1. 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

2. Outline of this talk ● Introduction ● Role of magnetic field for jet production ● Role of magnetic field for disk radiation ● Some work to be done

3. Quasars and Microquasars
1. Introduction
Quasars and Microquasars
Fig. 1
Schematic drawings
for quasars
and microquasars

4. Three basic ‘ingredients’：
(1) a spinning black hole
(2) an accretion disk
(3) collimated jet

5. Magnetic Field in Black Hole Accretion Disks
Fig. 2.
Different types of magnetic field lines in black hole magnetosphere.
From Blandford (2002)

6. 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.

7. 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.

8. 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 electro- magnetic field.

9. Fig. 3a — Schematic drawing for interpreting the
magnetic torque exerted at the current flowing
in the disk.

10. Fig. 3b — Schematic drawing for interpreting the
magnetic torque exerted at the current flowing
in the disk.

11. 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.

12. A critical angle of field line with the normal to the disk
Is required for launching particles centrifugally.
Fig. 4 Bead-on-a-wire analogy for centrifugal acceleration
by a magnetic field

13. Ustyugova et al. (2000) gave MHD simulation,
Cao (1997) found that the critical angle for launching particles centrifugally could be
for a fast-rotating BH.
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.

14. Lyutikov (2009) found, for prograde rotating disks around Kerr black holes, the angle decreases and becomes 00 for footpoints anchored to the disk near the horizon of an extreme Kerr black hole.

15. How to determine the ratio of EM to matter in the outflow from disk?

16. 2.3 Energy exchange in outflow
Analysis in BP82
Specific energy and specific angular
momentum
Conservation law of energy
Conservation law of angular momentum

17. The energy and angular momentum
in an outflow contain the contributions from outflow matter and Poynting flux.

18. The toroidal magnetic field is essential
for Poynting flux.
and
Thus
are interpreted as the contribution to the energy and angular momentum due to Poynting flux.

19. If
and
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.

20. It is required by the conservation law:
and or
decrease continually
in the outflow.
Based on Ampere’s law
decrease continually
in the outflow.

21. 2.4 An interpretation for decrease of
Fig. 5 A schematic representation of a possible
field geometry close to the disk (adapted from BP82)

22. Based on
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.

23. Fig.6 Interpret the decrease of Red solid arrow: disk current
(a) (b)
Fig.6 Interpret the decrease of
Red solid arrow: disk current
Blue dashed arrow: coronal current

24. 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)

25. The interior viscous process is dominated by tangled small-scale magnetic field, the viscous pressure is comparable to magnetic pressure (Balbus & Hawley 1991)

26. The conservation of energy and angular momentum for a disk with magnetic coupling (MC) is

27. is released in the disk,
heats corona and maintains its relativistic temperature via magnetic reconnection.

28. 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.

29. Fig. 7. A schematic drawing of disk-corona model

30. Fig. 8. A schematic drawing of radiation of disk-corona

31. Magnetic reconnection (MR) and corona
heating are related to small-scale magnetic
field:
Rapid variation of magnetic
field due to MR
Accelerating
Induced E electrons
Energy transferred from the spinning BH
to the inner disk via MC process.

32. The X-ray spectra of GRO J1655−40 and XTE 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.

33. Fig. 9. –– GRO J1655-40 in low/hard state (2005.03.06).

34. Fig. 10. –– XTE 1118+480 in low/hard state.

35. Fig. 11. – GX 339−4 in SPL state.

36. 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.

37. 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.

38. (a)
(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.

39. 4.2 A model for low/hard states with jets in black hole X-ray binaries as shown in Fig. 13.

40. for low/hard state in BH binaries
Fig. 13 Schematic drawing of the magnetic field configuration
for low/hard state in BH binaries

41. Fitting LH state in GX 339-4