1. Angular momentum evolution of low-mass stars The critical role of the magnetic field Jérôme Bouvier

2. 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. 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 ?

4. 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 ?

5. Star-disk magnetic coupling Zanni et al. 2009 Bessolaz et al. 2008 M star = 0.8M o ; R star =2R o B dipole = 800 G; dM acc /dt = 10 -8 M o /yr 2D MHD simulation of disk accretion onto an aligned dipole

6. 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 ?

7. 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 ?

8. Observational constraints Tremendous progress in the last years…

9. Observational constraints Wichmann et al. 1998

10. Observational constraints Irwin & Bouvier 2009 0.9-1.1 Mo

11. Observational constraints 0.9-1.1 Mo Gallet & Bouvier, in prep. Today’s update…

12. Irwin et al. (2010) PMS MS

13. 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

14. Models vs. observations What have we learnt so far ?

15. 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 τ c (core-envelope decoupling)

16. 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)

17. Core-envelope decoupling (τ c ) Radiative core Convective envelope τ c : core-envelope coupling timescale Differential rotation between the inner radiative core and the outer convective

18. 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 > ω sat to allow for “ultra-fast rotators” on the ZAMS Weak, starts to dominate only at the end of PMS contraction

19. 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)

20. Wind braking Matt & Pudritz’s (2008) prescription Calibrated onto numerical simulations of stellar winds Mass-loss : Cranmer & Saar 2011Dynamo : Reiners et al. 2009

21. Wind braking 1Mo M&P08 braking Gallet & Bouvier, in prep.

22. Core-envelope decoupling Models with a constant coupling timescale between the core and the envelope cannot reproduce the observations τ c =10 6 yr for fast rot τ c =10 8 yr for slow rot Bouvier 2008

23. 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 ?)

24. Long et al. 2007

25. Star-disk interaction C. Zanni’s magnetospheric ejection model Numerical simulations On-going work…

26. Star-disk interaction Gallet, Zanni & Bouvier, in prep.

27. 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

28. How to further constrain the angular momentum evolution models ? Investigate magnetic field evolution

29. “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)

30. 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)

31. “The magnetic Sun in time” Donati et al. Marsden et al. Petit, Morin, et al. Young open clusters

32. 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