Leibniz-Institut für Astrophysik Potsdam The existence of the Λ effect indicated by SDO data G....
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Leibniz-Institut für Astrophysik Potsdam The existence of the Λ effect indicated by SDO data G. Rüdiger, M. Küker Göttingen 2014
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Transcript of Leibniz-Institut für Astrophysik Potsdam The existence of the Λ effect indicated by SDO data G....
Leibniz-Institut für Astrophysik PotsdamLeibniz-Institut für Astrophysik Potsdam
The existence of the Λ effectindicated by SDO data
G. Rüdiger, M. Küker
Göttingen 2014
ROTATING TURBULENCEBoussinesq (1897), Taylor (1915):
Stress-strain relation, eddy viscosity
for rotation
negative through the whole convection zone
Göttingen 2014
MAGNETIC OBSERVATIONSMAGNETIC OBSERVATIONS
BUT: no confirmation by observations Ward 1965, Gilman & Howard 1984, Balthasar et al. 1986, Vrsnak et al. 2004
Göttingen 2014All tracers are magnetic-defined
Nesme-Ribes et al. 1993
Q𝜃𝜙 ≈ 107 cm2/s2
SDO DATASDO DATA
Göttingen 2014
Hathaway et al. 2013
Giant cells, 200 Mm,
Persisting over months
GIANT CELLS GIANT CELLS
Göttingen 2014
Hathaway et al. 2013
ROTATING & ANISOTROPIC TURBULENCEROTATING & ANISOTROPIC TURBULENCE
Rigid rotation: two possible tensors (odd in 𝛺, even in g )
Käpylä et al. 2011
Q𝜃𝜙 >0Q𝜃𝜙 <0Q𝜃𝜙 =0
Göttingen 2014
ANGULAR MOMENTUM TRANSPORTANGULAR MOMENTUM TRANSPORT
Göttingen 2014
V, H are functions of the Coriolis number 𝛺* =2𝜏corr 𝛺
• V < 0 for small 𝜏corr (inward transport)• H > 0 always (equatorial transport)
SOCA theory:RKH 2013
THE BASIC MODELTHE BASIC MODEL
Göttingen 2014
Solution of the conservation law of angular momentum
without meridional flow div (r sin𝜃 𝜚Q )=0.equation cubic in 𝛺, H=1, V=0, 𝜚=const:
No dependence on the viscosity, inner part: W>0. outer part: W<0
IMPROVED MODELIMPROVED MODEL
Göttingen 2014
V=-0.1, H= 1 for x<0.95, strong density gradient
W>0 in the bulk of the convection zone
COMPLETE MODELS WITH MERIDIONAL COMPLETE MODELS WITH MERIDIONAL CIRCULATIONCIRCULATION
Göttingen 2014
With 𝜦, meridional flow(polewards ) Without 𝜦, only meridional flow(equatorwards) Kippenhahn, Köhler, Pitadella et al., Balbus et al.Küker & R. 2012
Göttingen 2014
MERIDIONAL CIRCULATIONMERIDIONAL CIRCULATION
Schad et al. ´12
One-cell
meridional circulation?
HORIZONTAL REYNOLDS STRESSHORIZONTAL REYNOLDS STRESS
Göttingen 2014
withΛ effect,W=0.14
without Λ effect,W<0
Göttingen 2014
MAIN-SEQUENCE MODELSMAIN-SEQUENCE MODELS
MOST stars: ε Eri, Prot= 11 days, k=0.11. κ1 Ceti, Prot=9 days, k=0.09
kmod =0.12kmod =0.13
Theory: Weak dependence of δ𝛺 on 𝛺
OBSERVATIONSOBSERVATIONS
Göttingen 2014
Barnes et al. 2005
Reinhold et al. 2013
Kepler data
CONCLUSIONCONCLUSION
Göttingen 2014
If a mean-field formulation is possible
and if Hathaways measurements reflect
the horizontal Reynolds stress
the Λ effect exists
