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Millisecond Pulsar and kHz QPOs of LMXB

Millisecond Pulsar and kHz QPOs of LMXB. Chengmin ZHANG, NAOC. Collaborators: J. Wang, L.M. Song, Y.J. Lei, F. Zhang. 2011 – NAOC. 1967, 1st PSR, spin P= 1.33 s 1982, 1st MSP, spin P=1.56 ms.

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Millisecond Pulsar and kHz QPOs of LMXB

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  1. Millisecond Pulsar and kHz QPOs of LMXB Chengmin ZHANG, NAOC Collaborators: J. Wang, L.M. Song, Y.J. Lei, F. Zhang 2011 – NAOC

  2. 1967, 1st PSR, spin P= 1.33 s 1982, 1st MSP, spin P=1.56 ms 1st PSR Discovery -- 1967; J Bell 1st MSP Discovery – 1982; D Backer (died 2010)

  3. SUPERNOVA EXPLOSION Chinese Astronomer recorded Crab Nebula in 1054 AD, Song Dynasty. It is a great glory of Chinese Ancient SUPERNOVA EXPLOSION – Crab Pulsar P=33 ms

  4. Pulsar - Rotating Neutron/Quark Star Pulsar Beacon

  5. Pulsar:Magnetic field--period (1) Two types： Normal PSR - Recycled MSP (2) 716 Hz; ~10^8 G; why not 10^7 G ? Crab Pulsar ATNF PSR data Catlog ： PSR/MSP PSR: 2000+ MSP: ~ 200; BPSR: ~140 LMXB 毫秒脉冲星 MSP

  6. Pulsar status (see Manchester Talk) • Pulsar： ~2000 (radio) + ~ 200 (X-ray) • PSR in Binary：~160, NS/WD/Planet • MSP: ~200， P<30ms，half/binary • Magnetic Field: 108 G - 1015 G;~1012 G • Spin period: 1.4 ms,10s, <P>=0.5s • Bands: Radio, Optical, X-ray First MSP in 1982 (670 Hz); Fastest MSP in 2006 (716 Hz) RXTE: 24 spins, Max=619 Hz, X-ray band

  7. Two kinds： Normal and Millisecond Pulsar ? • Bimodal distribution: Magnetic B and Spin-P • On ATNF PSR data, see Hobbs & Manchester 2005

  8. Differences between PSR & MSP • Spin up： P=1.4 ms – 30 ms； • Field low： B= 10**8 G • Stable： Pdot=10**（-20） s/s • Mass: >1.4 M⊙ ? • Binary: MSP (Li XD talk)

  9. Two kinds of PSRs Normal Pulsars: SN • associated with supernova • Spin Periods 0.033 – 8.5 s • Young ? T=P/Pdot < 107 yrs • Mostly non-binary 双星系中子星X 射线源 • MSPs old ? P/Pdot~109 yrs • Half binary； B-P low 低 • ‘recycled’ by accretion from binary Millisecond Pulsars (MSPs): 1982, Recycled, Srinivasan & Radhakrishnan (died 2011) 蟹状星云 • accretion spins up NS to MSP • Evidence of MSP in binary ?

  10. MSP & Binary - 1st Evidence Accreting X-ray MSP-SAX J1808.4-3658 (2.49 ms) Wijnands and van der Klis, 1998

  11. MSP & Binary - 2nd Evidence Double Pulsars PSRJ0737-3039A Parkes + GBT radio telescope DNS (double pulsar) : M=1.25 M⊙, M=1.34 M⊙ (Lyne et al. 2004) PSR 1913+16 : M=1.38 M⊙, M=1.4 M⊙ (see Manchester & Taylor book) P=22.7 ms， B~109 Gauss, 1.34 M⊙, ; MSP - Recycled P=2.8 s， B~1012 Gauss, 1.25 M⊙ PSR - Normal

  12. MSP is recycled in Accreting Binary, Proposed by Srinivasan & Radhakrishnan 1982 中子星 Neutron Star Radhakrishnan died 2011

  13. Theoretical model: Magnetic neutron star in Binary system For a strong NS magnetic field, disk is disrupted in inner parts, where most radiation is produced. NS spinning => X-ray pulsar Material is channeled along field lines and falls onto star at magnetic poles

  14. Millisecond Pulsar (MSP) formation Millisecond Pulsar Heavier ! Mean value <M> = 1,57 +/-0.2 M⊙ MSP spun-up by accretion: e.g. Alpar et al 1982 • Accreted matters spin-up neutron star (Wang & Zhang 2011) • Buried NS magnetic field（van den Heuvel 2004; Zhang & Kojima 2006）

  15. Magnetic Field of MSP X-rays Zhang & Kojima 2006, ~1012 GStrong magnetic field channels gas to magnetic poles Drag field lines to equator region

  16. Spherical Accretion-Bottom magnetic field 10**8 G ~108 G Magnetic field makes gas allover star surface No drag field lines Strong Magnetic field equator region: ~1014 G

  17. MSP – Bottom magnetic field10^7.5 G ? Bottom magnetic field is defined ; Alfven radius equalsStar radius, B proportional to accretion rate Initial field: 1012 G and 1013 G， Field decays with accreting mass， reaches the bottom value after accreting ~0.2 M⊙

  18. Magnetic field vs. Spin Period relation MSP spun-up in binary accretion Wang & Zhang 2011 Evolution track in B-P diagram ； Initially, spin-up and field little decays； Later, almost follow the spin-up line

  19. Magnetar (磁星) Bottom field: 10^7.5 G • If magnetar accretes 0.2 solar mass, the bottom field of 10^7.5 Gauss ! Bottom field is independent of initials Wang, Zhang,.. et al. 2011

  20. MSP mass：average ~1.6 M⊙ > 1.4 M⊙ • 63 average mass M=1.46+/-0.30 M⊙ • （Zhang & Wang et al 2011） (Lattimer & Prakash 2006)

  21. Statistics of 63 NS mass - Zhang et al 2011 • Histogram: Gaussian Distribution

  22. MSP Mass vs. spin period; Ps ~ 20 ms • MSP <mass> = 1.57+/-0.35 M⊙ • Slow NS <mass> = 1.37+/- 0.23 M⊙ • ~0.2 M⊙ accreted in Binary - MSP • added mass – spin relation: 0.43/(P/ms)^0.7 (M⊙)

  23. How about MSP mass < 1.4 M⊙ 1) initial mass is low, e.g. 1.2 M⊙; binding energy 2) AIC: Accretion Induced Collapse of White Dwarf find: < 20% BMPSs are involved AIC processes Dayal & Lilia (ANU) 2007

  24. （24/35） MSP： in Accreting BinaryX-ray Neutron Star kHz QPOs Twin QPO difference 300 Hz Typically: Twin KHz QPO Upper ν2 ~ 1000 (Hz) Lower ν1 ~ 700 (Hz) Power Density Spectra (PDS)

  25. NS/LMXBs kHz QPOs in Atoll and ZSources ~1% Eddington Accretion ~Eddington Accretion Accretion rate direction Z source Atoll source Hasinger & Van der Klis 1989; Hasinger 1990

  26. QPO bands Sco X-1 power • Low frequency QPOs (<100Hz) • hecto-hertz QPOs (100-200Hz) • kHz QPOs (~200-1200+Hz): • Lower and upper - twin peak QPOs frequency kHz QPO origin remains questionable, often expected associated to the orbital motion in the inner part of disc.

  27. RXTE: Spin and kHz QPO 1996—2011 kHz QPOs (35) 127 - 1200+ Hz, van der Klis 2008; max = 1329 Hz (4U 0614)?: max = 1224 Hz ?, Boutelier et al. (2010: 1860 Hz harmonic) Max kHz QPO > ISCO, NS surface > M – R Spin frequency ~ Burst oscillation (26); 95 - 619 Hz, Wijnands 2008 (45 Hz >552 Hz Galloway et al 2010) Max spin 619 Hz, MSP 716 Hz (Hessels et al. 2006). Max spin > GW: HBO Horizontal Branch Oscillation, ~ 15-70 Hz, EXOSAT 1985; RXTE 1996 NBO， ～ 5 Hz, see Yu & van der Klis 2001 BH QPO, ~ 40 - 450 Hz,McClintock & Remillard 2006

  28. Twin kHz QPO relation • separation is constant ? (beat) • Ratio is a constant : 3:2 ? difference Cir X-1 Non-linear relation: ν1 = ~700. (Hz)(ν2 /1000Hz)b b ~ 1.6 Atoll Source, e.g. 4U1728 b~ 1.8 Z Source, e.g. Sco X-1 BEAT ? Ratio const ? Ratio

  29. Twin kHz QPO distribution

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

  31. Spin Frequency – X-ray MSP by RXTE Spin frequency: Max: 619 Hz Min: 95 Hz 26 Spin sources 12 spin + kHz QPO sources spin

  32. fittings kHz QPO models： 1. relativistic precession 2. Alfven wave Cir X-1

  33. Theoretical Explanation for kHz QPOs Beat-frequency Model ? Relativity precession Model Alfven Wave Oscillation Model

  34. Summary: new Knowledge addedMSP in 30 years: Magnetism, Spin, Mass • Bottom field B = 10^7.5 G； • Atoll - 10^8 G ； Z - 10^9 G； • Spin P: 1.4 ms； Max spin 700 Hz ? • Mass : <M> = 1.4+0.2 M⊙ • kHz QPOs 1300 Hz >> sub-millisecond ? 0.5 ms

  35. Thanks To Dick Manchester for discussions On MSP Bottom Magnetic Field Prediction, it needs More MSPs. Dedicated to two MSP pioneers D. Backer & V. Radhakrishnan Both are right ! we cannot live as long as MSP

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