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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

Magnetic models of solar-like stars

Laurène Jouve

(Institut de Recherche en Astrophysique et Planétologie)

B-Cool meeting

December 2011

slide2

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>

slide3

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

slide4

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

more recent observations
More recent observations

Field configuration:

More and more toroidal

Multipolar field

Petit et al. 2008, MNRAS

ESPADONS/NARVAL

more recent observations cycles
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?

slide7

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

the babcock leighton flux transport model
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

the babcock leighton model for the sun
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

slide10

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

slide11

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

slide12

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

slide13

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

slide14

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

slide15

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

slide16

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

slide17

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

slide18

3D simulations

In the Sun:

Rossby number of

order unity.

Small values of the

magnetic diffusivities

are needed to get

cyclicbehaviour.

slide19

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

slide20

3D simulations: the solar case

Large-scale magnetic cycle!

Looks like an aW dynamo

BUT: no explicit diffusion coefficients!

slide21

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