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Magnetic models of solar-like stars

Magnetic models of solar-like stars. Laurène Jouve (Institut de Recherche en Astrophysique et Planétologie) B-Cool meeting December 2011. Solar type stars ( late F, G and early K-type ). Over 111 stars in HK project : 31 flat or linear signal 29 irregular variables

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Magnetic models of solar-like stars

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  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 earlyK-type) Over 111 stars in HK project: 31 flat or linear signal 29 irregular variables 51 + Sun possess a magneticcycle Wilson 1978 Baliunas et al. 1995 CaII H & K lines , <R’HK>

  3. Solar type stars (late F, G and earlyK-type) Pcyc=Prot1.25+/-0.5 They takeintoaccount the characteristics of convection (the convective overturning time via Rossbynumber: Ro=Prot/t): Pcyc=(1/Ro)1.28+/-0.48 Noyes et al. 1984

  4. Solar type stars (late F, G and earlyK-type) Independant fit: Pcyc ~Protn, n ~ 0.8 for active branch, 1.15 for inactive Single power lawcan fit data: w_cycle ~ W-0.09, but withmuchhigher dispersion in fit Saar & Brandenburg, 99; Saar 02, 05

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

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

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

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

  9. The Babcock-Leighton model for the Sun Standard model: single-celled meridional circulation Cyclic field Butterfly diagram close to observations Parameters: v0=6.4 m.s-1 t=5x1010cm2.s -1 s0=20 cm.s-1 eq=460 nHz Solar-like differential rotation Magneticperiodcruciallydepends on MC amplitude

  10. What prescriptions canwe use from 3D models? Dikpati et al. 2001 assumedVp~W Charbonneau & Saar 2001 assumedVpαWor log(W) Scaling of MC deducedfrom Brown et al. 2008: VpαW-0.9 DW increaseswithW

  11. Babcock-Leighton model and stars 0.5 Wsol StrongerBtor compared to Bpol time 5 Wsol Pcyc = 20 yr Slower cycle when Wincreased time Jouve, Brown, Brun, A&A 2010

  12. Babcock-Leighton model and stars Scaling of DWwithW? Observations are unclear: eitherstrong dependency (Donahue et al. 96) or weakdependency (Barnes et al. 2005). 3D modelsgivedifferentanswers in HD or MHD. We assume extremeobs value to maximizeeffect: DW~W0.7 Stronger DW = 3 DW sol 5 Wsol Pcyc = 20 yrstill, so no effect time

  13. Babcock-Leighton model and stars Can wereconcilethis model withstellar datausing a more complex MC? Multicell meridional flow 5 Wsol, Pcyc = 5.2 yr, better agreement time

  14. 3D simulations: HD vs MHD models DW reduced in the MHD case 3Wsol, with no tachocline, ASH MHD HD DW lessdependent on W than in the HD case

  15. 3D simulations: strongtoroidalbelts Emag/Ekin=10% MeanEmag=47% MeanEpol=4%Emag_tot Toroidal field mainly due to the Omega effect inside the CZ. Poloidal field due to the turbulent emf: <u’ x b’> No clear alpha effect: no relationship between the emf and the mean toroidal field. Brown et al, ApJ 2010

  16. 3D simulations: time-dependenttoroidalbelts Star rotating at 5Wsol: Toroidal structures migrate towards the poles. Reconnections occurat the Equator. Max Btor=40kG Brown et al, ApJ 2011

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

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

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

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

  21. Conclusions? • Mean-field models: • Magneticevolution of other stars: constrainingsolarmodels • Otherdifficulties for Babcock-Leightonmodels • Refinedmodelswithadditional transport processes • 3D numerical simulations: • Rapidlyrotating stars: dominant toroidalwreaths • Cycles obtained in modelswithouttachoclines • (fundamentalrole of gradients of Omega in the whole convection zone) • Dynamo not relying on a basic alpha effect

  22. Oui mais bon…

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