1. Thermal Emission from Isolated Neutron Stars and their surface magnetic field: going quadrupolar? Silvia Zane, MSSL, UCL, UK 35 th 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.

2. X-ray Pulsating Dim Isolated Neutron Star: 4 so far!  Soft X-ray sources in ROSAT survey  BB-like X-ray spectra, no non thermal hard emission  Low absorption, nearby (N H ~10 19 -10 20 cm -2 )  Constant X-ray flux over ~ years: BUT 0720!  No radio emission ?  No obvious association with SNR  Optically faint

3. 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)

4. Long term variations in RXJ 0720 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.

5. 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. No if we just assume isotropic (bb-like) emission + a dipolar B-field. Can pulsed fraction, skewness, time variations be Can pulsed fraction, skewness, time variations be explained in term of surface thermal emission? Greenstein and Hartke, 1983

6. In theory: 2) Computing atmospheric models at different magnetic inclinations 1) Assuming B-field topology and computing surface temperature profile 3) Ray-tracing in the strong gravitational field. + + = 4) Predicting: a) lc and b) spin variation of the line parameters! GOAL: probe the surface properties of the NS via timing and pulse-phase spectroscopy of cyclotron lines !  = 0 ˚  = 40 ˚  = 80 ˚

7. 1: Fix a given dipolar + quadrupolar configuration and compute consistently the thermal map of the surface We can fix 7 parameters and “see” the rotation of the thermal surface: b quad i = B quad i /B dip i=0,…4  = angle between LOS and spin axis  = angle between magnetic and spin axis

8. 2: build an archive of Atmospheric models at different T, B,  (magnetic inclination angle) By using the matrix I we can associate at every patch of the neutron star surface the frequency dependent emissivity. First compute all models spanning (so far!): Then interpolate on a common grid and store the 6-D matrix:

9.  , , B i quad i=0…4:   (phase):    (coord. angles): Compute radial, polar and tangential components of B Integrate over the portion of the surface visible at Earth PHASE DEP. SPECTRUM Integrate over E LIGHT CURVE Compute ,  = photon angles (GR!) 1) | B | 2) cos  = B  n 3) T = T_ pol sqrt(cos  ) Interpolate I(E, , , T, B,  )

10. Effects of radiative beaming: B dip = 6 x 10 12 G T pol = 2.5 MK B 0 quad =0.5 Bdip B 2 quad =0.9 Bdip  = 90  = 30, 60, 90

11. 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 (z i ) (instead of 32 phases) The first 4 z i s account for 85 % of the total variance! z 1 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 B quad, ,  (non linear dependence.. Regression method does not work)

12. Can we identify families of “similar” curves in the parameter space? Cluster analysis.

13. Using the Principal Component’s space 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 From PCA we get the matrix Cij z i = C ij y j y j = observed intensity at phase  j

14. Reproducing the observed lc’s: excellents fits for RXJ 0806 and RXJ 0420 Reproducing the observed lc’s: excellents fits for RXJ 0806 and RXJ 0420 Epic-PN lc of RXJ 0806, rev 618 (April 2003). (0.12-1.2 keV). Haberl et al, 2004 B 0 quad = -0.47 Bdip  = 0.06 B 1 quad = 0.11 Bdip  = 0.04 B 2 quad = -0.33 Bdip  = 0.03 B 3 quad = 0.44 Bdip  = 0.01 B 4 quad = -0.17 Bdip  = 0.02  = 44.9  = 1.6  = 90.6  = 1.2 Epic-PN lc of RXJ 0806, rev 570 (Jan 2003). (0.12-0.7 keV). Haberl et al, 2004 B 0 quad = 0.44 Bdip  = 0.06 B 1 quad = -0.36 Bdip  = 0.06 B 2 quad = 0.03 Bdip  = 0.06 B 3 quad = -0.42 Bdip  = 0.06 B 4 quad = 0.37 Bdip  = 0.06  = 58.1  = 2.3  = 0.0  = 0.1  2 = 0.002

15. Reproducing the observed lc’s: 1223 illustrates the degeneracy Epic-PN lc of RXJ 1223, rev. 561 (Jan 2003). (0.12-0.5 keV). Haberl et al, 2003 Fit 1: B 0 quad = 0.07 Bdip  = 0.02 B 1 quad = -0.08 Bdip  = 0.02 B 2 quad = 0.53 Bdip  = 0.03 B 3 quad = 0.45 Bdip  = 0.02 B 4 quad = 0.52 Bdip  = 0.02  = 98.2  = 1.2  = 0.1  = 0.2  2 = 0.02 Fit 2: B 0 quad = -1.27 Bdip  = 0.31 B 1 quad = 0.95 Bdip  = 0.12 B 2 quad = 1.00 Bdip  = 0.12 B 3 quad = 0.43 Bdip  = 0.12 B 4 quad = -0.11 Bdip  = 0.12  = 58.6  = 4.5  = 80.9  = 3.3  2= 0.007

16. Reproducing the observed lc’s: what about the variations of 0720? Rev. 78:  2= 0.001 B 0 quad = 0.32 Bdip  = 0.03 B 1 quad = 0.45 Bdip  = 0.01 B 2 quad = -0.21 Bdip  = 0.03 B 3 quad = -0.28 Bdip  = 0.03 B 4 quad = -0.48 Bdip  = 0.02  = 70.2  = 0.9  = 5.6  = 2.1 Rev. 711:  2= 0.02 B 0 quad = 0.38 Bdip  = 0.04 B 1 quad = 0.50 Bdip  = 0.04 B 2 quad = -0.06 Bdip  = 0.04 B 3 quad = -0.08 Bdip  = 0.04 B 4 quad = -0.20 Bdip  = 0.02  = 95.2  = 3.6  = 0.1  = 0.8 Rev. 78 From Rev 78 to Rev 711,   only From Rev 78 to Rev 711, B i quad only Rev 711

17. Summary Source | B/B| | B tot quad /B dip |  (degrees)  (degrees) 22 RX J0806 0.800.0258.20.002 RX J0420 0.7544.990.10.002 RBS 1223 0.870.098.30.02 RX J0720 (rev. 78) 0.815.670.20.001 0.660.190.00.02

18. 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!