1. The formation of stars and planets Day 4, Topic 1: Magnetospheric accretion jets and outflows Lecture by: C.P. Dullemond

2. Boundary layer At inner radius of disk: Assume disk goes all the way down to the stellar surface If star rotates at less than breakup speed: Frictional energy release in boundary layer:

3. Boundary layer Friction between disk and star tends to spin up star until This means that star would rotate at breakup speed (almost zero local gravity at the equator) For non-rotating star: Ae and Be stars rotate fast Most stars, however, rotate far below breakup speed F star accr disk bnd layer

4. Magnetospheric accretion Ghosh & Lamb (1978) for neutron stars. Camenzind (1990), Königl (1991), Shu et al. (1994), Wang (1995) for TT stars Magnetic pressure: Dynamic pressure: Gas is loaded onto magnetic field lines (disk is destroyed) at the radius r i where P m =P dyn. Alfvén radius r i Königl (1991) (Here  * is stellar magnetic moment, and  <1 is a fudge factor, typically  =0.5 )

5. Magnetospheric accretion Corotation radius Spin-up/spin-down Very rough estimate for spin-up/spin-down: Spin-up Spin-down Ghosh & Lamb (1977,1978,1979) Königl (1991) Equilibrium sets stellar rotation rate (if braking/spin-up time is shorter than stellar formation time) (The concept of magnetic breaking of the sun was already suggested in 1960 by Hoyle, and in a somewhat less plausible way by Alfvén 1954)

6. Magnetospheric accretion Free-fall and accretion shock Free-fall region Accretion shock riri From r A down to star: matter is in supersonic free-fall. Near the star the matter gets to a halt in a stand-off shock. Shock velocity: Dissipated energy (=accretion luminosity from shock):

7. (  m) 120.40.2 Magnetospheric accretion Radiation from accretion shock Calvet & Gullbring (1998) Stellar spectrum Radiation from accretion shock

8. Measuring the accretion rate Veiling of atmospheric lines by continuum of the accretion layer Broad (FWHM ~ 200 km/s) H  line emission

9. Bipolar outflows / jets

10. Bipolar outflows HH47

11. Bipolar outflows HH34

12. Bipolar outflows Outflows also seen in molecular lines: Molecular outflows Bachiller et al.

13. Bipolar outflows Jets originate from inner regions of protoplanetary disks Hubble Space Telescope image

14. Bipolar outflows Optically detected jets: –Very collimated streams of gas, moving at supersonic speed (~~100 km/s) –Mostly bipolar, mostly perpendicular to disk –Jet outflow rate typically 10 -9... 10 -7 M . Molecular outflows: –Detected in CO lines –Often associated with optical jets (i.e. same origin) –Derived mass: 0.1...170 M  : large! Most of accelerated mass must have been swept up from the cloud core, rather than originating in mass ejected from the star

15. Bipolar outflows Terminal shock Hydrodynamic confinement? Magnetic confinement Magneto-centrifugal launching (<AU scale) Swept-up material (molecular outflow) Hot bubble of old jet material

16. Magnetically threaded disks Suppose disk is treaded by magnetic field: Inward motion of gas in disk drags field inward: B-field aquires angle with disk

17. Disk winds Slingshot effect. Blandford & Payne (1982) Gravitational potential: Use cylindrical coordinates r,z Effective gravitational potential along field line (incl. sling-shot effect): (courtesy: C. Fendt)

18. Disk winds Blandford & Payne (1982) InfallOutflow Critical angle: 60 degrees with disk plane. Beyond that: outflow of matter. Gas will bend field lines

19. Disk + star: X-wind model of Frank Shu Shu 1994

20. Magnetic field winding - confinement C. Fendt

21. Magnetic field winding - confinement Right-hand rule: force points inwards (courtesy: C. Fendt)

22. Hydromagnetic launch of jet from disk Kudoh, Matsumoto & Shibata (2003)

23. Hydrodynamic structure of jets Jets are surrounded by cocoon of pressurized gas –Cocoon partly made of old jet material, partly by swept up material from the environment –Jet material moves supersonically Head of jet (‘hot spot’) drills through ISM: shock Often knots seen (Herbig-Haro objects) Stone & Norman (1993)

24. Observed knot movement

25. Hydrodynamic confinement in jet: Shock only reduces the velocity component perpendicular to shock front. Therefore obliquely shocked gas is deflected toward the shock plane.

26. Hydrodynamic confinement in jet:

27. Head of the jet: Stand-off shock (most of jet energy dissipated here) Contact discontinuity (boundary between jet and external medium) Bow shock Back flow Turbulent mixing between old jet material and swept-up environment (entrainment) Shocked external medium gas (molecular outflow) Jet flow much faster than propagation of bow shock. Jet material much more tenuous than external medium