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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