Interplanetary propagation of relativistic solar protons

Particle fluxes and pitch angle distributions of relativistic solar protons at Earth's orbit have been determined by Monte Carlo calculations. The analysis covers two hours after the release of the particles from the Sun and total of 8 × 10⁶ particle trajectories were simulated. The pitch angle scattering was assumed to be isotropic and the scattering mean free path was varied from 0.1 to 4 AU.The intensity-time profiles after a delta-like injection from the Sun show that the interplanetary propagation is clearly non-diffusive at scattering mean-free paths above 0.5 AU. All pitch angle distributions have a steady minimum at 90 °, and they become similar about 20 min after the arrival of first particles.As an application, the solar injection profile and the interplanetary scattering mean-free path of particles that gave rise to the GLE on 7 May, 1978 were determined. In contrast to the values of 3–5 AU published by other authors, the average scattering mean-free path was found to be about 1 AU.     

Monte Carlo model of the highly anisotropic solar proton event of 20 April 1971

The anisotropy of the particle distribution and its variation with time at 1 AU early in a solar cosmic ray event can provide information on the pitch-angle scattering of the particles in the interplanetary medium. The proton event of 20 April 1971 is described in which the anisotropy of the 7.6–55 MeV energy channel remained large (? 100%) and field-aligned well into the decay phase of the event. A Monte Carlo technique, which gives the pitch-angle distribution, is employed to investigate two models put forward to explain this sustained anisotropy. It is shown that the observed event is consistent with one model in which the injection of particles at the Sun decayed with ane-folding time of 7 hr. In this model the parallel propagation is determined by small-angle scattering in a diverging field equivalent to a uniform diffusion coefficient of 2.1 × 10²² cm² s^?1 (the corresponding classical mean free path is 0.90 AU). A model with impulsive injection and in whichκ(r) increases strongly with distance from the Sun cannot satisfactorily explain the observations.     

On the ground level enhancement beginning

Based on our analysis of the data fromthe global network of neutronmonitors for several events, we have found the times of the first increases in count rate at individual stations that precede the main solar cosmic-ray enhancement. The onset time of proton acceleration at the Sun has been determined from the appearance of a broad gamma-ray line with its maximum near 70 MeV that is generated during the decay of neutral pions, which, in turn, are produced when protons with energies above 300 MeV interact with the solar atmosphere. The time of the first recording of energetic protons at the Earth is delayed relative to the time at which these protons appeared at the Sun by 60–300 s, i.e., by a value comparable to the difference between the direct photon and particle propagation times. At least two conclusions follow from the existence of such “precursors”. First, the protons begin to escape from the solar atmosphere into interplanetary space immediately after their acceleration. Second, some of the protons traverse a path shorter than the nominal length of interplanetary magnetic field lines.     

Balloon observations of solar protons on September 29–30, 1968, over Iceland

On September 29, 1968 a proton event has been recorded during three balloon flights performed at Reykjavik, Iceland (64.2 N, 21.7 W) with GM telescopes and scintillation detector. Solar X-rays have been recorded at 1620 UT when a flare of Importance 2B occurred at N 16, W 52. A comparison between X-rays and microwave emissions is made; the time of the maximum of X-ray intensity is taken as the time of the acceleration and ejection of the particles. The beginning of the proton event is at 1650 UT, and particles were observed for almost 24 h. The spectrum of solar protons E>120 MeV is given for several periods between 7 and 20 h after the flare using three independent methods. The solar particle source spectrum is found as: 321-01 (particles/MeV ster), which implies that (1.2±0.1) × 10³¹ protons (E>120 MeV)/ster have been ejected by the Sun.The time behaviour of the event fits well with Krimigis' model for solar particles diffusion in the interplanetary space. Comparison with other events shows that the radial dependence of the diffusion coefficient is the same (1) on September 28, 1961, July 7, 1966 and September 29, 1968. The diffusion mean free path at 1 AU is 0.11 AU for 1966, period of low solar activity, and decreases with solar activity (0.08 AU for 1961 and 1968). The fit of the time behaviour of the event with Burlaga's ADB model is also discussed.     

The Large Longitudinal Spread of Solar Energetic Particles During the 17 January 2010 Solar Event

We investigate multi-spacecraft observations of the 17 January 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at the two STEREO spacecraft and SOHO, suggesting a longitudinal spread of nearly 360 degrees at 1?AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and only small or no anisotropies in the intensity measurements at all three locations. The presence of a coronal shock is evidenced by the observation of a type II radio burst from the Earth and STEREO-B. In order to describe the observations in terms of particle transport in the interplanetary medium, including perpendicular diffusion, a 1D model describing the propagation along a magnetic field line (model 1) (Dr?ge, Astrophys. J. 589, 1027??C?1039, 2003) and the 3D propagation model (model 2) by Dr?ge et?al. (Astrophys. J. 709, 912??C?919, 2010) including perpendicular diffusion in the interplanetary medium have been applied. While both models are capable of reproducing the observations, model 1 requires injection functions at the Sun of several hours. Model 2, which includes lateral transport in the solar wind, reveals high values for the ratio of perpendicular to parallel diffusion. Because we do not find evidence for unusual long injection functions at the Sun, we favor a scenario with strong perpendicular transport in the interplanetary medium as an explanation for the observations.     

The 1990 May 24 solar cosmic-ray event

This paper presents an integrated analysis of GOES 6, 7 and neutron monitor observations of solar cosmic-ray event following the 1990 May 24 solar flare. We have used a model which includes particle injection at the Sun and at the interplanetary shock front and particle propagation through the interplanetary medium. The model does not attempt to simulate the physical processes of coronal transport and shock acceleration, therefore the injections at the Sun and at the shock are represented by source functions in the particle transport equation. By fitting anisotropy and angle-average intensity profiles of high-energy (>30 MeV) protons as derived from the model to the ones observed by neutron monitors and at GOES 6 and 7, we have determined the parameters of particle transport, the injection rate and spectrum at the source. We have made a direct fit of uncorrected GOES data with both primary and secondary proton channels taken into account.The 1990 May 24–26 energetic proton event had a double-peaked temporal structure at energies 100 MeV. The Moreton (shock) wave nearby the flare core was seen clearly before the first injection of accelerated particles into the interplanetary medium. Some (correlated with this shock) acceleration mechanism which operates in the solar corona at a height up to one solar radius is regarded as a source of the first (prompt) increase in GOES and neutron monitor counting rates. The proton injection spectrum during this increase is found to be hard (spectral index 1.6) at lower energies ( 30 MeV) with a rapid steepening above 300 MeV. Large values of the mean free path ( 1.8 AU for 1 GV protons in the vicinity of the Earth) led to a high anisotropy of arriving protons. The second (delayed) proton increase was presumably produced by acceleration/injection of particles by an interplanetary shock wave at height of 10 solar radii. Our analysis of the 1990 May 24–26 event is in favour of the general idea that a number of components of energetic particles may be produced while the flare process develops towards larger spatial/temporal scales.Visiting Associate from St. Petersburg State Technical University, St. Petersburg 195251, Russia.     

Energetic Particle Fluxes during the Bastille Day Solar Eruption

We report on our observations of solar energetic particle fluxes of p, He, C, O, Ne, Mg, Si, and Fe ions measured by the Energetic and Relativistic Nucleon and Electron (ERNE) experiment associated with the Bastille Day solar flare and coronal mass ejection (CME) on 14 July 2000. We observed two clear maxima of the Fe/O ratio at the energies 8.5–15 MeV nucl⁻¹. The first Fe/O maximum occurred ∼ 3 hours after the beginning of the particle event, and the second maximum ∼ 22 hours after the first one at the arrival of the shock associated with the Bastille Day eruption. We also observed a change in the energy spectrum of oxygen concurrent with a change in the direction of the interplanetary magnetic field at the start of the second enhancement of the Fe/O ratio. We propose an interpretation of the particle event where observed interplanetary particle fluxes are associated with two different particle sources near the Sun and in interplanetary space. We suggest that heavy ions observed during the first period of the Fe/O enhancement were released when a coronal shock reached a magnetic foot point connected to 1 AU. The second maximum of Fe/O occurred when spacecraft encountered Fe-rich material stored in magnetic field flux tubes early in the event and was possibly reaccelerated by the interplanetary shock.     

Adiabatic Deceleration of Solar Energetic Particles as Deduced from Monte Carlo Simulations of Interplanetary Transport

Monte Carlo simulations of interplanetary transport are employed to study adiabatic energy losses of solar protons during propagation in the interplanetary medium. We consider four models. The first model is based on the diffusion-convection equation. Three other models employ the focused transport approach. In the focused transport models, we simulate elastic scattering in the local solar wind frame and magnetic focusing. We adopt three methods to treat scattering. In two models, we simulate a pitch-angle diffusion as successive isotropic or anisotropic small-angle scatterings. The third model treats large-angle scatterings as numerous small-chance isotropizations. The deduced intensity–time profiles are compared with each other, with Monte Carlo solutions to the diffusion-convection equation, and with results of the finite-difference scheme by Ruffolo (1995). A numerical agreement of our Monte Carlo simulations with results of the finite-difference scheme is good. For the period shortly after the maximum intensity time, including deceleration can increase the decay rate of the near-Earth intensity essentially more than would be expected based on advection from higher momenta. We, however, find that the excess in the exponential-decay rate is time dependent. Being averaged over a reasonably long period, the decay rate of the near-Earth intensity turns out to be close to that expected based on diffusion, convection, and advection from higher momenta. We highlight a variance of the near-Earth energy which is not small in comparison with the energy lost. It leads to blurring of any fine details in the accelerated particle spectra. We study the impact of realistic spatial dependencies of the mean free path on adiabatic deceleration and on the near-Earth intensity magnitude. We find that this impact is essential whenever adiabatic deceleration itself is important. It is also found that the initial angular distribution of particles near the Sun can markedly affect MeV-proton energy losses and intensities observed at 1 AU. Computations invoked during the study are described in detail.     

Perpendicular Transport in the Inner Heliosphere: A Quick and Dirty Approach

In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ _⊥ /κ _‖ between 0.02 and 0.1 at 1 AU scaled with r ² as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.     

Coronal and interplanetary transport of solar energetic protons and electrons

We present a new method to separate interplanetary and coronal propagation, starting from intensity variations observed by spaceprobes at different heliolongitudes. In general, a decrease in absolute intensities is observed simultaneously with an increase in temporal delays. The coupling of these two effects can be described by Reid's model of coronal diffusion and can in principle be used to determine the two coronal time constants, diffusion time t _c and escape time A. In addition, a least-squares fit method is used to determine the parameters of interplanetary transport, assuming a radial dependence as (r) = ₀(r/1 AU)^b. The method is applied to the two solar events of 27 December, 1977 and 1 January, 1978 which were observed by the spaceprobes Helios 1, Helios 2, and Prognoz 6. Energetic particle data are analysed for 13–27 MeV protons and -0.5 MeV electrons. For the regions in space encountered during these events the mean free path of electrons is smaller than that of protons. Straight interpolation between the two rigidities leads to a rather flat rigidity dependence (P) P ⁿ with n = 0.17–0.25. This contradicts the prediction of a constant mean free path or of the transition to scatter-free propagation below about 100 MV rigidity. In three of the four cases the mean free path of 13–27 MeV protons is of the order 0.17 AU, the mean free path of electrons of the order 0.06 AU. For protons we find b - 0.7 for the exponent of the radial variation.The concept of two different coronal propagation regimes is confirmed. It is remarkable that in both regimes electrons are transported more efficiently than protons. This holds for the temporal delay as well as for the amplitude decrease. This is in contrast with the long existing concept of rigidity independent transport and puts severe limits to any model of coronal transport. For the December event all three spaceprobes are in the fast propagation regime up to an angular distance of 62°. For protons we find a finite delay even in the fast propagation region, corresponding to a coronal delay rate of about 0.8 hr rad^-1 up to 60° angular distance. In contrast, relativistic electrons may reach this distance within a few minutes.The fast transport of electrons and the different behaviour of electrons and protons is in contradiction to the expanding bottle concept. An explanation of coronal transport by shock acceleration directly on open field lines could in principle work in case of protons in the fast propagation region, but would fail in case of the electrons. The fast and efficient transport of electrons is most likely due to a region of field lines extending over a wide range of longitudes directly from the active region into interplanetary space. The much slower transport of both particle types at large azimuthal distances can neither be explained by direct access to open field lines not by the direct shock acceleration concept. A possible explanation is the loop reconnection model in a modified version, allowing for a faster lateral transport of electrons.Now at AEG, 2000 Wedel, F.R.G.     

Observation of shock-accelerated protons by GIOTTO and IMP-8 under solar minimum conditions in February 1986

Solar and shock-accelerated protons were observed by the interplanetary S/C GIOTTO and aboard the Earth orbiting satellite IMP-8 during solar minimum conditions in February 1986. Forward and reverse shock configurations developed on 9–11 February, 1986 and could be recognized by sunward and anti-sunward proton propagation. The results are consistent with a general east-west asymmetry in particle fluxes observed within a distance of 1 AU from the Sun and caused by quasi-perpendicular and quasi-parallel shock configurations in the interplanetary magnetic field. The high-energy protons (>1 GeV) measured simultaneously by ground-based neutron monitors showed a complementary enhanced amplitude in the diurnal variation on 9 February, 1986.     

Solar flare injection and propagation of low-energy protons and electrons in the event of 7–9 July, 1966

Simultaneous observations of the 7–9 July 1966 solar particle event by energetic particle detectors on three satellites, IMP-III, OGO-III and Explorer 33 are utilized to show that large spatial gradients are present in the fluxes of 0.5–20 meV protons and 45 keV electrons. The event is divided into three parts: the ordinary diffusive component, the halo, and the core. The core corotates with the interplanetary field, and therefore it and the surrounding halo are interpreted as spatial features which are connected by the interplanetary magnetic field lines to the vicinity of the flare region. Upper limits to the interplanetary transverse diffusion coefficient for 4–20 meV protons at 1 AU are derived from the width of the halo. These are at least two orders of magnitude less than the parallel diffusion coefficient for the same energy particles.It is argued that the observed flux variations cannot be explained by an impulsive point source injection for any physically reasonable diffusion model. Instead, since the interplanetary transverse-diffusion coefficient is small for these low-energy particles, the observed spatial features are interpreted as the projection to 1 AU by the interplanetary field lines of an extensive injection profile at the sun. The geometry of the injection mechanism is discussed and it is suggested that some temporary storage of the flare particles occurs near the sun.Now at NASA, Goddard Space Flight Center, Greenbelt, Md., U.S.A.     

The Solar Wind at 1 AU During the Declining Phase of Solar Cycle 23: Comparison of 3D Numerical Model Results with Observations

We present results of solar-wind parameters generated by 3D MHD models. The ENLIL inner-heliosphere solar-wind model together with the MAS or Wang – Sheeley – Arge (WSA) coronal models, describe the steady solar-wind stream structure and its origins in the solar corona. The MAS/ENLIL and WSA/ENLIL models have been tuned to provide a simulation of plasma moments as well as interplanetary magnetic-field magnitude and polarity in the absence of disturbances from coronal transients. To investigate how well the models describe the ambient solar wind structure from the Sun out to 1 AU, the model results are compared to solar-wind measurements from the ACE spacecraft. We find that there is an overall agreement between the observations and the model results for the general large-scale solar-wind structures and trends, such as the timing of the high-density structures and the low- and high-speed winds, as well as the magnetic sector structures. The time period of our study is the declining phase of Solar Cycle 23 when the solar activity involves well-defined stream structure, which is ideal for testing a quasi-steady-state solar-wind model.     

Influence of finite injections and of interplanetary propagation on time-intensity and time-anisotropy profiles of solar cosmic rays

For an observer in space the intensities and anisotropies of solar cosmic-ray events are governed by the duration and the functional shape of the injection processes near the Sun and by the propagation along the interplanetary magnetic field from the Sun to the observer. We study the influence of four different types of solar injections (Gaussian, exponential, step-function and coronal diffusion), and of a purely diffusive interplanetary propagation, where the diffusion coefficient has a power law dependence on the radial distance from the Sun, =Mr on both the time-intensity and the time-anisotropy profiles at 1 AU. The main results are as follows: A slow quasi-exponential decay of the intensity can be modelled in some cases; all finite injections produce high anisotropies during the main phase of an event; an effective solar injection length can be determined from simultaneous inspection of the intensities and anisotropies; the intensities and anisotropies do to first order not depend on the analytic shape of the various injection profiles. The model is applied to the November 18, 1968 solar event as observed by Pioneer 9 in the 7.5–21.5 MeV and 21.5–60 MeV energy channels. We obtain local diffusion coefficients in the range M= (2.5–5) × 10²¹ cm² s^–1 and injection periods of the order of 10–20 hr. Closer inspection reveals the change of interplanetary propagation conditions during the event.     

Solar wind heating beyond 1 AU

The effect of an interplanetary atomic hydrogen gas on solar wind proton, electron and α-particle temperatures beyond 1 AU is considered. It is shown that the proton temperature (and probably also the α-particle temperature) reaches a minimum between 2 AU and 4 AU, depending on values chosen for solar wind and interstellar gas parameters. Heating of the electron gas depends primarily on the thermal coupling of the protons and electrons. For strong coupling (whenT _p ≳T _e ), the electron temperature reaches a minimum between 4 AU and 8 AU, but for weak coupling (Coulomb collisions only), the electron temperature continues to decrease throughout the inner solar system. A spacecraft travelling to Jupiter should be able to observe the heating effect of the solar wind-interplanetary hydrogen interaction, and from such observations it may be possible of infer some properties of the interstellar neutral gas. Currently a National Research Council Resident Research Associate.     

Thermal Emission From The Dust Coma Of Comet Hale-Bopp And The Composition Of The Silicate Grains

The dust coma of comet Hale-Bopp was observed in the thermal infrared over a wide range in solar heating (R = 4.9–0.9 AU) and over the full wavelength range from 3 μm to 160 μm. Unusual early activity produced an extensive coma containing small warm refractory grains; already at 4.9 AU, the 10 μm silicate emission feature was strong and the color temperature was 30% above the equilibrium blackbody temperature. Near perihelion the high color temperature, strong silicate feature, and high albedo indicated a smaller mean grain size than in other comets. The 8–13 μm spectra revealed a silicate emission feature similar in shape to that seen in P/Halley and several new and long period comets. Detailed spectral structure in the feature was consistent over time and with different instruments; the main peaks occur at 9.3, 10.0 and 11.2 μm. These peaks can be identified with olivine and pyroxene minerals, linking the comet dust to the anhydrous chondritic aggregate interplanetary dust particles. Spectra at 16–40 μm taken with the ISO SWS displayed pronounced emission peaks due to Mg-rich crystalline olivine, consistent with the 11.2 μm peak. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the mean free path of solar cosmic rays – I. Protons

The spatial transport of charged particles in the presence of pure slab Alfvén waves, pure isotropic magnetosonic waves and their mixture is considered using Monte Carlo particle simulations. We show that the mean free path of solar cosmic ray protons strongly depends on the assumed spectrum and amplitude of MHD turbulence but much less on the type of the considered waves. It is demonstrated that, for realistic solar wind parameters, the presented wide range wave spectrum models can reproduce the observed mean free path in a particular SEP event but not in a wide range of rigidity characterized by the Palmer's `consensus'.     

Cosmic Ray Nonlinear Processes in Space Plasma: Applications to the Dynamic Heliosphere

Influence of cosmic ray pressure and kinetic stream instability on space plasma dynamics and magnetic structure are considered. It is shown that in the outer Heliosphere are important dynamics effects of galactic cosmic ray pressure on solar wind and interplanetary shock wave propagation as well as on the formation of terminal shock wave of the Heliosphere and subsonic region between Heliosphere and interstellar medium. Kinetic stream instability effects are important on distances more than 40–60 AU from the Sun: formation of great anisotropy of galactic cosmic rays in about spiral interplanetary magnetic field leads to the Alfven turbulence generation by non isotropic cosmic ray fluxes. Generated Alfven turbulence influences on cosmic ray propagation, increases the cosmic ray modulation, decreases the cosmic ray anisotropy and increases the cosmic ray pressure gradient in the outer Heliosphere (the later is also important for terminal shock wave formation). This revised version was published online in July 2006 with corrections to the Cover Date.     

Multi-spacecraft Study of the 8 November 2000 SEP Event: Electron Injection Histories 100° Apart

We present the analysis of a large solar near-relativistic electron event observed by the Ulysses and the ACE spacecraft on 8 November 2000, when Ulysses was located at a heliocentric distance of 2.4 AU and at a heliographic latitude of ??80° S. We use a particle propagation model to infer the local interplanetary transport conditions and the injection histories of the near-relativistic electrons observed by both spacecraft. We find different local transport conditions for each set of observations. The inferred injection profiles for both spacecraft extend for several hours; but the injection at Ulysses was smaller and started later. The association with type II radio emission suggests that the heliospheric electrons were provided by coronal shock acceleration. An analysis of the in situ magnetic field and plasma measurements indicates that the global configuration of the heliosphere (disturbed by transient structures) could play a role in shaping the characteristics of solar energetic particle events observed from different locations.     

Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks

We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.