magnetic field & mass of neutron stars 中子星的磁场和质量
DESCRIPTION
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 ?. - PowerPoint PPT PresentationTRANSCRIPT
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
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 ?