Kinetic and Magnetic Helicities of Solar Active Regions

Ram Ajor Maurya, Ashok Ambastha

And

Vema Reddy

Udaipur Solar Observatory

Physical Research Laboratory, India

Outline

Objectives

Introduction and background

The Data and Sample of Active Regions

Measurement of Helicities – Kinetic and Magnetic

Results

Evolution of Helicity in NOAA 10930 : 8-15 Dec 2006

Hemispheric Distribution

Association of Kinetic and Magnetic Helicities

Variations in Helicities and transient activities

Summary and Conclusions

Objective

Evolution of Kinetic and Magnetic Helicities in ARs

Variation in Helicities During Energetic Transients

Latitudinal distribution of Kinetic and Magnetic Helicities

Association of Kinetic and Magnetic Helicities?

Active regions: 3D magnetic structure extending from sub-photosphere to coronal heights

magnetic helicity observed at the photosphere is due to shear at larger depths and strong turbulence in the convection zone (Pevtsov, et al. 1994).

The kinetic helicity of turbulent flows twists the rising flux tube (Longcope et al. 1998).

The other possibility of twist in the rising tube is dynamo action (Choudhuri 2003) .

flux tube created at the base of the convection zone, rises toward the photosphere where turbulent flows braid and intertwine (Priest and Forbes 2002).

Kinetic helicity of

sub-photospheric flow

Magnetic helicity of

photospheric magnetic fields

Introduction

What is Helicity ?

Helicity of a vector field is a measure of linkage and twistedness of the field lines.

V

dVWXH

Kinetic Helicity ?dVuH

Vk

dVABHVm

Magnetic Helicity ?

Hemispheric Trend of Helicity Parameters:

Reference Helicity Parameter

North

(-ve)

%(no.)

South

(+ve)

%(no.)

Total Date

Hale (1926) HV 64(16) 50(13) 51 1901-1944

Richardson (1941) HV 71 66 141 1901-1944

Seehafer (1990) hc 91(11) 75(3) 16 SC21-22

Martin, et al. (1994) FC 100(26) 72(34) 47 SC22

Pevtsov, et al. (1995) αbest 76(25) 69(25) 69 1991-1995

Abramenko, et al. (1996) hc 79(15) 86(18) 40 1988-1994

Bao and Zhang (1998) hc 84(169) 79(177) 422 1988-1997

Longocope, et al. (1998) αbest 62(58) 66(73) 203 1991-1995

Bao, et al. (2000) αav 59(152) 65(26) 87 SC23

Pevtsov, et al. (2003) FC 80(558) 86(633) 2310 2000-2001

Lim and Chae (2009) FC 95(19) 100(18) 45 1996-2001

Hk ?

Some background

HV - Hα sunspot vorticity, hc – current helicity, FC - Hα filament chirality, αav, αbest force free parameter

Kinetic Helicity .. Some background

Komm et. al. 2007: Kinetic helicity on average is negative (positive) in northern (southern) hemisphere

Zhao and Kosovichev (2004): sub-surface kinetic helicity have a prepondence opposite to the current helicity.

Komm et al. (2004): strong signal in kinetic helicity at the location of the active region during the epoch when flares occur.

Kinetic helicity and Flares

(Maurya, Ambastha and Tripathy, 2009, Astrophys. J., 706, L235)

GOES-12 flux for 1.0 - 0.8Å (solid line) and 0.5 - 0.4Å (dotted line). The horizontal lines with labels Ri, i = 1, . . . 5, represent time span taken for the five data sets.

Solar oscillations could be excited by the mechanical impulse of large flare (Wolf 1972).

Flare related effects on p-modes: Chaplin et al. (2000), Ambastha et al.(2003), Howe et al. (2004).

presence of three sheared layers in the depth range 0 to 10 Mm of 44 ARs

two extrema in meridional velocity profiles of these ARs were found to be located at the depths of 1.92±0.15 and 4.69±0.30 Mm.

ARs having two extrema possessed as large as twice the mean magnetic field (MI) and mean GOES X-ray flux.

presence of steep gradients in meridional velocity at depths ranging from 1.5 to 5 Mm

hemispheric trend of gradient: negative (positive) signs in the northern (southern) hemisphere.

ARs of larger MI possessed steeper gradient in meridional velocity profiles.

flaring activity of ARs are associated with depth of the first extremum of vertical vorticity.

(Maurya and Ambastha, 2010, Astrophys. J., 714, L196)

Observational Data and Active Regions

Total : 91 North: 32 South: 59

GONG: Jul 2001- Aug 2007 MSFC: Jul 2001- Oct 2004 Hinode: Nov 2006 – Aug 2007

Local Helioseismology: Ring Diagram Analysis

Full disctime series

y

x

Tracked and filtered time series

Data Cube 3DFFT Ring-Fitting

Inversion

30

20

),,(k

b

UkUk

AkkP

yyxxyx

iii dzKzuU )(

Horizontal: ux, uy

Vertical: uz

(cont. eqn., Komm, et al. 2004)

∆ω = kx Ux + ky Uy

(Hill, 1988)

Measurement of Helicity

dVuHVk

dVABHVm

y

u

x

uu

Nh xy

zavzk

1)(

y

B

x

B

BNxy

z

zav

11

Vertical and helical fluctuations are an integral part of any turbulent fluid

Average flow in the Active Region NOAA 10486

3D Flow Structure Beneath the NOAA 10486

Kinetic Helicity in the Active Region NOAA 10486

Velocity and Magnetic Fields in NOAA 10486

Evolution of Kinetic and Magnetic Helicities in NOAA 10930

Latitudinal Distribution of Magnetic Helicity

Hemispheric Trend:Hemispheric Trend:

North: North: αzav< 0 (66%)< 0 (66%)

SouthSouth: αzav> 0 (63%)> 0 (63%)

Max. PDF: -9.37×10-9 (+1.72×10-9) m-1

Average αzav: -1.39×10-9 (+3.05×10-9) m-1

Latitudinal Distribution of Vertical Kinetic Helicity

Hemispheric Trend:Hemispheric Trend:

North: (North: (hk1z))av< 0 (47%)< 0 (47%)

SouthSouth: ((hk1z))av > 0 (53%)> 0 (53%)

Max. PDF: +2.50×10-8 (-4.48×10-9) ms-2

Average ((hk1z))av: 1.88×10-9 (-7.62×10-9) ms-2

North: (North: (hk2z))av< 0 (69%)< 0 (69%)

SouthSouth: ((hk2z))av > 0 (56%)> 0 (56%)

Max. PDF: -4.37×10-8 (3.44×10-9) ms-2 Average ((ω2

z))av : -6.99×10-8 (1.69×10-8) ms-2

Relation Between Kinetic and Magnetic Helicities

Par. Corr. Coeff.

(hk1z)av -0.07

(hk2z)av +0.23

Summary and Conclusions

Magnetic helicity parameter αzav shows significant hemispheric trend - in agreement with earlier

reports.

The average vertical vorticity for the depth range 2.5-12 Mm shows an opposite hemispheric trend while there is no hemispheric trend for the depth range 0.0-2.5 Mm.

There is no clear hemispheric preponderance for the average vertical kinetic helicity for the depth range 0.0-2.5 Mm while strong hemispheric trend is discernible for the depth range 2.5-12 Mm.

We do not find any clear association between the twists of surface magnetic fields and sub-surface flows.

Absolute mean magnetic field of ARs shows a mild correlation with the twist of magnetic fields while no association with the twist of sub-surface flows.

The GOES XHR flux also shows a mild correlation with vertical vorticity averaged over depths 2.5-12 Mm.

photospheric magnetic helicity has not a cause and effect relation with the sub-photospheric kinetic helicity in the depth range 0-12 Mm.

Latitudinal Distribution of Current Helicity

Hemispheric Trend:Hemispheric Trend:

North: (North: (hcz))av< 0 (56%)< 0 (56%)

SouthSouth: ((hcz))av > 0 (47%)> 0 (47%)

Max. PDF: 0.00×10-9 ( 0.00×10-9) m-1

Average ((hcz))av : -1.93×10-9 (+0.00×10-9) m-1

Latitudinal Distribution of Vertical Vorticity

Hemispheric Trend:Hemispheric Trend:

North: (North: (ω1z))av< 0 (56%)< 0 (56%)

SouthSouth: ((ω1z))av > 0 (51%)> 0 (51%)

Max. PDF: -1.12×10-7 (+8.62×10-9) s-1

Average ((ω1z))av : -2.56×10-9 (+3.83×10-8) s-1

North: (North: (ω2z))av< 0 (41%)< 0 (41%)

SouthSouth: ((ω2z))av > 0 (39%)> 0 (39%)

Max. PDF: +3.50×10-7 (-1.17×10-7) s-1

Average ((ω2z))av : +9.89×10-9 (-9.99×10-8) s-1

Relation Between Kinetic and Current Helicities

Par. Corr. Coeff.

(ωz1)av -0.10

(ωz1)av +0.04

(hk1z)av -0.05

(hk2z)av +0.26

Current Helicity ? dVJBHVc

dVJBHVc

y

B

x

BB

Nh xy

zavzc

1)(