1 Space Weather Magnetic Field Origins Helioseismology Dynamo Theory

2 Motivation Solar magnetic fields are the driver of space weather; without the magnetic field there is no space weather. Can someone tell me why that is? Magnetic fields originate under the solar surface. There are short and long term changes in the fields. How can we predict these changes?

3 Outline Helioseismology –What is it –What are the measurements –What is the mathematics –What do the results look like Solar Dynamo –Basic concept What is a dynamo? –Current understanding (pun not intended)

4 Solar Structure

5 Pressure and Gravity Mode Rays Courtesy Juri Toomre and Douglas Gough

6 Helioseismology Phenomenon 5 minute oscillations of the visible surface Sound waves resonantly trapped below the surface excited by convection just below the surface Methodology 10 7 normal modes of varying radial/latitudinal extent Comparison of frequencies with model calculations Inverse methods Local helioseismology and running waves Results Physics: GR, neutrinos, EoS, opacities, diffusion, Stellar Structure: temperature, density, abundances, rotation, flows, "turbulence",... Implies stellar evolution. Variability: modes, 3-D structures Frontier Asteroseismology Gravity Modes

7 The Solar Surface Courtesy of Luc Rouppe van der Voort, Oslo, from the Swedish Solar Telescope, La Palma

8 “Wiggle Line” Spectrum Wavelength [ Ångstroms ]

9 Telescope Ordinary white light telescope, need not be very large, good enough for 1” resolution Blocking filter to isolate one desirable spectral line Tunable interference filter to make measurements in several locations through line to make Doppler line profiles. CCD detector. Output is a line profile at each 1” element on the Sun

10 Data-Velocity Image

11 Disentangling the Modes    = = = Courtesy Frank Hill

12 Mathematical Form From Annual Reviews of Astronomy and Astrophysics 1984, 22, 593, Deubner and Gough

13 Equation of Motion

14 Surface velocity changes Steve Musman and Dave Rust, Solar Physics

15 Temporal Power Spectrum Courtesy Dick White and Milton Cha

16 A Testable Prediction p-modes g-modes

17 The Outcome Courtesy Franz-Ludwig Deubner

18 And Rapid Improvement Courtesy Franz-Ludwig Deubner, Roger Ulrich, and Ed Rhodes

19 Caricature of the “Scientific Method” Serendipitous Discovery Many Different Descriptions Testable Prediction of Unobserved Phenomenon Confirmation Use Remaining Small Deviations as Tool

20 A Typical ℓ - Diagram ℓ (Spherical Harmonic Degree) (Frequency)

21 The Global Rotation Picture Tachocline Surface Shear Courtesy of Rachel Howe

22 Sub-surface Flows Jesus Patron et al.

23 Structure of Sunspot Courtesy Tom Ducall

24 High Resolution Near Surface Flows Courtesy of Junwei Zhao

25 The Farside Courtesy Doug Braun

26 What we have learned, are learning, and hope to learn Successes –The phenomenon itself, Neutrinos, J 2, Internal Rotation, Helium abundance, Opacities, Depth of Convection Zone, Structures, etc, etc, etc… Challenges –Origins of solar magnetism –Differential rotation, torsional oscillations, and meridional circulation –Sub-surface inhomogeneities –How all of this should manifest itself in other stars –How these tools can contribute to a predictive understanding of space weather. Frontiers –Asteroseismology & G-modes

27 Dynamo

28 Coexistence of magnetic fields consisting of widely different length scales, magnitudes and temporal scales  Network fields ~ 100 km size Hierarchy in length scale: Hierarchy in flux and/or field strength: Hierarchy in temporal variations:  Spots, active regions, network fields ~ a few thousand Gauss  Persistent, cyclic features: butterfly diagrams, polar reversal, active longitudes  Sunspots, ephemeral regions, plage ~ km diameter  Unipolar regions ~ 100,000 km extent  Plage ~ a few hundred Gauss  Large-scale diffuse fields ~ a few tens of Gauss  Random features: small-scale mixed-polarity turbulent fields

29 What is a dynamo? A dynamo is a process by which the magnetic field in an electrically conducting fluid is maintained against Ohmic dissipation

30 Let’s Build A Homopolar-disc Dynamo A copper disc that can rotate about its axis

31 Let’s Build A Homopolar-disc Dynamo Supply kinetic energy to rotate the disc

32 Let’s Build A Homopolar-disc Dynamo Introduce magnetic fields; an electromotive force between the axis and the rim will be generated

33 A Homopolar-disc Dynamo (Complete) Connect a wire twisted in the same sense as the sense of rotation; magnetic fields will grow

34 Observational signature for systematic, cyclic evolution of solar magnetic fields Courtesy: D.H. Hathaway Many evidences for coexistence of small-scale and large-scale dynamos

35 Large-scale dynamo: historical background (i)Generation of toroidal field by shearing a pre-existing poloidal field by differential rotation (Ω-effect )

36 Large-scale dynamo: historical background (contd.) (ii) Re-generation of poloidal field by lifting and twisting a toroidal flux tube by helical turbulence (α-effect) Proposed by Parker (1955) Mathematically formulated by Steenbeck, Krause & Radler (1969)

37

38 Large-scale dynamo: historical background (contd.) In 1960’s and 70’s, equatorward propagating dynamo wave was obtained by assuming a radial differential rotation increasing inward throughout the convection zone. Equatorward propagation of dynamo wave was obtained by satisfying Parker-Yoshimura Sign Rule; α dΩ/dr < 0, In North-hemisphere Sunspots were identified as that formed from strong toroidal flux tubes which rise to the surface due to their magnetic buoyancy Equatorward migration of sunspot-belt was explained by an equatorward propagating dynamo wave for the subsurface toroidal fields

39 Historical Background (contd.) But, In 1980’s, helioseismic analysis inferred that there is no radial shear in the convection zone, and the strong radial shear at or below the base of the convection zone is decreasing inward at sunspot latitudes. Therefore, Convection Zone Dynamos Do Not Work With Solar-like Ω (Courtesy: Thierry Corbard)

40 FLUX-TRANSPORT DYNAMO Choudhuri, Schüssler, & Dikpati, Meridional circulation Wang & Sheeley, 1991 Durney, 1995 Dikpati & Charbonneau, 1999 Küker, Rüdiger & Schültz, 2001 And certainly many others <

41 Mathematical Formulation Under MHD approximation (i.e. electromagnetic variations are nonrelativistic), Maxwell’s equations + generalized Ohm’s law lead to induction equation : Applying mean-field theory to (1), we obtain the dynamo equation as, Differential rotation and meridional circulation Displacing and twisting effect by kinetic helicity Diffusion (turbulent + molecular) (1) (2)

42 Evolution of Magnetic Fields In a Babcock-Leighton Flux-Transport Dynamo Dikpati & Charbonneau 1999, ApJ, 518, 508 Dynamo cycle period ( T ) primarily governed by meridional flow speed

43 Calibrated Flux-transport Dynamo Model Dikpati, Corbard, Thompson & Gilman, 2001, ApJ, 575, L41 Above value of supergranular diffusivity is consistent with that of Wang, Shelley & Lean, 2002; Schrijver 2002 N-Pole S-Pole Red: α -effect location Green: rotation contours Blue: meridional flow

44 Contours: toroidal fields at CZ base Gray-shades: surface radial fields Observed NSO map of longitude-averaged photospheric fields Validity test of calibration (Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)

45 Predicting the onset of cycle 24 Simulated solar cycles Next cycle will start late in 2007 or early in 2008 (Dikpati et al., 2004, AAS/SPD) 23 (Delayed onset of cycle 24 has also been predicted by Sello 2003 using a different method)

46 Can we go beyond decadal time-scale? Maunder minimum is the absence of sunspots, but not the absence of cycle Can we predict Maunder minima or Medieval maxima?

47 The origin of magnetic fields in the solar interior Dikpati, Gilman & MacGregor (2005, in preparation)  Could solar cycle dynamo be a source for deep interior magnetic fields?  Noticed flux-transport dynamo model diffusing toroidal field into low-diffusivity domain below tachocline. Artifact, or reality?  Long-term transient or permanent?  Nonreversing fields, but structure dependent on initial phase of cycle when diffusion starts?