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 meetingDecember 2011
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
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
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)
More recent observations
Petit et al. 2008, MNRAS ESPADONS/NARVAL
Field configuration:
More and more toroidal
Multipolar field
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?
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
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
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
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
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
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
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
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
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
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
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
3D simulations
In the Sun:Rossby number of order unity.Small values of themagnetic diffusivitiesare needed to get cyclic behaviour.
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)
Large-scale magnetic cycle!
Looks like an W dynamo
3D simulations: the solar case
BUT: no explicit diffusion coefficients!
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
Oui mais bon…
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