张承民， 尹红星 National Astronomical Observatories Chinese Academy of Sciences, Beijing

QPOs ，准周期振荡 in Black Hole ， Neutron Star X-ray Sources:

X-ray bursts, accreting-powered pulsarsEinstein’s Relativity in Strong Gravitation

张承民， 尹红星

National Astronomical Observatories

Chinese Academy of Sciences, Beijing

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

Binary X-ray Sources

Normal Star + Compact Star 10,000 lyr, 300Hz/450Hz

Micro-quasar, Radio jet

7 solar mass/optical

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

Atoll and Z Sources --- LMXB CCD

Accretion rate direction

~Eddington Accretion~1% Eddington Accretion

Discovery: typical twin KHZ QPOs

Sco x-1, van der Klis et al 1997

Separation ~300 Hz

Typically: Twin KHz QPO

Upper ν2 = 1000 (Hz)

Lower ν1 = 700 (Hz)

18/25 sources

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

最大值 Max ： νmax=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？

kHz QPOs of Z Sources

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

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

Parallel Line Phenomenon 　kHz QPO － luminosity

relationSimilarity/Homogeneous ?

Among the different sources, same source at the different time

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

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

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

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

Spectrum of Type-I X-ray Burst frequency

4U1702-43, van der Klis 2006; Strohmayer and Bildsten 2003

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: 1039-40 erg. Eddington luminosity !

4U1728-34, (363 Hz) Strohmayer et al 1996

362.5 Hz --- 363.9 Hz, in 10 second

Burst Oscillations

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

Burst and Spin frequency

X

X

X

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

11 burst sources ， Muno 2004

25 kHz QPO 源

3rd kHz QPO ?

Low frequency QPO---kHz QPO 关系

Psaltis et al 1998, 1999

Belloni et al 2002; 2005

Empirical Relation

νHBO = 50. (Hz)(ν2 /1000Hz)1.9-2.0

νHBO = 42. (Hz) (ν1/500Hz)0.95-1.05

νqpo = 10. (Hz) (ν1/500Hz)

Low frequency QPO< 100 Hz

FBO/NBO = 6-20 (Hz)

HBO = 15-70 (Hz)

ν1 = 700. (Hz)(ν2 /1000Hz)1.9-2.0

Twin kHz QPO relations

ν1 = ~700. (Hz)(ν2 /1000Hz)b

b ~ 1.6 Atoll Source 4U1728

b ~ 1.8 Z Source Sco X-1

Zhang et al. 2006

Twin kHz QPO distribution

Twin kHz QPO distribution

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

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

νk= (1/2π)(GM/r3)1/2

= (c/2πr) (Rs/2r)1/2

νk (ISCO) = 2.2 (kHz) (M/Mּס) -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

High Frequency QPOs in Black Hole LMXBs

Name BH Mass(Msun) HF QPO (Hz) References

GRO J1655-40 ~6 300,450 1,2

XTE J1550-564 ~10 184,276188,249~276

3,45

GRS 1915+105 ~14 41,67113,165328165

67(?)8(?)9

H 1743-322 ~ 160,240166,242

1011

XTE J1859+226 ~9 150~200 12

4U 1630-472 ~ 184100~300

813

XTE J1650-500 ~ 110~270 14

(Astro-ph/0408402[8])

H 1743-322[10]

XTE J1650-500[14]

160

240

250

A comparison between high-frequency QPOs in BH LMXBs and those in NS LMXBs

QPOs in NS LMXBs

QPOs in BH LMXBs

Twin kHz QPOs Yes Yes

Ratio Not a constant ~3:2

Spectra index Soft Hard, saturation

Pulsations Yes No

Type I X-ray bursts Yes No

1/M scaling No? yes

Changes Increase with Lx Relatively stable

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

QPO and Break Frequency

Theoretical Consideration

Strong Gravity: Schwarzschild Radius: Rs=2GM/c2

Innermost Stable Circular Orbit RIsco= 3Rs

Strong Magnetic: 108-9 Gauss (Atoll, Z-sources) Beat Model: Kepler Frequency Difference to Spin frequency

Accretion Flow around NS/BH

Hard surface ?

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

Theoretical Models

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 = ν2 - ν1 = νspin

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

X-X- 射线源准周期振荡射线源准周期振荡 QPO, Beat ?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

Einstein’s Prediction: Perihelion Motion of Orbit

Perihelion precession of Mercury orbit = 43” /century, near NS, ~10^16 times large

Neutron Star Orbit

N. Copernicus

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 = ν2 - ν1 is not constant

ISCO Saturation

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

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., 2nd Fairbank W., Rome U, organized by R.Ruffini, 1998

Book “Gravitation and Inertia” by Ciufolini and Wheeler, 1995

Problems ?

Vacuum ?Kerr rotation ? Magnetic Field ? Inner Accretion Disk ?

Similarity: common parameter: accretion rate/radius

Alfven wave oscillation MODEL

(in Schwarzschild spacetime):

Zhang 2004; Li & Zhang 2005

Keplerian Orbital frequency resonance

MHD Alfven wave Oscillation in the orbit

ν2 = 1850 (Hz) A X3/2

ν1 = ν 2X (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

NS

M

ass 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 ?

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

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