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kHz QPOs of LMXBs Constrains on Pulsar Parameters

kHz QPOs of LMXBs Constrains 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

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kHz QPOs of LMXBs Constrains on Pulsar Parameters

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  1. kHz QPOs of LMXBsConstrains on Pulsar Parameters Chengmin Zhang & Hongxing Yin National Astronomical Observatories, Beijing

  2. 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

  3. 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

  4. 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.

  5. 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

  6. kHz QPOs in Atoll and ZSources -- CCD ~1% Eddington Accretion ~Eddington Accretion Accretion rate direction

  7. QPO v.s. Accretion rate relation QPO frequency increases with the accretion rate SCO X-1, Van der Klis, 2006 kHz QPO profile; Mendez 2005

  8. KHz QPO Data，Atoll and Z sources Max：νmax=1329 Hz, van Straaten & van der klis 2000 min: ~200 Hz Distribution of kHz QPOs：QPO (Atoll) ~ QPO（Z） Zhang et al 2006 MNRAS;

  9. Table: kHz QPO, spin 8

  10. separation of twin kHz QPOs = const?Beat ? Strohmayer et al 1996; Miller, Lamb & Psaltis 1998;

  11. 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

  12. Parallel Line PhenomenonkHz QPO－luminosity relation Similarity/Homogeneous ? Among the different sources, same source at the different time

  13. kHz QPO v.s. Count rate kHz QPO corresponds to the position in CCD, to accretion rate Mdot; QPO ~ Mdot

  14. 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 difference Cir X-1 Zhang，et al. 2006，MNRAS Ratio

  15. 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

  16. Twin kHz QPO distribution

  17. Twin kHz QPO distribution; ratio

  18. 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

  19. Type-I X-ray Burst frequency 4U1728-34, (363 Hz) Strohmayer et al 1996 ApJ 362.5 Hz --- 363.9 Hz 17 burst sources, van der Klis 2006; Strohmayer and Bildsten 2006

  20. kHz QPO separation and spin relation 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 Slow rotator; separation/spin ~ 1 Fast rotator; separation/spin ~ 0.5 Linares & van der Klis 2007

  21. Spin Frequency Distribution Spin frequency: Max: 1122 Hz, Kaaret et al 2007 ApJ Min: 45 Hz Villarreal & Strohmayer2004 8+11+4=23 Spin sources Radio MSP：Max Spin=716 Hz Yin, Zhang, Zhao et al 2007 AA

  22. kHz QPO & spin relation

  23. Radio Pulsar:Magnetic field--period diagram (1) Why B-P ? B evolves ? Recycled ? (2) 716 Hz; ~10^8 G; why not 10^7 G ? PSR: 1750, X-ray NS: 200 magnetar: 5SGR+11AXP MSP: 175 BPSR: 130, recycled LMXB Van den Heuvel 2004, Science

  24. Low frequency QPO---kHz QPO 关系 Belloni et al 2002 ApJ 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)1.6-2.0

  25. Low-high frequency QPO relation in WD/NS/BH Similarity in WD/NS/BH ? Neutron stars Black holes ？ White dwarfs, Cvs Zhang et al 2007, PASP Warner 2006 MNARS; Warner & Woudt 2004 MNRAS; Mauche 2002 ApJ; Titarchuk & Wood 2002 ApJ + 27 CVs, 5 magnitude orders in QPO frequency

  26. 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) 3:2 mechanism: Abramowicz et al 2003; Li & Narayan 2003; Wang et al, 2003/06, MNRAS Frequency at ISCO Schwarzschild νk= (1/2π)(GM/r3)1/2 = (c/2πr) (Rs/2r)1/2 νk (ISCO) = 2.2 (kHz) (M/Mסּ) -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 Measuring BH spin by QPO: Cui et al. 1998; Zhang SN et al 1997

  27. High frequency pair QPO BH: ~3:2 --- NS: varied near 3:2

  28. Theoretical Models Miller, Lamb, Psaltis 1998; Strohmayer et al 1996 Lamb & Miller 2003 Beat Model for KHz QPO ν2 = νkepler ν1 = νkepler - νspin ∆ν = ν2 - ν1 = νspin …Constant

  29. Relativistic precession model by Stella & Vietri 1999 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

  30. Problems: • Vacuum • Circular orbit • Test particle • Predicted 2 M⊙ • 5. 30 sources, NS mass ~ 1.4 solar mass Theoretical model Stella and Vietrie, 1999, Precession model

  31. Alfven wave oscillation MODEL Zhang 2004 AA; Li & Zhang 2005 ApJ; Keplerian Orbital frequency MHD Alfven wave Oscillation in the orbit Some radius: Lai 1998 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

  32. Migliari, van der Klis, Fender, 2003 MNRAS Boutloukos，van der Klis 2006 ApJ Cir X-1

  33. 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

  34. Mass-Radius relations Measuring NS Mass & Radius by kHz QPO, gravitational redshift and apparent radius • 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

  35. Measuring NS Mass-Radius by kHz QPO, gravitational redshift and apparent radius Zhang, Yin, Kojim, Li XD, Xu RX, Zhang B, Kiziltan B 2007 MNRAS AqlX-1， EXO 0748-676 Samples CN1/CN2: normal neutron matter, CS1/CS2: quark star CPC: Bose-Einstein condensate of pions

  36. Fastest Pulsar XTE J1739-285 1122 Hz Mass & Radius Kaaret et al. 2007 Quark Star ? Xu, MNRAS, 2005 Xu, Qiao, Wang, CPL, 2003 Li et al 1999 PRL Sub-millisecond PSR : high mass, Burderi et al. 2003 Quark Star ?

  37. 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

  38. Estimating NS spin by spin-kHz QPO relation Spin frequency is less than the minimum upper-frequency of twin kHz QPOs

  39. Summary • 1. kHz QPOs NS/LMXBs • 2. BH/WD/NS • 3. Constraints M,R,B,spin

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