# (a * ) Jets?

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15 Νοε 2013 (πριν από 4 χρόνια και 6 μήνες)

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WINDS AND
JETS FROM
ACCRETION FLOWS

Ramesh Narayan

Pre
-

Shapiro, Lightman & Eardley (1976):
hot 2T solution

thermally unstable

Ichimaru (1977):
Hint that there are
two hot 2T solutions

Rees et al. (1982):
Ion torus model

unclear which 2T solution (unstable?)

Narayan & Yi (1995), Abramowicz et al.
(1995):
stability, etc.

and Jets

Narayan & Yi (1994, Abstract):

… the
Bernoulli parameter
-
dominated flows are susceptible to producing outflows … We
-
dominated accretion may provide an
explanation for … the widespread occurrence of outflows and jets
in accreting systems

Narayan & Yi (1995, Title):
-
Dominated
Accretion: Self
-
Similarity and
Bipolar Outflows

Strong outflows confirmed in numerical simulation

WINDS, JETS

-
Dimensional

2
s
R
R
2
R
2 2
R s
P K c,w P/( 1)
dv
d 1 dP d d w
v
dR dR dR dR dR
dBe d 1 w
v 0
dR dR 2
1
Be v c Constant
2 1

   
 
 

   
 
     
 
 
 
   
 
 
   

Be
: Bernoulli parameter

Bernoulli Parameter

Be

For the self
-
similar
solution,

Be

is positive
(for

< 5/3
)
which means that the
gas is not
bound to the BH

it can expand to infinity and flow out

Hence strong
outflows/winds

are expected in an

Outflow speed:
v

~ (2Be)
1/2
~ 0.3v
K

In contrast, gas in a
thin disk

is tightly bound:
Be ~
-
v
K
2
/2

2 2 2 2
R s
2 2
K K
1 1 GM
Be v R c
2 2 R 1
5 3
2 v 0.12v
9 5

   

 

Convection

Narayan

& Yi (1994, Abstract):

… Convection is likely in many of these flows and, if present,
will tend to enhance the above effects
(winds, outflows)…

Narayan

& Yi (1995, Abstract):

… In addition, all the solutions are convectively unstable,
and the convection is particularly important along the
rotation axis…we suggest that a bipolar flow will develop
along the axis of these flows, fed by material from the
surface layers of the equatorial inflow.

WINDS, JETS

Why is there Convection?

Accreting gas is steadily heated by
viscous dissipation

But it is not radiating any of the energy

Entropy increases with decreasing
R
:
P/

~ R
-
(5
-
3

)/2
~ R
-
1/4

Satisfies the classic
Schwarzschild
criterion

for convective instability

Outflows/Convection
in
Viscous Rotating Flows

Numerical simulations of
inefficient hydro flows reveal
considerable convective activity
(Igumenshchev et al. 1996,
2001; Stone et al. 1999;
Igumenshchev & Abramowicz
1999, 2000)

These flows are called
convection
-
dominated
accretion flows (
CDAFs
)

Abramowicz et al. (2001)

Computer
Simulations

2D MHD: Stone & Pringle (2001)

3D MHD: Igumenshchev et al. (2003)

3D hydro: Igumenshchev et al. (2000)

GRMHD
Simulation
of a
Magnetized

The simulation spontaneously
generates:

1.
geometrically thick flow

2.
strong wind

3.
magnetized relativistic jet

McKinney & Gammie (2004)

Mass Loss in the Wind

If mass is injected at a rate
Mdot
inj

at some
R
inj
, accretion rate decreases
with decreasing
R

Less mass reaches the center than is
supplied on the outside

inj
inj
( ),0 1
s
R
M R M s
R
 
  
 
 
 
How Much Mass Does the
BH Actually Accrete?

Less than what is supplied

SMBH
: Assuming
Bondi flow
on the
outside, which circularizes at some
r
circ

r
Bondi
, then

Mdot
BH

~ Mdot
Bondi
/r
circ
s

BHXRB
:
Mdot

Mdot
BH

~ Mdot(r
tr
)/r
tr
s

The value of
s

is highly uncertain…

Cooling

Flow

External

Medium

r
circ

r
Bondi

r
tr

Why are Quiescent BHs
Extraordinarily Dim?

Why are quiescent
XRBs

and quiescent
SMBHs

like
Sgr A*

so dim?

Is it because they have

Low mass accretion rate?

Both?

Inefficient
vs

Mass
Outflow

Sgr A*

is extremely underluminous
because of
3

(roughly equal) factors
(Yuan et al. 2003):

Low mass supply:

Mdot
Bondi
~ 10
-
4

Mdot
Edd

Mass Outflow:
Mdot
BH

~ 10
-
2.5
Mdot
Bondi

L
acc

~ 10
-
2

(0.1 Mdot
BH

c
2
)

All part of the

Mdot
BH
=Mdot
Bondi
)

Nuclear SMBHs and Feedback

Bright AGN
have
thin disks
,

LLAGN
have

SMBHs

produce most of their
luminosity

in the
thin disk

phase (
quasars
,
bright AGN
)

SMBHs

spend most of their
time

(
90
-
99%
) in the

phase (
quiescence
)

SMBHs

accrete most of their
mass
in the

thin disk

phase
(Hopkins et al. 2005)

SMBHs
probably produce a lot of their
outflow energy

in
the

phase

100%

coupled to the external medium

Energy Output in the Wind

The
wind
will carry substantial
kinetic energy

which might have an
important effect on the
surroundings

Energy is of order a few percent of
the outflow mass energy

AGN

could modify mass supply from
external medium (
AGN feedback
)

Disk

outflow

during core collapse
may drive
SNe

(Kohri et al. 2005)

inj
inj
inj
1
inj
1
2
inj
inj
in
( )
Be
2(1 )
s
w
s s
w w
w
s
s
S
w
S
R
M R M
R
s M
d M dR
R R
GM
dL d M d M
R
R
R
s M c
L
s R R

 

 
 
 
 
 

 
 
 
 
 
 
 
 

 
 

 
 

Mechanical feedback from
SMBH

during super
-
Eddington accretion phase

AGN

during bright
quasar phase

Mechanical feedback through winds (and jets)

Causes reduced accretion

important for
understanding
AGN evolution

Strongly affects galaxy formation

is related to

physics

and Jets

Narayan & Yi (1994, Abstract):

… the
Bernoulli parameter
-
dominated flows are susceptible to producing outflows … We
-
dominated accretion may provide an
explanation for … the widespread occurrence of
outflows

and
jets

in accreting systems

The connection to outflows/winds was obvious

The connection to jets was a wild guess!!

Relativistic Jets

The power in an accretion flow is
~ 0.1 Mdot c
2

If a substantial fraction of this energy
goes into a substantial fraction of the
mass, expect only subrelativistic outflow

To get a
relativistic jet
, we have to
concentrate the accretion energy in a
small fraction of the mass

Even better:
extra source of energy

Relativistic Jets

“Superluminal” Motion

3C273

GRS
1915+105

Two Kinds of Jets

BH XRBs
have two kinds of jets:

-
power jet in the hard state

Impulsive high
-
power jet ejections

-
loud quasars
come in two types

-
power

FRII sources: blobby(?) high
-
power

Perhaps the physics is the same for
both classes of objects

connection for
Hard State/FRI

BH Accretion

Narayan 1996; Esin et al. (1997)

Fender, Belloni & Gallo (2003)

BH XRBs:
strong connection between
and

jets

Hysteresis

in low
-
high
-
low state transitions not fully understood

emission/Jet activity
seen in low
-
luminosity
AGN (
LLAGN
)

= L/L
Edd

R’ = 6 cm /B band

-
quiet AGN

probably have no
, only
thin disks

Ho (2002)

vs

Jet

are clearly associated with
Jets

Observed radiation is a combination of
emission from

and
Jet

thermal electrons
likely
to be from the

power
-
law electrons
likely to be from the
Jet

vs

Jet

is almost always from
PL

relativistic electrons in the
jet

X
-
rays

in the
hard state
look very
thermal, and must be from the

But, at lower accretion rates, the jet
may dominate even in X
-
rays

IR/optical

could be from outer
thin disk
,
or from
, or from
jet

Ingredients Needed for
Relativistic Jets

Impressive observational evidence for a
connection between

and
relativistic jets

At the same time there is considerable
evidence that
thin disks
are not
conducive to producing jets

Therefore, the accretion mode is clearly
one major factor behind jet activity

BH spin
?

Horizon shrinks: e.g.,
R
H
=GM/c
2

for
a
*
=1

Singularity becomes ring
-
like

Particle orbits are modified

Frame
-
dragging
---

Ergosphere

Energy can be extracted from
BH

Free Energy

Area Theorem
: The surface area of a
BH

can never decrease

A
BH

of mass
M

and spin
a
*

has less area
than a non
-
spinning
BH

of the same mass

Therefore, by reversible processes, this
BH

can be converted to a non
-
spinning
BH

of
lower mass, thereby releasing energy

How
Much
Energy?

1/2
2 2
2 2
*
2
*
8
8 1 1
16 if 0
A M M M a
M a
M a

 
  
 
 
  
 

2
initial final
*
2
*
Maximum Energy Available
0 (if 0)
0.29 (if 1)
E M M c
a
Mc a
 
 
 
Spinning Black Hole as an
Energy Source

A spinning
BH

has free energy that can
in principle be extracted
(Penrose 1969)

Can be done with specially designed
particles
(Penrose 1969)
,

but this is
unlikely to happen in a real system

Is there a natural way to
“grip”
a
BH

to
extract the free energy?

Magnetic fields are promising

Magnetic Penrose Process
(Meier 2000)

MHD Jet Simulations

Numerical
MHD

simulations of
around
rotating BHs

produce
impressive
jets/outflows

(Koide et al. 2002; de Villiers et al. 2003;
McKinney & Gammie 2004; Komissarov 2004; Semenov et al. 2004;
McKinney 2006; …)

OUTFLOW

JET

McKinney & Gammie (2004), McKinney (2006)

40M

400M

a*=
0.94

Other papers:
De Villiers et al. (2003); McKinney & Gammie (2004);
Komissarov et al. (2004), Tchekhovskoy et al. (2008)…

Semenov et al. (2004)

Jets from Spinning Black Holes

Semenov et al. (2004)

Role of the Black Hole

The accretion disk produces a mass
-
relativistic speed even from inner edge

Field lines from the
ergosphere

region
inside the disk inner edge are much
cleaner and are
magnetically dominated
(
Poynting
-
dominated
)

Rotation of these field lines is favorable
for producing a relativistic jet

Magnetic Hoop Stress and
Jet Collimation

A popular picture of jet collimation
is that the
hoop stress
of a helical
magnetic field provides the inward
collimating force

But this does not really work for
relativistic jets, especially in the
force
-
free regime

Force
-
Free
Magnetodynamics

Force
-
Free
: An approximation in which
we have
charges
,
currents

and strong
magnetic fields
, but no
mass
density/inertia

That is, we assume that the
charged

particles are
massless

This is a reasonable
first approximation
for studying
ultra
-
relativistic jets

Spinning Split Monopole

Michel (1973)
derived an
exact solution for a
spinning split monopole
with a
force
-
free
magnetosphere

Strong acceleration

But
no collimation
!

Field lines are swept back,
but they do not collimate
in the poloidal plane

How are Jets Collimated?

Self
-
collimation is apparently not feasible
with relativistic jets

We need some
external medium
to
collimate the spinning magnetic fields

In the case of a
Gamma
-
Ray Burst
, the
envelope of the star provides collimation

For other accreting
BHs
, the accretion
disk has to do it

Strong Outflow

Cartoon of a Jet System

Gamma
-
Ray Burst

XRB or AGN

Necessary Ingredients:
A Proposal

Powerful jet requires

Spinning BH/Star

Magnetic field

Currents (conducting)

Low inertia

Confining medium

(Tchekhovskoy
et al. 2008)

Axisymmetric force
-
free

jet from a
spinning magnetized star
surrounded
by a
magnetized disk

(Tchekhovskoy et al. 2008)

Toy Model
: Numerical simulation of a force
-
free jet surrounded by a stellar
envelope or a disk wind

Near Zone:
~
10
2
r
BH

5

2

4

3

1

0

40

-
40

80

Lorentz factor
increases
moves out:

jet

~ z
1/2

Rotation
hardly affects
the poloidal
structure of
the field even
tho’
B

B
z

Far Zone:
~
10
6
r
BH

log
10

3

2

1

0

Lorentz factor
continues to
increase and
reaches
~10
3

by a distance
of
10
6
r
BH

Jet is naturally
collimated:

jet

~ few
degrees

5x10
4

-
5x10
4

2x10
6

10
6

0

Main Results

Acceleration and collimation of a
force
-
free jet

depend on the radial profile of
the confining external pressure

A profile
P ~ r
-
5/2
, as expected for a
stellar envelope or an
,
seems to be favorable

Terminal Lorentz factor

depends on
how far out the confinement operates:

max

~ (r
max
)
1/2

vs

Thin Disk

Nearly all simulation results to date are
for non
-

Produce strong outflows and jets

What kind of jets/winds do
thin disks

produce?

Preliminary indication is that the jet is
absent and the wind is relatively weak
(e.g., Shafee et al. 2008)

Consistent with observations…

Unresolved Issues

How different are
mass
-
jets
compared to
force
-
free
jets?

Are their
terminal Lorentz
factors and
collimation angles
very different?

Given that
B

B
z
, why are jets
stable

over such enormous distances (e.g.,
Kruskal
-
Shafranov

criterion)?

BH Spin and Jets

There has been much speculation that jets are powered
by
BH

spin

Microquasar GRS 1915+105

has remarkable
relativistic
jets:

~ 2.7

(
Mirabel & Rodriguez
)
---

and it

has

a
*

1

---

looks like evidence for spin
-
jet connection…

GRO J1655
-
45

is also a
microquasar
:

~ 2.7
---

but it
has a more modest spin:
a
*

~ 0.65

0.75

So, is there really a connection between rapid
BH

spin
and powerful
jets
? Not clear …

BH Masses, Spins and Jets

Source Name

BH Mass (M

)

BH Spin (a
*
)

Jets?

LMC X
-
3

5.9

9.2

~0.25

X

XTE J1550
-
564

8.4

10.8

(~0.5)

GRO J1655
-
40

6.0

6.6

0.7
±

0.05

M33 X
-
7

14.2

17.1

0.77
±

0.05

X

4U1543
-
47

7.4

11.4

0.8
±

0.05

X

GRS 1915+105

10
--
18

0.98

1

Summary

and
strong outflows