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