What QPOs of NS tell us ?:
Neutron Star X-ray Sources
Chengmin Zhang
National Astronomical Observatories
Chinese Academy of Sciences, Beijing
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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
 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
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
RXTE
 a/Periodic, transient, and burst phenomena in the Xray emission
 The characteristics of X-ray binaries, masses, orbital,
matter exchange.
Strong Gravity, GR,
 Property of neutron star, nuclear matter composition,
equation of state (EOS), M-R relation, magnetic field
Precession, LS
 The behavior of matter into a black hole,
EOS,
M,R,Spin,
Thermonuclear
 Strong Gravity of general relativity near a black hole,
 Mechanisms causing the emission of X-rays
Binary X-ray Sources
10,000 lyr, 300Hz/450Hz
Normal Star + Compact Star
Microquasar, Radio jet
7 solar mass/optical
Albert Einstein and Black Hole
Century Person, 2005: 100
years of Special Relativity
GR, 1915,
Redshift
Precession
Deflection
Delay
BH-No hair Theorem
G wave
Mass/Spin/Charge
Black Hole
Galaxy Black Hole Myths
Stellar BH, 3-100 M‫סּ‬
1,000,000 Solar Mass
Milky Way’s Black Hole
Solar System
Midmass BH, 100-1000 M‫סּ‬
QPO discovered by RXTE since 1996-2005
review see van 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.
QPO:
Quasi Periodic
Oscillation
Atoll and Z Sources---LMXB
~1% Eddington Accretion
Accretion rate direction
~Eddington Accretion
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
QPO=Quasi Periodic Oscillation
LMXB
4U1728-34, Sco X-1
NASA/GSFC, 1996
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 frequency increases with
increasing of the accretion rate
SCO X-1, Van der Klis, 2004
QPO
KHz QPO Data，
Atoll
最大值：νmax=1329 Hz,
van Straaten 2000
平均值：QPO（Atoll） 〉QPO（Z）
原因？
KHz QPO of Z Sources
Twin KHz QPO difference=con ？
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
hard？
Parallel Line Phenomenon
kHz QPO－luminosity
Similarity/Homogeneous ?
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)
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
IGR J00291+5934
598.88 Hz, Markwardt
2004, 6 MSP sources
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
Wijnands and van der Klis 1998, Nature
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, 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
Burst Oscillations
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
Burst Oscillation Frequency
11 bursts， Muno 2004
25 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)
 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
Magnetosphere-disk instability noise:
mechanism：？
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
νk= (1/2π)(GM/r3)1/2
= (c/2πr) (Rs/2r)1/2
νk (ISCO) = 2.2 (kHz) (M/M‫ )סּ‬-1
Miller, et al 1998
STELLAR Black Hole--Microquasar
GRS 1915+105
10,000 lyr, 300Hz:450Hz=2:3
67 Hz, 33 solar mass
Microquasar, Radio jet
7 solar mass/optical
QPO and Break Frequency
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
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
Relativistic precession model
by Stella & Vietri
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
Theoretical Models
What modulate X-ray Flux ?
Why quasi periodic, not periodic ?
Parameters: M/R/Spin, B?--Z/Atoll
Beat Model (HBO),
ν =ν - ν
Alpar, M., Shaham, J., 1985, Nature
HBO
ν
ν
kepler
spin
Kepler
≈ r-3/2 is the Kepler Frequency of the orbit
spin
Constant, is the spin Frequency of the star
r ~ 1/Mdot ,
νHBO ~ Mdot
Beat Model for KHz QPO
Miller, Lamb, Psaltis 1998; Strohmayer et al 1996
ν2 = νkepler
Lamb & Miller 2003
ν1 = νkepler - νspin
∆ν = ν2
- ν1 = νspin
…Constant
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
ISCO Saturation
Einstein’s General Relativity: Perihelion precession
Precession Model for KHz QPO, Stella and Vietri, 1999
ν2 = νkepler
ν1 = νprecession
∆ν = ν2
= ν2 [1 – (1 – 3Rs/r)1/2]
- ν1 is not constant
Problems:
1. Vacuum
Theoretical model
2. Circular orbit
3. Test particle
4. Predicted 2 M⊙
5. 30源， 中子星质量≈1。3太阳质量
Stella and Vietrie, 1999, Precession model
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
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 = 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
Migliari, van der Klis, Fender, 2003
Difference of kHz QPOs
Lower kHz QPOs
Constrain on Star EOS , mass & radius
Kerr spacetime ?
NS
Mass 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
Now, we are standing on the edge of new discovery
THANKS