Download Where is the Magnetic field

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
[email protected]
After SUPERNOVA EXPLOSION
A Pulsar 。。。
SUPERNOVA EXPLOSION - Pulsar formed ?
Discoveries of 1st PSR and MSP
PSR -- 1967; P= 1.33 s ; by J Bell
MSP – 1982; P= 1.56 ms ; by D Backer (2011)
OUTLINE OF TALK
Pulsar (1967 - 2013)
magnetic field
Mass
Conclusions
Normal Pulsar at birth spin P ~ 30ms
Rotating 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)
Magnetars
Pulsars
Spin-up line by
van den Heuvel
Death line by Ruderman
MSPs
Bottom Field
2160PSRs (261 MSPs), data from ATNF Pulsar Catalogue in March of 2013.
212 binary pulsars including 160 MSPs.
Bimodal： Normal 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/Planet
 MSP:
~261， P<20ms，40% in 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 (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
年轻的正常脉冲星银道面集中
Young PSR - Galactic plane
老年的毫秒脉冲星银心区集中
old MSP - Galactic core
MSP
PSR-MSP（毫秒脉冲星） 两类
Normal Pulsars: SNR 超新星爆发
• Formed in supernova
• Periods between 0.03 and 10 s
Crab 蟹状星云
• Relatively young (< 107 years)
Millisecond Pulsars: accreting spinup in binary 双星系中吸积加速
• Mostly single (non-binary)
• MSPs are very old (~109 years).
• Mostly binary； B-P low 低
• ‘recycled’ by accretion from binary
• accretion spins up NS to milliseconds
MSP in binary
双星系中子星X 射线源
• During the accretion X-ray binary
Formation of MSP: recycled in Accreting Binary,
Proposed by Alpar et al. 1982; Srinivasan & Radhakrishnan 1982
Proved in this decade: AMXP, DNS, etc.
中子星 Neutron Star
Radhakrishnan died 2011
Magnetic, Spin, mass increases > 1.4 M⊙
MSP formation: X-Ray Binary
Pulsar Features：Magnetic
NS Magnetic field ~ 1012 G
Magnetic field of SUN ~ 100 Gauss 》》 NS ~ 1012
Magnetic flux conserved
BR  Const
2
B1  R2 
  
B2  R1 
2
G
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
NS Populations
15
Surface Magnetic Field (G)
10
Magnetars/AXPs?
14
10
10
13
10
12
10
11
Crab-like Pulsars
Binary X-ray Pulsars
Radio
Pulsars
10
10
2160 PSRs+200 X-ray NS
9
10
ms Pulsars
0.001
0.01
0.1
Rotation Period (sec)
1
10
100
1000
X-ray Pulsars
Rotation-powered: single, Radio + X-ray
Accretion-powered: binary, X-ray
Nuclear-powered: LMXB, X-ray burst frequency
Pulsars： magnetic dipole radiation
Magnetic field estimation
DNS binaries live here
Origination of neutron star magnetic field
(1)
generated by convective motions in
the core of the star, in same way as the Earth's magnetic field.
Dynamo MHD: thermomagnetic effect, Blandford et al 1983,
(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.
Core: 10^16 Gauss
Surface: 10^12 Gauss
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
11
2
6
progenitor star, R〜10 cm, B〜10 G → R〜10 cm,
12
B〜10 G
2
(2) Assume –d(Iω /2)/dt = mag. dipole radiation; → B
∝
sqrt(P*Pdot)
〜 10
11~13
G (dependence of I,M,R)
(3) Detection of X-ray spectral features due to (electron)
cyclotron resonance ;
12
Ea = heB/2πme = 11.6 (B/10 G) keV
8
(4) LMXB, magnetosphere radius，~10 (G), SAXJ
1808.4-3658
Observatoins with BeppoSAX
Fundamental and
2nd harmonic in
4U 1909+07
4 harmonics
in 4U 0115+63
Cusmano et al.
Astron. Astrophys
338, 79 (1998)
Santangelo et al.
Astrophys. J.
523, L85 (1998)
10
20
30
50
100
1
2
5
Energy (keV)
10
20
50
Observations with RXTE
Makishima et al 1992, describe
cyclotron scattering resonance features
14 cyclotron line pulsars
6 discovered by RXTE/BEPSAX,
Swank et al 2004(proposal)
B=3.6*1012
41 kev,
in Her X-1
(G)
Gruber et al, APJ, 562, 449 (2001)
36 kev, B=3.*1012 (G)
in MX0656-072
Heindl et al 2004
Evolution of NS Magnetic Field,
A scenario before the 1990s
 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 ?, Age of Pulsars
Characteristic age: T=P/Pdot, Pdot=dP/dt
Not 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:
Ohmic dissipation effect:
Geppert & Urpin 1995;
Chanugam 1992;
many others, etc.
Hall drift effect:
Kojima 1994; Naito & Kojima
1994; Geppert et al 2003;
Rheihardt & Geppert 2002; Jones
2003; Cumming et al 2004: Hall
cascade ; etc.
Since middle of 1980’s
B decay, automatic ? P/Pdot=age ?
1986, Kulkarni, PSR+WD, 200Myrs
1986, Taam & van den Heuvel
1989, Shibazaki, Murakami, Shaham, Nomoto, Nature
WD
B=Bo/(1+ ∆M/mB)
PSR
Magnetic evolution observations
Taam & Heuvel 1986
B=Bo/(1+ ∆M/mB)
Shibazaki, Murakami, Shaham & Nomoto 1989
HMXBs, binary pulsars, LMXBs
Magnetic evolution observations
Heuvel & Bitzaraki 1995
Bottom magnetic field
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.
Accretion induced magnetic field decay
 Zhang et al, 1994, Ferromagnetic screening





Urpin, Geppert, 1994, Ohmic dissipation
Cheng, Zhang, 1998, accretion flow, Bottom B
Cheng, Zhang, 2000, Bottom period
Bhattacharya, 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)
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
• Accreted matters spin-up X-ray neutron star (NS)
• Buried NS magnetic field
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, screening
 Urpin & 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.
Material is
channeled
along field lines
and falls onto
star at magnetic
poles
This is where most radiation is produced.
Compact object spinning => X-ray pulsator
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
Quasi Spherical Accretion
Bottom magnetic field formed
~108 G Magnetic field makes
gas allover star surface
No drag field lines
Strong Magnetic field equator region: ~1014 G
Final Magnetic field structure of recycled
neutron star
Large scale field: weak 108 Gauss
Local field: strong 1014-15 Gauss
MSP: Bottom magnetic field
Bottom magnetic field is defined
by the condition; Alfven radius
equals Star radius,
B is proportionally related to the
accretion rate
Initial field: 1012 G and 1013 G ， Field decays with the accreting the
mass， reaches the bottom value after accreting ~0.2 M⊙
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 G
Cyclotron line, 10^13 G
AXP, SGR, 10^14-15 G ?
Mc^2, 10^18 G
Gravity energy, 10^17 G
Gravitational wave limit, 10^16 G
GW 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 s
 magnetic field 10^15 G
 Normal 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
中子星磁场- CONCLUSIONS
 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。
Part 2. Pulsar 质量
Pulsar 质量测量意义？
1.
2.
3.
4.
SNR 约束
M-R 强引力
物态EOS
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
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


60+ NSs, M=1.4 M , R= 10 - 30 km ?
⊙
Radio pulsars, X-ray NS, binary systems
(MT77)
(Stairs 2004)
(Lattimer & Prakash 2004，2006)
NS mass determined in Binary system
？； Nice et al. 2004
⊙
(Jonker et al 2003); M=1.74 M⊙ (2008）
MSP, PSR J0751+1807, M = 2.1(2) M
2A1822-371, M>0.97+-0.24 M
⊙
DNS (double pulsar) : M=1.25M⊙, M=1.34 M⊙ (Lyne et al. 2004)
PSR J0737-3039A/B Post-Keplerian Effects
.
.
R: Mass ratio
w: periastron advance
g: gravitational redshift
r & s: Shapiro delay
P : orbit decay
b
• Six measured parameters
– only two
independent
with general relativity
• Fully consistent(0.1%)
A: 1.34 M
⊙
; B: 1.25 M
⊙
(Kramer et al. 2005)
No direct measure of NS radius !
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 0748-676
Rs=2GM/c2: Schwarzschild radius
Photon Spectra: Measuring NS Radius
Perfect Black Body d = distance to earth
Obs Total Flux:
F = 4 R 2 
T 4/d2
∞
SB ∞
R 
R
1 - 2GM/Rc 2
T  1 - 2GM/Rc 2 T
( 1 - 2GM/Rc 2  (1  z ) -1 )
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
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
 Apparent radius R =16.5 km (d/117pc), Truempet 2005
∞
 True radius 14 km (1.4 M ), stiff EOS, rule out quark star
⊙
Measuring M/R – Gravitational redshift
Redshifted absorption lines from a NS surface
Cottam, Paerels & Mendez (2002)- z=0.35
NS Mass-Radius
Exotic Stars
Gravitational Red-shift: observation of
spectral lines (Cottam, et al 2002).
QPOs indicate ISCO
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 ν ~ 1000 (Hz)
2
Lower ν ~ 700 (Hz)
1
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
Excluded
kHz QPO maximum frequency constrains NS equations of
states (EOSs)
Sco X-1
Relativistic precession model by Stella & Vietri 1999
M inferred from twin kHz QPOs
Maximum frequency at ISCO
ISCO Saturation
Einstein’s General Relativity: Perihelion precession
Precession Model for KHz QPO, Stella and Vietri, 1999
ν =ν
2
kepler
ν =ν
= ν [1 – (1 – 3Rs/r)1/2]
1
precession
2
∆ν = ν
- ν is not constant
2
1
M/R3 inferred from twin kHz QPOs
Maximum frequency at Star Surface R
Kepler frequency ν = (GM/4π2r3)0.5
k
ν = 1850 (Hz) A X3/2
k
ν = ν X (1- (1-X)1/2)1/2
1
2
A2=m/R 3; X=R/r, m=M/M , R = R/106 cm
6
⊙
6
Zhang 2004, AA
Maximum kHz QPO occurs at R or ISCO=3Rs
A> ν /1850 (Hz) and m < 2200 (Hz)/ ν
k
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-binary
9 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
Hot Spot ?
QUARK STAR ?
Aql X-1 ,
Apparent radius=14 km, single kHz QPO
EXO 0748-676 ,
gravitational redshift, kHz QPO
Measuring NS Mass & Radius
Mass-Radius relations
by kHz QPO, gravitational redshift and apparent radius
 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 STAR Mass-Radius
by kHz QPO, gravitational redshift and apparent radius
Zhang, et al, 2007
AqlX-1， EXO 0748-676 Samples
CN1/CN2: normal neutron matter, CS1/CS2: quark star
CPC: Bose-Einstein condensate of pions
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 - 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
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
1.
2.
3.
4.
5.
6.
PSR Mass, measured <M~1.4>
MSP mass 《M-1.6 》
Spectra, M-R relation
Redshift, M/R
kHz QPO, M/R^3, constraints
Other M-R relation
Not clear: fuzzy in M-R
EOS: Quark or Neutron ?
THANKS