PowerPoint Presentation - Isolated Neutron Stars_ solid crust by sdfwerte

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									   Thermal Emission from Isolated Neutron Stars
and their surface magnetic field: going quadrupolar?
                     Silvia Zane, MSSL, UCL, UK
         35th   Cospar Symposium - Paris, 18-25 July 2004


 Dim Isolated neutron stars
 are key in compact objects
 astrophysics: these are the
 only sources in which we can
 see directly the “surface” of
 the compact star.

  If pulsations and/or long term variations are detected:

   Study the shape and evolution of the pulse profile of
  the thermal emission

   Information about the thermal and magnetic map of
  the star surface.
X-ray Pulsating Dim Isolated Neutron Star:
                 4 so far!
 OBJECT                 KT/eV   P/ s       SEMIAMPL.   OPT.
 RX J0420.0-5022        44      3.45       12%         B>25.5
 RX J0720.4-3125        85      8.39       11%         B=26.6
 RX J0806.4-4123        96      11.37      6%          B>24
 RBS 1223               86      10.31      18%         m=28.6
 RBS 1556               96                             m=26.8
 RX J1856.5-3754        60                 <1%         V=25.7
 RBS 1774               (90)                           R>23

 RX J1836.2+5925 ?      (43)                           V>25.2
 (variable?)
           Soft X-ray sources in ROSAT survey
           BB-like X-ray spectra, no non thermal hard emission
           Low absorption, nearby (NH ~1019-1020 cm-2)
           Constant X-ray flux over ~years: BUT 0720!
           No radio emission ?
           No obvious association with SNR
           Optically faint
   Pulsating neutron stars: 4 so far!
1) LC’s may be asymmetric (skewness)

2) Relatively large pulsed fractions: 12%-35%

3) All cases: hardness ratio is max at the pulse
   maximum: counter-intuitive!
      Beaming effects ? (Cropper et al. 2001)
      Phase-dependent cyclotron absorption?
          (Haberl et al., 2003)
              Multiple abs. lines observed in 1E1207.4-5209
              are more important at the light curve trough.
              The peak of the total light curve corresponds
              to the phase-interval where lines are at their
              minimum.
                               (Bignami et al., 2003, Nature)
  Long term variations in RXJ 0720
                                             De Vries et al., 2004
                                             Vink, et al, 2004


A gradual, long term change in
the shape of the X-ray
spectrum AND in the pulse
profile

From rev. 78 (13 May 2000) to
rev.711 (27-10-2003) the
pulse profile become narrower
and the pulsed fraction
increases from ~20% to ~ 35%



   Pulse profile of 0720 in the 0.1-1.2 keV band and hardness ratio.
   The best sinusoidal fit to rev. 0078 (solid line) is overplotted on the
   light curve of rev. 0711 for comparison.
   Can pulsed fraction, skewness, time variations be
   explained in term of surface thermal emission?
                                                Greenstein and Hartke, 1983
    No if we just assume
    isotropic (bb-like) emission
    + a dipolar B-field.


         K  (4  K ) cos 2 
T ( ) 
            1  3 cos 2 
Relatively large pulsed fraction (up to 20%) are achieved accounting for:

 Shibanov et al, 1995: radiative beaming (atmo models and field assumed
dipolar)
 Page, D. 1995, Page and Sarmiento, 1996: quadrupolar B- components
(emission assumed bb-like and isotropic)


Can we account for both effects today?
          Zane, Turolla, et al, 2004 in prep.
                           In theory:
1) Assuming B-field         2) Computing atmospheric        3) Ray-tracing in
topology and computing      models at different             the strong
surface temperature         magnetic inclinations           gravitational field.
profile

                                             = 0˚
                                              = 40˚
                       +                       = 80˚   +



   GOAL: probe the                                                  =
   surface
   properties of the                                    4) Predicting:
   NS via timing and
                                                        a) lc and b) spin
   pulse-phase
   spectroscopy of                                      variation of the
   cyclotron lines!                                     line parameters!
1: Fix a given dipolar + quadrupolar
                                       T  Tpol cos
configuration and compute consistently           
the thermal map of the surface         cos  B  n




   We can fix 7 parameters and “see” the rotation of the thermal surface:
             b quadi = Bquadi /Bdip   i=0,…4
              = angle between LOS and spin axis
              = angle between magnetic and spin axis
2: build an archive of Atmospheric models at
different T, B,  (magnetic inclination angle)

First compute all models
spanning (so far!):
  0.01keV  E  10keV                     Then interpolate on a
                                          common grid and store
  0   , cos  1                        the 6-D matrix:
  0    2
  5.4  log T  6.6                       I  E ,  ,  , T , B,  
  12  log B  13.5

      By using the matrix I we can associate at every patch of the
      neutron star surface the frequency dependent emissivity.
 , , B i quad i=0…4:
             (phase):
                 (coord. angles):


              Compute radial, polar and          Compute ,  =
              tangential components of B         photon angles (GR!)

                     1) | B |
                     2) cos  = B  n
Integrate over       3) T = T_pol sqrt(cos  )
the portion of
the surface
visible at Earth                 Interpolate I(E, , , T, B, )


  PHASE DEP. SPECTRUM

                       Integrate over E             LIGHT CURVE
     Effects of radiative beaming:

Bdip = 6 x 1012 G
Tpol = 2.5 MK
B0quad =0.5 Bdip
B2quad =0.9 Bdip
 = 90
 = 30, 60, 90
        Principal Component analysis.
        A grid of 78000 models varying Bquad_i
        and the LOS, magnetic angles
Tipically lc’s are reproduced using only
the first ~20-21 more significant PCs
(zi) (instead of 32 phases)

The first 4 zis account for 85 % of
the total variance!

z1 easy meaning = mean value of the lc

Different def of “distance” used in
the PC’s space

BUT it is difficult to relate the PCs to
the physical variables Bquad, , 
(non linear dependence.. Regression
method does not work)
Can we identify families of “similar”
curves in the parameter space?
Cluster analysis.
  Using the Principal Component’s space

From PCA we get the matrix Cij

           zi = Cij yj

yj= observed intensity at phase j


For every observed LC we can
compute the PC’s!

Does it make sense to try a fit?

If so, from the nearest lc in the
PC’s space we obtain a “good”
trial lc
     Reproducing the observed lc’s:
excellents fits for RXJ 0806 and RXJ 0420




Epic-PN lc of RXJ 0806, rev 618 (April       Epic-PN lc of RXJ 0806, rev 570 (Jan 2003).
2003). (0.12-1.2 keV). Haberl et al, 2004    (0.12-0.7 keV). Haberl et al, 2004


B0quad = 0.44 Bdip     = 0.06                    B0quad = -0.47 Bdip    = 0.06
B1quad = -0.36 Bdip    = 0.06                    B1quad = 0.11 Bdip     = 0.04
B2quad = 0.03 Bdip     = 0.06                    B2quad = -0.33 Bdip    = 0.03
B3quad = -0.42 Bdip    = 0.06                    B3quad = 0.44 Bdip     = 0.01
B4quad = 0.37 Bdip     = 0.06                    B4quad = -0.17 Bdip    = 0.02

 = 58.1    = 2.3                                 = 44.9    = 1.6
 = 0.0     = 0.1               2= 0.002         = 90.6    = 1.2               2= 0.002
     Reproducing the observed lc’s:
     1223 illustrates the degeneracy
                                               Fit 1:

                                               B0quad = 0.07 Bdip       = 0.02
                                               B1quad = -0.08 Bdip      = 0.02
                                               B2quad = 0.53 Bdip       = 0.03
                                               B3quad = 0.45 Bdip       = 0.02
                                               B4quad = 0.52 Bdip       = 0.02

                                                = 98.2     = 1.2
                                               = 0.1       = 0.2

                                               2= 0.02

                                               Fit 2:

                                               B0quad = -1.27 Bdip      = 0.31
                                               B1quad = 0.95 Bdip       = 0.12
Epic-PN lc of RXJ 1223, rev. 561 (Jan 2003).   B2quad = 1.00 Bdip       = 0.12
(0.12-0.5 keV). Haberl et al, 2003             B3quad = 0.43 Bdip       = 0.12
                                               B4quad = -0.11 Bdip      = 0.12

                                                = 58.6       = 4.5
                                                = 80.9       = 3.3

                                               2= 0.007
       Reproducing the observed lc’s:
       what about the variations of 0720?
Rev. 78                 From Rev 78 to      Rev. 78:               2= 0.001
                        Rev 711,   only
                                            B0quad = 0.32 Bdip  = 0.03
                                            B1quad = 0.45 Bdip  = 0.01
                                            B2quad = -0.21 Bdip  = 0.03
                                            B3quad = -0.28 Bdip  = 0.03
                                            B4quad = -0.48 Bdip  = 0.02

                                             = 70.2     = 0.9
                                            = 5.6       = 2.1

From Rev 78 to                              Rev. 711:               2= 0.02
Rev 711, Biquad only   Rev 711
                                            B0quad = 0.38 Bdip  = 0.04
                                            B1quad = 0.50 Bdip  = 0.04
                                            B2quad = -0.06 Bdip  = 0.04
                                            B3quad = -0.08 Bdip  = 0.04
                                            B4quad = -0.20 Bdip  = 0.02

                                             = 95.2     = 3.6
                                             = 0.1       = 0.8
                      Summary


Source      | Btotquad/Bdip|  (degrees)    (degrees)   2


RX J0806    0.80            0.02           58.2          0.002


RX J0420    0.75            44.9           90.1          0.002


RBS 1223    0.87            0.0            98.3          0.02


RX J0720    0.81            5.6            70.2          0.001
(rev. 78)
RX J0720    0.66            0.1            90.0          0.02
(rev. 78)
        Summary and Future work

 We can reproduce a single observed lc’s with a combination
of quadrupolar B-field components and viewing angles

 But although in most cases this fit certainly exists, it is in
general not unique: degeneracy and non-linear dependence on
physical variables !

 Therefore, it is difficult to reproduce variations observed
in a single source

 Reduce the degeneracy:

           a)   learning more about the clustering of models

           b)   looking at the lc’s in different colour bands
                and/or line variations with spin pulse

                       Need to increase the grid of models!

								
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