Proton acceleration in flares and magnetohydrodynamic solar activity

The possibility of accelerated protons in solar flares having a sharp change in their spectral index is discussed. The analysis is based on the Tsytovich (1982, 1984, 1987a, b, c) acceleration model by MHD turbulence, which is shown to have different resonant conditions for non-relativistic and relativistic particles. The different resonant condition is shown to result in a sharp change in the accelerated proton spectral index, even in the absence of any peculiarity in the spectra of the MHD turbulence. Time scales for accelerated protons to relativistic energies are also derived, and shown to be consistent with observations. We also show that the threshold energy for electron acceleration by low frequency MHD turbulence is much greater than for proton acceleration. The turbulence therefore preferentially accelerates protons.     

Particle Acceleration in Reconnecting Current Sheets in Impulsive Electron-Rich Solar Flares

Electron and proton acceleration in reconnecting current sheets in electron-rich solar flares is considered. A significant three-dimensional magnetic field is assumed in the current sheet where the particles are accelerated by the DC electric field. The tearing instability of a pre-flare current sheet leads to the formation of multiple singular lines of magnetic field where the electric and magnetic fields are coaligned. Magnetized electrons are shown to be accelerated to a few tens of MeV before they leave the vicinity of a singular line. The acceleration time is estimated to be less than 10^–3 s. By contrast, much heavier protons are unmagnetized and their energy gain is more modest. The model explains a high electron-to-proton ratio and the unusually intense gamma-ray continuum above 1 MeV observed in the electron-rich flares.     

Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

Acceleration and Storage of Energetic Electrons in Magnetic Loops in the Course of Electric Current Oscillations

A mechanism of electron acceleration and storage of energetic particles in solar and stellar coronal magnetic loops, based on oscillations of the electric current, is considered. The magnetic loop is presented as an electric circuit with the electric current generated by convective motions in the photosphere. Eigenoscillations of the electric current in a loop induce an electric field directed along the loop axis. It is shown that the sudden reductions that occur in the course of type IV continuum and pulsating type III observed in various frequency bands (25?–?180 MHz, 110?–?600 MHz, 0.7?–?3.0 GHz) in solar flares provide evidence for acceleration and storage of the energetic electrons in coronal magnetic loops. We estimate the energization rate and the energy of accelerated electrons and present examples of the storage of energetic electrons in loops in the course of flares on the Sun or on ultracool stars. We also discuss the efficiency of the suggested mechanism as compared with the electron acceleration during the five-minute photospheric oscillations and with the acceleration driven by the magnetic Rayleigh–Taylor instability.     

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.     

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.     

Energy Spectra of Accelerated Solar Protons From Different Sources – I. Reconstruction and Properties of the Source Spectrum

It is widely accepted now that a significant fraction of the solar energetic particles (SEPs) observed at 1 AU after major solar flares are actually accelerated at a CME-driven shock. In addition, in the emerging new paradigm for SEP acceleration in different sources at or near the Sun, the existence of two types of flares – impulsive and gradual – is recognized. Within this concept, it is tempting also to separate SEPs into two groups – interacting and escaping – and to derive their 'source spectra' from observational data on various flare emissions (protons, gamma rays, neutrons, etc.). By different techniques, those spectra have been reconstructed for 80 solar proton events (SPE) in 1949–1991. In this paper, all available data on the source spectra of solar protons are summarized and revised. We discuss in detail existing uncertainties in the derived spectral indexes, consider other methodological problems involved in this study, and suggest several possible lines for the future investigations of solar flares and SCRs using the source spectrum data. It is noted that some peculiarities of the spectra, for instance, spectral steepening for high energies, may be characteristic of large events of the 23 February 1956 type.     

The Calculation of Solar Gamma-Rays by TALYS

Solar gamma-ray lines, produced from nuclear reactions of accelerated particles interacting with the solar atmospheric medium, are the most direct diagnosis for the acceleration and transportation of energetic electrons and ions in solar flares. Much information about composition, spectrum, and angular distribution of the accelerated ions, as well as the elemental abundances of the ambient solar atmosphere can be derived from solar gamma-ray line spectra. A new gamma-ray calculation program has been developed by using an efficient nuclear code − TALYS. The theory of gamma-ray production in solar flares is treated in detail. The characteristics of gamma-ray spectrum are also presented.     

Proton activity of the Sun in current solar cycle 24

We present a study of seven large solar proton events in the current solar cycle 24(from 2009 January up to the current date). They were recorded by the GOES spacecraft with the highest proton fluxes being over 200 pfu for energies 10 Me V. In situ particle measurements show that:(1) The profiles of the proton fluxes are highly dependent on the locations of their solar sources, namely flares or coronal mass ejections(CMEs), which confirms the "heliolongitude rules" associated with solar energetic particle fluxes;(2) The solar particle release(SPR) times fall in the decay phase of the flare emission, and are in accordance with the times when the CMEs travel to an average height of 7.9 solar radii; and(3) The time differences between the SPR and the flare peak are also dependent on the locations of the solar active regions. The results tend to support the scenario of proton acceleration by the CME-driven shock,even though there exists a possibility of particle acceleration at the flare site, with subsequent perpendicular diffusion of accelerated particles in the interplanetary magnetic field. We derive the integral time-of-maximum spectra of solar protons in two forms: a single power-law distribution and a power law roll-over with an exponential tail. It is found that the unique ground level enhancement that occurred in the event on 2012 May 17 displays the hardest spectrum and the largest roll-over energy which may explain why this event could extend to relativistic energies.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Relativistic acceleration of protons in reconnecting current sheets of solar flares

Acceleration of protons in a reconnecting current sheet (RCS), which forms as a consequence of filament eruption in the corona, is considered as a possible mechanism of generation of the relativistic particles during the late phase of solar flares. In order to explain the acceleration of protons and heavier ions up to several GeV in a time of < 0.1 s, the transverse electric field outside the RCS must be taken into account. Physically, this field is always present as a consequence of electric charge separation owing to the difference in the electron and proton masses. The new effect demonstrated in this paper is that the transverse electric field efficiently locks nonthermal ions in the RCS, thus allowing their acceleration by the direct electric field in the RCS. The mechanism considered may be useful in construction of a model for generation of relativistic ions in large gamma-ray/proton flares.     

Particle Acceleration and Propagation in Strong Flares without Major Solar Energetic Particle Events

Solar energetic particles (SEPs) detected in space are statistically associated with flares and coronal mass ejections (CMEs). But it is not clear how these processes actually contribute to the acceleration and transport of the particles. The present work addresses the question why flares accompanied by intense soft X-ray bursts may not produce SEPs detected by observations with the GOES spacecraft. We consider all X-class X-ray bursts between 1996 and 2006 from the western solar hemisphere. 21 out of 69 have no signature in GOES proton intensities above 10 MeV, despite being significant accelerators of electrons, as shown by their radio emission at cm wavelengths. The majority (11/20) has no type III radio bursts from electron beams escaping towards interplanetary space during the impulsive flare phase. Together with other radio properties, this indicates that the electrons accelerated during the impulsive flare phase remain confined in the low corona. This occurs in flares with and without a CME. Although GOES saw no protons above 10 MeV at geosynchronous orbit, energetic particles were detected in some (4/11) confined events at Lagrangian point L1 aboard ACE or SoHO. These events have, besides the confined microwave emission, dm-m wave type II and type IV bursts indicating an independent accelerator in the corona. Three of them are accompanied by CMEs. We conclude that the principal reason why major solar flares in the western hemisphere are not associated with SEPs is the confinement of particles accelerated in the impulsive phase. A coronal shock wave or the restructuring of the magnetically stressed corona, indicated by the type II and IV bursts, can explain the detection of SEPs when flare-accelerated particles do not reach open magnetic field lines. But the mere presence of these radio signatures, especially of a metric type II burst, is not a sufficient condition for a major SEP event.     

Particle Acceleration in the Presence of Weak Turbulence at an X-Type Neutral Point

We simulate the likely noisy situation near a reconnection region by superposing many 2D linear reconnection eigenmodes. The superposition of modes on the steady state X-type magnetic field creates multiple X- and O-type neutral points close to the original neutral point and so increases the size of the non-adiabatic region. We study test particle trajectories of initially thermal protons in these fields. Protons become trapped in this region and are accelerated by the turbulent electric field to energies up to 1 MeV in time scales relevant to solar flares. Higher energies are achieved due to the interaction of particles with increasingly turbulent electric and magnetic fields.     

Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet

Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.

     

The Influence of Ion-Acoustic Turbulence on the Electron Acceleration in the Reconnecting Current Sheet

Through solving the single electron equation of motion and the Fokker-Planck equation including the terms of electric field strength and ion-acoustic turbulence, we study the influence of the ion-acoustic wave on the electron acceleration in turbulent reconnecting current sheets. It is shown that the ion-acoustic turbulence which causes plasma heating rather than particle acceleration should be considered. With typical parameter values, the acceleration time scale is around the order of 10^-6 s, the accelerated electrons may have approximately a power-law distribution in the energy range 20 ～100 keV and the spectral index is about 3～10, which is basically consistent with the observed hard X-ray spectra in solar flares.     

Multiple acceleration of protons on the Sun and their free propagation to the Earth on January 20, 2005

We analyze the observations of solar protons with energies >80 MeV near the Earth and the January 20, 2005, solar flare in various ranges of the electromagnetic spectrum. Within approximately the first 30 min after their escape into interplanetary space, the solar protons with energies above 80 MeV propagated without scattering to the Earth and their time profiles were determined only by the time profile of the source on the Sun and its energy spectrum. The 80–165 MeV proton injection function was nonzero beginning at 06:43:80 UT and can be represented as the product of the temporal part, the ACS (Anticoincidence System) SPI (Spectrometer on INTEGRAL) count rate, and the energy part, a power-law proton spectrum ～E ^?4.7±0.1. Protons with energies above 165 MeV and relativistic electrons were injected, respectively, 4 and 9 min later than this time. The close correlation between high-energy solar electromagnetic emission and solar proton fluxes near the Earth is evidence for prolonged and multiple proton acceleration in solar flares. The formation of a posteruptive loop system was most likely accompanied by successive energy releases and acceleration of charged particles with various energies. Our results are in conflict with the ideas of cosmic-ray acceleration in gradual solar particle events at the shock wave driven by a coronal mass ejection.     

On the problem of power-law spectrum of particles accelerated in solar flares

The formation of power-law energy spectrum of particles accelerated in solar flares is investigated. The distinct difference between the mechanism and the model of acceleration is pointed out. It is shown that Fermi's model is described by linear differential equation of the first order and therefore a power-law spectrum is formed only for some special conditions which apparently are not fulfilled for flares. A satisfactory alternative to Fermi's model hasn't yet been found. In conclusion the connection between the mechanism of acceleration and a charge spectrum of accelerated particles is examined.     

Interstellar pickup protons and solar wind heating in the outer heliosphere

The ionization of hydrogen atoms that penetrate into the heliosphere from the interstellar medium gives rise to a peculiar population of energetic protons (interstellar pickup protons) in the solar wind. The short-wavelength Alfvènic turbulence in the outer heliosphere is entirely attributable to the source associated with the instability of the initial anisotropic pickup proton velocity distribution. The bulk of the generated turbulent energy is subsequently absorbed by the pickup protons themselves through the cyclotron-resonance particle-wave interaction, and only an insignificant fraction of this energy can be transferred to the solar wind protons and heat them up.     

Energetic Particle Acceleration and Propagation in Strong CME-Less Flares

Flares and coronal mass ejections (CMEs) contribute to the acceleration and propagation of solar energetic particles (SEP) detected in the interplanetary space, but the exact roles of these phenomena are yet to be understood. We examine two types of energetic particle tracers related with 15 CME-less flares that emit bright soft X-ray bursts (GOES X class): radio emission of flare-accelerated electrons and in situ measurements of energetic electrons and protons near 1 AU. The CME-less flares are found to be vigorous accelerators of microwave-emitting electrons, which remain confined in low coronal structures. This is shown by unusually steep low-frequency microwave spectra and by lack of radio emission from the middle and high corona, including dm?–?m wave type IV continua and metre-to-hectometre type III bursts. The confinement of the particles accelerated in CME-less flares agrees with the magnetic field configuration of these events inferred by others. Two events produced isolated metric type II bursts revealing coronal shock waves. None of the seven flares in the western hemisphere was followed by enhanced particle fluxes in the GOES detectors, but one, which was accompanied by a type II burst, caused a weak SEP event detected at SoHO and ACE. Three of the CME-less flares were followed within some hours by SEP-associated flares from the same active region. These SEP-producing events were clearly distinct from the CME-less ones by their association with fast and broad CMEs, dm?–?m wave radio emission, and intense DH type III bursts. We conclude that radio emission at decimetre and longer waves is a reliable indication that flare-accelerated particles have access to the high corona and interplanetary space. The absence of such emission can be used as a signal that no SEP event is to be expected despite the occurrence of a strong soft X-ray burst.     

周期性撕裂模的加速机制与射电尖峰的时间尺度

本文讨论了经典撕裂模理论的局限性,提出在考虑撕裂模的周期振荡后,其感应电场的大小及时空尺度均能满足太阳耀斑中的毫秒级射电尖峰所提供的高能粒子的信息,从而给耀斑粒子的一次加速提出了一种可能的机制。另一方面,撕裂模的周期与单个尖峰的宽度可对应,而撕裂模指数增长的特征时间又恰好与射电尖峰群的典型宽度具有同一量级,因此,快速尖峰辐射的时间结构很可能是由高能粒子流即加速电场本身的准周期性所决定。