Transcript Measuring Magnetic Fields of Neutron Stars

Observation of Neutron Stars
Kazuo Makishima
Department of Physics,
University of Tokyo
[email protected]
Let’s enjoy physics….
Jan. 16, 2007
Strongly-Correlated Many-Body Systems
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Topics with NSs
• Superfluid states, vorrtex strings
• Nuclear Pastas -- Dr. Sonoda
• Pion condensations in the central regions
• QGP, quark matter -- Prof.G. Baym
• The origin of strong magnetic fields
• …
Jan. 16, 2007
Strongly-Correlated Many-Body Systems
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Birth and Death of Stars
10-４
10-3
Initial Mas (M◎)
0.01
0.1
1
H-fusion
10
Time
Protostars
ブラックホール
classical gas pressure
N.S.
10-3
e-degeneracy
0.1
0.01
Final Mas (M◎)
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1
Black Holes
Brown
Dwarft
Coulomb
repulsion
10-４
Supernova
Main Seq.Stars
Planets
10
Nucleon degeneracy
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Radius R (R◎)
Mass-Radius Relations of Stars
1
0.1
Nucleons/Electrons
=1.2 (H+He)
Grav.contraction
evolution
Uranus
0.01
0.001
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Saturn Jupiter
Neptune
Chandrasekhar
limit (M◎)
Nucleons/Electrons
=2.0 (He, C, O, ,,)
10-４
10-3
0.01
0.1
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Mass M (M◎)
4
Synthesis of Carbon
A dying star with a white
dwarf forming at its core
106 R◎
Suzaku soft X-ray spectrum
(Murashima et al. 2006, ApJL)
C5+
O6+
O7+
Ne8+
Optical (Hubble Sp.Telescope.)
wind
He burning
(3α→12C)
C+O
He
H
0.3
0.5
1.0 1.5
Energy (keV)
13.6 eV×0.75×62 = 0.37 keV
C/O ratio is ~90 times enhanced
than the average cosmic matter
Direct evidence of He→ C fusion
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White Dwarfs (1)
A star of which the gravity is counter-balanced by the
electron degenerate pressure
M=WD mass, R=WD radius, n=particle density
1/ 3
P

h
/d

h
n
Fermi momentum
F
PF 2 h 2 n 2 / 3
h2M 2/3
F 


2/3
2me
2me
2me mp R 2
Fermi energy (e-)
GMm p
 (p+)
Grav. Energy
G 
Virial theorem

F  G
1
R  
G
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R
“Gravitational fine structure
constant” (by Prof. Y. Suto)
1/ 3
2


h M
Gmp
39





5.9
10
G

ch
mec 
m
 p 
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White Dwarfs (2)
If relativistic …
Fermi momentum
Fermi energy
(e-)
PF  h /d  h n1/ 3
F  cPF  chn1/ 3
GMm p
 (p+)
Grav. Energy
G 
Virial theorem

F  G
R
chM1/ 3

1/ 3
mp R
Cancel out
Chandrasekhar mass
2 / 3
Mmax  
(num.factor)  G mp = 1.47 M◎
2
Gmp
M◎ = 2.0×1030 kg = solar mass

 5.9 1039
ch
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Neutron Stars
WDs
1/ 3


1 h M
R



 G mec mp 

2/ 3
Mmax  (num.f.)  G
mp 1.4M
Change WDs to NSs, by changing electrons to nucleons

RWD
RNS
Mmax
1/ 3


mp M WD



me  M NS 
NS
RNS ~ (M/M◎)-1/3×10 km
 Mmax  3M
(corrected for gen. relativity & nuclear force)
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WD
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The NS Interior
“Outer Crust”
Nuclei + electrons
“Inner Crust”
Nuclei, free neutrons,
and electrons, possibly
with “pasta” phases
“Core”
Uniform nuclear matter,
possibly an exotic phase at
the very center
Magnetism provides one of the few
diagnostic tools with which we can
probe into the NS interior
Jan. 16, 2007
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11
Neutron Star Population
Surface Magnetic Field (T)
10
Magnetars?
10
10
10
9
10
8
10
7
Crab-like Pulsars
Binary X-ray Pulsars
Radio
Pulsars
6
10
5
10
0.001
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Msec
Pulsars
0.01
Rotation Period (sec)
0.1
1
10
100
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1000
10
The King of NSs -- the Crab pulsar
The remnant of the 1054 supernva. Emitting 30 Hz pulses from
radio to gamma-ray energies, and accelerating particles to 1015 eV
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An X-ray view from Chandra
Jan. 16, 2007
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How To Measure the NS Mass
Use radio pulsars in
binary systems.
Measure orbital
Doppler effects of
their radio pulses.
Measure optical
Doppler effects of
their primary stars.
Use Kepler’s law.
Thorsett & Chakrabarty1999
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How To Measure the NS Radius
 Sometimes, a burst-like nuclear
fusion (H → He or He→ C)
occurs on a certain class of NSs.
 The heated NS surface emits
blackbody X-rays, and gradually
cools down.
 The blackbody temp. T and
luminosity L can be measured.
 Use Stefan-Boltzmann’s law to
estimate the radius R
2.0
1.5
1.0
0.5
15
L  4 R T
10
2
4
Measuring a NS radius is equiv.
to measuring the size of a Hatom on Mt. Fuji from Tokyo
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6
4
2
0
5
0
Luminosity
Temperature (keV)
Radius (km)
10 sec
Kuulkers & van der Klis (2000)
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Atmospheric Transparency for EM Waves
e-
Free coherent
(plasma cutoff)
Free e- incoherent
Molecular Bound e-’s
(Compton)
(rot. vib.) (photoelectric)
Ozone absorp.
Blanket effect
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Japanese X-ray Satellites
Hakucho (1979)
Ginga (1987)
Tenma (1983)
Suzaku (Astro-E2)
(2005 July 10)
ASCA (1993)
Hard X-ray Detector
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Suzaku Launch
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How To Measure the NS Mag. Field
(1) A simple-minded estimate;
Landau levels
flux conservation from the progenitor
star
9
-2
4
8
R〜10 m, B〜10 T → R〜10 m, B〜10 T
2
(2) Assuming –d(Iω /2)/dt = mag.
 1 
E n  hn  e
 2 
dipole radiation;
7-9
→ B ∝ sqrt(P dP/dt) 〜 10 T
Electron cyclotorn
(3) Detection
of X-rayfrequency
spectral features due to

(electron) cyclotron resonance, or equivalently,
transitions between Landau levels;
8
Ea = hΩe = h(eB/me ) = 11.6 (B/10 T) keV
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An Accretion-Powered X-ray Pulsar (XRP)
A supersonic accretion
flow from companion
A standing
shock
An X-ray
emitting hot
(kT~20 keV)
accretion
column
A strongly
magnetized NS
Jan. 16, 2007
A strongly magnetized
NS with a rotation period
of 0.1〜1000 sec, in a
close binary with a massdonating companion star.
Electrons in the accretion column
resonantly scatter X-ray photons,
when they make transitions
between adjacent Landau levels.
→ The X-ray spectrum will bear a
strong spectral feature, called a
Cyclotron Resonance Feature .
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Cyclotron Resonances in XRPs (1)
Before 1990, only two examples were known (Truemper et al. 1978)
of discoveries
with the Ginga
Satellite (Makishima
et al. 1999)
Counts/s/cm2/keV
A series
A transient
X-ray
pulsar X0331+53
Makishima et al. (1990)
Ea = 28 keV →
B = 2.4×108 T
1
2
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5
10
New
20
Energy (keV)
50
measurements
currently carried out
with the Suzaku Hard
100 X-ray Detector (e.g.,
Terada et al. 2006).
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Cyclotron Resonances in XRPs (2)
Her X-1
X0331+53
Ea=33
keV
Ea=28
keV
4U 1538-52
Ea=21
keV
4U 0115+63
12 &
23
keV
Cep X-4
Ea=29
keV
SMC X-1
No
feature
Makishima et al. Astrophys. J. 525, 978 (1999)
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Higher Harmonic Resonances
Why is the 2nd harmonic deeper
than the fundamental?
 An absorbed 1Ω photons is
soon re-emitted --> scattering
 If a 2Ω photon is absorbed, the
excited electron returns to g.s.
by emitting two 1Ω photons in
cascade--> pure absorption
4 harmonics
in 4U 0115+63
Santangelo et al. (1998)
10
20
30
50
Energy (keV)
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 The cascade photons will fill
100 up the fundamental absorption.
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Distribution of Magnetic Fields
log[ B /(1+z )] (T)
Number
10
8
Ginga
8
ASCA
9
BeppoSAX
RXTE
Suzaku HXD
Surface magnetic
fields of ~15 binary
XRPs are tightly
concentrated over
(1-4)×108 T.
6
4
2
(Makishima et al. 1999)
0 2
5 10 20 50 100
Cyclotron Resonance Energy (keV)
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The Origin of NS Magnetic Field
~A scenario before the 1990s ~
 All neutron stars are born with strong magnetic
fields (〜108 T).
 The magnetic field is sustained by permanent
superconducting ring current 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 fields.
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The Origin of NS Magnetic Field
~A new scenario (Makishima et al. 1999) ~
1. If m.f. were decaying, the measured surface field
would exhibit a continuous distribution toward
lower fields --> contradict with the X-ray results.
2. Strong-field and weak-field NSs are likely to be
genetically different.
3. Strong-field and weak-field objects are connected
to each other by some phase transitions.
→ Magnetic field may be a manifestation
+ of nuclear ferrro-magnetism.
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Ferro-magnetic and para-magnetic NSs?
Magnetic moments of neutrons may align due to exchange
interaction, which must be repulsive on the shortest range.
If all the neutrons align, we expect B〜 4×1012 T.
A small volume fraction (~10-4) is ferro-magnetic
→ strong-field NSs (108 T)
Entirely para-magnetic → weak-filed NSs (＜104~5 T)
Phase transitions may occur depending on, e.g., age,
temperature, accretion history, etc.
A large fraction of the volume is ferro-magnetic
→ magnetars (1010~11 T) ?
The release of latent heat at the transition may explain
some soft gamma-ray repeaters?
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Magnetars
Proton cyclotron rsonance
E = 6.3 (B/1015G) [keV]
About two dozen X-ray pulsars, with periods of 6-12
sec, are known as Anomalous X-ray Pulsars (AXP).
Their spin-down rate, with plausible assumption,
yields B~1011 T, but their X-ray luminosity >> kinetic
energy output due to spin down.
They are rotating too slow to be rotation-powered,
but
SGR 1806-20
they do not have companions (no accretion), either.
Ibrahim et al.(2002)
The only energy source is strong m.f.
Some of them are identified with “Soft Gamma-Ray
Repeaters”, emitting enormous gamma-ray flasehs.
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Enigmatic Hard X-rays from AXPs
Den Hartog et al. (2006)
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Diagnosing Accretion Column
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