1. QPOs of LMXBs kHz QPO, millisecond pulsar
张承民 尹红星
National Astronomical Observatories
Chinese Academy of Sciences

2. Nobel Prize for Pulsar: Rotating Neutron Star
脉冲星发现40年:
1974, A. Hewish, Cambridge U, First Pulsar
1993, R. Hulse, J.A. Taylor, Princeton U, Binary Pulsar
Nobel Prize for Pulsar: Rotating Neutron Star

3. Pulsar Froms: SUPERNOVA EXPLOSION
Chinese Astronomer recorded Crab Nebula in 1054 AD, Song Dynasty.
It is a great glory of our forefather
SUPERNOVA EXPLOSION

4. Neutron Star
10km, solar mass

5. Neutron Star (NS) in Low Mass X-ray Binary
OUTLINE OF TALK
Neutron Star (NS) in Low Mass X-ray Binary
KHz Quasi Periodic Oscillation (QPO)
Millisecond accreting-powered X-ray Pulsar
Type-I X-ray Burst Oscillation
Other QPOs of NS & BH
Theoretical Mechanisms---QPOs
Further Expectations

6. RXTE INTRODUCTION Rossi X-ray Timing Explorer (RXTE): NASA
Named after the astronomer, Bruno Rossi, died in 1993
3000+ kg RXTE satellite
Launched on Dec. 30, 1995
Delta II rocket into earth orbit
600 km and 23 deg inclination
Time const = ms

7. Basic Physical Parameters
动力学时间尺度， 强引力场
Characteristic Velocity: (GM/R)1/2 ~ 0.5c
Schwarzschild Radius: Rs = 2GM/c2
Characteristic Time Scale: 2π(R3/GM)1/2 ~ 0.6 (ms)
G: Gravitational Const, c: Speed of Light
M: Mass, R: Radius
Rs = 5 km, for M= 1.4 Mסּ, solar mass
Rs = 3 cm, for M= 1.0 Me, earth mass
Rs /R = 0.3 : Gravitational Strength

8. RXTE Instruments Proportional Counter Array (PCA)
sensitive to X-rays keV. collecting area (6250 cm2)
High Energy X-ray Timing Experiment (HEXTE)
The All Sky Monitor (ASM) scan most of the sky every 1.5 hours

9. RXTE Target A/Periodic, transient, and burst in X-ray emission
Characteristics of X-ray binaries, masses, orbital, matter exchange
Property: nuclear matter composition, M-R relation, neutron/strange star ? magnetic field
Behavior of matter into/onto a black hole/NS
Strong Gravity of GR near a black hole
Mechanisms causing X-ray emission
Strong Gravity, GR,
Precession, LS
M,R,Spin,
EOS,
Thermonuclear

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

11. QPO frequencies discovered by RXTE 1996—2007， reviewed by van der Klis 2006
FBO/NBO, ~5-20 Hz, Yu et al
HBO, ~15-70 Hz
Hundred, ~100 Hz
kHz, ~1000-Hz(27)
Burst oscillation, ~400 Hz(16)
Spin frequency, ~400 Hz (7)
Low, high QPO, ~0.1 Hz
Others.
QPO: Quasi Periodic Oscillation 准周期振荡

12. Typical twin KHZ QPOs （21/27）
Separation ~300 Hz
Typically: Twin KHz QPO
Upper ν2 = 1000 (Hz)
Lower ν1 = 700 (Hz)
21/27 sources； ~290 对
Sco x-1, van der Klis 2006

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

14. QPO v.s. Accretion rate relation
QPO frequency increases with the accretion rate
SCO X-1, Van der Klis, 2006
QPO轮廓随吸积率变宽/低，消失
Mendez 2005

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

16. kHz QPOs of Z Sources

17. Difference of twin kHz QPOs = const
Difference of twin kHz QPOs = const? Beat model by Miller, Lamb & Psaltis 1998; Strohmayer etal 1997

18. Saturation of kHz QPO frequency ?
4U , 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

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

20. kHz QPO v.s. Count rate kHz QPO corresponds to the position in CCD,
to accretion rate Mdot;
QPO ~ Mdot
B ~ Mdot, proportional
Zhang & Kojim, 2006, MNRAS

21. kHz QPO Distribution :
Twin frequency difference/ratio is not a constant
difference
Cir X-1
ν1 = ~700. (Hz)(ν2 /1000Hz)b
b ~ 1.6 Atoll Source 4U1728
b ~ 1.8 Z Source Sco X-1
Ratio
Zhang，Yin，Zhao，et al ，MNRAS

22. Twin kHz QPO distribution

23. Twin kHz QPO distribution

24. Spin Frequency：SAX J1808.4-3658 Millisecond Radio Pulsar, X-ray MSP
Bhattacharya and van den Heuvel, 1991
Millisecond Radio Pulsar, X-ray MSP
Rule : burst vs. pulsation is exclusive ?
Sax J : 401 Hz (2.49 ms)
Binary Parameters of SAX J
Orbital period: 2 hr
Orbital radius: 63 lms
Mass function: 3.8× 10-5 Mסּ
Magnetosphere radius: 30 km
Magnetic field : (2-6)×108 Gauss
Chakrabaty and Morgan 1998 Nature
Wijnands and van der Klis 1998, Nature

25. Accreting X-ray millisecond 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

26. Radio Pulsar: Magnetic field--period diagram
(1) Why B-P ? B evolves ? Recycled ?
(2) 716 Hz; ~10^8 G; why not 10^7 G ?
PSR: 1750, X-ray NS: 200
magnetar: 5SGR+11AXP
MSP: 175
BPSR: 130, recycled
LMXB
Van den Heuvel 2004, Science

27. Accretion-powered X-ray PSR, (7),185-599 Hz
Radio Millisecond PSR is recycled，Alpar， et al 1982 Nature
IGR J Hz, Markwardt 2004, 7 MSP sources

28. 差频和自旋关系
SAXJ ，Twin kHz QPOs ：700 Hz, 500 Hz；Burst/spin: 401 Hz； Wijnands et al 2003， Nature
Burst frequency ~ spin frequency
XTE 1807, twin kHz QPO, 191 Hz,
Linares , van der Klis, Wijnands 2005 ApJ；
F. Zhang，J Qu，C Zhang，W.Chen, T.P. Li, ApJ

29. 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: second
Burst decay time: second
Total energy: erg. Eddington luminosity !
4U , (363 Hz) Strohmayer et al 1996
362.5 Hz Hz, in 10 second

30. Spectrum of Type-I X-ray Burst frequency
4U , Strohmayer 1996 and Markwardt 1999, van der Klis 2006; Strohmayer and Bildsten 2003

31. Burst Oscillations

32. 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

33. Spin Frequency Distribution
Spin 1122 Hz, Kaaret et al 2006
7+11+4=22 Spin sources Hz
Radio MSP：716 Hz
Yin et al 2007 AA

34. kHz QPO & spin relation

35. Burst and Spin frequency
Burst and Spin frequency are similar，401 Hz X
17 burst sources, Muno et al 2004；van der Klis 2006
X-ray pulsars, Wijnands 2004; Chakrabarty 2004
Spin sources=7+(17-2)=22

36. burst sources， Muno 2004

37. 3rd kHz QPO ?
25 kHz QPO 源

38. Low frequency QPO---kHz QPO 关系
Belloni et al 2002 ApJ
Low frequency QPO< 100 Hz
FBO/NBO = 6-20 (Hz)
HBO = (Hz)
Empirical Relation
νHBO = 50. (Hz)(ν2 /1000Hz)
νHBO = 42. (Hz) (ν1/500Hz)
νqpo = 10. (Hz) (ν1/500Hz)
ν1 = 700. (Hz)(ν2 /1000Hz)

39. Low-high frequency QPO 关系
Neutron stars
Black holes ？
White dwarfs, Cvs
Zhang et al 2007, PASP
Warner 2006 MNARS; Warner & Woudt 2004 MNRAS; Mauche 2002 ApJ
+ 27 CVs, 5 magnitude orders in QPOs

40. Black Hole High Frequency QPOs
HFQPO: (Hz)
Constant (stable) in frequency (M/S) Luminosity
Pair frequency relation 3:2
Frequency-Mass relation: 1/M
7 BH sources, van der Klis 2006
Jets like Galactic BHs ~10Ms
(McClintock & Remillard 2003;2006)
Different from those of NS’s
GRO J , XTE J
XTE , 4U
XTE , H
GRS , 7 Sources
Van der Klis 2006
νk= (1/2π)(GM/r3)1/2
= (c/2πr) (Rs/2r)1/2
νk (ISCO) = 2.2 (kHz) (M/Mסּ) -1
Magnetosphere-disk instability noise:
mechanism：？Abramowicz et al AA; MNRAS ; Wang et al, 2003/06, MNRAS
Miller, et al 1998
Cui et al. 1998; Zhang SN et al 1997, APJ

41. BH QPO - spectral indices, flux, color
Zhang GB, et al APJ 2007, swift 1753

42. ~ High Frequency QPOs in Black Hole LMXBs Name BH Mass(Msun)
HF QPO (Hz)
References
GRO J ~6
300,450
1,2
XTE J
~10
184,276
188,249~276
3,4 5
GRS
~14
41,67
113,165
328
165 6
7(?)
8(?) 9 H ~
160,240
166,242 10 11
XTE J ~9
150~200 12 4U
184
100~300 8 13
XTE J
110~270 14

43. STELLAR Black Hole—Micro-quasar
GRS
165 Hz, 14 solar mass
10,000 lyr, 300Hz:450Hz=2:3
Microquasar, Radio jet
6 solar mass/optical

44. QPO and Break Frequency

45. Theoretical Consideration
Accretion Flow around NS/BH
Hard surface ?
Strong Gravity:
Schwarzschild Radius: Rs=2GM/c2
Innermost Stable Circular Orbit RIsco= 3Rs
Strong Magnetic:
Gauss (Atoll, Z-sources)
Beat Model:
Kepler Frequency
Difference to Spin frequency

46. QPO Models
Miller, Lamb & Psaltis ’ Beat Model, developed from Alpar & Shaham 1985 Nature ; Lamb et al 1985 Nature
Abramovicz et al ： Model
non-linear resonance between modes of accretion disk oscillations
HFQPO: Stellar black hole QPO, 3:2 relation
Wang et al 2003/06
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
Relativistic precession model by Stella & Vietri 1999

47. Theoretical Models Beat Model (HBO), νHBO = νkepler - νspin
What modulate X-ray Flux ?
Why quasi periodic, not periodic ?
Parameters: M/R/Spin, B?--Z/Atoll
Beat Model (HBO),
νHBO = νkepler νspin
νKepler ≈ r-3/2 is the Kepler Frequency of the orbit
νspin Constant, is the spin Frequency of the star
Alpar, M., Shaham, J., 1985, Nature
r ~ 1/Mdot , νHBO ~ Mdot
Beat Model for KHz QPO
ν2 = νkepler
ν1 = νkepler νspin
∆ν = ν ν1 = νspin
Miller, Lamb, Psaltis 1998; Strohmayer et al 1996
Lamb & Miller 2003
…Constant

48. X-射线源准周期振荡QPO RXTE：罗西X-射线卫星1996年发现 kHz QPO：积累近十年观测结果 中子星 kHz QPO，成对出现
黑洞 QPO，100Hz，3：2
HBO，15-70Hz，互相关联
理论解释：
拍模型
重要意义：
爱因斯坦理论，强引力场
黑洞的视界，最小稳定轨道
中子星质量半径，核物态
中子星磁场演化/结构
机制研究：
阿尔文波振荡模型
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。

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

50. Neutron Star Orbit N. Copernicus ISCO Saturation
Einstein’s General Relativity: Perihelion precession
Precession Model for KHz QPO, Stella and Vietri, 1999
ν2 = νkepler
ν1 = νprecession = ν2 [1 – (1 – 3Rs/r)1/2]
∆ν = ν ν1 is not constant

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

52. Lense-Thirring Precession
BH precession ？
L.Stella, M.Vietri, 1998
Cui et al 1998; Zhang SN et al. 1997
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

53. Alfven wave oscillation MODEL Zhang 2004 AA; Li & Zhang 2005 ApJ;
Zhang et al 2007 AN
Keplerian Orbital frequency resonance
MHD Alfven wave Oscillation in the orbit
ν2 = 1850 (Hz) A X3/2
ν1 = ν2X (1- (1-X)1/2)1/2
A=m1/2/R63/2; X=R/r,
m: Ns mass in solar mass
R6 is NS radius in 10^6 cm

54. Migliari, van der Klis, Fender, 2003 MNRAS
Boutloukos，van der Klis ApJ

55. Neutron Star Mass-Radius
Zhang et al MNRAS
AqlX-1， EXO Samples
CN1/CN2: normal neutron matter, CS1/CS2: Strange matter
CPC: core becomes Bose-Einstein condensate of pions

56. Fastest Pulsar XTE J1739-285 1122 Hz by Kaaret et al. 2006
Radio pulsar 716 Hz , Hessels et al. 2006
XTE , 1122 Hz
kHz QPO: Hz
Quark Star ?

57. 11-year RXTE - where are we now ?
观测，进展较大，QPO关系明确
理论，进展缓慢，很多模型?
物理实验室
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？

58. Discussion and Problems
Now, we are standing on the edge of new discovery ?
THANKS

59. Have no X-ray pulsation & type-II X-ray bursts
A comparison between high-frequency QPOs in BH LMXBs and those in NS LMXBs
QPOs in BH LMXBs
QPOs in NS LMXBs
Hard spectral
Relatively soft
Break
Have no X-ray pulsation & type-II X-ray bursts
Have X-ray pulsation &type-II X-ray bursts
~3:2 ratio
Not constant
Relatively stable
Systemically change with Luminosity
1/M scaling ?
Spin? No observational evidence.
Spin! X-ray pulsation & type-II X-ray bursts