QPOs of LMXBs kHz QPO, millisecond pulsar 张承民 尹红星 National Astronomical Observatories Chinese Academy of Sciences

Nobel Prize for Pulsar: Rotating Neutron Star 脉冲星发现40年: 1967-2007 1974, A. Hewish, Cambridge U, First Pulsar 1993, R. Hulse, J.A. Taylor, Princeton U, Binary Pulsar Nobel Prize for Pulsar: Rotating Neutron Star

Pulsar Froms: SUPERNOVA EXPLOSION Chinese Astronomer recorded Crab Nebula in 1054 AD, Song Dynasty. It is a great glory of our forefather SUPERNOVA EXPLOSION

Neutron Star 10km, solar mass

Neutron Star (NS) in Low Mass X-ray Binary OUTLINE OF TALK Neutron Star (NS) in Low Mass X-ray Binary KHz Quasi Periodic Oscillation (QPO) Millisecond accreting-powered X-ray Pulsar Type-I X-ray Burst Oscillation Other QPOs of NS & BH Theoretical Mechanisms---QPOs Further Expectations

RXTE INTRODUCTION Rossi X-ray Timing Explorer (RXTE): NASA Named after the astronomer, Bruno Rossi, died in 1993 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 动力学时间尺度， 强引力场 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 Mסּ, 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 Target A/Periodic, transient, and burst in X-ray emission Characteristics of X-ray binaries, masses, orbital, matter exchange Property: nuclear matter composition, M-R relation, neutron/strange star ? magnetic field Behavior of matter into/onto a black hole/NS Strong Gravity of GR near a black hole Mechanisms causing X-ray emission Strong Gravity, GR, Precession, LS M,R,Spin, EOS, Thermonuclear

Binary X-ray Sources Normal Star + Compact Star 10,000 lyr, 300 - 450Hz QPOs, Micro-quasar, Radio jet, 7 solar mass/optical

QPO frequencies discovered by RXTE 1996—2007， reviewed by van der Klis 2006 FBO/NBO, ~5-20 Hz, Yu et al 2001-06 HBO, ~15-70 Hz Hundred, ~100 Hz kHz, ~1000-Hz(27) Burst oscillation, ~400 Hz(16) Spin frequency, ~400 Hz (7) Low, high QPO, ~0.1 Hz Others. QPO: Quasi Periodic Oscillation 准周期振荡

Typical twin KHZ QPOs （21/27） Separation ~300 Hz Typically: Twin KHz QPO Upper ν2 = 1000 (Hz) Lower ν1 = 700 (Hz) 21/27 sources； ~290 对 Sco x-1, van der Klis 2006

Atoll and Z Sources --- LMXB CCD ~1% Eddington Accretion ~Eddington Accretion Accretion rate direction

QPO v.s. Accretion rate relation QPO frequency increases with the accretion rate SCO X-1, Van der Klis, 2006 QPO轮廓随吸积率变宽/低，消失 Mendez 2005

KHz QPO Data，Atoll sources 最大值Max：νmax=1329 Hz, van Straaten 2000 min: ~200 Hz 平均值/Distribution of kHz QPOs：QPO (Atoll) ~ QPO（Z） Zhang et al 2006 MNRAS; 原因？

kHz QPOs of Z Sources

Difference of twin kHz QPOs = const Difference of twin kHz QPOs = const? Beat model by Miller, Lamb & Psaltis 1998; Strohmayer etal 1997

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 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 B ~ Mdot, proportional Zhang & Kojim, 2006, MNRAS

kHz QPO Distribution : Twin frequency difference/ratio is not a constant difference Cir X-1 ν1 = ~700. (Hz)(ν2 /1000Hz)b b ~ 1.6 Atoll Source 4U1728 b ~ 1.8 Z Source Sco X-1 Ratio Zhang，Yin，Zhao，et al. 2006，MNRAS

Twin kHz QPO distribution

Twin kHz QPO distribution

Spin Frequency：SAX J1808.4-3658 Millisecond Radio Pulsar, X-ray MSP Bhattacharya and van den Heuvel, 1991 Millisecond Radio Pulsar, X-ray MSP Rule : burst vs. pulsation is exclusive ? Sax J1808.4-3658: 401 Hz (2.49 ms) Binary Parameters of SAX J1804.5-3658 Orbital period: 2 hr Orbital radius: 63 lms Mass function: 3.8× 10-5 Mסּ Magnetosphere radius: 30 km Magnetic field : (2-6)×108 Gauss Chakrabaty and Morgan 1998 Nature Wijnands and van der Klis 1998, Nature

Accreting X-ray millisecond pulsar --- SAX J1808.4-3658 (7 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

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

Accretion-powered X-ray PSR, (7),185-599 Hz Radio Millisecond PSR is recycled，Alpar， et al 1982 Nature IGR J00291+5934 598.88 Hz, Markwardt 2004, 7 MSP sources

差频和自旋关系 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, twin kHz QPO, 191 Hz, Linares , van der Klis, Wijnands 2005 ApJ； F. Zhang，J Qu，C Zhang，W.Chen, T.P. Li, 2006 ApJ

Type-I X-ray Burst Type-I X-ray Burst, Lewin et al 1995/Bildsten 1998 Thermonuclear reaction on accreting NS surface (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

Spectrum of Type-I X-ray Burst frequency 4U1702-43, Strohmayer 1996 and Markwardt 1999, van der Klis 2006; Strohmayer and Bildsten 2003

Burst Oscillations

On the burst frequency Burst frequency increases ~ 2 Hz, drift. Decreasing is discovered From hot spot on neutron star kHz QPO separation ~ burst/spin frequency

Spin Frequency Distribution Spin 1122 Hz, Kaaret et al 2006 7+11+4=22 Spin sources 45-1122 Hz Radio MSP：716 Hz Yin et al 2007 AA

kHz QPO & spin relation

Burst and Spin frequency Burst and Spin frequency are similar，401 Hz X 17 burst sources, Muno et al 2004；van der Klis 2006 X-ray pulsars, Wijnands 2004; Chakrabarty 2004 Spin sources=7+(17-2)=22

burst sources， Muno 2004

3rd kHz QPO ? 25 kHz QPO 源

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

Low-high frequency QPO 关系 Neutron stars Black holes ？ White dwarfs, Cvs Zhang et al 2007, PASP Warner 2006 MNARS; Warner & Woudt 2004 MNRAS; Mauche 2002 ApJ + 27 CVs, 5 magnitude orders in QPOs

Black Hole High Frequency QPOs HFQPO: 40-450 (Hz) Constant (stable) in frequency (M/S) Luminosity Pair frequency relation 3:2 Frequency-Mass relation: 1/M 7 BH sources, van der Klis 2006 Jets like Galactic BHs ~10Ms (McClintock & Remillard 2003;2006) Different from those of NS’s 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 2006 νk= (1/2π)(GM/r3)1/2 = (c/2πr) (Rs/2r)1/2 νk (ISCO) = 2.2 (kHz) (M/Mסּ) -1 Magnetosphere-disk instability noise: mechanism：？Abramowicz et al 2003 AA; MNRAS ; Wang et al, 2003/06, MNRAS Miller, et al 1998 Cui et al. 1998; Zhang SN et al 1997, APJ

BH QPO - spectral indices, flux, color Zhang GB, et al APJ 2007, swift 1753

~ High Frequency QPOs in Black Hole LMXBs Name BH Mass(Msun) HF QPO (Hz) References GRO J1655-40 ~6 300,450 1,2 XTE J1550-564 ~10 184,276 188,249~276 3,4 5 GRS 1915+105 ~14 41,67 113,165 328 165 6 7(?) 8(?) 9 H 1743-322 ~ 160,240 166,242 10 11 XTE J1859+226 ~9 150~200 12 4U 1630-472 184 100~300 8 13 XTE J1650-500 110~270 14

STELLAR Black Hole—Micro-quasar GRS 1915+105 165 Hz, 14 solar mass 10,000 lyr, 300Hz:450Hz=2:3 Microquasar, Radio jet 6 solar mass/optical

QPO and Break Frequency

Theoretical Consideration Accretion Flow around NS/BH Hard surface ? Strong Gravity: Schwarzschild Radius: Rs=2GM/c2 Innermost Stable Circular Orbit RIsco= 3Rs Strong Magnetic: 108-9 Gauss (Atoll, Z-sources) Beat Model: Kepler Frequency Difference to Spin frequency

QPO Models Miller, Lamb & Psaltis ’ Beat Model, developed from Alpar & Shaham 1985 Nature ; Lamb et al 1985 Nature Abramovicz et al ： Model non-linear resonance between modes of accretion disk oscillations HFQPO: Stellar black hole QPO, 3:2 relation Wang et al 2003/06 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 0.08 ratio Relativistic precession model by Stella & Vietri 1999

Theoretical Models Beat Model (HBO), νHBO = νkepler - νspin What modulate X-ray Flux ? Why quasi periodic, not periodic ? Parameters: M/R/Spin, B?--Z/Atoll 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

X-射线源准周期振荡QPO RXTE：罗西X-射线卫星1996年发现 kHz QPO：积累近十年观测结果 中子星 kHz QPO，成对出现 黑洞 QPO，100Hz，3：2 HBO，15-70Hz，互相关联 理论解释： 拍模型 重要意义： 爱因斯坦理论，强引力场 黑洞的视界，最小稳定轨道 中子星质量半径，核物态 中子星磁场演化/结构 机制研究： 阿尔文波振荡模型 间隔常数？NO！ 拍模型预言:间隔常数=自旋 Alpar和Shaham，1985，Nature。 Lamb et al 1985， Nature。 Miller et al 1998， ApJ。

进动模型：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 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

Theoretical model 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

Lense-Thirring Precession BH precession ？ L.Stella, M.Vietri, 1998 Cui et al 1998; Zhang SN et al. 1997 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

Alfven wave oscillation MODEL Zhang 2004 AA; Li & Zhang 2005 ApJ; Zhang et al 2007 AN Keplerian Orbital frequency resonance 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

Migliari, van der Klis, Fender, 2003 MNRAS Boutloukos，van der Klis 2006 ApJ

Neutron Star Mass-Radius Zhang et al 2007 MNRAS AqlX-1， EXO 0748-676 Samples CN1/CN2: normal neutron matter, CS1/CS2: Strange matter CPC: core becomes Bose-Einstein condensate of pions

Fastest Pulsar XTE J1739-285 1122 Hz by Kaaret et al. 2006 Radio pulsar 716 Hz , Hessels et al. 2006 XTE 1739-285, 1122 Hz kHz QPO: 700-850 Hz Quark Star ?

11-year RXTE - where are we now ? 观测，进展较大，QPO关系明确 理论，进展缓慢，很多模型? 物理实验室 强引力广义相对论验证 中子星结构检验核物理 开普勒运动 近星点进动 LT 进动/引力磁 引力红移 黑洞/Kerr 时空 引力波 光线弯曲 质量 半径 核物态（中子/夸克） 磁场 旋转 吸积流动 QPO机制？ 数据处理？ 新物理？

Discussion and Problems Now, we are standing on the edge of new discovery ? THANKS

Have no X-ray pulsation & type-II X-ray bursts A comparison between high-frequency QPOs in BH LMXBs and those in NS LMXBs QPOs in BH LMXBs QPOs in NS LMXBs Hard spectral Relatively soft Break Have no X-ray pulsation & type-II X-ray bursts Have X-ray pulsation &type-II X-ray bursts ~3:2 ratio Not constant Relatively stable Systemically change with Luminosity 1/M scaling ? Spin? No observational evidence. Spin! X-ray pulsation & type-II X-ray bursts