V.I. Abramenko, V.B. Yurchyshyn, H. Wang, T.R. Spirock, P.R. Goode Big Bear Solar Observatory, NJIT Crimean Astrophysical Observatory, Ukraine 34 th Meeting of SPD June 2003

INTRODUCTION Analysis of the non-thermal broadening of soft X-ray spectral lines in solar flares observed with Yohkoh (Alexander et al. 1998, Harra et al. 2001) showed that the non-thermal velocity begins to rise before the flare onset and peaks often before the Hard X-ray emission. There are changes in the turbulent state of an active region, leading to the flare onset, in other words, there is a preflare turbulent phase. The non-thermal velocity COES X-ray flux   = 11 min - the growth time of the non-thermal velocity

INTRODUCTION Due to the magnetic coupling between the corona and the photosphere (Parker 1979, 1996), preflare turbulent phase may involve the photosphere, too. Photospheric plasma is in a state of highly developed turbulence, where the vertical component of the magnetic field, Bz, diffuses in the same way as a passive scalar in a turbulent flow (Parker 1979, Petrovay and Szakaly 1993). Thus, we can apply methods of the theory of turbulence to the longitudinal magnetic field of an active region measured near the center of the solar disk.

OBSERVATIONAL DATA from Big Bear Solar observatory : Video (upper penal) and Digital (lower penal) Magnetograph Systems  B Longitudinal magnetic field Pixel sise: 0.6 x 0.6 arcsec The X9.4 flare The M8.4 flare The X1.6 flare The M8.7 flare Measurements covered the time periods before, during and after a major flare with an appropriate time cadence.

METHOD A. The degree of intermittency of the magnetic field An increase in the turbulence implies that the turbulence becomes more intermittent. Intermittency characterizes a tendency of a turbulent field to concentrate into widely spaced very intense small-scale features. Frisch, 1995: An example of highly intermittent structure:

METHOD A. The degree of intermittency of the magnetic field The degree of intermittency may be estimated by determining structure functions of high statistical orders: Non-intermittent turbulence Here, q is the order of a statistical moment, r is a separation vector, x is the current point on a magnetogram. denotes the averaging over a magnetogram.  q  is a slope within the inertial range of scales. The routine was proposed by Abramenko et al. ApJ 577, 2002

METHOD A. The degree of intermittency of the magnetic field Non-intermittent turbulence Highly intermittent turbulence  -1 

METHOD B. Correlation length of the magnetic energy dissipation field For the longitudinal component of the photospheric magnetic field the energy dissipation, per unit mass in a unit of time, can be written (Monin & Yaglom 1975): For every magnetogram we calculated the magnetic energy dissipation structure,  x,y . The correlation length of these these clusters,, was determined using the method of the turbulence theory (Monin and Yaglom 1975).

RESULTS

CONCLUSIONS Our results - support the existence of the preflare turbulent phase in an active region (Alexander et al. 1998, Harra et al. 2001) - are in agreement with the concept that a solar flare is the collective energy released by an avalanche of reconnection events at small-scale discontinuities of the magnetic field (the self-organized criticality concept ) (Parker 1987; Longcope and Noonan 2000 ; Charbonneau, McIntosh, Liu and Bogdan 2001) - show that statistical properties of a flare-related nonlinear dissipative process in an active region can be studied by using the photospheric longitudinal magnetic field.

The X9.4 flare The X1.6 flare

The M8.7 flare The M8.7 flare

First, we calculated the correlation function: We have to normalize B(r) by the variance of dissipation: b(r) = B(r) / B(0) B(r ) =  (  (x+r) -    )·(  (x)-    )  By integrating b(r), over all scales r, we obtain a correlation length of the energy dissipation structure: =  b(r) dr max  r Correlation length of the magnetic energy dissipation cluster

The M8.4 flare on Nov 5, 1998 in active region NOAA 8375 GOES HH Flux c 

The M8.7 flare on July 26, 2002 in active region NOAA 0039 HH GOES c Flux

The X1.6 flare on October 19, 2001 in active region NOAA 9661 GOES HH Flux c 

The X9.4 flare on March 22, 1991 in active region NOAA 6555 GOES Flux c 

Table 1.

Table 2.

1.In all of the cases we found a peak in , which was followed by a peak in. During the time interval between them, , a rapid growth of the soft X-ray and H  flux occurred. 2.The peak in beta was preceded by a period of gradual growth of , . Maximum in  occurred earlier than the peak of the hard X-ray emission.  3. The maximum of tends to follow or to occur nearly simultaneously (with the accuracy of about 2-5 min) with the maximum of the Hard X-ray emission. 4. Based on limited examples, we conclude that the time intervals  and  are inversely proportional to impulsivity and intensity of flares.  CONCLUSIONS