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Workshop for Black Hole Accretion
April 26 - 28, 2008, Shanghai, China
Ding-Xiong Wang
Huazhong University of Science & Technology
Relationship betweenjet production
and disk accretion
Outline of this talk
1. Two main regimes for jets driven from accretion disks
2. Connection between energy and angular momentum in the jet driven by the BP process.
3. Application to astrophysics
1. Two main regimes for jet driven from accretion 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 electro- magnetic field.
• Hydromagnetic regime of jet formation in BH accretion disk was proposed by Blandford & Payne (1982, hereafter BP82)
• Poynting flux models for the origin of jets in BH accretion disk was proposed by Lovelace (1976) and Blandford (1976).
Both matter outflow and Poynting fl
ux are produced by the large-scale magnetic field.
What is the relation between matter outflow and Poynting flux?
Analysis in BP82
A critical angle of the magnetic field line with the normal to the disk surface is required based on the effective potential.
2
2 2
1.
2d
effd d
rGM rconst
r r z r
Fig. 1 Bead-on-a-wire analogy for centrifugal acceleration by a magnetic field with critical angle 030FL
030FL
Centrifugal force
Gravitational force
Constraint force
Fig. 2a Poynting flux coexists with the matter outflow, and is driven by the rotating disk around a black hole. The energy is extracted by the magnetic torque exerted on the disk current.
P PE
S E B
P F P E B
Poynting flux
P F P E B
P PE
S E B
Fig. 2b Poynting flux coexists with the matter outflow, and is driven by the rotating disk around a black hole. The energy is extracted by the magnetic torque exerted on the disk current.
Poynting flux
Disk rotationMagnetic torquePointing fluxField line velocity
F
remain unchanged !
,PB PE and disk currentDirections of
are opposite in Figs.2a and 2b
Directions of
BZ-MC-BP model (Wang et al. 2008)
A natural extension of BZ-MC
model
Fig. 3 Magnetic field configuration of BZ-MC-BP model.
(2) The model could be used to interpret the hard state of BH X-ray binaries or radio loud quasars.
(1) A Jet is driven by the BZ and BP processes, and disk accretion is suppressed by the MC process.
The feature of our model:
The critical radii rSIBZ and rSIMC can be determined by the following criterions:
2 1p TSIBZ BZ L Lr L B B
2 1p TSIMC MC d dr L B B
for SIBZ
for SIMC
The critical angle can be determined by
1tanFL SIBZ SIMC cr r H
A detailed calculation shows either hydromagnetic flux with αFL > 300 or Poynting flux with αFL < 300 is possible for jet production with the values given in the parameter space as shown in
Fig. 4.
Fig. 4. Region A for Poynting flux with
AA
B B
030FL Region B for hydromagnetic flux with
030FL
2. Connection between the two types of outflows
2.1 Specific energy and specific angular momentum
Conservation of energy
Conservation of angular momentum
(along each field line)
Poynm tat inter ge nsee co t
Poynm tat inter gl nsll co t
Poynting
matterl
l rB k
r
The energy and angular momentumin an outflow contain the contributions from matter outflow and Poynting flux.
2 2
Poyntin
matter
ge rB k
e h
4 P Pk B
2.2 The physical picture of the BP process
The role of the large scale magnetic field anchored on the disk:
The poloidal magnetic field: (1) exerting a torque on the current flowing o
n the disk; (2) transferring the kinetic energy of the disk
to the outflow matter centrifugally
4
4
pL P
P P
S r
B
B B
k
pL PBS r k
pL
P
SrB k
pE
P
SkrB
PoyntingePoyntingl
Corresponding to matter flux: P
1 1
4 4p F pE P P LS E E SB B
The toroidal magnetic field is dragged backward and is essential for Poynting flux.
According to BP82
The ratio is 58 for
λ=30 near the disk surface.
The ratio is 2 near the Alfven surface
About 1/3 Poynting energy is converted into the kinetic energy in the outflow.
1 2
d
l
GMr
Why is decreasing in the outflow? rB
2 4 Id rB B l
According to Maxwell equations,
The decrease of could arise from the variation of the corona current, which might be created by poloidal electric field
rB
Pcorj E
Fig. 5 A schematic representation of a possible field geometry close to the disk (adapted from
BP82)
(a) (b)
Fig.6 Interpretation for the variation of -rBφ in the outflow. Red solid arrow: disk current; Blue dashed arrow: coronal current; Green solid arrow: displacement current.
3. Application to astrophysics
3.1 Interpreting a spine/sheath jet structure.
The hydromagnetic outflow powered by the BP process corresponds to the sheath with lower Lorentz factor away from the axis.
The Poynting flux powered by the BZ process
corresponds to the spine with higher Lorentz
factor near the axis.
(2) The broad Fe Kα lines can be fitted by invoking the MC process as argued by Wilms (2001), Li (2002b) and Wang et al. (2003).
Different Lorentz factor in the jet can be fitted by adjusting the ratio of the BP power to the BZ power
The BZ and BP powers can be calculated based on the magnetic field configuration given in Fig. 3.
32
0 20
1 sin2
2 1 sin
S
BZ BZ
k k dP P P a
q
2 1
0 2
112
1
Sout
BP BP mSIMC ms
S xqP P P
S
2 2 2 2 28 10 4 6.59 10p
H HP B M B m erg s
Table 1 The powers and torques in the BZ and BP processes
It is shown in Table 1 that the BP power is greater than the BZ power and the ratio of varies with the parameters,
and
BP BZP P, and ca n h
jet BZ BPP P P
1BP BZP P Fig. 7 The inequality
region for (a) s=0.4 and (b) s=0.6
and (c)
.
holds in the shaded
3.2 Interpreting a universal radio-X-ray correlation in low/hard state black hole binaries
The states of BHXBs:
(1) low/hard state associated with jet;
(2) high/soft state without jet;
(3) SPL (Intermediate) state associated with QPOs
Fig. 8 A fundamental plane of black hole activity(Merloni, Heinz, & Di Matteo, 2003, MNRAS)
Fig. 9. Schematic illustrationof the high-energy emitting jet model. (from Levinson 2006)
Fig.10 BZ-MC-BP model for Interpreting a universal radio-X-ray correlation
下一步工作思路 :1. 进一步讨论MC 机制(1)黑洞转移能量和角动量到盘内区 , 能量和角动量的分配关系 ;
(2) MC过程对吸积的抑制作用 ;(3) 螺旋不稳定性限制磁场位形 , 盘冕的加热机制 ;2. 拟合黑洞系统的射电光度与 X射线光度的关系 :(1)一部分硬 X射线由高温冕产生 , 另一部分硬 X射线由穿出冕的软光子与喷流的相对论电子通过逆康普顿散射产生 .
(3) 射电光度由喷流产生 .
Thanks
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