Transcript The Nonmagnetic Field Surface Thermal Emission Model

Model Spectra of
Neutron Star Surface
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
The Nonmagnetic Field Surface Thermal Emission Model
Oppenheimer-Volkoff
Structure of neutron star atmosphere
Improved Feautrier
Radiation transfer equation
Flux ≠const
Unsold Lucy process
Temperature correction
Flux = const
Spectrum
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.
The Nonmagnetic Field Surface Thermal Emission Model
The delT derived from Unsold-Lucy process
 J   H
 H 
H ( ')d ' 2H (0)]  R
 [3






P
R
P
0

T  
4 T 3

dH  J

J PB
d  R
R
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.
The Nonmagnetic Field Surface Thermal Emission Model
Physical depth
dP
  g*
dz
P
 g*z
z
kT
mp g *
P
2kT 
mp
1016 106
1024 1014
1cm
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
P~424ms
P derivative~1.4*10-14ss-1
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.
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.
Four absorption features have central
energies colse to the ratio 1:2:3:4
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
.
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)
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 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
normalization has been performed.
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, 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.
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 absorptionlike 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.
1RXS J130848.6+212708 (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.
RX J1605.3+3249 (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.
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).
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 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.
The Magnetic Field Surface Thermal Emission Model
Wave Propagation n a Cold Magnetized Plasma
Assumptions:
1.Fully ionized hydrogen gas
2.w >> wpe,wpi
w >> wci
4 ne 2 12
)
m
eB
c 
mc
p (
 pe  1.6  104 n
1
 pi  3.7  104 n
1
2
( Hz )  3.8  1011~16 ( Hz )
as n  6  1014~ 24 (1/ cm3 )
2
( Hz )  8.9  109~14 ( Hz )
as n  6  1014~ 24 (1/ cm3 )
ci  1.5  1015 ( Hz )
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.
The Magnetic Field Surface Thermal Emission Model
From Maxwell equations and some formula derivations, we have below
results. (Meszaros 1992)
Ex1,2
E y1,2
1
2
2u (  v) cos 
i
u sin   [u sin   4u (  v) cos  ]
2
2
4
1
2
2
2
1
2
 u v sin 
uv cos  sin 
E

Ex
y
2
2
2
2
 u   (  v)  uv cos 
 u   (  v)  uv cos 
p 2
c 2
2e 2
u(
)
v(
)
 
c
  1  i
3


3me c
Ez  i
1:extraordinary mode , 2:ordinary mode
The Magnetic Field Surface Thermal Emission Model
z
k
B
θ
y
x
The Magnetic Field Surface Thermal Emission Model
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.
The Magnetic Field Surface Thermal Emission Model
z
B
k
X-mode
O-mode
y
x
The Magnetic Field Surface Thermal Emission Model
z
k
O-mode
X-mode
y
B
x
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….