The Log-normal Distributions of Physical Quantities of Flare associated   Coronal Mass Ejections (CMEs), and Flare/CME Model of Gamma-ray Bursts
  We investigated the statistical distributions of physical quantities of solar flares and associated coronal mass ejections (CMEs). We found that the distributions of the X-ray peak fluxes of CME-related flares, their time intervals, and speeds of associated CMEs are in good agreement with log-normal distributions. One possible interpretation of this is that only large energetic mass ejections can escape from the solar corona, which become CMEs in the interplanetary space. This ``filtering effect'' may be the reason why statistical distributions of some physical quantities are similar to log-normal distribution. It is known that the distributions of several physical quantities of gamma-ray bursts (GRBs) are also log-normal distributions, and that the time variations of gamma-ray intensity in GRBs are very similar to those of hard X-rays of solar flares. On the basis of these similarities and physical consideration of magnetohydrodynamic properties of an accretion disk around a black hole, which is supposed to be situated in the central engine of a GRB, we propose a new model of the central engine of GRBs, the {\it flare/CME model}, in which GRBs are formed by nonsteady jets consisting of intermittent ejections of mass (like solar CMEs) associated with reconnection events (like solar flares) in the accretion disk corona. Such nonsteady MHD jets would produce many shocks as well as local reconnection events far from the central engine. In this model, only large energetic mass ejections can escape from the accretion disk corona, so that statistical distributions of some physical quantities are similar to log-normal distributions. 
Seiichiro I. Aoki, Seiji Yashiro, & Kazunari Shibata