2. QPOs ，准周期振荡 in Black Hole ， Neutron Star X-ray Sources: X-ray bursts, accreting-powered pulsars Einstein’s Relativity in Strong Gravitation 张承民， 尹红星 National Astronomical Observatories Chinese Academy of Sciences, Beijing

3. OUTLINE OF TALK Introduction of RXTE Black Hole (BH) and Neutron Star (NS) in Low Mass X-ray Binary (LMXB) KHz Quasi Periodic Oscillation (QPO) Millisecond accreting-powered X-ray Pulsar Type-I X-ray Burst Oscillation QPOs of NS/BH X-ray Sources Theoretical Mechanisms---Strong Gravity Further Expectation

4. Binary X-ray Sources Normal Star + Compact Star 10,000 lyr, 300Hz/450Hz Micro-quasar, Radio jet 7 solar mass/optical

5. QPO frequencies discovered by RXTE 1996—2006 ， reviewed by van der Klis 2005, 06 NBO, ~5 Hz HBO, ~20-70 Hz Hundred, ~100 Hz kHz, ~1000-Hz Burst oscillation, ~300 Hz Spin frequency, ~300 Hz Low, high QPO, ~0.1 Hz Etc. QPO: Quasi Periodic Oscillation 准周期振荡

6. Atoll and Z Sources --- LMXB CCD Accretion rate direction ~Eddington Accretion ~1% Eddington Accretion

7. Discovery: typical twin KHZ QPOs Sco x-1, van der Klis et al 1997 Separation ~300 Hz Typically: Twin KHz QPO Upper ν 2 = 1000 (Hz) Lower ν 1 = 700 (Hz) 18/25 sources

8. QPO v.s. Accretion rate relation SCO X-1, Van der Klis, 2005, 06 QPO frequency increases with the accretion rate QPO 轮廓随吸积率变宽 / 低，消失

9. 最大值 Max ： ν max =1329 Hz, van Straaten 2000 min: ~200 Hz KHz QPO Data ， Atoll sources 平均值 /Distribution of kHz QPOs ： QPO (Atoll) ~ QPO （ Z ） Zhang et al 2006; 原因？

10. kHz QPOs of Z Sources

11. Difference of twin kHz QPOs = const? Beat model by Miller, Lamb & Psaltis 1998

12. Saturation of kHz QPO frequency ? 4U1820-30, NASA W. Zhang et al, 1998 Kaaret, et al 1999 Swank 2004; Miller 2004 BH/ISCO: 3 Schwarzschild radius Innermost stable circular orbit NS/Surface: star radius, hard surface

13. Parallel Line Phenomenon kHz QPO － luminosity relation Similarity/Homogeneous ? Among the different sources, same source at the different time

14. kHz QPO v.s. Count rate kHz QPO corresponds to the position in CCD, to the accretion rate Mdot; QPO ~ Mdot, 1/B B ~ Mdot, proportional Cheng & Zhang, 1998/2000 Zhang & Kojima, 2006

15. Accreting millisecond X-ray pulsar --- SAX J1808.4-3658 (7 sources) Wijnands and van der Klis, 1998 Nature Wijnands et al 2003 Nature 4 sources by Markwardt et al. 2002a, 2003a, 2003b, Galloway et al. 2002

16. SAXJ 1808.4-3658 Twin kHz QPOs 700 Hz, 500 Hz Burst/spin: 401 Hz See, Wijnands 2006 Burst frequency ~ spin frequency ? ， 2003 XTE 1807, kHz QPO, 191 Hz, Linares et al. 2005 F. Zhang et al. 2006

17. IGR J00291+5934 598.88 Hz, Markwardt 2004, 7 MSP sources

18. Spectrum of Type-I X-ray Burst frequency 4U1702-43, van der Klis 2006; Strohmayer and Bildsten 2003

19. Type-I X-ray Burst Type-I X-ray Burst, Lewin et al 1995/Bildsten 1998 Thermonuclear reaction on accreting NS surface (T/P, spot) Burst rise time: 1 second Burst decay time: 10-100 second Total energy: 10 39-40 erg. Eddington luminosity ! 4U1728-34, (363 Hz) Strohmayer et al 1996 362.5 Hz --- 363.9 Hz, in 10 second

20. Burst Oscillations

21. On the burst frequency Burst frequency increases ~ 2 Hz, drift. Decreasing is discovered From hot spot on neutron star kHz QPO separation ~ burst/spin frequency

22. Burst and Spin frequency XXXXXX 11 burst sources, Muno et al 2004 7 X-ray pulsars, Wijnands 2004; Chakrabarty 2004 kHz QPO separation=195 Hz/(spin=401 Hz) Burst and Spin frequency are similar

23. 11 burst sources ， Muno 2004

24. 25 kHz QPO 源 3 rd kHz QPO ?

25. Low frequency QPO---kHz QPO 关系 Psaltis et al 1998, 1999 Belloni et al 2002; 2005 Empirical Relation ν HBO = 50. (Hz)(ν 2 /1000Hz) 1.9-2.0 ν HBO = 42. (Hz) (ν 1 /500Hz) 0.95-1.05 ν qpo = 10. (Hz) (ν 1 /500Hz) Low frequency QPO< 100 Hz FBO/NBO = 6-20 (Hz) HBO = 15-70 (Hz) ν 1 = 700. (Hz)(ν 2 /1000Hz) 1.9-2.0

26. Twin kHz QPO relations ν 1 = ~700. (Hz)(ν 2 /1000Hz) b b ~ 1.6 Atoll Source 4U1728 b ~ 1.8 Z Source Sco X-1 Zhang et al. 2006

27. Twin kHz QPO distribution

29. Low-high frequency QPO 关系 Warner 2006; Warner & Woudt 2004; Mauche 2002 + 27 CVs, 5 magnitude orders in QPOs Black holes White dwarfs, Cvs Neutron stars ？ Zhang 2005: Model

30. Black Hole High Frequency QPOs HFQPO: 40-450 (Hz) Constant (stable) in frequency Mass/Spin/ Luminosity Pair frequency relation 3:2 Frequency-Mass relation: 1/M 7 BH sources, van der Klis 2006 Jets like Galactic BHs (McClintock & Remillard 2003) Different from those of NS’s ν k = (1/2π)(GM/r 3 ) 1/2 = (c/2πr) (R s /2r) 1/2 ν k ( ISCO ) = 2.2 (kHz) (M/Mסּ) -1 Miller, et al 1998 GRO J1655-40, XTE J1550-564 XTE 1650-5000, 4U1630-47 XTE 1859-226, H 1743-322 GRS 1915+105, 4/7 Sources Van der Klis 2006 Magnetosphere-disk instability noise: mechanism ：？ Genzel 2003; Auschenbach 2004; GC QPOs, 3:2

31. High Frequency QPOs in Black Hole LMXBs NameBH Mass(M sun )HF QPO (Hz)References GRO J1655-40~6300,4501,2 XTE J1550-564~10184,276 188,249~276 3,4 5 GRS 1915+105~1441,67 113,165 328 165 6 7(?) 8(?) 9 H 1743-322 ~ 160,240 166,242 10 11 XTE J1859+226~9150~20012 4U 1630-472 ~ 184 100~300 8 13 XTE J1650-500 ~ 110~27014

32. (Astro-ph/0408402[8]) H 1743-322[10] XTE J1650-500[14] 160 240 250

33. A comparison between high-frequency QPOs in BH LMXBs and those in NS LMXBs QPOs in NS LMXBs QPOs in BH LMXBs Twin kHz QPOsYes RatioNot a constant~3:2 Spectra indexSoftHard, saturation PulsationsYesNo Type I X-ray bursts YesNo 1/M scalingNo?yes ChangesIncrease with LxRelatively stable

34. STELLAR Black Hole—Micro-quasar GRS 1915+105 41:67 Hz, 33 solar mass 10,000 lyr, 300Hz:450Hz=2:3 Microquasar, Radio jet 7 solar mass/optical

35. QPO and Break Frequency

36. Theoretical Consideration Strong Gravity: Schwarzschild Radius: R s =2GM/c 2 Innermost Stable Circular Orbit R Isco = 3R s Strong Magnetic: 10 8-9 Gauss (Atoll, Z-sources) Beat Model: Kepler Frequency Difference to Spin frequency Accretion Flow around NS/BH Hard surface ?

37. QPO Models Titarchuk and cooperators ’ Model transition layer formed between a NS surface and the inner edge of a Keplerian disk, QPO: magnetoacoustic wave (MAW), Keplerian frequency. Low-high frequency relation 0.08 ratio Abramovicz and cooperators ’ Model non-linear resonance between modes of accretion disk oscillations HFQPO: Stella black hole QPO, 3:2 relation Wang, DX, 2003, positions Miller, Lamb & Psaltis ’ Beat Model, developed from Alpar & Shaham 1985 Nature ; Lamb et al 1985 Nature Relativistic precession model by Stella & Vietri 1999

38. Theoretical Models Beat Model (HBO), ν HBO = ν kepler - ν spin ν Kepler ≈ r -3/2 is the Kepler Frequency of the orbit ν spin Constant, is the spin Frequency of the star Alpar, M., Shaham, J., 1985, Nature r ~ 1/M dot, ν HBO ~ M dot Beat Model for KHz QPO ν 2 = ν kepler ν 1 = ν kepler - ν spin ∆ν = ν 2 - ν 1 = ν spin Miller, Lamb, Psaltis 1998; Strohmayer et al 1996 Lamb & Miller 2003 …Constant What modulate X-ray Flux ? Why quasi periodic, not periodic ? Parameters: M/R/Spin, B?--Z/Atoll

39. X- 射线源准周期振荡 QPO, Beat ? 间隔常数？ NO ！ 拍模型预言 : 间隔常数 = 自旋 Alpar 和 Shaham ， 1985 ， Nature 。 Lamb et al 1985 ， Nature 。 Miller et al 1998 ， ApJ 。 SAXJ 1808, Wijnands, Nat, 2003 XTEJ 1807, Zhang, F, Qu JL, Zhang CM, Li TP, Chen, W., 2006

40. Einstein’s Prediction: Perihelion Motion of Orbit Perihelion precession of Mercury orbit = 43” /century, near NS, ~10^16 times large

41. Neutron Star Orbit N. Copernicus Einstein’s General Relativity: Perihelion precession Precession Model for KHz QPO, Stella and Vietri, 1999 ν 2 = ν kepler ν 1 = ν precession = ν 2 [1 – (1 – 3Rs/r) 1/2 ] ∆ν = ν 2 - ν 1 is not constant ISCO Saturation

42. Theoretical model Stella and Vietrie, 1999, Precession model Problems: 1.Vacuum 2.Circular orbit 3.Test particle 4.Predicted 2 M ⊙ 5. 30 sources, NS mass ~ 1.4 solar mass

43. Lense-Thirring Precession From Einstein GR, frame dragging was first quantitatively stated by W. Lense and H. Thirring in 1918, which is also referred to as the Lense-Thirring effect Zhang, SN et al 1997; Cui et al 1998: BH precession ？ L.Stella, M.Vietri, 1998 Gravity Probe B, Gyroscope experiment, Stanford U, led by F.Everit, 2003 Gravitomagnetism Conf., 2 nd Fairbank W., Rome U, organized by R.Ruffini, 1998 Book “Gravitation and Inertia” by Ciufolini and Wheeler, 1995

44. Problems ? Vacuum ? Kerr rotation ? Magnetic Field ? Inner Accretion Disk ? Similarity: common parameter: accretion rate/radius

45. Alfven wave oscillation MODEL (in Schwarzschild spacetime): Zhang 2004; Li & Zhang 2005 Keplerian Orbital frequency resonance MHD Alfven wave Oscillation in the orbit ν 2 = 1850 (Hz) A X 3/2 ν 1 = ν 2 X (1- (1-X) 1/2 ) 1/2 A=m 1/2 /R 6 3/2; X=R/r, m: Ns mass in solar mass R 6 is NS radius in 10^6 cm

46. NS Mass in solar mass Ｎ S radius (km) Constrain on Star EOS, mass & radius CN1/CN2: normal neutron matter, CS1/CS2: Strange matter CPC: core becomes Bose-Einstein condensate of pions Kerr spacetime ?

47. 10 年 RXTE 探测总结 观测，进展较大， QPO 关系明确 理论，进展缓慢，很多模型 ? 强引力广义相对论验证中子星结构检验核物理 开普勒运动 近星点进动 LT 进动 / 引力磁 引力红移 黑洞 /Kerr 时空 引力波 光线弯曲 质量 半径 核物态 （中子 / 夸克） 磁场 旋转 吸积流动 QPO 机制？ 数据处理？ 新物理？ 物理实验室

48. References: 1: Remillard, R. A. et al. 1999, ApJ, 522, 397 2: Strohmayer, T. E. 2001, ApJ, 552, L49 3: Remillard, R. A. et al. 1999, ApJ, 517, L127 4: Remillard, R. A. et al. 2002, ApJ, 580, 1030 5: Miller, J. M. et al. 2001, ApJ, 563, 928 6: Strohmayer, T. E. 2001, ApJ, 554, L169 7: Remillard, R. A. 2003, abstract HEAD,7,3003 8: Remillard, R. A. 2002 (astro-ph/0208402) 9: Belloni, T. et al. 2006 (astro-ph/0603210) 10: Homan, J. et al. 2005, ApJ, 623, 383 11: Remillard, R. A. et al. 2006, ApJ, 637, 1002 12: Markwardt, C. 2001, ApSSS, 276,209 13: Klein-Wolt, M. et al. 2004, NuPhS, 132, 381 14: Homan, J. et al. 2003, ApJ, 586, 1262