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What QPOs of NS tell us ?: Neutron Star X-ray Sources. Chengmin Zhang National Astronomical Observatories Chinese Academy of Sciences, Beijing. Introduction of RXTE Black Hole and Neutron Star in Low Mass X-ray Binary (LMXB) KHz Quasi Periodic Oscillation (QPO) Millisecond X-ray Pulsar

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what qpos of ns tell us neutron star x ray sources
What QPOs of NS tell us ?:Neutron Star X-ray Sources

Chengmin Zhang

National Astronomical Observatories

Chinese Academy of Sciences, Beijing

Introduction of RXTE
  • Black Hole and Neutron Star in Low Mass X-ray Binary (LMXB)
  • KHz Quasi Periodic Oscillation (QPO)
  • Millisecond X-ray Pulsar
  • Type-I X-ray Burst Oscillation
  • QPO of Black Hole X-ray Sources
  • Theoretical Mechanisms---Strong Gravity
  • Further Expectation
Rossi X-ray Timing Explorer (RXTE): NASA

Named after Bruno Rossi

3000+ kg RXTE satellite

Launched on Dec. 30, 1995

Delta II rocket into earth orbit

600 km and 23 deg inclination

Time const = 0.5 ms

basic physical parameters
Basic Physical Parameters
  • 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
rxte instruments
RXTE Instruments

Proportional Counter Array (PCA)

sensitive to X-rays 2-60 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

  • a/Periodic, transient, and burst phenomena in the X-ray emission
  • The characteristics of X-ray binaries, masses, orbital, matter exchange.
  • Property of neutron star, nuclear matter composition, equation of state (EOS), M-R relation, magnetic field
  • The behavior of matter into a black hole,
  • Strong Gravity of general relativity near a black hole,
  • Mechanisms causing the emission of X-rays

Strong Gravity, GR,

Precession, LS




binary x ray sources
Binary X-ray Sources

10,000 lyr, 300Hz/450Hz

Microquasar, Radio jet

7 solar mass/optical

Normal Star + Compact Star

albert einstein and black hole
Albert Einstein and Black Hole

Century Person, 2005: 100 years of Special Relativity

GR, 1915,





G wave

Black Hole

BH-No hair Theorem


galaxy black hole myths
Galaxy Black Hole Myths

Stellar BH, 3-100 Mסּ

Midmass BH, 100-1000 Mסּ

1,000,000 Solar Mass

Solar System

Milky Way’s Black Hole

qpo discovered by rxte since 1996 2005 review see van der klis 2004
QPO discovered by RXTE since 1996--2005review seevan der Klis 2004
  • 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.


Quasi Periodic Oscillation

atoll and z sources lmxb
Atoll and Z Sources---LMXB

~1% Eddington Accretion

~Eddington Accretion

Accretion rate direction

typical twin khz qpos
Typical Twin KHZ QPOs

Separation ~300 Hz

Typically: Twin KHz QPO

Upper ν2 = 1000 (Hz)

Lower ν1 = 700 (Hz)

18/25 sources

Sco x-1, van der Klis et al 1997

discovery of khz qpo
Discovery of KHz QPO

QPO=Quasi Periodic Oscillation


4U1728-34, Sco X-1


Strohnayer et al, 1996

Van der Klis, et al 1996

25 Atoll/Z Sources

Van der Klis 2000, 2004; Swank 2004

See table

qpo v s accretion rate relation
QPO v.s. Accretion rate relation

QPO frequency increases with increasing of the accretion rate

SCO X-1, Van der Klis, 2004


KHz QPO Data,Atoll

最大值:νmax=1329 Hz,

van Straaten 2000

平均值:QPO(Atoll) 〉QPO(Z)


khz qpo saturation
KHz QPO saturation ?

4U1820-30, NASA

W. Zhang et al, 1998

Kaaret, et al 1999

Swank 2004; Miller 2004

ISCO: 3 Schwarzschild radius

Innermost stable circular orbit

Surface: star radius


khz qpo v s count rate
KHz QPO v.s. Count rate

Same source, kHz QPO and CCD,1-1

accreting millisecond x ray pulsar sax j1808 4 3658 6 sources
Accreting millisecond X-ray pulsar---SAX J1808.4-3658 (6 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

Burst frequency=spin frequency, 2003

sax j1808 4 3658
SAX J1808.4-3658
  • Bhattacharya and van den Heuvel, 1991
  • Millisecond Radio Pulsar, X-ray MSP
  • Rule : burst vs. pulsation is exclusive ?
  • Sax J1808.4-3658: 401 Hz (2.49 ms)

Binary Parameters of SAX J1804.5-3658

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

spectrum of type i x ray burst
Spectrum of Type-I X-ray Burst

4U1702-43, Strohmayer 1996 and Markwardt 1999, van der Klis 2004; Strohmayer and Bildsten 2003

type i x ray burst
Type-I X-ray Burst
  • Type-I X-ray Burst, Lewin et al 1995/Bilsten 1998
  • Thermonuclear (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

on burst
On burst
  • Burst frequency increases ~2 Hz, drift.
  • Decreasing is discovered
  • From hot spot on neutron star
  • kHz QPO relation
kHz QPO separation=195 Hz/(spin=401 Hz)

Burst and Spin frequency are same




11 burst sources, Muno et al 2004

6 X-ray pulsars, Wijnands 2004; Chakrabarty 2004

low frequency qpo khz qpo
Low frequency QPO---kHz QPO

Psaltis et al 1999,

Belloni et al 2002

Low frequency QPO< 100 Hz

FBO/NBO= 6-20 (Hz)

HBO =15-70 (Hz)

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)

ν1 = 700. (Hz)(ν2 /1000Hz)1.9-2.0

Low-high frequency QPO

Neutron stars

Black holes

White dwarfs, Cvs

Warner & Woudt 2004; Mauche 2002

+ 27 CVs, 5 magnitude orders in QPOs

bh high frequency qpo bh
BH High Frequency QPO (BH)

GRO J1655-40, XTE J1550-564

XTE 1650-5000, 4U1630-47

XTE 1859-226, H 1743-322

GRS 1915+105, 7 Sources

Van der Klis 2004

  • 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 2004
  • Jets like Galactic BHs

(McClintock & Remillard 2003)

Different from BH low frequency

QPOs and NS kHz QPOs

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:


Miller, et al 1998

stellar black hole microquasar
STELLAR Black Hole--Microquasar

GRS 1915+105

67 Hz, 33 solar mass

10,000 lyr, 300Hz:450Hz=2:3

Microquasar, Radio jet

7 solar mass/optical

theoretical consideration
Theoretical Consideration

Accretion Flow around NS/BH

Hard surface ?

  • Strong Gravity:
  • Schwarzschild Radius: Rs=2GM/c2
  • Innermost Stable Circular Orbit RIsco= 3Rs
  • Strong Magnetic:
  • 108-9 Gauss (Atoll, Z-sources)
  • Beat Model:
  • Keplerian Frequency
  • Difference to Spin frequency
qpo models
QPO Models

Miller, Lamb & Psaltis ’ Model

Beat model developed from Alpar & Shaham 1985 Nature

Abramovicz and cooperators ’ Model

non-linear resonance between modes of accretion disk oscillations

HFQPO: Stella black hole QPO, 3:2 relation

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

Relativistic precession model by Stella & Vietri

theoretical models
Theoretical Models

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-3/2is 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


einstein s prediction perihelion motion of orbit
Einstein’s Prediction: Perihelion Motion of Orbit

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

neutron star orbit
N. CopernicusNeutron Star Orbit

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 = ν2 - ν1 is not constant

theoretical model
Theoretical model
  • Problems:
  • Vacuum
  • Circular orbit
  • Test particle
  • Predicted 2 M⊙
  • 30源, 中子星质量≈1。3太阳质量

Stella and Vietrie, 1999, Precession model

lense thirring precession
Lense-Thirring Precession

W. Cui, S.N. Zhang, W. Chen, 1997 (MIT/NASA), 黑洞,进动?

L.Stella, M.Vietri, 1997 (Rome)

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

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

lense thirring precession frequency
Lense-Thirring Precession Frequency

Rs = 5 km, R = 15 -20 km,

Ω = 300 Hz

ΩLS = 30 Hz

Lense-Thirring Frequency estimation

ΩLS --- parameter * (Rs/R)2Ω

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

Similarity: common parameter: accretion rate/radius

Alfven wave oscillation MODEL

(in Schwarzschild spacetime): Zhang, 2004a,b

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

Migliari, van der Klis, Fender, 2003

Difference of kHz QPOs

Lower kHz QPOs

Constrain on Star EOS , mass & radius

Kerr spacetime ?

NSMass in solar mass

NS radius (km)

CN1/CN2: normal neutron matter, CS1/CS2: Strange matter

CPC: core becomes Bose-Einstein condensate of pions

discussion and problems
Discussion and Problems

Now, we are standing on the edge of new discovery