Yuri E. Litvinenko

Photospheric magnetic reconnection and canceling magnetic features on the Sun

Parameters describing quasi-steady reconnecting current sheets in the plasma of the solar photosphere and chromosphere are computed using the VAL-C atmospheric model. In particular, the inflow speed for the Sweet-Parker magnetic reconnection is found for a sheet whose width is determined by the density scale height. The resulting speed of several tens of meters per second corresponds closely to the speeds implied by observations of canceling magnetic features on the Sun. This and other arguments support photospheric magnetic reconnection as the cancellation mechanism. The reconnection process should be most efficient around the temperature minimum region about 600 km above the lower photospheric boundary.

Aspects of the Global MHD Equilibria and Filament Eruptions in the Solar Corona

This is a review of several promising approaches for analyzing the accumulation and release of magnetic energy in filament eruptions and coronal mass ejections in the solar corona. The importance of the magnetic virial theorem for understanding the role of slowly changing boundary conditions in the photosphere is stressed. A possible role of the magnetic expulsion force in the solar filament dynamics is also discussed.

Flux Pile-up Magnetic Reconnection in the Solar Photosphere

Magnetic reconnection in the temperature minimum region of the solar photosphere, observationally manifested as canceling magnetic features, is considered. Flux pile-up reconnection in the Sweet-Parker current sheet is analyzed. It is shown that the standard Sweet-Parker reconnection rate in the photosphere is too slow to explain the observed cancellation. Flux pile-up reconnection scalings, however, are shown to be in agreement with the speeds of canceling magnetic fragments, magnetic fields in the fragments, and the rates of magnetic flux cancellation, derived from SOHO MDI data. Pile-up factors in the range between 1 and 5 and local reconnecting magnetic fields of a few hundred G are calculated for the analyzed canceling features. The analysis shows that flux pile-up is a likely mechanism for adjusting the local parameters of reconnecting current sheets in the photosphere and for sustaining the reconnection rates that are determined by large-scale supergranular flows. The upward mass flux in the reconnection jet, associated with a large canceling feature, is predicted to exceed 1015 g hr-1. Hence, cancellation in a few photospheric patches over several hours can lead to the formation of a solar filament in the corona.

Particle acceleration scalings based on exact analytic models for magnetic reconnection

Observations suggest that particle acceleration in solar flares occurs in the magnetic reconnection region above the flare loops. Theoretical models for particle acceleration by the reconnection electric field, however, employ heuristic configurations for electric and magnetic fields in model current sheets, which are not solutions to the MHD reconnection problem. In the present study, particle acceleration is discussed within the context of a self-consistent MHD reconnection solution. This has the advantage of allowing poorly constrained local parameters in the current sheet region to be expressed in terms of the boundary conditions and electric resistivity of the global solution. The resulting acceleration model leads to energy gains that are consistent with those for high-energy particles in solar flares. The overall self-consistency of the approach is discussed.

Flare Energy Release by Flux Pile-up Magnetic Reconnection in a Turbulent Current Sheet

The power output of flux pile-up magnetic reconnection is known to be determined by the total hydromagnetic pressure outside the current sheet. The maximum energy-release rate is reached for optimized solutions that balance the maximum dynamic and magnetic pressures. An optimized solution is determined in this paper for a current sheet with anomalous, turbulent electric resistivity. The resulting energy dissipation rate Wa is a strong function of the maximum, saturated magnetic field Bs: Wa ~ B. Numerically, Wa can exceed the power output based on the classical resistivity by more than 2 orders of magnitude for three-dimensional pile-up, leading to solar flarelike energy-release rates of the order of 1028 ergs s-1. It is also shown that the optimization prescription has its physical basis in relating the flux pile-up solutions to the Sweet-Parker reconnection model.

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times Δt between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail ∼(Δt)γ for large waiting times (Δt>10 hours). It is shown that the power-law index γ varies with the solar cycle. For the minimum phase of the cycle the index is γ=−1.4±0.1, and for the maximum phase of the cycle the index is −3.2±0.2. For all years 1975–2001, the index is −2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate λ(t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(λ), the time distribution of the rate λ. If f(λ) has a power-law form ∼λα for low rates, the waiting time-distribution is predicted to have a power-law tail ∼(Δt)−(3+α) (α>−3). Distributions f(λ) are constructed from the GOES data. For the entire catalog a power-law index α=−0.9±0.1 is found in the time distribution of rates for low rates (λ<0.1 hours−1). For the maximum and minimum phases power-law indices α=−0.1±0.5 and α=−1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices −2.2±0.1 (1975–2001), −2.9±0.5 (maximum phase) and −1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.

Interpretation of particle acceleration in a simulation study of collisionless reconnection

A recent simulation study [Horiuchi and Sato, Phys. Plasmas 4, 277 (1997)] investigated collisionless magnetic reconnection in a sheared magnetic field. Theoretical models for particle acceleration in current sheets are used to interpret some of the simulation results, which are found to be consistent with analytical expressions for values of the electron energy gain, the acceleration time, and the longitudinal magnetic field giving rise to adiabatic particle motion. The simulation also identified an ion acceleration mechanism that will require additional theoretical study.A recent simulation study [Horiuchi and Sato, Phys. Plasmas 4, 277 (1997)] investigated collisionless magnetic reconnection in a sheared magnetic field. Theoretical models for particle acceleration in current sheets are used to interpret some of the simulation results, which are found to be consistent with analytical expressions for values of the electron energy gain, the acceleration time, and the longitudinal magnetic field giving rise to adiabatic particle motion. The simulation also identified an ion acceleration mechanism that will require additional theoretical study.

Viscous effects in planar magnetic X-point reconnection

The impact of viscous dissipation is considered on magnetic reconnection in closed line-tied magnetic X-points. It is shown that viscous effects can provide fast energy dissipation for disturbances which do not alter the initial X-point topology. If the X-point topology is altered, then the rate of viscous dissipation depends on both the perturbed topology and the relative magnitudes of viscosity and electric resistivity. New solutions are demonstrated, which derive from the combination of resistive and viscous effects. The solutions are characterized by monotonically decaying modes which are qualitatively different from the previously known oscillatory modes in nonviscous resistive X-point reconnection. These results suggest that viscous heating in magnetic X-points may be an important effect in solar flares.

Determination of Magnetic Diffusivity from High-Resolution Solar Magnetograms

The magnetic diffusivity in the solar photosphere is determined by applying a new method to the magnetic induction equation. The magnetic field evolution is specified by a time sequence of high-resolution magnetograms of plage regions, taken by Hinode/SOT and SOHO/MDI. The mean value of magnetic diffusivity determined from SOT magnetograms with the smallest pixel size of 116 km is about -->0.87 ? 0.08 km2 s?1. This is the smallest value that has been empirically determined so far. High-resolution and full-disk MDI magnetograms with the pixel sizes of 440 and 1400 km yielded larger values of -->4.4 ? 0.4 and -->18 ? 7.4 km2 s?1, respectively. The measured diffusivity values at different length scales are consistent with a turbulent cascade that ends at a resistive dissipation scale of about 30 km. The results suggest that turbulent magnetic diffusivity should be taken into account in the analysis of the observed rate of magnetic flux cancellation in the photosphere.

Three-dimensional fan magnetic reconnection and particle acceleration in the solar corona

Aims. Particle acceleration by the reconnection electric field in three-dimensional magnetic geometries in the solar corona is discussed. The acceleration times, defined by the particle escape from the vicinity of a magnetic null, and the corresponding energy gains are calculated. Methods. An exact global magnetohydrodynamic solution for fan magnetic reconnection is used to constrain the magnetic and electric fields in the vicinity of the null. Expressions for the particle acceleration times and energy gains are derived by applying the WKB approximation to the equation of motion in nonrelativistic and ultrarelativistic limits. Results. It is shown that the energies of the accelerated particles can be limited by the particle escape from the null rather than by the total electric potential at the reconnection site. For typical coronal parameters, the finite escape time limits proton energies if the Lundquist number is less than 10 12 and electron energies if the Lundquist number is less than 10 18 . Conclusions. Particle acceleration by the electric field, associated with fan magnetic reconnection in solar flares, can explain proton energies of the order of a few MeV and electron energies of the order of a few hundred keV in the case of classical electric resistivity. Energies up to a few hundred MeV can be reached if the resistivity at the reconnection site is turbulent. These estimates agree with typical solar flare observations.