Download Some progress in black hole accretion

The Role of Magnetic Fields in
Black Hole Accretion
Ding-Xiong Wang (汪定雄)
Zhao-Ming Gan (甘朝明)
Chang-Yin Huang (黄昌印)
Jiu-Zhou Wang (汪九洲)
Enshi, Hubei
2009. 9. 26
Outline of this talk
● Introduction
● Role of magnetic field
for jet production
● Role of magnetic field
for disk radiation
● Some work to be done
1. Introduction
Quasars and
Microquasars
Fig. 1
Schematic drawings
for quasars
and microquasars
Three basic ‘ingredients’：
(1) a spinning black hole
(2) an accretion disk
(3) collimated jet
Magnetic Field in Black Hole
Accretion Disks
Fig. 2.
Different types of
magnetic field lines in
black hole
magnetosphere.
From Blandford (2002)
BH
DISK
• The role of the following magnetic field
is discussed in this talk.
• Line 2: Magnetic reconnection  Disk
corona heating  X-ray Luminosity;
• Line 5: MC process for transferring E and
L from a spinning BH to inner disk;
• Line 3: BP process for driving jet;
• Line 6: BZ process for driving jet.
2. The Role of the Magnetic Field
for Jet Production (Lines 3 and 6)
There are two ingredients necessary for
the production of jets.
1. a source of material with sufficient
free energy to escape the gravitational
field of the compact object.
2. a way of imparting some directionality
to the escaping flow.
2.1 Two main regimes for jet
driven from disk
• Hydromagnetic regime:
Energy and angular momentum are
carried by both the electromagnetic
field and the kinetic flux of matter.
• Poynting flux regime:
Energy and angular momentum are
carried predominantly by electromagnetic field.
Fig. 3a — Schematic drawing for interpreting the
magnetic torque exerted at the current flowing
in the disk.
Fig. 3b — Schematic drawing for interpreting the
magnetic torque exerted at the current flowing
in the disk.
2.2 Launching matter centrifugally
from disk
Analysis in Blandford & Payne (1982,
BP82)
• A critical angle of the magnetic field
line with the normal to the disk surface
is required based on the effective
potential.
2

rd 
GM 1  r 
   
  const.
 eff  
2
2
rd  2  rd 

z

r

A critical angle of field line with the
0
normal to the disk  FL  30
Is required for launching particles
centrifugally.
 FL
BH
rd
z
Disk
r
Fig. 4 Bead-on-a-wire analogy for centrifugal acceleration
by a magnetic field
Cao (1997) found that the critical angle for
launching particles centrifugally could be
for a fast-rotating BH.
 FL  300
Ustyugova et al. (2000) gave MHD simulation,
a quasi-stationary collimated Poynting jet
from the inner disk;
a steady uncollimated hydromagnetic
outflow in the outer disk.
Lyutikov (2009) found, for prograde
rotating disks around Kerr black holes,
the angleαFL decreases and
becomes 00 for footpoints anchored
to the disk near the horizon of an
extreme Kerr black hole.
How to determine the ratio of
EM to matter in the outflow from
disk?
•
2.3 Energy exchange in outflow
Analysis in BP82
Specific energy and specific angular
momentum
e  ematter  ePoynting
l  lmatter  lPoynting
Conservation law of
energy
Conservation law of
angular momentum
ematter   2 2  h  
e
ePoynting    rB k

lmatter  r
l

lPoynting   rB k
The energy and angular momentum
in an outflow contain the contributions
from outflow matter and Poynting flux.
The toroidal magnetic field is essential
for Poynting flux.
S   rB BP 4 
p
L
Thus
S
p
L
 P
  rB k
S  rB P k
p
L
and
S Ep
P
  rB k
are interpreted as the contribution to
the energy and angular momentum
due to Poynting flux.
If
ematter and lmatter
increase in the outflow, while
e and l remains constant along each
field line,
we conclude:
Poynting flux is converted continually
into hydromagnetic flux
in the outflow.
It is required by the conservation
law:
 rB k and rB k
or  rB
decrease continually
in the outflow. Based on Ampere’s law
 B  dl 2 rB  4  I
 rB
 I
decrease continually
in the outflow.
2.4 An interpretation for decrease of rB
Fig. 5 A schematic representation of a possible
field geometry close to the disk (adapted from BP82)
• Based on E p    v F c   B p
we have the direction of the induced
electric field and that of the corona current
flowing into the magnetic surface, forming
a loop with the disk current as shown in
Fig. 6.
(a)
(b)
Fig.6 Interpret the decrease of  I
Red solid arrow: disk current
Blue dashed arrow: coronal current
3. The Role of Magnetic Field for
Disk Emission (Lines 2 and 4)
• Corona is induced for interpreting disk
emission.
• The tangled small-scale magnetic field BD
is related to the ordered large-scale BP by
(Livio et al. 1999)
h
B p ~    BD
r
The interior viscous process is dominated by
tangled small-scale magnetic field, the
viscous pressure is comparable to magnetic
pressure (Balbus & Hawley 1991)
tr   Pgas ~ Pmag  B / 8
2
D
The conservation of energy and angular
momentum for a disk with magnetic
coupling (MC) is
d
†
†
( M D L  g )  4 r (QL  H MC )
dr
d
( M D E †  g   D )  4 r (QE †  H MC  D )
dr

d

cor
Q  Q Q

cor
Q
/ f cor
Q  T

d
4
eff

cor
Q
is released in the disk,
heats corona and maintains its
relativistic temperature via magnetic
reconnection.
Gan et al. (2009) obtained the MC
configuration of the closed magnetic field
lines based on the conservation of energy,
angular momentum and magnetic flux as
shown in Fig. 7.
The emerged Spectra is obtained by using
Monte-Carlo Simulation as shown in Fig. 8.
Fig. 7. A schematic drawing of disk-corona model
Fig. 8. A schematic drawing of radiation of disk-corona
Magnetic reconnection (MR) and corona
heating are related to small-scale magnetic
field:
Rapid variation of magnetic
field due to MR
Induced E
Accelerating
electrons
Energy transferred from the spinning BH
to the inner disk via MC process.
The X-ray spectra of GRO J1655−40 and
XTE 1118+480 in low/hard state are fitted
in Figs. 9 and 10, and that of GX 339−4 in
SPL state is fitted in Fig, 11.
Fig. 9. –– GRO J1655-40 in low/hard state (2005.03.06).
Fig. 10. –– XTE 1118+480 in low/hard state.
Fig. 11. – GX 339−4 in SPL state.
4. Some new works to be done
4.1 A modified resonance model for
3:2 HFQPO pairs
Two uncertainties in resonance model
(e.g., see a review in MR06).
(1) Whether epicyclic resonance could
overcome the severe damping forces?
(2) Emit X–rays with sufficient amplitude
and coherence to produce the QPOs.
Resonance model for QPO pairs could be
improved by introducing MC effects in two
aspects:
(1) Association of QPO pairs with SPL
state of BH binaries;
(2) Inputting energy to the resonance
mode in the inner disk via the MC process.


 


ΩH

Corona







(a)

Disk
BH
(b)
Fig. 12 Poynting energy flux (blue thick arrows) in (a) a steady direct current
circuit and (b) a magnetosphere with closed field lines connecting a BH with
its surrounding disk.
• 4.2 A model for low/hard states with
jets in black hole X-ray binaries as
shown in Fig. 13.
Fig. 13 Schematic drawing of the magnetic field configuration
for low/hard state in BH binaries
Fitting LH state in GX 339-4