Waiting Times of Solar Hard X-Ray Flares

From RHESSI Wiki

Nugget
Number:	123
1st Author:	Markus Aschwanden
2nd Author:	Jim McTiernan
Published:	15 March 2010
Next Nugget:	TBD
Previous Nugget:	Narrowband radio signal correlated with early hard X-ray flux during a microflare
List all

Contents 1 Introduction 2 Waiting times for solar flares 3 Conclusions 4 References 5 Biographical note

Introduction

You might drive a car in a foreign city and have to stop at many red traffic lights (e.g., Figure 1). From the statistics of waiting times you probably can quickly figure out which signals operate independently and which ones operate the smart way with inductive-loop traffic detectors in a so-called demand-actuated mode. Thus, the statistics of waiting times bears crucial information how a system works, either having independent elements that act randomly, or consisting of elements with long-range connections that enable coupling and synchronization. In geophysics, aftershocks have been found to exhibit different waiting time statistics (Omori’s law) than the main shocks of earthquakes. In magnetospheric physics, waiting time statistics is used to identify Poisson random processes, self-organized criticality, intermittent turbulence, finite system size effects, or clusterization, such as in auroral emission, the auroral electron jet (AE) index, or in substorms at the Earth’s magnetotail. Waiting time statistics is studied intensely in solar physics, where most flares are found to be produced by a Poissonian random process, but there are also so-called sympathetic flares that have a causal connection or trigger each other Waiting time statistics of solar flares was studied in hard X-rays in soft X-rays for coronal mass ejections (CMEs) for solar radio bursts, and for the solar wind. In astrophysics, waiting time distributions have been studied for flare stars as well as for black-hole candidates, such as Cygnus X-1.

Waiting times for solar flares

In this study (Aschwanden and McTiernan 2010) we focus on waiting time distributions of solar flares detected in hard X-rays. The most comprehensive sampling of solar flare waiting times was gathered in soft X-rays so far, using a 25-year catalog of GOES flares (Wheatland 2000a; Boffetta et al. 1999; Lepreti et al. 2001), but three different interpretations were proposed, using the very same data: (i) a not-stationary (time-dependent) Poisson process (Wheatland 2000a), (ii) a shell-model of MHD turbulence (Boffetta et al. 1999), or (iii) a L´evy flight model of self-similar processes with some memory (Lepreti et al. 2001). All three interpretations can produce a powerlaw-like distribution of waiting times. On the other side, self-organized criticality models predict a Poissonian random process, which has an exponential distribution of waiting times for a stationary (constant) flare rate, but can produce powerlaw-like waiting time distributions with a slope of p < ! 3 for nonstationary variations of the flare rate (Wheatland and Litvinenko 2002). Therefore, the finding of a powerlaw-like distribution of waiting times of solar flares has ambiguous interpretations. The situation in solar flare hard X-rays is very discordant, from powerlaws, near-exponential, to double-hump distribution with an overabundance of short waiting times. In this study we analyze flare catalogs from HXRBS/SMM, BATSE/CGRO and RHESSI and are able to model all observed hard X-ray waiting time distributions with a unified model in terms of a nonstationary Poisson process in the limit of high intermittency. We resolve also the discrepancy between exponential and powerlaw-like waiting time distributions, in terms of selected fitting ranges. It can be shown analytically that nonstationary Poisson processes with slowly-varying flare rates produce a waiting time distribution that has a powerlaw tail with a slope of p < ! 3, while highly intermittently fluctuating flare rates produce a powerlaw tail with a slope of p ! 2). The observations from HXRBS/SMM, BATSE/CGRO, and RHESSI are closer to the latter case and can all be fitted with the same waiting time distribution (Fig. 1). Thus the waiting time distribution indicates a highly intermittent flare productivity in short clusters with high flare rates, separated by quiescent intervals with very low flare rates. A similar intermittent behavior is obseved in earthquakes and in X-ray pulses from accretion disks.

Conclusions

References

[1] Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays

[2] Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

[3] Solar Flare Waiting Time Distribution: Varying-Rate Poisson or Lévy Function?

Biographical note

Wheatland, M.S. 2000a, Astrophys. J. 536, L109.