Millisecond Pulsar and kHz QPOs of LMXBChengmin ZHANG, NAOC 2011 NAOCCollaborators: J. Wang, L.M. Song, Y.J. Lei, F. Zhang

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

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

Pulsar - Rotating Neutron/Quark Star Pulsar Beacon

Pulsar: Magnetic field--period ATNF PSR data Catlog PSR/MSPPSR: 2000+MSP: ~ 200; BPSR: ~140(2) 716 Hz; ~10^8 G; why not 10^7 G ?(1) Two types Normal PSR - Recycled MSPLMXBCrab Pulsar MSP

Pulsar status (see Manchester Talk)Pulsar ~2000 (radio) + ~ 200 (X-ray)PSR in Binary~160, NS/WD/PlanetMSP: ~200 P

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

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

Two kinds of PSRs MSPs old ? P/Pdot~109 yrs Half binary B-P low 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 < 107 yrs Mostly non-binary Millisecond Pulsars (MSPs): 1982, Recycled, Srinivasan & Radhakrishnan (died 2011)X

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

Double Pulsars PSRJ0737-3039A Parkes + GBT radio telescope P=22.7 ms B~109 Gauss, 1.34 M, ; MSP - Recycled P=2.8 s B~1012 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

Neutron StarMSP is recycled in Accreting Binary, Proposed by Srinivasan & Radhakrishnan 1982Radhakrishnan died 2011

Theoretical model: Magnetic neutron star in Binary systemFor a strong NS magnetic field, disk is disrupted in inner parts,

where most radiation is produced.NS spinning => X-ray pulsarMaterial is channeled along field lines and falls onto star at magnetic poles

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

Zhang & Kojima 2006, ~1012 G Strong magnetic field channels gas to magnetic polesX-raysDrag field lines to equator region

Magnetic Field of MSP

~108 G Magnetic field makes gas allover star surfaceNo drag field lines Spherical Accretion-Bottom magnetic field 10**8 GStrong Magnetic field equator region: ~1014 G

MSP Bottom magnetic field 10^7.5 G ?Initial field: 1012 G and 1013 G Field decays with accreting mass reaches the bottom value after accreting ~0.2 MBottom magnetic field is defined ; Alfven radius equals Star radius, B proportional to accretion rate

Magnetic field vs. Spin Period relationEvolution track in B-P diagram Initially, spin-up and field little decays Later, almost follow the spin-up lineMSP spun-up in binary accretion Wang & Zhang 2011

Magnetar () Bottom field: 10^7.5 GIf 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

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

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

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

How about MSP mass < 1.4 M1) initial mass is low, e.g. 1.2 M; binding energy2) AIC: Accretion Induced Collapse of White Dwarf find: < 20% BMPSs are involved AIC processes Dayal & Lilia (ANU) 2007

24/35Typically: Twin KHz QPOUpper 2 ~ 1000 (Hz)Lower 1 ~ 700 (Hz)Twin QPO difference 300 HzPower Density Spectra (PDS) MSP in Accreting BinaryX-ray Neutron Star kHz QPOs

NS/LMXBs kHz QPOs in Atoll and Z Sources Accretion rate direction~Eddington Accretion~1% Eddington Accretion

Hasinger & Van der Klis 1989; Hasinger 1990Z sourceAtoll source

Low frequency QPOs (

RXTE: Spin and kHz QPO 19962011 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

Twin kHz QPO relationNon-linear relation: 1 = ~700. (Hz)(2 /1000Hz)b

b ~ 1.6 Atoll Source, e.g. 4U1728b ~ 1.8 Z Source, e.g. Sco X-1Cir X-1differenceRatioseparation is constant ? (beat)Ratio is a constant : 3:2 ? BEAT ?Ratio const ?

Twin kHz QPO distribution

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

Spin Frequency X-ray MSP by RXTE26 Spin sources12 spin + kHz QPO sourcesSpin frequency: Max: 619 Hz Min: 95 Hz spin

Cir X-1fittings

kHz QPO models 1. relativistic precession 2. Alfven wave

Theoretical Explanation for kHz QPOsBeat-frequency Model ?Relativity precession ModelAlfven Wave Oscillation Model

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 : = 1.4+0.2 M kHz QPOs 1300 Hz >> sub-millisecond ? 0.5 ms

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

Smarr & Blandford 1976