kHz QPOs of LMXBsConstrains on Pulsar Parameters

Chengmin Zhang & Hongxing Yin

National Astronomical Observatories, Beijing

OUTLINE OF TALK

KHz Quasi Periodic Oscillation (QPO) in NS/LMXB Millisecond accreting-powered X-ray Pulsar

Type-I X-ray Burst Oscillation Other QPOs of NS & BH Theoretical Mechanisms---kHz QPOs Constrains on Mass, Radius, Magnetic of compact object

RXTE Target

A/Periodic, transient, and burst in X-ray X-ray binaries, masses, orbital, matter

exchange nuclear matter in compact objects, M-R

relation, magnetic field Behavior of matter into/onto a NS/BH Strong Gravity of GR near a NS/BH Mechanisms causing X-ray emission

Rossi X-ray Timing Explorer (RXTE): NASA, Launched on Dec. 30, 1995

QPO frequencies by RXTE 1996—2007

kHz QPOs (27) van der Klis 2006; Belloni et al. 2005; Zhang et al. 2007

Spin frequency - Burst oscillation (23); 45-1122 Hz Villarreal & Strohmayer. 2004; Strohmayer & Bildsten 2006; Kaaret 2007

HBO, ~15-70 Hz, van der Klis 2006

FBO/NBO, ~5-20 Hz, Yu et al 2003; van der Klis 2006

Others.

Typical twin kHz QPOs （ 21/27 ）

Z: Sco x-1, van der Klis et al 1996;

Atoll: 4U 1728-34 Strohmayer et al 1996

Separation ~300 Hz

~Spin ?

Typically: Twin KHz QPO

Upper ν2 ~ 1000 (Hz)

Lower ν1 ~ 700 (Hz)

Twin 21/27 sources ； ~290

kHz QPOs in Atoll and Z Sources -- CCD

Accretion rate direction

~Eddington Accretion~1% Eddington Accretion

QPO v.s. Accretion rate relation

SCO X-1, Van der Klis, 2006

QPO frequency increases with the accretion rate

kHz QPO profile; Mendez 2005

Max ： νmax=1329 Hz,

van Straaten & van der klis 2000

min: ~200 Hz

KHz QPO Data ， Atoll and Z sources

Distribution of kHz QPOs ： QPO (Atoll) ~ QPO （ Z ）

Zhang et al 2006 MNRAS;

Table: kHz QPO, spin

8

separation of twin kHz QPOs = const?Beat ? Strohmayer et al 1996; 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 accretion rate Mdot;

QPO ~ Mdot

Zhang ， et al. 2006 ， MNRAS

kHz QPO Distribution :

separation /ratio is not a constant

ν1 = ~700. (Hz)(ν2 /1000Hz)b

b ~ 1.6 Atoll Source 4U1728

b ~ 1.8 Z Source Sco X-1

Cir X-1

dif

fere

nce

Rat

io

AMXP: XTE1807-294, SAXJ1808.4-365: special cases 1.5 shift

XTE1807-294, Linares et al 2006; Zhang et al 2006

SAXJ1808.4-365: Wijnands & van der Klis 2003

Twin kHz QPO distribution

Twin kHz QPO distribution; ratio

Accreting X-ray millisecond pulsar --- SAX J1808.4-3658 (8 AXMPs); 401 Hz (2.49 ms)

Wijnands and van der Klis, 1998 Nat; Wijnands et al 2003 Nat

Type-I X-ray Burst frequency

17 burst sources, van der Klis 2006; Strohmayer and Bildsten 2006

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

362.5 Hz --- 363.9 Hz

SAXJ 1808.4-3658 ， Twin kHz QPOs ： 700 Hz, 500 Hz ； Burst/spin: 401 Hz ； Wijnands et al 2003 ， Nature

Burst frequency = spin frequency

XTE 1807-294, twin kHz QPOs, 191 Hz,

Linares, et al 2006 ; Zhang ， et al, 2006

kHz QPO separation and spin relation

Slow rotator; separation/spin ~ 1 Fast rotator; separation/spin ~ 0.5

Linares & van der Klis 2007

Spin Frequency Distribution

8+11+4=23 Spin sources

Radio MSP ： Max Spin=716 Hz

Yin, Zhang, Zhao et al 2007 AA

Spin frequency:

Max: 1122 Hz, Kaaret et al 2007 ApJ

Min: 45 Hz Villarreal & Strohmayer 2004

kHz QPO & spin relation

Radio Pulsar: Magnetic field--period diagram

PSR: 1750, X-ray NS: 200

magnetar: 5SGR+11AXP

MSP: 175

BPSR: 130, recycled

(2) 716 Hz; ~10^8 G; why not 10^7 G ?

(1) Why B-P ? B evolves ? Recycled ?

LMXB

Van den Heuvel 2004, Science

Low frequency QPO---kHz QPO 关系

Belloni et al 2002 ApJ

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)1.6-2.0

Low-high frequency QPO relation in WD/NS/BH

Warner 2006 MNARS; Warner & Woudt 2004 MNRAS; Mauche 2002 ApJ; Titarchuk & Wood 2002 ApJ

+ 27 CVs, 5 magnitude orders in QPO frequency

Black holes

White dwarfs, Cvs

Neutron stars

？

Zhang et al 2007, PASP

Similarity in WD/NS/BH ?

Black Hole High Frequency QPOs

HFQPO: 40-450 (Hz) Frequency stable with Luminosity Pair relation 3:2 Frequency-Mass relation: 1/M Jets like Galactic BHs ~10Msun

Different: NS/LMXB kHz QPOs (McClintock & Remillard 2003;2006)

Frequency at ISCO Schwarzschild

νk= (1/2π)(GM/r3)1/2

= (c/2πr) (Rs/2r)1/2

νk (ISCO) = 2.2 (kHz) (M/Mּס) -1

GRO J1655-40, XTE J1550-564

XTE 1650-5000, 4U1630-47

XTE 1859-226, H 1743-322

GRS 1915+105, 7 microquasars

Van der Klis 2006

3:2 mechanism:

Abramowicz et al 2003; Li & Narayan 2003; Wang et al, 2003/06, MNRAS

Measuring BH spin by QPO:

Cui et al. 1998; Zhang SN et al 1997

High frequency pair QPO

BH: ~3:2 --- NS: varied near 3:2

Theoretical Models

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

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

Relativistic precession model by Stella & Vietri 1999

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

Alfven wave oscillation MODEL

Zhang 2004 AA; Li & Zhang 2005 ApJ;

Keplerian Orbital frequency

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

Some radius: Lai 1998

Migliari, van der Klis, Fender, 2003 MNRAS

Boutloukos ， van der Klis 2006 ApJ

Cir X-1

Constrains star mass radius by kHz QPOs

Inner boundary to emit kHz QPO: ISCO, R > MAX M, R

M<2.2 M⊙ (1kHz/freq)

R<19.5 km (1kHz/freq) M/R3 relation known by model for twin kHz QPOs

SAXJ 1808.4: M/R3 by Burderi & King 1998

Mass-Radius relations

Apparent Radius: R∞=R/(1-Rs/R)1/2 Haensel 2001

Gravitational redshift: z=(1-Rs/R)-1/2 -1 Cottam et al 2003, z=0.35

Mass density: M/R3 (by kHz QPOs) Zhang 2004

1E1207.4-5209, Aql X-1 and EXO 0748-676

Rs=2GM: Schwarzschild radius

Measuring NS Mass & Radius

by kHz QPO, gravitational redshift and apparent radius 　　

Measuring NS Mass-Radius

by kHz QPO, gravitational redshift and apparent radius 　　

CN1/CN2: normal neutron matter, CS1/CS2: quark star

CPC: Bose-Einstein condensate of pions

Zhang, Yin, Kojim, Li XD, Xu RX, Zhang B, Kiziltan B 2007 MNRAS

AqlX-1 ， EXO 0748-676 Samples

Fastest Pulsar XTE J1739-285 1122 Hz Mass & Radius Kaaret et al. 2007

Quark Star ?

Quark Star ?

Xu, MNRAS, 2005

Xu, Qiao, Wang, CPL, 2003

Li et al 1999 PRL

Sub-millisecond PSR : high mass, Burderi et al. 2003

Estimating Magnetic filed - LMXB

Spin > corotation radius ~40 km > ~108 G Spin variation: torque > ~108 G Wijnands & van der Klis 1998; Burderi, de Salvo.. 2006; Chou Y, poster

kHz QPO distribution for Atoll/Z > similar magnetosphere ~108 G (Mdot)1/2

Zhang & Kojim 2006; Burderi et al 1996, 1997; White & W Zhang 1998

Z source has a stronger field than Atoll’s

Estimating NS spin by spin-kHz QPO relation

Spin frequency is less than

the minimum upper-frequency of twin kHz QPOs

Summary

1. kHz QPOs NS/LMXBs2. BH/WD/NS3. Constraints M,R,B,spin