THE SOLAR DYNAMO Mausumi Dikpati High Altitude Observatory, NCAR - PowerPoint PPT Presentation

THE SOLAR DYNAMO Mausumi Dikpati High Altitude Observatory, NCAR High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

Organization • Motivation (comes from observations) • Historical Background (first global solar dynamo models half a century ago) • Recent Models; Flux-transport Dynamos (compatible with recent advances in helioseismology) • Comparison Of Model Output With Observations (suitable proxies need to be developed from model output) • Summary (successes; difficulties; possible refinements) • Where Are We Now? (can we predict solar cycle features?)

Manifestations of Solar Activity Cycle • Appearance and variations in the number of sunspots with an 11-year periodicity • Reversal of the Sun’s polar field after every 11-year • Large-scale coronal variations

Observed butterfly diagram Courtesy: D.H. Hathaway • Sunspots are believed to be formed from strong toroidal flux tubes that 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

Historical Background Click to see movie (i) Generation of toroidal field by shearing a pre-existing poloidal field by differential rotation ( Ω -effect )

Historical Background (contd.) Click to see movie (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)

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 d Ω /dr < 0, In North-hemisphere

Observational constraints • 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. (Courtesy: Thierry Corbard) Therefore, Convection Zone Dynamos Do Not Work With Solar-like Ω

More Observational Constraints Evolution of large-scale, diffuse fields • Weak diffuse fields drift poleward in contrast to equatorward migration of sunspot belt • But maintain a 90-deg phase relation with the sunspots • Polar reversal takes place during sunspot maximum • Polar field changes sign from negative to positive when subsurface toroidal field is positive Dikpati & Choudhuri 1995, SolP, 161, 9 [Data source: How ard (NSO) and Wang (NRL)]

Flux-transport Models Click to see movie Poleward drift of large-scale diffuse fields was explained by invoking a meridional circulation. A θ - Φ surface model by NRL Group in 1989 An r- θ model : Dikpati’s thesis 1996

What is a Flux-transport Dynamo? Pole + Meridional circulation 0.6R 1R 0.7R ⇒ FLUX-TRANSPORT DYNAMO Equator (Wang & Sheeley, 1991, ApJ, 375, 761) (Choudhuri, Schüssler, & Dikpati, 1995, A&A, 303, L29.) (Durney, 1995, SolP, 160, 213.) (Dikpati & Charbonneau, ApJ, 1999, 518, 508) (Küker, Rüdiger & Schültz, A&A, 2001, 374, 301)

Observational Evidence of Meridional circulation and Differential rotation Doppler measurements: Equator Duvall, 1979 Helioseismic inversions: Ulrich et al. 1988 Brown et al. 1989 Cavallini, Ceppatelli & Righini 1993 Goode et al. 1991 Hathaway 1996 Tomczyk, Chou & Thompson 1995 Hathaway et al. 1996 Kosovichev 1996 Magnetic tracer : Charbonneau et al. 1997 Komm, Howard & Harvey 1993 Corbard et al. 1998 Helioseismic inversions: Giles et al. 1997 Braun & Fan 1998

Mathematical Formulation Under MHD approximation (i.e. electromagnetic variations are nonrelativistic), Maxwell’s equations + generalized Ohm’s law lead to induction equation : ∂ B ( ) . = ∇ × × − ∇ × η U B B (1) ∂ t Applying mean-field theory to (1), we obtain the dynamo equation as, ∂ B ( ) , = ∇ × × + − ∇ × α η (2) U B B B ∂ t Diffusion Differential rotation (turbulent + molecular) and meridional circulation Displacing and twisting effect by kinetic helicity

Mathematical Formulation (continued) Under the assumption of axisymmetry, we write; ( ) , ( ) ( ) ( ) ( ) = + ∇ × = + B r , θ , t ˆ A r , θ , t ˆ r , θ r sin θ Ω r , θ ˆ , B e e U u e φ φ φ φ Toroidal field Poloidal field Meridional Differential circulation rotation We obtain the following two scalar equations: ∂ ( ) ⎛ ⎞ A 1 1 ( )( ) 2 + ⋅ ∇ = ∇ − + ⎜ ⎟ r sin θ A η A S r , θ , B φ B u (3a) φ , ∂ 2 2 t r sin θ ⎝ ⎠ r sin θ ∂ ∂ ( ) ∂ ( ) ⎥ B φ 1 ⎡ ⎤ + + ru B u B ⎢ r φ θ φ ∂ ∂ ∂ ⎣ ⎦ t r r θ ( ) ⎛ ⎞ 1 2 = ⋅ ∇ − ∇ × ∇ × + ∇ − ⎜ ⎟ r sin θ Ω η B ˆ η B B e p φ φ φ , (3b) 2 2 ⎝ ⎠ r sin θ

Mathematical Formulation (continued) Schematic diagram Babcock 1961, ApJ, 133, 572 A Babcock-Leighton type poloidal source-term can be represented as, − 1 ( ) ⎡ ⎤ 2 ⎡ ⎤ ⎡ ⎤ ⎛ − ⎞ ⎛ − ⎞ ( ) 1 r r r r B φ r , θ , t 3 2 = + ⎜ ⎟ − ⎜ ⎟ × + S r , θ , B S sin θ cos θ 1 erf 1 erf ⎢ 1 ⎥ . ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ φ 0 4 d d B ⎝ ⎠ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 2 3 0 Latitude Confines in a thin layer Quenching dependence near the surface Amplitude

Boundary Conditions Diffusivity profile ( ∇ A=0, B φ =0 2 - 1 / r 2 s i n 2 θ ) A = 0 , Polar Axis B φ = A 0 = 0 , B φ = 0 0.7 R 1 R 0.6 R Equator ∂ A = = 0 , B 0 φ ∂ θ

Evolution of Magnetic Fields In a Babcock-Leighton Flux-Transport Dynamo Click to see movie

Time-latitude Diagrams Produced from the Babcock-Leighton Flux-transport Dynamo Solution Toroidal Field at r = 0.7R • Equatorward migrating Pole sunspot belts Latitude (degree) • Poleward drifting large-scale radial fields Equator • Correct phase relation 0 10 20 30 40 50 between these two fields t (yr) Surface Radial Field Pole • Dynamo cycle period ( T ) Latitude (degree) primarily governed by meridional flow speed − − = 0 . 89 0 . 13 0 . 22 T 56 . 8 υ s η , m 0 t Equator → υ max. flow speed 0 10 20 30 40 50 m → s surface poloidal source t (yr) 0 → η turbulent diffusivit y T Dikpati & Charbonneau, 1999, ApJ, 518, 508

Difficulties 1. A Babcock-Leighton dynamo is not self-excited; how can it revive after Maunder minima? 2. Furthermore, N & S hemispheres are coupled by an antisymmetric magnetic field about the equator, as inferred from Hale’s polarity rule But, a full-spherical-shell Babcock-Leighton dynamo relaxes to symmetric magnetic fields about the equator

Full Spherical Shell Solutions Dynamo driven by Babcock-Leighton alpha-effect produces Click to see movie incorrect field symmetry, violating Hale’s polarity rule Dynamo driven by tachocline alpha-effect produces Click to see movie solar-like field symmetry, satisfying Hale’s polarity rule Dikpati & Gilman, 2001, ApJ, 559, 428 Bonanno et al, 2002, A&A, 390, 673

Summary • Large-scale solar dynamo mechanism involves 3 basic processes; (i) Ω -effect, (ii) α -effect, (iii) flux-transport by meridional circulation • Mean meridional flow sets the solar clock • Sun is likely to have both Babcock-Leighton type and tachocline α -effect.

“Peculiar” Features Of Cycle 23 Sunspot index graphics The monthly (blue) & monthly smoothed (red) sunspot numbers for the latest five cycles 250 Sunspot Number Monthly 200 Smoothed Spot Number 150 100 19 20 21 22 23 50 0 1960 1970 1980 2000 1990 Time (years) • Rise of this cycle was slow compared to other odd cycles • It never reached the expected strength • It showed a second peak during its declining phase, unusual for an odd cycle

Building A Flux-transport Dynamo-based Prediction Scheme We postulate that “magnetic persistence”, or the duration of the Sun’s “memory” of its own magnetic field, is controlled by meridional circulation.

Correlation Between Polar Field And Sunspot Field Derived From A Stochastic Flux-transport Dynamo Charbonneau & Dikpati, 2000, ApJ, 543, 1027 Observationally verified by Hathaway et al, 2002

Polar Field Features Of Cycle 23 Polar field pattern • Polar reversal in cycle 23 was unusually slow • After the reversal, polar field build-up was slow • S-polar field reversed ~1 yr after the N-polar field • During 1993-1999, N- and S-polar field patterns show distinctly different features • S-polar fields were stronger than N-polar fields during minima of 21 and 22