyzed from the modern standpoint. We adopt a purely phenomenological approach to this very intricate problem, discussing spatial scales that range from the magnetospheres of Earth and other planets of the Solar System to the Sun’s atmosphere, the heliosphere, supernovae, and extragalactic objects responsible for the generation of ultra-high-energy cosmic rays. We demonstrate a great variety of acceleration mechanisms operating in the Universe. However, data on the nuclear composition of accelerated particles obtained in numerous experiments may be indicative of a global nature of the Fermi-type stochastic acceleration mechanism inherent in various astrophysical objects. This mechanism may well be dominant over others, but a number of experimental observations are nevertheless inconsistent with that idea. It is possible that a hierarchy of accelerating mechanisms operates in some space objects, with preliminary acceleration by one mechanism followed by other mechanisms, acting sequentially or alternatively. We therefore discuss all currently available data for and against the global ‘presence’ of a Fermi-type acceleration mechanism.

From the Fermi Blazar Sequence to the Relation between Fermi Blazars and γ-Ray Narrow-line Seyfert 1 Galaxies

Abstract We use the third catalog of blazars detected by Fermi/LAT (3LAC) and γ-ray narrow-line Seyfert 1 Galaxies (γ-NLSy1s) to study the blazar sequence and relationship between them. Our results are as follows. (i) There is a weak anticorrelation between synchrotron peak frequency and peak luminosity for both Fermi blazars and γ-NLSy1s, which supports the blazar sequence. However, after Doppler correction, the inverse correlation disappeared, which suggests that anticorrelation between synchrotron peak frequency and peak luminosity is affected by the beaming effect. (ii) There is a significant anticorrelation between jet kinetic power and synchrotron peak frequency for both Fermi blazars and γ-NLSy1s, which suggests that the γ-NLSy1s could fit well into the original blazar sequence. (iii) According to previous work, the relationship between synchrotron peak frequency and synchrotron curvature can be explained by statistical or stochastic acceleration mechanisms. There are significant correlations between synchrotron peak frequency and synchrotron curvature for whole sample, Fermi blazars and BL Lac objects, respectively. The slopes of the correlation are consistent with statistical acceleration. For FSRQs, LBLs, IBLs, HBLs, and γ-NLS1s, we also find a significant correlation, but in these cases the slopes cannot be explained by previous theoretical models. (iv) The slope of the relation between synchrotron peak frequency and synchrotron curvature in γ-NLS1s is larger than that of FSRQs and BL Lac objects. This result may imply that the cooling dominates over the acceleration process for FSRQs and BL Lac objects, while γ-NLS1s is the opposite.

Two Phases of Solar Flares and a Stochastic Mechanism for Acceleration of Electrons and Protons

The hypothesis of two phases of charged particle acceleration in solar flares is well known, with subrelativistic electrons accelerated in the first phase and relativistic electrons and protons in the second. Both phases are distinguished in the solar proton events and their parent flares of December 26, 2001 (M7.1), November 2, 2003 (X8.3), and August 9, 2011 (X6.9), while in the interplanetary space only electrons were observed from the first phase and electrons and protons from the second. The temporal profiles of the electrons and protons from the second phase are similar; hence, it is concluded that the relativistic electrons and protons observed in the interplanetary space are predominantly accelerated in flares, rather than in the shock front of a coronal mass ejection. Most likely a stochastic acceleration mechanism is realized in flares where protons and electrons gain energy in many elementary events over the entire duration of the flare which lasts much longer than an elementary event. To ensure consistency of a stochastic acceleration process with the existence of two phases in solar flares it is necessary to consider gyrosynchronous radiative electron losses in the second phase which can be neglected in the first phase. The energy of the accelerated protons in the first phase is small for their detection in processes taking place on the sun, but in the second phase it may be sufficient to produce gamma lines, both nuclear and from pion decay.

Wakefield acceleration towards ZeV from a black hole emanating astrophysical jets

We consider that electromagnetic pulses produced in the jets of this innermost part of the accretion disk accelerate charged particles (protons, ions, electrons) to very high energies via wakefield acceleration, including energies above 10[Formula: see text] eV for the case of protons and nucleus and 10[Formula: see text] eV for electrons by electromagnetic wave-particle interaction. Thereby, the wakefield acceleration mechanism supplements the pervasive Fermi’s stochastic acceleration mechanism (and overcomes its difficulties in the highest energy cosmic ray generation). The episodic eruptive accretion in the disk by the magneto-rotational instability gives rise to the strong Alfvenic pulses, which acts as the driver of the collective accelerating pondermotive force. This pondermotive force drives the wakes. The accelerated hadrons (protons and nuclei) are released to the intergalactic space to be ultra-high energy cosmic rays. The high-energy electrons, on the other hand, emit photons to produce various non-thermal emissions (radio, IR, visible, UV, and gamma-rays) of active galactic nuclei in an episodic manner, giving observational telltale signatures.

Novel approach to stochastic acceleration of electrons in colliding laser fields

The mechanism of stochastic electron acceleration in colliding laser waves is investigated by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative laser wave is absent. The performed analytical analysis clearly reveals the physical picture of stochastic electron dynamics. It shows that when the amplitude of the perturbative laser field exceeds some critical value, stochastic electron acceleration occurs within some electron energy range. The conditions, at which the maximum electron energy gained under stochastic acceleration greatly exceeds the ponderomotive energy scaling based on the amplitude of the dominant laser, are derived.

LOFAR Observations of 4C+19.44: On the Discovery of Low-frequency Spectral Curvature in Relativistic Jet Knots

Abstract We present the first LOFAR observations of the radio jet in the quasar 4C+19.44 (a.k.a. PKS 1354+19) obtained with long baselines. The achieved resolution is very well matched to that of archival Jansky Very Large Array observations at higher radio frequencies as well as the archival X-ray images obtained with Chandra. We found that, for several knots along the jet, the radio flux densities measured at hundreds of MHz lie well below the values estimated by extrapolating the GHz spectra. This clearly indicates the presence of spectral curvature. Radio spectral curvature has already been observed in different source classes and/or extended radio structures, and it has been often interpreted as due to intrinsic processes, as a curved particle energy distribution, rather than absorption mechanisms (Razin–Tsytovich effect, free–free or synchrotron self absorption to name a few). Here, we discuss our results according to the scenario where particles undergo stochastic acceleration mechanisms also in quasar jet knots.

Curvature of the spectral energy distribution, the inverse Compton component and the jet in Fermi 2LAC blazars

We fit the spectral energy distributions (SEDs) of members of a large sample of Fermi 2LAC blazars to synchrotron and inverse Compton (IC) models. Our main results are as follows. (i) As suggested by previous works, the correlation between peak frequency and curvature can be explained by statistical or stochastic particle acceleration mechanisms. For BL Lacs, we find a linear correlation between synchrotron peak frequency and its curvature. The slope of the correlation is consistent with the stochastic acceleration mechanisms and confirm previous studies. For FSRQs, we also find a linear correlation, but its slope cannot be explained by previous theoretical models. (ii) We find a significant correlation between IC luminosity and synchrotron luminosity. The slope of the correlation of FSRQs is consistent with the EC process. And the slope of the correlation of BL Lac is consistent with the SSC process. (iii) We find several significant correlations between IC curvature and several basic parameters of blazars (black hole mass, broad line luminosity, the Lorentz factor of jet). We also find significant correlations between bolometric luminosity and these basic parameters of blazars which suggest that the origin of jet is a mixture of the mechanisms proposed by Blandford $\&$ Znajek and by Blandford $\&$ Payne.

CURVATURE OF THE SPECTRAL ENERGY DISTRIBUTIONS OF BLAZARS

The SED of blazars show significant curvature. In this paper, we study the curvature properties for a large sample of Fermi/LAT bright blazars based on quasi-simultaneous SED. Both SEDs of synchrotron and inverse Compton (IC) components are fitted by a log-parabolic law in log_v-log_vfv diagram. The second-degree term of log-parabola measures the curvature of SED. We find a statistically significant correlation between synchrotron peak frequency and its curvature. This result is in agreement with the theoretical prediction, and confirms previous studies, which dealt with single source with various epoch observations or a small sample. If a broken power-law is employed to fit the SED, the difference between the two spectral indexes (alpha2-alpha1) can be considered as a "surrogate" of the SED curvature. We collect spectral parameters of a sample blazars from literature, and find a correlation between the synchrotron peak frequency and the spectral difference. We do not find a significant correlation between the IC peak frequency and its curvature, which may be caused by complicated seed photon field. It is also found that the synchrotron curvatures are on average larger than that of IC curvatures, and there is no correlation between these two parameters. As suggested by previous works in literature, both the log-parabolic law of SED and above correlation can be explained by statistical and/or stochastic particle accelerations. Stochastic particle acceleration predicts a different slope of the correlation from that of statistical one, and our result seems favor stochastic acceleration mechanisms and emission processes. Some of other evidences also seem to support that the electron energy distribution (and/or synchrotron SED) may be log-parabolic, which include SED modeling, particle acceleration simulation, and comparisons between some predictions and empirical relations/correlations.

Stochastic electron acceleration in plasma waves driven by a high-power subpicosecond laser pulse

The mechanism of stochastic electron acceleration and heating by a picosecond laser pulse in underdense plasma is studied using particle-in-cell simulations and theoretical models. The formation of wide electron energy spectra in the simultaneously acting laser and plasma fields is analyzed. It is shown that electron scattering by turbulent plasma fluctuations excited through stimulated forward Raman scattering plays a governing role in the formation of high-energy tails in the electron distribution function.

Stochastic electron motion driven by space plasma waves

Abstract. Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is responsible for the dynamical balance between the accelerating process and relativistic electron precipitation events. We have also considered the efficiency of the mechanism of stochastic surfing acceleration of cosmic electrons at the supernova remnant shock front, and the accelerating process driven by a Langmuir wave packet in producing cosmic ray electrons. The dynamics of cosmic electrons is formulated in terms of a dissipative map involving the effect of synchrotron emission. We present analytical and numerical methods for studying Hamiltonian chaos and dissipative strange attractors, and for determining the heating extent and energy spectra.

PROBING DYNAMICS OF ELECTRON ACCELERATION WITH RADIO AND X-RAY SPECTROSCOPY, IMAGING, AND TIMING IN THE 2002 APRIL 11 SOLAR FLARE

Based on detailed analysis of radio and X-ray observations of a flare on 2002 April 11 augmented by realistic 3D modeling, we have identified a radio emission component produced directly at the flare acceleration region. This acceleration region radio component has distinctly different (i) spectrum, (ii) light curves, (iii) spatial location, and, thus, (iv) physical parameters from those of the separately identified, trapped or precipitating electron components. To derive evolution of physical parameters of the radio sources we apply forward fitting of the radio spectrum time sequence with the gyrosynchrotron source function with 5 to 6 free parameters. At the stage when the contribution from the acceleration region dominates the radio spectrum, the X-ray- and radio- derived electron energy spectral indices agree well with each other. During this time the maximum energy of the accelerated electron spectrum displays a monotonic increase with time from ~ 300 keV to ~ 2 MeV over roughly one minute duration indicative of an acceleration process in the form of growth of the power-law tail; the fast electron residence time in the acceleration region is about 2 - 4 s, which is much longer than the time of flight and so requires a strong diffusion mode there to inhibit free-streaming propagation. The acceleration region has a relatively strong magnetic field, B ~ 120 G, and a low thermal density, less than 2x10^9 cm^-3. These acceleration region properties are consistent with a stochastic acceleration mechanism.

REVISITING ACCELERATION OF CHARGED GRAINS IN MAGNETOHYDRODYNAMIC TURBULENCE

We study the acceleration of charged grains by magnetohydrodynamics (MHD) turbulence in the interstellar medium (ISM). We begin with revisiting gyroresonance acceleration by taking into account the fluctuations of grain guiding center along a uniform magnetic field (i.e. nonlinear theory--NLT). We calculate grain velocities due to gyroresonance by fast MHD modes using the NLT for different phases of the ISM, and compare with results obtained using quasi-linear theory (QLT). We find for the parameters applicable to the typical ISM phases that the fluctuations of grain guiding center reduce grain velocities by less than 15 percent, but they can be important for more special circumstances. We confirm that large grains can be accelerated to super-Alfvenic velocities through gyroresonance. For such super-Alfvenic grains, we investigate the effect of further acceleration via transit time damping (TTD) by fast modes. We find that due to the broadening of resonance condition in the NLT, the TTD acceleration is not only important for the cosines of grain pitch angle relative to the magnetic field mu>V_{A}/v, but also for mu<V_{A}/v where v is the grain velocity and V_{A} is the Alfven speed. We show that the TTD acceleration is dominant over the gyroresonance for large grains, and can increase substantially grain velocities induced by gyroresonance acceleration. We quantify another stochastic acceleration mechanism arising from low frequency Alfven waves. We discuss the range of applicability of the mechanisms and their implications.

X-RAY AND TeV EMISSIONS FROM HIGH-FREQUENCY-PEAKED BL LAC OBJECTS

The majority of the extragalactic sources yet detected at TeV photon energies belong to the class of "high frequency peaked BL Lacs" (HBLs) that exhibit a spectral energy distribution with a lower peak in the X-ray band. Such spectra are well described in terms of a log-parabolic shape with a considerable curvature, and widely interpreted as synchrotron emission from ultrarelativistic electrons outflowing in a relativistic jet; these are expected to radiate also in gamma-rays by the inverse Compton process. Recently we have compared the X-ray spectral parameter distributions of TeV detected HBLs (TBLs) with those undetected (UBLs), and found that the distributions of the peak energies E_p are similarly symmetric around a value of a few keVs for both subclasses, while the X-ray spectra are broader for TBLs than for UBLs. Here we propose an acceleration scenario to interpret both the E_p and the spectral curvature distributions in terms of a coherent and a stochastic acceleration mechanisms, respectively. We show how the curvature parameter b< 0.3 - 0.7 of the synchrotron X rays, that depends only on the latter acceleration component, can be related to the inverse Compton luminosity in gamma-rays, so introducing a link between the X-ray and the TeV observations of HBLs.

Which radio galaxies can make the highest energy cosmic rays?

Numerous authors have suggested that the ultra-high energy cosmic rays (UHECR) detected by the Pierre Auger Observatory and other cosmic-ray telescopes may be accelerated in the nuclei, jets or lobes of radio galaxies. Here I focus on stochastic acceleration in the lobes. I show that the requirement that they accelerate protons to the highest observed energies places constraints on the observable properties of radio lobes that are satisfied by a relatively small number of objects within the Greisen-Zat'sepin-Kuzmin (GZK) cutoff; if UHECR are protons and are accelerated within radio lobes, their sources are probably already known and catalogued radio galaxies. I show that lobe acceleration also implies a (charge-dependent) upper energy limit on the UHECR that can be produced in this way; if lobes are the dominant accelerators in the local universe and if UHECR are predominantly protons, we are unlikely to see cosmic rays much higher in energy than those we have already observed. I comment on the viability of the stochastic acceleration mechanism and the likely composition of cosmic rays accelerated in this way, based on our current understanding of the contents of the large-scale lobes of radio galaxies, and finally discuss the implications of stochastic lobe acceleration for the future of cosmic ray astronomy.

The acceleration of Anomalous Cosmic Rays by stochastic acceleration in the heliosheath

Stochastic acceleration in the heliosheath appears to be a likely mechanism by which Anomalous Cosmic Rays (ACRs) are accelerated. However, most stochastic acceleration mechanisms are not appropriate. The energy density in the ACRs and in the interstellar pickup ions out of which the ACRs are accelerated greatly exceeds the energy density in the turbulence in the heliosheath. Thus, a traditional stochastic acceleration mechanism in which particles are accelerated by damping the turbulence will not work. A stochastic acceleration mechanism has been developed in which the total energy of the pickup ions and the ACRs is conserved. Energy is redistributed from the core pickup ions into a suprathermal tail to create the ACRs. A model for the acceleration of the ACRs in the heliosheath, based on this stochastic acceleration mechanism, is presented. The model provides reasonable fits to the spectra of suprathermal particles and ACRs observed by Voyager.

Stochastic and direct acceleration mechanisms in the Earth's magnetotail

Ion beams with energies of the order of several tens of keV are frequently observed in the Earth's magnetotail. Here we consider two possible acceleration mechanisms, the cross tail electric field Ey and the stochastic acceleration due to the electromagnetic fluctuations present in the magnetotail. Electromagnetic perturbations are generated by random oscillating “clouds” moving in the x − y plane. A test particle simulation has been performed in order to reproduce the interaction between protons and electromagnetic fluctuations and the constant dawn‐dusk electric field, Ey, in the magnetotail current sheet. Protons are accelerated via a stochastic Fermi‐like process and, by varying the features of the electromagnetic fluctuations, the combined effect of Ey and of the moving clouds can explain the typical energy range of ion observations from 20 to 100 keV, and the characteristic acceleration times of several minutes.

Beamlets from stochastic acceleration

We investigate the dynamics of a realization of the stochastic Fermi acceleration mechanism. The model consists of test particles moving between two oscillating magnetic clouds and differs from the usual Fermi-Ulam model in two ways. (i) Particles can penetrate inside clouds before being reflected. (ii) Particles can radiate a fraction of their energy during the process. Since the Fermi mechanism is at work, particles are stochastically accelerated, even in the presence of the radiated energy. Furthermore, due to a kind of resonance between particles and oscillating clouds, the probability density function of particles is strongly modified, thus generating beams of accelerated particles rather than a translation of the whole distribution function to higher energy. This simple mechanism could account for the presence of beamlets in some space plasma physics situations.