Millisecond Pulsar and kHz QPOs of LMXB

Chengmin 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 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

Pulsar - Rotating Neutron/Quark Star

Pulsar Beacon

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

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

Two kindsTwo kinds ： ： Normal and Millisecond Normal and Millisecond Pulsar ?Pulsar ?

Bimodal distribution: Magnetic B and Spin-P On ATNF PSR data, see Hobbs & Manchester 2005

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 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 < 107 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

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

中子星 Neutron Star

MSP is recycled in Accreting Binary,

Proposed by Srinivasan & Radhakrishnan 1982

Radhakrishnan died 2011

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

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 <M> = 1,57 +/-0.2 M⊙

Zhang & Kojima 2006, ~1012 G Strong magnetic field channels gas to magnetic poles

X-rays

Drag field lines to equator region

Magnetic Field of MSP

~108 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: ~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 M⊙

Bottom magnetic field is defined ;

Alfven radius equals Star radius,

B proportional to accretion rate

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

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

(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 ）

Statistics of 63 NS mass - Zhang et al 2011

Histogram: Gaussian Distribution

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⊙)

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

（ 24/35 ）

Typically: Twin KHz QPO

Upper ν2 ~ 1000 (Hz)

Lower ν1 ~ 700 (Hz)

Twin QPO difference 300 Hz

Power 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 1990

Z sourceAtoll source

• Low frequency QPOs (<100Hz)

• hecto-hertz QPOs (100-200Hz)

• kHz QPOs (~200-1200+Hz): Lower and upper - twin peak QPOs

frequency

pow

er

Sco X-1

kHz QPO origin remains questionable, often expected associated to the orbital motion in the inner part of disc.

QPO bands

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

Twin kHz QPO relation

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

Cir X-1

dif

fere

nce

Rat

io

1. separation is constant ? (beat)

2. 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 RXTE

26 Spin sources

12 spin + kHz QPO sources

Spin frequency:

Max: 619 Hz

Min: 95 Hz

spin

Cir X-1

fittings

kHz QPO models ：

1. relativistic precession

2. Alfven wave

Theoretical Explanation for kHz QPOs

Beat-frequency Model ?

Relativity precession Model

Alfven Wave Oscillation Model

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 : <M> = 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