The Absorption Features in X-ray Emission

from Isolated Neutron Stars

2004 / 04 / 15

Assumptions & Global Model

Gravitation Effect (see Isothermal NS Case)

Canonical Model & Line profile

INS: 1E 1207.4-5209

Results & Discussions

OH MY!! What’s going on??

Outline

Lensing Red-shift

Strong M field Effect

Anisotropy of the surface temperature Beaming

Assumption

Spherical symmetry typical neutron star.

Photons are emitted from the surface of an opaque sphere.

LTE: Iν= Bν.

Global modelChanging coordinate

Z axisθθ

θmθm

Magnetic Axis

θbθb

θpθpSurface normal

Magnetic Axis

Rotation Axis

θθ00

ββ

γγ

Flux(t): (Lightcurve)∫I(t) cosθ’ dΩ’

Spec.:∫Iν(t) cosθ’ dΩ’

∫Iν(t) cosθ ’ dt dΩ’

Note: cosθ’ isqual to 1

Gravitational Effects

Self-Lensing

Gravitational redshift

5.05.02122

RM

R/M M/R4

0.25e30 0

1

2

4ddB

ddB

Relative total flux v.s ωt

R/M M/R

40.25

e30 0

15.0)5.01log(21log

R

M

ν’ ν

dB

1

2

3dB ν ’ ν

Relative specific flux v.s Freq.

Strong Magnetic field effects• Anisotropy of the surface temperature

• Beaming ( In magnetized electron-ion plasma, the scattering and

free-free absorption opacities depend on the direction of propagation and the normal modes of EM waves) Dong Lai etc. MNRAS 327,1081 2001

core

envelope

atmosphereνcyclotron

=eB/2πme

K

Ion cyclotron resonance occurs whenThe E field of the mode rotates in the same direction as the ion gyration

4 22 )(sin0264.0)(cos02.1 bbeff TPT

Heyl etc. MNRA 324,292 2001Best-fitting model for (a*cos 2θ +b*sin 2θ) for 1012G

4effTFlux

Relative T v.s. θb

Isotropic :

Iν ( T1)

Iν ( T2)

Iν ( T3)

Iν ( T4) Iν ( T5) Iν ( T4)

Iν ( T3)

Iν ( T2)

Iν ( T1)T 1 = T eff

Iν ( T1)

Iν ( T1)

Iν ( T1)

Iν ( T1)

Iν ( T1)

θbθb

4 cos cos

: assume

effbb TddIFluxtotal

BI

Harding etc. ApJ 500:862 1998 Pavlov etc. A&A 297,441 1995

Beaming due to B field :

B field

3D Angles…..|=.=|“

. .

θmθm

Magnetic Axis

θbθb

θpθp

Need to calculate Θm Θm θB_field θB_field surface surface temperaturetemperatureΘphoton Θphoton Limb-darkening Limb-darkeningθphoton&B_fieldθphoton&B_field Magnetic beaming Magnetic beaming

Surface normal

Canonical ModelM=1.4M⊙ R=10km T =1 secRs=2GM/C2 ~ 0.267R θMAX~132∘

1E1207.4-5209

XMM PN observationBignami et al. Nature 423:725 2003

Results

Simple Dipole Model Limb-darkening Model Magnetic Beaming Model

Cyclotron Resonance Lines

23

2

222

4

1

3

2 frequency) resonance sn' (the

)(

)(

nnn

nnTn

nn

mC

e

mC

eBn

eIf

Ex. B=1011Gauss @ pole

Binning

Photon number

Line profile in units of σ

Line (line1+line2) Conti.

0.5KeV 1KeV3x1017 Hz

5KeV

50 bin 50 bin

(Log Scale)

Given:1. Observing time2. Effective area3. Distance to the source

case continuumin number photon ltheoretica:

case linein number photon ltheoretica:

conti

line

line

contiline

N

N

N

NN

N~106

Stellar absorption by NH~1021cm-2

N~103

Numerical Results Observation

0.2~4KeV

208,000 photons

& Lack of photon ~1KeV and higher energy

Note that although we lack of photon at ~ 1KeV and higher energy (“lack” means in our calculus, the theoretical photon number is lower than “1” photon), we can still calculate the residual in units of σ

40:25

~102 :1

As a reasonable try , we multiply 103 in each bin to get a similar total photon number with observation.

The ratio of the first line and the second line is even worse. (about 103:1)

DiscussionOur results show that a direct approach to reproduce the line features for 1E1207.4-5209is not work well. Photon number problem The photon number problem might be solved

by higher temperature in polar cap or the larger neutron star radius in our model.

Ratio problem The ratio problem is essentially difficult to

solved for our considerations.