PowerPoint Presentation - Isolated Neutron Stars, solid crust

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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.

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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 (NH 1019-1020 cm-2)
• Constant X-ray flux over years BUT 0720!
• No radio emission ?
• No obvious association with SNR
• Optically faint

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Pulsating neutron stars 4 so far!

1. LCs 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)

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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.
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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.

• 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.

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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.


GOAL probe the surface properties of the NS via
timing and pulse-phase spectroscopy of cyclotron
lines!


4) Predicting a) lc and b) spin variation of
the line parameters!
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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 quadi
Bquadi /Bdip i0,4 ?
angle between LOS and spin axis
? angle between magnetic and spin axis
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2 build an archive of Atmospheric models at
different T, B, ? (magnetic inclination angle)
First compute all models spanning (so far!)
Then interpolate on a common grid and store the
6-D matrix
By using the matrix I we can associate at every
patch of the neutron star surface the frequency
dependent emissivity.
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? ?, ?, B i quad i04
? ? (phase)
? ? ? (coord. angles)
Compute ?, ? photon angles (GR!)
Compute radial, polar and tangential components
of B
1) B 2) cos ? B ? n 3) T T_pol
sqrt(cos ? )
Integrate over the portion of the surface
visible at Earth
Interpolate I(E, ?, ?, T, B, ?)
PHASE DEP. SPECTRUM
LIGHT CURVE
Integrate over E
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Effects of radiative beaming
Bdip 6 x 1012 G Tpol 2.5 MKB0quad 0.5
Bdip B2quad 0.9 Bdip ? 90 ? 30, 60, 90
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Principal Component analysis.A grid of 78000
models varying Bquad_i and the LOS, magnetic
angles
Tipically lcs 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 PCs space BUT it is difficult to
relate the PCs to the physical variables Bquad,
?, ? (non linear dependence.. Regression method
does not work)
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Can we identify families of similar curves in
the parameter space?Cluster analysis.
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Using the Principal Components 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 PCs!
Does it make sense to try a fit? If so, from
the nearest lc in the PCs space we obtain a
good trial lc
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Reproducing the observed lcsexcellents
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
Epic-PN lc of RXJ 0806, rev 570 (Jan 2003).
(0.12-0.7 keV). Haberl et al, 2004
B0quad -0.47 Bdip ? 0.06 B1quad 0.11
Bdip ? 0.04 B2quad -0.33 Bdip ?
0.03 B3quad 0.44 Bdip ? 0.01 B4quad
-0.17 Bdip ? 0.02 ? 44.9 ? 1.6 ?
90.6 ? 1.2
B0quad 0.44 Bdip ? 0.06 B1quad -0.36
Bdip ? 0.06 B2quad 0.03 Bdip ?
0.06 B3quad -0.42 Bdip ? 0.06 B4quad
0.37 Bdip ? 0.06 ? 58.1 ? 2.3 ?
0.0 ? 0.1
?2 0.002
?2 0.002
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Reproducing the observed lcs1223 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 B2quad 1.00 Bdip
? 0.12 B3quad 0.43 Bdip ? 0.12 B4quad
-0.11 Bdip ? 0.12 ? 58.6 ? 4.5
? 80.9 ? 3.3 ?2 0.007
Epic-PN lc of RXJ 1223, rev. 561 (Jan 2003).
(0.12-0.5 keV). Haberl et al, 2003
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Reproducing the observed lcswhat about the
variations of 0720?

• Rev. 78 ?2 0.001
• 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, ? ? only
Rev. 78
From Rev 78 to Rev 711, Biquad only
Rev. 711 ?2 0.02 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
Rev 711
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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 (rev. 78) 0.81 5.6 70.2 0.001
RX J0720 (rev. 78) 0.66 0.1 90.0 0.02
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Summary and Future work

• We can reproduce a single observed lcs 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

• learning more about the clustering of models
• looking at the lcs in different colour bands
  and/or line variations with spin pulse
• ? Need to increase the grid of
  models!