Propagation of solar cosmic rays: Diffusion versus focused diffusion

This paper is designed to bring to the attention the fact that the effect of focusing of solar energetic particles is always essential as compared with scattering, no matter how small the value of the mean free path may be. That is why, an ordinary (focusing-free) diffusion approach can not be applied to the solar cosmic ray transport. In the case of high-energy solar particles, the focused diffusion is demonstrated to lead to a power law decay of energetic particle intensity much like an ordinary diffusion. However, the power law index of the decay is renormalized by the focusing.     

Global Heliospheric Parameters and Cosmic-Ray Modulation: An Empirical Relation for the Last Decades

We study empirical relations between the modulation of galactic cosmic rays quantified in terms of the modulation potential and the following global heliospheric parameters: the open solar magnetic flux, the tilt angle of the heliospheric current sheet, and the polarity of the heliospheric magnetic field. We show that a combination of these parameters explains the majority of the modulation potential variations during the neutron monitor era 1951 – 2005. Two empirical models are discussed: a quasi-linear model and a model assuming a power-law relation between the modulation potential and the magnetic flux. Both models describe the data fairly well. These empirical models provide a simple tool for evaluating various cosmic-ray related effects on different time scales. The models can be extended backwards in time or used for predictions, if the corresponding global heliospheric variables can be independently estimated.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

An Upper Limit on Sunspot Activity During the Maunder Minimum

We have estimated the upper and lower limits of sunspot activity, in terms of active day fraction during the Maunder minimum (1645–1710), using raw information on individual daily observations (Hoyt and Schatten, 1998). Establishing the relation between the sunspot activity and active day fraction after 1850, we evaluate the upper limit of annual group sunspot number during the deep Maunder minimum (1645–1700) which does not exceed 4. The earlier finding of a dominant 22-year periodicity during the Maunder minimum is verified and shown to be robust. Also we confirm that the start of the Maunder minimum was very abrupt.     

Neutron monitor data on the 15 June 1991 flare: Neutrons as a test for proton acceleration scenario

Response of Alma-Ata neutron monitor for solar neutrons from the 15 June 1991 was studied. We considered this response as a test for various scenarios of proton acceleration during the flare. The analysis of neutron monitor is an evidence in favour of the assumption of two acts of proton acceleration at impulsive and post-impulsive phases of the flare.     

A Test of the Active-Day Fraction Method of Sunspot Group Number Calibration: Dependence on the Level of Solar Activity

The method of active-day fraction (ADF) was proposed recently to calibrate different solar observers to standard observational conditions. The result of the calibration may depend on the overall level of solar activity during the observational period. This dependency is studied quantitatively using data of the Royal Greenwich Observatory by formally calibrating synthetic pseudo-observers to the full reference dataset. It is shown that the sunspot group number is precisely estimated by the ADF method for periods of moderate activity, may be slightly underestimated by 0.5?–?1.5 groups (\({\leq}\,10\%\)) for strong and very strong activity, and is strongly overestimated by up to 2.5 groups (\({\leq}\,30\%\)) for weak-to-moderate activity. The ADF method becomes inapplicable for the periods of grand minima of activity. In general, the ADF method tends to overestimate the overall level of activity and to reduce the long-term trends.     

Ground-level energetic solar particle event on 24 May 1990: Possibility of direct solar neutron detection

The first increase in neutron monitor count rate during the ground-level event on 24 May 1990 was interpreted by Shea et al. (1991) as a consequence of an arrival of flare neutrons. Debrunner et al. (1991) rejected the neutron hypothesis and proposed that the first neutron monitor increase was due to the arrival of primary protons. We have show that neutron monitor data do not contradict the hypothesis of a neutron origin of the first increase of ground-level event on 24 May 1990.     

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.     

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.     

Neutron and electromagnetic emissions during the 1990 May 24 solar flare

In this paper, we are primarily concerned with the solar neutron emission during the 1990 May 24 flare, utilizing the counting rate of the Climax neutron monitor and the time profiles of hard X-rays and γ-rays obtained with the GRANAT satellite (Pelaezet al., 1992; Talonet al., 1993; Terekhovet al., 1993). We compare the derived neutron injection function with macroscopic parameters of the flare region as obtained from theHα and microwave observations made at the Big Bear Solar Observatory and the Owens Valley Radio Observatory, respectively. Our results are summarized as follows: (1) to explain the neutron monitor counting rate and 57.5–110 MeV and 2.2 MeV γ-ray time profiles, we consider a two-component neutron injection function,Q(E, t), with the form $$Q(E,t) = N_f {\text{ exp[}} - E/E_f - t/T_f ] + N_s {\text{ exp[}} - E/E_s - t/T_s ],$$ whereN _f(s),E _f(s), andT _f(s) denote number, energy, and decay time of the fast (slow) injection component, respectively. By comparing the calculated neutron counting rate with the observations from the Climax neutron monitor we derive the best-fit parameters asT _f ≈ 20 s,E _f ≈ 310 MeV,T _s ≈ 260 s,E _s ≈ 80 MeV, andN _f (E > 100 MeV)/N _s (E > 100 MeV) ≈ 0.2. (2) From the Hα observations, we find a relatively small loop of length ≈ 2 × 10⁴ km, which may be regarded as the source for the fast-decaying component of γ-rays (57.5–110 MeV) and for the fast component of neutron emission. From microwave visibility and the microwave total power spectrum we postulate the presence of a rather big loop (≈ 2 × 10⁵ km), which we regard as being responsible for the slow-decaying component of the high-energy emission. We show how the neutron and γ-ray emission data can be explained in terms of the macroscopic parameters derived from the Hα and microwave observations. (3) The Hα observations also reveal the presence of a fast mode MHD shock (the Moreton wave) which precedes the microwave peak by 20–30 s and the peak of γ-ray intensity by 40–50 s. From this relative timing and the single-pulsed time profiles of both radiations, we can attribute the whole event as due to a prompt acceleration of both electrons and protons by the shock and subsequent deceleration of the trapped particles while they propagate inside the magnetic loops.