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Astron. Astrophys. 344, 295-309 (1999)

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5. Surface - distributed characteristics of NSNR X-ray emission

5.1. Surface brightness in range [FORMULA]

We analyze here the surface brightness distribution [FORMULA] (in [FORMULA])

[EQUATION]

and surface distribution of spectral index

[EQUATION]

where the integrals are taken along the line of sight inside the remnant.

5.1.1. NSNRs in a medium with flat exponential density distribution

Figs. 8-11 demonstrate an evolution of surface brightness of NSNR in media with exponential density distribution (11). At the beginning of SNR evolution, the surface brightness map is very like the Sedov one (Fig. 9), but with age the differences become more considerable when the majority of emission arises from more dense regions. The brightness contrast [FORMULA] may increase with time up to [FORMULA] ([FORMULA] and [FORMULA] are the values of both the biggest and the smallest maxima in distribution of surface brightness).

[FIGURE] Fig. 8. Distribution of [FORMULA] surface brightness [FORMULA] along the NSNR symmetry axis in uniform and exponential Eq. (11) media for time moments [FORMULA] yrs (line 1), 5000 yrs (line 2), 40000 yrs (line 3). The model parameters are [FORMULA] [FORMULA] [FORMULA]

[FIGURE] Fig. 9. Distribution of surface brightness [FORMULA] of the Sedov SNR in uniform medium in the range [FORMULA]. The model parameters are [FORMULA]. The SNR characteristics are [FORMULA] [FORMULA] [FORMULA]. The lines of constant brightness are indicated by values of logarithm of flux [FORMULA]. The center of explosion hereafter is at the origin of the coordinates.

[FIGURE] Fig. 10. The same as in Fig. 9 for exponential medium Eq. (11) with [FORMULA]. The NSNR parameters at this time are [FORMULA]. The NSNR inclination angle to the plane of the sky equals [FORMULA] (upper case), [FORMULA] (center case) and [FORMULA] (lower case).

[FIGURE] Fig. 11. The same as in Fig. 10 for time [FORMULA] ([FORMULA]) and [FORMULA] ([FORMULA]).

In order to interpret an observation, it is necessary to take into account that projection effects also essentially affect the visible morphology of NSNR. Three cases of projection are shown. We can see that projection decreases real anisotropy and contrasts. For example, under condition of full disclosure of NSNR at the age [FORMULA] (Fig. 11) [FORMULA] but for inclination angle [FORMULA] this ratio is [FORMULA].

It is interesting also to compare Fig. 9 and a bottom case of Fig. 10 (when a visible shape of NSNR is spherical as result of projection). One can see that even spherically symmetric Sedov-like observational distribution of surface brightness does not guarantee an isotropic distribution of parameters inside SNR i.e., uniformity of ISM density and isotropy of explosion.

5.1.2. NSNRs in a medium with power-law density distribution

Fig. 12 shows three projections of NSNR in power-law density distribution (13) with [FORMULA] [FORMULA] [FORMULA]. Corresponding NSNR characteristics are [FORMULA] [FORMULA] [FORMULA]. It may be compared with values calculated for NSNRs which evolve in media with different density distribution, to show that different ISM density distributions give similar integral (surface-integrated) X-ray characteristics. For the same model parameters in case of SNR in uniform density, we obtain [FORMULA] [FORMULA] [FORMULA] and for exponential NSNR: [FORMULA] [FORMULA] [FORMULA]

[FIGURE] Fig. 12. Distribution of surface brightness [FORMULA] of NSNR in medium with power-law density distribution Eq. (13) in range [FORMULA]. Model parameters are: [FORMULA] [FORMULA] [FORMULA] [FORMULA]. The NSNR inclination angle to the plane of the sky equals [FORMULA] (upper case ), [FORMULA] (center case ), and [FORMULA] (lower case ).

As a result of projection, the maximum of surface brightness does not lie close to the edges of NSNR as in shell-like SNRs, but creates a compact region inside the visible projection. Therefore, the projection effect in case of the NSNR elongated predominantly along the line of sight is one possible sources of apparent filled-centre SNRs, especially when the search for a pulsar has no result.

5.2. Surface brightness in range [FORMULA]

Different photon energy ranges reveal different sensitivity to the non-uniformity of ISM. Fig. 13 shows the results of calculation of surface brightness of NSNR in an exponential density distribution (11) in range [FORMULA]. We may see that surface brightness contrast in this range is essentially smaller then in the wider range [FORMULA] where line emission dominates. So, for [FORMULA] (Fig. 11) the maximal surface brightness contrast is [FORMULA] for [FORMULA] and is only [FORMULA] for [FORMULA]. A contrast of surface brightness in range [FORMULA] is mainly caused by the contrast of the surrounding medium density distribution ([FORMULA]), but in range [FORMULA] it weakly depends on density contrast ([FORMULA]) (Hnatyk & Petruk 1996).

[FIGURE] Fig. 13. The same as in Fig. 10 for range [FORMULA] and time [FORMULA] ([FORMULA]) and [FORMULA] ([FORMULA]).

5.3. Surface distribution of spectral index

Plasma in different regions of NSNR is under different conditions which influence emission. Therefore, spectra from different NSNR regions must be different. The spectral index distribution for NSNR in an exponential medium is shown in Fig. 14. The contrast of values of spectral index increases with time but even for old adiabatic NSNR does not exceed a few times. Meantimes, the projection effects decrease both the index contrast and anisotropy of its distribution.

[FIGURE] Fig. 14. Surface distribution of spectral index [FORMULA] at 5keV for NSNR in exponential medium Eq. (11) with [FORMULA] [FORMULA] [FORMULA] for time [FORMULA] (spectral index from total SNR [FORMULA]), [FORMULA] ([FORMULA]) and [FORMULA] ([FORMULA]).

5.4. Discussion

We will summarize the results presented in this section.

  1. The distribution of surface brightness of NSNR differs essentially from a spherical one.

  2. The contrast of surface brightness increases with the age of the SNR and may reach a few ten of thousands.

  3. Projection effects hide real contrasts of surface characteristics of NSNR's emission. Observational morphology of NSNR depends essentially on its orientation to the line of sight.

  4. A harder X-ray range (e.g., [FORMULA]) is less sensitive to the influence of surrounding medium non-uniformity than a range which includes soft emission. This fact may be used for testing ISM non-uniformity.

  5. The surface distribution of spectral index [FORMULA] may also be an effective test for NSNR diagnostics.

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© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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