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.     

High abnormal rotation rates of sunspots and flare productivity

Solar activity, such as flares and CMEs, affect the interplanetary medium, and Earth’s atmosphere. Therefore, to understand the Space Weather, we need to understand the mechanisms of solar activity. Towards this end, we use 1135 events of solar H_α flares and the positional data of sunspots from the archive of Solar Geophysical Data (SGD) for the period January–April, 2000 and compute the abnormal rotation rates that lead to high flare productivity. We report that the occurrence of 5 or more flares in a day in association with a given sunspot group can be defined as high flare productivity and the sunspots that have an abnormal rotation rates of ～4–10 deg day^?1 trigger high flare productivity. Further, in order to compare the flare productivity expressed as the strength of the flux emitted, especially the soft X-ray (SXR) flares in the frequency range of 1–8 Å, we compute the flare index of SXR flares and find that 8 out of 28 active regions used in this study satisfy the requirement for being flare productive. This enables us to conclude that the high rotation rates of sunspots are an important mechanism to understand the flare productivity, especially numerical flare productivity that includes flares of all class.     

Longitudinal distribution of PCA sources on the sun

For 181 PCA's recorded during the years 1956–1969 the association with flares is studied. Both the number of events which cannot be associated with any flare on the visible hemisphere, as well as the longitude distribution of identified proton flares, lead to the conclusion that 25–30% of PCA's are caused by flares behind the western solar limb. PCA's of this kind are mostly small. During the investigated years no PCA > 13 dB and possibly no PCA > 8.5 dB were caused by flares behind the limb, while hardly 60% of PCA's < l dB had their origin on the visible hemisphere. While the sources of GLE's and of PCA's in general, are centered around 50°W which corresponds to the average curvature of the magnetic field lines in interplanetary space, the strongest PCA's (> 8.5 dB) show an anomalous longitude distribution centered around ∼ 20°W. It is suggested that this anomaly may be a consequence of the fact that in strong PCA events the kinetic energy density of protons below 100 MeV becomes comparable to the magnetic energy density in space, thus leading to a ‘straightening’ of the magnetic field lines.     

Vertical current and a 3B/X12 flare in a highly sheared active region (NOAA 6659) on June 9, 1991

NOAA active region 6659, during its June 1991 transit across the solar disk, showed highly sheared vector magnetic field structures and produced numerous powerful flares, including five white-light flares. Photospheric vector magnetograms of this active region were obtained at the Huairou Solar Observing Station of the Beijing Astronomical Observatory. After the resolution of the 180° ambiguity of the transverse magnetic field and transformation of off-center vector magnetograms to the heliographic plane, we have determined the photospheric vertical current density and discussed the relationship with powerful flares. The following results were obtained: (a) The powerful 3B/X12 flare on June 9, 1991 was triggered by the interaction between the large-scale electric current system and magnetic flux of opposite polarity. (b) The kernels of the powerful Hβ flare (sites of the white-light flare) were close to the peaks of the vertical electric current density. (c) Some small-scale structures of the vertical current relative to the magnetic islands of opposite polarity have not been found. This probably implies that the electric current is not always parallel to the magnetic field in solar active regions.     

Solar circumstances at the time of the cosmic ray increase on January 28, 1967

Solar circumstances have been evaluated for January 28, 1967, the date of an observed ground level enhancement of cosmic rays which was not preceded by observation of a suitably great Hα flare. On the visible solar hemisphere, a bright subflare at S23° E19° occurred in appropriate time association with the cosmic ray event, and was accompanied by weak X-ray enhancement and radio frequency emission. If this flare, alone, or in combination with other minor flares observed on the visible hemisphere on January 28 was the source of the energetic cosmic rays recorded on that date, then current thinking regarding the characteristics of cosmic ray flares must be modified. An initial study of probable circumstances on the invisible hemisphere did not lead to the immediate recognition of amajor center of activity as the probable source of a cosmic ray flare. Further evaluation of all centers of activity on the invisible hemisphere identified one region, McMath Plage No. 8687, 64° beyond the west limb, as the most plausible, possible site for the cosmic ray flare on January 28, 1967. The location of this region is in accord with the source-position deduced in Lockwood's analysis (1968) of the cosmic ray event. This center of activity could not have been more than 5 days old on January 28, 1967. The interval of major activity in the region was confined primarily to the invisible hemisphere. The occurrence of an ‘isolated’ major flare in the region on February 13, 1967 is discussed. The present study exemplifies the partial nature of solar observations which are limited to the visible hemisphere. The possible role of exceptional geomagnetic calm, 1963–1967, in permitting atypical cosmic ray enhancements, as on January 28, 1967, is mentioned.     

Forbush Decreases Associated with Western Solar Sources and Geomagnetic Storms: A Study on Precursors

As suggested in many studies the pre-increases or pre-decreases of the cosmic ray intensity (known as precursors), which usually precede a Forbush decrease, could serve as a useful tool for studying space weather effects. The events in this study were chosen based on two criteria. Firstly, the heliolongitude of the solar flare associated with each cosmic ray intensity decrease was in the 50°?–70°W sector and, secondly, the values of the geomagnetic activity index, Kp _max, were ≥?5. Twenty five events were selected from 1967 to 2006. We have used data on solar flares, solar wind speed, geomagnetic indices (Kp and Dst), and interplanetary magnetic field in our detailed analysis. The asymptotic longitudinal cosmic ray distribution diagrams were plotted using the “Ring of Stations” method for all the events. The results reveal clear signs of precursors in 60 % of selected events.     

The relationship between solar flares and solar sector boundaries

A superposed epoch analysis of 1964–1970 solar flares shows a marked increase in flare occurrence within a day (13° of longitude) of (- +) solar sector boundaries as well as a local minimum in flare occurrence near (+ -)sector boundaries. This preference for (- +) boundaries is more noticeable for northern hemisphere flares, where these polarities match the Hale polarity law, but is not reversed in the south. Plage regions do not show such a preference.     

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.     

X-ray observations of recurrence of eruptive flares and active regions

In a study of soft X-ray coronal images obtained with the Yohkoh spacecraft, two eruptive flares with remarkably similar X-ray structures were noted – most remarkably because the flares occurred at the same solar location (approximately 10 deg north latitude on the east limb) yet separated in time by three solar rotations. Between the times of the eruptions, the active region responsible for the first flare disappeared from Yohkoh images. An extremely similar X-ray active region replaced it by the third solar rotation. The recurring X-ray active region appearance and recurring flare activity after 86 days suggest that persistent subsurface flux emergence patterns might be responsible, and support previous arguments that active longitudes exist.     

North–south asymmetry of different solar activity features during solar cycle 23

A study on north–south (N–S) asymmetry of different solar activity features (DSAF) such as solar proton events, solar active prominences [total, low (?40°) and high (?50°) latitudes], Hα flare indices, soft X-ray flares, monthly mean sunspot areas and monthly mean sunspot numbers carried out from May 1996 to October 2008. Study shows a southern dominance of DSAF during this period. During the rising phase of the cycle 23 the number of DSAF approximately equals on both, the northern and the southern hemispheres. But these activities tend to shift from northern to southern hemisphere during the period 1998–1999. The statistical significance of the asymmetry time series using a χ²-test of goodness of fit indicates that in most of the cases the asymmetry is highly significant, meaning thereby that the asymmetry is a real feature in the N–S distribution of DSAF.     

Long-period pulsations of the Earth's magnetic field with periods more than 20 minutes before proton flares on the sun

Long-period (more than 20 min) quasi-periodic pulsations (QPP) occurring in the Earth's magnetic field (EMF) before the proton flare are studied by the method of spectral correlation analysis of geomagnetic field H-component. The corresponding data have been obtained at six stations located from 12°41'E up to 180° 52'E and from 52°04'N up to 68°52'N.QPP space-time distribution is shown to be correlated with that of the Earth's ionosphere current systems. The results obtained indicate that QPP of the EMF are influenced by QPP of the solar X-ray and ultraviolet radiation modulated by oscillation processes in the active solar region.     

High energetic solar proton flares on the declining phase of solar cycle 22

The year 1991 is a part of the declining phase of the solar cycle 22, during which high energetic flares have been produced by active regions NOAA/USAF 6659 in June. The associated solar proton events have affected the Earth environment and their proton fluxes have been measured by GOES space craft. The evaluation of solar activity during the first half of June 1991, have been carried out by applying a method for high energetic solar flares prediction on the flares of June 1991. The method depends on cumulative summation curves according to observed H-alpha flares, X-ray bursts, in the active region 6659 during one rotation when the energetic solar flares of June 1991 have occurred. It has been found that the steep trend of increased activity sets on several tens of hours prior to the occurrence of the energetic flare, which can be used, together with other methods, for forecasts of major flares. All the used data at the present work are received from NOAA, Boulder, Colorado, USA.     

A solar super‐flare as cause for the 14C variation in AD 774/5?

We present further considerations regarding the strong ¹⁴C variation in AD 774/5. For its cause, either a solar super‐flare or a short gamma‐ray burst were suggested. We show that all kinds of stellar or neutron star flares would be too weak for the observed energy input at Earth in AD 774/5. Even though Maehara et al. (2012) present two super‐flares with ∼10³⁵ erg of presumably solar‐type stars, we would like to caution: These two stars are poorly studied and may well be close binaries, and/or having a M‐type dwarf companion, and/or may be much younger and/or much more magnetic than the Sun – in any such case, they might not be true solar analog stars. From the frequency of large stellar flares averaged over all stellar activity phases (maybe obtained only during grand activity maxima), one can derive (a limit of) the probability for a large solar flare at a random time of normal activity: We find the probability for one flare within 3000 years to be possibly as low as 0.3 to 0.008 considering the full 1σ error range. Given the energy estimate in Miyake et al. (2012) for the AD 774/5 event, it would need to be ∼2000 stronger than the Carrington event as solar super‐flare. If the AD 774/5 event as solar flare would be beamed (to an angle of only ∼24°), 100 times lower energy would be needed. A new AD 774/5 energy estimate by Usoskin et al. (2013) with a different carbon cycle model, yielding 4 ot 6 time lower ¹⁴C production, predicts 4–6 times less energy. If both reductions are applied, the AD 774/5 event would need to be only ∼4 times stronger than the Carrington event in 1859 (if both had similar spectra). However, neither ¹⁴C nor ¹⁰Be peaks were found around AD 1859. Hence, the AD 774/5 event (as solar flare) either was not beamed that strongly, and/or it would have been much more than 4‐6 times stronger than Carrington, and/or the lower energy estimate (Usoskin et al. 2013) is not correct, and/or such solar flares cannot form (enough) ¹⁴C and ¹⁰Be. The 1956 solar energetic particle event was followed by a small decrease in directly observed cosmic rays. We conclude that large solar super‐flares remain very unlikely as the cause for the ¹⁴C increase in AD 774/5. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Evolution of the Net Twist Current and the Net Shear Current in Active Region NOAA 10930

The electric current exists because of the non-potential magnetic field in solar active regions. We present the evolution of net current in the solar active region NOAA 10930 as the sum of shear current and twist current by using 27 high-resolution vector magnetograms obtained with Hinode/SOT-SP during 9?–?15 December 2006. This active region was highly eruptive and produced a large number of flares ranging from B to X class. We derived local distribution of shear and twist current densities in this active region and studied the evolution of net shear current (NSC) and net twist current (NTC) in the N-polarity and S-polarity regions separately. We found the following: i) The twist current density was dominant in the umbrae. ii) The footpoint of the emerging flux rope showed a dominant twist current. iii) The shear current density and twist current density appeared in alternate bands around the umbrae. iv) On the scale of the active region, NTC was always larger than NSC. v) Both NTC and NSC decreased after the onset of an X3.4 class flare that occurred on 13 December 2006.     

The characteristics of the coronal mass ejections preceding the associated X-ray and γ-ray burst solar flares

In this study, investigated 14,786 coronal mass ejection (CME) events and 5092 Gamma-ray Burst Monitor (GBM) solar flare events (called γ-ray burst solar flare) recorded during 2008–2017, by using temporal and spatial conditions criteria, we found 845 (about 16%) CME events associated with γ-ray burst solar flare events only (hereafter, CME–γ-preflare). All the 845 events are associated with solar flares that are detected in both GBM and RHESSI simultaneously. Investigating the characteristics of these events, we found that the best time interval is 0–2 h before the flare's start time. The mean time interval for these CME–γ-preflare associated events is 61 min, with the flare's duration mean value of 12 min, which is greater than non-associated γ-ray solar flare's duration. CME width of CME-γ-preflare associated events 64° is slightly wider and slightly faster (remain lower than solar wind's speed) than non-associated CME 53°.     

Magnetic field of the solar wind

Relationship between the geoefficiency of the solar flares as well as of the active regions passing the central meridian of the Sun and the configuration of the large scale solar magnetic field is studied.It is shown that if the tangential component of the large scale magnetic field at the active region or at the flare region is directed southwards, that region and that flare produce geomagnetic storm. In case when the tangential magnetic field is directed northward, the active region and the flares occurring at that region do not cause any geomagnetic disturbance.An index of the geoefficiency of the solar flares and of the active regions is proposed.     

The Association of Solar Flares with Coronal Mass Ejections During the Extended Solar Minimum

We study the association of solar flares with coronal mass ejections (CMEs) during the deep, extended solar minimum of 2007?–?2009, using extreme-ultraviolet (EUV) and white-light (coronagraph) images from the Solar Terrestrial Relations Observatory (STEREO). Although all of the fast (v>900 km?s^?1), wide (θ>100^°) CMEs are associated with a flare that is at least identified in GOES soft X-ray light curves, a majority of flares with relatively high X-ray intensity for the deep solar minimum (e.g. ?1×10^?6 W?m^?2 or C1) are not associated with CMEs. Intense flares tend to occur in active regions with a strong and complex photospheric magnetic field, but the active regions that produce CME-associated flares tend to be small, including those that have no sunspots and therefore no NOAA active-region numbers. Other factors on scales similar to and larger than active regions seem to exist that contribute to the association of flares with CMEs. We find the possible low coronal signatures of CMEs, namely eruptions, dimmings, EUV waves, and Type III bursts, in 91 %, 74 %, 57 %, and 74 %, respectively, of the 35 flares that we associate with CMEs. None of these observables can fully replace direct observations of CMEs by coronagraphs.     

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)     

How Does Large Flaring Activity from the Same Active Region Produce Oppositely Directed Magnetic Clouds?

We describe the interplanetary coronal mass ejections (ICMEs) that occurred as a result of a series of solar flares and eruptions from 4 to 8 November 2004. Two ICMEs/magnetic clouds occurring from these events had opposite magnetic orientations. This was despite the fact that the major flares related to these events occurred within the same active region that maintained the same magnetic configuration. The solar events include a wide array of activities: flares, trans-equatorial coronal loop disappearance and reformation, trans-equatorial filament eruption, and coronal hole interaction. The first major ICME/magnetic cloud was predominantly related to the active region 10696 eruption. The second major ICME/magnetic cloud was found to be consistent with the magnetic orientation of an erupting trans-equatorial filament or else a rotation of 160° of a flux rope in the active region. We discuss these possibilities and emphasize the importance of understanding the magnetic evolution of the solar source region before we can begin to predict geoeffective events with any accuracy.     

Gamma-ray emission from solar flares of January 2005 observed by the AVS-F apparatus onboard the CORONAS-F satellite

Six solar flares were detected by the AVS-F apparatus onboard the CORONAS-F satellite in January 2005. We discuss the temporal profiles and energy spectra of the solar flares of January 20, 17, and 15, 2005 (class X7.1, X3.8, and X2.6, respectively) on the AVS-F data. The active region NOAA 10720 was the source of these flares. The spectra of the flares of January 17 and 20, 2005 contain nuclear lines, a positron line, and a line due to neutron capture line, while only the positron and neutron capture lines can be identified in the spectrum of the flare of January 15, 2005. The spectral features corresponding to these lines were observed during the whole duration of the flares. Analysis of the temporal profile of the flare of January 20, 2005 with a 1-ms temporal resolution in the energy range 0.1–20 MeV reveals the presence of a thin structure (at the 99% confidence level) with typical timescales of 7 to 35 ms.