1. A toy model for HFQPOs in XRBs Ye Yong-Chun ( 叶永春 ), Wang Ding-Xiong( 汪定雄 ) Department of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China

2. Content Background Description of model Discussion

3.  Background

4. HFQPOs in XRBs Quasi-periodic oscillations in X-ray binaries have become a very active research field since the launch of the Rossi X-Ray Timing Explorer (RXTE; Bradt, Rothschild & Swank 1993 ). A key feature in these sources is that some of high frequency quasi- periodic oscillations (HFQPOs) appear in pairs. Five black hole (BH) X-ray binaries exhibit transient HFQPOs. Thereinto, three sources have pairs occurring,

5. Some models GRO J1655-40 ( 450, 300Hz; Strohmayer 2001a; Remillard et al 1999 ) GRS 1915+105 ( 168, 113Hz; McClintock & Remillard 2003 ) XTE J1550-564 ( 276, 184, 92Hz; Miller 2001; Homan et al 2001; Remillard et al 2002a; Remillard et al 2002b ). Strohmayer ( 2001a; 2001b ) : The azimuthal and radial coordinate frequencies ; Wagoner et al. ( 2001 ) : Discoseismic oscillations in a relativistic accretion disc ; Abramowicz & Kluzniak ( 2001 ) : Resonance between orbital and epicyclic motion of accreting matter. Model The puzzling 3:2:1 ratio

6.  Description of model

7. Configuration of magnetic field (non- axisymmetric) Three processes are involved:  The magnetic coupling (MC) process  The Blandford-Znajek (BZ) process  The Disc accretion (DA) process Figure 1. The poloidal magnetic field configuration including the screw instability in the MC process (SIMC)

8. Figure 2. Azimuthal profile of the non-axisymmetric magnetic field on the BH horizon Non-axisymmetric

9. is the critical radius constrained by SIMC, which is determined by The formation of hotspot Considering the BZ power transferred through two adjacent magnetic surfaces between and on the horizon, and the mapping relation between and the cylindrical radius in the BZ process:

10. A hotspot is produced by the energy transferred from the BH to the disc at the place where attains its maximum( Nowak 1998; Wang 2003 )

12. The QPO frequencies Considering that the two hotspots are frozen at the disc, we have the QPO frequencies by substituting and into the Keplerian angular velocity as follow The QPO frequency corresponding to SIBZ is determined by the angular velocity of the magnetic field lines

13.  Discussion

14. The observations and our results Figure 3. The observations of XTE J1550-564 (Remillard 2002b) Table 1. The 3:2:1 ratio of HFQPOs produced by our model

15. The explanation for the X-ray QPOs It is believed that a disc is probably surrounded by a high- temperature corona analogous to the solar corona ( Liang & Price 1977; Haardt 1991; Zhang et al 2000 ). Very recently, some authors argued that the coronal heating in some stars including the Sun is probably related to dissipation of currents, and very strong X-ray emissions arise from variation of magnetic fields ( Galsgaard & Parnell 2004; Peter et al. 2004 ). Analogously, if the corona exists above the disc in our model, we expect that it might be heated by the induced currents due to SIMC and SIBZ. Therefore a very strong X-ray emission would be produced to form X-ray Hotspot

16. The astrophysics surrounding Figure 4. The observations of XTE J1550-564 ( Miller 2001:longer marks denote observation in which a HFQPO is found )

17. Abramowicz, M. A., & Kluzniak, W., 2001, A&A, 374, L19 Bradt, H. V., Rothschild, R. E., & Swank, J. H., 1993, A&AS, 97, 355 Galsgaard K., & Parnell C., Procedings of SOHO 15 Coronal Heating, ESA publication, astro-ph/0409562 Haardt F., & Maraschi L., 1991, ApJ, 380, L51 Homan J. et al., 2001, ApJS, 132, 377 Liang E. P. T., Price R. H., 1977, ApJ, 218, 247 McClintock J. E., & Remillard, R. A., 2003, in “Compact Stellar X-ray Sources,” eds. W. H. G. Lewin & M. van der Klis, (Cambridge U. Press), in press; astro-ph/0306213 Miller J. M. et al., 2001, ApJ, 563, 928 Nowak, M. A., Lehr, D. E., 1998, in Theory of Black Hole Accretion Disks, ed. M. A. Abramowicz, G. Bjornsson, & J. E. Pringle, (Cambridge: Cambridge Univ. Press), p.233, preprint (astro-ph/9812004) Reference

18. Peter H., Gudiksen B., & Nordlund A., Procedings of SOHO 15 Coronal Heating, ESA publication, astro-ph/0409504 Remillard, R. A., et al., 1999, ApJ, 522, 397 Remillard R. A. et al., 2002a, ApJ, 564, 962 Remillard R. A. et al., 2002b, ApJ, 580, 1030 Strohmayer, T. E., 2001a, ApJ, 552, L49 Strohmayer, T. E., 2001b, ApJ, 554, L169 Wagoner, R. V., Silbergleit, A. S., & Ortega-Rodriguez, M. 2001, ApJ, 559, L25 Wang D.-X., Lei W.-H., and Ma R.-Y. 2003, Mon. Not. R. Astron. Soc. 342, 851 Reference (continue)

19. Thank you!