1. Emerging Active Regions: turbulent state in the photosphere
Valentina I. Abramenko
Big Bear Solar Observatory of NJIT
This talk will be about an interesting relationship between observational parameters of emerging active regions.
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

2. Introduction E()   -
Photospheric magnetized plasma in a turbulent state Parker 1979,
Petrovay & Szakaly 1993,
Petrovay & Moreno-Insertis 1997
I analyzed line-of-sight magnetograms for 16 active regions obtained by MDI in high resolution mode.
Six of them were emerging ones, and now I will pay attention to them.
One of the way to analyze the turbulence
is to calculate the magnetic power spectrum,
in particular, the power spectrum of the
observed line-of-sight component of the magnetic field:
E()   -
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

3. Emerging of a Flare-quiet Active Region NOAA 9851
Emerging of a Flare-quiet Active Region NOAA 9851
This emerging active region possessed the power spectrum with a slope of 1.7 which is very close to the Kolmogorov-type spectrum with a power index of 5/3.
(Recall that in the turbulence theory the Kolmogorov-type spectrum characterizes a stationary homogeneous turbulent regime, when the energy input at large scales is equal to energy dissipated at small scales ).
This active region produced no flares during its passage across the disk.
E()   -
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

4. Emerging of a Flaring Active Region NOAA 0365
Emerging of a Flaring Active Region NOAA 0365
This is an emerging and very flaring active region The power spectrum for three magnetogram are shown.
At the very beginning of emergence, this magnetic structure possessed a very steep, non-Kolmogorov spectrum.
As the active region emerges, we observe the lifting of the spectrum at all scales, with nearly the same magnitude of the power index .
It looks like we observe unraveling , disentangling emergence of a very complicated, very tangled magnetic structure generated under the photosphere.
(in the real talk this slide will be replaced by two movies).
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

5. Emerging of a Flaring Active Region NOAA 0365
Emerging of a Flaring Active Region NOAA 0365
Other emerging active regions showed the similar result, namely,
the power index obtained before the beginning of the flare activity (from the first magnetogram) was very close to the averaged power index.
Moreover, the steeper the spectrum at the beginning of the emergence the higher the future flare productivity.
To quantify the flare productivity, we calculated the soft X-ray flare index for a given active region.

6. Soft X-ray Flare Index
The daily SRX flare index was first introduced by Anna Antalova in 1996 and later was applied by other authors to characterize the daily flare productivity of the Sun from the soft X-ray flux measured by GOES in the 1-8 A range. Discussions with Alexei and Dana helped me a lot in application of the idea to a single active region.
The flare index is constructed by weighting flares of classes X,M,C as 100, 10, 1 and summing over all flares occurred in a given active region during its passage across the disk. The result is divided by the duration of the passage, tau (measured in days) . And we obtain the specific flare productivity per day.
For example, ….
A=1 corresponds to one flare of C1 per day.
For all ARs analyzed in this study, tau was no less than 9 days – a time period sufficient enough to display the ability for flaring.
For example, during 13 days an active region launched flares:
X5.2 , M1.2 , C6.0
A=( ) / 13 = 41.4
(in units 10 W m ) -6 -2
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

7. Soft X-ray Flare Index versus Magnetic power index
Soft X-ray Flare Index versus Magnetic power index
This plot summarizes results obtained for 16 active regions. Each point corresponds to one active region.
The vertical axis is the magnitude of the flare index A ,
Horizontal axis is the power index of the magnetic power spectrum as averaged from several magnetograms registered in the high resolution mode by SOHO/MDI.
One can see a good correlation between the power index and the flare index. The data points may be successively fitted by such an analytical curve (red line), the reduced chi-square test is about 1. Active regions which produced X-class flares possessed a steep power spectrum with alpha higher than 2. Flare-quiet active regions display a Kolmogorov-type spectrum.
The most interesting point is the situation with emerging active regions red circles) . For all of them, the power index determined from the first magnetogram (before the start of the flare activity) got into the red circles, in other words, it was very close to the averaged magnitude . This means that the magnitude of the power index, determined at the beginning of the emergence, seems to be related to the future flare productivity of AR. This finding shows the way to distinguish at the very early stage
those solar spots that are ``born bad'' and have a potential to produce powerful flares.
So, this plot can help much in forecasting on oncoming flare activity , especially for emerging magnetic structures.
The very steep non-Kolmogorov spectra of flaring active regions imply the inhomogeneous non-stationary turbulence regime when the energy transport rate along the spectrum may not be constant. And the energy dissipation displays an intermittent(burst-like) behavior as in time so in spatial domains.
The Kolmogorov-type spectra of quiet active regions might suggest a nearly stationary turbulent regime , which provides premises for smooth evolution without catastrophes.
This study has demonstrated that structural and dynamical characteristics of the magnetic field as measured in the photosphere are relevant to the intensity of non-stationary processes in the entire magnetic configuration.
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

8. Additional info
The very steep non-Kolmogorov spectra of flaring active regions imply the inhomogeneous non-stationary turbulence regime when the energy transport rate along the spectrum may not be constant. And the energy dissipation displays an intermittent(burst-like) behavior as in time so in spatial domains.
The Kolmogorov-type spectra of quiet active regions might suggest a nearly stationary turbulent regime , which provides premises for smooth evolution without catastrophes.
This study has demonstrated that structural and dynamical characteristics of the magnetic field as measured in the photosphere are relevant to the intensity of non-stationary processes in the entire magnetic configuration.

9. Table 1: Active Regions

10. Magnetic Power Spectrum: calculationsk y k x
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005

11. Magnetic Power Spectrum
Flare-quiet active region 0061 (A=2.6)
Flaring active region 9077 (A=120)
Here I show typical examples of the power spectrum for two active regions.
The first one is flare-quiet AR and it displays the Kolmogorov-type spectrum of the power index close to five thirds.
The second AR was very flare-productive one. It shows the spectrum steeper than the Kolmogorov spectrum.

12. Magnetic Power Spectrum: time-variations of the power index
Flare-quiet
active region 0061:
This is the time variations of the power index for the same Ars (black lines). And red lines show the GOES flux.
For the quiet active region the power index waves around the dashed line which shows the state of Kolmogorov turbulence.
This is the result for flaring AR. The power index is considerably above the K41 line.
Both above mentioned active regions were developed ones. It would be interesting to check what is going on in emerging active regions.
Flaring
active region 9077:

13. Table: Emerging Active Regions
Table: Emerging Active Regions
Other emerging active regions showed the similar result, namely,
the power index obtained before the beginning of the flare activity (from the first magnetogram) was very close to the averaged power index.
Moreover, the steeper the spectrum at the beginning of the emergence the higher the future flare productivity.
To quantify the flare productivity, we calculated the soft X-ray flare index for a given active region.
NSO Workshop #23 Solar MHD: Theory and Observations July 18-22, 2005