DO SOLAR FLARES EXHIBIT AN INTERVAL–SIZE RELATIONSHIP?

Some models for flare statistics predict or assume that there is a relationship between the times between flares and the energy of flares. This question is examined observationally using the WATCH solar X-ray burst catalogue. A rank correlation test applied to the data finds strong evidence for a correlation between the time since the last event, t _b, and the size (peak count rate) of an event, and for a correlation between the time to the next event, t _a, and the size of an event. A more sophisticated statistical test, taking into account a probable bias in event selection, does not support the hypothesis that event size depends on t _b or t _a.     

Distinctions between the characteristics of before and after DH CMEs associated flares

A detailed analysis of characteristics of coronal mass ejections and flares associated with deca-hectometer wavelength type-II radio bursts (DH-CMEs and DH-flares) observed in the period 1997–2008 is presented. A sample of 62 limb events is divided into two populations known as after-flare CMEs (AF-CMEs) and before-flare CMEs (BF-CMEs) based on the relative timing of the flare and CME onsets. On average, AF-CMEs (1589 km s⁻¹) have more speed than the BF-CMEs (1226 km s⁻¹) and the difference between mean values are highly significant (P∼2%). The average CME nose height at the time of type-II start is at larger distance for AF-CMEs than the BF-CMEs (4.89 and 3.84 R _o, respectively). We found a good anti-correlation for accelerating (R _a=−0.89) and decelerating (R _d=−0.78) AF-CMEs. In the case of decelerating BF-CMEs, the correlation seems to be similar to that for decelerating AF-CMEs (R _d=−0.83). The number of decelerating AF-CMEs is 51% only; where as, the number of decelerating BF-CMEs is 83%. The flares associated with BF-CMEs have shorter rise and decay times than flares related to AF-CMEs. We found statistically significant differences between the two sets of associated DH-type-II bursts characteristics: starting frequency (P∼4%), drift rate (P∼1%), and ending frequency (P∼6%). The delay time analysis of DH-type-II start and flare onset times shows that the time lags are longer in AF-CME events than in BF-CME events (P≪1%). From the above results, the AF-CMEs which are associated with DH-type-II bursts are found to be more energetic, associated with long duration flares and DH-type-IIs of lower ending frequencies.     

Kinematics and Flare Properties of Radio-Loud CMEs

A detailed analysis of the characteristics of coronal mass ejections (CMEs) and flares associated with decameter-hectometer wavelength type-II radio bursts (hereafter DH-type-II radio bursts, DH-CMEs or radio-loud CMEs) observed in the period 1997??C?2008 is presented. A sample of 61 limb events is divided into two populations based on the residual acceleration: accelerating CMEs (a _r>0) and decelerating CMEs (a _r<0). We found that average speed (residual acceleration) of all limb DH-CMEs (called radio-loud CMEs) is nearly three (two) times greater than the average speed of the general population CMEs (radio-quiet CMEs). While the initial acceleration (a _i) of the accelerating DH-CMEs is smaller than that of decelerating DH-CMEs (0.79 and 1.62 km?s^?2, respectively), the average speed and magnitude of residual acceleration of the accelerating and decelerating DH-CMEs are similar (??V _CME??: 1254 km?s^?1 and 1303 km?s^?1; ??a _r??: 0.026 km?s^?2 and 0.028 km?s^?2, respectively). The accelerating DH-CMEs attain their peak speed at larger heights than decelerating DH-CMEs. A good positive and negative linear correlation for accelerating and decelerating DH-CMEs (R _a=0.74 and R _d=?0.77, respectively) is found. The flares associated with accelerating DH-CME events have longer rise times and decay times than flares of decelerating DH-CME. The accelerating and decelerating DH-CMEs events associated with DH-type-II bursts have similar ending frequencies. The analysis of time lags between DH-type-II start and the flare onset shows that the delays are longer in accelerating DH-CMEs than decelerating DH-CMEs (P??7 %). However, the time lags between the DH-type-II start and the CMEs onset are similar.     

Energetic protons from the solar flare of March 24, 1966

Ten to 100 meV protons from the solar flare of March 24, 1966 were observed on the University of California scintillation counter on OGO-I. The short rise and decay times observed in the count rates of the 32 channels of pulse-height analysis show that scattering of the protons by the interplanetary field was much less important in this event than in previously observed proton flares. A diffusion theory in which D = M _r is found to be inadequate to account for the time behavior of the count rates of this event. Small fluctuations of the otherwise smooth decay phase may be due to flare protons reflected from the back of a shock front, which passed the earth on March 23.     

Statistical Characteristics on SEPs,Radio-Loud CMEs,Low Frequency Type II and Type III Radio Bursts Associated with Impulsive and Gradual Flares

We have statistically analyzed a set of 115 low frequency (Deca-Hectometer wavelengths range) type II and type III bursts associated with major Solar Energetic Particle (SEP: E_p?>?10 MeV) events and their solar causes such as solar flares and coronal mass ejections (CMEs) observed from 1997 to 2014. We classified them into two sets of events based on the duration of the associated solar flares:75 impulsive flares (duration <?60 min) and 40 gradual flares (duration >?60 min).On an average, the peak flux (integrated flux) of impulsive flares?×?2.9 (0.32 J m^?2) is stronger than that of gradual flares M6.8 (0.24 J m^?2). We found that impulsive flare-associated CMEs are highly decelerated with larger initial acceleration and they achieved their peak speed at lower heights (??27.66 m s^?2 and 14.23 R_o) than the gradual flare-associated CMEs (6.26 m s^?2 and 15.30 R_o), even though both sets of events have similar sky-plane speed (space speed) within LASCO field of view. The impulsive flare-associated SEP events (R_t?=?989.23 min: 2.86 days) are short lived and they quickly reach their peak intensity (shorter rise time) when compared with gradual flares associated events (R_t?=?1275.45 min: 3.34 days). We found a good correlation between the logarithmic peak intensity of all SEPs and properties of CMEs (space speed: cc?=?0.52, SE_cc?=?0.083), and solar flares (log integrated flux: cc?=?0.44, SE_cc?=?0.083). This particular result gives no clear cut distinction between flare-related and CME-related SEP events for this set of major SEP events. We derived the peak intensity, integrated intensity, duration and slope of these bursts from the radio dynamic spectra observed by Wind/WAVES. Most of the properties (peak intensity, integrated intensity and starting frequency) of DH type II bursts associated with impulsive and gradual flare events are found to be similar in magnitudes. Interestingly, we found that impulsive flare-associated DH type III bursts are longer, stronger and faster (31.30 min, 6.43 sfu and 22.49 MHz h^?1) than the gradual flare- associated DH type III bursts (25.08 min, 5.85 sfu and 17.84 MHz h^?1). In addition, we also found a significant correlation between the properties of SEPs and key parameters of DH type III bursts. This result shows a closer association of peak intensity of the SEPs with the properties of DH type III radio bursts than with the properties DH type II radio bursts, atleast for this set of 115 major SEP events.

     

Peak-Size Distributions of Proton Fluxes and Associated Soft X-Ray Flares

A database combining information about solar proton enhancements (SPEs) near the Earth and soft X-ray flares (GOES measurements) has been used for the study of different correlations through the period from 1975 to May 2006. The emphasis of this work is on the treatment of peak-size distributions of SXR flares and SPEs. The frequency of SXR flares and solar proton events (>10 and >100 MeV, respectively) for the past three solar cycles has been found to follow mainly a power-law distribution over three to five orders of magnitude of fluxes, which is physically correct beyond the “sensitivity” problem with the smallest peak values. The absence of significant spectral steepening in the domain of the highest peak values demonstrates that during the period considered, lasting 30 years, the limit of the highest flare’s energy release has not yet been achieved. The power-law exponents were found to be −2.19±0.04, −1.34±0.02, and −1.46±0.04, for the total SXR flare distribution and the total SPE distributions (for both E _P>10 MeV and E _P>100 MeV), respectively. For SPEs associated with flares located to the West of 20° W, the exponents are −1.22±0.05 (E _P>10 MeV) and −1.26±0.03 (E _P>100 MeV). The size distribution for corresponding flares follows a power law with a slope of −1.29±0.12. Thus, X-ray and proton fluxes produced in the same solar events have very similar distribution shapes. Moreover, the derived slopes are not incompatible with a linear dependence between X-ray flare power and proton fluxes near the Earth. A similar statistical relation is obtained independently from the direct comparison of the X-ray and proton fluxes. These all argue for a statistically significant relationship between X-ray and proton emissions.     

The State of Self-organized Criticality of the Sun during the Last Three Solar Cycles. II. Theoretical Model

The observed power-law distributions of solar-flare parameters can be interpreted in terms of a nonlinear dissipative system in a state of self-organized criticality (SOC). We present a universal analytical model of an SOC process that is governed by three conditions: i) a multiplicative or exponential growth phase, ii) a randomly interrupted termination of the growth phase, and iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential growth model, which also includes a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence-frequency distributions and the scatter of correlated parameters more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar-cycle modulations of the power-law slopes of flare-frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.     

Frequency dependence of solar flare occurrence rates—inferred from power-law distribution

Based on the frequency dependence of the power-law distribution of the peak fluxes in 486 radio bursts in 1–35 GHz observed by Nobeyama Radio Polarimeters (see Song et al. in Astrophys. J. 750:160, 2012), we have first suggested in this paper that the events with power-law behaviors may be emitted from the optically-thin regions, which can be considered as a good measure for the flare energy release. This result is supported by that both the power-law and optical-thin events gradually increase with radio frequencies, which are well fitted by a power-law function with similar indices of 0.48 and 0.80, respectively. Moreover, a flare occurrence rate is newly defined by the power-law event number in per unit frequency. Its values in lower frequencies are evidently larger than those in higher frequencies, which just imply that most flares are trigged in higher corona. Hence, the frequency variation of power-law event number may indicate different energy dissipation rates on different coronal heights.     

The distribution of solar flares for the time period 1967–1985

The distribution of monthly counts of grouped solar flares N _f has been studied for the time period 1967–1985 and they have been compared to other solar activity index R _z , F ₂₈₀₀, and F ₃₇₅₀ i.e. intensities of solar radio flux at 2800 MH _z and 3750 MH _z . Seasonal variations have been found in the monthly distribution of solar flares.We have also studied the variation of the correlation coefficient for every year between N _F and R _z for the time period 1967–1985. The distribution of monthly counts of grouped solar flares N _f has also been compared to the number at high velocity solar-wind streamers for the same period.     

Studies on metric–decimetric Type II bursts in relation to soft X-ray flares

The relationship between metric type II radio bursts and soft X-ray (SXR) flares is studied. Type II bursts are highly associated with SXR flares. The duration and drift rate of type II bursts are found to depend on the duration, asymmetry in duration (ratio of rise time to duration), as well as on the peak flux of SXR bursts. Important results obtained are: (i) the durations of type II bursts are linearly correlated with the durations of associated SXR bursts in case of long-lived events (duration >40 min), whereas in short-lived flares such a correlation is not found, (ii) the durations of type II bursts do not depend upon the SXR peak flux, (iii) more durable type II radio bursts are correlated with more symmetric SXR bursts, (iv) average drift rates of type II bursts are larger in the events associated with more powerful and more symmetric SXR bursts.     

Properties of elementary flare bursts

From a study of eight hard X-ray flares, all with durations of less than five minutes, it is found that these flares can be completely decomposed into short-lived bursts, called Elementary Flare Bursts (EFB). For each one flare the individual EFB's have approximatively the same Full Width at Half Maximum (FWHM); average values range between 4 s (± 1 s) and 24 s (± 5 s) for the different flares. Yet there are significant differences between the FWHM's for the individual EFB's of a flare. The EFB's are slightly asymmetric; rise time is approx. 0.9 of the decay time. Their half-widths decrease with increasing photon energy, proportional to E ^-0.69±0.05.     

Close binary systems among very low‐mass stars and brown dwarfs

Using Monte Carlo simulations and published radial velocity surveys we have constrained the frequency and separation (a ) distribution of very low‐mass star (VLM) and brown dwarf (BD) binary systems.We find that simple Gaussian extensions of the observed wide binary distribution, with a peak at 4AU and 0.6 < σ _{log(a /AU)} < 1.0, correctly reproduce the observed number of close binary systems, implying a close (a < 2.6 AU) binary frequency of 17–30% and overall frequency of 32–45%. N‐body models of the dynamical decay of unstable protostellar multiple systems are excluded with high confidence because they do not produce enough close binary VLMs/BDs. The large number of close binaries and high overall binary frequency are also completely inconsistent with published smoothed particle hydrodynamical modelling and argue against a dynamical origin for VLMs/BDs. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray Flares Observed from Six Young Stars Located in the Region of Star Clusters NGC 869 and IC 2602

We present, for the first time, an analysis of seven intense X-ray flares observed from six stars (LAV 796, LAV 1174, SHM2002 3734, 2MASS 02191082+5707324, V553 Car, V557 Car). These stars are located in the region of young open star clusters NGC 869 and IC 2602. These flares detected in the XMM-Newton data show a rapid rise (10–40 min) and a slow decay (20–90 min). The X-ray luminosities during the flares in the energy band 0.3–7.5 keV are in the range of 10^29.9 to 10^31.7 erg s^?1. The strongest flare was observed with the ratio ～13 for count rates at peak of the flare to the quiescent intensity. The maximum temperature during the flares has been found to be ～100 MK. The semi-loop lengths for the flaring loops are estimated to be of the order of 10¹⁰ cm. The physical parameters of the flaring structure, the peak density, pressure and minimum magnetic field required to confine the plasma have been derived and found to be consistent with flares from pre-main sequence stars in the Orion and the Taurus-Auriga-Perseus region.     

Characteristics of DH type II bursts, CMEs and flares with respect to the acceleration of CMEs

A detailed investigation on DH-type-II radio bursts recorded in Deca-Hectometer (hereinafter DH-type-II) wavelength range and their associated CMEs observed during the year 1997–2008 is presented. The sample of 212 DH-type-II associated with CMEs are classified into three populations: (i) Group I (43 events): DH-type-II associated CMEs are accelerating in the LASCO field view (a>15 m s⁻²); (ii) Group II (99 events): approximately constant velocity CMEs (−15<a<15 m s⁻²) and (iii) Group III (70 events): represents decelerating CMEs (a<−15 m s⁻²). Our study consists of three steps: (i) statistical properties of DH-type-II bursts of Group I, II and III events; (ii) analysis of time lags between onsets of flares and CMEs associated with DH-type-II bursts and (iii) statistical properties of flares and CMEs of Group I, II and III events. We found statistically significant differences between the properties of DH-type-II bursts of Group I, II and III events. The significance (P _a ) is found using the one-way ANOVA-test to examine the differences between means of groups. For example, there is significant difference in the duration (P _a =5%), ending frequency (P _a =4%) and bandwidth (P _a =4%). The accelerating and decelerating CMEs have more kinetic energy than the constant speed CMEs. There is a significant difference between the nose height of CMEs at the end time of DH-type-IIs (P _a ≪1%). From the time delay analysis, we found: (i) there is no significant difference in the delay (flare start—DH-type-II start and flare peak—DH-type-II start); (ii) small differences in the time delay between the CME onset and DH-type-II start, delay between the flare start and CME onset times. However, there are high significant differences in: flare duration (P _a =1%), flare rise time (P _a =0.5%), flare decay time (P _a =5%) and CMEs speed (P _a ≪1%) of Group I, II and III events. The general LASCO CMEs have lower width and speeds when compared to the DH CMEs. It seems there is a strong relation between the kinetic energy of CMEs and DH-type-II properties.     

Characteristics of electron and high-energy proton flares

High-energy proton (E _p > 55 MeV) and electron (E _e > 50 keV) events were observed by University of Iowa experiments on the satellites Explorer 33 and 35. The solar X-ray (2–12 Å) flares associated with the energetic proton events were found to have in general higher peak fluxes, considerably longer decay times (t) and smaller rise to decay time ratios (r) than the X-ray flares associated with the electron events. The most common decay times and rise to decay time ratios are: 80 t 100 min, 0.1 r 0.2 for the proton X-ray flares and t 20 min, 0.3 r 0.7 for the electron ones.     

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.     

On the power-law distributions of X-ray fluxes from solar flares observed with GOES

The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality(SOC).In this paper,we first show that,so long as the shape of the normalized light curve is not correlated with the peak flux,the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the powerlaw frequency distribution of the peak flux,which may partially explain why power-law distributions are ubiquitous in the Universe.We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different:the higher energy channel has a harder distribution than the lower energy channel,which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites.The temperature(T) distribution,on the other hand,approaches a power-law distribution with an index of 2 for high values of T.Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.     

Simultaneous UBVRI observations of the cataclysmic variable AE Aquarii: Temperatures and masses of fireballs

We report simultaneous multicolour observations in 5 bands (UBVRI) of the flickering variability of the cataclysmic variable AE Aqr. Our aim is to estimate the parameters (colours, temperature, size) of the fireballs that produce the optical flares. The observed rise times of the optical flares are in the interval 220‐440 s. We estimate the dereddened colours of the fireballs as (U ‐B)₀∼0.8‐1.4, (B ‐V)₀∼0.03‐0.24, and (V ‐I)₀∼0.26‐0.78. We find for the fireballs temperatures of 10000‐25000 K, masses of (7‐90)x10¹⁹ g, and sizes of (3‐7)x10⁹ cm (using a distance of d = 86 pc). These values refer to the peak of the flares observed in the UBVRI bands. The data are available upon request from the authors (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Satellite motion in a non-singular gravitational potential

We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second order. This series contains three terms, the first been the Newtonian potential and the other two, here R ₁ (first order term) and R ₂ (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the second-order disturbing term R ₂ on the perigee and the mean anomaly are 4″.307×10⁻⁹/a, and −2″.533×10⁻¹⁵/a, respectively. These effects are far too small and most likely cannot easily be observed with today’s technology. Numerical evaluation of the low and high frequency effects of the disturbing term R ₂ on low Earth orbiters like GRACE are very small and undetectable by current observational means.     

Astron observations of the Rapid Burster MXB 1730-335 and constraints on burster parameters from spectra of trailing bursts

We report on eight X-ray bursts detected by ASTRON from the Rapid Burster (RB) on 13 and 28 April and 16 August, 1983. Six of them (trailing bursts), with durations of 1.5–2 min, rise times of 5–10 s and intervals of 1–1.5 hours, exhibit spectral softening during the burst decay and may be related to the type I bursts. Two of the bursts (triangle bursts) observed on 28 April at interval of 28 min with much longer rise times (30–50 s) and longer durations (3 min), do not show distinct spectral softening. Persistent flux from RB on 16 August was estimated asF _p(2.0–2.4)×10^–9 erg cm^–2 s^–1. Spectral evolution of two trailing bursts was investigated by fitting their spectra in consecutive time intervals with the blackbody (BB), isothermal scattering photosphere (SP) and thermal bremsstrahlung (TB) models. Around the burst maxima the SP model fits the data best whereas in the burst tails the TB model is generally better. The BB model is worse than at least one of the two others. Interpretation of the burst spectra in terms of the BB radiation leads to improbably small neutron star mass and radius (M<0.86M ,R _NS<5 km) if the peak luminosity does not exceed the Eddington limit. Interpretation of the spectra around the burst maxima (3–15 s from the burst onset) in terms of an isothermal SP yields reasonable constraints onM,R _NS, and distanceD. For instance, for the hydrogen photosphere we obtainedM=(1.0–2.1)M R _NS=(7.1–16.4) km ifD=11 kpc. If one postulatesM=1.4M , thenD=(8.5–13) kpc for hydrogen photosphere; if, besides,D=11 kpc, thenR _NS=(8.1–13.3) km. It follows also from the SP-interpretation that the photosphere radius may increase up to 20–30 km in maxima of the trailing bursts when the luminosity becomes close to the Eddington luminosity.