Recent Progress about kHz QPO and Spin in LMXB and their implications C.M. Zhang, H.X. Yin, Y. Yan, L.M. Song, F. Zhang National Astronomical Observatories, Beijing High Energy Physics Institute, Beijing Shandong University, Weihai High energy astrophysics Workshop, Shanghai, April 25-28, 2008

OUTLINE OF TALK QPO in LMXB – kHz QPOs Spins of accreting millisecond X-ray Pulsar Spin and kHz QPO relations BH QPOs, Miscs QPO, Mechanisms Implications and Conclusions

Spin and kHz QPO by RXTE 1996—2008 RXTE: NASA: Swank 1995 kHz QPOs (31) van der Klis 2006; Belloni, Mendez & Homan 2005/2007 max=1329 Hz: van Straaten, Ford, van der Klis, Mendez, Kaaret, 2000 Spin frequency - Burst oscillation (24); ? Hz, Wijnands 2005; Strohmayer & Bildsten 2006; Kaaret 2007 ?; Lamb & Boutloukos 2007; Yin, Zhang, Zhao et al 2007 Max=619 Hz ? Radio MSP 716 Hz (Hessels et al. 2006) HBO, ~15-70 Hz, van der Klis 2006 NBO, ~5-20 Hz, van der Klis 2006; Yu & van der Klis 2003 BH QPO, ~100 Hz, McClintock & Remillard 2006

kHz QPOs in Atoll and Z Sources -- CCD Accretion rate direction ~Eddington Accretion ~1% Eddington Accretion

Typical twin kHz QPOs （ 22/31 ） Typically: Twin KHz QPO Upper ν 2 ~ 1000 (Hz) Lower ν 1 ~ 700 (Hz) Twin 22/31 sources ； ~ 310

QPO v.s. Accretion rate relation SCO X-1, Van der Klis, 2006 QPO frequency increases with the accretion rate kHz QPO profile; e.g. Mendez 2005 Barret, Olive, Miller 2007

Accreting X-ray millisecond pulsar --- SAX J (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 U , Hz Hz, ~1Hz frequency drift

Table: sources with twin kHz QPO/spin 8 No Spin found in Z-sources ! Why ? Spins see: Muno 2001, Chakrabarty 2004; Wijnands 2005; Strohmayer & Bildsten 2006; Belloni, Mendez & Homan 2005/2007; Lamb & Boutlokos 2007; Yin, Zhang, Zhao et al 2007

separation of twin kHz QPOs = const? Simple beat model ?: Alpar & Shaham 1985; Strohmayer et al 1996; Miller, Lamb & Psaltis 1998; Improved beat model needed, e.g. Lamb 2001; Lamb & Miller 2003

Twin kHz QPO relation Non-linear relation by Psaltis et al. 1998; Zhang et al. 2006a for 290 pairs ν 1 = ~700. (Hz)(ν 2 /1000Hz) b b ~ 1.6 Atoll Source, e.g. 4U1728 b ~ 1.8 Z Source, e.g. Sco X-1 Cir X-1 difference Ratio 1. separation is constant ? (simple beat) 2. Linear relation: ν2 = A ν1 +B 3.Ratio is a constant : 3:2 ? Abramowicz, et al Cir X-1 : Boutloukos, van der Klis, Altamirano, Klein-Wolt, Wijnands,,Jonker, Fender: 2006

AMXP: special cases of 1.5 shift SAXJ ; XTE J SAXJ : Wijnands & van der Klis 1998; Chakrabarty, Morgan, Muno, Galloway,.Wijnands, Klis, Markwardt 2003 XTE , Linares et al 2006; Zhang et al 2006b

SAXJ ， Twin kHz QPOs ： ~700 Hz, ~ 500 Hz ； Burst/spin: 401 Hz Wijnands, van der Klis, 1998; Wijnands, van der Klis, Homan, Chakrabarty, Markwardt, Morgan, 2003 XTE J , twin kHz QPO sep ~ 200 Hz, spin=191 Hz, Linares, van der Klis, Altamilano, Markwardt 2005 ; Zhang et al, 2006b kHz QPO separation and spin relation Slow rotator (XTE 1807); separation/spin ~ 1 Fast rotator (SAX 1808); separation/spin ~ 0.5 Linares, van der Klis, Wijnands 2007 Lamb & Boutloukos 2007

Table 1. TWELVE sources with the twin kHz QPOs and spin frequencies. Millisecond pulsars sep spin ratio XTE J SAX J Atoll sources 4U U U U KS U IGR J SAX J U Aql X data: van der Klis 2006, Belloni, Mendez & Homan 2005, 2007, Zhang et al. 2006a, Yin, Zhang et al. 2007

Ratio of kHz QPO separation to Spin for 12 sources ratio

Spin Frequency Distribution 24 Spin sources Yin, Zhang, Zhao et al spin + kHz QPO sources Spin frequency: Max: 1122 Hz, Kaaret et al 2007 ? Min: 45 Hz Villarreal & Strohmayer 2004 spin

Lower of twin kHz QPO frequency > 1.1 spin frequency

SAJ 1808, XTE J 1807; 1.5 shift

kHz QPO & spin relation

Twin kHz QPO distribution

Twin kHz QPO distribution; ratio~1.5=3:2 Ave.

Magnetic filed – LMXB, Atoll & Z source Spin > corotation radius ~40 km > ~10 8 G Atoll, Z source has spin detected ? kHz QPO distribution for Atoll/Z > similar magnetosphere B ~ 10 9 G (Mdot-Ed) 1/2 Z source has a stronger field than Atoll’s B ~ 10 9 G (Z) ; B ~ 10 8 G (Atoll) e.g. Zhang & Kojima 2006; Burderi et al 1996, 1997; Konar & Bhatcharya 2003 Psaltis, Lamb & Miller 1998; Lamb & Yu 2006; Hasinger & Kils 1986

Maximum spin: gravitational wave ? NS break up frequency > 1000 Hz Max ~ 700 Hz (1122 Hz ?) GW ?

Radio Pulsar: Magnetic field--period diagram Radio PSR: magnetar: 5SGR+11AXP MSP: ~200 BPSR: 130, recycled (2) 716 Hz; ~10^8 G; why not 10^7 G ? (1) Why B-P ? B evolves ? Recycled ? LMXB

Low frequency QPO---kHz QPO relation Belloni, Psaltis & Klis 2002 Empirical Relation ν HBO = 50. (Hz)(ν 2 /1000Hz) ν HBO = 42. (Hz) (ν 1 /500Hz) ν qpo = 10. (Hz) (ν 1 /500Hz) Low frequency QPO< 100 Hz FBO/NBO = 6-20 (Hz) HBO = (Hz) ν 1 = 700. (Hz)(ν 2 /1000Hz)

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

Parallel Line Phenomenon kHz QPO － luminosity relation Similarity/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

Black Hole High Frequency QPOs HFQPO: (Hz) Frequency stable with Luminosity Twin QPO relation 3:2 (4 sources) Frequency-Mass relation: 1/M Jets like Galactic BHs ~10 Msun Different from: NS/LMXB kHz QPOs (McClintock & Remillard 2003;2006) Frequency at ISCO Schwarzschild ν k = (1/2π)(GM/r 3 ) 1/2 = (c/2πr) (R s /2r) 1/2 ν k ( ISCO ) = 2.2 (kHz) (M/Mסּ) -1 GRO J , XTE J XTE , 4U XTE , H GRS , 7 microquasars van der Klis :2 mechanism: Abramowicz et al 2003 Wang DX et al. 2003; 2006 Measuring BH spin by QPO, (Kerr SP): Cui et al. 1998; Zhang SN et al 1997 TorokTorok, Abramowicz, 2006 Abramowicz

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

Microquasar Jet formation condition Massi & Bernado 2008, P(mag)<P(flow) 1) Alfven radius ~ NS radius, Z sources: Cir X-1, Sco X-1 twin kHz QPOs and jets, no spins detected 2) Alfven radius ~ ISCO 7 microquasars: jets, 3:2 twin QPO ratios ( Hz)

Theoretical Models Beat Model for KHz QPO ν 2 = ν kepler ν 1 = ν kepler - ν spin ∆ν = ν 2 - ν 1 = ν spin Alpar & Shaham 1985; Miller, Lamb, Psaltis 1998; Strohmayer et al 1996; Lamb & Miller 2001; 2003 …Constant

Einstein’s General Relativity: Perihelion precession Precession Model for KHz QPO, ν 2 = ν kepler ν 1 = ν precession = ν 2 [1 – (1 – 3Rs/r) 1/2 ] ∆ν = ν 2 - ν 1 is not constant ISCO Saturation Relativistic precession model by Stella & Vietri 1999

Theoretical model Stella and Vietrie, 1999, Precession model Problems: = 3 M ⊙. For SAJ NS ~ 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 ν 2 = 1850 (Hz) A X 3/2 ν 1 = ν 2 X (1- (1-X) 1/2 ) 1/2 A=m 1/2 /R 6 3/2; X=R/r, m: Ns mass in solar mass R 6 is NS radius in 10^6 cm

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/R 3 relation known by model for twin kHz QPOs SAXJ : M/R 3 by Burderi & King 1998

Mass-Radius relations Apparent Radius: R ∞ =R/(1-R s /R) 1/2 Haensel 2001 Gravitational redshift: z=(1-R s /R) -1/2 -1 Cottam et al 2003, z=0.35 Mass density: M/R 3 (by kHz QPOs) Zhang E , Aql X-1 and EXO 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, et al MNRAS AqlX-1 ， EXO Samples

Estimating Magnetic filed - LMXB Spin > corotation radius ~40 km > ~10 8 G Spin variation: torque > ~10 8 G Wijnands & van der Klis 1998; Burderi, de Salvo ; kHz QPO distribution for Atoll/Z > similar magnetosphere ~10 8 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

Conclusions Spin - kHz QPO relation (a) slow/fast rotator ½-1.0 ? (b) occur kHz QPO – Spin ? Predicts Z spin (c) Av. kHz QPO – spin relation Constraints on kHz QPOs Model twin kHz QPOs – nonlinear relation NS magnetic implications: Z/Atoll Low-high QPO ratio = similarity in NS/BH/WD; GR is a role ? Thanks many friends here for thoughtful discussions, which arouses my interest of understanding spins and kHz QPOs.

QPO Frequency vs. Flux MagnifiedFull range

Fastest Pulsar XTE J Hz Mass & Radius Kaaret et al Quark Star ? Xu, MNRAS, 2005 Xu, Qiao, Wang, CPL, 2003 Li et al 1999 PRL Cheng et al. 1998, Sci Sub-millisecond PSR : high mass, Burderi et al. 2003