1. Helicity: basic properties, open geometries 2. Observations of helicity and helicity flux 3. Twist and Writhe Mitchell Berger Review of Magnetic Helicity.

Slides:



Advertisements
Similar presentations
Free Magnetic Energy and Relative Helicity in Quiet Sun Regions and their role in Solar Dynamics Kostas Tziotziou IAASARS, National Observatory of Athens,
Advertisements

1 A New Model of Solar Flare Trigger Mechanism Kanya Kusano (Hiroshima University) Collaboration with T.Maeshiro (Hiroshima Univ.) T.Yokoyama (Univ. of.
The magnetic nature of solar flares Paper by E.R. Priest & T.G. Forbes Review presented by Hui Song.
Estimating the magnetic energy in solar magnetic configurations Stéphane Régnier Reconnection seminar on Thursday 15 December 2005.
Energy and Helicity Budget of Four Solar Flares and Associated Magnetic Clouds. Maria D. Kazachenko, Richard C. Canfield, Dana Longcope, Jiong Qiu Montana.
Study of Magnetic Helicity Injection in the Active Region NOAA Associated with the X-class Flare of 2011 February 15 Sung-Hong Park 1, K. Cho 1,
CME/Flare Mechanisms Solar “minimum” event this January For use to VSE must be able to predict CME/flare Spiro K. Antiochos Naval Research Laboratory.
Jan 13, 2009ISSI1 Modeling Coronal Flux Ropes A. A. van Ballegooijen Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A Collaborators:
3D Reconnection in Prominences. Gibson & Fan 2006 Negative Points: Pros and Cons of the Flux-Rope-Dip Model 4. Flux ropes are a basic element of low 
The Hemispheric Pattern of Filaments and Consequences for Filament Formation Duncan H Mackay Solar Physics Group University of St. Andrews.
Abstract On 2004 November 10, TRACE observed an X2.5 flare in NOAA Active Region The observations were taken at very short cadence (~3.7 s) in the.
Active Region Evolution and the Removal of Magnetic Helicity by CMEs Len Culhane Mullard Space Science Laboratory University College London.
Coronal Mass Ejections - the exhaust of modern dynamos Examples: systematic swirl (helicity) Measuring it quantitatively Connection with the dynamo Axel.
Current sheets formation along magnetic separators in 3d Dana Longcope Montana State University Thanks: I Klapper, A.A. Van Ballegooijen NSF-ATM.
Magnetic Helicity and Energetics in Solar Active Regions: Can we calculate them – why do we need them? Manolis K. Georgoulis JHU/APL Whistler, CA, 08/01/07.
Magnetic Tongues, Magnetic Helicity and Twist in Active Regions. É. Pariat & P. Démoulin LESIA, CNRS, Observatoire de Paris, France Flux Emergence Workshop.
Evolution of Magnetic Helicity in the Corona During Flux Emergence Anna Malanushenko, Humed Yusuf, Dana Longcope.
What can helicity redistribution in solar eruptions tell us about reconnection in these events? by Brian Welsch, JSPS Fellow (Short-Term ), Space Sciences.
Chip Manchester 1, Fang Fang 1, Bart van der Holst 1, Bill Abbett 2 (1)University of Michigan (2)University of California Berkeley Study of Flux Emergence:
September 2006 CISM All Hand Meeting Properties of Solar Active Regions and Solar Eruptive Events Yang Liu -- Stanford University
Flux emergence: An overview of thin flux tube models George Fisher, SSL/UC Berkeley.
SHINE The Role of Sub-Surface Processes in the Formation of Coronal Magnetic Flux Ropes A. A. van Ballegooijen Smithsonian Astrophysical Observatory.
MSU Team: R. C. Canfield, D. W. Longcope, P. C. H. Martens, S. Régnier Evolution on the photosphere: magnetic and velocity fields 3D coronal magnetic fields.
1 SDO/HMI Products From Vector Magnetograms Yang Liu – Stanford University
Free Energies via Velocity Estimates B.T. Welsch & G.H. Fisher, Space Sciences Lab, UC Berkeley.
Magnetic Helicity • Magnetic helicity measures
Magnetic Helicity Generation Inside the Sun
Dec. 2, 2008 Bangalore, India Active region emergence and its effect on the solar corona Dana Longcope Montana State University, Bozeman, MT Isaac Klapper.
Dr. Alexei A. Pevtsov Helicity on the Sun. If you worry about publicity Do not speak of Current Helicity Jan Stenflo.
High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University.
Kinetic and Magnetic Helicities of Solar Active Regions Ram Ajor Maurya, Ashok Ambastha And Vema Reddy Udaipur Solar Observatory Physical Research Laboratory,
Active Region Flux Transport Observational Techniques, Results, & Implications B. T. Welsch G. H. Fisher
B. T. Welsch Space Sciences Lab, Univ. of California, Berkeley, CA J. M. McTiernan Space Sciences.
Sung-Hong Park Space Weather Research Laboratory New Jersey Institute of Technology Study of Magnetic Helicity and Its Relationship with Solar Activities:
Knots and Bolts of Solar Helicity Dr. Alexei A. Pevtsov “If You are after good publicity, You should not speak about current helicity” – Jan Stenflo.
Twist & writhe of kink-unstable magnetic flux ropes I flux rope: helicity sum of twist and writhe: kink instability: twist  and writhe  (sum is constant)
Helicity: where it comes from and what it tells us Dana Longcope, MSU Anna Malanushenko, MSU/LMSAL 8/11/10Canfield-fest Thanks: Graham Barnes, CoRA B.
The Occurrence and Speed of CMEs Related to Magnetic Helicity Injection in Their Source Regions Sung-Hong Park Solar and Space Weather Research Group Korea.
1 Mei Zhang ( National Astronomical Observatory, Chinese Academy of Sciences ) Helicity Transport from the convection zone to interplanetary space Collaborators:
Coronal Mass Ejection As a Result of Magnetic Helicity Accumulation
1Yang Liu/Magnetic FieldHMI Science – 1 May 2003 Magnetic Field Goals – magnetic field & eruptive events Yang Liu Stanford University.
Helicity as a Constraint on the Solar Dynamo Alexei A. Pevtsov If you worry about publicity Do not speak of Current Helicity Jan Stenflo.
Helicity Observations by Huairou Vector Magnetograph Mei Zhang National Astronomical Observatory, Chinese Academy of Sciences Plan of the Talk: 1.Huairou.
Helicity Condensation: The Origin of Coronal/Heliospheric Structure S. K. Antiochos, C. R. DeVore, et al NASA/GSFC Key features of the corona and wind.
Practical Calculation of Magnetic Energy and Relative Magnetic Helicity Budgets in Solar Active Regions Manolis K. Georgoulis Research Center for Astronomy.
Long-term Helicity Evolution in AR 8100 A. The relative magnetic helicity content of the coronal field B. The magnetic helicity injected by photospheric.
I. INTRODUCTION Gas Pressure Magnetic Tension Coronal loops are thin and bright structure of hot plasma emitting intense radiation in X-ray and EUV. (1)
3D simulations of solar emerging flux ISOBE Hiroaki Plasma seminar 2004/04/28.
3D Spherical Shell Simulations of Rising Flux Tubes in the Solar Convective Envelope Yuhong Fan (HAO/NCAR) High Altitude Observatory (HAO) – National Center.
SHINE 2006 David Alexander Rice University Exploring the dynamics of flux-emergence in magnetically-complex solar active regions David Alexander and Lirong.
1 Mei Zhang ( National Astronomical Observatory, Chinese Academy of Sciences ) Solar cycle variation of kinetic helicity Collaborators: Junwei Zhao (Stanford,
SHINE Formation and Eruption of Filament Flux Ropes A. A. van Ballegooijen 1 & D. H. Mackay 2 1 Smithsonian Astrophysical Observatory, Cambridge,
Evolutionary Characteristics of Magnetic Helicity Injection in Active Regions Hyewon Jeong and Jongchul Chae Seoul National University, Korea 2. Data and.
Thought in 2000: Magnetic helicity is an important theoretical concept Pascal Démoulin but there is no way to estimate it from observations.
Magnetic Helicity and Solar Eruptions Alexander Nindos Section of Astrogeophysics Physics Department University of Ioannina Ioannina GR Greece.
Introduction to Space Weather Jie Zhang CSI 662 / PHYS 660 Spring, 2012 Copyright © The Sun: Magnetic Structure Feb. 16, 2012.
What we can learn from active region flux emergence David Alexander Rice University Collaborators: Lirong Tian (Rice) Yuhong Fan (HAO)
2. Method outline2. Method outline Equation of relative helicity (Berger 1985): - : the fourier transform of normal component of magnetic field on the.
Axel Brandenburg & Jörn Warnecke NorditaStockholm  loop emergence –Buoyant rise –Many scale heights –Twist needed Dynamo –bi-helical field Emergence.
Helicity Thinkshop 2009, Beijing Asymmetry of helicity injection in emerging active regions L. Tian, D. Alexander Rice University, USA Y. Liu Yunnan Astronomical.
Thought in 2000: Magnetic helicity is an important theoretical concept Pascal Démoulin but there is no way to estimate it from observations.
CMEs: Taking magnetic helicity from low corona
Magnetic Helicity in Emerging Active Regions
Solar magnetic fields: basic concepts and magnetic topology
Magnetic Helicity in Emerging Active Regions: A Statistical Study
Thought in 2000: Magnetic helicity is an important theoretical concept
Introduction to Space Weather
Preflare State Rust et al. (1994) 太陽雑誌会.
Introduction to Helicity
Magnetic Helicity in Solar Active Regions: Some Observational Results
Presentation transcript:

1. Helicity: basic properties, open geometries 2. Observations of helicity and helicity flux 3. Twist and Writhe Mitchell Berger Review of Magnetic Helicity and Field Topology

L = 5

Equivalently, we set the helicity of the potential field to zero (and assume helicity is bilinear). Open volumes True FieldReference Field

Helicity Dissipation

Reconnection of two flux tubes converts mutual helicity to self (twist + writhe) helicity Linton, Dahlburg and Antiochos 2001

Relaxation

(Nandy, Hahn, Canfield, & Longcope 2003)

Relaxation But … relaxation to linear force-free state requires 1. Confinement (The only linear force-free field in infinite space outside a sphere is a potential field) e.g. relaxation in one flux tube, or under one helmet streamer 2. Killing all subhelicities (through widespread reconnection – but does line-tying make this less likely than in laboratory plasmas?)

Decompositions of Magnetic Helicity 1. Fourier Spectra 2. Poloidal-Toroidal 3. Regions of Space 4. Self and Mutual Helicity 5. Twist and Writhe

1. Fourier Spectra Physical Meaning: Represent field as sum of circularly polarized modes. Each mode has self linking, but there is no net linking between modes.

Fourier helicity spectra do not always detect helical structure … Helicity spectrum is identically zero!

Example – twisted ring of flux Asgari-Targhi & B 2009

2. Poloidal - Toroidal Physical Meaning: Poloidal and Toroidal Fields link each other, but not themselves. B85, Low 2010

3. Self and Mutual Helicity Suppose we divide the coronal magnetic field into two pieces. In each piece, the field lines begin and end at the photosphere. We can write the helicity as a sum of self helicities H 1 and H 2, and mutual helicities H 12 : H = H 1 + H 2 + 2H 12. H 1 = 1.5  1 2 H 2 = -1.2  2 2 H 12 = 0.22  1  2

Individual twist helicity may be difficult to observe. The total mutual helicity of a collection of threads may be easier. Example: a set of sheared loops (each of unit flux) H = 6.1

A simple prominence model Here the self helicity of the barbs is of opposite sign to the helicities of the spine and overlying arcade Self HelicitiesMutual Helicities barbs H b = 6.1 spine H a = -2.2 arcade H s = -5.1 H sa = H ba = -5.5 H bs = -2.9

Self Helicity of one flux tube The self helicity arises as a sum of twist within the tube and writhe of the tube axis. Choosing the volume to just contain the flux tube gives only the twist helicity. Implications for onset of kink instability for fat flux tubes. Longcope & Malanushenko 2008; Malanushenko et al 2009

Helicity Flow through the photosphere

Helicity Observations Current helicity j z /B z from vector magnetograms (Abramenko et al 1997; Pevtsov & Latushko 2002) Effects of differential rotation on active regions (van Ballegooijen et al 1998; Devore 2000; Green et al 2002; Nindos et al 2003) Helicity flow through photosphere (Kusano et al 2002; Tian 2003; Démoulin and Berger 2003; Chae et al 2004; Kusano et al 2005; Longcope, Ravindra, & Barnes 2007; Kazachenko et al 2010) Magnetograms plus best-fit force-free extrapolations (Démoulin et al 2002; Aulanier et al 2002; Georgoulis & LaBonte 2007)

A combination of LCT and time evolution of vector magnetograms can reconstruct the velocity field, giving the best observation of helicity flow (Welsh et al 2004; Longcope 2004; Kusano et al 2005) There is a gauge-invariant and physically meaningful way of mapping a helicity flow density (Pariat, Démoulin &B 2005; Pariat, Nindos, Démoulin & B 2006) – leads to much more coherent maps. 3. Helicity flow into active regions more coherent than previously thought. Helicity Flow through the photosphere

On the largest scales, differential rotation injects helicity into each hemisphere.

Helicity Flow through the photosphere

Getting the helicity flux right Single footpoint moving in a straight line Helicity Flux negative Helicity Flux positive Some non-helical motions can have large fluctuations in helicity flux, creating noise

When practical, a different formula for helicity flux is much less noisy! The θ ij braiding terms measure braiding of the tubes connected to foot points i and j (unless these belong to same tube). The θ ii spinning terms measure twisting of the tube connected to foot point i. (Longcope, Ravindra, & Barnes 2007)

Field line helicity flux can be mapped! (In practice, each of the two footpoints must be treated separately)

Twist and Writhe Universal language for describing tubes ribbons, and curves Biology: DNA and proteins (Fuller 1971, Ricca & Maggioni 2006) Engineering: elastic rods (van der Heijden & Thompson 2000) Fluid Mechanics: magnetic tubes and vortex filaments (Ricca 1995)

W=-0.72 Tw=0 L=-1 W=-0.72 Tw=6 L=5

Supercoiled DNA (R. Friddle)

Helicity Decomposition Magnetic Helicity for (thin) flux tube with axial flux Φ : Writhe can be determined by subtracting twist from helicity

Writhe Writhe = 2.68Writhe = 0.46 Helix with three turns:

Writhe of Magnetic Fields Kink instability: internal twist converted to writhe (Ricca & Moffatt 1995, Rust 1996, Turok, Berger and Kliem 2010) Stretch-Twist-Fold Dynamos: large scale positive writhe helicity, small scale negative twist helicity (Gilbert 2003) Outer Convection Zone: coriolis force on rising tubes creates large scale positive writhe helicity, small scale negative twist helicity (in North) ‘bihelical fields’ (Blackman & Brandenburg)  effect (Longcope & Pevtsov) : helicity source in active regions?

Winding Number method A simpler and more efficient method for calculating writhe divides the writhe into local and nonlocal terms (Berger & Prior 2006):

This methods divides up a curve into pieces at its maxima and minima, then computes the “local writhe” of each piece, and the “nonlocal writhes” between pieces. Nonlocal = winding number between the two pieces = 0.02 local writhe = local writhe = -1.36

Vertical Helical Tube with n turns Writhe = 2.68 Writhe = 0.46

Kinked Loop: Sine Height profile Two loops with identical Writhe = -0.2

You need height to calculate writhe!

Following the writhe of an erupting filament.