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

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

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 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

Binary X-ray Sources

Normal Star + Compact Star10,000 lyr, 300Hz/450Hz

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

G wave

Black Hole

BH-No hair Theorem

Mass/Spin/Charge

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

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

Accretion rate direction

~Eddington Accretion~1% Eddington Accretion

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

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

QPO v.s. Accretion rate relation

SCO X-1, Van der Klis, 2004

QPO frequency increases with increasing of the accretion rate

QPO

最大值： νmax=1329 Hz,

van Straaten 2000

KHz QPO Data ， Atoll

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

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

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 starkHz QPO relation

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

Burst Oscillation Frequency

11 bursts ， Muno 2004

25 kHz QPO

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

Low-high frequency QPO

Warner & Woudt 2004; Mauche 2002

+ 27 CVs, 5 magnitude orders in QPOs

Black holes

White dwarfs, Cvs

Neutron stars

？

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 ：？

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

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: Keplerian 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

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

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

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 源，　中子星质量≈ 1 。 3 太阳质量

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

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

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

Lower kHz QPOs

Difference of kH

z QP

Os

Migliari, van der Klis, Fender, 2003

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 ?

Discussion and Problems

THANKS

Now, we are standing on the edge of new discovery