Diagnostics of flare activity level from turbulence parameters of photospheric plasma

Diagnostics of flare activity level from turbulence parameters of

photospheric plasmaAbramenko, Valentyna

Big Bear Solar Observatory of [email protected]

www.bbso.njit.edu/~avi

RHESSI/SOHO/TRACE WorkshopPre-event Physics

December 8-11, 2004,Sonoma, California

Introduction

RHESSI/SOHO/TRACE Workshop/ WG 1: Pre-event Physics Dec 8-11, 2004, Sonoma, California

A solar flare may be triggered as a chain reaction in a stressed coronal magnetic configuration.

Flares occur as an unavoidable phase in evolution of a complex non-linear dynamical system of magnetized plasma (Parker 1988, a review by Charbonneau et al. 2001)

The system extents from the convective zone to the corona through layers of plasma of different physical conditions.

Introduction


Introduction


Essential properties of the photospheric plasma:

Magnetized plasma in a turbulent state (Parker 1979),

very intermittent (or, in other words, multifractal) medium (Lawrence et al. 1993, Abramenko et al. 2002),

where the magnetic helicity may have an inverse cascade (Biskamp 1993)

Introduction


Situation in the photosphere – flaring in the corona:

Magnetic helicity transport in the photosphere (Rust & LaBonte 2003; Georgoulis, Rust & LaBonte – present meeting; Chae 2001; Romano – present meeting ).

Statistical properties of electric currents, current helecity, magnetic flux, etc., derived from vector-magnetograms (Leka & Barnes 2004).

Introduction

Fractal dimensions of the photospheric magnetic fields (Tarbell et al. 1990; Balke et al. 1993; Meunier 1999;

Ireland, Gallagher & McAteer 2003).


Situation in the photosphere – flaring in the corona: we propose to analyze

3. Multifractality (intermittency) of the photospheric magnetic fields – poster at the current meeting. (Abramenko, Yurchyshyn, Wang, Goode, ApJ 577, 2002).

2. Turbulence state of the photospheric magnetic field as derived from magnetic power spectrum – present talk.

Introduction

1. Distribution functions of the magnetic flux in elements of the magnetic field in active regions – present talk. (Abramenko & Longcope, ApJ, 2005)

Distribution functions of the magnetic flux


Flare-quiet active region 0061 (C2) Flaring active region 9077 (X5.7)

(Abramenko & Longcope, ApJ, 2005)


Distribution functions of the magnetic flux(Abramenko & Longcope, ApJ, 2005)

Magnetic Power Spectrum:


Flare-quiet active region 0061 Flaring active region 9077


Flare-quiet active region 0061

Flaring active region 9077 Magnetic Power Spectrum:


Flare-quiet emerging active region NOAA 9851

No X-ray flares during the passage across the disk



Flaring emerging active region NOAA 0365

The most powerful flare during the passage across the disk: X3.6


Multifractality vs. Turbulence


9773/M9.5

9866/M5.7

9077/X5.7

0515/ -

0306/C19851/ -

0061/C2

Jul 13Jul 14

Flaring ARs

Flare-Quiet ARs

Classical Kolmogorov Turbulence state

Conclusions


1. Parameters of the turbulence state (the power index ) and of the structural organization (the distribution

functions and the degree of multifractality, h) of the photospheric magnetic field correlate with flaring productivity of an active region.


2. The turbulence state of the magnetic field at the phase of emergence seems to determine the ongoing flare productivity of an active region.

3. Further study on a large statistics is needed: the catalog of active regions observed in a high resolution mode by SOHO/MDI will be used

(Paolo Romano & Vasyl Yurchyshyn, www.bbso.njit.edu/~vayur/MDI_catalog.htm)

Conclusions

Calculation of Multifractality


Structure functions were first introduced by Kolmogorov (1941). They were defined as statistical moments of the field increments:

Classical Kolmogorov theory

Refined Kolmogorov theory, multifractal structure

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.

Calculation of Multifractality


Historically accepted terminology:Historically accepted terminology:Analysis of Time series : intermittencyAnalysis of Spatial arrays : multifractality

h(q)= d(q)/dq D(h(q))=2+qh(q)- (q)

Examples of different multifractality

Calculation the Power Spectrum


Calculation the Power Spectrum


Documents

Diagnostics of flare activity level from turbulence parameters of photospheric plasma