Gennady A. Kovaltsov

Grand minima and maxima of solar activity: new observational constraints

Aims. Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. Methods. We present an updated reconstruction of sunspot number over multiple millennia, from 14 C data by means of a physicsbased model, using an updated model of the evolution of the solar open magnetic flux. A list of grand minima and maxima of solar activity is presented for the Holocene (since 9500 BC) and the statistics of both the length of individual events as well as the waiting time between them are analyzed. Results. The occurrence of grand minima/maxima is driven not by long-term cyclic variability, but by a stochastic/chaotic process. The waiting time distribution of the occurrence of grand minima/maxima deviates from an exponential distribution, implying that these events tend to cluster together with long event-free periods between the clusters. Two different types of grand minima are observed: short (30–90 years) minima of Maunder type and long (>110 years) minima of Sporer type, implying that a deterministic behaviour of the dynamo during a grand minimum defines its length. The duration of grand maxima follows an exponential distribution, suggesting that the duration of a grand maximum is determined by a random process. Conclusions. These results set new observational constraints upon the long-term behaviour of the solar dynamo.

The AD775 cosmic event revisited: the Sun is to blame

Aims. Miyake et al. (2012, Nature, 486, 240, henceforth M12) recently reported, based on 14 C data, an extreme cosmic event in about AD775. Using a simple model, M12 claimed that the event was too strong to be caused by a solar flare within the standard theory. This implied a new paradigm of either an impossibly strong solar flare or a very strong cosmic ray event of unknown origin that occurred around AD775. However, as we show, the strength of the event was significantly overestimated by M12. Several subsequent works have attempted to find a possible exotic source for such an event, including a giant cometary impact upon the Sun or a gamma-ray burst, but they are all based on incorrect estimates by M12. We revisit this event with analysis of new datasets and consistent theoretical modelling. Methods. We verified the experimental result for the AD775 cosmic ray event using independent datasets including 10 Be series and newly measured 14 C annual data. We surveyed available historical chronicles for astronomical observations for the period around the AD770s to identify potential sightings of aurorae borealis and supernovae. We interpreted the 14 C measurements using an appropriate carbon cycle model. Results. We show that: (1) The reality of the AD775 event is confirmed by new measurements of 14 C in German oak; (2) by using an inappropriate carbon cycle model, M12 strongly overestimated the event’s strength; (3) the revised magnitude of the event (the global 14 C production Q = (1.1−1.5) × 10 8 atoms/cm 2 ) is consistent with different independent datasets ( 14 C, 10 Be, 36 Cl) and can be associated with a strong, but not inexplicably strong, solar energetic particle event (or a sequence of events), and provides the first definite evidence for an event of this magnitude (the fluence >30 MeV was about 4.5 × 10 10 cm −2 ) in multiple datasets; (4) this interpretation is in agreement with increased auroral activity identified in historical chronicles. Conclusions. The results point to the likely solar origin of the event, which is now identified as the greatest solar event on a multimillennial time scale, placing a strong observational constraint on the theory of explosive energy releases on the Sun and cool stars.

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.

Heliospheric modulation of cosmic rays and solar activity during the Maunder minimum

Modern models and direct cosmic ray experiments deal with heliospheric modulation of cosmic rays only during the recent times of rather high overall solar activity level. On the other hand, the question of cosmic ray modulation during the exceptional conditions of very quiet heliosphere is important. In the present paper we compare the variations of cosmic ray intensity with solar and auroral activity during the Maunder minimum (1645-1715) when the Sun was extremely quiet. We use the newly presented group sunspot number series as a measure of early solar activity, the auroral observations in central Europe as an indicator of transient phenomena in the inner heliosphere, and the radiocarbon data as a proxy of cosmic ray intensity. We find that both cosmic ray intensity and auroral activity closely follow the dominant 22-year cyclicity with sunspot activity during the Maunder minimum. Moreover, the strict antiphase between the 22-year variation of cosmic ray intensity and sunspot activity suggests that the 22-year variation in cosmic ray intensity can be explained by the diffusion-dominated terms of cosmic ray modulation without significant drift effects. We also discuss the possible origin of the behavior of the 10 Be data which is different from all other parameters during the Maunder minimum.

OCCURRENCE OF EXTREME SOLAR PARTICLE EVENTS: ASSESSMENT FROM HISTORICAL PROXY DATA

The probability of occurrence of extreme solar particle events (SPEs) with proton fluence (>30 MeV) F 30 ≥ 1010 cm–2 is evaluated based on data on the cosmogenic isotopes 14C and 10Be in terrestrial archives covering centennial-millennial timescales. Four potential candidates with F 30 = (1-1.5) × 1010 cm–2 and no events with F 30 > 2 × 1010 cm–2 are identified since 1400 AD in the annually resolved 10Be data. A strong SPE related to the Carrington flare of 1859 AD is not supported by the data. For the last 11,400 years, 19 SPE candidates with F 30 = (1-3) × 1010 cm–2 are found and clearly no event with F 30 > 5 × 1010 cm–2 (50 times the SPE of 1956 February 23) has occurred. These values serve as observational upper limits on the strength of SPEs on the timescale of tens of millennia. Two events, ca. 780 and 1460 AD, appear in different data series making them strong candidates for extreme SPEs. We build a distribution of the occurrence probability of extreme SPEs, providing a new strict observational constraint. Practical limits can be set as F 30 ≈ 1, 2-3, and 5×1010 cm–2 for occurrence probabilities ≈10–2, 10–3, and 10–4 yr–1, respectively. Because of the uncertainties, our results should be interpreted as a conservative upper limit on the SPE occurrence near Earth. The mean solar energetic particle (SEP) flux is evaluated as ≈40 (cm2 s)–1, in agreement with estimates from lunar rocks. On average, extreme SPEs contribute about 10% to the total SEP fluence.

The Maunder minimum (1645–1715) was indeed a grand minimum: A reassessment of multiple datasets

Aims. Although the time of the Maunder minimum (1645–1715) is widely known as a period of extremely low solar activity, it is still being debated whether solar activity during that period might have been moderate or even higher than the current solar cycle #24. We have revisited all existing evidence and datasets, both direct and indirect, to assess the level of solar activity during the Maunder minimum. Methods. We discuss the East Asian naked-eye sunspot observations, the telescopic solar observations, the fraction of sunspot active days, the latitudinal extent of sunspot positions, auroral sightings at high latitudes, cosmogenic radionuclide data as well as solar eclipse observations for that period. We also consider peculiar features of the Sun (very strong hemispheric asymmetry of the sunspot location, unusual differential rotation and the lack of the K-corona) that imply a special mode of solar activity during the Maunder minimum. Results. The level of solar activity during the Maunder minimum is reassessed on the basis of all available datasets. Conclusions. We conclude that solar activity was indeed at an exceptionally low level during the Maunder minimum. Although the exact level is still unclear, it was definitely lower than during the Dalton minimum of around 1800 and significantly below that of the current solar cycle #24. Claims of a moderate-to-high level of solar activity during the Maunder minimum are rejected with a high confidence level.

Revisited Sunspot Data: A New Scenario for the Onset of the Maunder Minimum

The Maunder minimum forms an archetype for the Grand minima, and detailed knowledge of its temporal development has important consequences for the solar dynamo theory dealing with long-term solar activity evolution. Here, we reconsider the current paradigm of the Grand minimum general scenario by using newly recovered sunspot observations by G. Marcgraf and revising some earlier uncertain data for the period 1636-1642, i.e., one solar cycle before the beginning of the Maunder minimum. The new and revised data dramatically change the magnitude of the sunspot cycle just before the Maunder minimum, from 60-70 down to about 20, implying a possibly gradual onset of the minimum with reduced activity started two cycles before it. This revised scenario of the Maunder minimum changes, through the paradigm for Grand solar/stellar activity minima, the observational constraint on the solar/stellar dynamo theories focused on long-term studies and occurrence of Grand minima.

Correlative study of solar activity and cosmic ray intensity

We perform a correlative study of solar activity (sunspot numbers) and cosmic ray intensity (neutron monitor count rates) for the last four solar cycles. Analysis of the running cross correlation between the two series shows that the behavior of cosmic ray modulation is similar, in general, for particles with different energy. However, a strong rigidity dependence as well as an unusual behavior of the cross correlation function is found for the descending phase of cycle 20. We study the evolution of cosmic ray and solar activity cycles in a three-dimensional phase space by means of the delayed component method. While all solar activity cycles and most cosmic ray cycles are planar, cosmic ray cycle 20 is significantly three-dimensional. A concept of the momentary phase of a cycle is introduced, and the phase evolution of cosmic ray and solar activity cycles is studied. We also discuss the heliospheric conditions responsible for the unusual behavior of cosmic ray modulation in the descending phase of cycle 20.

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.

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.