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