The most powerful explosions on the Sun – in the form of bright flares, intense storms of solar energetic particles (SEPs), and fast coronal mass ejections (CMEs) – drive the most severe space‐weather storms. Proxy records of flare energies based on SEPs in principle may offer the longest time base to study infrequent large events. We conclude that one suggested proxy, nitrate concentrations in polar ice cores, does not map reliably to SEP events. Concentrations of select radionuclides measured in natural archives may prove useful in extending the time interval of direct observations up to ten millennia, but as their calibration to solar flare fluences depends on multiple poorly known properties and processes, these proxies cannot presently be used to help determine the flare energy frequency distribution. Being thus limited to the use of direct flare observations, we evaluate the probabilities of large‐energy solar events by combining solar flare observations with an ensemble of stellar flare observations. We conclude that solar flare energies form a relatively smooth distribution from small events to large flares, while flares on magnetically active, young Sun‐like stars have energies and frequencies markedly in excess of strong solar flares, even after an empirical scaling with the mean coronal activity level of these stars. In order to empirically quantify the frequency of uncommonly large solar flares extensive surveys of stars of near‐solar age need to be obtained, such as is feasible with the Kepler satellite. Because the likelihood of flares larger than approximately X30 remains empirically unconstrained, we present indirect arguments, based on records of sunspots and on statistical arguments, that solar flares in the past four centuries have likely not substantially exceeded the level of the largest flares observed in the space era, and that there is at most about a 10% chance of a flare larger than about X30 in the next 30 years.
We present a detailed analysis of the geometric and physical parameters of 281 EUV nanoflares, simultaneously detected with the TRACE telescope in the 171 and 195 Å wavelengths. The detection and discrimination of these flarelike events is detailed in the first paper in this series. We determine the loop length l, loop width w, emission measure EM, the evolution of the electron density ne(t) and temperature Te(t), the flare decay time τdecay, and calculate the radiative loss time τloss, the conductive loss time τcond, and the thermal energy Eth. The findings are as follows: (1) EUV nanoflares in the energy range of 1024-1026 ergs represent miniature versions of larger flares observed in soft X-rays (SXR) and hard X-rays (HXR), scaled to lower temperatures (Te ≲ 2 MK), lower densities (ne ≲ 109 cm-3), and somewhat smaller spatial scales (l ≈ 2-20 Mm). (2) The cooling time τdecay is compatible with the radiative cooling time τrad, but the conductive cooling timescale τcond is about an order of magnitude shorter, suggesting repetitive heating cycles in time intervals of a few minutes. (3) The frequency distribution of thermal energies of EUV nanoflares, N(E) ≈ 10-46(E/1024)-1.8 (s-1 cm-2 ergs-1) matches that of SXR microflares in the energy range of 1026-1029, and exceeds that of nonthermal energies of larger flares observed in HXR by a factor of 3-10 (in the energy range of 1029-1032 ergs). Discrepancies of the power-law slope with other studies, which report higher values in the range of a = 2.0-2.6 (Krucker & Benz; Parnell & Jupp), are attributed to methodical differences in the detection and discrimination of EUV microflares, as well as to different model assumptions in the calculation of the electron density. Besides the insufficient power of nanoflares to heat the corona, we find also other physical limits for nanoflares at energies ≲1024 ergs, such as the area coverage limit, the heating temperature limit, the lower coronal density limit, and the chromospheric loop height limit. Based on these quantitative physical limitations, it appears that coronal heating requires other energy carriers that are not luminous in EUV, SXR, and HXR.
In this book, the term solar dynamo refers to the complex of mechanisms that cause the magnetic phenomena in the solar atmosphere. Usually, however, that complex is broken down into three components: (1) the generation of strong, large-scale fields of periodically reversing polarity, (2) the rise of these fields to the photosphere, and (3) the processing in, spreading across, and removal from the photosphere of magnetic flux. Components (2) and (3) are discussed in Chapters 4–6; in this chapter, we concentrate on aspect (1). Even on this limited topic, there is a stream of papers, but, as Rüdiger (1994) remarked, “it is much easier to find an excellent… review about the solar dynamo… than a working model of it.”
The magnetic field in solar active regions forms a highly structured pattern without an apparent length scale. We study this pattern in detail for a plage and its surroundings observed with the Swedish Solar Observatory on La Palma. The magnetogram has a resolution of about 1,, after image optimisation. We analysed the geometric properties of isolated patches of magnetic flux. Patches with a linear size up to 3 appear to be statistically self-similar, with a fractal dimension of Dj,= 1.54 _+ 0.05 for the relation between area and linear size. This value agrees very well with the dimension D r = 1.56 which is found in percolation theory for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas also agrees with that of clusters on such a random lattice. The correspondence between properties of observations and of clusters on randomly filled lattices suggests that - well after emergence - the magnetic flux on the Sun is randomly distributed at least up to sizes of about 3 and possibly larger.
Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of pre-existing atmospheric magnetic flux subject to surface plasma flows, or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with 4 different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~10^32 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.
