III- Star-disc interaction: ejections

unkindnesskindΠολεοδομικά Έργα

15 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

149 εμφανίσεις

III
-

Star
-
disc

interaction:
ejections

A
numerical

coincidence



Stellar

spin down =>
zero

torque condition





Jet
asymptotics

(if
connected

to disc)




V
jet

~ 200 to 500 km/s => J ~ 3 to 14 =>
f ~ 0.07 to 0.4


So, YSO jets
seem

to
allow

«

naturally

» a spin
equilibrium
… if
they

are
causally

connected

to the star AND the disc

Shu

et al 94

(
Uchida

&
Low

81,
Hirose

97)

Ferreira, Pelletier,
Appl

00

Camenzind

90

Shu

et al 94a, 95

Matt
&
Pudritz

05

Two simple configurations

-

Assumes
R
t
=
R
co

-

«

X
-
wind

»:
assumed

to
possibly

spin down the
protostar

(or in spin
equilibrium
)

-

Assumes
R
t
< R
X

=
R
co

-

«

Reconnection

X
-
winds

»
at

the
magnetic

neutral

line:
very

efficient
stellar

spin down (but
unsteady

wind

=
bullets
)

R
t

R
X

III.1
-

Steady
-
state

X
-
winds

X
-
winds

: back to basics

Shu

et al 94a,b
Shu

et al 95

Najita

&
Shu

94, Shang et al 98,02

Cai

et al 08

Ostriker

&
Shu

95

Mohanty

&
Shu

08

-

Y
-
type

magnetic

interaction (scenario for the
origin

of B)

-

Magnetosphere

is

assumed

to
be

potential

-

Cold
wind

calculations
:
super
-
SM

flow
from

point source to A surface (
prescribed
),
matched

to
cylindrical

asymptotics
;

-

unknown

method

(interpolation of invariants?): Shang et al

-

Variational

method
:
Cai

et al 08 (
See

also

Rosso & Pelletier 94)



Shu
et al
94c

Shang
et al
98, 02

Open questions:

-

Can
the disc
afford

the
imposed

mass
flux and
field

geometry
?

-

Is
the
transfied

equilibrium

satisfied
?

-

How
is

energy

transferred

to the MHD
wind

?

Cold
fan
-
shaped

winds
:
T
-
winds
,
M
-
winds

Ferreira & Casse 12, in
press

Terminal or
T
-
wind

Magnetospheric

or
M
-
wind

Look
at

all
a
-
disc

+ jet
equations

and
verify

if
boundary

conditions
can

be

satisfied
:


m
i

~1,
m
e

<<1 and

3 cases for
M
-
winds
:


r
i

<
r
co
: «

regular

»


r
i

>
r
co
: «

propeller

»


r
i

<
r
co
: «

X
-
wind

»


Governing

MHD
equations
,
applied

on a
thin

disc
annulus



Mass




Momentum




Energy




Perfect gas




Diffusion Bp




Induction B
f


With

3
anomalous

transport coefficients:
viscosity

(
n
v
),
magnetic

diffusivity

(
n
m
,
n
m
’)

Given

the fan
geometry
, the dominant
cemf

term

is


At

the surface (
ideal

MHD)





The
magnetic

shear

is

therefore



The
magnetic

configuration

Steady
-
state

Ohm’s

law
:


with





The
magnetic

bending

is


J
f

The
poloidal

structure

Since


m
< 1 in the
annulus

by
assumption
:



-

Radial balance
mostly

keplerian

in a
thin

disc (
annulus
)








-

Quasi
-

MHS vertical balance




Properties

of
stationary

fan
-
shaped

winds

Spherical

dilution of the
magnetic

flux


Since

only

published

F
-
shaped

wind

is

X
-
wind
, use
same

notations


where


The
definition

of the disc
magnetization

brings

(mass + mg flux conservation)

Angular

momentum
:




Specific

energy

(Bernoulli)

F
-
wind

power and
velocity

Najita

&
Shu

94,
Cai

et al 08

Wind power
is




where






Thus
,






Defining

an
average

jet
velocity
:


Wind
with

keplerian

speed
requires

q ~
D
r/r = h/r << 1

Local
energy

conservation
writes

for a cold flow:





Integrated

over the volume



Accretion

power












Energy

budget of the
annulus

(1/4)

r
i

r
e

Note: in
X
-
wind

theory



f = 0.1 to 0.4 and 2P
wind

≈ GMM
a
/2r
i


D
r/r=h/r= 0.05



Viscous

power












«

difference

factor

»


Note:
in SAD
theory
, torque
assumed

=0
at

r
i

and
r
e

>> r
i


To
get

power, a
F
-
Wind

requires

D>0 and of
order

unity

=>
Energy

must
be

flowing

from

the
inner

radii

through

viscous

(turbulent)
means
,
more
efficiently

than

it

leaks

out
at

the
outer

radius



Energy

budget of the
annulus

(2/4)

r
i

r
e

Disc
luminosity

(dissipation)







The
viscous

contribution
is


The
magnetic

contribution (Joule
heating
)



=>
Negligible

wrt

viscous

dissipation


The total power
lost

by the
annulus





Energy

budget of the
annulus

(3/4)

r
i

r
e

The power
available

to the
wind

can

be

derived

by
applying

the
energy

budget









On the
other

hand,
ideal

MHD
equations

for the
wind

give





Combining

the
two

provides

the relations,
valid

for all
fan
-
shaped

winds



Energy

budget of the
annulus

(4/4)

r
i

r
e

M
-
winds

below

co
-
rotation

We

identify

r
i

<
r
co

as the base of the
columns


-

Stellar

magnetic

torque
brakes

down the disc

-

Boundary

conditions:






R
m,i

~r/h




R
e,e
= 3/2






Unless

Pm>> 1, D <0:
unphysical

situation


Relax
steady
-
state

approximation or
allow

for
re

~ri (but not a fan
shape

anymore
…)


NB:
Same

conclusion for
T
-
winds

M
-
winds

beyond

co
-
rotation

Situation
with

r
co


<
r
t


<

r
i


-

No
accretion

columns

(
propeller

regime
)

-

In
that

case,
steady
-
state

only

for
f=1

-

viscous

stress must transport
angular

momentum

from

r
t


to

r
i
:
viscous

torque
accelerates

the disc









The
energy

feeding

the
wind

is

the
rotational

energy

of the star, if
D > ½



namely

comparable
viscosities
. Ok.



But to
redirect

entirely

the
accretion

flow, mass conservation
requires

an
incoming

velocity

u
e

~Cs.
Since

u
e

~
a
v
Cs

h/r,
this

implies

a
v

~r/h >> 1



M
-
winds

at

co
-
rotation
:
X
-
winds

Situation
with

r
t


<

r
i

r
co



-

Accretion

columns

possible
below

r
i
=> f <1

-

Possibility

to
be

powered

by
stellar

rotation




viscous

stress must transport
angular

momentum

from

r
t


to

r
i
:
viscous

torque
accelerates

the
annulus

(
z
i

~r/h and <0)




Magnetic

torque due to
X
-
wind

deccelerates

it
,
so

that

the
actual

disc
accretion

speed
is

tiny


(2) All
models

computed

with


b
~
unity
, J
between

2 and 7






=
> q = 1/
a
m

~ h/r



(1) This
requires

an
almost

perfect

matching

between

the
two

torques

Comments

on
X
-
wind

(1) All
considerations

here

are consistent
with

ideal

MHD
wind

dynamics

published

Differences

are



-

Induction
equation

for
B
j

(q) not
used

in
X
-
wind

theory



-

Disc
angular

momentum

conservation not
used


(2)
M
-
winds

(
whatever
)
never

obtained

in simulations: but out of range of
parameter

space


(3)
Could

X
-
winds

be

realized

?



-

issue of turbulence



-

issue of
allowing

accretion

column

formation



(
needs

m
s
~ 1
whereas

m
s

~ (h/r)
2
)



(4)
Note: YSO jet
kinematics

inconsistent

with

current

(
published
)
wind

calculations

(Ferreira et al 06,
Cabrit

et al 07)




-

range in
poloidal

speeds not
explained




-

steep

decline

in
spedd

towards

jet
edge

not
explained

III.2
-

ReX
-
winds

Reconnection X
-
winds: Interplay of dynamo +
fossil fields


Protostellar core at break
-
up (Class 0)


Bipolar fossil field


t=0: dynamo produces a dipole field


Magnetic neutral line at R
X
= R
*


Contraction of the protostar, spin
-
down by the ReX
-
wind + accretion funnels


r
x
≈ r
co
increases (magnetosphere expands)


Accretion rate onto the star is regulated


Stellar open field increases (Class I, II?)

The global
picture

Ferreira, Pelletier, Appl 00, MNRAS

1.
Stationary extended disc wind, providing open magnetic flux to the
star

2.
Unsteady ejection

above the reconnection zone, allowing to brake
down the contracting protostar

3.
Basic features remain if stellar dipole is inclined (precessing bullets
channeled by the outer disc wind)

The
role

of a
reconnection

belt

Ostriker & Shu 95

Both

configurations
require

an
equatorial

reconnection

zone (
interesting

for
energy

dissipation and CAI in
chondrules

-
Calcium

Aluminium
Inclusions
-

Gounelle

et
al 06
)

-
«

ReX
-
wind

» model:

enforced
, due
to
opposedly

directed

magnetic

fields

(
disc+star
)

-

«

X
-
wind

» model:

no justification (?)


Several

numerical

attempts

but large
scale

reconnection

is

major issue


Ferreira, Pelletier, Appl 00

Shu et al 94a

(1)
Virial

theorem
:



(2)
Energy

conservation
with





Provides

the contraction rate of the
protostar


(3) Mass conservation



(4)
Angular

momentum

conservation



with

always

verified

on long (KH) time
scales



Governing

equations

(L3
level
)

Consider

a
sphere

of mass M
*

initially

at

break
-
up

R
*
=
r
co
,
with

a dynamo,
evolving

following

the
Hayashi

track

(T
*
=
Cte
),
embedded

in an ambiant
magnetic

field
,
surrounded

by an
accretion

disc in JED state.

Governing

equations

The
co
-
rotation

radius
is

assumed

to
follow

r
co
=
r
X



R
x

is

the
reconnection

line
with

so

a prescription for
the
field

must
be

used


Disc
field

(
equipartition
)
:




Depends

on M
a
. If star spins down,
r
co
=
r
x

increases
,
so

must do B
MAES
,
hence

M
a



Stellar

field
:



where

n free
parameter

and
Bcl

is

the
closed

(
initially

dipolar
)
magnetic

field

linking

the
star to the disc.



Normalized

to the t=0 values, one has



where

is

the
stellar

closed

magnetic

flux.


which

needs

to
be

prescribed

in time…(or impose
some

time
evolution

for M
a
).


The
stellar

magnetic

flux

The total
stellar

magnetic

flux (
open+closed
)


Assuming

dynamo contribution to open flux
negligible


with






(B
MAES
varies as
r
-
b
,
b
=3/4).

This contribution of the open
stellar

flux
grows

in time as


What

about
F
cl
(t) ?


-

scenario 1: dynamo
provides

closed

flux
at

same

rate



-

scenario 2: no dynamo
at

all,
closed

flux
is

only

the
inital

flux


which

can

be

parametrized

by




where

is

a
measure

of the
amount

of
closed

flux
at

t=0



Stellar

spin
evolution

Free
parameters
:




(+
a

in the
no
-
dynamo

scenario)



n > 3
magnetic

field

exponent


f =
M
x
/M
a

mass flux in
ReX
-
wind


l
= (r
A
/r
x
)
2

magnetic

lever arm
parameter

Reconnection

X
-
winds

Stellar

field


n = 4

Dynamo scenario

T
*

= 3000 K

Reconnection

X
-
winds

Stellar

field


n = 4

Dynamo scenario

T
*

= 3000 K

Reconnection

X
-
winds

Dynamo scenario

T
*

= 3000 K


n=4


l

= 3


Influence of f


solid

: f=0.01


dashed
: f=0.027


dotted
: f=0.07


dash
-
dot
: f= 0.19

Long
-
dash
: f=0.5



Reconnection

X
-
winds

Stellar

field


n =

3

NO
-
dynamo

scenario

T
*

= 3000 K


a
=0.01


a
=0.5

Momentum flux Vs Bolometric luminosity

Bontemps
et al.

95

Class 0

Class I

10
3

yr

10
4

yr

10
5

yr

Ferreira
et al.

00

Saturation mechanism for B
*
?


ReX
-
wind

is

not a «

wind

» (or
only

in a
very

long time
averaged

sense
)


power
diminishes

in time
with

W
*


The disc
magnetic

flux
F

must
be

limited

otherwise

B
*

too

large,
W
*

too

low


If disc
magnetic

flux
ceases
,
both

Disc
wind

+
ReX
-
wind

stop (but APSW dominant)


One
would

expect

a
correlation

between

W
*

and
F


Does

the
weak

dispersion in

stellar

periods

reflect

a
weak

dispersion in disc
magnetic

flux ? (
remember

F


M
)


n = 4

III.3
-

Steady
-
state

conical

winds

Romanova et al 09

Konigl

et al 11

Lii

et al 12

Rt

<
rco

Rt

>
rco
:
propeller

«

discovery

» of
conical

jets
along

opened

stellar

field

lines

-

dense flow
attached

to the disc (=
conical

wind
)

-

stellar

wind

(=
fast

axial jet)

-

stellar

magnetosphere

is

compressed
:
m

~1

-

high

mass flux
M
w
/M
a

~10
-
30%

-

flow
driven

by gradient of
toroidal

magnetic

field

(== dense config)

-

propeller

case:
rapid

spin down of the
protostar

-

Accretor

case: spin up of the
protostar

-

depending

on turbulence
parameters
,
steady
-
state

wind

or not


=> A new class of
ejections

?


Romanova et al 09

Time
normalized

to
keplerian

period

at

r=1

N
q

=50, N
R

=120

Lii

et al 12

Same

as in Romanova et al 09, but
computational

domain

3 times
larger

=>
launching

+
collimation
studies


Simulations
done

with

Pm= 2
-
3,
typical

a
v
=0.3 and
a
m
=0.1

No
stellar

wind

allowed

this

time.


Lii

et al 12

Launching

zone
requires

equipartition

large
scale

(open)
field

-

same

as in disc
winds


-

magnetic

topology

different

from

M
-
wind

(no fan: Pm
too

low
)


-

The
outer

part
is

not a
SAD: m
s

larger
, due to
open
field

lines

Lii

et al 12

-

Accretion

rate onto the star,
expelled

in the
wind

(no
stellar

wind

here
)

-

Ang
mom
. fluxes
measured

at

the
stellar

surface (
red
) AND
at

R=20 (green).



Star spins up



Wind
is

matter

dominated
:
resembles

a «

warm disc
wind

»


Note:
Steady
-
state

is

«

demonstrated

» by
these

curves
, not by
showing

invariants

Projection of the forces:

-

wind

acceleration

is

done

at

the
expense

of
poloidal

current

I
p

-

Wind collimation idem (
current

closure

outside

the box)



Romanova et al 09

The
conical

winds

remain

axisymmetric

even

with

inclined

dipole

Comments

Romanova et al 09

(
Appendix

D2)


Steady
-
state

conical

winds

are
formed

whenever

P
m
>1, but large
viscosity

required
:
share

many

properties

of «

warm disc
winds

» (
steady
,
familiar

dynamics
,
axisymmetric
)


But the oscillations
were

unexplained



a
m
=1 P
m
=0.3 : no
wind


a
m
=0.3 P
m
=1 :
steady
-
state

conical

wind


a
m
=0.1 P
m
=3 : «

oscillations

»


a
m
=0.01 P
m
=30: ??


Onto the star

Onto the
wind

III.4
-

Magnetospheric

Ejections

ME =
Magnetospheric

Ejections

Zanni & Ferreira 12, in
press

-

simulation
with

a
v
=0.3 and
a
m
=0.1


-

MEs

+
stellar

wind

provide

efficient
spin
-
down

of
the star



-

MEs

are
time
-
dependent

and
depend

on
stellar

field

structure (
variability
,
asymmetry
). Collimation
depends

on
outer

disc
wind


Time unit=
stellar

period

N
R

x
N
q

= 214 x 100 (
twice

resolution

R09)

Mass fluxes:


Onto the star




In the
MEs




Dot: disc
wind

Long
dash
: ME,
from

star

Dash
:
Stellar

Wind

ME’s

are
loaded

from

both

sides

(but
most

of the mass
from

disc)

(plots= time
average

over 54
stellar

periods
)

-

From

disc:
centrifugal

+
magnetic

-

From

star: «

thermal

» push

-

at

r=7,
stellar

material

encounters

disc
materia

-

magnetic

field

is

azimuthaly

accelerating

material
:
magnetic

slingshot

Forces
from

disc surface to
cusp

Forces
from

stellar

surface to
cusp

Ejecta transport
away

a
significant

fraction of the disc
angular

momentum


=>
huge

decrease

of the
accretion

torque
onto the star

Torques on the star

Accretion


Dash
: ME

Dot:
Stellar

wind



Combination

of ME +
Stellar

wind

alows

a net spin down torque

-

But
does

not
compensate

for contraction…

-

Need

to
rely

on more massive
ejecta

and/or
some

propeller

phases

ME ≠ EMI =
Episodic

Magnetospheric

Inflation ?

Goodson

et al
97, 99

Matt et al 2002

Concluding

remarks
/questions

1
-

The
old

Ghosh

& Lamb
picture

is

in real trouble


-

accretion

funnel

flows

along

a
dipole

are
well

understood
.
With

complex

fields
,
another

story…


-

disc
interacts

with

the
dipole

only

on a
small

radial
extent


-

star must
loose

its

angular

momentum

through

ejection


2
-

The
idea

of a single model for BOTH jet
phenomenon

and
stellar

braking

is

getting

more and more
problematic


=> multi (
interacting
) components



-

disc
winds

are
probably

needed
:
most

of the mass flux in YSO jets and good
collimation
properties
. But issue of the
magnetic

flux
history

of the disc


-

X
-
winds
: no


-

Conical

winds
:
behave

exactly

like

disc
winds

from

a
small

radial
extent



-

ReX
-
winds
:
need

dynamical

calculations


-

ME’s

are «

perfect

»:
magnetic

slingshot

mechanism

braking

down the star
and
introducing

natural

variability


-

APSW:
certainly

do
exist

and
play

some

role
. Issue of
energy

conversion
must
be

worked

out.


Multiple MHD ejection sites in young stars

Adapted from Camenzind 1990

accretion powered

stellar wind

Unsteady

Magnetospheric ejections

(disk
-
star interaction)

Accretion shocks

disk

wind

Ferreira etal 06
: argue
that 3 components
coexist in YSO jets:


Which one dominates
the jet mass
-
flux and
power? Try to better
constrain role of disk
wind

Courtesy

S.
Cabrit