Neutron Star X-ray Sources: Quasi Periodic Oscillations (QPOs) in NS-NS and NS-BH binaries

1. What QPOs of NS tell us ?:Neutron Star X-ray Sources Chengmin Zhang National Astronomical Observatories Chinese Academy of Sciences, Beijing

2. 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

3. 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

4. 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 Mסּ, solar mass • Rs = 3 cm, for M= 1.0 Me, earth mass • Rs /R = 0.3 : Gravitational Strength

5. 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

6. 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

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

8. 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

9. Galaxy Black Hole Myths Stellar BH, 3-100 Mסּ Midmass BH, 100-1000 Mסּ 1,000,000 Solar Mass Solar System Milky Way’s Black Hole

10. QPO discovered by RXTE since 1996--2005review seevan 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

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

12. Typical Twin KHZ QPOs Separation ~300 Hz Typically: Twin KHz QPO Upper ν2 = 1000 (Hz) Lower ν1 = 700 (Hz) 18/25 sources Sco x-1, van der Klis et al 1997

13. Discovery of KHz QPO QPO=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

14. QPO v.s. Accretion rate relation QPO frequency increases with increasing of the accretion rate SCO X-1, Van der Klis, 2004 QPO

15. KHz QPO Data，Atoll 最大值：νmax=1329 Hz, van Straaten 2000 平均值：QPO（Atoll） 〉QPO（Z） 原因？

16. KHz QPO of Z Sources

17. Twin KHz QPO difference=con ？

18. 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？

19. Parallel Line PhenomenonkHz QPO－luminosity Similarity/Homogeneous ?

20. KHz QPO v.s. Count rate Same source， kHz QPO and CCD,1-1

21. 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

22. SAXJ 1808.4-3658 Twin kHz QPOs 700 Hz, 500 Hz Burst/spin: 401 Hz Burst frequency=spin frequency， 2003

23. IGR J00291+5934 598.88 Hz, Markwardt 2004, 6 MSP sources

24. SAX J1808.4-3658 • 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

25. Spectrum of Type-I X-ray Burst 4U1702-43, Strohmayer 1996 and Markwardt 1999, van der Klis 2004; Strohmayer and Bildsten 2003

26. 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

27. Burst Oscillations

28. On burst • Burst frequency increases ~2 Hz, drift. • Decreasing is discovered • From hot spot on neutron star • kHz QPO relation

29. kHz QPO separation=195 Hz/(spin=401 Hz) Burst and Spin frequency are same X X X 11 burst sources, Muno et al 2004 6 X-ray pulsars, Wijnands 2004; Chakrabarty 2004

30. Burst Oscillation Frequency

31. 11 bursts， Muno 2004

32. 25 kHz QPO

33. Low frequency QPO---kHz QPO Psaltis et al 1999, Belloni et al 2002 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)1.9-2.0

34. Low-high frequency QPO Neutron stars Black holes ？ White dwarfs, Cvs Warner & Woudt 2004; Mauche 2002 + 27 CVs, 5 magnitude orders in QPOs

35. BH High Frequency QPO (BH) 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 • 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/Mסּ) -1 Magnetosphere-disk instability noise: mechanism：？ Miller, et al 1998

36. 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

37. QPO and Break Frequency

38. 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: • Keplerian Frequency • Difference to Spin frequency

39. QPO Models Miller, Lamb & Psaltis ’ Model Beat model developed from Alpar & Shaham 1985 Nature Abramovicz and cooperators ’ Model non-linear resonance between modes of accretion disk oscillations HFQPO: Stella black hole QPO, 3:2 relation 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 Relativistic precession model by Stella & Vietri

40. Theoretical Models 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-3/2is 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

41. Einstein’s Prediction: Perihelion Motion of Orbit Perihelion precession of Mercury orbit = 43” /century, near NS, ~10^16 times large

42. N. Copernicus Neutron Star Orbit 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

43. Theoretical model • Problems: • Vacuum • Circular orbit • Test particle • Predicted 2 M⊙ • 30源，　中子星质量≈1。3太阳质量 Stella and Vietrie, 1999, Precession model

44. Lense-Thirring Precession W. Cui, S.N. Zhang, W. Chen, 1997 (MIT/NASA)，　黑洞，进动？ L.Stella, M.Vietri, 1997 (Rome) 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 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

45. Lense-Thirring Precession Frequency Rs = 5 km, R = 15 -20 km, Ω = 300 Hz ΩLS = 30 Hz Lense-Thirring Frequency estimation ΩLS --- parameter * (Rs/R)2Ω

46. Problems ? • Vacuum ? • Kerr rotation ? • Magnetic Field ? • Inner Accretion Disk ? Similarity: common parameter: accretion rate/radius

47. 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 = 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

48. Migliari, van der Klis, Fender, 2003 Difference of kHz QPOs Lower kHz QPOs