Transcript Globular Cluster Formation in CDM Cosmologies

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 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),
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)


M w / M a  0.1
2. Evidence for universality: CO flows
Measure thrust
in swept-up CO;
FCO
 250( Lbol / 103 L ) 0.3
Lbol / c
(Cabrit &
Bertout1992)
 Correlation works
for both low and
high mass stars
For 391 outflows: Wu et al (2004) same index
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
v p

d Mw
k

 const
Bp
d
* Function k 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

The toroidal field in rotating flows
- from induction equation:
B 

k
(v  r o )
 0 = 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)
2. Angular momentum conservation:
* Angular momentum per unit mass conserved
along each field line (depends on mass load)
l  (rv 
rB
4k
)  const
Regular behaviour of flow through “critical
(Alfven) point” on field line;
mA  v p / v A  1
2
2
2
l  o rA  (rA / ro ) lo
2
2
- Angular momentum is extracted from rotor
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:
v  2 o rA  (rA / ro )vesc,o
1/ 2
Use conservation laws (Anderson et al 2003) to
deduce point of origin of outflow from disk from
j  e   o l  const
observed disk rotation profile
  o  v p , /(2v , r )
2

Angular momentum extraction from disk:
- assume thin disk, neglect viscosity
- angular momentum flow due to external torque
of threading field:
- after vertical integration:

Ma
d (ro v )
dro
 ro B Bz |ro , H
2
Disk angular momentum equation (Pudritz & Norman 1986,
Pelletier & Pudritz 1992):


M a  [rA (ro ) / ro ] M w
2
Accretion and ejection coupled through magnetic
torque exerted on disk


Lever arm: rA (ro ) / ro  3 (numerics) and
observations (Anderson et al 2003): 1.8 – 2.6 for
DG Tau)
Disk angular momentum equation (Pudritz &
Norman 1986, Pelletier & Pudritz 1992):


M w / M a  0.1
Jet Collimation


Collimation of flows – force balance perpendicular to field line
a every point (eg. Heyvaerts 2003)
Hoop-stress provided by toroidal field:
FLorentz,r  J z B

Current carried by a jet – depends on mass load!
r
I (r , z )  2  J z (r , z )dr   (c / 2)rB (r , z )

0
Cylindrical collimation (Heyvaerts & Norman 1987) if:
lim I (r )  0
r 

If current finited – then Parabolic collimation (ie wide-angle)
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)
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:
Bz (ro ,0)  bro
 1
potential;   0
Blandford-Payne;
Pelletier-Pudritz   1 / 2 yet steeper
This prescribes mass loadings:
 o v p ,o
1 
k
 ro
B p ,o
1
 ro ,
ro
3 / 4
,
ro
1 / 2
,
ro
1 / 4
  1 / 4
  3 / 4
Last 2 give wideangle disk wind
Initial Magnetic Field Configurations
1. Potential
  0.0
2. Blandford-Payne
  0.25
3. Pelletier-Pudritz
  0.5
4. yet steeper..
  0.75
r
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 B p
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…
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 circumplanetary subdisk (eg. Kley et al 2001):

5

M Planet  6 10 M Jup yr 1
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)
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)
Best fit,
stationary,self-similar
solution that is better
match to
observations: warm
outflow (Casse &
Ferreira 2002) – a
disk corona involved?
  h(ro ) / ro  0.1
T
m 
1
v Ah

  d ln M a / d ln ro  0.004
Casse & Keppens 2004
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:

M  2 107 M  / yr
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 (dotdash)
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
Low mass model:
M = 2.1 solar masses,
R = 12,500 AU,
T = 16K; free-fall time 67,000 yr.
(Banerjee & Pudritz 2006; ApJ)
  6.5
t ff  0.4
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?

 accrete  M a (vK ,t rt )
Possibilities:
- disk-locking (Konigl 1991),
- X-wind (Shu et al 1994)
- accretion powered, stellar wind (Matt &
Pudritz, 2005 ApJ)
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

 w   M w * R2 (rA / R* ) 2
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