Measuring Magnetic Fields of Neutron Stars

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					   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.”

  Jan. 6, 2003         Tokyo-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
Jan. 6, 2003       Tokyo-Adelaide Conference
  The Origin and Evolution of NS Magnetic Field
        〜A scenario before the 1990s 〜
 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.
    Jan. 6, 2003    Tokyo-Adelaide Conference
                                 15
                                               NS Populations
                            10
    Surface Magnetic Field (G)
                            10
                                 14                               Magnetars?
                                          Crab-like Pulsars
                                 13
                            10

                                 12                  Binary X-ray Pulsars
                            10

                            10
                                 11
                                                  Radio
                                 10
                                                  Pulsars
                            10
                                 9
                            10           Msec
                                         Pulsars          Rotation Period (sec)
                                 0.001     0.01     0.1     1       10    100   1000
Jan. 6, 2003                                  Tokyo-Adelaide Conference
     Estimates of NS Magnetic Fields
(1) A simple-minded estimate;
  flux conservation from the progenitor star
            9           2                 4                12
  R〜10 m, B〜10 G → R〜10 m, B〜10 G
                            2
(2) Assuming –d(Iω /2)/dt = mag. dipole radiation;
                                               11~13
       →         B ∝ sqrt(P dP/dt) 〜 10                G
(3) Detection of X-ray spectral features due to
  (electron) cyclotron resonance ;
                                          12
      Ea = heB/2πme = 11.6 (B/10 G) keV
  Jan. 6, 2003         Tokyo-Adelaide Conference
An Accretion-Powered Binary X-ray Pulsar
                A supersonic accretion      A strongly magnetized
                flow from companion
                                            NS with a rotation period
                                            of 0.1〜1000 sec, in a
                                            close binary with a mass-
                                            donating companion star.
                            A standing
                            shock
                             Electrons in the accretion column
 An X-ray                    resonantly scatter X-ray photons,
 emitting hot                when they make transitions
 (kT~20                      between adjacent Landau levels.
 keV)
 accretion                   → The X-ray spectrum will bear a
 A strongly                  strong spectral feature, called a
 column
 magnetized NS               Cyclotron Resonance Scattering
                             Feature (CRSF).
 Jan. 6, 2003           Tokyo-Adelaide Conference
    Cosmic X-ray Studies in Japan




ASCA (Advanced Satellite for ASTRO-E2 Scheduled
Cosmology & Astrophysics)
1993.2〜2000.7                for launch in 2005
                                                   M-5 launch
                                                   vehicle of ISAS




  Ginga (Galaxy)            Tenma (Pegasus)
  1987.2〜1991.10            1983.2〜1984.8          Hakucho (Cygnus)
                                                   1979.2〜1984.4
      Jan. 6, 2003     Tokyo-Adelaide Conference
                        X-ray Observations of CRSFs
        Before 1990, only two examples were observed
        (e.g., Truemper et al. 1978, Astrophys. J. 219, L105; 1978)

                                                                  A series of dis-
                                                                   coveries with the
Counts/s/cm2/keV




                                                                   Ginga Satellite
                                                                   (1987-1991)
                                                                  A transient X-ray
                                                                   pulsar X0331+53
                        Er = 28 keV →                              Makishima et al.
                                                                   Astrophys. J. 365,
                        B = 2.4×1012 G                             L59 (1990)
                    1      2      5    10      20       50 100
                                  Energy (keV)
                   Jan. 6, 2003       Tokyo-Adelaide Conference
      Discoveries of CRSFs with Ginga
        Her X-1          X0331+53              Cep X-4


    Er=33               Er=28                 Er=29
     keV                 keV                   keV



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


                        12 &
    Er=21                23                    No
     keV                keV                   CRSF



   Makishima et al. Astrophys. J. 525, 978 (1999)
Jan. 6, 2003      Tokyo-Adelaide Conference
Observatoins with the Rossi X-ray Timing Explorer

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


                                                     f (E) = (aE -p + bE +q)
                                                     ×exp(-E /kT)
                                                        × exp(-S )

    Fit residuals with exp{-S}                       S =E 2/{(E-Er)2+W 2 }
     Fit residuals w/o exp{-S}                       Makishima et al.
                                                     (1999)


   Jan. 6, 2003          Tokyo-Adelaide Conference
                    Observatoins with BeppoSAX




                                               Fundamental and
4 harmonics                                    2nd harmonic in
in 4U 0115+63                                  4U 1909+07
Santangelo et al.                              Cusmano et al.
Astrophys. J.                                  Astron. Astrophys
523, L85 (1998)                                338, 79 (1998)

10       20         30   50         100    1    2         5   10   20   50
                         Energy (keV)
     Jan. 6, 2003             Tokyo-Adelaide Conference
Cyclotron Resonances and the Spectral Continuum
Cyclotron Resonance Energy Er (keV)


                                      60
                                                                              A0535+26
                                      50
                                                                              4U1626-67
                                      40
                                                                  GX301-2
                                                                                 Her X-1
                                      30                   X0331+53
                                                                            Cep X-4
                                                                 Cen X-3      Vela X-1
                                                         4U1538-52
                                      20
                                                                 4U1907+09                       Energy     Ec Er
                                                         4U0115+63 (1991)
                                                      4U0115+63(1990)                         Even if CRSF is not
                                      10                                                      detected, we can
                                           6      8      10                 20           30   estimate the field
                                               Cutoff Energy Ec (keV)                         intensity from the X-
                                                                                              ray continuum shape
                          Jan. 6, 2003                        Tokyo-Adelaide Conference
          Distribution of Magnetic Field
                                     Surface magnetic fields of
          log[ B /(1+z )] (Gauss)
                 12           13      〜15 binary X-ray pulsars
    10                                are
                               BeppoSAX tightly12 concentrated over
       Ginga                  RXTE    (1-4)×10 G.
Number



     8
          ASCA             ASTRO-E2 CRSF is yet to be detected
                                      from the remaining 〜20
                           HXD
                                      binary X-ray pulsars, but the
     6                                continuum shape suggests
                                      that they have comparable
     4                                field intensities.
                                     Higher-field side of the
     2                                distribution may be subject
                                      to selection effects. → The
                                      Hard X-ray Detector (HXD)
     0 2                              onboard ASTRO-E2 (laumch
             5 10 20 50 100
   Cyclotron Resonance Energy (keV)   in 2005) is of great value.
         Jan. 6, 2003   Tokyo-Adelaide Conference
            Does the Magnetic Field Decay?
                         10

A fast field decay                                                           A0535+26




                    B (1012G)
                                  1626-67                                       GX302-1
                                                     Her X-1
 is unlikely.                                                      0331+53
                                                               Cep X-4     Vela X-1    Cen X-3
                                                                 1907-09
 New radio-pulsar                                               0115-63
                                                                            1538-52

 statistics support 1
 field-non-decay
 hypothesis (Itoh et
 al. Astrophys. J.                    Half Lifetime in the Main Sequence (yr)
 455, 244; 1995)                             1010       109    108      107      106      105
                        0.10.1                      1                 10                    100
                                            Companion Mass (M◎)
     Jan. 6, 2003               Tokyo-Adelaide Conference
 The Origin and Evolution of NS Magnetic Field
          〜An alternative scenario 〜

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.                 + -


    Jan. 6, 2003   Tokyo-Adelaide Conference
   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〜 4×1016 G.
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?
    Jan. 6, 2003    Tokyo-Adelaide Conference
                                Proton cyclotron rsonance
Magnetars?                      E = 6.3 (B/1015G) [keV]
                                  Is this soft γ-ray
                                   repeater a
                                   “magnetar” with B ~
                                   1015 G, and the burst
                                   energy is supplied by
                                   magnetic phase
                                   transitions ?
            SGR 1806-20
                                  We urgently need to
        Ibrahim et al., Astrophys. search for objects
        J. 574, L51 (2002)         with B~ 1014 G →
                                   electron CRSF at
                                   ~100 keV

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




   Jan. 6, 2003   Tokyo-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.


    Jan. 6, 2003   Tokyo-Adelaide Conference

				
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