W. Dröge

ANISOTROPIC THREE-DIMENSIONAL FOCUSED TRANSPORT OF SOLAR ENERGETIC PARTICLES IN THE INNER HELIOSPHERE

We investigate the combined effects of solar energetic particle propagation, parallel and perpendicular to the large-scale magnetic field in the solar wind. Numerical methods employing stochastic differential equations are used incorporating pitch-angle diffusion, focusing, and pitch-angle-dependent diffusion perpendicular to the magnetic field. We compute spatial distributions of ~100?keV electrons and 4?MeV protons in the inner heliosphere, assuming impulsive injection near the Sun over a limited range of solar longitude and latitude. In addition, spatial distributions and intensity-time profiles for various combinations of the parallel and perpendicular mean free path, with different assumptions for the dependence of ?? on the radial distance and pitch angle, are investigated. We find that realistic results can be obtained when we assume that the perpendicular mean free path scales in the inner heliosphere with the gyroradius of the particles. Step-like decreases of particle intensities as frequently observed in impulsive events at 1?AU can be reproduced for a ratio of ??/?? a few times 10?5.

Statistical survey of widely spread out solar electron events observed with STEREO and ACE with special attention to anisotropies

Context. In February 2011, the two STEREO spacecrafts reached a separation of 180 degrees in longitude, offering a complete view of the Sun for the first time ever. When the full Sun surface is visible, source active regions of solar energetic particle (SEP) events can be identified unambiguously. STEREO, in combination with near-Earth observatories such as ACE or SOHO, provides three well separated viewpoints, which build an unprecedented platform from which to investigate the longitudinal variations of SEP events. Aims. We show an ensemble of SEP events that were observed between 2009 and mid-2013 by at least two spacecrafts and show a remarkably wide particle spread in longitude (wide-spread events). The main selection criterion for these events was a longitudinal separation of at least 80 degrees between active region and spacecraft magnetic footpoint for the widest separated spacecraft. We investigate the events statistically in terms of peak intensities, onset delays, and rise times, and determine the spread of the longitudinal events, which is the range filled by SEPs during the events. Energetic electron anisotropies are investigated to distinguish the source and transport mechanisms that lead to the observed wide particle spreads. Methods. According to the anisotropy distributions, we divided the events into three classes depending on different source and transport scenarios. One potential mechanism for wide-spread events is efficient perpendicular transport in the interplanetary medium that competes with another scenario, which is a wide particle spread that occurs close to the Sun. In the latter case, the observations at 1 AU during the early phase of the events are expected to show significant anisotropies because of the wide injection range at the Sun and particle-focusing during the outward propagation, while in the first case only low anisotropies are anticipated. Results. We find events for both of these scenarios in our sample that match the expected observations and even different events that do not agree with the scenarios. We conclude that probably both an extended source region at the Sun and perpendicular transport in the interplanetary medium are involved for most of these wide-spread events.

Wide longitudinal distribution of interplanetary electrons following the 7 February 2010 solar event: Observations and transport modeling

We analyze 65–105 keV electrons in the 7 February 2010 solar electron event observed simultaneously by STEREO-A, STEREO-B, and ACE. A method to reconstruct the full-electron pitch angle distributions from the four Solar Electron and Proton Telescope sensors on STEREO-A/B and the Solar Electron and Proton Telescope instrument on ACE in the energy range of approximately 60–300 keV for periods of incomplete angular coverage is presented. A transport modeling based on numerical solutions of a three-dimensional particle propagation model which includes pitch angle scattering and focused transport is applied to the intensity and anisotropy profiles measured on all three spacecraft. Based on an analysis of intensity gradients observed between the three spacecraft, we find that the lateral transport of the electrons occurs partially close to the Sun, due to effects of nonradial divergence of magnetic field lines or particle diffusion, and partially in the interplanetary medium. For the mean free paths characterizing the electron diffusion parallel and perpendicular to the interplanetary magnetic field, we derive values of λ∥∼ 0.1 AU and λ⟂∼ 0.01 AU. In comparison with results from other particle events which we had previously analyzed in a similar manner we discuss whether the diffusion mean free paths parallel and perpendicular to the average magnetic field might be related with each other, and whether the particle transport perpendicular to the average magnetic field is more likely due to particles following meandering magnetic field lines, or due to particles being scattered off individual field lines.

Evidence of a Two-Temperature Source Region in the 3He-Rich Solar Energetic Particle Event of 2000 May 1

Using instruments on the ACE and Wind spacecraft, we investigate the temporal evolution, spectra, and ionization states of solar energetic particle (SEP) Fe in the impulsive event of 2000 May 1. Proton and electron intensities and anisotropies were used to help constrain the characteristics of the interplanetary propagation, taking into account focusing, pitch-angle scattering, adiabatic deceleration, and convection. We find that the event was nearly scatter-free, with an interplanetary scattering mean free path larger than 1 AU. The Fe spectrum spectral form is consistent with stochastic acceleration, but the observed increase of the ionization state of Fe between 200-600 keV nucleon-1 is larger than can be explained using a single temperature source even after including the effect of adiabatic deceleration in the solar wind. A two-temperature source region is required to fit the observed range of Fe charge states, with the bulk (>80%) of the particles coming from a T ~ 106 K region, and the remainder from a region with T ~ 1.6 × 107 K.

Latitudinal distribution of >106 MeV protons and its relation to the ambient solar wind in the inner southern and northern heliosphere: Ulysses Cosmic and Solar Particle Investigation Kiel Electron Telescope Results

We present observations and model calculations of the modulated intensities of galactic cosmic ray protons above 106 MeV/n along the Ulysses trajectory. Data are taken by the Cosmic and Solar Particle Investigation (COSPIN) Kiel Electron Telescope (KET) from spring 1993 to fall 1996. During this time period solar activity decreased and galactic cosmic rays recovered. To separate spatial from temporal variations we used the University of Chicago measurements from IMP 8 near Earth and compare the residual spatial variation with time independent modulation models. According to standard drift dominated modulation model, one would expect a radial gradient of ≈2%/AU and a latitudinal gradient of ≈1.2%/degree in both hemispheres. The measured mean radial gradient of «3%/AU is within the uncertainties in good agreement with the model predictions. However, the measured mean latitudinal gradient has a value of (0.33 ± 0.04)%/degree in both hemispheres at intermediate latitudes and is by a factor of 4 lower than expected. In the modified models the latitudinal gradient is in agreement with the measured ones when we increase the diffusion coefficient κθθ perpendicular to the magnetic field in polar direction to a value of 15% of the diffusion coefficient parallel to the magnetic field. The latitudinal gradients >106 MeV protons calculated by modified modulation models are in very good agreement with the measured ones at intermediate latitudes. At lower latitudes, when Ulysses is embedded in the streamer belt, the models predict approximately the same latitudinal gradient than at intermediate latitudes, whereas the measured ones are significant smaller, or even vanishing. The observations support the previous conclusion from Paizis et al. [1995] that a significant latitudinal gradient is only observed when Ulysses is outside the streamer belt. Another remarkable observation is the difference of the radial gradient Gr at ∼3.5 AU in the southern (Gr≈3.5%/AU) and in the northern hemisphere (Gr≈2.3%/AU). Probable reasons for the significantly lower radial gradient in the northern hemisphere can be either a spatial asymmetry of the heliosphere or temporal variations.

Acceleration and Transport Modeling of Solar Energetic Particle Charge States for the Event of 1998 September 9

The 1998 September 9 solar particle event was a 3He-rich solar particle event that showed a strong increase of Fe ionization states in the energy range below 1 MeV nucleon-1. We have investigated this event by fitting Wind and ACE observations using a model of acceleration and stripping near the Sun, followed by particle transport in the interplanetary medium taking into account particle focusing, pitch-angle scattering, adiabatic deceleration, and convection. The simulation provides a reconstruction of the injection function of the energetic particles released from the Sun and their time, energy, and charge dependence. We find that electrons and Fe ions are injected almost impulsively, whereas the injection of protons takes place on a much longer timescale or even consists of two distinct injection processes. We are able to obtain good overall fits to the observations. This suggests that our model can be used to obtain information about the conditions in the acceleration region such as density, temperature, and the timescales of the acceleration process, if sufficiently accurate modeling of the particle transport in the solar wind is possible.

Solar origin of in-situ near-relativistic electron spikes observed with SEPT/STEREO

During 2010–2011 the Solar Electron Proton Telescope (SEPT) onboard the twin STEREO spacecraft detected a number of typical impulsive electron events showing a prompt intensity onset followed by a long decay, as well as several near-relativistic so-called electron spike events. These spikes are characterized by a very short duration of below 10–20 min at FWHM, almost symmetric time profiles, velocity dispersion and strong anisotropy, revealing a very weak scattering during particle propagation from the Sun to STEREO. Spikes are detected at energies below 300 keV and appear simulateneously with type III radio bursts detected by SWAVES/STEREO and narrow EUV jets in active regions. Using particle, EUV and radio imaging observations we found that nearrelativistic electrons were accelerated simultaneously and at the same location as the electrons emitting the accompanying type III radio bursts and together with coronal EUV jets. Furthermore, the sources of type III radio bursts match very well the locations and the trajectories of the associated EUV jet. Applying a particle propagation model we demonstrate that the spike characteristics reflect both, properties of the accelerator and effects of interplanetary propagation.

MULTI-SPACECRAFT OBSERVATIONS AND TRANSPORT MODELING OF ENERGETIC ELECTRONS FOR A SERIES OF SOLAR PARTICLE EVENTS IN AUGUST 2010

During August 2010 a series of solar particle events, origin ating from the adjacent active regions 11093 and 11099, was observed by the two STEREO as well as by ne ar-Earth spacecraft. For the events occurring on the August 7 and 18 we combine in-situ and remote-sensing observations with predictions from our model of three-dimensional aniso tropic particle propagation in order to investigate the physical processes which cause the large an gular spreads of the energetic particles during these events. In particular, we address the effects o f lateral transport of the electrons in the solar corona as well as due to diffusion perpendicular to the average magnetic field in the interplanetary medium. We also study the influence of two Cor onal Mass Ejections and associated shock waves on the electron propagation, and a possible long itudinal variation in space of the transport conditions during the above period. For the Augus t 18 event we additionally utilize electron observations from the MESSENGER spacecraft at a di st nce of 0.31 AU from the Sun for an attempt to separate between radial and longitudinal d ependencies in the transport process.

CHARGE STATE FORMATION OF ENERGETIC ULTRAHEAVY IONS IN A HOT PLASMA

We introduce a simplified method to calculate the cross sections and rates of ionization and recombination of accelerated ions with arbitrary nuclear charge Z and atomic mass number A. Calculations of equilibrium and nonequilibrium charge states of the element Tellurium (Te, Z = 52) are presented for the first time. The validity of the proposed method is demonstrated by showing that predictions for Si and Fe are in agreement at energies characteristic for energetic (≥0.15 MeV nucleon−1) ultraheavy ions with the results of a more sophisticated model. We find that while the charge states for Te come out higher than those for Fe under similar conditions, the Q/A values for Te fall consistently below those for Fe over the entire energy range and under all comparable conditions, thus extending the trend in Q/A that is observed when going to higher mass elements. Implications of our results for the observed enrichments of ultraheavy ions in solar energetic particle events are discussed.

Dependence of the Spectrum of Shock-Accelerated Ions on the Dynamics at the Shock Crossing

Diffusive shock acceleration (DSA) of ions occurs due to pitch-angle diffusion in the upstream and downstream regions of the shock and multiple crossing of the shock by these ions. The classical DSA theory implies continuity of the distribution at the shock transition and predicts a universal spectrum of accelerated particles, depending only on the ratio of the upstream and downstream fluid speeds. However, the ion dynamics at the shock front occurs within a collision-free region and is gyrophase dependent. The ions fluxes have to be continuous at the shock front. The matching conditions for the gyrophase-averaged distribution functions at the shock transition are formulated in terms of the transition and reflection probabilities. These probabilities depend on the shock angle and the magnetic compression as does the power spectrum of accelerated ions. Their spectral index is expressed in terms of the reflectivity. The spectrum is typically harder than the spectrum predicted by the classical DSA theory.