The DiskJet Connection

1
The Disk-Jet Connection

• Ralph Pudritz
• Robi Banerjee
• (McMaster University)
• IAUS 227,
• Catania, 2005

2
Overview

• A. Observational clues low vs. high mass
  outflows
• B. Disk winds universal scalings
• C. Outflows and jet formation during
  gravitational collapse
• - 3D AMR global
  simulations
• Points 1. Disk wind mechanism is universal (low
  and high
• mass)
• 2. Outflows and jets (low and high
  mass) are inevitable
• consequences of magnetized
  collapse
• 3. Outflows and jets commence even
  before final
• protostar assembled
• (Recent review Pudritz 2003, NATO ASI - Les
  Houches lectures Beskin et al eds.
  Springer-Verlag also Koenigl Pudritz 2000)

3
A. Observations

• Measure thrust
• in swept-up CO
• (well resolved flow,
• accurate masses,
• inclination corrected)
• (Cabrit Bertout 1992)
• excludes radiative
• and thermal
• driving
• Universal mechanism?

For 391 outflows Wu et al (2004) same index
4
CO outflows in low mass systems jet diagnostics

• CO flows trace interaction between jet and
  molecular cloud
• - Reviews Cabrit et al (1997), Richer et al
  (2000)
• Models 1. jet-driven bow-shock (Raga Cabrit
  1993, Masson Chernin 1993)?
• 2. wide-angle wind-driven shell
  from X-wind (Shu et al 2000, Li Shu 1996)?

5
CO outflows in high mass systems
CO flows in regions of massive star formation
(Shepherd Churchwell 1996, review Richer et al
2000) - Collimation of outflows in high and low
mass systems similar? collimation factors 2-10
(eg. Beuther et al 2002, 2003) - Outflows precede
the appearance of ultracompact HII region (eg.
Gibb et al 2004)
Beuther et al 2004, high mass outflow
6
Disks universal drivers of
jets/outflows ? - high spatial resolution
observations detect massive disk (eg. Cesaroni et
al 1999)

• Initial conditions, Bonnor-Ebert-Spheres?
• ( high mass cores turbulent 3D collapse of
  logatropes? Reid et al 2002, ApJ)
• Low and high mass stars from collapse of low
  and high mass gas cores?
• (IMF arises from CMF)

IR Observation of Bok globule Barnard 68, from
Alves, Lada Lada, Nature 2001 Mgas 2.1 MSol
Omega Nebula (M 17) from Chini et al. Nature
2004 Mdisk 100 MSol
7
Strong evidence for jets as centrifugally
driven disk winds 1. jet rotation

• (Bacciotti et al 2003, Coffey et al 2004, Pesenti
  et al 2004)
• High resolution (0.1) observations of emission
  line profiles of DG Tau
• - Line asymmetries on either side of jet axis
• jet rotation at 0.5 (110 AU) from source of
• 6-15 km/sec
• Footpoints for launch of jet extended over disk
  surface
• Detailed fits (Anderson et al 2003) show LV
  originates from disk region ranging from 0.3-4.0
  AU

8
2. accretion and jet mass loss rates coupled

• 
  TTS(a) FU Ori(b)
• a) Hartmann et al (1998)
• b) Hartmann (1997), Hartmann Kenyon
  (1996)
• High accretion rates in FU Ori systems will
  crush stellar magnetosphere (Hartmann 1997)

9
B. Universality of hydromagnetic disk winds
Blandford Payne (1982), Pelletier Pudritz
(1992)
10

• Conserved fluxes along a field line
• 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

11

• 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)

12

• Angular momentum flow in wind
• Angular momentum per unit mass conserved
  along each field line

Regular behaviour of flow through critical
(Alfven) point on field line
- Angular
momentum is extracted from rotor
13

• Bernoulli theorem total energy conserved along
  any field line in rotating, magnetized flow
• - Terminal speed scales with depth of
  gravitational potential well
• Use conservation laws (Anderson et al 2003) to
  deduce point of origin of outflow from disk from
  observed disk rotation profile

14

• Disk angular momentum equation
• - assume thin disk, neglect viscosity
• - angular momentum flow due to external
  torque
• of threading field
• - after vertical integration
• - sub for toroidal field (using 3.), for
  vertical field (2.),
• for l using (5.)

15

• Disk angular momentum equation (Pudritz Norman
  1986, Pelletier Pudritz 1992)
• 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)

16

• Total mechanical energy carried by jet scales
  with depth of potential (Pudritz 2003)
• For Class 0 protostars
• Total thrust carried by jet, scales with depth
  of potential

17

Jet Collimation

• Collimation of flows force balance
  perpendicular to field line a every point the
  intractable Grad-Shafranov equation
• Hoop-stress provided by toroidal field
• Current carried by a jet
• Cylindrical collimation (Heyvaerts Norman 1987)
  if
• So jet collimation depends on mass loading
  through toroidal field ( Pudritz 2003, Pudritz et
  al 2005 )

18
2D Numerical Simulations - how is jet
collimation controlled?

• I. Disks as platforms for jets
• - underlying accretion disk provides fixed
  boundary conditions for jet
• - 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),
• II. Global simulations
• - disk and jet evolution both simulated
• - eg. Uchida Shibata (1985), Stone Norman
  (1994), Bell Lucek (1995), Tomisaka (1999),
  Kudoh et al (2002), von Rekowski Brandenburg
  (2004),

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• Ouyed Pudritz (1997) Accretion disk boundary
  conditions outflow from a magnetized disk
  corona
• - 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

20

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

21
Initial Magnetic Field Configurations

• Potential
• 2. Blandford-Payne
• 3. Pelletier-Pudritz
• 4. yet steeper..
• r

z
22
Potential poloidal field
density
23
BP poloidal field
density
24
PP poloidal field
density
25
-0.75 poloidal field
density
26
Potential config poloidal velocity field
27
BP Poloidal velocity field
28
PP poloidal velocity field
29
-0.75 poloidal velocity vectors
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C. Outflows and jets during star formation
global simulations

• First simulations Uchida Shibata (1985)
• - magnetized disk sub-Keplerian rotation
• rapid radial collapse, winding of
  field creating
• strong toroidal field launch vertical
  torsional
• wave flux - powers outflow transient
• Tomisaka (1998) collapse of core in magnetized,
  filament, in nested grid simulations collapse
  and outflow.

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Tomisaka (1998) collapse of cylinder
32
3D hydro collapse of rotating, cooling BE
spheres(Banerjee, Pudritz, Holmes, MNRAS 2004)
Molecular Clouds in hydrostatic equilibrium
follow a Bonnor-Ebert-Profile
Critical BE-Sphere xcrit 6.451
Barnard 68, from Alves, Lada Lada, Nature 2001

• Other observational evidence
• Coalsack globule 2, M 4.5 Msol,
  Racca, Gomez Kenyon, ApJ 2002
• Dark globule B335, M 14 Msol,
  Harvey et al. ApJ 2001

Dust column density profile in terms of visual
extinction follows a BE-Profile
33

• Initial Conditions
• Pressure confined, rigidly rotating, B-E model
• MOLECULAR COOLING, using data from Neufeld et al.
  (1995)

High mass M 168 solar masses R 330,000 AU T
20K
Low mass model M 2.1 solar masses, R
12,500 AU, T 16K free-fall time 67,000
yr.
34
FLASH useful approach to Adaptive Mesh
Refinement (AMR)

• - Code developed at
• U. Chicago ASCI/
• Alliance center
• - Solves coupled hydro
• gravity on Eulerian Grid
• - Dynamically, self adjusting grid
• Grid adjusts to resolve local Jeans length
  (Truelove et al 1997) we use 12 pixels rather
  than 4
• - Parallel code/MPI
• - Image has 16 million grid
• points, resolves 0.3 AU.

Each block has 83 pixels
35
Disk formation with cooling has double shock
structure (eg. Yorke Bodenheimer,)
M 170 Msol, W tff 0.1
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Bars, Rings, and Fragmentation cont.
Low mass cloud (Barnard 68), tff W 0.2,
ring/bar, M 0.1 Msol
37
Bars, Rings, and Fragmentation cont.
high mass cloud, tff W 0.2, ring gt binary ring
size 1016 cm (cf. torus in M 17 Chini et al.
2004)
38
Disk Formation High and low mass disk accretion
low mass (M 2.1 MSol) cloud, e.g. Barnard 68
high mass (M 170 MSol) cloud
Mass accretion of high mass cloud high enough to
feed a high mass protostar (M 10 Msol) in 104
years
39
The Onset of jets and
outflowsMHD simulations of collapsing,
magnetized B-E spheres Low mass Banerjee
Pudritz, 2005, Nature, submitted)

• Initial conditions as in hydro except for
  addition of additional, uniform, magnetic field
  ? 84 on midplane
• Spin parameter

40
Earliest signature of outflow toroidal
magnetic tower launched near position of outer
shock 160 AU- Upper panel 68,000yr.into
collapse, outflow just starts- End of
simulation, 1400 yrs later, outflow well
developed.- Super Alvenic outflow velocity at
400 AU about 0.5 km per sec.
41
Onset of jet/disk wind, on scales interior to
0.7 AU- snapshots zoomed in by factor of 1000
compared to previous- upper collapse into
central regions- lower start of disk wind on
favourably distorted field lines- SuperAlvenic
jet flow at this stage is 3 km per sec.at 0.4 AU
greater than escape speed
42
3D Visualization of field lines, disk, and
outflow- Upper magnetic tower flow- Lower
zoomed in by 1000, centrifugally driven disk wind
43
Protodisk and prostar(s) side and top views
inside of
10(12) cm
Jets are initiated even though central object(s)
are only 1/100th of a solar mass jets are true
products of disk accretion
44
Physical quantities across disk. Note, stellar
fossil field of 3000G, Hiyashi law for disk
column density
45
Disk-wind and jet connection outflow across
spherical shell (top left).. Effect of double
shock (R1AU, and 600 AU, clearly seen
46
High mass collapse earliest phases of
protostellar core assembly same physics

• Onset of magnetic tower outflow on large scales

47

• 3D Visualization of field lines, tower flow, and
  disk, in massive outflow simulation.

48
Magnetic tower flow shock structure as flow
pushes through infall envelop
49

• Bar still forms in disk although at very small
  scales compared to pure hydro simulation.

50
Higher accretion rates than in pure hydro
caseInner jet dominates angular momentum
transport by an order of magnitude!
51

• Summary
• - Magnetized collapse in clumps expected to be
  universal (ie BE calculation is a good guide even
  to more complex situation).
• - Outflows and jets (low and high mass systems)
  get started even before complete star is
  assembled!
• - Dynamics and collimation of outflow universal,
  does not depend on mass.. Should pertain to
  understand early outflows in formation of massive
  stars.

Turbulent fragmentation of a magnetized
clump Tilley Pudritz 2005