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Solar Flare Occurrence Rate and Waiting Time Statistics

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Abstract

We use Renewal Theory for the estimation and interpretation of the flare rate from the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare catalogue. It is found that, in addition to the flare rate variability with the solar cycles, a much faster variation occurs. The fast variation on time scales of days and hours down to minute scale appears to be comparable with time intervals between two successive flares (waiting times). The detected fast non-stationarity of the flaring rate is discussed in the framework of the previously published stochastic models of the waiting time dynamics.

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Notes

  1. http://www.ngdc.noaa.gov/stp/solar/solarflares.html .

  2. We use the mathematically strict definition of the density as the differential quantity with respect to the distribution, which is often used in a misleading way instead.

  3. This time interval is also called the age of a device, i.e., its lifetime without any failure.

  4. An abstract picture is considered here: a broken device replacement (repair) is thought to be a very instant, in such a way that the time required for the repair is zero. A continuous operation is meant, and provided, for instance, by multiple hardware availability.

  5. This function is also known as the hazard function, hazard rate or failure rate.

  6. The smoothing is the same as for the graphs in Figure 7.

  7. Here by “event” we mean the event as defined in Probability Theory.

  8. per unit time (minute).

  9. Recall that memoryless stochastic processes are those with h=const, i.e. the probability of an event is independent of neither the waiting time elapsed before it occurs nor the preceding event.

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Acknowledgements

We thank the GOES teams at NOAA and SIDC for data management and availability and Christoph Keller for useful comments and discussions. M.M. acknowledges the support of the Italian Space Agency (ASI) and COST Action ES0803. Mrs. S. Fabrizio (INAF-OATS) is gratefully acknowledged for careful proofreading.

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Authors and Affiliations

  1. Sterrekundig Instituut, Utrecht University, Postbus 80000, 3508 TA, Utrecht, The Netherlands

    A. Gorobets

  2. INAF-Astronomical Observatory of Trieste, Loc. Basovizza 302, 34012, Trieste, Italy

    M. Messerotti

  3. Department of Physics, University of Trieste, Via A. Valerio 2, 34127, Trieste, Italy

    M. Messerotti

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  1. A. Gorobets
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  2. M. Messerotti
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Correspondence to A. Gorobets.

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Gorobets, A., Messerotti, M. Solar Flare Occurrence Rate and Waiting Time Statistics. Sol Phys 281, 651–667 (2012). https://doi.org/10.1007/s11207-012-0121-7

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  • DOI: https://doi.org/10.1007/s11207-012-0121-7

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