Physics 778 - 2009 Jets and Outflows

1. Physics 778 - 2009 Jets and Outflows Ralph Pudritz

2. Clues and Questions: 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: is jet production mechanism same - from disks from brown dwarfs to massive stars? Hypothesis: Jets harness accretion power in all systems, from extended disk down to stellar surface..

3. YSO Optical Jet Gallery

4. 1.3 YSO jets – relation to disks SED classification: - Class 0: infalling envelope – fast CO outflow + bright submm core ( ) - Class 1: evolved protostar + thick disk + jet: SED dominated by disk ( ) - Class 2: (CTTS) star + thick disk + jet: SED dominated by star ( ) - Class 3: (WTTS) no obvious disk – no jet - ( )

5. High resolution studies: 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. Hartmannet al 1998)

6. Jet Dynamics: (DG Tau – HST) - Top image: two distinct bow shocks (at MV) - Velocity range: + 50 to 450 km per sec - widths of velocity bins; ~ 125 km per sec Find: - Jet density increases towards star and axis - HVC jet emission traced to within 15 AU (0.1”) - Continuous velocity variation in jet in transverse direction: highest near jet axis, lowest farther away - Collimation of HVC is better DG Tau - Bacciotti et al (2002)

7. Velocity asymmetriescompatible with rotation: Shifts in range 5 – 25 km/sec; at slit positions 20-30 AU from axis of flow (0.1” = 14 AU at this distance) Angular momentum transport: 60-100% of that in inner disk -> jets as major transport of disk angular momentum Coffey et al 2004

8. Direct observed links between accretion and outflow TTS(a) FU Ori(b) a) Hartmann et al (1998) b) Hartmann (1997), Hartmann & Kenyon (1996)

9. 3.1 Theory of disk winds Blandford & Payne (1982; BP), Pelletier & Pudritz (1992)

10. Basic stationary, ideal MHD equations (Chandrasekhar, Mestel,..): (mass conservation, EOM, induction, & no monopoles) • Convenience – employ poloidal & toroidal fields:

11. Why universal solutions are possible: Conservation laws for ideal, 2-D flow • General solution to induction equation: where is an “electrostatic” potential. • Assume axisymmetry: - Toroidal comp (5): poloidal velocity is along poloidal field lines - Take : along field lines

12. 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

13. 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)

14. Angular momentum carried by the flow: - from toroidal component EOM: • Application 1: Flow along a field line - (6) & (7) imply - angular momentum per unit mass conserved

15. 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

16. Energetics - Bernoulli theorem – rotating, magnetized flow - take : - Terminal speed – scales with depth of gravitational potential well: - eg. If inner disk edge at twice radius of central object:

17. 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

18. 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):

19. For viscous disks – compare wind and viscous torque: • Vertical torque exerted by wind - radial torque exerted by disk turbulence - MHD disk wind: co-rotation of accelerating gas with disk – enforced out to Alfven point - Viscous torque in disk (Shakura-Sunyaev): torque ratio:

20. 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):

21. Jet Collimation • 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)

22. Jet collimation depends on mass loading through toroidal field (PRO): - 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)

23. Self-similar models for jets and disks i) the only velocity scale in problem is Keplerian ii) disk structure: iii) wind structure: Blandford & Payne (1982)

24. Consequences of self-similarity: (i) (ii) (iii) From (i) and density scaling (iv) Mass loading of wind:

25. Flow becomes strongly toroidal beyond Alfven surface. • Flow strongly super-Alfvenic • Rotation of flow decreases as jet widens out

26. 4. Numerical simulations of disk winds

27. 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),…

28. A. 2-D Jets from Keplerian disk + corona • Numerical model – (Ouyed & Pudritz 1997) - accretion disk: surface pressure matches pressure of overlying, non-rotating corona - corona: initial hydrostatic equilibrium in (unsoftened) gravitational potential of star - initial B field: exerts no force on initial state – choose • Some numerical tests: - No B; analytic equilibrium maintained to machine accuracy

29. Accretion disk boundary conditions: - specify 5 flow variables at all points of disk surface – at all times: - ; fixed by solendoidal condition - ; smaller than sound speed in Keplerian disks • Inner radius of disk - basic length scale - no rotation to interior - time, measured in units of

30. Episodic jet: Ouyed, Pudritz, & Stone, Nature, 1997

31. Poloidal velocity, top frame: density below, OPS94

32. Toroidal field, top frame: density, lower frame, OPS97

33. 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

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

35. Potential: poloidal field density

36. BP: poloidal field density

37. PP: poloidal field density

38. BP: Poloidal velocity field

39. 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 (Klaassen et al 2005, Banerjee & Pudritz 2005) - Disk winds many punch hole in envelop - allowing radiation to escape ( Krumholz et al 2004)