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.     

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.     

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.     

Upper cutoff of high energy solar protons

By studying the data from the worldwide neutron monitor network the spectra of most of the solar proton events in cycles 19–20 have been determined. These spectra are best represented by a power law with an upper cutoff R _m . This holds over a wide range in energy or rigidity. For the events examined R _m had values between 3 GV and 20 GV. It is shown that there is no correlation between R _m and the amplitude of the events.The equation describing continuous particle acceleration in a confining medium is solved in the non-stationary case. This solution shows the existence of a cutoff in the spectrum, and is compared with the experimental results in connection with the problem of particle acceleration time.Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico.     

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.     

Propagation of flare protons in the solar atmosphere

The velocity dispersion for a large number of solar proton events is analyzed in the energy regime of 10–60 MeV. It is found for all events that the time from the flare to particle maximum t _m is well represented by a sum of two components. The first component which is energy independent describes the propagation in the solar atmosphere, the second component describes the propagation in the interplanetary medium giving a velocity dispersion v × t _m = const. The additional study of time intensity profiles, onset times, and multispaceprobe observations reveals that the propagation in the solar atmosphere consists of three processes: (1) A rapid transport process in the initial ( 1 h) phase after the event fills up a fast propagation region (FPR), which may extend up to 60° from the flare site and which is tentatively identified with a large unipolar magnetic cell as seen on H synoptic charts, (2) a large-scale drift process which is energy independent with drift velocities v _D in the range 1° v _D 4°h^-1, and simultaneously (3) a diffusion process which yields the general broadening of the intensity time profiles for eastern hemisphere events, which is, however, of less importance than previously assumed.     

Shock versus stochastic acceleration of impulsive solar flare protons

The two major candidates for proton acceleration in impulsive -ray producing flares, shock and stochastic acceleration, are considered in light of recent observations of mass motions and turbulence in flares. Starting with the basic problem of energies required, energy storage and the currents which must be involved, it is concluded that the primary energy release must occur close to the temperature minimum region. It is shown that energy can propagate upwards in the form of fast magnetosonic waves which become evanescent in the transition region, converting a large fraction of their energy to mass motions and turbulence. Present observations are mostly of rather coarse (7000 km) spatial resolution and it is quite possible that significantly higher velocities than those observed were present. Using the results of recent simulations of parallel shocks and the well tested theory of Lee (1983) for parallel shock acceleration in the interplanetary medium, it is shown that shock acceleration is a viable candidate at velocities slightly higher than present observations. It is also shown that shocks must be driven by a mass of material which would be visible in coronal lines such as Caxix for them to be energetically important in proton acceleration.Stochastic acceleration is examined using the hypothesis that there is an equipartition of energy between observed turbulence and magnetic field fluctuations. It is shown that this is a viable acceleration mechanism within a large range of presently observed turbulence provided that the above equipartition hypothesis is valid and the turbulent elements are of small scale (1–200 km). Since turbulence is observed in many flares without any evidence of -rays, one of the above conditions must not be satisfied in general. It is concluded that although present observations favor stochastic acceleration, no definitive conclusion can be made without higher spatial resolution observations and additional theoretical work.     

The entry of solar protons over the polar caps

Observations of solar protons at energies from 1 MeV to 360 MeV are examined in relation to the information that these particles give about the magnetosphere, magnetotail and magnetopause. Trajectory integrations in a realistic model of the geomagnetic field out to 25R_E and a tail field model fitted to observations from 15R_E to 80R_E are used to obtain a better understanding of the particle motion. The mean free path of protons in the tail is found to be 700R_E and 200R_E for 100 MeV and 1 MeV protons respectively, which indicates that trajectory calculations in a static field model are valid.     

Interstellar pickup protons and solar wind heating in the outer heliosphere

The ionization of hydrogen atoms that penetrate into the heliosphere from the interstellar medium gives rise to a peculiar population of energetic protons (interstellar pickup protons) in the solar wind. The short-wavelength Alfvènic turbulence in the outer heliosphere is entirely attributable to the source associated with the instability of the initial anisotropic pickup proton velocity distribution. The bulk of the generated turbulent energy is subsequently absorbed by the pickup protons themselves through the cyclotron-resonance particle-wave interaction, and only an insignificant fraction of this energy can be transferred to the solar wind protons and heat them up.     

The solar origin of geomagnetic storms

A recent study of associations between geomagnetic storms and solar phenomena has found more associations with solar flares than with coronal holes (Garcia and Dryer, 1987). This disagrees with observations of earthbound transients obtained from IPS imaging which showed that nearly all geomagnetically effective disturbances originated from coronal holes at low latitudes. The discrepancy has arisen because the former study failed to take into account the large angular extent of transient eruptions from coronal holes. It is highly probable that the intense geomagnetic storm of February 1986, discussed by Garcia and Dryer, was caused by a low-latitude coronal hole which was present at that time. This answers their question concerning moderately strong flares that apparently cause major storms, while much larger flares often do not; flares may sometimes be associated with eruptions from coronal holes, but only as peripheral events.     

Directional diffusion coefficients of solar protons inside and outside the bow shock

The directional diffusion coefficients of low-energy (? 0.3 MeV) solar protons inside and outside the bow shock are examined during the solar flare event of 24 January 1969. The data are derived from simultaneous observations obtained by Explorer 33 inside the magnetosheath and by Explorer 35 in the interplanetary medium. Although the gross properties of the spin-averaged intensities on a diffusion-type plot appear to be the same in both media, the directional intensities show significant variations. It is shown that directional intensities of low-energy protons can be described reasonably well by anisotropic diffusion with an associated diffusion coefficient. Directional diffusion coefficients are found to differ by a factor as much as three among different directions in space, and from the spin-averaged diffusion coefficient. This suggests that anisotropic diffusion does indeed take place and that so called ‘isotropic’ diffusion coefficients derived in the past from spin-averaged intensities may actually be directional diffusion coefficients in cases where substantial anisotropies (> 50 per cent) exist. The typical postulated ratio of field aligned to cross-field diffusion coefficients is $\text{κ⊥}\text{κ∥}\text{< 0.1}$. The present data would indicate a ratio of ?0.3. This value of the anisotropy is to be taken only as an upper limit of the ratio because of the limitations introduced by the wide field of view of the detectors (~90°) and the lack of directional measurements over the entire sphere. Comparison between directional diffusion coefficients in the interplanetary medium and magnetosheath derived from identical directions in space implies changes in the parameters of the interplanetary magnetic field as it interacts with the bow shock.     

Relativistic acceleration of protons in reconnecting current sheets of solar flares

Acceleration of protons in a reconnecting current sheet (RCS), which forms as a consequence of filament eruption in the corona, is considered as a possible mechanism of generation of the relativistic particles during the late phase of solar flares. In order to explain the acceleration of protons and heavier ions up to several GeV in a time of < 0.1 s, the transverse electric field outside the RCS must be taken into account. Physically, this field is always present as a consequence of electric charge separation owing to the difference in the electron and proton masses. The new effect demonstrated in this paper is that the transverse electric field efficiently locks nonthermal ions in the RCS, thus allowing their acceleration by the direct electric field in the RCS. The mechanism considered may be useful in construction of a model for generation of relativistic ions in large gamma-ray/proton flares.     

Line diagnostics for Ne V and Mg V solar ions

Spectroscopic diagnostics for the Nev and Mgv solar ions have been investigated. The theoretical forbidden line ratios from these ions are presented for estimating the Ne/Mg variation in different solar structures. Calculations for density and temperature line diagnostics of these ions are given for the several spectral line ratios and their applications are discussed with the help of available solar observations in space. Future observations from the CDS and the SUMER experiments aboard the SOHO satellite are also discussed.     

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.     

A dominant role for protons at the onset of solar flares

The energetics of the onset of the impulsive phase of solar flares are examined on the premise that a single acceleration mechanism is operating in the corona. From considerations of recent observations of plasma turbulence and upflows, and nuclear gamma-rays it is concluded that a model where the bulk of the energy resides in a non-thermal electron beam with a low energy cut-off at 20–25 keV is incompatible with many of the observations. Conversely, a model where the bulk of the energy resides in non-thermal protons is consistent with the majority, if not all, of the observations. It is suggested that the bulk of the energy in the impulsive phase is initially transferred to 10²–10³ keV protons. Acceleration by a series of small shocks is an energy transfer mechanism which gives particles increments in velocity rather than energy and would naturally favour protons over electrons. An important consequence of this result is that the hard X-ray burst must be thermal. At this time the precise mechanism for thermal X-ray production is unclear; however recent theoretical plasma physics results have indicated promising avenues of research in this context.     

Energetic protons from the solar flare of March 24, 1966

Ten to 100 meV protons from the solar flare of March 24, 1966 were observed on the University of California scintillation counter on OGO-I. The short rise and decay times observed in the count rates of the 32 channels of pulse-height analysis show that scattering of the protons by the interplanetary field was much less important in this event than in previously observed proton flares. A diffusion theory in which D = M _r is found to be inadequate to account for the time behavior of the count rates of this event. Small fluctuations of the otherwise smooth decay phase may be due to flare protons reflected from the back of a shock front, which passed the earth on March 23.     

The temperature anisotropy and adiabatic cooling of the protons in the solar wind

A simple theoretical expression for the mean kinetic temperature of the protons in a steady state as a function of heliocentric distance is derived. The basic assumption is that the temperature anisotropy of the protons is invariant in space where binary encounters are rare. For an assumed base temperature of 5 × 10⁵K at a distance of 0.05 AU, the calculated temperature at a distance of 1 AU is in the range (2–4) × 10⁴K for an average anisotropy factor of 3: this range of temperatures is close to the observed average value under so-called ‘quiet’ conditions. Measurement of the anisotropy factor at different heliocentric distances is required to test the basis of the model.