Big Bear Solar Observatory

Intermittency and Turbulence of the Solar Magnetic Field

In recent decades, Solar Physics research demonstrated considerable progress in understanding of macro-scale processes (e.g., the magneto-hydrodynamic modeling of the heliosphere, modeling of large-scale coronal magnetic structures, etc.), on one hand and micro-scale phenomena (e.g., turbulence of solar plasma) on the other hand. Further progress seems to be associated with the realization of how various micro-scale processes are involved and manifested in the macro-scale behavior of the entire Sun. Thus, the problem of multi-scale interactions arises. The problem can be tackled in the framework of intermittency and multifractality. This approach seems to be a very promising one in efforts to understand the underlying laws that govern the behavior of solar activity. In the Big Bear Solar Observatory, this project is lead by Dr. Valentyna Abramenko since 2000.

What is intermittency? The notion of intermittency comes from turbulence theory and denotes the ability of small-scale turbulent features to concentrate into high-intensity separated blobs surrounded by extended areas of much lower fluctuations (inverse cascade process). This property exists in both spatial and temporal domains, so that highly intermittent structures are prone to reveal a burst-like, explosive behavior. More details in Abramenko (2008).

Fig. 1. -

Intermittency in solar surface magnetic structures. Turbulent motion of the solar plasma creates complex, highly intermittent structures observable in the surface magnetic fields.(0365.mpg)

How to measure the intermittency?

Calculate the high-order structure functions. Details are in: Abramenko et. al. 2002, Astrophys. J. 577 , 487 and Abramenko et. al. 2008, Astrophys. J. 681, 1669.
Calculate the Power Spectrum (second-order momentum). Detail are in Abramenko, V. 2005, Astrophys. J. 629, 1141

Predicted consequences of intermittency for solar active regions: eruptive energy releases and creation of a self-organized criticality state. Our goal: to check this on real data and, possibly, to use for flare forecast.

Intermittency of the photospheric magnetic fields versus flaring productivity of active regions (ARs)

Fig. 2. - Time variations of the intermittency index, κ, determined for NOAA AR 10930 (observed on Dec 8 -13, 2006) from i) photospheric magnetograms (Hinode SOT/FG data), ii) Hinode XRT data, iii) Nobeyama radio data, and iv) GOES flux. Thin black line represents the GOES flux data. The data show that gradual increase of coronal intermittency occurred after the peak of the photospheric intermittency. The time delay between the peak of photospheric intermittency and the occurrence of the first strong (X3.4) flare was approximately 1.3 days. Thus, the enhancement of intermittency/complexity first occurs in the photosphere and is later transported toward the corona. The full text is here.

Fig. 3 - Power index a versus flare index A plotted for 16 active regions. The dashed straight line indicates the power index α = 5/3 for the stationary non-intermittent Kolmogorov turbulence K41. The curve shows the best fit to the data: A(α) = 409.5(α - 5/3)2.5. We found that the magnitude of the power index at the stage of emergence of an AR reflects its future flare productivity. Detail are in here.

The Project Intermittency Bibliography can be found here.
Talks delivered at meetings can be seen here.
More details on the intermittency and turbulence can be found in Frisch (1995) .