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Mass & Radius of Compact Objects F astest pulsar and its stellar EOS

Mass & Radius of Compact Objects F astest pulsar and its stellar EOS. CHENGMIN ZHANG National Astronomical Observatories Chinese Academy of Sciences, Beijing. Significance of Measuring Star mass and radius – Neutron or Quark.

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Mass & Radius of Compact Objects F astest pulsar and its stellar EOS

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  1. Mass & Radius of Compact Objects Fastest pulsar and its stellar EOS CHENGMIN ZHANG National Astronomical Observatories Chinese Academy of Sciences, Beijing

  2. Significance of Measuring Star mass and radius – Neutron or Quark • we can measure physical parameters of star,mass and radius, probethe nuclear physics and understand EOS • we can study the strong gravitational field, where Einstein GR might be tested

  3. Neutron Stars？ • 40+ NSs, M=1.4 M⊙ , R= 10 -30 km ? • Radio pulsars, X-ray NS, binary systems (MT77) (Stairs 2004) (Lattimer & Prakash 2004，2006)

  4. NS mass determined in Binary system MSP, PSR J0751+1807, M = 2.1(2) M⊙ ？； Nice et al. 2004 2A1822-371, M>0.97+-0.24 M⊙; Jonker et al 2003 ； （1.74 M⊙ ，2008） DNS: M=1.25M⊙, M=1.34 M⊙ , double pulsars (2004)

  5. PSR J0737-3039A/B Post-Keplerian Effects R: Mass ratio w: periastron advance g: gravitational redshift r & s: Shapiro delay Pb: orbit decay . . • Six measured parameters – only two independent • Fully consistent with general relativity (0.1%) A: 1.34 M⊙ ; B: 1.25 M⊙ (Kramer et al. 2005)

  6. No direct measure of radius ! Measured M-R relations • Apparent Radius: R∞=R/(1-Rs/R)1/2 • Gravitational redshift: z=(1-Rs/R)-1/2 -1 • Mass density: M/R3 • g=~M/R2 • 1E1207.4-5209, Aql X-1 and EXO 0748-676 Rs=2GM: Schwarzschild radius

  7. For perfect Black Body: Observed Total Flux: F=4 R∞2SB T∞4/d2 Photon Spectra: Key to Measuring Radius RX J1856.5-3754 (Fred Walter’s Star !) Spectra are seldom black body: Neutron Stars have atmospheres ! Composition and Magnetic field shape the spectra. Other issues: Is the surface temperature and radiation isotropic ?

  8. The Mass-Radius Exotic Stars Gravitational Red-shift: observation of spectral lines (Cottam, et al 2002). QPOs indicate ISCO

  9. Typical twin kHz QPOs （24/35） Z: Sco x-1, van der Klis et al 2006 Separation ~300 Hz ~Spin ? Typically: Twin KHz QPO Upper ν2 ~ 1000 (Hz) Lower ν1 ~ 700 (Hz) Twin 21/27 sources； ~290

  10. Constrain star M_R 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

  11. kHz QPOs from LMXBs: R-ISCO Sco X-1 Excluded kHz QPO maximum frequency constrains NS equations of state

  12. Striking case of RX J1856.5-3754Truempet et al. 2004; Burwitz et al. 2003 This is an isolated neutron star (INS), valuable because: We can see the surface There are minimal magnetospheric complications If we can see the surface, we can determine the angular diameter The parallax gives the radius R spectral lines give the surface composition, T, and g R and g give M M/R constrains the EOS of matter at nuclear densities Gravitational light bending effect: R/M <~10 km/M⊙ ; Ransom et al 2004  Apparent radius R∞=16.5 km (d/117pc), Truempet 2005  True radius 14 km (1.4 M⊙), stiff EOS, rule out quark star (Pons et al, 2002; Walter & Lattimer, 2002 )

  13. Relativistic precession model by Stella & Vietri 1999 M inferred from twin kHz QPOs Max frequency – ISCO 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

  14. M/R3 inferred from twin kHz QPOs Max frequency – Star Surface R Kepler frequency νk = (GM/4π2r3)0.5 νk = 1850 (Hz) A X3/2 ν1 = ν2X (1- (1-X)1/2)1/2 A2=m/R63; X=R/r, m=M/M⊙ , R6 = R/106 cm Zhang 2004, AA; Li & Zhang 2005 Maximum kHz QPO occurs at R or ISCO=3Rs A> νk /1850 (Hz) and m < 2200 (Hz)/ νk Miller et al 1998

  15. Constraining M – R by R∞ and z • 1E 1207.4-5209: • R∞=4.6 km, Bignami et al 2004 • z=0.12-0.23; Sanwal et al 2002 ? • R 6 =R∞6 /(1+z) • M=f(z)R∞6 /(1+z) • F(z)=(20/3)z(1+z/2)/(1+z)2

  16. Constraining M – R by R∞ and A~M/R3 • Aql X-1 : • 9 km<R∞<18 km, Rutledge et al 2001 • one kHz QPO: 1040 Hz; van der Klis 2006 • R6 =R∞6 /(1+0.15(A/0.7)2 R2∞6 )0.5 • m=AR36

  17. Constraining M – R by A=M/R^3 and z • EXo 0728-676: • z=0.35; Cottam et al 2002 • One kHz QPO 695 Hz; Homan & van der Klis 2000 • R6 =1.43f0.5(z)(0.7/A) • m=1.43f1.5(z)(0.7/A) • f(z)=(20/3)z(1+z/2)/(1+z)2

  18. 1E1207.4-5209, Apparent radius, gravitational redshift QUARK STAR ?

  19. Aql X-1 , Apparent radius=14 km, single kHz QPO

  20. EXO 0748-676 , gravitational redshift, kHz QPO

  21. Measuring NS Mass & Radius by kHz QPO, gravitational redshift and apparent radius 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

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

  23. How about the Sub-millisecond Pulsar XTE J1739285, spin=1122 Hz • Spin=1122 Hz • Radio PSR, 716 Hz Quark Star, FAST target Cheng et al 1998, Li 1999; Xu, Qiao, Wang 2002 Horvath 2002 Harko, 2005 Zhang, ..Li, 2007 More……

  24. ISCO condition, m ≤ 2200 (Hz)/spin • Keplerian at R, crust split

  25. Max kHz QPO 1330 Hz Zhang et al. 2006 difference Cir X-1 Ratio

  26. Spin Frequency - LMXBs Spin frequency: Max: 1122 Hz, Kaaret et al 2007 Min: 45 Hz Villarreal & Strohmayer2004 23 Spin sources, Av ~ 400 Hz Radio MSP：Max Spin=716 Hz

  27. kHz QPO & spin relation

  28. List of the Low-Mass X-Ray Binaries Simultaneously Detected Twin Kilohertz QPO and Spin Frequencies • QPO (Hz) spin Dnu/spin • 4U 160852 . . . . . . . . 802–1099 619 1.3 • 4U 163653 . . . . . . . . 971–1192 581 1.7 • 4U 170243 . . . . . . . . . 1055 330 3.2 • 4U 172834 . . . . . . . . . 582–1183 363 1.6 • KS 1731260 . . . . . . . . 1169 524 2.2 • 4U 191505 . . . . . . . . . 514–1055 270 1.9 • XTE J1807294 . . . . . . 353–587 191 1.8 • SAX J1808.43658 . . . .694 401 1.7 • QPO data, Belloni et al. (2005), van der Klis (2006)

  29. Fastest Pulsar XTE J1739-285 spin = 1122 Hz M – R Kaaret et al. 2007 Quark Star = sub-MSP ? Quark Star ?

  30. Summary • Conclusions: M-R relations • Mass, measured • Radius, not measured directly • Spectra, MR relation • Redshift, M/R • kHz QPO, M/R^3, constraints • Others… Ozel 2006 Not clear: fuzzy in M-R EOS: Quark or Neutron ? THANKS

  31. Saturation of kHz QPO frequency ?ISCO – Star Mass 4U1820-30, NASA Swank 2004; Miller 2004 BH/ISCO: 3 Schwarzschild radius Innermost stable circular orbit NS/Surface: star radius, hard surface

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