Cycle 23 Variation in Solar Flare Productivity

The NOAA listings of solar flares in cycles 21?–?24, including the GOES soft X-ray magnitudes, enable a simple determination of the number of flares each flaring active region produces over its lifetime. We have studied this measure of flare productivity over the interval 1975?–?2012. The annual averages of flare productivity remained approximately constant during cycles 21 and 22, at about two reported M- or X-flares per region, but then increased significantly in the declining phase of cycle 23 (the years 2004?–?2005). We have confirmed this by using the independent RHESSI flare catalog to check the NOAA events listings where possible. We note that this measure of solar activity does not correlate with the solar cycle. The anomalous peak in flare productivity immediately preceded the long solar minimum between cycles 23 and 24.     

Re-Evaluation of the Flare–Type II–CME Association

We have re-evaluated the association of type II solar radio bursts with flares and/or coronal mass ejections (CMEs) using the year 2000 solar maximum data. For this, we consider 52 type II events whose associations with flares or CMEs were absent or not clearly identified and reported. These events are classified as follows; group I: 11 type IIs for which there are no reports of GOES X-ray flares and CMEs; group II: 12 type IIs for which there are no reports of GOES X-ray flares; and group III: 29 type IIs for which the flare locations are not reported. By carefully re-examining their association from GOES X-ray and H, Yohkoh SXT and EIT-EUV data, we attempt to answer the following questions: (i) if there really were no X-ray flares associated with the above 23 type IIs of groups I and II; (ii) whether they can be regarded as backside events whose X-ray emission might have been occulted. From this analysis, we have found that two factors, flare background intensity and flare location, play important roles in the complete reports about flare–type II–CME associations. In the above 23 cases, for more than 50% of the cases in total, the X-ray flares were not noticed and reported, because the background intensity of X-ray flux was high. In the remaining cases, the X-ray intensity might be greatly reduced due to occultation. From the H flare data, Yohkoh SXT data and EIT-EUV data, we found that ten cases out of 23 might be frontside events, and the remaining are backside events. While the flare–type II association is found to be nearly 90%, the type II–CME association is roughly around 75%. This analysis might be useful to reduce some ambiguities regarding the association among type IIs, flares and CMEs.     

Interpretation of Statistical Flare Data using Magnetic Reconnection Models

The ability of magnetic reconnection solutions to explain statistical flare data is discussed. It is assumed that flares occur at well-defined, isolated sites within an active region, determined by the null points and separators of the coronal magnetic field (Craig, 2001). Statistical flare observations then derive from a multiplicity of independent sites, flaring in parallel, that produce events of widely varying output (Wheatland, 2002). Given that the `separator length' at an individual site controls the event frequency and the mean energy release, it is shown that the observed frequency-energy spectrum N(E)can be inverted to yield a source function that relates directly to the distribution of separator lengths. It is also pointed out that, under the parallel flaring model, inferred waiting-time distributions are naturally interpreted as a superposition of individual point processes. Only a modest number of flaring separators is required to mimic a Poisson process.     

The Radio Supernebula in NGC 5253

It was recently pointed out that the distribution of times between solar flares (the flare waiting-time distribution) follows a power law for long waiting times. Based on 25 years of soft X-ray flares observed by Geostationary Operational Environmental Satellite instruments, it is shown that (1) the waiting-time distribution of flares is consistent with a time-dependent Poisson process and (2) the fraction of time the Sun spends with different flaring rates approximately follows an exponential distribution. The second result is a new phenomenological law for flares. It is shown analytically how the observed power-law behavior of the waiting times originates in the exponential distribution of flaring rates. These results are argued to be consistent with a nonstationary avalanche model for flares.     

Statistical Models for the Solar Flare Interval Distribution in Individual Active Regions

This article discusses statistical models for the solar flare interval distribution in individual active regions. We analyzed solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to derive probability density functions from any data set and propose a new procedure, which uses the maximum likelihood method and Akaike Information Criterion (AIC) to objectively compare some competing probability density functions. Previous studies of the solar flare interval distribution in individual active regions only dealt with constant or time-dependent Poisson process models, and no other models were discussed. We examine three models – exponential, lognormal, and inverse Gaussian – as competing models for probability density functions in this study. We found that lognormal and inverse Gaussian models are more likely models than the exponential model for the solar flare interval distribution in individual active regions. The possible solar flare mechanisms for the distribution models are briefly mentioned. We also briefly investigated the time dependence of probability density functions of the solar flare interval distribution and found that some active regions show time dependence for lognormal and inverse Gaussian distribution functions. The results suggest that solar flares do not occur randomly in time; rather, solar flare intervals appear to be regulated by solar flare mechanisms. Determining a solar flare interval distribution is an essential step in probabilistic solar flare forecasting methods in space weather research. We briefly mention a probabilistic solar flare forecasting method as an application of a solar flare interval distribution analysis. The application of our distribution analysis to a probabilistic solar flare forecasting method is one of the main objectives of this study.     

Subsurface Vorticity of Flaring <Emphasis Type="Italic">versus</Emphasis> Flare-Quiet Active Regions

We apply discriminant analysis to 1023 active regions and their subsurface-flow parameters, such as vorticity and kinetic helicity density, with the goal of distinguishing between flaring and non-flaring active regions. We derive synoptic subsurface flows by analyzing GONG high-resolution Doppler data with ring-diagram analysis. We include magnetic-flux values in the discriminant analysis derived from NSO Kitt Peak and SOLIS synoptic maps binned to the same spatial scale as the helioseismic analysis. For each active region, we determine the flare information from GOES and include all flares within 60° central meridian distance to match the coverage of the ring-diagram analysis. The subsurface-flow characteristics improve the ability to distinguish between flaring and non-flaring active regions. For the C- and M-class flare category, the most important subsurface parameter is the so-called structure vorticity, which estimates the horizontal gradient of the horizontal-vorticity components. The no-event skill score, which measures the improvement over predicting that no events occur, reaches 0.48 for C-class flares and 0.32 for M-class flares, when the structure vorticity at three depths combined with total magnetic flux are used. The contributions come mainly from shallow layers within about 2 Mm of the surface and layers deeper than about 7 Mm.     

Photospheric Magnetic Evolution in the WHI Active Regions

Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Sun??s disk during the Whole Heliosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated several parameterizations of magnetic structure and evolution that have previously been associated with flare and CME activity, including total unsigned magnetic flux, magnetic flux near polarity-inversion lines, amount of canceled flux, the ??proxy Poynting flux,?? and helicity flux. To catalog flare events, we used flare lists derived from both GOES and RHESSI observations. By most such measures, AR 10988 should have been the most flare- and CME-productive active region, and AR 10989 the least. Observations, however, were not consistent with this expectation: ARs 10988 and 10989 produced similar numbers of flares, and AR 10989 also produced a few CMEs. These results highlight present limitations of statistics-based flare and CME forecasting tools that rely upon line-of-sight photospheric magnetic data alone.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.     

Irradiance observations of the 1–8 Å solar soft X-ray flux from goes

The solar 0.5–8 soft X-ray flux was monitored by the NOAA Geostationary Operational Environmental Satellites (GOES) from 1974 to the present, providing a continuous record over two solar activity cycles. Attempts have been made to determine a soft X-ray (SXR) background flux by subtracting out solar flares (using the daily lowest flux level). The SXR background flux represents the quiescent SXR flux from heated plasma in active regions, and reflects similar (intermediate-term) variability and periodicities (e.g. 155-day period) as the SXR or hard X-ray (HXR) flare rate, although it is determined in non-flaring time intervals. The SXR background flux peaks late in Solar Cycle 21 (2–3 years after the sunspot maximum), similar to the flare rate measured in SXR, HXR, or gamma rays, possibly due the increasing complexity of coronal magnetic structures in the decay phase of the solar cycle. The SXR background flux appears to be dominated by postflare emission from the dominant active regions, while the contributions from the quiet Sun are appreciable in the Solar Minimum only (A1-level). Comparisons with full-disk integrated images from YOHKOH suggest that the presence of coronal holes can decrease the quietest SXR irradiance level by an additional order of magnitude, but only in the rare case of absence of active regions.Presented at IAU Colloquium No. 143, The Sun as a Variable Star: Solar and Stellar Irradiance Variations, Boulder, CO, June 20–25, 1993     

High-temperature flares observed in broadband soft X-rays

Broadband soft solar X-rays monitored by the GOES satellites have been used to detect high-temperature flares (> 25 MK). The data suggest that there are two general categories of high-temperature flares: those that are intrinsically hot and recur repeatedly in particular active regions and those that show enhanced temperatures because of their proximity to the solar limb. Intrinsically hot flares associate with gamma-ray flares and impulsive hard X-ray flares. Hot flares show a small incidence with gradual hard X-ray flares, but those cases are either extremely intense flares or limb flares. The apparently hot flares occur near the visible limb, which suggests the strong thermal stratification of flare plasmas as demonstrated by over-the-limb events; even on the visible disk near the limb, the lower, cooler plasmas are somehow partially occulted.     

Solar Flare Occurrence Rate and Waiting Time Statistics

We use Renewal Theory for the estimation and interpretation of the flare rate from the Geostationary Operational Environmental Satellite (GOES) soft X-ray?flare catalogue. It is found that, in addition to the flare rate variability with the solar cycles, a much faster variation occurs. The fast variation on time scales of days and hours down to minute scale appears to be comparable with time intervals between two successive flares (waiting times). The detected fast non-stationarity of the flaring rate is discussed in the framework of the previously published stochastic models of the waiting time dynamics.     

On the origin of solar metric type II bursts

The vast majority of solar flares are not associated with metric Type II radio bursts. For example, for the period February 1980–July 1982, corresponding to the first two and one-half years of the Solar Maximum Mission, 95% of the 2500 flares with peak >25 keV count rates >100 c s^–1lacked associated Type II emission. Even the 360 largest flares, i.e., those having >25 keV peak count rates >1000 c s^–1, had a Type II association rate of only 24%. The lack of a close correlation between flare size and Type II occurrence implies the need for a 'special condition' that distinguishes flares that are accompanied by metric Type II radio bursts from those of comparable size that are not. The leading candidates for this special condition are: (1) an unusually low Alfvén speed in the flaring region; and (2) fast material motion. We present evidence based on SMM and GOES X-ray data and Solwind coronagraph data that argues against the first of these hypotheses and supports the second. Type II bursts linked to flares within 30° of the solar limb are well associated (64%; 49/76) with fast (>400 km s^–1) coronal mass ejections (CMEs); for Type II flares within 15° of the limb, the association rate is 79% (30/38). An examination of the characteristics of 'non-CME' flares associated with Type IIs does not support the flare-initiated blast wave picture that has been proposed for these events and suggests instead that CMEs may have escaped detection. While the degree of Type II–CME association increases with flare size, there are notable cases of small Type II flares whose outstanding attribute is a fast CME. Thus we argue that metric Type II bursts (as well as the Moreton waves and kilometric Type II bursts that may accompany them) have their root cause in fast coronal mass ejections.     

The Free Energy of NOAA Solar Active Region AR 11029

The NOAA active region (AR) 11029 was a small but highly active sunspot region which produced 73 GOES soft X-ray flares during its transit of the disk in late October 2009. The flares appear to show a departure from the well-known power law frequency-size distribution. Specifically, too few GOES C-class and no M-class flares were observed by comparison with a power law distribution (Wheatland, Astrophys. J. 710, 1324, 2010). This was conjectured to be due to the region having insufficient magnetic energy to power the missing large events. We construct nonlinear force-free extrapolations of the coronal magnetic field of AR 11029 using data taken on 24 October by the SOLIS Vector SpectroMagnetograph (SOLIS/VSM) and data taken on 27 October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP). Force-free modeling with photospheric magnetogram data encounters problems, because the magnetogram data are inconsistent with a force-free model. We employ a recently developed “self-consistency” procedure which addresses this problem and accommodates uncertainties in the boundary data (Wheatland and Régnier, Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of the self-consistent solution, which provides a model for the coronal magnetic field of the active region. The free energy of the region was found to be ≈?4×10²⁹?erg on 24 October and ≈?7×10³¹?erg on 27 October. An order of magnitude scaling between RHESSI non-thermal energy and GOES peak X-ray flux is established from a sample of flares from the literature and is used to estimate flare energies from the observed GOES peak X-ray flux. Based on the scaling, we conclude that the estimated free energy of AR 11029 on 27 October when the flaring rate peaked was sufficient to power M-class or X-class flares; hence, the modeling does not appear to support the hypothesis that the absence of large flares is due to the region having limited energy.     

Proton Enhancements and Their Relation to the X-Ray Flares During the Three Last Solar Cycles

Energetic proton measurements obtained from the GOES and IMP-8 satellites as well as from ground-based neutron monitors are compared with the GOES soft X-ray measurements of the associated solar flares for the period 1975–2003. The present study investigates a broad range of phenomenology relating proton events to flares (with some references to related interplanetary disturbances), including correlations of occurrence, intensities, durations and timing of both the particle event and the flare as well as the role of the heliographic location of the designated active region. 1144 proton events of > 10 MeV energy were selected from this 28-year period. Owing primarily to the low particle flux threshold employed more than half of this number was found to be reliably connected with an X-ray flare. The statistical analysis indicates that the probability and magnitude of the near-Earth proton enhancement depends critically on the flare's importance and its heliolongitude. In this study all flares of X-ray importance > X5 and located in the most propitious heliolongitude range, 15^∘W to 75^∘W, were succeeded by a detectable proton enhancement. It was also found that the heliolongitude frequently determines the character of the proton event time profile. In addition to intensity, duration and timing, proton events were found to be related to the other flare properties such as lower temperatures and longer loop lengths.     

Repeated Flaring from Loop–Loop Interaction

A series of solar flares was observed near the same location in NOAA active region 8996 on 18–20 May 2000. A detailed analysis of one of these flares is presented where the emitting structures in soft and hard X-rays, EUV, H, and radio at centimeter wavelengths are compared. Hard X-rays and radio emission were observed at two separate loop footpoints, while soft X-rays and EUV emission were observed mainly above the nearby positive polarity region. The flare was confined although the observed type III bursts at the time of the flare maximum indicate that some field lines were open to the corona. No flux emergence was evident but moving magnetic features were observed around the sunspot region and within the positive polarity (plage) region. We suggest that the flaring was due to loop–loop interactions over the positive polarity region, where accelerated electrons gained access to the two separate loop systems. The repeated radio flaring at the footpoint of one loop was visible because of the strong magnetic fields near the large sunspot region while at the footpoint of the other loop the electrons could precipitate and emit in hard X-rays. The simultaneous emission and fluctuations in radio and X-rays – in two different loop ends – further support the idea of a single acceleration site at the loop intersection.     

A statistical analysis of sunspot groups hosting M and X flares

In this paper we present the results obtained from a statistical analysis carried out by correlating sunspot‐group data collected at the INAF‐Catania Astrophysical Observatory and in the NOAA reports with data on Mand X flares obtained by the GOES‐8 satellite in the soft X‐ray range during the period January 1996–June 2003. These results allow us to provide a quantitative estimate of the parameters typical for an active region with very energetic flares. Moreover, the analysis of the flare productivity as a function of the group evolutionary stage indicates that the flaring probability of sunspots slightly increases with the spot age during the first passage across the solar disk, and that flaring groups are characterized by longer lifetimes than non‐flaring ones. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-Dependent Stochastic Modeling of Solar Active Region Energy

A time-dependent model for the energy of a flaring solar active region is presented based on an existing stochastic jump-transition model (Wheatland and Glukhov in Astrophys. J. 494, 858, 1998; Wheatland in Astrophys. J. 679, 1621, 2008 and Solar Phys. 255, 211, 2009). The magnetic free energy of an active region is assumed to vary in time due to a prescribed (deterministic) rate of energy input and prescribed (random) jumps downwards in energy due to flares. The existing model reproduces observed flare statistics, in particular flare frequency – size and waiting-time distributions, but modeling presented to date has considered only the time-independent choices of constant energy input and constant flare-transition rates with a power-law distribution in energy. These choices may be appropriate for a solar active region producing a constant mean rate of flares. However, many solar active regions exhibit time variation in their flare productivity, as exemplified by NOAA active region (AR) 11029, observed during October – November 2009 (Wheatland in Astrophys. J. 710, 1324, 2010). Time variation is incorporated into the jump-transition model for two cases: (1) a step change in the rates of flare transitions, and (2) a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The model exhibits flare-like event statistics. In each case the frequency – energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. The rollover is not observed if the mean free energy of the system is sufficiently large. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case 1 are presented which confirm the estimate for the relaxation time and the expected forms of the frequency – energy and waiting-time distributions. The simulation results provide a qualitative model for observed flare statistics in AR 11029.     

A Rate-Independent Test for Solar Flare Sympathy

Solar flare sympathy is the triggering of a flare in one active region by a flare in another. Statistical tests for flare sympathy have returned varying results. However, existing tests have relied on flaring rates in active regions being constant in time, or else have attempted to model the rate variation, which is a difficult task. A simple test is described which is independent of flaring rates. The test generalizes the approach of L. Fritzová-Švestkova, R.C. Chase, and Z. Švestka [Solar Phys. 48, 275, 1976], and examines the distribution of flare coincidences in pairs of active regions as a function of coincidence interval τ. The test is applied to available soft X-ray and Hα flare event listings. The soft X-ray events exhibit a deficit of flare coincidences for τ≤;20 min, which is most likely due to an event-selection effect whereby the increased soft X-ray emission due to one flare prevents a second flare being identified. The Hα events show an excess of flare coincidences for τ≤; 10 min, suggesting flare sympathy. The number of Hα event pairs occurring within 10 min of one another is higher than that expected on the basis of random coincidence by a fraction 0.12± 0.02. Nearby active regions (spatial separation <50˚) show a greater excess of coincidences for τ≤; 10 min than do active regions which are far apart (spatial separation ≥50˚). However, the active regions which are far apart still show some evidence for an excess of coincidences at very short coincidence intervals (τ≤; 2 min), which appears to exclude the possibility of a coronal disturbance propagating from one region to another.     

A search for hard X-ray microflares near solar minimum

Near solar maximum, hard X-ray microflares with peak 20 keV fluxes of 10^–2 (cm² s keV)^–1, more than ten times smaller than for typical flares and subflares, can occur at the rate of about once every five minutes. We report here on a search for hard X-ray microflares made on a long duration balloon flight in February 1987 near solar minimum, at a time when no active regions were on the Sun. No microflares were observed over a total observing time of 16.5 hours spread over three days, implying a statistical upper limit to their rate of occurrence about a factor often lower than observed near solar maximum. Thus hard X-ray microflaring appears to be an active region phenomenon, and apparently not associated with flaring of soft X-ray bright points.     

The Coronal Mass Ejection Waiting-Time Distribution

The distribution of times t between coronal mass ejections (CMEs) in the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for the years 1996–2001 is examined. The distribution exhibits a power-law tail (t) with an index –2.36±0.11 for large waiting times (t>10 hours). The power-law index of the waiting-time distribution varies with the solar cycle: for the years 1996–1998 (a period of low activity), the power-law index is –1.86±0.14, and for the years 1999–2001 (a period of higher activity), the index is –2.98±0.20. The observed CME waiting-time distribution, and its variation with the cycle, may be understood in terms of CMEs occurring as a time-dependent Poisson process. The CME waiting-time distribution is compared with that for greater than C1 class solar flares in the Geostationary Operational Environmental Satellite (GOES) catalog for the same years. The flare and CME waiting-time distributions exhibit power-law tails with very similar indices and time variation.