Valentina AbramenkoBig Bear Solar Observatory of NJIT

Multi-fractality of Solar Magnetic Fields: New Progress with HMIMulti-fractality of Solar Magnetic Fields: New Progress with HMI

Abstract.Abstract. The SDO/HMI instrument allows us to address temporal variations of magnetic field parameters. Higher sensitivity, lower noise level and smaller The SDO/HMI instrument allows us to address temporal variations of magnetic field parameters. Higher sensitivity, lower noise level and smaller pixel size, as compared to MDI data, improve our estimations of multi-scale parameters of magnetic structures. Here we compare spectra of multi-fractality pixel size, as compared to MDI data, improve our estimations of multi-scale parameters of magnetic structures. Here we compare spectra of multi-fractality obrained for the same area on the Sun using the MDI/hires and HMI data. We find that while at scales below 4-5 Mm, MDI does not detect any signature of obrained for the same area on the Sun using the MDI/hires and HMI data. We find that while at scales below 4-5 Mm, MDI does not detect any signature of milti-fractality, HMI data, instead, display a multi-fractal ogranization of the magnetic field. About a day before a strong flare, we observe a period of inflation milti-fractality, HMI data, instead, display a multi-fractal ogranization of the magnetic field. About a day before a strong flare, we observe a period of inflation of multi-fractality (complexity) in the photosphere.of multi-fractality (complexity) in the photosphere.

AR NOAA 11166 AR NOAA 11158Feb 12/00:00 UT Feb 13/03:00 UT Feb 14/22:48 UTHMI: Mar 07/00:00 UT HMI: Mar 08/15:22 UT MDI: Mar 08/15:08 UT HMI: Mar 09/18:00 UT

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Small-scale range2 -5 Mm : multi-fractality indexon small scales

Large-scale range5 – 20 Mm :Multi-fractality indexon large scales

Spectrum cutoff due to noise

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Sq(r) = <|B(x+r) – B(r )|q>

Spectra from Magnetograms:

An increase of the flatness function with the decreasing scale implies the multi-fractal magnetic field. The degree of multi-fractality at small scales (<5 Mm) is correlated to the flaring productivity of ARs (Abramenko et al.2010,ApJ722). A steep power-law flatness was very poor pronounced in MDI data, whereas it is well detectable in HMI data.

Both time profiles (the left – for AR 11166, and the right for AR 11158) show that the multi-fractality index on large scales reflects the overall enlargement of the active region. At the same time, the magnetic power spectrum index, α, and the multi-fractality index on small scales, κ, show a waving behavior with well well pronounced peaks in multi-fractality approximately pronounced peaks in multi-fractality approximately 1-2 days before the strongest (in the AR) flare 1-2 days before the strongest (in the AR) flare occurs.occurs.

Time variations of the magnetic power spectrum index α, and the multi-fractality index on small scales, κ, reflect the reorganizations of the magnetic field at small scales. These parameters are not responsible for, say, reinforcement/separation of large sunspots, but they are rather reflect appearance of strong field gradients, extended threads and filament-like magnetic features, inner delta-structures inside the AR, etc. For slow evolving, low-flaring ARs, these parameters are not varying with time. However, for rapidly growing, complex and flaring ARs, there are intriguing peculiarities in their time profiles. Thus, a 1-2 days before the strong flare onset, we observe periods of enhanced multi-fractality in the magnetic field (see plots for ARs 11158 and 11166).Note that for very stable, quiet and low-flaring ARs, the variations in these parameters are much smaller.

Time, days of February 2011

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