Statistical study of short quiescent times between flares

The study of the statistical distribution of short quiescent times (≤ 30 minutes) between solar flares has been investigated on a 1D MHD model. A power law behaviour is found which indicates the existence of sympathetic flaring. This prediction is supported by recent observations. Solar flares are the most violent phenomena observed in the solar system. It is believed that they play a fundamental role in maintaining a “hot” corona. Statistical analyses of observational data (Dennis, 1985; Crosby et al., 1993; Pearce et al., 1993), in terms of probability distribution functions (pdfs), revealed the scale-invariance property of solar flares: 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 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 physical ingredients, like the magnetic field in the case of flares, with simple rules they are able to reproduce well the statistical properties observed. The limitation of SOC models in the predictability of flares statistics was however recently discussed by Boffetta et al. (1999). The authors have studied the pdf of long quiescent times (also called waiting times), τ (for τ ≥ 6 hours), defined as the time intervals between two successive bursts. This observational analysis, based on 20 years of data obtained from the GOES sensors shows clearly a power law behaviour with an index ατ ≈ 2.4. This kind of behaviour is an indication of the existence of sympathetic flaring (i.e. the triggering of one flare by another) on long time-scales. It corroborates what we already knew for short quiescent times (Pearce et al., 1993; Wheatland et al., 1998). Then Boffetta et al. (1999) concluded that this result was in contradiction with SOC models of solar flares, where the system is driven at a constant rate (Lu and Hamilton, 1991), and thus for which events occur randomly in time as a Poisson process. Note that there are many SOC models in the literature like nonconservative models (Christensen and Olami, 1992) which are able to produce power laws for the distribution of quiescent times. Therefore the distinction discussed above between SOC and turbulence is not so obvious (although it is for many other aspects!). SolarPhys3.tex; 1/02/2008; 13:25; p.1