Flare Frequency Distribution Research Articles

X-ray flaring from the young stars in Cygnus OB2

Aims. We characterize individual and ensemble properties of X-ray flares from stars in the Cygnus OB2 and ONC star-forming regions. Methods. We analyzed X-ray lightcurves of 1003 Cygnus OB2 sources observed with Chandra for 100 ks and of 1616 ONC sources detected in the “Chandra Orion Ultra-deep Project” 850 ks observation. We employed a binning-free maximum likelihood method to segment the light-curves into intervals of constants signal and identified flares on the basis of both the amplitude and the timederivative of the source luminosity. We then derived and compared the flare frequency and energy distribution of Cygnus OB2 and ONC sources. The effect of the length of the observation on these results was investigated by repeating the statistical analysis on five 100 ks-long segments extracted from the ONC data. Results. We detected 147 and 954 flares from the Cygnus OB2 and ONC sources, respectively. The flares in Cygnus OB2 have decay times ranging from <0.5 to about 10 h. The flare energy distributions of all considered flare samples are described at high energies well by a power law with index α = −(2.1 ± 0.1). At low energies, the distributions flatten, probably because of detection incompleteness. We derived average flare frequencies as a function of flare energy. The flare frequency is seen to depend on the source’s intrinsic X-ray luminosity, but its determination is affected by the length of the observation. The slope of the high-energy tail of the energy distribution is, however, affected little. A comparison of Cygnus OB2 and ONC sources, accounting for observational biases, shows that the two populations, known to have similar X-ray emission levels, have very similar flare activity. Conclusions. Studies of flare activity are only comparable if performed consistently and taking the observation length into account. Flaring activity does not vary appreciably between the age of the ONC (∼1 Myr) and that of Cygnus OB2 (∼2 Myr). The slope of the distribution of flare energies is consistent with the micro-flare explanation of the coronal heating.

Different Power-Law Indices in the Frequency Distributions of Flares with and without Coronal Mass Ejections

We investigated the frequency distributions of flares with and without coronal mass ejections (CMEs) as a function of flare parameters (peak flux, fluence, and duration of soft X-ray flares). We used CMEs observed by the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO) mission and soft X-ray flares (C3.2 and above) observed by the GOES satellites during 1996 to 2005. We found that the distributions obey a power-law of the form: dN/dX~X^-alpha, where X is a flare parameter and dN is the number of events recorded within the interval [X, X+dX]. For the flares with (without) CMEs, we obtained the power-law index alpha=1.98+-0.05 (alpha=2.52+-0.03) for the peak flux, alpha=1.79+-0.05 (alpha=2.47+-0.11) for the fluence, and alpha=2.49+-0.11 (alpha=3.22+-0.15) for the duration. The power-law indices for flares without CMEs are steeper than those for flares with CMEs. The larger power-law index for flares without CMEs supports the possibility that nanoflares contribute to coronal heating.

Latitudinal Distribution of Solar Flares and Their Association with Coronal Mass Ejections

Major solar flare events have been utilised to study the latitudinal frequency distribution of solar flares in northern and southern hemispheres for the period of 1986 to 2003. A statistical analysis has been performed to obtain the correlation between Coronal Mass Ejections (CMEs) and Forbush decrease (Fds) of cosmic ray intensity. Almost the same flares distribution in both hemispheres is found in association with CMEs. In a further analysis, it is noted that a larger number of CME-associated solar flares located in the northern hemisphere are found to be more effective in producing Forbush decreases.

Temporal aspects and frequency distributions of solar soft X-ray flares

A statistical analysis of almost 50 000 soft X-ray (SXR) flares observed by GOES during the period 1976–2000 is presented. On the basis of this extensive data set, statistics on temporal properties of soft X-ray flares, such as duration, rise and decay times with regard to the SXR flare classes is presented. Correlations among distinct flare parameters, i.e. SXR peak flux, fluence and characteristic times, and frequency distributions of flare occurrence as function of the peak flux, the fluence and the duration are derived. We discuss the results of the analysis with respect to statistical flare models, the idea of coronal heating by nanoflares, and elaborate on implications of the obtained results on the Neupert effect in solar flares.

Flare Frequency Distributions Based on a Master Equation

The Rosner & Vaiana model for flares is generalized to allow for flares that do not deplete all free energy from the system, a step that overcomes a number of objections to the original model. We obtain a probability balance equation, or master equation, describing the free energy E of an active region subject to a prescribed growth rate, Ė, and a prescribed distribution, α(E), of stochastic decay events. We argue that the solution appropriate to flares involves an energy-independent growth rate and a power-law form for α(E), which may be the result of an underlying avalanche process. The resulting model produces power-law flare frequency distributions below a high-energy rollover corresponding to the largest energy the system is likely to attain, which is set by the balance between the rate of growth and the rate of stochastic decay. There is a close correspondence between the resulting model and the avalanche model for flares.

Evidence for a Cutoff in the Frequency Distribution of Solar Flares from Small Active Regions

In this paper, we present evidence that active regions with small sunspot areas have an upper limit to the energy of the flares they produce. This result is consistent with predictions of the avalanche model of Lu et al.

A new model for the distribution of flare energies

A new model is presented for the distribution of solar (and stellar) flare energies. Flares are assumed to result from energy release in multiple reconnecting current sheets (RCSs) in the solar corona. The model takes into account both the dynamical evolution of separate RCSs and their interaction by virtue of coalescence. Thus an attempt is made to generalize previously suggested avalanche and RCS models for the flare frequency distribution. The number of RCSs is not specified and the strength of their interaction is governed by a coalescence parameter. Under quite general assumptions, the resulting distribution can be approximated by a power law with the slope 3/2 < α < 7/4, as required by numerous observations. A softer distribution of numerous ‘nanoflares’, responsible for the coronal heating, is also possible under suitable choice of parameters.

An explanation for the flare frequency - energy dependence

The reconnecting current sheet model for energy accumulation and release during solar flares results in the flare frequency distribution that is a power-law function of total flare energy, with the index 7/4 for sufficiently large energies. The distribution is predicted to be much steeper in the low-energy region, implying the significance of microand nanoflares for coronal heating.

Solar flares and avalanches in driven dissipative systems

The contention of Lu and Hamilton (1991) that the energy release process in solar flares can be understood as avalanches of many small reconnection events is further developed. The dynamics of the complex magnetized plasma of solar active regions is modeled with a simple driven dissipative system, consisting of a vector field with local instabilities that cause rapid diffusion of the field. It is argued that the avalanches in this model are analogous to solar flares. The distributions of avalanches in this model are compared with the solar flare frequency distributions obtained from ISEE 3/ICE satellite observations. Quantitative agreement is found with the energy, peak luminosity, and duration distributions over four orders of magnitude in flare energy, from the largest flares down to the completeness limit of the observations. It is predicted that the power-law solar flare frequency distributions will be found to continue downward with the same logarithmic slopes to an energy of about 3 x 10 exp 25 ergs and duration of about 0.3 s, with deviations from power-law behavior below these values.