Model Spectra of Neutron Star Surface Thermal Emission Soccer 2005.4.21.

Model Spectra of Model Spectra of Neutron Star Surface Neutron Star Surface

Thermal Emission Thermal Emission

Model Spectra of Model Spectra of Neutron Star Surface Neutron Star Surface

Thermal Emission Thermal Emission

Soccer 2005.4.21

Outline

• The nonmagnetic field surface thermal emission model (finished)

• About 1E 1207-5209• The magnetic field surface thermal

emission model

Structure of neutron star atmosphere

Radiation transfer equation

Temperature correction

Flux ≠const

Flux = const SpectrumImproved Feautrier

Unsold Lucy process

Oppenheimer-VolkoffOppenheimer-Volkoff

The Nonmagnetic Field Surface Thermal Emission Model

Temperature profile after 20 times temperature correction

1.The result is different from those of others.

2.Adding correction times will let temperature profile diverge.

03

[3 ( ') ' 2 (0)]

4

J H R

P R P

HH d H

TT

J P

R R

dHJ B

d

The delT derived from Unsold-Lucy process


Frequency=1e17(Hz)

limb-darkening

Frequency=1e17(Hz)

Theta=0

Theta=0.628

The order of rho is similar with that of tau.

The spectra reveal limb-darkening and high energy tail and are different from Plank function significantly.

Physical depth

*

*

16 6

* 24 14

2

10 101

10 10

p

p

dP kTg P

dz m

P g z

kTz cmm g

z~1cm << R~10^6cm , thus the assumption of plane-parallel is good.


Different effective temperatures

Different gravitations

About 1E 1207-5209 In August 2002 by XMM-Newton from De Luca, Mereghetti, Caraveo, Moroni, Mignani, Bignami, 2004, ApJ 418.

supernova remnant G296.5+10.0

1E 1207.4-5209

Red represents photons in the 0.3-0.6 keV band, green and blue correspond to the 0.6-1.5 keV and 1.5-8 keV bands respectively.

P~424ms

P derivative~1.4*10-14ss-1

Figure 5: Fit of the phase-integrated data. The model (double blackbody plus line components) is described in the text. From top to bottom, the panels show data from the pn, the MOS1 and the MOS2 cameras. In each panel the data are compared to the model folded through the instrumental response (upper plot); the lower plot shows the residuals in units of sigma.

Figure 6: Residuals in units of sigma obtained by comparing the data with the best fit thermal continuum model. The presence of four absorption features at ~0.7 keV,~1.4 keV, ~2.1 keV and ~2.8 keV in the pn spectrum is evident. The three main features are also independently detected by the MOS1 and MOS2 cameras.

From pn: 0.68/0.24 : 1.36/0.18

Four absorption features have central energies colse to the ratio 1:2:3:4

About 1E 1207-5209

The feature is naturally explained by cyclotron absorption.

If these lines are caused by the electron or proton cyclotron resonance,

the magnetic filed are ~8*1010G or ~1.6*1014G, respectively.

But from the magneto-dipole braking assumption, B is about (2.6±0.3)*1012G.

About 1E 1207-5209

Other INSs have been detected with absorption features:

GEMINGA (Mignani et al. 1998, A&A, 332)

SGR 1806-20 (Ibrahim et al. 2002, ApJ, 574 & 2003, ApJ, 584)

AXP 1RXS J170849-400910 (Rea et al. 2003, ApJ, 586)

1RXS J130848.6+212708 (RBS 1223) (Haberl et al. 2003, A&A, 403)

RX J1605.3+3249 (Kerkwijk 2003, arXiv:astro-ph/0310389)

RX J0720.4-3125 (Haberl et al. 2003, arXiv:astro-ph/0312413)

Others….??

Ps: For neutron stars in binary systems, direct measures of the magnetic fields were reported by Trumper et al. in 1978.

GEMINGA (From HST and other telescopes during 1987 ~ 1996)

Fig. 1a-c. Ten-year evolution of the I-to-UV photometry of Geminga. a Situation in 1987, with 3 ground-based (CFHT, ESO 3.6m) points (R,V,B) clearly not compatible with a black-body curve (Bignami et al. 1988). b By the end of 1995, several points were added (see Bignami et al. 1996 where, indeed, a numerical error of a factor 4 is present in Figs. 2 and 3, where all the black-body fits should be revised downwards) both from the ground (I) and from HST (555W, 675W, 342W). c New HST/FOC data (430W, 195W) presented here. The lines shown represent best fit backbody curves to the ROSAT/EUVE data for an INS at d=157 pc (Caraveo et al. 1996). The two cases shown correspond to R=10 km and T=4.5e5 K (ROSAT 1991 fit-dotted) and to R=15 km and T= 2.5e5 K (EUVE fit-dashed). Note the absolute scale: no normaliz

ation has been performed.

An emission feature is at ~ 6000 Å, which is explained by the proton cyclotron emission close to the surface of a a neutron star.

Spectrum and best-fit continuum model for the second precursor interval, with

four absorption lines (RXTE/PCA, 2~30 keV). Bottom: Pulse-height spectrum with the model predicted counts (histogram). Top: Model (histogram) and the

estimated photon spectrum for the best-fit model.

SGR 1806-20 (From the RXTE in 1996)~5.0 keV, ~11.2 keV, ~17.5 keV are due to proton cyclotron resonances. (The slight deviation is because of the emission region with different magnetic B or redshift z)

~7.5 keV is due to a-patticle resonance. (The fundamental line is at ~2.4 keV.)

AXP 1RXS J170849-400910 (From the BeppoSAX in 2001)

MECS and LECS spectra from the 0.4 - 0.58 phase interval fitted with the "standard

model" (the sum of a blackbody and power law with absorption) plus a cyclotron line. Residuals are relative to the

standard model alone in order to emphasize the absorption-like feature at ~ 8.1 keV: (a) the BeppoSAX observations merged together; (b) the 2001 observation alone; and (c) the phase intervals contiguous to that showing the cyclotron absorption feature in the merged observations.

The absorption line at ~ 8.1 keV is explained by the electron or proton cyclotron resonance.

1RXS J130848.6+212708 (From observation of XMM-Newton in 2003)

Figure 1: Blackbody model fits to EPIC-pn (upper pair), EPIC-MOS (middle pair) and RGS spectra of RBS1223. The four RGS spectra were combined in the plot for clarity. While the pure blackbody model fit (left) is unacceptable, including a broad Gaussian absorption line at ~ 300 eV (right) can reproduce the data. The residuals (bottom panels) show consistent behavior for all instruments.

The absorption line center at an energy of ~ 300 keV, which is explained by proton cyclotron absorption line.

RX J1605.3+3249 (From the XMM-Newton in 2003)

Comparison of the data taken with Chandra ACIS-I and XMM EPIC through the thick filter with the best fit inferred from the EPIC data taken through the thin filter (Fig. 3). Both data sets confirm that a strong absorption feature is present near 0.4 keV.

The absorption is at ~0.45 keV which is explained by proton cyclotron line.

RX J0720.4-3125 (From XMM in 2000,2002)

Figure 1: Simultaneous fits using models A ( left) and B ( right) to the XMM-Newton spectra of RX J0720.4-3125. For model definition see Table 2. For each model the best fit (histogram) to the spectra (crosses) is plotted in panels a). Panels b)- d) show the residuals for EPIC-pn, -MOS and RGS spectra, respectively. For model B panel e) illustrates the best fit model with the absorption line removed. The three EPIC-pn spectra obtained with thin filter were combined for clarity in the plots, as well as all the eight RGS spectra. The MOS data below 300 eV were not used for the spectral fits. The residuals increasing with energy above 800 eV in the EPIC spectra are probably caused by pile-up (see Sect. 3.3).

The absorption is at ~ 271 eV which is explained by proton cyclotron line.

About 1E 1207-5209

We assume that the absorption lines from the 1E 1207 are due to electron cyclotron resonance.

Then………

The Magnetic Field Surface Thermal Emission Model

Nonmagnetic magnetic field model

Magnetic field model and n=1 fundamental line from Q.M.

Magnetic field model and n=2,3,4 lines from Q.E.D.

The opacity which is due to Thomson scattering and free-free process in nonmagnetic field has to replace by that in the magnetic field.


Wave Propagation n a Cold Magnetized Plasma

Assumptions:

1.Fully ionized hydrogen gas

2.w >> wpe,wpi

w >> wci

3.The plasma is charged-neutral:

ρ0=0, J0=0

4.The volume magnetic moment is negtected:

M=0, μ=1

5.The cold plasma means kT 0, hence thermal electron motion is

neglected compared to those induced by the wave.

122

14 11~16 14~24 32

14 9~14 14~24 32

15

4( )

1.6 10 ( ) 3.8 10 ( ) 6 10 (1/ )

3.7 10 ( ) 8.9 10 ( ) 6 10 (1/ )

1.5 10 ( )

p

c

pe

pi

ci

ne

meB

mc

n Hz Hz as n cm

n Hz Hz as n cm

Hz


From Maxwell equations and some formula derivations, we have below results. (Meszaros 1992)

1

21,2

12 2 4 2 21,2 2

1

2

2 2 2 2

22 2

3

2 ( )cos

sin [ sin 4 ( ) cos ]

sin cos sin

( ) cos ( ) cos

2( ) ( ) 1

3

x

y

z y x

pcc

e

E u vi

Eu u u v

u v uvE i E E

u v uv u v uv

eu v i

m c

1:extraordinary mode , 2:ordinary mode


x

z

y

θ

kB


As theta=0 andλ=1:

Ex1/Ey1=i for X-mode, Ex2/Ey2=-i for O-mode and Ez=0.

As theta=pi/2 and λ=1:

Ex1/Ey1=0 for X-mode, Ex2/Ey2=i∞ for O-mode and Ez is proportional to Ey.


x

z

y

k

B

X-modeO-mode


x

z

y

k

B

X-modeO-mode


NEXT TIME……

Thomson scattering cross section and free-free cross section…

Some results of the magnetic field model….


Model Spectra of Neutron Star Surface Thermal Emission Soccer 2005.4.21.

Documents

b slide

1e17hz slide

magnetic field model

1e17hz limbdarkening

e x2 e y2

e x1 e y1

b xmode omode

extraordinary mode