1. CHARACTERISTICS OF TURBULENT PROCESS IN THE SOLAR PHOTOSPHERE
R.Kostik1, L.Kozak2,3, O.Cheremnykh3
¹Main Astronomical Observatory of the National Academy of Sciences of Ukraine
²Kyiv National Taras Shevchenko University, Department of Astronomy and Space Physics
³Space Research Institute of the National Academy of Sciences of Ukraine and State Space Agency of Ukraine
Abstract—Observations obtained at the 70 cm vacuum tower telescope (VTT) at Izaña (Tenerife, Spain) are analyzed to show that turbulent processes in the solar photosphere have two distinct spectra of turbulence. The first is the well known Kolmogorov spectrum, which describes plasmas with a zero mean magnetic field, and the second is the Kraichnan spectrum with a nonzero mean magnetic field. The transition from one spectrum type to another is found to occur at a scale of 3 Mm. This scale is consistent with the typical size of mesogranular structures, which indicates a transition to large scale self organizing magnetic structures.
OBSERVATIONS
RESULTS OF OBSERVATIONS
Observations were obtained in July 21, 2004 (a quiet region) and November 17, 2007 (faculae) near the solar disk center at the German Vacuum Tower Telescope located at the Observatorio del Teide in Izana, Tenerife. The spectral region was centered on the Ba II 4554 Å line. Following the standart procedure (Kostik, R. & Khomenko, E. 2007, A&A, 476, 341) we obtained convective and oscillatory variations of the velocity and intensity along the photosphere from h=0 km to h=650 km. The dimensions of the convective elements were found from the change of sign of the velocity along the spectrograph slit.
Convective (left panel) and oscillatory (right panel) of the velocity field as a function of the slit position and time. Quiet region.
METHOD
The turbulence of the solar plasma is characterized by a large number of degrees of freedom and non linearly interacting modes. Scientists typically use statistical physics and the theory of probability to describe such a medium. This way they can obtain information about average variations in the macroscopic parameters of the plasma medium in time or space.
To determine the type of turbulent processes, we analyzed the moments of the probability density function for different orders, and also, in order to refine the scale of the turbulent processes, we investigated the spectral dependences of the changes in velocity.
In the turbulence theory, this commonly used analysis is referred to as extended selfsimilarity (ESS) analysis. In the general case, the main idea of this approach is to find dependences of the form Sq(l) = |υ(x+l)-υ(x)|q ~ lζ(q), where … is averaging over an ensemble. For Kolmogorov’s theory of turbulence ζ(q) = q/3 and the dependence of the energy flux spectrum on the wave number can be written as Ek(k) ∝ k–5/3. For model of Iroshnikov–Kraichnan ζ(q) = q/4 and the dependence of the energy flux spectrum on the wave number can be written as Eik(k) ∝ k–3/2. In comparison with the Kolmogorov spectrum, this spectrum exhibits a significantly reduced level of energy transfer on small scales, perturbations of MHD variables propagate at a speed of the order of the Alfven speed..
m/sec
m/sec
Convective velocity fluctuations in quiet (left panel) and in active (right panel) regions at height h = 650 km.
TWO SPECTRA OF TURBULENCE ON THE SUN
The cascade according to the Kolmogorov 1941 theory of the turbulence. Notice that at each step the eddies are space-filling.
Schematic representation of the Kolmogorov 1941 picture of turbulence showing the spatial energy spectrum as an example.
Spectral density E of the convective velocity field component for the active region at h = 650 km (solid line) and h = 0 (dashed line)
Spectral density E of the convective velocity field component for the quiet region at h = 650 km (solid line) and h = 0 (dashed line)
CONCLUSIONS
The statistical and spectral analysis of the convective velocity field component found that:
1. For the solar quiet regions the spectrum of turbulence corresponds to the Kolmogorov turbulence model.
2. Solar active regions exhibit two fundamentally different spectra of the turbulence. The Kolmogorov type turbulent processes dominate on the small scales, and the Iroshnikov–Kraichnan type turbulent processes are observed on the large scales.
3. The transfer from the Kolmogorov spectrum to the Iroshnikov–Kraichnan spectrum takes place on a scale of approximately 3 Mm. This scale corresponds to the scale of mesogranulation and points to nonzero mean magnetic field. Moreover, it indicates the possibility of development of self-organized magnetic plasma structures (spots, bipolar groups, active regions, activity complexes, etc.).
ACKNOWLEDGMENTS. The work is done in the frame of complex program of NAS of Ukraine on space researches for , and under a support of the grant Az from the Volkswagen Foundation («VW-Stiftung»).