![Page 1: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/1.jpg)
What QPOs of NS tell us ?:Neutron Star X-ray Sources
Chengmin Zhang
National Astronomical Observatories
Chinese Academy of Sciences, Beijing
![Page 2: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/2.jpg)
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
![Page 3: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/3.jpg)
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
![Page 4: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/4.jpg)
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 Mס, solar mass
Rs = 3 cm, for M= 1.0 Me, earth mass
Rs /R = 0.3 : Gravitational Strength
![Page 5: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/5.jpg)
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
![Page 6: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/6.jpg)
RXTE
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
M,R,Spin,
EOS,
Thermonuclear
![Page 7: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/7.jpg)
Binary X-ray Sources
Normal Star + Compact Star10,000 lyr, 300Hz/450Hz
Microquasar, Radio jet
7 solar mass/optical
![Page 8: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/8.jpg)
Albert Einstein and Black Hole
Century Person, 2005: 100 years of Special Relativity
GR, 1915,
Redshift
Precession
Deflection
Delay
G wave
Black Hole
BH-No hair Theorem
Mass/Spin/Charge
![Page 9: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/9.jpg)
Galaxy Black Hole Myths
1,000,000 Solar Mass
Stellar BH, 3-100 Mס
Milky Way’s Black Hole
Solar SystemMidmass BH, 100-1000 Mס
![Page 10: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/10.jpg)
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
![Page 11: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/11.jpg)
Atoll and Z Sources---LMXB
Accretion rate direction
~Eddington Accretion~1% Eddington Accretion
![Page 12: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/12.jpg)
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
![Page 13: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/13.jpg)
Discovery of KHz QPOQPO=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
![Page 14: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/14.jpg)
QPO v.s. Accretion rate relation
SCO X-1, Van der Klis, 2004
QPO frequency increases with increasing of the accretion rate
QPO
![Page 15: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/15.jpg)
最大值: νmax=1329 Hz,
van Straaten 2000
KHz QPO Data , Atoll
平均值: QPO ( Atoll ) 〉 QPO ( Z)
原因?
![Page 16: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/16.jpg)
KHz QPO of Z Sources
![Page 17: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/17.jpg)
Twin KHz QPO difference=con ?
![Page 18: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/18.jpg)
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 ?
![Page 19: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/19.jpg)
Parallel Line Phenomenon kHz QPO - luminosity
Similarity/Homogeneous ?
![Page 20: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/20.jpg)
KHz QPO v.s. Count rate
Same source , kHz QPO and CCD,1-1
![Page 21: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/21.jpg)
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
![Page 22: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/22.jpg)
SAXJ 1808.4-3658
Twin kHz QPOs
700 Hz, 500 Hz
Burst/spin: 401 Hz
Burst frequency=spin frequency , 2003
![Page 23: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/23.jpg)
IGR J00291+5934 598.88 Hz, Markwardt 2004, 6 MSP sources
![Page 24: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/24.jpg)
Bhattacharya and van den Heuvel, 1991Millisecond Radio Pulsar, X-ray MSP Rule : burst vs. pulsation is exclusive ? Sax J1808.4-3658: 401 Hz (2.49 ms)
SAX J1808.4-3658
Binary Parameters of SAX J1804.5-3658
Orbital period: 2 hr
Orbital radius: 63 lms
Mass function: 3.8× 10-5 Mס
Magnetosphere radius: 30 km
Magnetic field : (2-6)×108 Gauss
Chakrabaty and Morgan 1998/Nature
Wijnands and van der Klis 1998, Nature
![Page 25: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/25.jpg)
Spectrum of Type-I X-ray Burst
4U1702-43, Strohmayer 1996 and Markwardt 1999, van der Klis 2004; Strohmayer and Bildsten 2003
![Page 26: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/26.jpg)
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
![Page 27: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/27.jpg)
Burst Oscillations
![Page 28: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/28.jpg)
On burst
Burst frequency increases ~2 Hz, drift. Decreasing is discovered From hot spot on neutron starkHz QPO relation
![Page 29: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/29.jpg)
X
X
X
11 burst sources, Muno et al 2004
6 X-ray pulsars, Wijnands 2004; Chakrabarty 2004
kHz QPO separation=195 Hz/(spin=401 Hz)
Burst and Spin frequency are same
![Page 30: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/30.jpg)
Burst Oscillation Frequency
![Page 31: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/31.jpg)
11 bursts , Muno 2004
![Page 32: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/32.jpg)
25 kHz QPO
![Page 33: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/33.jpg)
Low frequency QPO---kHz QPO
Psaltis et al 1999,
Belloni et al 2002
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
![Page 34: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/34.jpg)
Low-high frequency QPO
Warner & Woudt 2004; Mauche 2002
+ 27 CVs, 5 magnitude orders in QPOs
Black holes
White dwarfs, Cvs
Neutron stars
?
![Page 35: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/35.jpg)
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
νk= (1/2π)(GM/r3)1/2
= (c/2πr) (Rs/2r)1/2
νk (ISCO) = 2.2 (kHz) (M/Mס) -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, 7 Sources
Van der Klis 2004
Magnetosphere-disk instability noise:
mechanism :?
![Page 36: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/36.jpg)
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
![Page 37: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/37.jpg)
QPO and Break Frequency
![Page 38: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/38.jpg)
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: Keplerian Frequency Difference to Spin frequency
Accretion Flow around NS/BH
Hard surface ?
![Page 39: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/39.jpg)
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
Abramovicz and cooperators ’ Model
non-linear resonance between modes of accretion disk oscillations
HFQPO: Stella black hole QPO, 3:2 relation
Miller, Lamb & Psaltis ’ Model
Beat model developed from Alpar & Shaham 1985 Nature
Relativistic precession model by Stella & Vietri
![Page 40: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/40.jpg)
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
![Page 41: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/41.jpg)
Einstein’s Prediction: Perihelion Motion of Orbit
Perihelion precession of Mercury orbit = 43” /century, near NS, ~10^16 times large
![Page 42: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/42.jpg)
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
![Page 43: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/43.jpg)
Theoretical model
Stella and Vietrie, 1999, Precession model
Problems:
1. Vacuum
2. Circular orbit
3. Test particle
4. Predicted 2 M⊙
5. 30 源, 中子星质量≈ 1 。 3 太阳质量
![Page 44: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/44.jpg)
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
W. Cui, S.N. Zhang, W. Chen, 1997 (MIT/NASA) , 黑洞,进动?
L.Stella, M.Vietri, 1997 (Rome)
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
![Page 45: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/45.jpg)
Lense-Thirring Precession Frequency
Lense-Thirring Frequency estimation
ΩLS --- parameter * (Rs/R)2Ω
Rs = 5 km, R = 15 -20 km,
Ω = 300 Hz
ΩLS = 30 Hz
![Page 46: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/46.jpg)
Problems ?
Vacuum ?Kerr rotation ? Magnetic Field ? Inner Accretion Disk ?
Similarity: common parameter: accretion rate/radius
![Page 47: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/47.jpg)
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
![Page 48: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/48.jpg)
Lower kHz QPOs
Difference of kH
z QP
Os
Migliari, van der Klis, Fender, 2003
![Page 49: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/49.jpg)
![Page 50: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/50.jpg)
![Page 51: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/51.jpg)
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 ?
![Page 52: What QPOs of NS tell us ?: Neutron Star X-ray Sources](https://reader036.vdocuments.mx/reader036/viewer/2022062410/5681591f550346895dc64889/html5/thumbnails/52.jpg)
Discussion and Problems
THANKS
Now, we are standing on the edge of new discovery