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
Young, low-mass stars rotate at
10% of the break-up velocity
How to get stellar spin down from
the star-disk interaction ?
Camenzind 1990
• Accretion-driven winds (Matt & Pudritz)
• Propeller regime (Romanova et al.)
• Magnetospheric ejections (Zanni & Ferreira)
Star-disk magnetic coupling
2D MHD simulation of disk accretion
onto an aligned dipole
Zanni et al. 2009
Bessolaz et al. 2008
Mstar = 0.8Mo; Rstar=2Ro
Bdipole = 800 G; dMacc/dt = 10-8 Mo/yr
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 constraints
Wichmann et al. 1998
Observational constraints
Irwin & Bouvier 2009
0.9-1.1 Mo
Observational constraints
Today’s update…
0.9-1.1 Mo
Gallet & Bouvier, in prep.
PMS
Irwin et al. (2010)
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 stardisk 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
ZAMS
PMS
MS
Wind
braking
PMS
spin up
Disk
locking
Surface rotation is
dictated by the initial
velocity + disk lifetime +
magnetic winds
(+ core-envelope
decoupling)
Core-envelope decoupling (τc)
Radiative core
τc : core-envelope
coupling timescale
Convective
envelope
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
Wind braking
• Modified Kawaler’s prescription
Suitable for solar-type stars
1 Mo
But fails for VLM stars
0.25 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
1Mo
M&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 rot
τc=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
On-going work…
• C. Zanni’s magnetospheric ejection model
Numerical simulations
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)
“The magnetic Sun in time”
(J. Bouvier, F. Gallet, P. Petit, J.-F. Donati, A. Morgenthaler, E. Moraux)
• 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”
Marsden
et al.
Young open
clusters
Donati
et al.
Petit, Morin, et al.
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 longlived 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