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Astron. Astrophys. 331, 821-828 (1998)

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2. Observations and results

We used the archival ROSAT and ASCA data of 1E1207.4-5209  (see MBC96 and V97 for a detailed description). Four ROSAT Position Sensitive Proportional Counter (PSPC) pointings (obtained in July 1993, with exposure times about 5-6 ks each - see Table 2 in MBC96) were centered at different positions (off-axis angles between [FORMULA] and [FORMULA]). We checked that the spectra of 1E1207.4-5209  extracted from each of the four data sets and properly corrected for the PSPC response are consistent with each other. For the combined analysis with the ASCA data we chose the ROSAT PSPC observation with the minimum off-axis angle [FORMULA] (exposure time [FORMULA]  ks). With the aid of the MIDAS/EXSAS package (Zimmermann et al. 1994) we extracted a raw spectrum from a region with a radius [FORMULA] centered on the source and subtracted the background spectrum estimated from an annulus with the inner radius r and outer radius [FORMULA]. (The backgrounds for observations with other ROSAT and ASCA instruments were estimated in the same manner). The (off-axis) source count rate is [FORMULA]  s-1. We binned the source spectrum in the 0.1-2.4 keV energy range into 24 spectral bins with signal-to-noise ratios greater than 5. The ROSAT HRI counts for each of the three on-axis pointings (obtained in August 1992 and July 1994; total exposure time [FORMULA]  ks) were selected from the circles of [FORMULA]. The corresponding source count rate is [FORMULA]  s-1, in agreement with MBC96.

The ASCA data were obtained in July 1994, with two Solid State Imaging Spectrometers, SIS0 and SIS1, in the "2-CCD bright" mode, and two Gas Scintillation Imaging Spectrometers, GIS2 and GIS3, in the "pulse-height" mode. The SIS1 image of 1E1207.4-5209  is too close to the edge of the CCD chip for a reliable spectral analysis. To reduce the ASCA data, we used the FTOOLS/XSELECT software (v. 3.5). The SIS0 source counts collected in [FORMULA]  ks (with "high" and "medium" bit rates) were extracted from the circle of [FORMULA], the total source count rate is [FORMULA]  s-1. The SIS0 spectrum was binned into 38 spectral bins (with minimum number of counts equal 20) in the 0.4-10.0 keV range. The GIS2 and GIS3 source counts were extracted from circles of [FORMULA] (exposure [FORMULA]  ks for the high plus medium bit rates). The source count rates are [FORMULA] (GIS2) and [FORMULA]  s-1 (GIS3). The spectra were binned into 39 and 46 spectral bins (with the same binning scheme as for SIS0) in the 0.2-10.0 keV range for GIS2 and GIS3, respectively. The total source count rates for all the three ASCA instruments are somewhat lower than those reported by V97, perhaps because of different screening criteria we applied. The SIS0 and GIS spectral responses (redistribution matrix and ancillary response files) were created with the standard FTOOLS codes "sisrmg" and "ascaarf".

For our spectral analysis we used the XSPEC package (v. 9.01) with its standard [FORMULA] fitting. As a first step, we fitted the count rate spectra simultaneously for the four instruments, ROSAT PSPC and ASCA SIS0, GIS2, and GIS3, with the traditional power-law and BB models. Fig. 1 shows the results of these fits. The power-law fit yields a photon index [FORMULA] and a hydrogen column density, [FORMULA] (minimum [FORMULA], [FORMULA] ; the uncertainties hereafter are at a 90% confidence level). These values of [FORMULA] and [FORMULA] are better constrained than those obtained by MBC96 from the PSPC data alone, [FORMULA] and [FORMULA] (minimum [FORMULA], [FORMULA]). The photon index is unusually large in comparison with typical values, [FORMULA], observed from, e.g., X-ray emitting radio pulsars (Becker & Trümper 1997), and the hydrogen column density significantly exceeds the values obtained by independent measurements (see below). These discrepancies imply that the power-law interpretation is inadequate.

[FIGURE] Fig. 1. 68%, 90% and 99% confidence contours ([FORMULA], 6.3 and 11.3, respectively) for the power-law and blackbody simultaneous fits to the ROSAT PSPC and ASCA SIS0, GIS2 and GIS3 spectra of 1E1207.4-5209. The lines in the right panel correspond to constant values of radius of emitting area at a distance [FORMULA]  kpc.

The BB temperature (as measured by a distant observer), [FORMULA]  K, the apparent radius of the emitting area, [FORMULA]  km, and the bolometric luminosity, [FORMULA]  erg s-1, obtained from the combined fit (Fig. 1) are very close to the values from the separate fits of the ROSAT and ASCA data by MBC96 and V97. The hydrogen column density in the combined fit, [FORMULA], is compatible with [FORMULA] inferred from the separate ROSAT PSPC spectrum. Although the quality of the BB fit is better than the quality of the power law fit, the [FORMULA] values look surprisingly low in comparison with the [FORMULA]  cm-2 obtained from independent estimates (see Sect. 1).

Since thermal NS spectra, as well as spectra of ordinary stars, cannot exactly coincide with the BB spectra because of the effects of radiative transfer in the emitting layers, it is natural to compare them with more realistic model spectra of NS atmospheres (e.g., Pavlov et al. 1995). Strongest deviations from the BB spectrum are expected if the NS surface is covered with a hydrogen atmosphere. Hydrogen may appear at the NS surface as a result of, e.g., accretion of interstellar matter or post-supernova accretion of a fraction of the ejected envelope. Due to the huge surface gravity (typical gravitational acceleration [FORMULA]  cm s-2), heavier chemical elements sink down in deeper layers and do not affect the properties of emitted radiation, whereas hydrogen remains at the surface. The shape of the spectrum emitted by an atmosphere depends on the strength B of the NS surface magnetic field. The lack of pulsations does not allow one to estimate B using the pulsation period and its derivative, as is usually done for pulsars. The absence of statistically reliable features in the observed spectra (see Fig. 2), which could be associated with an electron cyclotron line at [FORMULA]  keV, prevents one to make a direct estimation of B. Therefore, one has to try the atmosphere models with both low ([FORMULA]  G) and high magnetic fields. (In the former case, the field does not affect the properties of emergent radiation [Zavlin et al. 1996], so that we can merely put [FORMULA]). In the case of strong nonuniform field ([FORMULA]  G), the NS should have a nonuniform temperature distribution along its surface because of the high anisotropic thermal conductivity in the NS crust (e.g., Shibanov & Yakovlev 1996). However, since we have no information about the field geometry, we assume that the magnetic field has the same strength and is directed radially everywhere at the surface, and that the effective temperature is uniform. This assumption reduces the number of fitting parameters and can be considered as a reasonable first approximation for investigating the atmosphere effects.

[FIGURE] Fig. 2. Count rate spectra observed from 1E1207.4-5209, together with the best-fit hydrogen atmosphere model spectra for [FORMULA]  G (cf. Fig. 3). The residuals (in units of [FORMULA]) are shown separately for the four instruments. The spectra of SIS0 and GIS3 are reduced for clarity by factors of 10 and 20, respectively.

Fig. 3 shows results of fits of the combined ROSAT and ASCA data with hydrogen atmosphere models for three fixed values of the magnetic field. In these fits we assume canonical values for the NS mass and radius, [FORMULA] and [FORMULA]  km, and consider the distance as a fitting parameter. The models with [FORMULA] (left panels) and [FORMULA]  G (right panels) result in close values of the distance, effective temperature at the NS surface and bolometric luminosity, [FORMULA]  kpc, [FORMULA]  K, [FORMULA]  erg s-1, and [FORMULA]  kpc, [FORMULA]  K, [FORMULA]  erg s-1, for [FORMULA] and [FORMULA]  G, respectively. Since the nonmagnetic spectra are softer at lower energies, the hydrogen column density at [FORMULA], [FORMULA], is lower than for the strong magnetic field, [FORMULA]. We checked that folding the models within the 90% confidence region with the ROSAT HRI response yields count rates compatible with those observed. When the field strength varies in the range [FORMULA]  G, the fitting parameters remain approximately the same because the model spectra are almost insensitive to the B value in the corresponding domain of energies and effective temperatures. When B exceeds [FORMULA]  G, the proton cyclotron line centered at [FORMULA]  keV (cf. Bezchastnov et al. 1996) enters the SIS energy range, which makes the fits statistically unacceptable. (This line moves above [FORMULA]  keV, the maximum energy where the NS flux is still above the background [Fig. 2], at superstrong magnetic fields, [FORMULA], for which the models we used here are not directly applicable.) When B falls below [FORMULA]  G, the low-energy wing of the electron cyclotron line gets into the ASCA range, and the model spectra become softer at [FORMULA]  keV. As a result, the confidence contours in the [FORMULA] -d and [FORMULA] - [FORMULA] planes move to greater d and [FORMULA], and lower [FORMULA], towards the BB contours. An example is shown in the middle panels of Fig. 2 for [FORMULA]  G, for which the best-fit distance is about 50% larger than at [FORMULA]  G. When the field is lower than [FORMULA]  G, but greater than [FORMULA]  G, the atmosphere model fits become statistically unacceptable because the core of the electron cyclotron line gets into the ASCA /ROSAT range.

[FIGURE] Fig. 3. 68%, 90% and 99% confidence contours for the NS hydrogen atmosphere fits to the the combined ROSAT and ASCA data for [FORMULA], [FORMULA]  km, and three values of the surface magnetic field B.

The atmosphere models depend not only on B, but also on the NS mass and radius which determine the gravitational acceleration (one of our model parameters) and the gravitational redshift factor [FORMULA], where [FORMULA], [FORMULA]. To illustrate this effect, we present in Fig. 4 the best-fit parameters at [FORMULA]  G in a wide range of R and M allowed by equations of state of the NS matter. Although the effective temperature at the NS surface, [FORMULA], varies by about [FORMULA] in the allowed R -M domain, the apparent effective temperature (as measured by a distant observer), [FORMULA], remains almost constant, [FORMULA]  K, because the redshift is compensated by the change of the unredshifted NS spectrum (it softens in the Wien tail with increasing M and decreasing R at given [FORMULA]). Owing to the approximate constancy of [FORMULA], the apparent and "true" bolometric luminosities depend on R and M as [FORMULA] and [FORMULA]. The latter dependence explains the non-monotonous behavior of [FORMULA] at higher M. The best-fit d and [FORMULA] are almost independent of M at higher R, when [FORMULA] is close to 1. At lower R the variations are stronger, albeit within the statistical uncertainties of these parameters (cf. Fig. 2). The distance inferred at assumed R and M can be approximately described, in the allowed mass-radius domain, by a linear equation: [FORMULA] (in kpc); it grows with R faster than for the BB interpretation. Notice that if d is determined more accurately in future observations of the SNR and its central source, this equation would delimit a band in the M -R plane constraining equation of state of the NS matter.

[FIGURE] Fig. 4. Dependences of the best-fit parameters for the atmosphere fits on the NS radius R at different values of the NS mass, [FORMULA]. The thick dashed lines delimit the ranges of the apparent temperature and luminosity (upper and lower dashed curves correspond to [FORMULA] and 0.8, respectively).

Since the hydrogen atmosphere fits yield [FORMULA] greater than the BB fit by a factor of 3-5, it is important to estimate this parameter independently. For this purpose, we fitted the SNR emission with various models for thermal plasma radiation. We extracted the SNR spectrum from a bright region of the ROSAT PSPC image of the remnant shell within the [FORMULA] circle centered at [FORMULA], [FORMULA]. Three models available with the XSPEC package, "vraymond", "vmeka", and "vmekal" (Raymond-Smith, Mewe-Gronenschild-Kaastra, and Mewe-Kaastra-Liedahl models with variable abundances) give satisfactory fits ([FORMULA]) with the column density to the SNR in the range of [FORMULA]  cm-2, consistent with the hydrogen atmosphere fits of 1E1207.4-5209, but certainly in excess of the BB fits. The inferred plasma temperature is [FORMULA]  K. These results were obtained with a moderate excess of abundances of Al and Si whose emission lines are prominent in the SIS spectra of the SNR shell. Abundances of other elements are close to standard values. The SNR parameters inferred from our fits are consistent with those obtained by Kellett et al. (1987) from the EXOSAT data. The lower hydrogen density, [FORMULA], obtained by V97, is likely associated with fixed cosmic abundances adopted, which resulted in lower statistical quality of their fits ([FORMULA]). Note, however, that the emission models we and V97 used assume a single-temperature plasma in collisional ionization equilibrium. Both the temperature nonuniformity and nonequilibrium ionization may significantly affect the SNR X-ray emission (see, e.g., Bocchino et al. 1997, and references therein), so that the inferred SNR parameters, particularly the element abundances and temperature, may not be very accurate.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998