Model Spectra of Neutron Star Surface Thermal Emission Soccer

Outline The nonmagnetic field surface thermal emission model (finished) About 1E The magnetic field surface thermal emission model

Structure of neutron star atmosphere Radiation transfer equation Temperature correction Flux ≠const Flux = const Spectrum Improved Feautrier Unsold Lucy process Oppenheimer-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.

The delT derived from Unsold-Lucy process The Nonmagnetic Field Surface Thermal Emission Model

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 z~1cm << R~10^6cm, thus the assumption of plane-parallel is good. The Nonmagnetic Field Surface Thermal Emission Model

Different effective temperatures

Different gravitations

About 1E In August 2002 by XMM-Newton from De Luca, Mereghetti, Caraveo, Moroni, Mignani, Bignami, 2004, ApJ 418. supernova remnant G E Red represents photons in the keV band, green and blue correspond to the keV and keV bands respectively. P~424ms P derivative~1.4* ss -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 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*10 10 G or ~1.6*10 14 G, respectively. But from the magneto-dipole braking assumption, B is about (2.6±0.3)*10 12 G.

About 1E Other INSs have been detected with absorption features: GEMINGA (Mignani et al. 1998, A&A, 332) SGR (Ibrahim et al. 2002, ApJ, 574 & 2003, ApJ, 584) AXP 1RXS J (Rea et al. 2003, ApJ, 586) 1RXS J (RBS 1223) (Haberl et al. 2003, A&A, 403) RX J (Kerkwijk 2003, arXiv:astro-ph/ ) RX J (Haberl et al. 2003, arXiv:astro-ph/ ) 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 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.Bignami et al. 1988Bignami et al. 1996Caraveo et al 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 (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 J (From the BeppoSAX in 2001) MECS and LECS spectra from the 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 J (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.RBS1223 The absorption line center at an energy of ~ 300 keV, which is explained by proton cyclotron absorption line.

RX J (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.Fig. 3 The absorption is at ~0.45 keV which is explained by proton cyclotron line.

RX J (From XMM in 2000,2002) Figure 1: Simultaneous fits using models A ( left) and B ( right) to the XMM-Newton spectra of RX J 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).RX J The absorption is at ~ 271 eV which is explained by proton cyclotron line.

About 1E 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. The Magnetic Field Surface Thermal Emission Model

Wave Propagation n a Cold Magnetized Plasma Assumptions: 1.Fully ionized hydrogen gas 2.w >> w pe,w pi w >> w ci 3.The plasma is charged-neutral: ρ 0 =0, J 0 =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) 1:extraordinary mode, 2:ordinary mode The Magnetic Field Surface Thermal Emission Model

x z y θ k B

As theta=0 andλ=1: E x1 /E y1 =i for X-mode, E x2 /E y2 =-i for O-mode and E z =0. As theta=pi/2 and λ =1: E x1 /E y1 =0 for X-mode, E x2 /E y2 =i∞ for O-mode and E z is proportional to E y. The Magnetic Field Surface Thermal Emission Model

x z y k B X-mode O-mode The Magnetic Field Surface Thermal Emission Model

x z y k B X-mode O-mode 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 …. The Magnetic Field Surface Thermal Emission Model