grand minima and the predictability of the solar cyclebidya_karak/hao_talk.pdf · grand minima and...
TRANSCRIPT
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Bidya Binay KarakPhD student
Indian Institute of ScienceCollaborators:Prof. Arnab Rai Choudhuri (IISc, Bangalore)Dr. Dibyendu Nandy (IISER, Kolkata)
Grand minima and
the predictability of the solar cycle
Bidya Binay KarakPhD student at Indian Institute of Science
Presently at HAO/NCAR
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Layout of the talk:Observational data of solar cycle in
past.Then use flux transport dynamo model
to explain the irregular features of solar cycle.
Karak & Nandy submitted to Physical Review Letters
Choudhuri & Karak submitted to Physical Review Letters8
Karak 2010, ApJ, 724, 1021
Choudhuri & Karak 2009, Res. Astron. Astrophys., 9, 953
References:
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Maunder minimum period = 1645 to 1715 (Eddy, 1976; Foukal, 1990; Wilson, 1994)
It is a real phenomenon! (Sokoloff & Nesme-Ribes 1994; Hoyt & Schatten 1996)
Maunder minimum
Hadsfddfa
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North-South Asymmetry:
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13.5-15.5yrs (14.4yrs)
Frequency(1/yr)
Periods were longer (Δ14C results) – Miyahara et al. (2004)
0.20
0.16
0.12
0.08
0.041640 1660 1680 1700 1720
How to study solar activity in past?
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27 grand minima in last 11,000 years(from C14 data by Usoskin et al. 2007)
C14data:
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Yearly Averaged Sunspot Numbers 1610-2000
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Modeling grand minima and
Understanding the predictability
of the solar cycle
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Toroidal fieldPoloidal field
Dynamo theory
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Toroidal fieldPoloidal field
How?
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Toroidal Field Generation (ω Effect)
Observationally verified(Schou et al. 1998; Charbonneau et al. 1999)
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Toroidal fieldPoloidal field
How?
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1. The Mean Field α-effect or classical α-effect
• Buoyantly rising toroidal field is twisted by helical turbulent convection, creating loops in the poloidal plane• The small-scale loops diffuse to generate a large-scale poloidal field
α-effect – works only if B is not very strong
Earlier dynamo models were mostly based on this alpha effect!
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2. Poloidal Field Generation:–Babcock–Leighton alpha effect: (Babcock 1961; Leighton 1969; Dasi-Espuig et al. 2010)
Not self excited!
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Toroidal fieldPoloidal field
Differential rotation
Helical alpha effect + Babcock-Leighton mechanism
Dynamo theory
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Building dynamo model
• Induction equation:
2( )B v B Bt
Evolution of mean (large scale) field is given by
2( )l Tl l l lB v B B Bt
Our approach is kinematics (velocity field is given)
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Velocity field= ( , ) s i n r rr r e v e v e angular frequency meridional circulation
Poloidal field evolution:
Toroidal field evolution:
In axisymmetry case
( , ) [ ( , ) ]lB B r e A r e
22
1 1( ) ( ) ( ) ( . )
1 ( )
r t p
t
B rv B v B B s Bt r r s
rBr r r
22
1 1( . )( ) ( )pA v sA A Bt s s
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Region of toroidal field
generation
Region of poloidal field
generation
Flux Transport Dynamo(Durney 1995; Choudhuri, Schussler & Dikpati 1995;
Dikpati & Charbonneau 1999)
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ƞ ~ (1/3) l v = 1012-1013 cm2/s ???
Turbulent diffusivity (ηt)
Important ingredients of flux transport dynamo
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Meridional circulation:Near the surface its value ~ 20 m/s and it is poleward. (Hathaway 1996; Haber et al. 2002; Basu & Antia 2000)
Use mass conservation principle to construct the full profile of the meriodional circulation
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Poloidal field evolution:
Toroidal field evolution:
Dynamo simulation:
22
1 1( ) ( ) ( ) ( . )
1 ( )
r t p
t
B rv B v B B s Bt r r s
rBr r r
22
1 1( . )( ) ( )pA v sA A Bt s s
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Chatterjee et al. (2004)
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Regular process Random process+
Solar cycle
Hadsfddfa
???
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Solar cycle
Or
Nonlinear chaotic system?The modulation of the solar cycle is due to the chaotic nature of the dynamo process?
???
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α-quenching: ;
Long history – Stix 1972; Ivanova & Ruzmaikin 1977; Yoshimura 1978; Schmitt & Schussler 1989, Krause & Meinel 1988; Brandenburg et al. 1989 ……….
Has a stabilizing effect instead of producing irregularities
Weiss, Cattaneo & Jones (1984) found chaos in some highly truncated models
Nonlinearity is definitely there!Because magnetic field acts on the velocity field
22
1.. . ( )pA A Bt s
Charbonneau, St-Jean & Zacharias (2005), Charbonneau, Beaubien & St-Jean (2007) – The odd-even effect (Gnevyshev-Ohl rule) may be due to period doubling just beyond bifurcation point
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Regular process Random process+
Solar cycle
Hadsfddfa
Our point of view:
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Are the grand minima merely extremes of cycle irregularities?
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How to model Maunder minimum?
Hadsfddfa
Well, find out the sources of randomness in dynamo model.
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Region of toroidal field
generation
poloidal field generation
Sources of randomness in flux transport dynamo
Fluctuations inBabcock-Leighton process of
poloidal field generation
Fluctuations inmeridional circulation
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Fluctuations in Babcock-Leighton process
Depends on: Tilt angle, total magnetic flux from active regions, meridional circulation
Dikpati & Charbonneau (2000); Choudhuri et al. (2007); Jiang et al. (2007); Dasi-Espuig et al. (2010) Kitchatinov & Olemskoy (2011)
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Charboneau, Blais-Laurier & St-Jean (2004) – Low diffusivity dynamo simulation with fluctuations in α (100% level)
Intermittencies over several periods
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Modeling Maunder minimum?
Give a large fluctuation in the poloidal field!
To reproduce Maunder minimum:
1. stop the code at a solar minimum.
2. change the poloidal field in the following way:AN = 0.0ANAS = 0.4AS
3. run the code for several cycles.
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ballTheoretical
Observed
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ball Theoretical
Observational
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Fluctuations in meridional circulation
Hathaway & Rightmire (2010)
Coming from slight imbalance between two large terms – the centrifugal term and
the latitudinal temperature gradient term
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Indirect evidence of variation of meridional circulation
Wang et al. (2002)
Hathaway et al. (2003)
Javaraiah & Ulrich (2006)
Passos & Lopes (2008)
Karak (2010)
Karak & Choudhuri (2011)
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Did the meridional circulation vary largely?
In flux transport dynamo:
0.890
1v
Period
(Dikpati & Charbonnea 1999)
0.8850
1v
Period
(Yeates, Nandy & Mackey 2008)
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Effect of fluctuations of meridional circulation
In high diffusivity modelIn low diffusivity model
More time toinduct toroidal field
More timefor the diffusion
Weaker cycleStronger cycle
Meridional circulation
(Yeates, Nandy & Mackey 2008)
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ball
Can a large fluctuation in meridional circulation lead to a Maunder-like minimum?
Close
close
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close
Observed
Theoretical
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Maunder-like grand minimum
Modeling Maunder minimum
Large decrease of the poloidal field
Large decrease of themeridional circulation
Meridional circulation (m/s)
Polo
idal
fiel
d st
reng
th
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Observational result:
27 grand minima in last 11,000 years
1,000 solar cycle in last 11,000 years
So the probability that a solar cycle will trigger to agrand minima
= (27/1000)×100 = 2.7%
What will be this value from a dynamo model?
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Observational data:
27 grand minima of different durations
Grand minimaof length ~ 20 yrs
Meridional circulation (m/s)
Polo
idal
fiel
d st
reng
th
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How to find out the strength of the meridional circulation?
In flux transport dynamo:
0.890
1v
Period
(Dikpati & Charbonnea 1999)
0.8850
1v
Period
(Yeates, Nandy & Mackey 2008)
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Meridional circulation of last 28 cycle
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How to find the strength of the poloidal field?
Polar field data
Polar field is a measure of the next sunspot cycle!
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Poloidal field
Toroidal field
ModelObservation
Jiang et al. (2007)Yeates et al. (2008)Charbonneau & Barlet(2011)
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How to find out the strength of the poloidal field?
Assume a perfect correlation between the peak sunspot numberand the polar field of the previous cycle
Sunspot number
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How to find out the strength of the poloidal field?
Assume a perfect correlation between the peak sunspot numberand the polar field of the previous cycle
Sunspot number
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Poloidal field strength
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Distributions of
Meridional circulation poloidal field strength
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0 0( , )p v d dv
Grand minimaof length ~ 20 yrs
Meridional circulation (m/s)
Polo
idal
fiel
d st
reng
th Theoretical value = 1.8%
Observational value= 2.7%
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Simulation of grand minima
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Results of simulation of grand minima
We get 24–30 grand minima in 11,000 years
28 grand minima
Observational value = 27
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Region of toroidal field
generation
Region of poloidal field
generation
Memory of solar cycle and predictability
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How long is the memory?Is it one cycle?i.e.Toroidal field of cycle n = F(poloidal field of cycle n-1)?
Or
Is it many cycles?i.e.Toroidal field of cycle n = F(poloidal field of
cycle n-1, n-2, n-3, ………)?
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Jiang, Chatterjee & Choudhuri (2007); Yeates, Nandy & Mackey (2008)
Diffusion dominated regime
Advection dominated regime
Short memoryi.e.Toroidal field of cycle n = F(poloidal field of cycle n-1)
Long memoryi.e.Toroidal field of cycle n = F(poloidal field of cycle n-1, n-2, n-3, ………)
Prediction of the future solar cycle strongly depends on the regime where the dynamo is operating!
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Turbulent flux pumping:
Tobias et al. (2001)
(Petrovay & Szakaly 1993; Brandenburg et al. 1996; Tobias et al. 1998; Tobias et al. 2001; Dorch & Nordlund 2001; Ossendrijver 2002; Ziegler & R udiger 2003; K apyl a et al. 2006; Rogachevskii et al. 2011).
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Flux transport timescales:
Advection by meridional circulation:~ 10 years (with v0 = 20 m/s)
αΩ
Jadsaasdfsd
Jadsaasdfsd Turbulent diffusion:
~ 2.8 years (with η = 5 1012cm2/s~ 276 years (with ƞ = 5 1010cm2/s)
Turbulent pumping:~ 3.3 years (with v pump = 2 m/s)
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From stochastically forced dynamo model with turbulent pumping
Advection regime
Short memory!Long term prediction is not possible!
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What have we learnt?
Maunder minimum
Frequency of grand minima
Memory of the solar cycle and its predictability
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Which alpha effect is dominated in real Sun?Babcock-Leighton alpha effect?Parker’s mean field alpha effect?Alpha-effect due to buoyancy instability?Tachocline alpha effect?
Open issues
Is the solar dynamo:Advection dominated?Diffusion dominated?Turbulent pumping dominated?
Is the meridional circulation as variable as we find in flux transport dynamo model?Waldmeier effect (Dikpati et al. 2008, Cameron & Schussler 2008) can only be explained using variable meridional circulation (Karak & Choudhuri 2011)
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Full MHD simulations?
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Thank you for your kind attention