1. The Disk-Jet Connection: A Universal Picture for Protostellar Jets Ralph Pudritz McMaster University Western Workshop: From Protostellar Disks to Planetary Systems

2. Outline 1. Theory of disk winds 2. Numerical simulations – disks as jet engines 3. Coupled disk-jet evolution 4. Disks and outflows during gravitational collapse 5. Jets and star-disk interaction Collaborators: Robi Banerjee (pdf), Sean Matt (pdf), Rachid Ouyed (U. Calgary), Conrad Rogers (summer student),

3. Major Advances in the field: - High resolution spectro-imaging of jets - Computational advances – large class of new solutions - Disk/Jet paradigm being uncovered in massive stars & brown dwarfs. (Reviews; eg. Pudritz 2003, Les Houches; and Pudritz et al, 2006, PPV)

4. Points of Principle: 1. Jets and disks are coupled: (in large measure, operation of a disk wind for observed jets) - outflow rate scales with accretion rate - jet rotation and angular momentum extraction from disk measured 2. Universality: jet production mechanism same - from disks from brown dwarfs to massive stars (eg. massive stars: Konigl 1999) Jets harness accretion power in all systems, from extended disk down to stellar surface..

5. 1. Evidence for jet/disk coupling: (i) jet rotation (Bacciotti et al 2003, Coffey et al 2004, Pesenti et al 2004) jet rotation, 110 AU from source, at 6-15 km/sec Footpoints for launch of jet *extended over disk surface* (Anderson et al 2003) LV originates from disk region: 0.3-4.0 AU (ii) accretion and jet mass loss rates coupled (wide variety of systems (eg. Hartmann et al 1998)

6. Measure thrust in swept-up CO; (Cabrit & Bertout1992) Correlation works for both low and high mass stars For 391 outflows: Wu et al (2004) same index 2. Evidence for universality: CO flows

7. I. Theory of disk winds Blandford & Payne (1982; BP), Pelletier & Pudritz (1992)

8. Conservation laws in steady, axisymmetric flow: 1. Conservation of mass and magnetic flux * Function is mass load, per unit time, per unit magnetic flux - requires input physics. The way that an accretion disk mass loads field lines at each disk radius plays critical role in jet dynamics

9. The toroidal field in rotating flows - from induction equation: = ang. velocity at mid-plane of disk Strength of toroidal field: - depends on mass loading : stronger toroidal field for smaller k inertial effect - mass load has an important effect on the collimation and variability of jets (Ouyed & Pudritz 1999, MNRAS; Anderson et al 2005)

10. 2. Angular momentum conservation: * Angular momentum per unit mass conserved along each field line (depends on mass load) Regular behaviour of flow through “critical (Alfven) point” on field line; - Angular momentum is extracted from rotor

11. 3. Energy conservation: Bernoulli theorem - energy conserved along each field line Terminal speed – (i) scales with depth of gravitational potential well at point of launch; (ii) has “onion-like” kinematic structure: Use conservation laws (Anderson et al 2003) to deduce point of origin of outflow from disk from observed disk rotation profile

12. Angular momentum extraction from disk: - assume thin disk, neglect viscosity - angular momentum flow due to external torque of threading field: - after vertical integration: Disk angular momentum equation (Pudritz & Norman 1986, Pelletier & Pudritz 1992):

13. Accretion and ejection coupled through magnetic torque exerted on disk Lever arm: (numerics) and observations (Anderson et al 2003): 1.8 – 2.6 for DG Tau) Disk angular momentum equation (Pudritz & Norman 1986, Pelletier & Pudritz 1992):

14. Collimation of flows – force balance perpendicular to field line a every point (eg. Heyvaerts 2003) Hoop-stress provided by toroidal field: Current carried by a jet – depends on mass load! Cylindrical collimation (Heyvaerts & Norman 1987) if: If current finited – then Parabolic collimation (ie wide-angle) Jet Collimation

15. - Gradually decreasing field (BP): collimated jet - Steeply decreasing field (eg. monopolar): wide angle outflow Models: 1. jet-driven bow-shock (Raga & Cabrit 1993, Masson & Chernin 1993)? 2. wide-angle wind-driven, X-wind (Shu et al 2000, Li & Shu 1996)? - Both types observed (eg. Lee et al 2000) Jet collimation depends on mass loading through toroidal field (PRO):

16. II. Numerical simulations – disks as jet engines Underlying accretion disk provides fixed boundary conditions for jet – check physics of *ejection, acceleration, collimation, stability* eg. Ustyugova et al (1995), Ouyed et al (Nature 1997), Ouyed & Pudritz (1997a,b, 1999), Romanova et al (1997), Meir et al (1997), Krasnopolsky et al (1999),…

17. Krasnopolsky et al (1999) - treatment near outflow axis: core “jet” – no equilibrium - cold gas – pressure small - constant density maintained at disk boundary

18. Outflow from initial split –monopole initial field: Poloidal field and velocities isodensity contours Beta = 1; flow not collimated Romanova et al (1997)

19. Mass loading controls jet collimation ( Pudritz, Rogers, & Ouyed, 2005, PRO ) - assume power-law disk field: potential; Blandford-Payne; Pelletier-Pudritz yet steeper This prescribes mass loadings: Last 2 give wide- angle disk wind

20. 1.Potential 2. Blandford-Payne 3. Pelletier-Pudritz 4. yet steeper.. r Initial Magnetic Field Configurations z

21. Potential: poloidal field density

22. BP: poloidal field density

23. PP: poloidal field density

24. -0.75: poloidal field density

25. BP: Poloidal velocity field

26. -0.75: poloidal velocity vectors

27. Collimation better for shallow slope in Collimation due to hoop stress Dense jet near axis in all models - low density, wide-angle outflow from larger radii for steeper distribution - Shu et al (1994), Romanova et al (1996) as limiting cases – they are highly concentrated fields that should give wide-angle flow…

28. 3D simulation of jet from initially vertical field threading accretion disk - Find nonlinear saturation of K-H modes…jets are stable! (Ouyed, Clarke & Pudritz 2003)

29. Universality – applications of disk winds: 1. Protoplanetary jets: Jovian planets accrete from circum- planetary subdisk (eg. Kley et al 2001): Fendt (2003) – disk wind model for planetary outflows - T up to 2000K: good coupling of field - feasible - Outflow of order escape speed: 60 km/sec (X-wind model: Quilling & Trilling 1998) 2. Massive YSO jets: precede radiative driven outflows ( Banerjee & Pudritz 2006, in prep.) - Disk winds many punch hole in envelop - allowing radiation to escape ( Krumholz et al 2004)

30. III. Coupled Disk-Jet Evolution Self-consistent mass loading, magnetic field, etc. – requires disk-jet interaction. Questions: launch mechanism? Origin of disk field? Disk and jet evolution both simulated - Non-equilibrium system: Uchida & Shibata (1985), pioneering simulations… - Stone & Norman (1994), Bell & Lucek (1995), Tomisaka (1999), Kudoh et al (2002), Casse & Keppens (2002), von Rekowski & Brandenburg (2004),…

31. How are jets actually launched? Magnetic field squeezes matter towards disk plane below concave region: pushes matter upwards in convex region Change of curvature because accretion drags field lines inward Turbulent diffusivity in disk – ideal MHD in jet Ferreira (1997)

32. Casse & Keppens 2004 Best fit, stationary,self-similar solution that is better match to observations: warm outflow (Casse & Ferreira 2002) – a disk corona involved?

33. Disk and stellar wind (von Rekowski & Brandenburg 2004) – B field generation through dynamo action Interaction of stellar magnetosphere and dynamo generated disk field: For standard case (1KGauss stellar field) Fast, centrifugally driven disk wind to 240 km/sec - Highly episodic accretion onto central star; averaging:

34. Purely dynamo generated fields: conical outflows Mass loading effect? Need for ambient field too? von Reskowski & Brandenburg 2004

35. Direct detection of disk magnetic field in FU Ori: Uses high res, spectropolarimetry..direct Zeeman measurements. 1kG at 0.05 AU – far too strong to be stellar dipole field… a.Unpolarized disk profile (solid); Kepler speed of 65 km/sec at 0.05AU (dot- dash) b. Zeeman signature (top); with antisymm and symm components (middle, bottom) Donati et al, 2005, Nature

36. IV. Disks and outflows during gravitational collapse MHD simulations of collapsing, magnetized B-E spheres (FLASH AMR MHD code) (Misaligned B and rotation axis rapidly align Matsumoto & Tomisaka 2004) Initial conditions as in hydro; except for addition of additional, uniform, magnetic field:  = 84 on midplane Low mass model: M = 2.1 solar masses, R = 12,500 AU, T = 16K; free-fall time 67,000 yr. (Banerjee & Pudritz 2006; ApJ)

37. Onset of large scale outflow: 100 AU scales… magnetic tower flow (eg. Lynden-Bell..)

38. Jets as disk winds (Pudritz & Norman 1986): - launch inside 0.07 AU (separated by 5 month interval) - jets rotate and carry off angular momentum of disk - spin of protostellar core at this early time?

39. 3D Visualization of field lines, disk, and outflow: - Upper; magnetic tower flow - Lower; zoomed in by 1000, centrifugally driven disk wind

40. Physical quantities across disk. Note, stellar fossil field of 3000G, Hiyashi law for disk column density

41. Collapse of massive core, all coolants included; launch of outflow (Banerjee & Pudritz 2006, in prep)

43. V. Jets and star-disk interaction Field lines beyond Rco: shear and inflate; disconnect from star – feeds flux into disk to become disk-wind field lines (eg. Fendt & Elstner, 2000) Romanova et al (2002)

44. Magnetosphere; funnel flow onto star – what cancels the spin-up torque? Possibilities: - disk-locking (Konigl 1991), - X-wind (Shu et al 1994) - accretion powered, stellar wind (Matt & Pudritz, 2005 ApJ)

45. Accretion powered stellar wind (Matt & Pudritz, ApJL, 2005): operates even for rather weak stellar fields Numerical work shows dipolar lines open: - MHD wind maintains stellar spin at small values through accretion powered wind

46. Conclusions - theory and simulations converge Universality: - magnetized, rotating collapse produces central object + disk + jet - jets feed on accretion power Coupling: - reflects jets transport of angular momentum Consequences: - planetary  O star outflows