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Angular momentum evolution of low-mass stars. The critical role of the magnetic field. Jérôme Bouvier. Stellar rotation : a window into fundamental physical processes . Star formation : initial angular momentum distribution (collapse, fragmentation) - PowerPoint PPT Presentation
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Angular momentum evolution of low-mass stars
The critical role of the magnetic field
Jérôme Bouvier
Stellar rotation : a window into fundamental physical processes
• Star formation : initial angular momentum distribution (collapse, fragmentation)
• Star-disk interaction during the PMS• Rotational braking by magnetized winds• AM transfer in stellar interiors• Binary system evolution, stellar dynamos and
magnetic activity, chemical mixing, etc.
3 major physical processes
The evolution of surface rotation from the PMS to the late-MS (1 Myr – 10 Gyr) is dictated by :
Star-disk interaction (early PMS) : magnetospheric accretion/ejection
Wind braking (late PMS, MS) : magnetized stellar winds
Core-envelope decoupling (late PMS, MS) : internal magnetic fields ?
Magnetic star-disk interaction
• Accretion-driven winds (Matt & Pudritz)• Propeller regime (Romanova et al.)• Magnetospheric ejections (Zanni & Ferreira)
Camenzind 1990
Young, low-mass stars rotate at 10% of the break-up velocity
How to get stellar spin down from the star-disk interaction ?
Star-disk magnetic couplingZanni et al. 2009 Bessolaz et al. 2008
Mstar = 0.8Mo; Rstar=2Ro
Bdipole = 800 G; dMacc/dt = 10-8 Mo/yr
(.mpg)
2D MHD simulation of disk accretion onto an aligned dipole
Magnetized wind braking
Once the disk has disappeared (~5 Myr), wind braking is the dominant process to counteract PMS contraction and later on for MS spin down :
• Kawaler’s (1988) semi-empirical prescription • Magnetized stellar winds (Matt & Pudritz 2008)• PMS wind braking (Vidotto et al. 2010)
How does (dJ/dt)wind vary in time ?
Core-envelope decoupling
Surface velocity measured at the top at the convective envelope while radiative core’s velocity unknown (except for the Sun)
How much angular momentum is exchanged ? On what timescale ?
• Turbulence, circulation (Denissenkov et al. 2010)• Magnetic coupling (Eggenberger et al. 2011)• Internal gravity waves (Talon & Charbonnel 2008)
How rigidly is a star rotating ?
Observational constraints
Tremendous progress in the last years…
Observational constraintsWichmann et al. 1998
Observational constraintsIrwin & Bouvier 2009
0.9-1.1 Mo
Observational constraints
0.9-1.1 Mo
Gallet & Bouvier, in prep.
Today’s update…
Irwin et al. (2010) PMS MS
Observational constraints
• Several thousands of rotational periods now available for solar-type and low-mass stars from ~1 Myr to a ~10 Gyr (0.2-1.2 Msun)
• Kepler still expected to yield many more rotational periods for field stars
• Several tens of vsini measurements available for VLM stars and brown dwarfs
Models vs. observations
What have we learnt so far ?
AM evolution : model assumptions
Accreting PMS stars are braked by magnetic star-disk interaction (~fixed angular velocity)
Non-accreting PMS stars are free to spin up as they contract towards the ZAMS
Low mass main sequence stars are braked by magnetized winds (saturated dynamo)
Radiative core / convective envelope exchange AM on a timescale τc (core-envelope decoupling)
Grids of rotational evolution models
Disk locking
MS
PMS spin up
Wind braking
PMS
ZAMS
Surface rotation is dictated by the initial velocity + disk lifetime + magnetic winds
(+ core-envelope decoupling)
Core-envelope decoupling (τc)
Radiative core
Convective envelope
τc : core-envelope coupling timescale
Differential rotation between the inner radiative core and the outer convective
Angular momentum loss: I. Solar-type winds• Most modellers use the Kawaler (1988) formulation with n = 3/2 to reproduce the Skumanich (1972) t-1/2 law
• Introduce saturation for ω > ωsat to allow for “ultra-fast rotators” on the ZAMS
• Weak, starts to dominate only at the end of PMS contraction
• Modified Kawaler’s prescription
Wind braking
But fails for VLM stars
0.25 Mo
Suitable for solar-type stars
1 Mo
Irwin & Bouvier (2009) Irwin et al. (2010)
Wind braking• Matt & Pudritz’s (2008) prescription• Calibrated onto numerical simulations of stellar
winds
Mass-loss : Cranmer & Saar 2011 Dynamo : Reiners et al. 2009
Wind braking
1MoM&P08 braking
Gallet & Bouvier, in prep.
Core-envelope decoupling• Models with a constant coupling timescale between the core
and the envelope cannot reproduce the observations
τc=106yr for fast rotτc=108yr for slow rot
Bouvier 2008
Core-envelope decoupling
• Models with a constant coupling timescale between the core and the envelope cannot reproduce the observations
• Need for a rotation-dependent core-envelope coupling timescale : weak coupling in slow rotators, strong coupling in fast rotators
• Still need to identify the physical origin of this rotation-dependent coupling (hydro ? B ? waves ?)
Long et al. 2007
Star-disk interaction
• C. Zanni’s magnetospheric ejection model
Numerical simulations
On-going work…
Star-disk interaction
Gallet, Zanni & Bouvier, in prep.
Star-disk interaction
• Strong observational evidence that accreting stars are prevented from spinning up in the first few Myr
• Still no fully consistent PMS stellar spin down from star disk interaction models (e.g. Matt et al. 2010)
• Angular momentum has to be removed from the star, and not only from the disk
How to further constrain the angular momentum evolution models ?
Investigate magnetic field evolution
“The magnetic Sun in time” (on-going project, TBL/NARVAL, CFHT/ESPADONS)
• Investigate the magnetic field topology of young stars in open clusters in the age range from 30 to 600 Myr
• Expectations : the topology of the surface magnetic field depends on the shear at the tachocline
• Goal : use surface magnetic field as a proxy for internal rotation and test the model predictions (e.g., core-envelope decoupling)
• Targets : G-K stars in young open clusters• Clusters :– Coma Ber (600 Myr)– Pleiades (120 Myr)– Alpha Per (80 Myr)– IC 4665 (30 Myr)
• Preliminary results (2009-2011), on-going analysis
“The magnetic Sun in time”(J. Bouvier, F. Gallet, P. Petit, J.-F. Donati, A. Morgenthaler, E. Moraux)
“The magnetic Sun in time”
Donati et al.
Marsden et al.
Petit, Morin, et al.
Young open clusters
Conclusion• Still need to identify the physical process(es) by which
internal angular momentum is transported (core-envelope coupling)
• Still need to understand the origin of the long-lived dispersion of rotation rates in VLM stars (dynamos bifurcation?)
• Still awaiting a fully consistent physical description of PMS stellar spin down from the star-disk interaction : (dJ/dt)net < 0 !
• Still lacking constraints on the internal rotation profile (e.g. tachocline) and its evolution