On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

Particle acceleration during the explosive phase of a solar flare

Starting with the quasi-linear equation of the distribution function of particles in a regular electric field, a combined diffusion coefficient in the momentum space conbining the effects of the regular field and a turbulent field is obtained and a combined mechanism of acceleration by the regular and turbulent fields in the neutral sheet of solar proton flares is proposed. It is shown by calculation that conditions in solar proton flares are such that the charged particles can be effectively accelerated to tens of MeV, even ~1 GeV. It is shown that the combined acceleration by a regular electric field and ion-acoustic turbulence pumps the protons and other heavy ions into ranges of energy where they can be accelerated by Langmuir turbulence. By considering the combined acceleration by Langmuir turbulence and the regular electric field, the observed spectrum of energetic protons and the power-law spectrum of energetic electrons can be reproduced.     

Physical conditions in radio jets and re-acceleration of relativistic electrons by MHD turbulence

Based on the observed features and physical conditions in the radio jets of several low-luminosity radio galaxies, I discuss the re-acceleration of relativistic electrons. On assuming a Fermi type acceleration, an acceleration coefficient of ～10^?15 s^?1 was obtained, which can well explain the radio brightness distribution in the jets and their spectrum. I further discuss the possibility of MHD turbulence providing the acceleration, and find that the turbulence energy spectral index must be restricted to the very narrow range 1.6–1.7.     

Acceleration of Relativistic Protons During the 20 January 2005 Flare and CME

The origin of relativistic solar protons during large flare/CME events has not been uniquely identified so far. We perform a detailed comparative analysis of the time profiles of relativistic protons detected by the worldwide network of neutron monitors at Earth with electromagnetic signatures of particle acceleration in the solar corona during the large particle event of 20 January 2005. The intensity – time profile of the relativistic protons derived from the neutron monitor data indicates two successive peaks. We show that microwave, hard X-ray, and γ-ray emissions display several episodes of particle acceleration within the impulsive flare phase. The first relativistic protons detected at Earth are accelerated together with relativistic electrons and with protons that produce pion-decay γ rays during the second episode. The second peak in the relativistic proton profile at Earth is accompanied by new signatures of particle acceleration in the corona within ≈1R _⊙ above the photosphere, revealed by hard X-ray and microwave emissions of low intensity and by the renewed radio emission of electron beams and of a coronal shock wave. We discuss the observations in terms of different scenarios of particle acceleration in the corona.     

Nonresonant generation of MHD disturbances during supernova explosions in an inhomogeneous interstellar medium

We analyze the nonresonant generation of large-scale magnetic inhomogeneities near a shock front by accelerated particles. The MHD disturbances are generated by the electric current excited by relativistic particles in the preshock medium in the presence of weak large-scale density inhomogeneities. The MHD modes considered can be amplified by other resonant and nonresonant mechanisms related to the presence of relativistic particles. We estimate the magnetic fields and the energies to which charged particles can be accelerated in different phases of the interstellar medium by taking into account the random magnetic fields generated by the mechanism considered.     

Acceleration of particles by electron plasma waves in a moderate magnetic field

A general scheme is established to examine any magnetohydrodynamic (MHD) configuration for its acceleration potential including the effects of various types of plasma waves. The analysis is restricted to plasma waves in a magnetic field with electron cyclotron frequency less than, but comparable to, the electron plasma frequency (moderate field). The general role of electron plasma waves is examined in this paper independent of a specific MHD configuration or generating mechanism in the weak turbulence limit. The evolution of arbitrary wave spectra in a non-relativistic plasma is examined, and it is shown that the nonlinear, process of induced scattering on the polarization clouds of ions leads to the collapse of the waves to an almost one-dimensional spectrum directed along the magnetic field. The subsequent acceleration of non-relativistic and relativistic particles is considered. It is shown for non-relativistic particles that when the wave distribution has a negative slope the acceleration is retarded for lower velocities and enhanced for higher velocities compared to acceleration by an isotropic distribution of electron plasma waves in a magnetic field. This change in behavior is expected to affect the development of wave spectra and the subsequent acceleration spectrum.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Investigation of the possible source for the solar energetic particle event on 2017 September 10

According to the solar proton data observed by Geostationary Operational Environmental Satellites(GOES), ground-based neutron monitors on Earth and near-relativistic electron data measured by the ACE spacecraft, the onset times of protons with different energies and near-relativistic electrons have been estimated and compared with the time of solar soft and hard X-ray and radio burst data.The results show that first arriving relativistic and non-relativistic protons and electrons may have been accelerated by the concurrent flare. The results also suggest that release times of protons with different energies may be different, and the protons with lower energy may have been released earlier than those with higher energy. Some protons accelerated by concurrent flares may be further accelerated by the shock driven by the associated CME.     

On the threshold effect of proton acceleraton in solar flares

Based on the reconnection theory of a flare and on recent observational and statistical findings, the problem of the initial acceleration of solar cosmic rays (SCR) is discussed. Simple estimates of the electric fields required to start the electron acceleration are obtained and the problem of proton ionization losses for overcoming the Coulomb barrier is considered. We take into account also the possible differences between proton and electron spectra from the very beginning of the acceleration process. Special attention is paid to the distribution functions of solar flare events in various parameters (peak fluxes and/or energy fluences in X-ray and radio wave bursts, in proton and electron emissions, etc.). It is shown that the distribution functions allow the interpretation of some scale and time flare parameters in terms of expected threshold effects. However, these functions are still insufficient to evaluate the relative share of different emissions in the global energy budget of a flare. In this context, a more promising approach is to derive the direct ratio between the number of accelerated protons,N _p, and total flare energy,W _f, within the frame of a certain acceleration model. It is argued that an absolute threshold for proton production (in Hudson's formulation) does not exist. Meanwhile, the flux and threshold energy of accelerated protons overcoming the Coulomb loss maximum, in fact, may depend heavily on the global output of flare energy.     

Prompt particle acceleration around moving X-point magnetic field during impulsive phase of solar flares

We present a model for high-energy solar flares to explain prompt proton and electron acceleration, which occurs around moving X-point magnetic fields during the implosion phase of the current sheet. We derive the electromagnetic fields during the strong implosion of the current sheet, which is driven by the converging flow toward the center of the magnetic arcade. We investigated a test particle motion in the strong electromagnetic fields derived from the MHD equations. It is shown that both protons and electrons can be promptly (within 1 s) accelerated to 70 and 200 MeV, respectively. This acceleration mechanism can be applicable for the impulsive phase of the gradual gamma-ray and proton flares (gradual GR/P flare), which have been called two-ribbon flares.     

The multi-band non-thermal emission from the supernova remnant RX J1713.7−3946

Non-thermal X-rays and very high energy (VHE) γ-rays have been detected from the supernova remnant (SNR) RX J1713.7−3946, and the recent observations with the Suzaku satellite clearly reveal a spectral cut-off in the X-ray spectrum, which directly relates to the cut-off of the energy spectrum of the parent electrons. However, whether the origin of the VHE γ-rays from the SNR is hadronic or leptonic is still in debate. We studied the multi-band non-thermal emission from RX J1713.7−3946 based on a semi-analytical approach towards the non-linear shock acceleration process by including the contribution of the accelerated electrons to the non-thermal radiation. The results show that the multi-band observations on RX J1713.7−3946 can be well explained in the model with appropriate parameters, and the TeV γ-rays have hadronic origin, i.e. they are produced via proton–proton interactions as the relativistic protons accelerated by the shock collide with the ambient matter.     

Acceleration of particles in the vicinity of a massive black hole

Recent results of the gamma-ray Cherenkov astronomy definitely prove the existence of fast variability in the very high energy (V.H.E.) gamma-ray flux of some active galactic nuclei. The BL Lac PKS 2155-304 for instance showed variations down to a few minutes time scale. From standard light travel time argument, these variations put extremely strong constraints on the size of the TeV emitting zone, which has to be of the order of a few Schwarzschild radius, even for high values of the relativistic Doppler factor of the emitting jets. Such discovery is a challenge for particle acceleration scenarios, which have to imagine efficient acceleration processes at work in a very compact zone. Eventually, the immediate vicinity of the central black hole appears as the most conservative choice for the location of the TeV emission region of active galactic nuclei. In this paper, we propose a two-step mechanism for charged particle acceleration in the magnetosphere of a massive black hole surrounded by an accretion disk. Particles first gain energy by a stochastic process during the accretion phase. It is shown that effective proton acceleration up to energies 10¹⁷–10¹⁹ eV is possible in a low-luminosity magnetized accretion disk with 2D turbulent motion. The distribution function of energetic protons over energies is a power law function with typical index ≃−1. Here electrons are not very efficiently accelerated because of their drastic losses by synchrotron radiation. In a second time, part of the fast particles escape from the disk and are then entrained by the magnetic structure above the disk, in the rotating black hole magnetosphere. They thus gain additional energy by direct centrifugal mechanism, up to about 10²⁰ eV for the protons and to 10–100 TeV for the electrons when they cross the light cylinder surface. Such energetic particles can further radiate in the TeV spectral range observed by Cherenkov experiments as HESS, MAGIC and VERITAS. Energetic protons can produce γ-radiation in the energy band 1 GeV–100 TeV and above mainly by nuclei collisions with the disk matter, clouds, or ambient low energy photons. Energetic electrons can also reach the required spectral range by inverse Compton emission. However their acceleration is less efficient due to heavy radiation losses, and only gained by centrifugal process during the second phase of the whole mechanism we describe. Our present analysis would therefore favor hadronic scenarios for TeV emission of active galactic nuclei. It is tempting to relate long term variability over years of TeV active galactic nuclei to the first stochastic acceleration phase, which also provides the needed power law particle distributions, while short term variability over minutes is more likely due to perturbations of the second fast direct acceleration phase.     

Diffusion of cosmic rays in a multiphase interstellar medium swept-up by a supernova remnant blast wave

Supernova remnants (SNRs) are one of the most energetic astrophysical events and are thought to be the dominant source of Galactic cosmic rays (CRs). A recent report on observations from the Fermi satellite has shown a signature of pion decay in the gamma-ray spectra of SNRs. This provides strong evidence that high-energy protons are accelerated in SNRs. The actual gamma-ray emission from pion decay should depend on the diffusion of CRs in the interstellar medium. In order to quantitatively analyse the diffusion of high-energy CRs from acceleration sites, we have performed test particle numerical simulations of CR protons using a three-dimensional magnetohydrodynamics (MHD) simulation of an interstellar medium swept-up by a blast wave. We analyse the diffusion of CRs at a length scale of order a few pc in our simulated SNR, and find the diffusion of CRs is precisely described by a Bohm diffusion, which is required for efficient acceleration at least for particles with energies above 30 TeV for a realistic interstellar medium. Although we find the possibility of a superdiffusive process (travel distance ∝ t^0.75) in our simulations, its effect on CR diffusion at the length scale of the turbulence in the SNR is limited.     

Stochastic acceleration of electrons in solar flares

The generation of lower-hybrid waves by cross-field currents is applied to reconnection processes proposed for solar flares. Recent observations on fragmentation of energy release and acceleration, and on hard X-ray (HXR) spectra are taken into account to develop a model for electron acceleration by resonant stochastic interactions with lower-hybrid turbulence. The continuity of the velocity distribution is solved including collisions and escape from the turbulence region. It describes acceleration as a diffusion process in velocity space. The result indicates two regimes that are determined by the energy of the accelerating electrons which may explain the double power-law often observed in HXR spectra. The model further predicts an anticorrelation between HXR flux and spectral index in agreement with observations.     

Fermi acceleration and particle pitch angle scattering

We suggest that sharp velocity gradients will exist in fluid-like turbulence in nearly collisionless plasma. This implies effective quenching of Fermi acceleration of thermal particles, but the Fermi acceleration coefficient for relativistic particles remains essentially unchanged.     

A Kinetic Model of Coronal Heating and Acceleration by Ion-Cyclotron Waves: Preliminary Results

We present a kinetic model of the heating and acceleration of coronal protons by outward-propagating ion-cyclotron waves on open, radial magnetic flux tubes. In contrast to fluid models which typically insist on bi-Maxwellian distributions and which spread the wave energy and momentum over the entire proton population, this model follows the kinetic evolution of the collisionless proton distribution function in response to the combination of the resonant wave-particle interaction and external forces. The approximation is made that pitch-angle scattering by the waves is faster than all other processes, resulting in proton distributions which are uniform over the resonant surfaces in velocity space. We further assume, in this preliminary version, that the waves are dispersionless so these resonant surfaces are portions of spheres centered on the radial sum of the Alfvén speed and the proton bulk speed. We incorporate the fact that only those protons with radial speeds less than the bulk speed will be resonant with outward-propagating waves, so this rapid interaction acts only on the sunward half of the distribution. Despite this limitation, we find that the strong perpendicular heating of the resonant particles, coupled with the mirror force, results in substantial outward acceleration of the entire distribution. The proton distribution evolves towards an incomplete shell in velocity space, and appears vastly different from the distributions assumed in fluid models. Evidence of these distinctive distributions should be observable by instruments on Solar Probe.     

Electromagnetic and corpuscular emission from the solar flare of 1991 June 15: Continuous acceleraton of relativistic particles

Data on X-,γ-ray, optical and radio emission from the 1991 June 15 solar flare are considered. We have calculated the spectrum of protons that producesγ-rays during the gradual phase of the flare. The primary proton spectrum can be described as a Bessel-function-type up to 0.8 GeV and a power law with the spectral index ≈3 from 0.8 up to 10 GeV or above. We have also analyzed data on energetic particles near the Earth. Their spectrum differed from that of primary protons producingγ-ray line emission. In the gradual phase of the flare additional pulses of energy release occurred and the time profiles of cm-radio emission andγ-rays in the 0.8–10 MeV energy band and above 50 MeV coincided. A continuous and simultaneous stochastic acceleration of the protons and relativistic electrons at the gradual phase of the flare is considered as a natural explanation of the data.     

Test particle acceleration in torsional spine magnetic reconnection

Three-dimensional (3D) magnetic reconnection is taking place commonly in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. One of the proposed mechanisms for steady-state 3D magnetic reconnection is “torsional spine reconnection”. By using the magnetic and electric fields for “torsional spine reconnection”, we numerically investigate the features of test particle acceleration with input parameters for the solar corona. We show that efficient acceleration of a relativistic proton is possible near the null point where it can gain up to 100 MeV of kinetic energy within a few milliseconds. However, varying the injection position results in different scenarios for proton acceleration. A proton is most efficiently accelerated when it is injected at the point where the magnetic field lines change their curvature in the fan plane. Moreover, a proton injected far away from the null point cannot be accelerated and, even in some cases, it is trapped in the magnetic field. In addition, adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.     

Energetic particle acceleration in a three-dimensional magnetic field reconnection model: the role of magnetohydrodynamic turbulence

The role of magnetohydrodynamic (MHD) turbulence in the cosmic ray acceleration process in a volume with a reconnecting magnetic field is studied by means of Monte Carlo simulations. We performed modelling of proton acceleration, with the three-dimensional analytic model of stationary reconnection of Craig et al. providing the unperturbed background conditions. Perturbations of particle trajectories resulting from a turbulent magnetic field component were simulated using small-amplitude pitch-angle momentum scattering, enabling modelling of both small- and large-amplitude turbulence in a wide wavevector range. Within the approach, no second-order Fermi acceleration process is allowed. Comparison of the acceleration process in models involving particle trajectory perturbations with the unperturbed model reveals that the turbulence can substantially increase the acceleration efficiency, enabling much higher final particle energies and flat particle spectra.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.