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The Solar Cycle: Observations and Dynamo Modeling

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The Solar Cycle: Observations and Dynamo Modeling The Solar Cycle: Observations and Dynamo Modeling Mausumi Dikpati HAO/NCAR 1 Some milestones in defining solar cycle 1611: discovery of sunspot with telescope Some milestones in defining the solar cycle (contd.) Heinrich Schwabe 1843: Sunspot cycle with periodicity of ~10 year (Astronomische Nachrichten, vol. 20., no. 495, 1843) Richard Christopher Rudolf Wolf Carrington 1860: 1848: Differential rotation from Historical sunspots reconstruction of sunspot cycle Some milestones in defining the solar cycle (contd.) Edward Maunder 1890: Butterfly diagram; signature of cycle (original diagram resides at HAO) Latitude Time George Ellery Hale 1908: Strong magnetic fields in sunspots What causes solar cycle? If solar magnetic fields were primordial, they wouldn’t vary cyclically Furthermore if there wouldn’t have been regeneration of magnetic fields, all would have vanished from the convection zone in just 10 years Hypothesis: There must be an oscillatory dynamo inside the Sun which is responsible for generation and cyclic evolution of magnetic fields What is the nature of that dynamo? Milestones in understanding the solar cycle Eugene Parker (1955) proposed the first solar dynamo model by including the Sun’s differential rotation and helical turbulence Parker’s model can be understood if the Sun’s vector magnetic fields be decomposed into its toroidal and poloidal components Generation of toroidal field by shearing a pre-existing poloidal field by differential rotation (Ω-effect ) Milestones in understanding the solar cycle To close the dynamo loop, it is necessary to regenerate the poloidal fields from toroidal fields Parker proposed the re- twisting generation of poloidal field by lifting and lifting twisting a toroidal flux Field line tube by helical turbulence (α-effect) • Parker obtained an equatorward-propagating oscillatory dynamo-wave solution from his model • He introduced the concept of “magnetic buoyancy” to explain how magnetic flux rises to the surface of the Sun • Identifying the sunspots as the toroidal fluxtubes risen to the surface, their equatorward propagation was explained by the dynamo wave Evidence of twisted loops from 3D MHD simulations Nelson, Brown, Brun, Miesch & Toomre, 2014, Solar Phys. Conditions for equatorward propagation of dynamo wave German school (Steenbeck, Krause & Radler 1969) developed mean-field formalism to mathematically solve for equatorward dynamo wave solution •Rising convective plume expands into lower density layers •Coriolis force (NH) turns flow vectors to their right •Thus , curl V < 0, clockwise vorticity is generated dΩ/dr < 0 •For rising plume, w > 0 •So kinetic helicity < 0 in NH α > 0 •For isotropic turbulence, α ~ -(kinetic helicity) So α > 0 (NH) The first theoretical solution of solar cycle from an oscillatory αω dynamo In 1960’s and 70’s, equatorward propagating dynamo wave was obtained by assuming a radial differential rotation increasing inward throughout the convection zone. 3D mean-field αω dynamo Stix (1971) formulated a classical 3D αω dynamo with the aim of understanding sector boundary structure, which shows a certain large-scale longitude dependence that varies with solar cycle An alternative concept for identifying the poloidal field generation developed by Babcock (1961) and Leighton (1969) Identifying the poloidal source as arising from the decay of tilted, bipolar active regions α > 0 Babcock and Leighton showed the poleward dispersal of the large-scale poloidal fields, and dΩ/dr < 0 hence the polar reversal every 11 -year can be α-effect works explained by preferential poleward drift of near the surface, trailing flux by a random walk from Ω-effect in the convection zone supergranules. Long-term modulation of amplitude of 11-year solar cycle Jack Eddy (1976) reexamined historical sunspot records as well as geomagnetic and C14 concentration to definitively show the existence of multicycle time durations of extremely low solar activity The grand minimum occurred between 1645-1715 he named the “Maunder minimum” Little Ice age and Maunder minimum A new search for differential rotation and dynamo model Gilman & Miller (1981): development of first full 3D convective dynamo Helicity Differential rotation negative at (cylindrical contours): sunspot Taylor-Proudman state latitudes ∂Ω∕∂r > 0 α > 0 Poleward migration of toroidal fields was found (Gilman 1983) So either the differential rotation or the dynamo was wrong ! This new challenge led to further development of full 3D convective models; therefore solar dynamo model developments proceeded on two parallel tracks since 1980s: (i) mean-field approach and (ii) full 3D convective simulation Biggest challenge posed by helioseismology in 1990s Thompson (1991) and colleagues showed: convection zone base is located at 0.713R; below is radiative zone, and above is subadiabatic overshoot zone Tim Brown (1989) and colleagues showed there is almost no ∂Ω∕∂r in convection zone, and strong ∂Ω∕∂r > 0 exists at convection zone base at low latitudes Biggest challenge posed by helioseismology in 1990s Thompson (1991) and colleagues showed: convection zone base is located at 0.713R; below is radiative zone, and above is subadiabatic overshoot zone Tim Brown (1989) and colleagues showed there is almost no ∂Ω∕∂r in convection zone, and strong ∂Ω∕∂r > 0 exists at convection zone base at low latitudes Mean-field αω convection zone dynamos do not work for the Sun ! Storage issue of strong toroidal field in the turbulent convection zone became highlighted. Can toroidal fields be stored long enough at cz base to be amplified to the strength needed to produce sunspot fields at the surface? Plausible remedy I: Thin-layer dynamos Ed DeLuca Cherri Morrow Axel Brandenburg (PhD thesis) (Grad Student (HAO Postdoc in 1990s) in 1990s) Explored thin-layer dynamos, locating the shear layer as well as α-effect in a thin layer at the base of the convection zone See De Luca & Gilman 1986 Gilman, Morrow & De Luca 1989 Brandenburg & Charbonneau 1992 Ferriz-Mas, Schmitt & Schuessler 1994 Plausible remedy II: Interface dynamos Paul Charbonneau Keith Macgregor Colin Roald (Grad student in late 1990s) Explored interface dynamos, locating the shear layer below the core-envelope interface and α-effect above that See Parker 1993 MacGregor & Charbonneau 1996 Tobias 1996 Charbonneau & Macgregor 1997 Roald 1997 Another big challenge from magnetogram . Sunspot-belt migrates equatorward . Large-scale diffuse fields drift poleward . There is a phase relationship between these two components; polar reversal happens during sunspot maximum A paradigm shift: Babcock-Leighton flux-transport 1R dynamos Observed NSO map of Pole 0.7R longitude-averaged 0.6R photospheric fields Meridional + circulation Equator Wang & Sheeley, 1991 Choudhuri, Schüssler, & Dikpati, 1995 Durney, 1995 Dikpati & Charbonneau, 1999 Dick White Küker, Rüdiger & Schültz, 2001 And many others Giuliana Contours: toroidal fields at CZ base de Toma Gray-shades: surface radial fields Dikpati, de Toma, Gilman, Arge & White 2004 2D dynamical Babcock-Leighton flux-transport dynamos Matthias Rempel Lorentz force (jXB) back- Combining reaction creates thermal effect curvature stress which along with jXB creates, in turn, prograde back-reaction, and retrograde jets on top mean-field flux- of average rotation – can transport explain torsional dynamos can oscillation at high simulate low- latitudes. latitude torsional oscillation 2D Babcock-Leighton flux-transport dynamo-based prediction scheme 3 predictions were Delayed onset of cycle 24 ✓ issued for solar Strong cycle 24 ✗ cycle 24: South stronger than North ✓ Dikpati, De Toma & Gilman 2006 Dikpati et al. 2007 Dikpati et al. 2010 2D Babcock-Leighton flux-transport dynamo-based prediction scheme 3 predictions were Delayed onset of cycle 24 ✓ issued for solar Strong cycle 24 ✗ cycle 24: South stronger than North ✓ Reasons for failure in amplitude prediction: Dikpati et al. Bernadett Belucz is investigating N/S (2006) did not asymmetry in solar cycle (her PhD thesis) consider phase- shift between North and South Wrong tilts of a few large spots at the end of cycle 23 may have reduced the poloidal seed field Data was nudged for entire 12 cycles without frequent updates 3D Babcock-Leighton flux-transport dynamos At low latitudes, small- scale features appear due to eruption of tilted bipolar spots, but their dispersal by diffusion, meridional circulation and differential rotation produces mean poloidal Mark Miesch fields • Trailing flux drifts towards the poles in a series of streams and cause polar reversal • Toroidal field butterfly diagram shows equatorward migration, cycle period is governed by meridional circulation Miesch & Dikpati (2014); See also Yeates & Munoz-Zaramillo (2013) Nelson et al. (2013) Full 3D convective dynamo simulations I. Miesch & colleagues Augustson et al. (2015) Grand Minimum! Kyle Augustson (ASP Postdoc) Origins of Flux Emergence! Full 3D convective dynamo simulations II. Fan & Fang Solar convective dynamo: self-consistent maintenance of the solar differential rotation and emerging flux (Fan and Fang 2014, ApJ, 789, 35) Summary First solar dynamo model was built 70 years ago Babcock-Leighton flux-transport solar dynamos were created as a paradigm shift to overcome challenges posed by helioseismology and magnetic butterfly diagram, and remain as a leading class of solar dynamo models Full 3D convective dynamos are continuing in a parallel track since the first model of Gilman & Miller (1981), and have reached the level that they self-consistently produce cycles and flux emergence HAO has always been one of the leaders in both dynamo approaches 3D Babcock-Leighton dynamo models are progressing for operating in data- assimilative mode and hence are showing prospects for improvements in predictions Ultimate goal is to merge the two parallel approaches and build a grand solar dynamo model .
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