Jan. 6, 2003Tokyo-Adelaide Conference Measuring Magnetic Fields of Neutron Stars Kazuo Makishima Department of Physics, University of Tokyo [email protected]

Jan. 6, 2003 Tokyo-Adelaide Conference

Measuring Magnetic Fields of Neutron Stars

Kazuo MakishimaDepartment of Physics,

University of [email protected]

“How the strong magnetic field of neutron stars is sustained, and how it evolves.”


Interior of a NS“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

Manetism provides one of the few diagnostic tools with which we

can probe into the NS interior


All neutron stars are born with strong 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.

The Origin and Evolution of NS Magnetic Field〜 A scenario before the 1990s 〜

+ -


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

Msec Pulsars

Radio Pulsars

Binary X-ray Pulsars

Magnetars?

Crab-like Pulsars

NS Populations


Estimates of NS Magnetic Fields(1) A simple-minded estimate;

flux conservation from the progenitor star　 R 〜 109m, B 〜 102 G → R 〜 104m,

B 〜 1012 G

(2) Assuming –d(Iω2/2)/dt = mag. dipole radiation; → 　 B ∝ sqrt(P dP/dt) 〜 1011~13 G

(3) Detection of X-ray spectral features due to (electron) cyclotron resonance ; Ea = heB/2πme = 11.6 (B/1012 G) ke

V


An Accretion-Powered Binary X-ray Pulsar

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 shockElectrons 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 Scattering Feature (CRSF).


Hakucho (Cygnus)1979.2 〜 1984.4

Cosmic X-ray Studies in Japan

Tenma (Pegasus)1983.2〜 1984.8

Ginga (Galaxy)1987.2 〜 1991.10

ASCA (Advanced Satellite for Cosmology & Astrophysics)1993.2〜 2000.7

ASTRO-E2 Scheduled for launch in 2005

M-5 launch vehicle of ISAS


1 2 5 10 20 50 100

Energy (keV)

Coun

ts/s

/cm

2 /k

eV

A series of dis-coveries with the Ginga Satellite (1987-1991)

A transient X-ray pulsar X0331+53 Makishima et al. Astrophys. J. 365, L59 (1990)

X-ray Observations of CRSFsBefore 1990, only two examples were observed(e.g., Truemper et al. 1978, Astrophys. J. 219, L105; 1978)

Er = 28 keV → 　 B = 2.4×1012

G


Discoveries of CRSFs with Ginga

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

Er=33 keV

Er=28 keV

Er=29 keV

Er=21keV

12 & 23 keV

No CRSF

Her X-1 X0331+53 Cep X-4

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


Heindl et al. Astrophys. J. 563, L35 (2001)

Observatoins with the Rossi X-ray Timing Explorer

Inferred model spectrum

Data with the PCA Data with the HEXTEf (E) = (aE -p + bE +q) 　 ×exp(-E /kT)　 × exp(-S )

S =E 2/{(E-Er)2+W 2 }

Makishima et al. (1999)

Fit residuals w/o exp{-S}Fit residuals with exp{-S}


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)


Energy Ec Er

Cyclotron Resonances and the Spectral Continuum

10

20

30

40

5060

Cycl

otro

n Re

sona

nce

Ener

gy E

r (ke

V)

Cutoff Energy Ec (keV)

4U1538-52

Cep X-4

Vela X-1

Her X-1

A0535+26

Cen X-3

4U1907+09

4U1626-67

X0331+53

4U0115+63(1990)

4U0115+63 (1991)

GX301-2

6 8 10 20 30

E r=1.7

E c

Even if CRSF is not detected, we can estimate the field intensity from the X-ray continuum shape


Distribution of Magnetic Field

0

2

4

6

8

10

Cyclotron Resonance Energy (keV)

Num

ber

10 100202 5 50

log[B /(1+z )] (Gauss)12 13

Surface magnetic fields of 〜 15 binary X-ray pulsars are tightly concentrated over (1-4)×1012 G.

CRSF is yet to be detected from the remaining 〜 20 binary X-ray pulsars, but the continuum shape suggests that they have comparable field intensities.

Higher-field side of the distribution may be subject to selection effects. → The Hard X-ray Detector (HXD) onboard ASTRO-E2 (laumch in 2005) is of great value.

BeppoSAXGinga RXTE

ASTRO-E2 HXD

ASCA


0.1

1

10

0.1 1 10 100Companion Mass (M◎)

Does the Magnetic Field Decay?

B (

1012

G)

τ=10

6 yr

τ=10

7 yr

τ=10

8 yrτ=

109 y

r

1626-67

0115-631538-52

Vela X-1 Cen X-3

1907-09

Her X-10331+53

GX302-1

A0535+26

Cep X-4

Half Lifetime in the Main Sequence (yr)

107 106 1051010 108109

A fast field decay is unlikely.

New radio-pulsar statistics support field-non-decay hypothesis (Itoh et al. Astrophys. J. 455, 244; 1995)


1.The field decay occurs on a very long time scale. → difficult to explain the weak-field NSs.

2.Strong-field and weak-field NSs are 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.

The Origin and Evolution of NS Magnetic Field〜 An alternative scenario 〜

+ -N S


Ferro-magnetic and para-magnetic NSs?

A small volume fraction (~10-3) is ferro-magnetic → strong-field NSs (1012 G) ?

Entirely para-magnetic → weak-filed NSs ( ＜ 108~9 G) ?

Phase transitions may occur depending on, e.g., age, temperature, accretion history, etc.

A large fraction of the volume is ferro-magnetic → magnetars (1014~15 G) ?

The release of latent heat at the transition may explain some soft gamma-ray repeaters?

N S

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 〜 4×1016 G.


Magnetars?

SGR 1806-20

Ibrahim et al., Astrophys. J. 574, L51 (2002)

Is this soft γ-ray repeater a “magnetar” with B ~ 1015 G, and the burst energy is supplied by magnetic phase transitions ?

We urgently need to search for objects with B~ 1014 G → electron CRSF at ~100 keV

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


The Hard X-ray Detector (HXD) Experiment onboard ASTRO-E2

Unprecedented sensitivity in 10~600 ke

VASTRO-E2 Scheduled for launch in 2005


Summary

1.X-ray observations are uncovering interesting inference that the magnetic field of NSs is sustained by nuclear ferro-magnetism

2.Theoretical studies of magnetic phase diagram of nuclear matter is encouraged.

3.Search for cyclotron resonances in the ~100 keV energy range is an important task.

Documents

Jan. 6, 2003Tokyo-Adelaide Conference Measuring Magnetic Fields of Neutron Stars Kazuo Makishima Department of Physics, University of Tokyo [email protected]