Magnetic Field & Mass of Neutron Stars中子星的磁场和质量

CHENGMIN ZHANG 张承民 National Astronomical Observatories

Chinese Academy of Sciences, Beijing

zhangcm@bao.ac.cn

After SUPERNOVA EXPLOSIONA Pulsar 。。。

SUPERNOVA EXPLOSION - Pulsar formed ?

PSR -- 1967; P= 1.33 s ; by J Bell MSP – 1982; P= 1.56 ms ; by D Backer (2011)

Discoveries of 1st PSR and MSP

OUTLINE OF TALK

Pulsar (1967 - 2013)

magnetic field

Mass

Conclusions

Normal Pulsar at birth spin P ~ 30msRotating Neutron Star - Quark Star

Pulsar Beacon

Pulsars 1967-2013

Ground-Space ， ~ 2160 radio pulsars

Optiacl, X-ray (Accretion NS 100 ?),

Gam- ray (FERMI > 125)

Part 1. Pulsar （ PSR ）磁场 - 周期

Magnetic-Period diagram and 2160 PSRs (March 2013)

2160PSRs (261 MSPs), data from ATNF Pulsar Catalogue in March of 2013.

212 binary pulsars including 160 MSPs.

Death line by Ruderman

Spin-up line by van den Heuvel

Bottom Field

Pulsars

Magnetars

MSPs

BimodalBimodal ： ： Normal and Millisecond PulsarNormal and Millisecond Pulsar

Bimodal distribution: Magnetic B and Spin-P

Pulsar status (1967-2013)

Pulsar ： ~2160 (radio) + ~ 200 (X-ray)PSR in Binary ： ~ 212, NS/WD/PlanetMSP: ~261 ， P<20ms ， 40% in binaryMagnetic Field: 108 G - 1015 G; ~1012 GSpin period: 1.4 ms,10s, <P>=0.5sBands: Radio, Optical, X-ray

First MSP in 1982 (spin 670 Hz); Fastest MSP in 2006 (716 Hz)

RXTE: 26 spins, Max=619 Hz, X-ray band;

precisely measured 2 solar masses: PSR 2010

Galactic Distribution of Pulsars脉冲星空间分布 – 自行运动 proper motion of PSR & MSP

MSP

年轻的正常脉冲星银道面集中

老年的毫秒脉冲星银心区集中

Young PSR - Galactic plane

old MSP - Galactic core

PSR-MSP （毫秒脉冲星） 两类

• MSPs are very old (~109 years).

• Mostly binary ； B-P low 低• ‘recycled’ by accretion from binary

• accretion spins up NS to milliseconds

• During the accretion X-ray binary

Normal Pulsars: SNR 超新星爆发• Formed in supernova

• Periods between 0.03 and 10 s

• Relatively young (< 107 years)

• Mostly single (non-binary)

Millisecond Pulsars: accreting spin-up in binary 双星系中吸积加速

Crab 蟹状星云

MSP in binary

双星系中子星 X 射线源

中子星 Neutron Star

Formation of MSP: recycled in Accreting Binary, Proposed by Alpar et al. 1982; Srinivasan & Radhakrishnan 1982

Proved in this decade: AMXP, DNS, etc.

Radhakrishnan died 2011

Magnetic, Spin, mass increases > 1.4 M ⊙

MSP formation: X-Ray Binary

NS Magnetic field ~ 1012 GMagnetic field of SUN ~ 100 Gauss 》》 NS ~ 1012 GMagnetic flux conserved

ConstBR 2

2

1

2

2

1

R

R

B

B

Pulsar Features ： Magnetic

Magnetic Strength of Astronomical Objects

NS Magnetic B ~ 108 G - 1015 G Sun B ~ 100-1000 G Earth B~ 1 G

100,000 G - man made

Sur

face

Mag

neti

c F

ield

(G

)

0.001 0.01 0.1 1 　 10 　 100 1000

Rotation Period (sec)

1015

1014

1013

1012

1011

1010

109

ms Pulsars

Radio Pulsars

Binary X-ray Pulsars

Magnetars/AXPs?Crab-like Pulsars

NS Populations

2160 PSRs+200 X-ray NS

Rotation-powered: single, Radio + X-rayAccretion-powered: binary, X-rayNuclear-powered: LMXB, X-ray burst frequency

X-ray Pulsars

Pulsars ： magnetic dipole radiationMagnetic field estimation

DNS binaries live here

Origination of neutron star magnetic field(1) Dynamo MHD: thermomagnetic effect, Blandford et al 1983, generated by convective motions in

the core of the star, in same way as the Earth's magnetic field.

Core: 10^16 Gauss

Surface: 10^12 Gauss

(2) Collapsed from main sequence star,'fossil field hypothesis' , (J. Braithwaite and H.C. Spruit: 2004, Nature, 431, 819-821 )

Solar Radius: 697,000 km, B=10^3 Gauss, collapsed to NS radius 10 km with

magnetic flux conservation, 10^12 Gauss field can be obtained.

(3) Permanent magnet: neutron intrinsic spin magnetic

moment aligned.

Where is the Magnetic field ?

Neutron Star Parameters:

Mass:= 1.25 M⊙

; 30 measured, (PSR

1913+16: 1.41&1.38).

Radius: 15 km, inferred.

Surface temperature 10^6k

Magnetic field = 10^8-15 G

Period=1.5ms – 10 s

Position of magnetic field:

Outer crust : decay fast

Whole crust: : Sang & Chanmugam 87

Core: no decay

Estimates of NS Magnetic Fields

(1) A simple estimate, flux conservation from the

progenitor star, R 〜 1011cm, B 〜 102 G → R 〜106cm, B 〜 1012 G

(2) Assume –d(Iω2/2)/dt = mag. dipole radiation; →

B ∝ sqrt(P*Pdot) 〜 1011~13 G (dependence of I,M,R)

(3) Detection of X-ray spectral features due to (electron)

cyclotron resonance ;

Ea = heB/2πme = 11.6 (B/1012 G) keV

(4) LMXB, magnetosphere radius ， ~108 (G), SAXJ

1808.4-3658

Observatoins with BeppoSAX

4 harmonics in 4U 0115+63Santangelo et al. Astrophys. J. 523, L85 (1998)

Fundamental and 2nd harmonic in 4U 1909+07Cusmano et al. Astron. Astrophys 338, 79 (1998)

10 20 30 50 100 1 2 5 10 20 50Energy (keV)

Observations with RXTE

36 kev, B=3.*1012 (G) in MX0656-072Heindl et al 2004

41 kev, B=3.6*1012 (G) in Her X-1Gruber et al, APJ, 562, 449 (2001)

14 cyclotron line pulsars

6 discovered by RXTE/BEPSAX,

Swank et al 2004(proposal)

Makishima et al 1992, describe cyclotron

scattering resonance features

All NSs are born with magnetic fields (1012 G).

The magnetic field is sustained by permanent ring current, flowing possibly in the crust.

The magnetic field decays exponentially with time, due to Ohmic loss of the ring current.

Radio pulsar statistics suggest a field decay timescale of τ 〜 107 yr.

The older NSs (e.g., millisecond pulsars) have the weaker magnetic field.

Evolution of NS Magnetic Field, A scenario before the 1990s

Evolution ?, Age of Pulsars

Characteristic age: T=P/Pdot, Pdot=dP/dtNot a good indicator for PSR age, initial period ?

Crab PSR, from 1054, ok./ MSP ? T~ Hubble age?

T>t=real age ? Dipole radiation torque ?

T~Z/v, Z vertical position in Galaxy, v=proper velocity. But initial Z=0?

SNR age. Discrepancy ? Dipole spin down age ? PSRB1757-24/SNR G5.4-1.2, SNR age=40kyrs, T=16kyrs

Magnetic field decay main mechanisms:

Hall drift effect:

Kojima 1994; Naito & Kojima 1994;

Geppert et al 2003;

Rheihardt & Geppert 2002; Jones

2003; Cumming et al 2004: Hall

cascade ; etc.

Ohmic dissipation effect:

Geppert & Urpin 1995;

Chanugam 1992;

many others, etc.

Since middle of 1980’s

B decay, automatic ? P/Pdot=age ?1986, Kulkarni, PSR+WD, 200Myrs1986, Taam & van den Heuvel1989, Shibazaki, Murakami, Shaham, Nomoto, Nature

B=Bo/(1+ ∆M/mB)

WD

PSR

Taam & Heuvel 1986

Shibazaki, Murakami, Shaham & Nomoto 1989

B=Bo/(1+ ∆M/mB)

Magnetic evolution observations

HMXBs, binary pulsars, LMXBs

Magnetic evolution observations

Observations:

Becker et al 2003: 3.05-ms pulsar B1821—24 in Globular Cluster M28

by Chandra, 3.3 kev line,implying B=3*10^11 Gauss.

Heuvel & Bitzaraki 1995

Bottom magnetic field

Accretion induced magnetic field decay

Zhang et al, 1994, Ferromagnetic screeningUrpin, Geppert, 1994, Ohmic dissipationCheng, Zhang, 1998, accretion flow, Bottom BCheng, Zhang, 2000, Bottom periodBhattacharya, 2000; spin up effects. Melatos & Phinney, Payne, Konar, Urpin, Geppert,

….2000’s

Double Pulsars in Binary System

PSRJ0737-3039A , J0737-3039B

two pulsars lie (500-600 pc) away in our Galaxy 800,000 km, about twice the distance of Earth-Moon.

orbit period 2.4 hours ， 85 Myrs combining 。PSR J0737-3039 10-times closer to Earth than is PSR

1913+16 P=22 。 7 ms ， B=10**9 Gauss, 1.34 solar mass P=2 。 77 s ， B=10**12 Gauss, 1.25 solar mass

Formation of millisecond pulsar (MSP)

• Accreted matters spin-up X-ray neutron star (NS)• Buried NS magnetic field

Millisecond X-ray pulsar by RXTE: SAXJ 1808.4-3658, P=2.49 (ms), Wijnands & van der Klis 1998

MSP is recycled by accretion: Alpar et al 1982

Sample: magnetic field decay in the binary phase, Double Pulsars PSRJ0737-3039A

Parkes ： Lyne et al Sci, 2004; Burgay et al. 2003, Nat; van den Heuvel, Sci 2004

Firstly formed PSR,

P=22.7 ms ， B~109 Gauss, 1.34 M⊙

P=2.8 s ， B~1012 Gauss, 1.25 M⊙

RXTE: Spin Frequency of X-ray PSR

Spin sources: 8+12+4=24

Frequency: 190 - 619 Hz

Radio MSP ： 716 Hz （ GBT）

Accretion induced NS magnetic field decay in binary phase: theories

Wijers, Hartman & Verbundt 1992 Zhang et al. 1994, screeningUrpin & Geppert, 1998, Ohmic Wijers 1998, accretion rate ?,Bhattacharya & Konar 2002,Payne & Melatos 2004; Lovelace et al 2005, Zhang & Kojima 2006, Alfven R=R*

Magnetic neutron stars

For neutron star with a strong magnetic field, disk is disrupted in inner parts.

This is where most radiation is produced.

Compact object spinning => X-ray pulsator

Material is channeled along field lines and falls onto star at magnetic poles

X-Ray Blusters

磁场演化演示Zhang & Kojim 2006, ~1012 G Strong magnetic field channels gas to magnetic poles

X-rays

Drag field lines to equator region

~108 G Magnetic field makes gas allover star surface

No drag field lines

Quasi Spherical Accretion

Bottom magnetic field formed

Strong Magnetic field equator region: ~1014 G

Final Magnetic field structure of recycled neutron star

Large scale field: weak 108 GaussLocal field: strong 1014-15 Gauss

MSP: Bottom magnetic field

Initial field: 1012 G and 1013 G ， Field decays with the accreting the mass ， reaches the bottom value after accreting ~0.2 M⊙

Bottom magnetic field is defined by

the condition; Alfven radius equals Star radius,

B is proportionally related to the

accretion rate

Magnetic field vs. Period relation

Evolution track in B-P diagram ； Initially, spin-up and field little decays ； Later, almost follow the spin-up line

Main Conclusion on Pulsar ： Future detection

~107 (G) MSP, exists ?

Magnetar accreted 0.2 solar mass >> MSP !

Maximum Magnetic Field of NS

Crust modulus, 10^13 GCyclotron line, 10^13 GAXP, SGR, 10^14-15 G ? Mc^2, 10^18 G Gravity energy, 10^17 G Gravitational wave limit, 10^16 GGW braking index n=4, Obs n<3.

Magnetic Field and EOS

Magnetic pressure B^2 ~ 10^29 B15^2

Crust structure of NS/QS ? Quark or electron degenerate ?

Magnetar 10^15 G

Soft Gamma Repeater (SGR)

Magnetar: a super-strong magnetic field ?

Theory by Dr.Robert Duncan (1992)Observation: Crysa Kouveliotou (2003)SGR 1806-20 T=7.5 smagnetic field 10^15 GNormal radio pulsars reach 10^12 G

Magnetar

At the surface of the star a chunk of magnetizable metal like iron would feel a force equal to 150 million times the Earth's gravitational pull on it

magnetism itself can keep the star hot - about 10 million degrees C

吸积质量相关， 双星系磁场和吸积物质反比；底部磁场 10**8G ，吸积饱和

孤立中子星磁场不变。

中子星磁场 - CONCLUSIONS

Part 2. Pulsar 质量

Pulsar 质量测量意义？

1. SNR 约束2. M-R 强引力3. 物态 EOS4. 吸积演化约束

Significance of Measuring Star mass and radius – Neutron or Quark Matter

we can measure physical star parameters, mass and radius, probe nuclear physics at highdensity ， equation of state (EOS)

we can study strong gravitation field, and Einstein GR is tested

Pulsar 质量测量： 双星系统 & 模型估计

1. 双星参数2. 相对论效应

Status of Neutron Star Mass

measurements

(Stairs 2004)

(MT77)

(Lattimer & Prakash 2004 ， 2006)

60+ NSs, M=1.4 M⊙

, R= 10 - 30 km ?

Radio pulsars, X-ray NS, binary systems

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); M=1.74 M (2008⊙ ）

DNS (double pulsar) : M=1.25M , M=1.34 ⊙ M (Lyne et al. 2004)⊙

PSR J0737-3039A/B Post-Keplerian Effects

R: Mass ratio

: periastron advance

: gravitational redshift

r & s: Shapiro delay

Pb

: orbit decay

(Kramer et al. 2005)

.

.

• Six measured parameters – only two

independent

• Fully consistent with general relativity

(0.1%)

A: 1.34 M⊙

; B: 1.25 M⊙

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 Gravity acceleration g=~M/R2

1E1207.4-5209, Aql X-1 and EXO 0748-676Rs=2GM/c2: Schwarzschild radius

No direct measure of NS radius !

Photon Spectra: Measuring NS Radius

Perfect Black Body d = distance to earth

Obs Total Flux: F = 4 R∞

2 SB

T∞

4/d2

))1(/2-1(

/2-1

/2-1

1-2

2

2

zRcGM

TRcGMT

RcGM

RR

Spectra seldom black body: NSs have atmospheres !

Composition and Magnetic field shape spectra.

Surface temperature and radiation isotropic ?

d: distance of NS-earth - error

RX J1856.5-3754

Striking case of RX J1856.5-3754

Truempet et al. 2004; Burwitz et al. 2003

Apparent radius RApparent radius R∞∞

=16.5 km (d/117pc), =16.5 km (d/117pc), Truempet 2005Truempet 2005

True radius 14 km (1.4 MTrue radius 14 km (1.4 M⊙⊙

), stiff EOS, rule out quark star), stiff EOS, rule out quark star

This is an isolated neutron star (INS), valuable because:

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 (temperature), and g (gravity

acceleration);

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

Redshifted absorption lines from a NS surface

Cottam, Paerels & Mendez (2002)- z=0.35

Measuring M/R – Gravitational redshift

NS Mass-Radius

Gravitational Red-shift: observation of

spectral lines (Cottam, et al 2002).

QPOs indicate ISCO

Exotic Stars

Measure M/R3 by kHz QPOs （ 24/35)

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 24/35 sources ； ~300

Orbital Keplerian frequency ~M/r3

Constrain star M_R by kHz QPOs

Inner boundary to emit a MAXIMUM kHz QPO frequency (1) ISCO=3Rs, (ISCO=Innermost stable circular orbit) (2) NS surface R

M < 2.2 M⊙ (1kHz/frequency)R < 19.5 km (1kHz/frequency) M/R3 relation known by a model for twin kHz QPOs

SAXJ 1808.4: M/R3 by Burderi & King 1998

kHz QPOs from LMXBs: Maximum frequency at ISCO or R

kHz QPO maximum frequency constrains NS equations of states

(EOSs)

Excluded

Sco X-1

Einstein’s General Relativity: Perihelion precession

Precession Model for KHz QPO, Stella and Vietri, 1999

ν2 = ν

kepler

ν1 = ν

precession = ν

2 [1 – (1 – 3Rs/r)1/2]

∆ν = ν2

- ν1 is not constant

ISCO Saturation

Relativistic precession model by Stella & Vietri 1999

M inferred from twin kHz QPOs

Maximum frequency at ISCO

M/R3 inferred from twin kHz QPOs

Maximum frequency at Star Surface R

Kepler frequency νk = (GM/4π2r3)0.5

νk = 1850 (Hz) A X3/2

ν1

= ν 2X (1- (1-X)1/2)1/2

A2=m/R63; X=R/r, m=M/M

⊙ , R

6 = R/106 cm

Zhang 2004, AA

Maximum kHz QPO occurs at R or ISCO=3Rs

A> νk /1850 (Hz) and m < 2200 (Hz)/ ν

k

Miller et al 1998

Constraining M – R by R∞ and z

Source: 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

Constraining M – R by R∞ and A~M/R3

Aql X-1 : LMXB-binary9 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

Constraining M – R by A~M/R3 and z

EXO 0748-676: LMXB z=0.35; Cottam et al 2002

One kHz QPO 695 Hz; Homan & 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

1E1207.4-5209,

Apparent radius, gravitational redshift

QUARK STAR ?

Hot Spot ?

Aql X-1 ,

Apparent radius=14 km, single kHz QPO

EXO 0748-676 ,

gravitational redshift, kHz QPO

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

Measuring NS Mass & Radius

by kHz QPO, gravitational redshift and apparent radius 　　

Measuring STAR Mass-Radius

by kHz QPO, gravitational redshift and apparent radius 　

CN1/CN2: normal neutron matter, CS1/CS2: quark star

CPC: Bose-Einstein condensate of pions

Zhang, et al, 2007

AqlX-1 ， EXO 0748-676 Samples

Statistics of 65 NS mass

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 - MSPadded 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

Mass Statistics of MSP: 1.5-1.6Mʘ

MSP (Pspin<20ms):1.48Mʘ PSR less recycled(Pspin>20 ms):1.35Mʘ

毫秒脉冲星质量 ~1.6 Mʘ

吸积物质 ~ 0.2 Mʘ accreted

(Lattimer & Prakash 2006)

2R ～ 20 km ； M~Msun

Summary

THANKS

1. PSR Mass, measured <M~1.4>

2. MSP mass 《 M-1.6 》

3. Spectra, M-R relation

4. Redshift, M/R

5. kHz QPO, M/R^3, constraints

6. Other M-R relation

Not clear: fuzzy in M-R

EOS: Quark or Neutron ?