黑洞X射线双星的高频准周期振荡(HFQPO)与喷流(Jet)的 相关性 汪定雄, 叶永春, 黄昌印 华中科技大学 2nd workshop on black hole accretion 2007 Beijing April 21-23

1. Introduction 2. A brief review of the BZMC Model 3. Correlation between jets and HFQPOs 4. Estimate the BH spin based on 3:2 QPO pairs 5. State Transition in BHXB and jet line in HID 6. Some puzzles in the evolving BHXBs

1. Introduction Four sources exhibit 3:2 pairs of HFQPOs in which three BHXBs and one BH transient are included. The jets are also observed in these sources. How to explain the correlation between HFQPOs and Jet?

Fig. 1 银河系16个黑洞双星的示意图 The Sun–Mercury distance (0.4 AU) is shown at the top.

Fig. 2 Four pairs of HFQPOs observed in three black–hole binary systems. The energy band is 6–30 keV.

BHXBs: GRO J1655-40 (450 and 300 Hz); XTE J1550-564 (276 and 184 Hz); GRS 1915+105 (168 and 113 Hz). BH Transient: H1743-322 (240 and 160 Hz). In addition, jets are observed in the above sources.

Fig. 3 喷流现象普遍出现类星体，微类星体和伽玛射线暴中.

Fig. 4 黑洞吸积盘 已成为类星体和微类星体高能辐射和喷流产生的标准模型.

The jets can be observed in hard states, but can not in soft states, and a jet line in HID divides the hard state from the soft state (Fender et al. 2004).

Fig. 5 A schematic of our simplified model for the jet-disk coupling in black hole binaries (From Fender et al. 2004).

Fig. 6. Hardness-Intensity diagram of the 2002/2003 outburst of GX 339-4 (From Belloni 2005).

A consistent interpretation for the state transitions in BHXBs remains controversial. Belloni et al. (1997a, b; 2000) : The transition between State C and States A/B is caused by the disappearance and reappearance of the inner accretion disk due to a disk instability mechanism.

(2) Livio et al. (2003) In one state, the accretion energy is dissipated locally to produce the observed disk luminosity. In another state the energy liberated in the accretion is converted efficiently into magnetic energy in the form of a magnetically dominated outflow or jet.

Questions: 1. Is there any correlation between HFQPOs with jets in BHXBs? 2. How to interpret the jet line in HID? These issues can be explained naturally based on BZMC model (Wang et al. 2003, 2004, 2005).

磁场的引入对提取黑洞的旋转能量和喷流的准直起到非常关键的作用； 确定黑洞吸积盘的磁场位形是一个关键问题

2. A brief review of the BZMC Model Fig. 7 Magnetic field Configuration with the BZ and MC processes

Energy and angular momentum are transferred from the BH to the disk by virtue of a large scale non-axisymmetric magnetic field (Wang et. 2003, 2005).

Screw instability (kink instability) of the magnetic field is invoked to determine the angular boundary of the open and closed magnetic field lines at the horizon: Two rotating hotspots are produced in the inner disk by the non-axisymmetric field.

Inner hotspot corresponds to the upper frequency of the HFQPO pair, arising from the peak value of transferred energy flux. Outer hotspot corresponds to the lower frequency of the HFQPO pair, arising from the screw instability.

3. Correlation between jets and HFQPOs The coexistence of the BZ and MC processes always accompanies the screw instability (Wang et al. 2004). Fig. 8 Critical line for the MC with BZ jet and without BZ jet in parameter space.

4.1 Estimate the BH spin based on 3:2 QPO pairs The upper and lower frequencies are expressed by

Table 1 The fitting results for 3:2 ratio in HFQPOs

Comparison of the estimated BH spins J1655-40: Authors Methods Spin Z97 X-ray continuum fitting 0.7-0.95 G01 X-ray continuum fitting 0.68-0.88 S06 X-ray continuum fitting 0.65-0.75 M06 X-ray continuum fitting 0.65-0.80 AK01 Resonance 0.2-0.67 W07 3:2 QPO pair 0.667-0.709 Z97 -- Zhang et al. 1997, ApJ, 482, L155, G01 --Cierlinski, 2001, MNRAS, 325, 1253 S06 -- Shafee et al. 2006, ApJ, 636, L113, M06-- McClintock et al. astro-ph/0606076, AK01--Abramowicz & Kluzniak, 2001, A&A, 374, L19 W07 -- Wang et al. 2007, ApJ, 657, 428,

4.2 Estimate BH mass and spin of H1743-322 H1743-322 is a BH transient with 3:2 HFQPO pair: (240 and 160 Hz), whose mass is uncertain. FIG. 9 The characteristic line of the 3:2 QPO pair (240, 160Hz) for H1743-322 in the parameter space.

From Fig. 9 we obtain the value ranges of the BH mass and spin as follows. Although the constraint is rather loose, it is a starting point for further study, and can be improved by observations.

4.3 Estimate BH spin in XTE J1859+226 based on one-component QPO (190Hz) FIG. 10 Two contours of corresponding to the lower and upper BH masses of XTE J1859+226.

Belloni et al (astro-ph0603210): The maximum QPO frequency is inversely proportional to the BH mass, this result is consistent with the hotspot’s angular velocity.

Belloni (2005): 5. State Transition in BHXB and jet line in HID The states are reduced to only two basic states, a hard state and a soft one. Jets are observed in hard states, but can not in soft states.. A hard state and a soft state are divided by a jet line in HID.

Scenario: State transition between a hard state and a soft based on the variation of the current distribution in the disk. From Ampere’s law and the magnetic field profile: we have

A magnetic field of can be produced by the fluctuations in densities of the plasma coming from a companion star: where

Timescale estimate

State transition can be realized based on the variation of the current distribution Fig. 12

6. Some puzzles in the evolving BHXBs (1) Why the evolving paths of BHXBs in HID are always anti-clockwise? (2) Why the Lorentz factor increase abruptly before the jets disappear? (3) What is the real reason for setting the large scale magnetic field configurations in BH accretion?

There is a long way to go.

References Abramowicz, M. A., & Kluzniak, W., 2001, A&A, 374, L19 (AK01) Abramowicz, M. A., & Kluzniak, W., 2004, in AIP Conf. Proceedings, 714, X-ray Timing 2003: Rossi and Beyond, ed. P Kaaret, F K. Lamb, J H. Swank. (NY: AIP), 21 (AK04) Aschenbach, B., et al. 2004a, A&A, 417, 71 (A04a) —. 2004b, A&A, 425, 1075 (A04b) —. 2006, updated version of a talk given at the 2005 Frascati Workshop, Vulcano, Italy, May 23 – 28, astro-ph/0603193 (A06) Belloni, T., Mendez, M., King, A. R., van der Klis, M., & van Paradijs, J. 1997a, ApJ, 479, L145 —.1997b, ApJ, 488, L109 Belloni, T., Klein-Wolt, M., Mendez, M., van der Klis, M., & van Paradijs, J. 2000, A&A, 355, 271 Belloni, T., 2005, Proceedings of COSPAR Colloquium "Spectra & Timing of Compact X-ray Binaries," January 17-20, 2005, Mumbai, India, astro-ph/0507556 (B05) Blandford, R. D., & Znajek, R. L. 1977, MNRAS, 179, 433 Blandford, R. D., 1999, in ASP Conf. Ser. 160, Astrophysical Discs: An EC Summer School, ed. J. A. Sellwood & J. Goodman (San Francisco: ASP), 265

Blandford, R. D., 2002, Lighthouses of the Universe: The Most Luminous Celestial Objects and Their Use for Cosmology Proceedings of the MPA/ESO/, p. 381. Bradt, H. V., Rothschild, R. E., & Swank, J. H., 1993, A&AS, 97, 355 Brown, G. E., et al. 2000, New Astronomy 5, 191 Bower, G. C., Falcke, H., Herrnstein, R. M., et al. 2004, Science, 304, 704 Bursa, M., 2005, in Proceedings of RAGtime 6/7: Workshops on black holes and neutron stars, ed. S. Hledík & Z. Stuchlík (Silesian University in Opava, Czech), 39 (Br05) Davis, S. W., Done, C., & Blaes, O. M., 2006, ApJ, 647, 525 (D06) Fender, R.P., Belloni, T., & Gallo, E., 2004, MNRAS, 355, 1105 (FBG04) Gierlinski, et al. 2001, MNRAS, 325, 1253 (G01) Homan, J., et al. 2005, ApJ, 623, 383 Kalemci, E. et al. 2006, ApJ, 640, 55 Kato, S., & Fukue, J., astro-ph/0608578 (KF06) Li, L. -X., 2000a, ApJ, 533, L115 —. 2000b, ApJ, 531, L111 —. 2002, ApJ, 567, 463

Livio, M., Pringle, J. E., & King, A. R., 2003, ApJ, 593, 184 (LPK03) Ma, R.-Y., Wang, D.-X., & Zuo, X.-Q., 2006, A&A, 453, 1 McClintock, J E, & Remillard R A 2006. In Compact Stellar X-ray Sources, ed. WHG Lewin, M van der Klis, pp. 157–214. Cambridge: Cambridge University Press. (astro-ph/0306213) (MR06) McClintock, J E et al. astro-ph/0606076 (M06) Middleton, M., et al. astro-ph/0601540 (MD06) Mirabel, I. F., & Rodriguez L. F., 1998, Nat, 392, 673 —. 1999, ARA&A, 37, 409 Miller, J. M. et al. 2001, ApJ, 563, 928 Page, D. N., & Thorne, K. S. 1974, ApJ, 191, 499 Remillard, R. A., et al., 1999, ApJ, 522, 397 Remillard, R. A., et al., 2002, ApJ, 564, 962 Remillard, R. A., & Muno, M. P., ApJ, 2002, 580, 1030 (RM02) Remillard, R. A., et al. 2006, ApJ, 637, 1002 Remillard, R. A., & McClintock J. E., 2006, ARA&A, 44, 49 (RM06) Shafee, R., et al. ApJ, 2006, 636, L113 (S06) Strohmayer, T. E., 2001a, ApJ, 552, L49 —. 2001b, ApJ, 554, L169 Thorne, K. S. 1974, ApJ, 191, 507 Torok, G., 2005, Astron. Nachr., 326, 9, 856

Wagoner, R. V. , Silbergleit, A. S. , & Ortega-Rodriguez, M Wagoner, R. V., Silbergleit, A. S., & Ortega-Rodriguez, M. 2001, ApJ, 559, L25 Wang, D.-X., Xiao K., & Lei W.-H. 2002, MNRAS, 335, 655 (W02) Wang, D.-X., et al., 2003a, ApJ, 595, 109 (W03) —. 2003b, MNRAS, 344, 473 —. 2004, ApJ, 601, 1031 (W04) Wang, et al., MNRAS, 2005, 359, 36 (W05) Zhang, S. N., Cui, W., & Chen, W., 1997, ApJ, 482, L155 (Z97)