1. Magnetic models of solar-like stars Laurène Jouve (Institut de Recherche en Astrophysique et Planétologie) B-Cool meeting December 2011

2. Solar type stars (late F, G and early K-type) Wilson 1978 Baliunas et al. 1995 CaII H & K lines, Over 111 stars in HK project: 31 flat or linear signal 29 irregular variables 51 + Sun possess a magnetic cycle

3. P cyc =P rot 1.25+/-0.5 Noyes et al. 1984 Solar type stars (late F, G and early K-type) They take into account the characteristics of convection (the convective overturning time via Rossby number: Ro=P rot /  P cyc =(1/Ro) 1.28+/-0.48 

4. Saar & Brandenburg, 99; Saar 02, 05 Independant fit: P cyc ~P rot n, n ~ 0.8 for active branch, 1.15 for inactive Single power law can fit data:  _cycle ~  -0.09, but with much higher dispersion in fit Solar type stars (late F, G and early K-type)

5. More recent observations Petit et al. 2008, MNRAS ESPADONS/NARVAL Field configuration: More and more toroidal Multipolar field

6. More recent observations: cycles? Donati et al, 2008, MNRAS; Fares et al, 2009, MNRAS:  boo: 2 years ? Petit et al, 2009, MNRAS: HD 190771 Garcia et al, 2010, Science: HD 49933: 120 days?

7. 1: magnetic field generation, self-induction 2: pumping of mag. field or 2’: transport by meridional flow 3: stretching of field lines through  effect 4: Parker instability 5: emergence+rotation 6: recycling through  - effect or 7: emergence of twisted bipolar structures at the surface Schematic theoretical view of the solar cycle

8. The Babcock-Leighton flux-transport model Source of poloidal field linked to the rise of toroidal flux concentrations Transport by meridional circulation within the convection zone (Babcock 1961, Leighton 1969, Wang & Sheeley 1991) 2 coupled PDEs: 8 Confinement at the surface Quenching « Ad hoc » latitudinal dependence Toroidal field at the base of the CZ Standard source term: 4

9. The Babcock-Leighton model for the Sun Standard model: single-celled meridional circulation Cyclic field Butterfly diagram close to observations Parameters: v 0 =6.4 m.s -1  t =5x10 10 cm 2.s -1 s 0 =20 cm.s -1  eq =460 nHz Solar-like differential rotation Magnetic period crucially depends on MC amplitude

10. What prescriptions can we use from 3D models? Scaling of MC deduced from Brown et al. 2008: Vp α W -0.9 Dikpati et al. 2001 assumed Vp ~ W Charbonneau & Saar 2001 assumed Vp α W or log( W )  increases with 

11. Babcock-Leighton model and stars 0.5  sol 5  sol Slower cycle when  increased Pcyc = 20 yr Jouve, Brown, Brun, A&A 2010 Stronger Btor compared to Bpol time

12. 5  sol Pcyc = 20 yr still, so no effect Stronger  = 3  sol Scaling of DW with W ? Observations are unclear: either strong dependency (Donahue et al. 96) or weak dependency (Barnes et al. 2005). 3D models give different answers in HD or MHD. We assume extreme obs value to maximize effect: DW ~ W 0.7 Babcock-Leighton model and stars time

13. Multicell meridional flow 5  sol, Pcyc = 5.2 yr, better agreement Can we reconcile this model with stellar data using a more complex MC? Babcock-Leighton model and stars time

14. 3D simulations: HD vs MHD models  reduced in the MHD case MHD HD  less dependent on  than in the HD case 3  sol, with no tachocline, ASH

15. 3D simulations: strong toroidal belts Emag/Ekin=10% Mean Emag=47% Mean Epol=4%Emag_tot Toroidal field mainly due to the Omega effect inside the CZ. Poloidal field due to the turbulent emf: No clear alpha effect: no relationship between the emf and the mean toroidal field. Brown et al, ApJ 2010

16. 3D simulations: time-dependent toroidal belts Star rotating at 5  sol: Toroidal structures migrate towards the poles. Reconnections occur at the Equator. Brown et al, ApJ 2011 Max Btor=40kG

17. 3D simulations: signs of cyclic activity Evidence of a 1500-day cycle Reversals as well as excursions Cycles due to spatial and temporal shifts between the source terms of poloidal and toroidal fields

18. 3D simulations In the Sun: Rossby number of order unity. Small values of the magnetic diffusivities are needed to get cyclic behaviour.

19. MHD simulation of a CZ with no tachocline Ghizaru et al., ApJ, 2010 Racine et al., ApJ, 2011 EULAG code 3D simulations: the solar case Developed convection Solar-like rotation Weak meridional flow (2m.s -1 at the surface)

20. Large-scale magnetic cycle! Looks like an  dynamo 3D simulations: the solar case BUT: no explicit diffusion coefficients!

21. Conclusions?  Mean-field models: Magnetic evolution of other stars: constraining solar models Other difficulties for Babcock-Leighton models Refined models with additional transport processes  3D numerical simulations: Rapidly rotating stars: dominant toroidal wreaths Cycles obtained in models without tachoclines (fundamental role of gradients of Omega in the whole convection zone) Dynamo not relying on a basic alpha effect

22. Oui mais bon…