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

Magnetic models of solar-like stars

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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 - PowerPoint PPT Presentation

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Page 1: Magnetic  models  of  solar-like  stars

Magnetic models of solar-like stars

Laurène Jouve(Institut de Recherche en Astrophysique et Planétologie)

B-Cool meetingDecember 2011

Page 2: Magnetic  models  of  solar-like  stars

Solar type stars (late F, G and early K-type)

Wilson 1978Baliunas et al. 1995

CaII H & K lines , <R’HK>

Over 111 stars in HK project:31 flat or linear signal29 irregular variables51 + Sun possess a magnetic cycle

Page 3: Magnetic  models  of  solar-like  stars

Pcyc=Prot1.25+/-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 timevia Rossby number: Ro=Prot/t): Pcyc=(1/Ro)1.28+/-0.48

Page 4: Magnetic  models  of  solar-like  stars

Saar & Brandenburg, 99; Saar 02, 05

Independant fit: Pcyc ~Protn, n ~ 0.8 for active branch, 1.15 for inactive

Single power law can fit data: w_cycle ~ W-0.09, but with much higher dispersion in fit

Solar type stars (late F, G and early K-type)

Page 5: Magnetic  models  of  solar-like  stars

More recent observations

Petit et al. 2008, MNRAS ESPADONS/NARVAL

Field configuration:

More and more toroidal

Multipolar field

Page 6: Magnetic  models  of  solar-like  stars

More recent observations: cycles?

Donati et al, 2008, MNRAS; Fares et al, 2009, MNRAS: t boo: 2 years ?

Petit et al, 2009, MNRAS: HD 190771

Garcia et al, 2010, Science: HD 49933: 120 days?

Page 7: Magnetic  models  of  solar-like  stars

1: magnetic field generation, self-induction2: pumping of mag. field or 2’: transport by meridional flow3: stretching of field lines through W effect

4: Parker instability5: emergence+rotation6: recycling through -effect or7: emergence of twisted bipolar structures at the surface

Schematic theoretical view of the solar cycle

Page 8: Magnetic  models  of  solar-like  stars

The Babcock-Leighton flux-transport model

Source of poloidalfield 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:

Confinement at the surface Quenching « Ad hoc » latitudinal

dependence

Toroidal field at the base

of the CZ

Standard source term:

4

Page 9: Magnetic  models  of  solar-like  stars

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

Weq=460 nHzSolar-like differential

rotation

Magnetic period crucially depends on MC amplitude

Page 10: Magnetic  models  of  solar-like  stars

What prescriptions can we use from 3D models?

Scaling of MC deduced fromBrown et al. 2008: Vp α W-0.9

Dikpati et al. 2001 assumed Vp ~WCharbonneau & Saar 2001assumed Vp α W or log(W)

DW increases with W

Page 11: Magnetic  models  of  solar-like  stars

Babcock-Leighton model and stars

0.5 Wsol

5 Wsol

Slower cycle when W increased

Pcyc = 20 yr

Jouve, Brown, Brun, A&A 2010

Stronger Btorcompared to Bpol

time

time

Page 12: Magnetic  models  of  solar-like  stars

5 Wsol Pcyc = 20 yr still, so no effect

Stronger DW = 3 DW 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 tomaximize effect: DW~W0.7

Babcock-Leighton model and stars

time

Page 13: Magnetic  models  of  solar-like  stars

Multicell meridional flow

5 Wsol, 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

Page 14: Magnetic  models  of  solar-like  stars

3D simulations: HD vs MHD models

DW reduced in the MHD case

MHD

HD

DW less dependent on W than in the HD case

3Wsol, with no tachocline, ASH

Page 15: Magnetic  models  of  solar-like  stars

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: <u’ x b’>No clear alpha effect: no relationship betweenthe emf and the mean toroidal field.

Brown et al, ApJ 2010

Page 16: Magnetic  models  of  solar-like  stars

3D simulations: time-dependent toroidal belts

Star rotating at 5Wsol:

Toroidal structures migratetowards the poles.Reconnections occur at theEquator.

Brown et al, ApJ 2011

Max Btor=40kG

Page 17: Magnetic  models  of  solar-like  stars

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 poloidaland toroidal fields

Page 18: Magnetic  models  of  solar-like  stars

3D simulations

In the Sun:Rossby number of order unity.Small values of themagnetic diffusivitiesare needed to get cyclic behaviour.

Page 19: Magnetic  models  of  solar-like  stars

MHD simulation of a CZ withno tachocline

Ghizaru et al., ApJ, 2010Racine et al., ApJ, 2011

EULAG code

3D simulations: the solar case

Developed convectionSolar-like rotationWeak meridional flow(2m.s-1 at the surface)

Page 20: Magnetic  models  of  solar-like  stars

Large-scale magnetic cycle!

Looks like an W dynamo

3D simulations: the solar case

BUT: no explicit diffusion coefficients!

Page 21: Magnetic  models  of  solar-like  stars

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

Page 22: Magnetic  models  of  solar-like  stars

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