1. Jan. 6, 2003Tokyo-Adelaide Conference Measuring Magnetic Fields of Neutron Stars Kazuo Makishima Department of Physics, University of Tokyo maxima@phys.s.u-tokyo.ac.jp “How the strong magnetic field of neutron stars is sustained, and how it evolves.”

2. Jan. 6, 2003Tokyo-Adelaide Conference 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

3. Jan. 6, 2003Tokyo-Adelaide Conference  All neutron stars are born with strong magnetic fields ( 〜 10 12 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 〜 10 7 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 〜 + -

4. Jan. 6, 2003Tokyo-Adelaide Conference Surface Magnetic Field (G) 0.001 0.01 0.1 1 10 100 1000 Rotation Period (sec) 10 15 10 14 10 13 10 12 10 11 10 9 Msec Pulsars Radio Pulsars Binary X-ray Pulsars Magnetars? Crab-like Pulsars NS Populations

5. Jan. 6, 2003Tokyo-Adelaide Conference Estimates of NS Magnetic Fields (1) A simple-minded estimate; flux conservation from the progenitor star R 〜 10 9 m, B 〜 10 2 G → R 〜 10 4 m, B 〜 10 12 G (2) Assuming –d( I ω 2 /2)/dt = mag. dipole radiation; → B ∝ sqrt(P dP/dt) 〜 10 11~13 G (3) Detection of X-ray spectral features due to (electron) cyclotron resonance ; E a = heB/2πm e = 11.6 (B/10 12 G) keV

6. Jan. 6, 2003Tokyo-Adelaide Conference 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 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 Scattering Feature (CRSF).

7. Jan. 6, 2003Tokyo-Adelaide Conference 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

8. Jan. 6, 2003Tokyo-Adelaide Conference 1 2 5 10 20 50 100 Energy (keV) Counts/s/cm 2 /keV  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 CRSFs Before 1990, only two examples were observed (e.g., Truemper et al. 1978, Astrophys. J. 219, L105; 1978) E r = 28 keV → B = 2.4×10 12 G

9. Jan. 6, 2003Tokyo-Adelaide Conference Discoveries of CRSFs with Ginga Makishima et al. Astrophys. J. 525, 978 (1999) E r =33 keV E r =28 keV E r =29 keV E r =21 keV 12 & 23 keV No CRSF Her X-1 X0331+53 Cep X-4 4U 1538-52 4U 0115+63SMC X-1

10. Jan. 6, 2003Tokyo-Adelaide Conference 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 HEXTE f (E) = (aE -p + bE +q ) × exp(-E /kT) × exp(-S ) S =E 2 /{(E-E r ) 2 +W 2 } Makishima et al. (1999) Fit residuals w/o exp{-S} Fit residuals with exp{-S}

11. Jan. 6, 2003Tokyo-Adelaide Conference Observatoins with BeppoSAX 4 harmonics in 4U 0115+63 Santangelo et al. Astrophys. J. 523, L85 (1998) Fundamental and 2nd harmonic in 4U 1909+07 Cusmano et al. Astron. Astrophys 338, 79 (1998) 10 20 30 50 1001 2 5 10 20 50 Energy (keV)

12. Jan. 6, 2003Tokyo-Adelaide Conference EnergyEcEc ErEr Cyclotron Resonances and the Spectral Continuum E r =1.7 E c Even if CRSF is not detected, we can estimate the field intensity from the X- ray continuum shape

13. Jan. 6, 2003Tokyo-Adelaide Conference Distribution of Magnetic Field 0 2 4 6 8 10 Cyclotron Resonance Energy (keV) Number 10100 202 550 log[ B /(1+z )] (Gauss) 12 13  Surface magnetic fields of 〜 15 binary X-ray pulsars are tightly concentrated over (1- 4)×10 12 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. BeppoSAX Ginga RXTE ASTRO-E2 HXD ASCA

14. Jan. 6, 2003Tokyo-Adelaide Conference 0.1 1 10 0.1110100 Companion Mass (M ◎ ) Does the Magnetic Field Decay? B (10 12 G) τ=10 6 yr τ=10 7 yr τ=10 8 yr τ=10 9 yr 1626-67 0115-63 1538-52 Vela X-1Cen X-3 1907-09 Her X-1 0331+53 GX302-1 A0535+26 Cep X-4 Half Lifetime in the Main Sequence (yr) 10 7 6 5 8 9  A fast field decay is unlikely.  New radio-pulsar statistics support field-non-decay hypothesis (Itoh et al. Astrophys. J. 455, 244; 1995)

15. Jan. 6, 2003Tokyo-Adelaide Conference 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

16. Jan. 6, 2003Tokyo-Adelaide Conference Ferro-magnetic and para-magnetic NSs?  A small volume fraction (~10 -3 ) is ferro-magnetic → strong-field NSs (10 12 G) ?  Entirely para-magnetic → weak-filed NSs ( ＜ 10 8~9 G) ?  Phase transitions may occur depending on, e.g., age, temperature, accretion history, etc.  A large fraction of the volume is ferro-magnetic → magnetars (10 14~15 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 〜 4×10 16 G.

17. Jan. 6, 2003Tokyo-Adelaide Conference Magnetars? SGR 1806-20 Ibrahim et al., Astrophys. J. 574, L51 (2002)  Is this soft γ-ray repeater a “magnetar” with B ~ 10 15 G, and the burst energy is supplied by magnetic phase transitions ?  We urgently need to search for objects with B~ 10 14 G → electron CRSF at ~100 keV Proton cyclotron rsonance E = 6.3 (B/10 15 G) [keV]

18. Jan. 6, 2003Tokyo-Adelaide Conference The Hard X-ray Detector (HXD) Experiment onboard ASTRO-E2 Unprecedented sensitivity in 10~600 keV ASTRO-E2 Scheduled for launch in 2005

19. Jan. 6, 2003Tokyo-Adelaide Conference 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.