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

3. 1st PSR Discovery -- 1967; J Bell 1st MSP Discovery – 1982; D Backer (died 2010) 1967, 1st PSR, spin P= 1.33 s 1982, 1st MSP, spin P=1.56 ms

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

5. Pulsar - Rotating Neutron/Quark Star Pulsar Beacon

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

7. 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: 10 8 G - 10 15 G; ~10 12 G Spin period: 1.4 ms,10s, =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

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

9. 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)

10. Two kinds of PSRs MSPs old ? P/Pdot~10 9 yrs Half binary ； B-P low 低 ‘recycled’ by accretion from binary accretion spins up NS to MSP Evidence of MSP in binary ? Normal Pulsars: SN associated with supernova Spin Periods 0.033 – 8.5 s Young ? T=P/Pdot < 10 7 yrs Mostly non-binary Millisecond Pulsars (MSPs): 1982, Recycled, Srinivasan & Radhakrishnan (died 2011) 蟹状星云 双星系中子星 X 射线源

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

12. Double Pulsars PSRJ0737-3039A Parkes + GBT radio telescope P=22.7 ms ， B~10 9 Gauss, 1.34 M ⊙, ; MSP - Recycled P=2.8 s ， B~10 12 Gauss, 1.25 M ⊙ PSR - Normal 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) MSP & Binary - 2nd Evidence

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

14. 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

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

16. Zhang & Kojima 2006, ~10 12 G Strong magnetic field channels gas to magnetic poles X-rays Drag field lines to equator region Magnetic Field of MSP

17. ~10 8 G Magnetic field makes gas allover star surface No drag field lines Spherical Accretion-Bottom magnetic field 10**8 G Strong Magnetic field equator region: ~10 14 G

18. MSP – Bottom magnetic field 10^7.5 G ? Initial field: 10 12 G and 10 13 G ， Field decays with accreting mass ， reaches the bottom value after accreting ~0.2 M ⊙ Bottom magnetic field is defined ; Alfven radius equals Star radius, B proportional to accretion rate

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

20. 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

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

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

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

24. 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

25. （ 24/35 ） Typically: Twin KHz QPO Upper ν 2 ~ 1000 (Hz) Lower ν 1 ~ 700 (Hz) Twin QPO difference 300 Hz Power Density Spectra (PDS) MSP ： in Accreting Binary X-ray Neutron Star kHz QPOs

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

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

28. 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

29. Twin kHz QPO relation Non-linear relation: 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 ? (beat) 2.Ratio is a constant : 3:2 ? BEAT ? Ratio const ?

30. Twin kHz QPO distribution

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

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

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

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

35. Summary : new Knowledge added MSP 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 : = 1.4+0.2 M ⊙ kHz QPOs 1300 Hz >> sub-millisecond ? 0.5 ms

36. 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