A Universal Picture for Protostellar Jets

velodromeryeΠολεοδομικά Έργα

15 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

130 εμφανίσεις


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)


1
.
0
/



a
w
M
M










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
.
0
3
)
10
/
(
250
/



L
L
c
L
F
bol
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



const
d
M
d
B
v
k
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)



)
(
o
r
v
k
B






0

2. Angular momentum conservation:



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

const
k
rB
rv
l



)
4
(



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







-

Angular momentum is extracted from rotor

o
o
A
A
o
l
r
r
r
l
2
2
)
/
(



1
/
2
2
2


A
p
A
v
v
m
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



o
esc
o
A
A
o
v
r
r
r
v
,
2
/
1
)
/
(
2




)
2
/(
,
2
,










r
v
v
const
l
e
j
p
o
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):



H
r
z
o
o
o
a
o
B
B
r
dr
v
r
d
M
,
2
|
)
(








w
o
o
A
a
M
r
r
r
M
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
/
)
(

o
o
A
r
r
r
1
.
0
/



a
w
M
M



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)




B
J
F
z
r
Lorentz

,
Jet Collimation






r
z
z
r
rB
c
r
d
z
r
J
z
r
I
0
)
,
(
)
2
/
(
)
,
(
2
)
,
(


0
)
(
lim



r
r
I
-

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
,
(



o
o
z
br
r
B
0


4
/
1



2
/
1



4
/
3



4
/
1
2
/
1
4
/
3
1
1
,
,
,
,
,









o
o
o
o
o
o
p
o
p
o
r
r
r
r
r
B
v
k



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…



p
B
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)



1
5
10
6






yr
M
M
Jup
Planet
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
.
0
ln
/
ln
1
1
.
0
/
)
(







o
a
A
T
m
o
o
r
d
M
d
h
v
r
r
h




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:


yr
M
M
/
10
2
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



ff
t

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)


)
(
,
t
t
K
a
accrete
r
v
M



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
*
)
/
(
R
r
R
M
A
w
w






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