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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
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:
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
North-South Asymmetry:
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?
27 grand minima in last 11,000 years(from C14 data by Usoskin et al. 2007)
C14data:
Yearly Averaged Sunspot Numbers 1610-2000
Modeling grand minima and
Understanding the predictability
of the solar cycle
Toroidal fieldPoloidal field
Dynamo theory
Toroidal fieldPoloidal field
How?
Toroidal Field Generation (ω Effect)
Observationally verified(Schou et al. 1998; Charbonneau et al. 1999)
Toroidal fieldPoloidal field
How?
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!
2. Poloidal Field Generation:–Babcock–Leighton alpha effect: (Babcock 1961; Leighton 1969; Dasi-Espuig et al. 2010)
Not self excited!
Toroidal fieldPoloidal field
Differential rotation
Helical alpha effect + Babcock-Leighton mechanism
Dynamo theory
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)
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
Region of toroidal field
generation
Region of poloidal field
generation
Flux Transport Dynamo(Durney 1995; Choudhuri, Schussler & Dikpati 1995;
Dikpati & Charbonneau 1999)
ƞ ~ (1/3) l v = 1012-1013 cm2/s ???
Turbulent diffusivity (ηt)
Important ingredients of flux transport dynamo
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
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
Chatterjee et al. (2004)
Regular process Random process+
Solar cycle
Hadsfddfa
???
Solar cycle
Or
Nonlinear chaotic system?The modulation of the solar cycle is due to the chaotic nature of the dynamo process?
???
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
Regular process Random process+
Solar cycle
Hadsfddfa
Our point of view:
Are the grand minima merely extremes of cycle irregularities?
How to model Maunder minimum?
Hadsfddfa
Well, find out the sources of randomness in dynamo model.
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
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)
Charboneau, Blais-Laurier & St-Jean (2004) – Low diffusivity dynamo simulation with fluctuations in α (100% level)
Intermittencies over several periods
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.
ballTheoretical
Observed
ball Theoretical
Observational
Fluctuations in meridional circulation
Hathaway & Rightmire (2010)
Coming from slight imbalance between two large terms – the centrifugal term and
the latitudinal temperature gradient term
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)
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)
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)
ball
Can a large fluctuation in meridional circulation lead to a Maunder-like minimum?
Close
close
close
Observed
Theoretical
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
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?
Observational data:
27 grand minima of different durations
Grand minimaof length ~ 20 yrs
Meridional circulation (m/s)
Polo
idal
fiel
d st
reng
th
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)
Meridional circulation of last 28 cycle
How to find the strength of the poloidal field?
Polar field data
Polar field is a measure of the next sunspot cycle!
Poloidal field
Toroidal field
ModelObservation
Jiang et al. (2007)Yeates et al. (2008)Charbonneau & Barlet(2011)
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
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
Poloidal field strength
Distributions of
Meridional circulation poloidal field strength
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%
Simulation of grand minima
Results of simulation of grand minima
We get 24–30 grand minima in 11,000 years
28 grand minima
Observational value = 27
Region of toroidal field
generation
Region of poloidal field
generation
Memory of solar cycle and predictability
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, ………)?
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!
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).
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)
From stochastically forced dynamo model with turbulent pumping
Advection regime
Short memory!Long term prediction is not possible!
What have we learnt?
Maunder minimum
Frequency of grand minima
Memory of the solar cycle and its predictability
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)
Full MHD simulations?
Thank you for your kind attention