Thermal Emission from Isolated Neutron Thermal Emission from Isolated Neutron StarsStarsand their surface magnetic field: going quadrupolar?and their surface magnetic field: going quadrupolar?

Silvia Zane, MSSL, UCL, UK35th 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 X-ray Pulsating Dim Isolated Neutron Star: Star: 4 so far! 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

Pulsating neutron stars: 4 so Pulsating neutron stars: 4 so far!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 Long term variations in RXJ 07200720

De Vries et al., 2004Vink, 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.

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.

ϑϑϑ

2

2

cos31

cos)4()(

+

−+∝

KKT

Can pulsed fraction, skewness, time Can pulsed fraction, skewness, time variations be variations be explained in term of surface thermal emission? Greenstein and Hartke, 1983

In theory: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˚

1: Fix a given dipolar + 1: Fix a given dipolar + quadrupolar configuration and quadrupolar configuration and compute consistently the compute consistently the thermal map of the surfacethermal map of the surface

We can fix 7 parameters and “see” the rotation of the thermal surface: b quad

i = Bquadi /Bdip i=0,…4

= angle between LOS and spin axis = angle between magnetic and spin axis

nB

TT pol

rr⋅=

=

α

α

cos

cos

2: build an archive of Atmospheric 2: build an archive of Atmospheric models at different T, B, models at different T, B, αα (magnetic (magnetic inclination angle)inclination angle)

( )αφμ ,,,,, BTEI

By using the matrix I we can associate at every patch of the neutron star surface the frequency dependent emissivity.

5.13log12

6.6log4.5

20

1cos,0

1001.0

≤≤≤≤

≤≤≤≤≤≤

BT

keVEkeV

πφαμ

First compute all models spanning (so far!):

Then interpolate on a common grid and store the 6-D matrix:

, , B i quad i=0…4:

(phase):

φ (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 μ, = photon angles (GR!)

1) | B |2) cos α = B n3) T = T_pol sqrt(cos α )

Interpolate I(E, μ, , T, B, α)

Effects of radiative Effects of radiative beaming:beaming:

Bdip = 6 x 1012 GTpol = 2.5 MKB0

quad =0.5 BdipB2

quad =0.9 Bdip = 90 = 30, 60, 90

Principal Component analysis.Principal Component analysis.A grid of 78000 models varying A grid of 78000 models varying Bquad_i and the LOS, magnetic Bquad_i and the LOS, magnetic anglesangles

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

Using the Principal Component’s Using the Principal Component’s spacespace

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

zi = Cij yj

yj= observed intensity at phase j

Reproducing the observed lc’s:Reproducing the observed lc’s:excellents fits for RXJ 0806 and RXJ excellents fits for RXJ 0806 and RXJ 04200420

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

B0quad = -0.47 Bdip = 0.06B1quad = 0.11 Bdip = 0.04B2quad = -0.33 Bdip = 0.03B3quad = 0.44 Bdip = 0.01B4quad = -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

B0quad = 0.44 Bdip = 0.06 B1quad = -0.36 Bdip = 0.06B2quad = 0.03 Bdip = 0.06B3quad = -0.42 Bdip = 0.06B4quad = 0.37 Bdip = 0.06

= 58.1 = 2.3 = 0.0 = 0.1 2= 0.0022= 0.002

Reproducing the observed Reproducing the observed lc’s:lc’s:1223 illustrates the 1223 illustrates the degeneracydegeneracy

Epic-PN lc of RXJ 1223, rev. 561 (Jan 2003). (0.12-0.5 keV). Haberl et al, 2003

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= 0.02Fit 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

Reproducing the observed lc’s:Reproducing the observed lc’s:what about the variations of what about the variations of 0720?0720?

Rev. 78: 2= 0.001

B0quad = 0.32 Bdip = 0.03 B1quad = 0.45 Bdip = 0.01B2quad = -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

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. 78 From Rev 78 to Rev 711, only

From Rev 78 to Rev 711, Bi

quad only Rev 711

SummarSummaryy

SourceSource | B| Btotquad/B/Bdip|| (degrees)(degrees) (degrees)(degrees) 2

RX J0806RX J0806 0.800.80 0.020.02 58.258.2 0.0020.002

RX J0420RX J0420 0.750.75 44.944.9 90.190.1 0.0020.002

RBS 1223RBS 1223 0.870.87 0.00.0 98.398.3 0.020.02

RX J0720 RX J0720 (rev. 78) (rev. 78)

0.810.81 5.65.6 70.270.2 0.0010.001

RX J0720 RX J0720 (rev. 78)(rev. 78)

0.660.66 0.10.1 90.090.0 0.020.02

Summary and Future Summary and Future workwork

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!