Large-scale Flows and Dynamo In Solar-Like Stars Gustavo Guerrero Physics Department Universidade Federal de Minas Gerais Brazil P. Smolarkiewicz (ECMWF) A. Kosovichev (NJIT), Elisabete M. de G. Dal Pino (IAG-USP) N. Mansour (NASA Ames) A. Stejko (NJIT)
Magnetic fields in late-type stars Magnetic field in late type stars, Ca II H (396.8nm) and K (393.4nm) (Baliunas et al. 1995)
u rms Ro= 2 Ω0 L 0.47 B R ' HK ( ) Beq From Brandenburg, Saar & Turpin (1998) Stellar magnetic activity is directly related to the stellar rotation rate
Petit+ (2008)
Large-scale magnetic fields in the Sun Poloidal (r,θ) Toroidal (φ) Poloidal (r,θ) Toroidal (φ) How does it work? Turbulent dynamo (mean-field theory), Flux-transport dynamo, Babcock-Leighton α
Solar Mean flows: differential rotation
Solar Mean flows: meridional circulation Surface Sub-surface old beliefs New findings Zhao+ (2103) Ulrich (2010) See also: Schad+ (2013)
Global models
Anelastic simulations with the MHD-EULAG code Anelastic approximation (Lipps & Helmer 1982, Lipps 1990) (Guizaru+ 2010, Racine+ 2011, Smolarkiewicz & Charbonneau 2013, Cossette+ 2013, Guerrero+ 2013, Guerrero+ 2015)
HD
Differential rotation in solar-like stars a) Ω0 = 0 b) Ω0 = Ω /2 c) Ω0 =Ω d) Ω0=2Ω Guerrero+ (2013)
a) T = 112d (Ω0=Ω /4 ) c) T = 28d (Ω0=Ω ) b) T = 56d (Ω0=Ω /2) d) T = 14d (Ω0=2Ω ) SOLAR DYNAMO FRONTIERS WORKSHOP HELIOSEISMOLOGY 3D MODELING AND DATAGuerrero+ ASSIMILATION (2013)
Differential rotation profile is defined by the balance between buoyancy and Coriolis forces defined by the Rossby number (Ro). Solar-like (fast equator) and anti-solar modes (faster poles) are obtained. (see Käpylä+ 2011, Guerrero+ 2013, Featherstone & Miesch, 2015) Ω eq Ω 60 Ω0 o Gastine+ (2014) Guerrero+ (2013) SOLAR DYNAMO FRONTIERS WORKSHOP HELIOSEISMOLOGY 3D MODELING AND DATA ASSIMILATION
MHD
Stellar Mean-flows and Dynamo a) T = 7d b) T = 14d d) T = 56d e) T = 112d c) T = 28d f) T = 224d
The differential rotation profile depends now on the balance between buoyancy, Coriolis and Lorentz forces Ω eq Ω 60 Ω0 o Rengarajan (1984) SOLAR DYNAMO FRONTIERS HELIOSEISMOLOGY 3D MODELING AND DATA ASSIMILATION Looking forward forworkshop Tim Reinhold's talk
Stellar Dynamos T = 7d T = 56d T = 14d T = 112d T = 28d T = 224d
B (surface) vs Ro
The role of tachoclines in stellar dynamo simulations (Guerrero+ 15)
Models without tachocline Models with tachocline
Models without tachocline (Butterfly diagrams at r=0.95r ) Models with tachocline
Turbulent coefficients FOSA (Northern hemisphere) T=14d T=28d T=56d
Shear source terms C θ Ω C r Ω T=14d T=28d T=56d
Model CZ02 Tc=2.2 yr Time [yr] θ Ω>0, r Ω> 0, α> 0 α> 0 Radial DW upwards Lat. DW poleward
Model RC02 Tc=34.5 yr Time [yr] Conv. Zone Tach. (Eq) Tach. (pole) NSSL θ Ω>0, r Ω> 0, r Ω< 0, r Ω< 0, α> 0 α> 0 α> 0 α< 0 upwards poleward equatorward poleward
Who process governs the cycle period? 13 2 1 9 2 1 According with MLT estimations, ηt 10 cm s =10 m s (mean field models result in periods ~2-8 yr), η-quenching does not help much with the cycle period (Rudiger+ 94, Tobias 96, Gilman & Rempel 05, Guerrero+ 09, Muñoz+11). MLT Christensen-Dalsgard 96 η-quenching effect on mean-field dynamo models + Beq = 104 Beq = 103 Muñoz+ (2011) Guerrero+ (2009)
2 τ ηt = urms ( FOSA) 3 t t RC d CZ d = 2 RC 2 CZ RC t CZ t L /η L /η 19 Despite the field production is distributed over the simulation domain, the dynamo period is regulated by the diffusion time of the magnetic field at the deeper, more stable layers
CONCLUSIONS LES & ILES are promising tools to explore turbulent problems. MHD-EULAG code is a powerful code to study solar/stellar mean-flows and dynamo Tachoclines play an important role un solar and stellar dynamos Due to the highly sub-adiabatic stable region, all the simulations exhibit the formation of a tachocline. Besides, by choosing the appropriate stratification, a near-surface shear layer is obtained. For all the simulations at the solar rotation rate the meridional flow is multicellular. The simulations that reproduce the NSSL develop a poleward meridional flow at the surface and higher latitudes. Dynamo models without tachocline result in oscillatory solutions with short cycle period (~2yr). Dynamo models including a tachocline result in oscillatory solutions with long cycle period (>30yr). The strongest field developed in this radial shear layers dominates the evolution of the global field.
Thanks
The Near Surface Shear Layer