Twisting and Writhing with George Ellery Hale

Magnetic Helicity: from Turbulent Convection to Space Weather

Richard C. CanfieldDepartment of Physics

Montana State University, Bozeman

Data courtesy Solar Dynamics Observatory AIA & HMIAR 11158 video courtesy Daniel Brown

W Loops and Turbulence

Convective Turbulence shreds loops• Assume Ω loops are rigid and rise through

the photosphere with constant velocity• Stack 800 HMI magnetograms• 1 mtgm every 7.5 min for 100 hours)• Red / blue: negative / positive polarity

Chintzoglou and Zhang ApJ 2013

National Geographic / Universe Today

Credit unknown

Hale’s “Vortices (1908)”

Hale discovered:

• Vortex direction depends on hemisphere.

• Vortex direction does not depend on cycle

Hale, ApJ 1927

Northern Hemisphere(left handed upwelling)

Southern Hemisphere(right handed upwelling)

?

Magnetic Helicity + Force-Free Fields

“We then, by the way, find … that A B is a constant of the motion.”

Elsasser, Rev Mod Phys 1956

Minimizing

where is a Lagrange multiplier, leads to the equation

for “force-free” ( j x B = 0 ) fields. N.B.: is a measure of twist (constant when E is minimum).

-------------------------------------------------------------------------

Woltjer, Proc Nat Acad Sci 1958; Berger, AGU Geophys. Mon. 111, 1999

H A B d3 x

where B = A

E = (1/8) { B2 - A B d3x }

B = B

Twist, Writhe, Linking, Self & Mutual Helicity and Conservation

Video courtesy Dana Longcope

Twist(T)

Writhe(W)

Moffatt & Ricca Proc. R. Soc. Lond. A, 1992

Wiegelmann & Sakurai LRSP

MagneticHelicityConservationH = T + W

H = Σ Σ Lij Φi Φj i=1 j=1

N N

i ≠ j : Mutual Helicity

Lij : Linking Number

i = j : Self Helicity

Hale’s Vortices Today:The Hemispheric Twist Rule

Pevtsov, Canfield, Latushko ApJ 2001

Solar Cycle 22203 Active Regions

Solar Cycle 23 263 Active Regions

B = B

Flux-Tube Twist from Helical Convective Turbulence

Effect Model:• Horizontal thin flux tube• Helical turbulence• Mixing length theory• Helicity conservation• Monte Carlo approach

Longcope, Fisher, Pevtsov ApJ 1998Pevtsov, Canfield, Metcalf ApJ 1996

Northern hemisphere

Southern hemisphere

Glatzmeier ApJ 1985

Model Predicts:• Hemispheric

sign trend• Amplitude of

scatter• Lack of cycle

dependence

Longcope, Fisher, Pevtsov ApJ 1998

“THE SOLUTIONS ALL ARE SIMPLE … AFTER YOU’VE ALREADY ARRIVED AT THEM.

BUT THEY’RE SIMPLE ONLY WHEN YOU ALREADY KNOW

WHAT THEY ARE”

Robert M. PirsigZen and the Art of Motorcycle Maintenance

Measuring Coronal Magnetic Energy and Helicity

Two alternative approaches1. Construct the instantaneous 3D coronal magnetic

field using a photospheric vector magnetogram

2. Calculate the flux of magnetic helicity and energy into the corona using magnetogram sequences

Related quantities• Free Magnetic Energy• Relative Magnetic Helicity

Woltjer (Proc Nat Acad Sci 1958)Berger & Field (JFM 1984)Finn & Antonsen (CPPCF 1985)Kusano et al (ApH 2002)

Tziotziou, Georgoulis, & Raouafi ApJ 2012

Data courtesy Solar Dynamics Observatory Helioseismic and Magnetic ImagerAR 11158 video courtesy Lucas Tarr

Helicity and Energy Fluxesfrom Magnetogram Sequences

Berger & Field (JFM 1984)Finn & Antonsen (CPPCF 1985)Kusano et al (ApJ 2002)Chae (ApJ 2001)November & Simon (ApJ 1988)Demoulin & Berger (SP 2003)Pariat et al (A&A 2005)

Emergence

Emergence

Shearing & Braiding

Shearing & Braiding

ADS Citations to Berger & Field (JFM 1984)

Sea Change: SDO HMI DataVector Magnetogram Sequences

Liu & Schuck ApJ 2012Liu & Schuck ApJ 2012

Reconnection: Mutual Helicity Self Helicity Flux Rope

Amari, Aly, Mikic, Linker ApJ L 2010

Coronal Mass Ejections(CMEs) Are Flux Ropes

Vourlidas et al ApJ 2012 Courtesy of Ben Lynch

The Space Weather Challenge for the helicity enthusiast:

Predict the leading-field orientation when these flux ropes arrive at Earth – i.e.,

predict the Magnetic Cloud helicity

The most severe space weather is associated with flux ropes whose leading magnetic field points South, pushing a sheath magnetic field that also points South.

Courtesy of Thomas Zurbuchen Li et al Solar Physics 2011

Energy and Helicity Storageon Topological Separators

Courtesy of Dana Longcope

Sweet IAU Symposium 6,1958

MINIMUM CURRENT CORONA (MCC)• As photospheric magnetic flux elements

shuffle around (shearing and braiding), the flux content of each domain changes only when reconnection occurs an/or when flux emerges or submerges.

• The constraint that fluxes in each individual domain do not change causes currents to build along separators:

• Physics: The separator currents follow from Faraday's Law & Ohm's Law in the presence of moving magnetic point changes -> separator energy and helicity.

• When flare reconnection occurs, these separator currents are fully dissipated.

• Use flare imaging to identify which separators flare.

Predicted (MCC) & observed flare energy (SDO/EVE) and MC helicity (ACE), 4 events

Canfield & Kazachenko 2013

Some interesting questionsin AR Helicity / Energetics

1. What will data-driven nonlinear force-free models tell us about where energy and helicity is released in flares, when compared to the topological models?

2. What is the contribution of distributed currents, as opposed to separator currents, to CME energetics?

3. Will continuous vector magnetogram sequences and helicity flux maps find dynamo effects, as opposed to just convection zone effects ( effect)?

4. What is the axial variation of magnetic helicity per unit length in Magnetic Clouds?

Summary

The conservation properties of magnetic helicity link the solar dynamo and convection zone to eruptive solar events and their interaction with the magnetic field of Earth, an important component of Space Weather.

Continuous high temporal and spatial resolution vector magnetogram sequences and new modeling techniques enable quantitative measurement and modeling of energy and helicity in erupting active regions, which is now and will continue to be a rich research field for decades to come.

• Thanks to the SPD, for this honor• Thanks to you, for your attention• Thanks to the following students &

Postdocs, of whom I am very proud:

PhD Students

•Robert E. Stencel, Ph.D. (Astronomy), University of Michigan, 1977•Richard C. Puetter, Ph.D. (Physics), University of California, San Diego, 1980•Paul J. Ricchiazzi, Ph.D. (Physics), University of California, San Diego, 1982•Todd A. Gunkler, Ph.D. (Physics), University of California, San Diego, 1984•George H. Fisher, Ph.D. (Physics), University of California, San Diego, 1984•David H. Tamres, Ph.D. (Physics), University of California, San Diego, 1989•Kenneth G. Gayley, Ph.D. (Physics), University of California, San Diego, 1990•Thomas R. Metcalf, Ph.D. (Physics), University of California, San Diego, 1990•Kimberly D. Leka Ph.D. (Astronomy), University of Hawaii, Honolulu, 1995•Angela C. Des Jardins, Ph.D. (Physics), Montana State University, 2007•Maria D. Kazachenko, Ph.D. (Physics), Montana State University, 2010

Postdoctoral Fellows

•Chang-Hyuk An, Ph.D. (Physics), University of Tennessee, 1979•Stanley Owocki, Ph.D. (Physics), University of Colorado, 1981•Jean-Pierre Wuelser, Ph.D. (Physics), University of Bern, 1988•Thomas R. Metcalf, Ph.D. (Physics), University of California, San Diego, 1990•Jean-Francoise de La Beaujardiere, Ph.D. (Astrophysical, Planetary, and Atmospheric Sciences), University of Colorado, 1990•Edward Lu, Ph.D. (Physics), Stanford University, 1990•Gianna Cauzzi, Ph.D. (Astronomy), University of Florence, 1992•Alexei Pevtsov, Ph.D. (Solar and Planetary Physics), Institute of Solar-Terrestrial Physics, Irkutsk, 1992•Tetsuya Magara, Ph.D. (Solar Physics), University of Kyoto, Japan 1998•Robert Leamon, Ph.D. (Physics), University of Delaware, Newark, 1999•Stephane Regnier, Ph.D. (Physics), Inst. d'Astrophysique Spatiale, Orsay, 2001

•Dibyendu Nandi, Ph.D. (Physics), Indian Institute of Science, Bangalore, 2003

Graduate and Undergraduate Research Students

•Marc Allen, University of Michigan•James Rhoads, Harvard University•Sean Sandborg, Montana State University•Keith Lambkin, University College Dublin•Tanya Freeman, Union College•Zachary Holder, Montana State University•Ji Son, University of California, Los Angeles•Crystal Fordyce, Clemson University•Emily McLinden, University of Chicago•Scott Waitukaitis, University of Chicago•Michael Hahn, Columbia University•Stacy Gaard, University of Indiana•Alexander Russell, University of St Andrews•Thomas Schad, University of Notre Dame•Christopher Lowder, Georgia Institute of Technology•Meghan Cassidy, University of Maryland•William Simpson, University of St. Andrews

Dedicated to the memory of Thomas R. Metcalf

Finis