Motion of solar cosmic rays in the coronal magnetic field

Trajectories of solar cosmic rays have been calculated in a static ninth-order coronal magnetic field. It is found that as a result of field curvature and gradients, protons drift across the field lines at a rate of up to 200 ² deg hr^–1. These drift rates are of the same order as, but somewhat smaller than, empirically derived rates. Localized enhancements of magnetic field have been inserted into the ninth-order field in order to model (in a highly idealized manner) the effects of the small-scale magnetic features which give rise to X-ray bright points. The motions of the particles in the presence of these scattering centers can be parameterized approximately by a cross-field diffusion coefficient. Our estimates of this coefficient, although crude, overlap with empirical values which have been deduced over a wide range of energies.We propose that coronal propagation of solar cosmic rays has two components. One is independent of particle velocity, and is associated with dynamic field phenomena (such as an expanding magnetic bottle): this is the only component which is important in flares which occur close to the foot-point of the Sun-Earth field line. The second component is velocity dependent, but is independent of mass, and is associated with scattering off (relatively static) magnetic inhomogeneities with scale sizes of at least 500 km: the second component contributes to coronal propagation if the flare occurs more than about 50–60 deg away from the Sun-Earth field line.     

Catastrophe of coronal magnetic rope in partly open multipolar magnetic field

Catastrophe of coronal magnetic rope embedded in a partly open multipolar background magnetic field is studied by using a 2-dimensional, 3-component ideal MHD model in spherical coordinates. The background field is composed of three closed bipolar fields of a coronal streamer and an open field with an equatorial current sheet. The magnetic rope lies below the central bipolar field, and it is characterized by its annular and axial magnetic fluxes. For a given annual flux, there is a critical value of the axial flux, and for a given axial flux, there is a critical value of annual flux such that, below the critical value, the magnetic rope is attached to the solar surface and the system stays in equilibrium, but when the critical value is exceeded, the magnetic rope breaks free and erupts upward. This implies that catastrophe can occur in a coronal magnetic rope embedded in a partly open multipolar background magnetic field. Our computation gives a threshold value of magnetic energy that is about 15% greater than the energy of the partly open magnetic field (the central bipolar field open and the fields on either side closed). The excess energy may serve as source for solar explosions such as coronal mass ejections.     

Dependence of the solar wind speed on the coronal magnetic field in cycle 23

The dependence of the position of the solar wind sonic point on the magnetic field in the solar corona during cycle 23 is studied. This dependence is shown to be rather strong in the rising phase and at the cycle maximum. As the coronal magnetic field grows, the distance to the sonic point decreases. Since the distance to the sonic point has been shown previously to anticorrelate with the solar wind speed, the result obtained suggests a strong positive correlation between the later and the coronal magnetic field. The situation changed dramatically two years after the calendar date of the cycle maximum. Beginning in 2004 the solar wind speed ceased to depend on the magnetic field up until the cycle minimum in December 2008. In 2009 a strong dependence of the wind speed on the coronal magnetic field was restored. It is hypothesized that this effect is associated with two different coronal heating mechanisms whose relative efficiency, in turn, depends on the contribution from magnetic fields of different scales.     

On the magnetic field line topology in solar active regions

The field lines of closed magnetic structures above the photosphere define a mapping from the photosphere to itself. This mapping is discontinuous, and the field line connectivity to the boundary can change discontinuously in response to continuous changes of field strength and direction, if field lines either end in a singular point of the field or are tangential to the photosphere at one end. Whereas the general existence of singular points is questionable, the field has typically a cell structure due to the presence of segments of the zero line of the photospheric longitudinal field on which the transversal field is directed from negative (pointing into the Sun) to positive fields. The cell boundaries are made up of field lines which all touch the photosphere on one of these line segments. Within each of the cells the field line mapping is continuous. When during a slow evolution a substantial part of a coronal loop or of an arcade has passed from one cell into another a fast dynamic instability may set in which was previously prevented by the anchoring of field lines in the dense photosphere.     

Evolution of the photospheric magnetic field and coronal null points before solar flares

Based on a topological model for the magnetic field of a solar active region (AR), we suggest a criterion for the existence of magnetic null points on the separators in the corona. With the problem of predicting solar flares in mind, we have revealed a model parameter whose decrease means that the AR evolves toward a major eruptive flare. We analyze the magnetic field evolution for AR 9077 within two days before the Bastille Day flare on July 14, 2000. The coronal conditions are shown to have become more favorable for magnetic reconnection, which led to a 3B/X5.7 eruptive flare.     

Skinning process stability of the magnetic field in the solar active regions

Skinning process stability of the magnetic field in homogeneous plasma is studied. A set of magnetohydrodynamic equations is used. Dependence of electrical conductivity on the plasma parameters and radiation intensity in grey-body approximation are taken into account. The investigation is carried out on the model problems in linear approximation and by means of numerical solution of MHD equations. Threshold of stability and critical gradient of magnetic field in skin-layer are obtained. The model of the phenomenon proposed in the paper indicates on overheating instability of plasma with electric current in large gradient magnetic field zones as a possible trigger mechanism of solar flare origin.     

Estimation of coronal magnetic field from razin effect in solar decametric continuum burst

A solar flare of importance 1B which occurred at 06:36 UT on April 27, 1979 on the solar disk (N 20, E 16) produced intense radio bursts. The most interesting feature of this event is the observation of a strong continuum radiation (type IV) starting at 06:53 UT and lasting for about 10 min in the decametric range. This continuum radiation displayed sharp low frequency cut-off, which varied from about 40 to 30 MHz in a quasiperiodic manner and could be attributed to Razin effect. The perturbation of this cut-off frequency is interpreted as that induced by the passing MHD shock wave through the region of the trapped energetic electrons. Assuming model electron density values and using the observed cut-off frequency, the magnitude of coronal magnetic field around 2R from Sun center works out to be about 6 G.     

Comment on coronal magnetic field models

A long-standing misconception about the mathematical validity of utilizing Green's function solutions to coronal magnetic fields is discussed. Although this type of solution does not fit the observed line-of-sight component of the photospheric magnetic field, but rather the net flux in a region, the solution does obey Laplace's equation in the inner corona.     

The proton temperature and the total hourly variance of the magnetic field components in different solar wind speed regions

A comparison has been made between the predictions of the theory for radial variations of both Alfvénic fluctuations and solar wind proton temperatures proposed by Tu (1987, 1988) and the statistical results of hourly averaged plasma and magnetic field data observed by Helios 1 and 2 from launch through 1980 for different solar wind speed regimes. The comparison shows that for speed ranges between 500–800 km s^-1, the radial variation of the proton temperature between 0.3 and 1 AU can be explained by heating from the cascade energy determined by the radial variation of the total variance of magnetic field vector. The explanation of the radial variations of both temperature and the total variance of magnetic fields for speed ranges less than 400 km s ^-1 is less clear.This project was supported by National Natural Science Foundation of China for Tu's part of the work.     

On the causes of the observed magnetic field imbalance in solar active regions

Based on a topological magnetic field model for active region (AR) 8086 observed on September 15–21, 1997, we calculate the evolution of the magnetic flux imbalance during its disk passage. We have established possible causes of the observed imbalance. Using model ARs produced by perfectly balanced magnetic field sources as examples, we show that even in this case, the observed imbalance can reach a significant value, depending on the AR size and location. The peculiar properties of the magnetic field imbalance in ARs predicted by the topological model must be taken into account when present-day magnetographic observations of the Sun are interpreted.     

Lifetime of solar flare particles in coronal storage regions

Most discussions of lifetime of flare particles in the solar corona have assumed that collision loss is the dominant means of slowing and stopping these particles. The customary formulas used to estimate the rate of collision loss assume individual fast particles interacting with relatively cold matter. However, it is quite possible that the solar cosmic rays are not imbedded in 10⁶ K coronal material but rather all particles in the storage region are energetic. Collision times are sufficiently short so that the energy spectrum may approach a maxwellian distribution with kT on the order of 30 keV. If this is the case, the rate of collision loss will be greatly reduced. Bremsstrahlung and magnetobremsstrahlung then will be the important energy losses. To account for the presence of appreciable numbers of MeV particles, it is probably necessary to postulate the existence of a non-thermal tail in the stored particle distribution.     

The source regions of solar coronal mass ejections

Knowledge of the origin of the solar coronal mass ejection (CME) may be crucial to our understanding of several active solar phenomena, such as flares, as well as to the structure and stability of the corona and the prediction of interplanetary disturbances. In recent years, two camps of opinion have emerged, based on the belief that CMEs either commonly originate from structures intimately linked to active regions or they originate from coronal hole regions. This present study investigates the locations of 95 CME events observed during 1984–1986 relative to coronal hole and active region features. We find no evidence to support the coronal hole hypothesis and many indications that active regions are indeed associated with the source regions of CMEs.     

A new technique of observing the magnetic field of solar active regions

By fitting a new type of polarization detector after the entrance slit of a solar spectrograph, the two dimensional magnetic field of solar active regions can be obtained. Not only the field intensity, but also the longitudinal map is obtained quickly. The simultaneous observation of a few lines will also provide data on the structure of the magnetic tubes etc.     

Modeling coronal magnetic field using spherical geometry: cases with several active regions

The magnetic fields in the solar atmosphere structure the plasma, store free magnetic energy and produce a wide variety of active solar phenomena, like flare and coronal mass ejections (CMEs). The distribution and strength of magnetic fields are routinely measured in the solar surface (photosphere). Therefore, there is considerable interest in accurately modeling the 3D structure of the coronal magnetic field using photospheric vector magnetograms. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Nonlinear force-free field (NLFFF) models are thought to be viable tools for those task. Usually those models use Cartesian geometry. However, the spherical nature of the solar surface cannot be neglected when the field of view is large. In this work, we model the coronal magnetic field above multiple active regions using NLFFF extrapolation code using vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph (VSM) as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with their respective coronal EUV-images from the Atmospheric Imaging Assembly (SDO/AIA) observed on October 15, 2011 and November 13, 2012. This study has found that the NLFFF model in spherical geometry reconstructs the magnetic configurations for several active regions which agrees to some extent with observations. During October 15, 2011 observation, there are substantial number of trans-equatorial loops carrying electric current.     

Methods for deriving the magnetic field in solar (radio) active regions

In the present paper, in terms of the theory about the mechanisms of radio radiation, we have briefly classified, induced, summarized and reviewed the methods for deriving the magnetic field in the solar (radio) active regions. This revised version was published online in July 2006 with corrections to the Cover Date. This revised version was published online in July 2006 with corrections to the Cover Date.     

Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partially open, consisting of a closed arcade in the center and an open field at the flank. The coronal magnetic flux rope is characterized by its magnetic properties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope axis, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magnetic field, the dependence of the geometrical features on the magnetic properties displays a catastrophic behavior, namely, there exists a certain critical point, across which an infinitesimal enhancement of the magnetic parameters causes a finite jump of the geometrical parameters for the rope. The amplitude of the jump depends on the extent to which the ambient magnetic field in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

On the possibility of determining the coronal magnetic field from solar type III radio burst observations

A simple method of estimating the coronal magnetic field is suggested. It is based on the observational fact that the duration of the highly polarized part in type III bursts can be different, varying from a small fraction of the burst length to its total duration. We suggest that this difference is determined by the relation between the size of the region where only the ordinary wave can propagate and the size of the region where the burst is generated at a fixed frequency. The magnetic field is estimated at several tens of gauss in regions emitting highly polarized type III bursts at frequencies over 200 MHz. Density and magnetic field scales are estimated.     

A comparison of the temperature and emission measure of X-ray active regions with coronal magnetic fields

The distribution of temperature and of emission measure in X-ray active regions relative to the coronal magnetic fields has been investigated. The position of maximum temperature and the position of maximum emission measure were found to lie along the magnetic neutral line, with the maximum temperature tending to lie above the position of an abrupt change in direction of the neutral line. Several simple structural models of these regions are compared to the emission measure. The total magnetic energy and the total emission measure appear to be related by a power law in the regions studied by us.     

Constraints on the magnetic field geometry of magnetars

We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.     

Predicting the evolution of photospheric magnetic field in solar active regions using deep learning

The continuous observation of the magnetic field by the Solar Dynamics Observatory(SDO)/Helioseismic and Magnetic Imager(HMI) produces numerous image sequences in time and space.These sequences provide data support for predicting the evolution of photospheric magnetic field. Based on the spatiotemporal long short-term memory(LSTM) network, we use the preprocessed data of photospheric magnetic field in active regions to build a prediction model for magnetic field evolution. Because of the elaborate learning and memory mechanism, the trained model can characterize the inherent relationships contained in spatiotemporal features. The testing results of the prediction model indicate that(1) the prediction pattern learned by the model can be applied to predict the evolution of new magnetic field in the next 6 hours that have not been trained, and predicted results are roughly consistent with real observed magnetic field evolution in terms of large-scale structure and movement speed;(2) the performance of the model is related to the prediction time; the shorter the prediction time, the higher the accuracy of the predicted results;(3) the performance of the model is stable not only for active regions in the north and south but also for data in positive and negative regions. Detailed experimental results and discussions on magnetic flux emergence and magnetic neutral lines finally show that the proposed model could effectively predict the large-scale and short-term evolution of the photospheric magnetic field in active regions. Moreover, our study may provide a reference for the spatiotemporal prediction of other solar activities.