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Modeling solar cycle irregularities
using flux transport dynamo modelsBidyaBidya BinayBinay KarakKarak
PhD studentIndian Institute of Science
Collaborators:Collaborators:Prof. Arnab Rai Choudhuri (IISc, Bangalore)Dr. Dibyendu Nandy (IISER, Kolkata)
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Sunspot number of last 300 years
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Dikpati et al. (2008) claim that the Waldmeier effect does not exist in sunspot area data
Karak & Choudhuri (2011)
Waldmeier effect:Inverse correlation between the rise time and the cycle amplitude
-- Waldmeier (1935)
WE1 => anti-correlation between the rise times and the amplitudesWE2 => positive correlation between the rise rates and the amplitudes
Sunspot number Sunspot area
WE1
WE2
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Maunder minimum period = 1645 to 1715 (Eddy, 1976; Foukal, 1990; Wilson, 1994)
68% of days were observed (Hoyt & Schatten 1996)
Maunder minimum:
Study of cosmogenic isotopes - C14: 27 grand minima in last 11,000 years (Usoskin et al. 2007)
Grand minima: => Periods of strongly reduced activity
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Flux Transport dynamo
High diffusivity model Low diffusivity modelηt = 1012 - 1013 cm2 s-1 ηt = 1010 - 1011 cm2
s-1
Mixing length theory gives cm2 s-112(1/ 3) 10l v
(Durney 1995; Choudhuri, Schussler & Dikpati 1995)
Time scale of turbulent diffusion: (where L = depth of the convection zone.)
~ 2.8 years (ηt = 5×1012cm2/s).
~ 276 years (ηt = 5×1010cm2/s).
2
t
L
Turbulent diffusivityηt
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Meridional circulation:Comes from the combination of Buoyancy forces, Reynolds stresses, Latitudinal pressure gradients and Coriolis forces acting on the mean zonal flow(Kitchatinov & Rudiger 1995; Miesch 2005)
Near the surface its value ~ 20 m/s and it is poleward. (Hathaway 1996; Haber et al. 2002; Basu & Antia 2000)
Taken from Yeates et al. (2008)
Using the mass conservationprinciple we construct the fullprofile of the MC.
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Did the meridional circulation vary largely?
In flux transport dynamo:
0.890
1v
Period
Taken from Karak & Choudhuri (2010)
(Dikpati & Charbonnea 1999)
Wang et al. (2002); Hathaway et al. (2003); Javaraiah & Ulrich (2006)---amplitude of MC varied largely with the solar cycle.
0.8850
1v
Period
(Yeates, Nandy Mackey 2008)
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Sources of irregularities in flux transport dynamo
Fluctuations inB-L process of generating
poloidal field
Fluctuations inmeridional circulation
High diffusivity
Can explain the correlation between thepolar field and the next sunspot cycle
Jiang, Chatterjee & Choudhuri (2007)
Low diffusivity High diffusivity Low diffusivity
? ?Yeates, Nandy & Mackey (2008)
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Effect of Fluctuations of Meriodional circulation
22
1... ( ) ( . )ptB B s Bt s
In high diffusivity modelIn low diffusivity model
More time toinduct toroidal field
More timefor the diffusion
Weaker cycleStronger cycle
Meriodinal circulation
(Yeates, Nandy & Mackey 2008)2
2
1... ( )tA A St s
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Modeling last 23 cycles using variable meridional circulationFrom High diffusivity Model (Chatterjee, Nandy & Choudhuri 2004)
Karak (2010)
0.700
1v
Period In this model,
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On repeating the same calculation in Low diffusivity Model(Dikpati & Charbonneau 1999)
Karak (2010)
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Introducing stochastic fluctuationsin poloidal field source term
Theoretical study of Waldmeier effect
Karak & Choudhuri (2011)
in meriodional circulation
WE1
WE2
WE1
WE2
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1) Fluctuation in meriodional circulation is required to explain WE.
2) Only high diffusivity model is able to explain WE.
Introducing stochastic fluctuations in
Karak & Choudhuri (2011)
WE2
WE1
WE2
WE1
meriodional circulationpoloidal field source term +
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ball
Karak (2010)
It reproduces the strong asymmetry(Ribes & Nesme-Ribes 1993; Sokoloff & Nesme-Ribes 1994).
Can a large fluctuation in meriodional circulation lead to a Maunder-like minimum?
Close
close
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close
Karak (2010)
Sudden initiation of MM but gradual recovery (Usoskin et al. 2000)
Observed
Theoretical
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If we decrease the poloidal field to a very low valueat the beginning of the Maunder minimum, then we can reproduce a Maunder-like grand minimum.
Choudhur & Karak (2009)
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Effect of Turbulent Pumping on Solar Cycles Memory: Investigations using a Kinematic Dynamo Model
Authors: Bidya Binay Karak & Dibyendu Nandy
Please visit the poster – P19on
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Repeat the same calculation in Low diffusivity model
Karak (2010)
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From the study of 14C data in tree rings, Miyahara et al. (2004, 2010) say that the solar cycle was continued during Maunder minimum, but with a period of 13–15 yr instead of regular 11-yr period
Karak (2010)
It explains the cyclic behaviour of solar activity (Schwabecycle) during MM (Beer et al. 1998, Miyahara et al. 2004)