Prompt acceleration of ions by oblique turbulent shocks in solar flares

Solar flares often accelerate ions and electrons to relativistic energies. The details of the acceleration process are not well understood, but until recently the main trend was to divide the acceleration process into two phases. During the first phase elctrons and ions are heated and accelerated up to several hundreds of keV simultaneously with the energy release. These mildly relativistic electrons interact with the ambient plasma and magnetic fields and generate hard X-ray and radio radiation. The second phase, usually delayed from the first by several minutes, is responsible for accelerating ions and electrons to relativistic energies. Relativistic electrons and ions interact with the solar atmosphere or escape from the Sun and generate gamma ray continuum, gamma ray line emission, neutron emission or are detected in space by spacecraft. In several flares the second phase is coincident with the start of a type 2 radio burst that is believed to be the signature of a shock wave. Observations from the Solar Maximum Mission spacecraft have shown, for the first time, that several flares accelerate particles to all energies nearly simultaneously. These results posed a new theoretical problem: How fast are shocks and magnetohydrodynamic turbulence formed and how quickly can they accelerate ions to 50 MeV in the lower corona? This problem is discussed

Energetic ion acceleration at collisionless shocks

An example is presented from a test particle simulation designed to study ion acceleration at oblique turbulent shocks. For conditions appropriate at interplanetary shocks near 1 AU, it is found that a shock with theta sub B n = 60 deg is capable of producing an energy spectrum extending from 10 keV to approx. 1 MeV in approx 1 hour. In this case total energy gains result primarily from several separate episodes of shock drift acceleration, each of which occurs when particles are scattered back to the shock by magnetic fluctuations in the shock vicinity

Simulating Flaring Events in Complex Active Regions Driven by Observed Magnetograms

We interpret solar flares as events originating from active regions that have reached the Self Organized Critical state, by using a refined Cellular Automaton model with initial conditions derived from observations. Aims: We investigate whether the system, with its imposed physical elements,reaches a Self Organized Critical state and whether well-known statistical properties of flares, such as scaling laws observed in the distribution functions of characteristic parameters, are reproduced after this state has been reached. Results: Our results show that Self Organized Criticality is indeed reached when applying specific loading and relaxation rules. Power law indices obtained from the distribution functions of the modeled flaring events are in good agreement with observations. Single power laws (peak and total flare energy) as well as power laws with exponential cutoff and double power laws (flare duration) are obtained. The results are also compared with observational X-ray data from GOES satellite for our active-region sample. Conclusions: We conclude that well-known statistical properties of flares are reproduced after the system has reached Self Organized Criticality. A significant enhancement of our refined Cellular Automaton model is that it commences the simulation from observed vector magnetograms, thus facilitating energy calculation in physical units. The model described in this study remains consistent with fundamental physical requirements, and imposes physically meaningful driving and redistribution rules.Comment: 14 pages; 12 figures; 6 tables - A&A, in pres

An observationally-driven kinetic approach to coronal heating

Coronal heating through the explosive release of magnetic energy remains an open problem in solar physics. Recent hydrodynamical models attempt an investigation by placing swarms of 'nanoflares' at random sites and times in modeled one-dimensional coronal loops. We investigate the problem in three dimensions, using extrapolated coronal magnetic fields of observed solar active regions. We apply a nonlinear force-free field extrapolation above an observed photospheric magnetogram of NOAA active region (AR) 11158. We then determine the locations, energy contents, and volumes of 'unstable' areas, namely areas prone to releasing magnetic energy due to locally accumulated electric current density. Statistical distributions of these volumes and their fractal dimension are inferred, investigating also their dependence on spatial resolution. Further adopting a simple resistivity model, we infer the properties of the fractally distributed electric fields in these volumes. Next, we monitor the evolution of 10^5 particles (electrons and ions) obeying an initial Maxwellian distribution with a temperature of 10 eV, by following their trajectories and energization when subjected to the resulting electric fields. For computational convenience, the length element of the magnetic-field extrapolation is 1 arcsec, much coarser than the particles collisional mean free path in the low corona. The presence of collisions traps the bulk of the plasma around the unstable volumes, or current sheets (UCS), with only a tail of the distribution gaining substantial energy. Assuming that the distance between UCS is similar to the collisional mean free path we find that the low active-region corona is heated to 100-200 eV, corresponding to temperatures exceeding 2 MK, within tens of seconds for electrons and thousands of seconds for ions. Fractally distributed, nanoflare-triggening fragmented UCS ...Comment: accepted by A&

Shell-models of RMHD turbulence and the heating of solar coronal loops

A simplified non-linear numerical model for the development of incompressible magnetohydrodynamics (MHD) in the presence of a strong magnetic field B0 and stratification, nicknamed Shell-Atm, is presented. In planes orthogonal to the mean field, the non-linear incompressible dynamics is replaced by 2D shell-models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long time integrations to obtain a good statistics at moderate computational cost. The shell-models of different planes are coupled by Alfven waves propagating along B0. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated via turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact non-linearly and form turbulent spectra in the directions perpendicular and, via propagation, also parallel to the mean field. A heating function is obtained, and is shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona, and is proportional to the aspect ratio of the loop to the power -1.5; characteristic properties of heating events are distributed as power-laws. Cross-correlations show a delay of dissipation compared to energy content.Comment: 12 pages, 16 figures, accepted for publication in Ap

Particle Acceleration in an Evolving Network of Unstable Current Sheets

We study the acceleration of electrons and protons interacting with localized, multiple, small-scale dissipation regions inside an evolving, turbulent active region. The dissipation regions are Unstable Current Sheets (UCS), and in their ensemble they form a complex, fractal, evolving network of acceleration centers. Acceleration and energy dissipation are thus assumed to be fragmented. A large-scale magnetic topology provides the connectivity between the UCS and determines in this way the degree of possible multiple acceleration. The particles travel along the magnetic field freely without loosing or gaining energy, till they reach a UCS. In a UCS, a variety of acceleration mechanisms are active, with the end-result that the particles depart with a new momentum. The stochastic acceleration process is represented in the form of Continuous Time Random Walk (CTRW), which allows to estimate the evolution of the energy distribution of the particles. It is found that under certain conditions electrons are heated and accelerated to energies above 1 MeV in much less than a second. Hard X-ray (HXR) and microwave spectra are calculated from the electrons' energy distributions, and they are found to be compatible with the observations. Ions (protons) are also heated and accelerated, reaching energies up to 10 MeV almost simultaneously with the electrons. The diffusion of the particles inside the active region is extremely fast (anomalous super-diffusion). Although our approach does not provide insight into the details of the specific acceleration mechanisms involved, its benefits are that it relates acceleration to the energy release, and it well describes the stochastic nature of the acceleration process.Comment: 37 pages, 10 figures, one of them in color; in press at ApJ (2004

The interaction of gravitational waves with strongly magnetized plasmas

We study the interaction of a gravitational wave (GW) with a plasma that is strongly magnetized. The GW is considered a small disturbance, and the plasma is modeled by the general relativistic analogue of the induction equation of ideal MHD and the single fluid equations. The equations are derived without neglecting any of the non-linear interaction terms, and the non-linear equations are integrated numerically. We find that for strong magnetic fields of the order of $10^{15}$G the GW excites electromagnetic plasma waves very close to the magnetosonic mode. The magnetic and electric field oscillations have very high amplitude, and a large amount of energy is absorbed from the GW by the electromagnetic oscillations, of the order of $10^{23}$erg/cm$^3$ in the case presented here. The absorbed energy is proportional to $B_0^2$, with $B_0$ the background magnetic field. The energization of the plasma takes place on fast time scales of the order of milliseconds. The amount of absorbed energy is comparable to the energies emitted in the most energetic astrophysical events, such as giant flares on magnetars and possibly even short Gamma ray bursts (GRB), for which the mechanism analyzed here also has the fast time-scales required.Comment: 5 pages, 7 figures, Eq. (7) and corresponding text is modifie

Particle acceleration and heating in regions of magnetic flux emergence

L.V. was partly supported by the European Union (European Social Fund) and the Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Frame Work Research Funding Program: Thales. Investing in Knowledge Society through the European Social Fund. V.A. acknowledges support by the Royal Society.The interaction between emerging and pre-existing magnetic fields in the solar atmosphere can trigger several dynamic phenomena, such as eruptions and jets. A key element during this interaction is the formation of large-scale current sheets, and eventually their fragmentation that leads to the creation of a strongly turbulent environment. In this paper, we study the kinetic aspects of the interaction (reconnection) between emerging and ambient magnetic fields. We show that the statistical properties of the spontaneously fragmented and fractal electric fields are responsible for the efficient heating and acceleration of charged particles, which form a power-law tail at high energies on sub-second timescales. A fraction of the energized particles escapes from the acceleration volume, with a super-hot component with a temperature close to 150 MK, and with a power-law high-energy tail with an index between −2 and −3. We estimate the transport coefficients in energy space from the dynamics of the charged particles inside the fragmented and fractal electric fields, and the solution of a fractional transport equation, as appropriate for a strongly turbulent plasma, agrees with the test-particle simulations. We also show that the acceleration mechanism is not related to Fermi acceleration, and the Fokker–Planck equation is inconsistent and not adequate as a transport model. Finally, we address the problem of correlations between spatial transport and transport in energy space. Our results confirm the observations reported for high-energy particles (hard X-rays, type III bursts, and solar energetic particles) during the emission of solar jets.Publisher PDFPeer reviewe