Model Spectra of Neutron Star Surface Thermal Emission

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Model Spectra of Neutron Star Surface Thermal
Emission
Soccer 2005.4.21
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Outline

• The nonmagnetic field surface thermal emission
  model (finished)
• About 1E 1207-5209
• The magnetic field surface thermal emission model

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The Nonmagnetic Field Surface Thermal Emission
Model

• Oppenheimer-Volkoff

Structure of neutron star atmosphere
Improved Feautrier
Flux const
Radiation transfer equation
Spectrum
Flux ?const
Unsold Lucy process
Temperature correction
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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.
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The Nonmagnetic Field Surface Thermal Emission
Model
The delT derived from Unsold-Lucy process
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Frequency1e17(Hz)
limb-darkening
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Frequency1e17(Hz)
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Theta0
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Theta0.628
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The order of rho is similar with that of tau.
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The spectra reveal limb-darkening and high energy
tail and are different from Plank function
significantly.
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The Nonmagnetic Field Surface Thermal Emission
Model
Physical depth
z1cm ltlt R106cm , thus the assumption of
plane-parallel is good.
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Different effective temperatures
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Different gravitations
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About 1E 1207-5209
In August 2002 by XMM-Newton from De Luca,
Mereghetti, Caraveo, Moroni, Mignani, Bignami,
2004, ApJ 418.
supernova remnant G296.510.0
P424ms P derivative1.410-14ss-1
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.
1E 1207.4-5209
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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.
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Four absorption features have central energies
colse to the ratio 1234
From pn 0.68/0.24 1.36/0.18
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.
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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 81010G or 1.61014G,
respectively. But from the magneto-dipole braking
assumption, B is about (2.60.3)1012G.
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About 1E 1207-5209
Other INSs have been detected with absorption
features GEMINGA (Mignani et al. 1998, AA,
332) SGR 1806-20 (Ibrahim et al. 2002, ApJ, 574
2003, ApJ, 584) AXP 1RXS J170849-400910 (Rea et
al. 2003, ApJ, 586) 1RXS J130848.6212708 (RBS
1223) (Haberl et al. 2003, AA, 403) RX
J1605.33249 (Kerkwijk 2003, arXivastro-ph/031038
9) RX J0720.4-3125 (Haberl et al. 2003,
arXivastro-ph/0312413) Others.??
Ps For neutron stars in binary systems, direct
measures of the magnetic fields were reported by
Trumper et al. in 1978.
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GEMINGA (From HST and other telescopes during
1987 1996)
An emission feature is at 6000 Å, which is
explained by the proton cyclotron emission close
to the surface of a a neutron star.
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 d157 pc (Caraveo et al. 1996). The two cases shown correspond to R10 km and T4.5e5  K (ROSAT 1991 fit-dotted) and to R15 km and T 2.5e5 K (EUVE fit-dashed). Note the absolute scale no normalization has been performed.

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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.)
Spectrum and best-fit continuum model for the
second precursor interval, with four absorption
lines (RXTE/PCA, 230 keV). Bottom Pulse-height
spectrum with the model predicted counts
(histogram). Top Model (histogram) and the
estimated photon spectrum for the best-fit model.
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AXP 1RXS J170849-400910 (From the BeppoSAX in
2001)
The absorption line at 8.1 keV is explained by
the electron or proton cyclotron resonance.
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.
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1RXS J130848.6212708 (From observation of
XMM-Newton in 2003)
The absorption line center at an energy of 300
keV, which is explained by proton cyclotron
absorption line.
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.
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RX J1605.33249 (From the XMM-Newton in 2003)
The absorption is at 0.45 keV which is explained
by proton cyclotron line.
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.
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RX J0720.4-3125 (From XMM in 2000,2002)
The absorption is at 271 eV which is explained
by proton cyclotron line.
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).
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About 1E 1207-5209
We assume that the absorption lines from the 1E
1207 are due to electron cyclotron
resonance. Then
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The Magnetic Field Surface Thermal Emission Model
Nonmagnetic magnetic field model
Magnetic field model and n1 fundamental line
from Q.M.
Magnetic field model and n2,3,4 lines from Q.E.D.
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The Magnetic Field Surface Thermal Emission Model
The opacity which is due to Thomson scattering
and free-free process in nonmagnetic field has
to replace by that in the magnetic field.
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The Magnetic Field Surface Thermal Emission Model
Wave Propagation n a Cold Magnetized Plasma
Assumptions 1.Fully ionized hydrogen gas 2.w gtgt
wpe,wpi w gtgt wci 3.The plasma is
charged-neutral ?00, J00 4.The volume
magnetic moment is negtected M0, µ1 5.The
cold plasma means kT ? 0, hence thermal electron
motion is neglected compared to those induced
by the wave.
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The Magnetic Field Surface Thermal Emission Model
From Maxwell equations and some formula
derivations, we have below results. (Meszaros
1992)
1extraordinary mode , 2ordinary mode
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The Magnetic Field Surface Thermal Emission Model
z
k
B
?
y
x
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The Magnetic Field Surface Thermal Emission Model
As theta0 and?1 Ex1/Ey1i for X-mode,
Ex2/Ey2-i for O-mode and Ez0.
As thetapi/2 and ?1 Ex1/Ey10 for X-mode,
Ex2/Ey2i8 for O-mode and Ez is proportional to
Ey.
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The Magnetic Field Surface Thermal Emission Model
z
B
k
O-mode
X-mode
y
x
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The Magnetic Field Surface Thermal Emission Model
z
k
X-mode
O-mode
y
B
x
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The Magnetic Field Surface Thermal Emission Model
NEXT TIME Thomson scattering cross section and
free-free cross section Some results of the
magnetic field model.