Numerical studies of the transport of solar protons in interplanetary space

Numerical solutions of the Fokker-Planck equation governing the transport of solar protons are obtained using the Crank-Nicholson technique with the diffusion coefficient represented by K_r=K₀r^b where r is radial distance from the Sun and b can take on positive or negative values. As b ranges from +1 to ?3, the time to the observation of peak flux decreases by a factor of 5 for 1 MeV protons when $\text{V}\text{K}{}_0\text{=}\text{3 AU}{}^{\mathrm{b?1}}$ where V is the solar wind speed. The time to peak flux is found to be very insensitive to assumptions concerning the solar and outer scattering boundary conditions and the presence of exponential time decay in the flux does not depend on the existence of an outer boundary. At $\text{V}\text{K}{}_0\text{? 15 AU}{}^{\mathrm{b?1}}$, 1 MeV particles come from the Sun by an almost entirely convective process and suffer large adiabatic deceleration at b?0 but for b=+1, large Fermi acceleration is possible at all reasonable $\text{V}\text{K}{}_0$ values. Implications of this result for the calculation and measurement of particle diffusion coefficients is discussed. At $\text{b?0}$, the pure diffusion approximation to transport overestimates by a factor 2 or more the time to peak flux but as b becomes more negative, the additional effects of convection and energy loss become less important.     

Angular distributions of solar protons and electrons

High angular-resolution measurements of directional fluxes of solar particles in space have been obtained with detectors aboard OGO-5 during the cosmic ray event of 18 November 1968. This is the only case on record for which sharply-defined directional observations of protons and electrons covering a wide rigidity range (0.3 MV to 1.5 GV) are available.The satellite experiment provided data for determining pitch-angle distributions with respect to the direction of the local interplanetary magnetic field lines during the lengthy highly anisotropic phase of the event. It was found that the unidirectional differential intensities j(θ) of 3- to 25-MeV protons varied in accordance with the relationship j(θ) = b₀ + b₁cosθ + b₂cos²θ, where b₀ and b₁ ? 0, and b₂, is positive, zero or negative. Soon after onset, 79–266-keV electrons arriving from the direction of the Sun displayed an anisotropic component with the intensity varying as cos θ. Later, a double-peaked distribution appeared at the lower energies, whereas the flux at the upper end of the range covered by the experiment became isotropic. These results have been interpreted in the light of the temporal flux profiles and the state of the interplanetary medium.The observation of the unusually large and long-lasting anisotropies lead to several conclusions including: (1) If injection of the solar particles was instantaneous, the diffusion coefficient was either constant or increasing with distance from the Sun. (2) If the solar source emitted particles over an extended period, and there is evidence to that effect, there was weak scattering in the region between the Sun and the Earth and a strong scattering region beyond the Earth's orbit. (3) Solar electrons were stored near the Sun. (4) The observed angular distribution of 200-MV protons in the magnetosheath was in good agreement with that deduced in an earlier analysis of polar orbiting satellite observations and trajectory calculations.     

Energetic solar electrons in the interplanetary medium

ISEE-3 measurements extending down to 2 keV energy have provided a new perspective on energetic solar electrons in the interplanetary medium. Impulsive solar electron events are observed, on average, several times a day near solar maximum, with 40% detected only below 15 keV. The electron energy spectra have a nearly power-law shape extending smoothly down to 2 keV, indicating that the origin of these events is high in the corona. These coronal flare-like events often produced ³He-rich particle events.In large solar flares which accelerate electrons and ions to relativistic energies, the electron spectrum appears to be modified by a second acceleration which results in a double power-law shape above 10 keV with a break near 100 keV and flattening from 10–100 keV. Large flares result in long-lived (many days) streams of outflowing electrons which dominate the interplanetary fluxes at low energies. Even in the absence of solar activity, significant fluxes of low energy electrons flow out from the Sun.Solar type-III radio bursts are produced by the escaping 2–10² keV electrons through a beam-plasma instability. The detailed ISEE-3 measurements show that electron plasma waves are generated by the bump-on-tail distribution created by the faster electrons running ahead of the slower ones. These plasma waves appear to be converted into radio emission by nonlinear wave-wave interactions.     

Propagation and confinement of energetic electrons in solar flares

The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements: (1) spatially resolved observations obtained by imaging instruments; (2) stereoscopic observations of partially occulted sources providing radial (vertical) spatial resolution; and (3) directivity of the emission measured through stereoscopic observations and the center-to-limb variation of the occurrence frequency of hard X-ray flares. The characteristics of the energetic electrons are found to be quite distinct in impulsive and gradual hard X-ray flares. In impulsive flares the non-thermal electron spectrum seems to extend down to 2 keV indicating that the total energy of non-thermal electrons is much larger than that assumed in the past.     

Electrons and protons in long-lived streams of energetic solar particles

In 1966 and 1967 many long-lived streams of low-energy solar electrons and protons were observed near Earth. These streams were sometimes associated with bright flares which occurred many hours earlier and sometimes no individual flare could be found. In the latter case the particles are evidently to be associated in a general way with solar active centers as Fan et al. (1968) have done. The long-lived solar events discussed here include energetic storm particles, delayed events and fluxes associated with solar active regions. It is suggested here that these are all probably the same basic phenomena viewed in somewhat different ways depending on the age of the region and its location on the solar disc. These events are usually associated with a depression in the sea-level neutron intensity and one or more sudden commencements or sudden impulses. Both electrons and protons are present in these events but in several cases electrons were not detected. The most unusual feature is that when both particle species are present, the electron flux is centered several hours before the proton flux.     

Propagation and confinement of energetic electrons in solar flares

Solar Physics - The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements:...     

Bidirectional distribution of energetic protons in the 18 February 1979 interplanetary shock event

Pitch angle distributions of 35–1000 keV protons in the 18 January 1979 interplanetary shock event are presented and discussed in this paper. The observed, apparently unusual distributions can be well explained by assuming a magnetic bottle configuration of the interplanetary magnetic field immediately prior to the shock passage. The implication of such a magnetic configuration on the acceleration of charged particles by shock waves is also discussed.     

Coronal expansion and the transfer of solar angular momentum to the interplanetary space

We discuss the question of loss of angular momentum through coronal expansion. From a large volume of data on Type-1 cometary tails we have confirmed the presence of a tangential component in the coronal expansion, which has not only a stochastic component but also a constant component of 9.8 km/s. Through coronal expansion the Sun has lost 80% of its angular momentum since it evolved on to the main sequence and the angular velocity of the Sun is decreasing exponentially. This result should have a large effect on the dynamical evolution of the Sun.     

A further search on waves generated by solar energetic protons

It has been suggested that in the interplanetary medium Alfvén waves may be significantly amplified or damped during large solar proton events. This implies the increase or decrease of the ambient magnetic fluctuations in concurrence with the presence of the streaming particles, that we have analysed in a first study at times of eight proton events observed by Helios spacecraft (Valdés-Galicia and Alexander, 1997). However, it is not possible with interplanetary magnetic field measurements only to distinguish between waves moving away or towards the Sun in the frame of reference of the spacecraft. Plasma data for these eight events have now been made available to us and hence the energetic content of inward and outward propagating waves may be found, which is an important aid in our search for signatures left by the energetic protons. In the present work we incorporate the new information into the analyses of those events that in our first study showed more favourable evidence and therefore try to give a more definite answer as to whether it might be observed. The new results do not reinforce the evidence of our previous work, as they seem to be mildly consistent with the presence of the proton self-generated waves in just one of the three cases studied.     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

Coronal magnetic structures associated with interplanetary clouds

Among all the signatures of solar ejecta in interplanetary space, magnetic clouds are particularly interesting. We have shown that they are associated with solar mass ejections that involve not only coronal heights, but also chromospheric heights and so, they are almost always associated with low-altitude solar activity such as H flares or filament eruptions. As a magnetic cloud is a very large structure, and not all the ejecta found in the interplanetary medium are clouds, it is interesting to investigate the characteristics of the large-scale coronal magnetic structures in the regions where the activity leading to a cloud takes place. In this paper we use Hoeksema's potential field model of the solar magnetosphere to obtain the magnetic structure of the site of the solar events associated with 35 interplanetary magnetic clouds. The position of the related solar activity was determined from the location of the near-surface solar explosive events (flares and filament eruptions) associated with each cloud, obtained in our previous study. We find that the solar activity associated with interplanetary magnetic clouds occurs in regions of low-altitude, magnetically closed structures lying between higher helmets, or between the highest helmets and coronal holes, where the magnetic field lines are longitudinally oriented.     

A comparison of energetic storm protons to halo protons

Satellite observations of solar proton events with a halo structure or an energetic storm proton event and an SSC are studied. It is pointed out that some SSC events are associated with a decrease in the few MeV cosmic ray fluxes while most are associated with a flux increase. The properties of halo protons and energetic storm protons are compared. It is hypothesized that the two events are similar in origin. The propagation mode of storm particles is discussed. Evidence is presented for a solar, rather than interplanetary origin of storm protons.     

The role of high-energy protons and electrons in powering the solar white-light flare emission

The temporal histories of three intense and impulsive gamma-ray flares, for which also white-light emission had been observed, are analyzed in order to test the role of high-energy particles- electrons and protons - in powering the optical continuum. By comparing the light curves at optical wavelengths and at X-ray and gamma-ray energies, we find a good correlation of the main peaks of emission, which confirms previous findings that the continuum emission is most likely associated with the energy loss of energetic particles. The power carried by the greater-than-50 keV nonthermal electrons may be sufficient to balance the optical emission. The power residing in protons or ions with energies greater than 1 MeV depends largely on the spectral shape of the particle distribution. Only if this is similar to a power law, may the energy carried by these high-energy particles be sufficient to balance the white-light flare emission.Operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. Partial support for the National Solar Observatory is provided by the USAF under a Memorandum of Understanding with the NSF.     

Noble gases in interplanetary dust particles,I: The excess helium‐3 problem and estimates of the relative fluxes of solar wind and solar energetic particles in interplanetary space

Abstract— We report mass‐spectrometric measurements of light noble gases pyrolytically extracted from 28 interplanetary dust particles (IDPs) and discuss these new data in the context of earlier analyses of 44 IDPs at the University of Minnesota. The noble gas database for IDPs is still very sparse, especially given their wide mineralogic and chemical variability, but two intriguing differences from isotopic distributions observed in lunar and meteoritic regolith grains are already apparent. First are puzzling overabundances of ³He, manifested as often strikingly elevated ³He/⁴He ratios—up to >40x the solar‐wind value—‐and found primarily but not exclusively in shards of some of the larger IDPs (“cluster particles”) that fragmented on impact with the collectors carried by high‐altitude aircraft. It is difficult to attribute these high ratios to ³He production by cosmic‐ray‐induced spallation during estimated space residence times of IDPs, or by direct implantation of solar‐flare He. Minimum exposure ages inferred from the ³He excesses range from ～50 Ma to an impossible >10 Ga, compared to Poynting‐Robertson drag lifetimes for low‐density 20–30 μm particles on the order of ～0.1 Ma for an asteroidal source and ～10 Ma for origin in the Kuiper belt. The second difference is a dominant contribution of solar‐energetic‐particle (SEP) gases, to the virtual exclusion of solar‐wind (SW) components, in several particles scattered throughout the various datasets but most clearly and consistently observed in recent measurements of a group of individual and cluster IDPs from three different collectors. Values of the SEP/SW fluence ratio in interplanetary space from a simple model utilizing these data are ～1% of the relative SEP/SW abundances observed in lunar regolith grains, but still factors of approximately 10–100 above estimates for this ratio in low‐energy solar particle emission.     

Fast solar electrons,interplanetary plasma and km-wave type-III radio bursts observed from the IMP-6 spacecraft

IMP-6 spacecraft observations of low frequency radio emission, fast electrons, and solar wind plasma are used to examine the dynamics of the fast electron streams which generate solar type-III radio bursts. Of twenty solar electron events observed between April, 1971 and August, 1972, four were found to be amenable to detailed analysis. Observations of the direction of arrival of the radio emission at different frequencies were combined with the solar wind density and velocity measurements at 1 AU to define an Archimedean spiral trajectory for the radio burst exciter. The propagation characteristics of the exciter and of the fast electrons observed at 1 AU were then conpared. We find that: (1) the fast electrons excite the radio emission at the second harmonic; (2) the total distance travelled by the electrons was between 30 and 70% longer than the length of the smooth spiral defined by the radio observations; (3) this additional distance travelled is the result of scattering of the electrons in the interplanetary medium; (4) the observations are consistent with negligible true energy loss by the fast electrons.     

Energetic electrons as an energy transport mechanism in solar flares

We review the observations and theory relating to the role of energetic electrons in the solar flare, with particular emphasis on discriminating between thermal and nonthermal origins of these electrons. We discuss diagnostics in hard X-rays, especially those relating to the recent observations of the SMM and HINOTORI satellites. We also briefly address the response of the atmosphere to energy input in the form of high energy electrons, in particular through the diagnostics of both the Fe K feature and optically thin transition region lines such as 0V. Finally, we discuss the relative roles of electron and proton heating in -ray flare events.     

MHD simulations of solar and interplanetary phenomena

Workers in the field of magnetohydrodynamics (MHD) have been interested in the hypothesis that observed solar activities can be utilized in a deterministic way to predict the bulk flow consequences of these activities in the three-dimensional heliosphere. Exploration of this hypothesis, using the conventional/classic initial boundary value approach, will be reviewed against the background of basic, ideal (except for shocks) one-fluid approximations. This work has been divided into two parts: near-Sun simulations in two dimensions of coronal mass ejections (CMEs) as well as interplanetary simulations in 2D and 3D of propagating shocks. In the latter case, the flows behind the shocks should be thought of as interplanetary ICMEs, i.e., the interplanetary, evolutionary consequences of the near-Sun simulations.Initialization of these simulations has been based on observations (optical, soft X-ray, radio) from both ground-and space-based instruments. Simulation outputs have been compared within situ plasma and field observations and interplanetary scintillations (IPS). Improvements in the initialization procedures — spatial/temporal variations of solar plasma and field parameters at the coronal base — are expected from YOHKOH, SOHO, CORONAS-I, and TRACE experiments. Ground truth observations from WIND, SOHO, ACE, and INTERBALL experiments should then be compared with three-dimensional MHD outputs in tests of the fluid hypothesis noted above.