The Disk-Jet Connection: A Universal Picture for Protostellar Jets

Ralph Pudritz McMaster University Western Workshop: From Protostellar Disks to Planetary Systems

Outline 1. Theory of disk winds2. Numerical simulations – disks as jet engines3. Coupled disk-jet evolution4. Disks and outflows during gravitational collapse5. Jets and star-disk interaction

Collaborators: Robi Banerjee (pdf), Sean Matt (pdf), Rachid Ouyed (U. Calgary), Conrad Rogers (summer student),

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)

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..

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)

1.0/

aw MM

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

3.03 )10/(250/

LL

cL

Fbol

bol

CO

2. Evidence for universality: CO flows

I. Theory of disk winds

Blandford & Payne (1982; BP), Pelletier & Pudritz (1992)

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

constd

Md

B

vk w

p

p

k

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)

)( orvk

B

0

2. Angular momentum conservation:

* Angular momentum per unit mass conserved along each field line (depends on mass load)

constk

rBrvl )

4(

Regular behaviour of flow through “critical (Alfven) point” on field line;

- Angular momentum is extracted from rotor

ooAAo lrrrl 22 )/(

1/ 222 ApA vvm

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

oescoAAo vrrrv ,2/1 )/(2

)2/( ,2

,

rvv

constlej

po

o

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):

Hrzoo

oa

oBBr

dr

vrdM ,

2 |)(

wooAa MrrrM 2]/)([

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):

3/)( ooA rrr

1.0/

aw MM

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)

BJF zrLorentz ,

Jet Collimation

r

z zrrBcrdzrJzrI0

),()2/(),(2),(

0)(lim rrI

- 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):

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),…

Krasnopolsky et al (1999)

- treatment near outflow axis:

core “jet” – no equilibrium

- cold gas – pressure small

- constant density maintained

at disk boundary

Outflow from initial split –monopole initial field: Poloidal field and velocities isodensity contours

Beta = 1; flow not collimated Romanova et al (1997)

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

1)0,( ooz brrB

0 4/12/1 4/3

4/12/14/31

1

,

,

,,,

oooo

oop

opo

rrrr

rB

vk

1. Potential

2. Blandford-Payne

3. Pelletier-Pudritz

4. yet steeper..

r

Initial Magnetic Field Configurations

0.0

25.0

5.0

75.0

z

Potential: poloidal field density

BP: poloidal field density

PP: poloidal field density

-0.75: poloidal field density

BP: Poloidal velocity field

-0.75: poloidal velocity vectors

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…

pB

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)

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)

15106

yrMM JupPlanet

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),…

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)

004.0ln/ln

1

1.0/)(

oa

A

Tm

oo

rdMd

hv

rrh

Casse & Keppens 2004

Best fit, stationary,self-similar solution that is better

match to observations: warm

outflow (Casse & Ferreira 2002) – a

disk corona involved?

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:

yrMM /102 7

Purely dynamo generated fields: conical outflows

Mass loading effect? Need for ambient field too?

von Reskowski & Brandenburg 2004

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

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

4.0

5.6

fft

Low mass model: M = 2.1 solar masses,

R = 12,500 AU, T = 16K; free-fall time 67,000 yr.

(Banerjee & Pudritz 2006; ApJ)

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

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?

3D Visualization of field lines, disk, and outflow:

- Upper; magnetic tower flow

- Lower; zoomed in by 1000, centrifugally driven disk wind

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

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

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)

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)

)( , ttKaaccrete rvM

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

2*

2* )/( RrRM Aww

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