Power-law spectra of energetic electrons in solar flares from the maximum entropy and dimensional considerations

The maximum entropy formalism and dimensional analysis are used to derive a power-law spectrum of accelerated electrons in impulsive solar flares, where the particles can contain a significant fraction of the total flare energy. Entropy considerations are used to derive a power-law spectrum for a particle distribution characterised by its order of magnitude of energy. The derivation extends an earlier one-dimensional argument to the case of an isotropic three-dimensional particle distribution. Dimensional arguments employ the idea that the spectrum should reflect a balance between the processes of energy input into the corona and energy dissipation in solar flares. The governing parameters are suggested on theoretical grounds and shown to be consistent with solar flare observations. The flare electron flux, differential in the non-relativistic electron kinetic energy E, is predicted to scale as $E^{-3}$. This scaling is in agreement with RHESSI measurements of the hard X-ray flux that is generated by deka-keV electrons, accelerated in intense solar flares.     

Relativistic proton production at the Sun in the 20 January 2005 solar event

Based on the concept of multiple acceleration of solar energetic particles (SEP) we analyzed the super-event of 20 January 2005 by the data of ground level, balloon and spacecraft observations. The main characteristics of relativistic solar protons (energy spectra, anisotropy directions and pitch-angle distributions) are derived and their dynamics during the event is studied. It is shown that the flux of relativistic solar protons may consist of two distinct components, the so-called prompt and delayed ones. Within a two-source model of particle generation, one of which is associated with an expanding magnetic loop, we solved the transport equation in energy phase space, including adiabatic losses simultaneously with the stochastic acceleration process, and calculate the expected spectra of the delayed component at the source. The confrontation of experimental spectra with theoretical ones shows that the delayed component may be correctly described by stochastic acceleration, but not the prompt component. The required acceleration efficiencies turned out to be rather high, so that, for this particular event, adiabatic cooling is practically negligible. Our results provide a new support to the existence of two populations of relativistic solar protons in some SEP events.     

To the problem on the reliability of solar energetic proton flux models

This work analyses basic issues of conformity of the most well-known models of solar energetic particles (SEP) fluxes to the experimental data. It is shown, that the postulates on neglecting SEP fluxes in quiet Sun years and on invariability SEP fluxes in active Sun years, underlying some models, contradict the experimental data.     

Driving major solar flares and eruptions: A review

This review focuses on the processes that energize and trigger M- and X-class solar flares and associated flux-rope destabilizations. Numerical modeling of specific solar regions is hampered by uncertain coronal-field reconstructions and by poorly understood magnetic reconnection; these limitations result in uncertain estimates of field topology, energy, and helicity. The primary advances in understanding field destabilizations therefore come from the combination of generic numerical experiments with interpretation of sets of observations. These suggest a critical role for the emergence of twisted flux ropes into pre-existing strong field for many, if not all, of the active regions that produce M- or X-class flares. The flux and internal twist of the emerging ropes appear to play as important a role in determining whether an eruption will develop predominantly as flare, confined eruption, or CME, as do the properties of the embedding field. Based on reviewed literature, I outline a scenario for major flares and eruptions that combines flux-rope emergence, mass draining, near-surface reconnection, and the interaction with the surrounding field. Whether deterministic forecasting is in principle possible remains to be seen: to date no reliable such forecasts can be made. Large-sample studies based on long-duration, comprehensive observations of active regions from their emergence through their flaring phase are needed to help us better understand these complex phenomena.     

Estimation of the solar proton spectrum in the GLE70 event

The GLE event on December 13, 2006 as observed by network station neutron monitor data is investigated (is considered). The GLE energetic spectrum suggested for this event is estimated taking into account the primary differential spectrum of galactic cosmic rays, coupling coefficients and integral multiplicities of concrete detectors at different latitudes and levels of observation. It is noted that the additional increase of solar protons is also manifested in the ionization chamber ASK-1 data at the Yakutsk station.     

Mode selection mechanism and magnetic diffusivity in a non-axisymmetric solar dynamo model

The generation of solar non-axisymmetric magnetic fields is studied based on a linear α²–Ω dynamo model in a rotating spherical frame. The model consists of a solar-like differential rotation, a magnetic diffusivity varied with depth, and three types of α-effects with different locations, i.e. the tachocline, the whole convective zone and the sub-surface. Some comparisons of the critical α-values of axisymmetric (m = 0) and longitude-dependent modes (m = 1,2,3) are presented to show the roles of the magnetic diffusivity in the problem of modes selection. With the changing of diffusivity intensity for the given solar differential rotation system, the dominant mode possibly changes likewise and the stronger the diffusivity is, the easier the non-axisymmetric modes are excited. The influence of the diffusivity and differential rotation on the configurations of the dominant modes are also presented.     

Properties of solar X-ray flares and proton event forecasting

X-ray flares and acceleration processes are in one complex of sporadic solar events (together with CMEs, radio bursts, magnetic field dissipation and reconnection). This supposes the connection (if not physical, but at least statistical) between characteristics of the solar energetic proton events and flares. The statistical analysis indicates that probability and magnitude of the near-Earth proton enhancement depends heavily on the flare importance and their heliolongitude. These relations may be used for elaboration of the forecasting models, which allow us to calculate probability of the solar proton events from the X-ray observations.     

Tilts and polarity separation in the sunspot groups and active regions at the ascending and descending phases of the cycle 23

The Solar Feature Catalogues for sunspots and active regions measured with SOHO/MDI instrument and Ca II K3 spectroheliograph of the Paris-Meudon Observatory are analyzed with the automated classification technique for sunspot groups and active region polarities. We report the first classification results for daily variations of tilt angles (normal and trigonometric ones) in sunspot groups (SG) and active (AR) regions in the cycle 23. The average normal tilts are presented for every year at the ascending and descending phases of the cycle 23 which are similar to those deduced by other authors for the cycles 19–22. The normal tilts of both the sunspot groups and active regions are shown to increase in the ascending phase and a decrease in the descending phase. Similar to SG and AR areas, the trigonometric tilts are shown to have the noticeable North–South asymmetry with the Southern hemisphere dominant in the selected ascending and descending periods. The normal tilt variations with latitude follow Joy’s law revealing a periodicity along the meridian of about 10° and reaching the maximum of 14° at the latitude of about 32° corresponding to the top of the ‘royal zone’ where the sunspots appear. The variations of polarity separation with a latitude are in an anti-phase with those of the tilts reaching a maximum at the latitude of 35° and showing a small positive separation for the groups/active regions in a vicinity of the average tilts ±40°. The ratio R of the polarity separation to the trigonometric tilt fits the linear function of a latitude φ as R = −0.0213φ − 0.1245 confirming positive separation for the polarities of active regions with the average tilts, or the dominance of activity in the Southern hemisphere activity, for the selected period of observations.     

Spectroscopic analysis of the solar flare event on 2002 August 3 with the use of RHESSI and RESIK data

We use simultaneous observations from RESIK and RHESSI instruments to compare plasma properties of a major solar flare in its rise and gradual phase. This event occurred on 2002 August 3 (peak time at 19:06 UT). The flare had a very good coverage with RESIK data and well-resolved soft and hard X-ray sources were seen in RHESSI images. Spectra of X-ray radiation from RHESSI images are studied and compared with RESIK measurements in different flare phases. Result shows large differences in flare morphology and spectra between flare rise and gradual phase.     

From solar nanoflares to stellar giant flares: Scaling laws and non-implications for coronal heating

In this study we explore physical scaling laws applied to solar nanoflares, microflares, and large flares, as well as to stellar giant flares. Solar flare phenomena exhibit a fractal volume scaling, V(L)  L^1.9, with L being the flare loop length scale, which explains the observed correlation between the total emission measure EM_p and flare peak temperature T_p in both solar and stellar flares. However, the detected stellar flares have higher emission measures EM_p than solar flares at the same flare peak temperature T_p, which can be explained by a higher electron density that is caused by shorter heating scale height ratios s_H/L ≈ 0.04–0.1. Using these scaling laws we calculate the total radiated flare energies E_X and thermal flare energies E_T and find that the total counts C are a good proxy for both parameters. Comparing the energies of solar and stellar flares we find that even the smallest observed stellar flares exceed the largest solar flares, and thus their observed frequency distributions are hypothetically affected by an upper cutoff caused by the maximum active region size limit. The powerlaw slopes fitted near the upper cutoff can then not reliably be extrapolated to the microflare regime to evaluate their contribution to coronal heating.     

Flaring loop parameters estimated from solar decimeter type U-like and type J-like fine structures

This work presents the analysis of five fine structures in the solar radio emission, observed between June 2000 and October 2001 by the Brazilian Solar Spectroscope (BSS), in the decimeter frequency band of 950–2500 MHz. Based on their morphological characteristics identified in the dynamic spectra, the fine structures had been classified as type U-like or type J-like bursts. Such emissions are variants of the type III bursts. They support the hypothesis of generation by plasma emission mechanism, from interaction of electron beams accelerated during solar flares, propagating along closed magnetic structures, within the trapped plasma of the solar corona. The spectral and temporal characteristics of the five fine structures had been obtained from the dynamic spectra and the parameters of the agent and the emitting source have been determined, assuming both fundamental and harmonic emissions. The analysis revealed the flux density of the structures is less than 20–80 s.f.u. For assumption of harmonic emission, the interval of values for the source parameters estimated are: the loop size is (0.3–5.1) × 10¹⁰ cm; the electron beam velocity is in the range of 0.16–0.53 c; the temperature of coronal loop top is of the order of (0.25–1.55) × 10⁷ K; and the low limit for the magnetic field is of 7–26 G. These results are in agreement with previous determinations reported in the literature.     

Particle acceleration and gamma rays in solar flares: Recent observations and new modeling

Experiments on SMM, GAMMA, Yohkoh, GRANAT, Compton GRO, INTEGRAL, RHESSI and CORONAS-F satellites over the past three decades have provided copious data for fundamental research relating to particle acceleration, transport and energetics of flares and to the ambient abundance of the solar corona, chromosphere and photosphere. We summarize main results of solar gamma-astronomy (including some results of several joint Russian–Chinese projects) and try to appraise critically a real contribution of those results into modern understanding of solar flares, particle acceleration at the Sun and some properties of the solar atmosphere. Recent findings based on the RHESSI, INTEGRAL and CORONAS-F measurements (source locations, spectrum peculiarities, ³He abundance etc.) are especially discussed. Some unusual features of extreme solar events (e.g., 28 October 2003 and 20 January 2005) have been found in gamma-ray production and generation of relativistic particles (solar cosmic rays, or SCR). A number of different plausible assumptions are considered concerning the details of underlying physical processes during large flares: (1) existence of a steeper distribution of surrounding medium density as compared to a standard astrophysical model (HSRA) for the solar atmosphere; (2) enhanced content of the ³He isotope; (3) formation of magnetic trap with specific properties; (4) prevailing non-uniform (e.g., fan-like) velocity (angular) distributions of secondary neutrons, etc. It is emphasized that real progress in this field may be achieved only by combination of gamma-ray data in different energy ranges with multi-wave and energetic particle observations during the same event. We especially note several promising lines for the further studies: (1) resonant acceleration of the ³He ions in the corona; (2) timing of the flare evolution by gamma-ray fluxes in energy range above 90 MeV; (3) separation of gamma-ray fluxes from different sources at/near the Sun (e.g., different acceleration sources/episodes during the same flare, contribution of energetic particles accelerated by the CME-driven shocks etc.); (4) asymmetric magnetic geometry and new magnetic topology models of the near-limb flares; (5) modeling of self-consistent time scenario of the event.     

The investigation of powerful solar flares characteristics by analysis of excited states of C and various neutrons capture lines

Accelerated energetic particles in solar flares produced nuclear γ-lines in interactions with ambient solar atmosphere. Analysis of intensity of ratios between various γ-lines allows us to make estimations of abundance of elements, parameters of surrounding media and other solar characteristics. In this article we discuss the flux ratio between two lines from excited states of ¹²C (f_15.11/f_4.44) and our results of preliminary calculation of intensity ratio between two neutron capture lines at ³He and ¹H (f_20.58/f_2.223). In particular we consider the opportunity to obtain n(³He)/n(¹H) ratio during solar flares and using high-energy gamma-emission studying, based on the satellite data. Possible interpretation of spectral features observed during the January 20, 2005 solar flare is discussed. Preliminary analysis of energy spectrum in the band of 2–21 MeV gives n(³He)/n(¹H) ∼ 8 × 10⁻⁴ for January 20, 2005 solar flare.     

Non-stationarity and cross-correlation effects in the MHD solar activity

The analysis of turbulent processes in sunspots and pores which are self-organizing long-lived magnetic structures is a complicated and not yet solved problem. The present work focuses on studying such magneto-hydrodynamic (MHD) formations on the basis of flicker-noise spectroscopy using a new method of multi-parametric analysis. The non-stationarity and cross-correlation effects taking place in solar activity dynamics are considered. The calculated maximum values of non-stationarity factor may become precursors of significant restructuring in solar magnetic activity. The introduced cross-correlation functions enable us to judge synchronization effects between the signals of various solar activity indicators registered simultaneously.     

Comparison of the transport codes HZETRN,HETC and FLUKA for a solar particle event

The protection of astronauts and instrumentation from galactic cosmic rays and solar particle events is one of the primary constraints associated with mission planning in low earth orbit or deep space. To help satisfy this constraint, several computational tools have been developed to analyze the effectiveness of various shielding materials and structures exposed to space radiation. These tools are now being carefully scrutinized through a systematic effort of verification, validation, and uncertainty quantification. In this benchmark study, the deterministic transport code HZETRN is compared to the Monte Carlo transport codes HETC-HEDS and FLUKA for a 30 g/cm² water target protected by a 20 g/cm² aluminum shield exposed to a parameterization of the February 1956 solar particle event. Neutron and proton fluences as well as dose and dose equivalent are compared at various depths in the water target. The regions of agreement and disagreement between the three codes are quantified and discussed, and recommendations for future work are given.     

First results of ozone profiles between 35 and 65 km retrieved from SCIAMACHY limb spectra and observations of ozone depletion during the solar proton events in October/November 2003

Ozone density profiles between 35 and 65 km altitude are derived from scattered sunlight limb radiance spectra measured by the SCIAMACHY instrument on the Envisat satellite. The method is based on the inversion of normalized limb radiance profiles in the Hartley absorption bands of ozone at selected wavelengths between 250 and 310 nm. It employs a non-linear Newtonian iteration version of Optimal Estimation (OE) coupled with the radiative transfer model SCIARAYS. The limb scatter technique combined with a classical OE retrieval in the short-wave UV-B and long-wave UV-C delivers reliable results as shown by a first comparison with MIPAS V4.61 profiles yielding agreement within 10% between 38 and 55 km. An overview of the methodology and an initial error analysis are presented. Furthermore the effect of the solar proton storm between 28 October and 6 November 2003 on the ozone concentration profiles is shown. They indicate large depletion of ozone of about 60% at 50 km in the Northern hemisphere, a weaker depletion in the Southern hemisphere and a dependence of the depletion on the Earth’s magnetic field.     

Bottom side profiles for two close stations at the southern crest of the EIA: Differences and comparison with IRI-2012 and NeQuick2 for low and high solar activity

Bottom side electron density profiles for two stations at the southern crest of the Equatorial Ionization Anomaly (EIA), São José dos Campos (23.1°S, 314.5°E, dip latitude 19.8°S; Brazil) and Tucumán (26.9°S, 294.6°E, dip latitude 14.0°S; Argentina), located at similar latitude and separated by only 20° in longitude, have been compared during equinoctial, winter and summer months under low (year 2008, minimum of the solar cycle 23/24) and high solar activity (years 2013–2014, maximum of the solar cycle 24) conditions. An analysis of parameters describing the bottom side part of the electron density profile, namely the peak electron density NmF2, the height hmF2 at which it is reached, the thickness parameter B₀ and the shape parameter B₁, is carried out. Further, a comparison of bottom side profiles and F-layer parameters with the corresponding outputs of IRI-2012 and NeQuick2 models is also reported. The variations of NmF2 at both stations reveal the absence of semi-annual anomaly for low solar activity (LSA), evidencing the anomalous activity of the last solar minimum, while those related to hmF2 show an uplift of the ionosphere for high solar activity (HSA). As expected, the EIA is particularly visible at both stations during equinox for HSA, when its strength is at maximum in the South American sector. Despite the similar latitude of the two stations upon the southern crest of the EIA, the anomaly effect is more pronounced at Tucumán than at São José dos Campos. The differences encountered between these very close stations suggest that in this sector relevant longitudinal-dependent variations could occur, with the longitudinal gradient of the Equatorial Electrojet that plays a key role to explain such differences together with the 5.8° separation in dip latitude between the two ionosondes. Furthermore at Tucumán, the daily peak value of NmF2 around 21:00 LT during equinox for HSA is in temporal coincidence with an impulsive enhancement of hmF2, showing a kind of “elastic rebound” under the action of the EIA. IRI-2012 and NeQuick2 bottom side profiles show significant deviations from ionosonde observations. In particular, both models provide a clear underestimation of the EIA strength at both stations, with more pronounced differences for Tucumán. Large discrepancies are obtained for the parameter hmF2 for HSA during daytime at São José dos Campos, where clear underestimations made by both models are observed. The shape parameter B₀ is quite well described by the IRI-2012 model, with very good agreement in particular during equinox for both stations for both LSA and HSA. On the contrary, the two models show poor agreements with ionosonde data concerning the shape parameter B₁.