A statistical study of quiescent times between flares

The study of the statistical distribution of the quiescent times between solar flares has been investigated on a 1D MHD model. The result shows a power law behaviour in agreement with the observations. This strong time correlation of flares is different from the SOC prediction unless overlap of events is allowed. Many observations e.g. Skylab, SMM, Yohkoh, GRANAT, SoHO or TRACE have shown the magnetic nature of the solar corona which is currently seen as a dynamical medium with a strong activity. This activity is characterised for instance by a spatio-temporal intermittent brightness in the X-ray domain (for a review see Priest, 1982). In its most violent form, the coronal activity consists in the flaring of magnetic loops and in the energy release of 10 erg to 10 erg over a range of time from seconds to hours. Although it is believed that the nature of solar flares is strongly correlated to the magnetic field (Parker, 1994), the precise mechanism by which the flares are generated is not yet fully understood, neither their role in maintaining a “hot” corona. The physical process that underlies the flaring is the impulsive dissipation of the magnetic energy by the formation of current sheets triggered by instabilities. The magnetic energy is previously stored in a coronal loop via the random shuffling of its magnetic foot-points generated by the sub-photospheric convective cells. Statistical analyses of observational data (Dennis, 1985; Crosby et al., 1993; Pearce et al., 1993), in terms of probability distribution functions (pdfs), have revealed the scale-invariance property of solar flares. Indeed, the pdfs N(x) of different quantities x, such as the peak luminosity (P), the total energy (E) or the duration (D) of flare events, follow widely extended power laws, viz. N(x) ∼ xx (x = P, E or D) with the indices αP ≈ 1.7, αE ≈ 1.5 and αD ≈ 2.2. This apparent absence of a characteristic length scale has allowed us to see solar flares in a new way, like a Self-Organised Critical (SOC) system (Lu and Hamilton, 1991; Vlahos et al., 1995). Although SOC models do not make a direct connection with the physical ingredients like the magnetic field in the case of flares, with simple rules they are able to reproduce well the statistical properties of flares. The limitation of SOC models in the predictability of flares statistics was however recently discussed (Boffetta et al., 1999) by emphasising a new type of statistics, that corresponding to the quiescent times, i.e. the time intervals between two successive bursts. This observational analysis, based on 20 years of SolarPhys.tex; 30/05/2008; 2:03; p.1