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