1. Solar Magnetic Field Reversal and the Role of Dynamo Families
Allan Sacha Brun
Service d’Astrophysique/UMR AIM,
CEA-Saclay
with M. Derosa and T. Hoeksema
Solar magnetic families
2-D mean field models

2. Cycles 22, 23, 24 Small vs Large Scale Dynamos Regions Quiet Actives
Butterfly Diagram
polar reversal
Small vs Large Scale
Dynamos
Equatorial branch
Regions
Quiet
Actives

3. What can we learn from other reversing magnetic field
in the solar system?
=> The case of the Earth

4. Earth’s Magnetic Field Reversal
Matuyama -> Bruhnes -780,000 yr
Leonhardt
& Fabian 2007
Dominant multipole over
dipole
Reversal takes about 8 kyr, with a precursor of ~2.5 kyr, a reversal of ~3 kyr and rebound of ~2.5 kyr (Valet et al )

5. Quadrupole vs Dipole strength during Earth’s reversal
Dominant quadrupole at dipole min
Dipole
Quadrupole
Dipole stay dominant during excursion!  Reversal =/= Excursions

6. Reversals vs Excursions
Petrelis & Fauve 2009 Rm
Limit cycle above
the saddle node
bifurcation, leads
Cyclic dynamo solution.
The Sun with large Rm
is above the instability,
whereas the Earth isn’t,
explaining the failed
reversals (excursions)
In order to get irregular
Cycles, one needs to have
a time dependent control
Parameter (Rm, Re…)
that makes the Sun goes
On and Off (Spiegel 2009)
Such behavior is expected
from the Sun’s nonlinear
dynamo, or by stochasticity
Coupling a Dipole to a Quadrupole => A= D + i Q yields
a dynamical system with a 2-D phase space describing
a saddle node bifurcation (with stable/unstable fixed points)
Coupling of both families via either nonlinear effects or symmetry
breaking in the flow (Roberts & Stix 1972, Mc Fadden et al. 1991)
See M. Derosa’s Talk for an example

7. Does the Sun exhibits a similar behavior?

8. Last 3 solar reversals: Takes about 1 to 2 years to reverse
No sign of excursion in the Sun
Dipole reverses ahead of full field
Derosa, Brun, Hoeksema 2011, 2012

9. Dipole and Quadrupole Evolution over cycle 21-23/24

10. Quadrupole vs Dipole Strength
Dominant quadrupole at reversal
Derosa, Brun, Hoeksema 2011

11. Axisymmetric Modes Quad ~ 25% Dip Except during Reversal where it is
dominant.
Derosa, Brun, Hoeksema 2011, 2012

12. Dynamo theory and the role of equatorial symmetry

13. Assessing Symmetries of Induction Equation
If V is symmetric: VS x BA -> CS so
VS x BS -> CA so
=> Generates fields of same family => Uncoupled Dynamo solutions (families)
If V is anti-symmetric: VA x BA -> CA so
VA x BS -> CS so
=> Generates field of the opposite family => Coupled Dynamo solutions
In current Babcock-Leigthon dynamo models ingredients yields uncoupled families
Gubbins & Zhang 1993

14. B-L Mean Field Solar Dynamo Model
B-L models:
Dikpati & Charbonneau 99
Charbonneau 2005
Jouve & Brun 2007, …
Poloidal
Toroidal
Meridional Circulation
S term is linked to tilt of active region (Joy’s law) and their later decay
Replace emf <v’ x b’> by surface source term S
Stenflo & Kosovishev 2008

15. 2-D Model: Babcock-Leighton
1 cell per hemisphere, symmetric flow
Jouve & Brun, 2007 A&A, 474, 239
Check International Benchmark: Jouve et al. 2008, A&A

16. Family decomposition of B-L model
Dipole
Very weak Quadrupole mode
not as observed
+40

17. Meridional Circulation
Mitra-Kaev & Thompson 2007
Meridional Circulation
More & more evidence for multi cellular MC
Influence of B
(active region)
on MC
N-S Asymmetry
N-S Asymmetry
Solar Min (1997)
N-S Asymmetry
Svanda et al. 2008
See also Hathaway et al. 1996, Gizon 2004, Zhao
& Kosovichev 2004, Zhao et al. 2012, …
(Haber et al. 2002)

18. Babcock-Leigthon source term. Similar for asymmetric meridional flow
Asymmetry e of 0.1% of
Babcock-Leigthon source term.
Similar for asymmetric meridional
flow
Dip + Quad !
Small N-S lag
Derosa, Brun, Hoeksema 2011, 2012

19. Asymmetry and Reversals in 3-D Convective Geo Dynamo
Symmetrized flows: No Reversals
Full 3-D or Turbulent case: reversals
Nishikawa & Kusano 2008
See also Olson, Glatzmaier et al. 2011

20. Asymmetry and Reversals in 3-D Convective Solar Dynamo
Note the dipolar, quadrupolar and multipolar states
Brun et al. 2004
see also Browning et al. 2006, Brown et al. 2011, Racine et al. 2010

21. CONCLUSIONS The Sun is not always dominated by its dipolar component
It does, as the Earth, possess a dominant quadrupolar component near
field reversal
Models need to possess such coupling of families
Most current mean field model don’t
0.1% asymmetry in ingredients used yields the right coupling
3-D models get such coupling naturally through asymmetric convective flow
and non linear coupling of dynamo families (Nishikawa & Kusano 2008,
Olson et al. 2011, Brun et al. 2004, Brown et al. 2010, 2011, Derosa, Brun &
Hoeksema 2012)