Jan. 16, 2007Strongly-Correlated Many-Body Systems 1 Observation of Neutron Stars Kazuo Makishima Department of Physics, University of Tokyo [email protected]

Jan. 16, 2007

Strongly-Correlated Many-Body Systems

1

Observation of Neutron Stars

Kazuo MakishimaDepartment of Physics,

University of [email protected]

Let’s enjoy physics….

Jan. 16, 2007


2

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


3

Birth and Death of Stars

ブラックホール

Initial Mas (M◎)10-3 0.01 0.1 110- ４ 10

Brown Dwarft

Time

Protostars

Coulomb repulsion

Main Seq.Stars

Red Gi

ants

White

Dwarfs

e-degeneracy

N.S.

Black Holes

Nucleon degeneracy

Supernov

a

H-fusion

Final Mas (M◎)10-3 0.01 0.1 110- ４ 10

Planets classical gas pressure

Jan. 16, 2007


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Mass-Radius Relations of Stars

0.01

0.1

1

0.001

JupiterSaturnNeptune

Uranus

Mass M (M◎)

White dwarfs

Brown dwarfs

Radius R (R

◎)

10-3 0.01 0.1 110- ４

Main Seq.Stars

Planet

sevolution

Grav.contraction

Nucleons/Electrons=2.0 (He, C, O, ,,)

Nucleons/Electrons=1.2 (H+He)

Chandrasekhar limit (M◎)R ∝ M1/

3

Jan. 16, 2007


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Synthesis of CarbonA dying star with

a white dwarf forming at its core

Optical (Hubble Sp.Telescope.)

106 R◎

C/O ratio is ~90 times enhanced than the average cosmic matterDirect evidence of He→ C fusion

0.3 0.5 1.0 1.5

Energy (keV)

C5+ O6+O7+ Ne8+

windHe burning(3α→12C)

HHe C+O

Suzaku soft X-ray spectrum (Murashima et al. 2006, ApJL)

13.6 eV×0.75×62 = 0.37 keV

Jan. 16, 2007


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White Dwarfs (1)

€

PF ≈ h /d ≈ h n1/ 3Fermi momentum

Fermi energy (e-)

€

εF =PF

2

2me

≈h 2n2 / 3

2me

≈h 2M 2 / 3

2me mp2 / 3R2

€

R ≈1

α G

h

mec

M

mp

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

−1/ 3

€

εG ≈GMmp

RGrav. Energy (p+)

Virial theorem

€

εF ≈ εG

A star of which the gravity is counter-balanced by the electron degenerate pressure M=WD mass, R=WD radius, n=particle density

€

αG ≡Gmp

2

ch ≡ 5.9 ×10−39

“Gravitational fine structure constant” (by Prof. Y. Suto)

Jan. 16, 2007


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White Dwarfs (2)

€

PF ≈ h /d ≈ h n1/ 3Fermi momentum

Fermi energy (e-)

€

εF = cPF ≈ ch n1/ 3 ≈ch M1/ 3

mp1/ 3R

€

Mmax ≈ (num.factor) ×α G−2 / 3mp€

εG ≈GMmp

RGrav. Energy (p+)

Virial theorem

€

εF ≈ εG

If relativistic …

Chandrasekhar mass= 1.47 M◎

Cancel out

M◎ = 2.0×1030 kg = solar mass

€

α ≡Gmp

2

ch ≡ 5.9 ×10−39

Jan. 16, 2007


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Neutron Stars

€

Mmax ≈ (num.f.) ×α G−2 / 3mp ≈1.4M⊗

€

R ≈1

α G

h

mec

M

mp

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

−1/ 3

WDs

Change WDs to NSs, by changing electrons to nucleons

€

RWD

RNS

≈mp

me

MWD

MNS

⎛

⎝ ⎜

⎞

⎠ ⎟

−1/ 3

€

MmaxNS ≈ Mmax

WD ≈ 3M⊗

(corrected for gen. relativity & nuclear force)

RNS ~ (M/M◎)-1/3×10 km

Jan. 16, 2007


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“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

centerMagnetism provides one of the few diagnostic

tools with which we can probe into the NS

interior

The NS Interior

Jan. 16, 2007


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Surf

ace

Magn

etic

Fie

ld (

T)

0.001 0.01 0.1 1 　 10 　 100 1000

Rotation Period (sec)

1011

1010

109

108

107

106

105

Msec Pulsars

Radio Pulsars

Binary X-ray Pulsars

Magnetars?

Crab-like Pulsars

Neutron Star Population

Jan. 16, 2007


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The King of NSs -- the Crab pulsar

QuickTime˛ Ç∆YUV420 ÉRÅ[ÉfÉbÉN êLí£ÉvÉçÉOÉâÉÄ

Ç™Ç±ÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

An X-ray view from Chandra

The remnant of the 1054 supernva. Emitting 30 Hz pulses from radio to gamma-ray energies, and accelerating particles to 1015 eV

Jan. 16, 2007


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How To Measure the NS Mass

Thorsett & Chakrabarty1999

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.

Jan. 16, 2007


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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

€

L = 4πR2σT 4

Kuulkers & van der Klis (2000)

6420

2.01.51.00.5

15

10

5

0

Radius (km)

Temperature (keV)

Luminosity

10 sec

Measuring a NS radius is equiv. to measuring the size of a H-atom on Mt. Fuji from Tokyo

Jan. 16, 2007


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Atmospheric Transparency for EM Waves

Blanket effect

Ozone absorp.

Bound e-’s (photoelectri

c)

Free e- incoherent (Compton)

Molecular(rot. vi

b.)

Free e- coherent (plasma cu

toff)

Jan. 16, 2007


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Japanese X-ray Satellites

Hakucho (1979) Tenma (1983)

Ginga (1987) ASCA (1993)

Suzaku (Astro-E2)

(2005 July 10)

Hard X-ray Detector

Jan. 16, 2007


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Suzaku Launch

QuickTime˛ Ç∆Sorenson Video 3 êLí£ÉvÉçÉOÉâÉÄ

Ç™Ç±ÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

Jan. 16, 2007


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(1) A simple-minded estimate;

flux conservation from the progenitor star 　 R 〜 109m, B 〜 10-2 T → R 〜 104m, B 〜 108 T

(2) Assuming –d(Iω2/2)/dt = mag. dipole radiation; → 　 B ∝ sqrt(P dP/dt) 〜 107-9 T

(3) Detection of X-ray spectral features due to (electron) cyclotron resonance, or equivalently, transitions between Landau levels; Ea = hΩe = h(eB/me ) = 11.6 (B/108 T) keV

How To Measure the NS Mag. Field

Electron cyclotorn frequency

Landau levels

€

En = h n +1

2

⎛

⎝ ⎜

⎞

⎠ ⎟Ωe

Jan. 16, 2007


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A strongly magnetized NS

A strongly magnetized NS with a rotation period of 0.1〜1000 sec, in a close binary with a mass-donating companion star.

A supersonic accretion flow from companion

An X-ray emitting hot (kT~20 keV) accretion column

A standing shock

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 .

An Accretion-Powered X-ray Pulsar (XRP)

Jan. 16, 2007


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1 2 5 10 20 50 100

Energy (keV)

Coun

ts/s

/cm2/k

eV

A series of discoveries with the Ginga Satellite (Makishima et al. 1999)

A transient X-ray pulsar X0331+53 Makishima et al. (1990)

New measurements currently carried out with the Suzaku Hard X-ray Detector (e.g., Terada et al. 2006).

Before 1990, only two examples were known (Truemper et al. 1978)

Ea = 28 keV → 　 B = 2.4×108

T

Cyclotron Resonances in XRPs (1)

Jan. 16, 2007


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Makishima et al. Astrophys. J. 525, 978 (1999)

Ea=33 keV

Ea=28 keV

Ea=29 keV

Ea=21keV

12 & 23 keV

No feature

Her X-1 X0331+53 Cep X-4

4U 1538-52 4U 0115+63 SMC X-1

Cyclotron Resonances in XRPs (2)

Jan. 16, 2007


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4 harmonics in 4U 0115+63Santangelo et al. (1998)

10 20 30 50 100Energy (ke

V)

Higher Harmonic Resonances

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

The cascade photons will fill up the fundamental absorption.

Why is the 2nd harmonic deeper than the fundamental?

Jan. 16, 2007


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0

2

4

6

8

10

Cyclotron Resonance Energy (keV)

Number

10 100202 5 50

log[B /(1+z)] (T)8 9

Surface magnetic fields of ~15 binary XRPs are tightly concentrated over (1-4)×108 T.

(Makishima et al. 1999)

BeppoSAXGinga RXTE

Suzaku HXDASCA

Distribution of Magnetic Fields

Jan. 16, 2007


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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.

~A scenario before the 1990s ~

+ -

The Origin of NS Magnetic Field

Jan. 16, 2007


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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.

+ -N S

The Origin of NS Magnetic Field~A new scenario (Makishima et al. 1999) ~

Jan. 16, 2007


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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?

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. N S

Ferro-magnetic and para-magnetic NSs?

Jan. 16, 2007


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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 they do not have companions (no accretion), either.

The only energy source is strong m.f.Some of them are identified with “Soft Gamma-Ray Repeaters”, emitting enormous gamma-ray flasehs.

Magnetars Proton cyclotron rsonanceE = 6.3 (B/1015G) [keV]

SGR 1806-20

Ibrahim et al.(2002)

Jan. 16, 2007


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Enigmatic Hard X-rays from AXPs

Den Hartog et al. (2006)

Jan. 16, 2007


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Diagnosing Accretion Column

Documents

Jan. 16, 2007Strongly-Correlated Many-Body Systems 1 Observation of Neutron Stars Kazuo Makishima Department of Physics, University of Tokyo [email protected]