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

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

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

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. 2008-2012)

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

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

Does the Sun exhibits a similar behavior?

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

Dipole and Quadrupole Evolution over cycle 21-23/24

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

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

Dynamo theory and the role of equatorial symmetry

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

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

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

Family decomposition of B-L model Dipole Very weak Quadrupole mode not as observed +40 +0.0004

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)

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

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

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

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)