5. Surface - distributed characteristics of NSNR X-ray emission
5.1. Surface brightness in range
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 may increase with time up to ( and are the values of both the biggest and the smallest maxima in distribution of surface brightness).
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 (Fig. 11) but for inclination angle this ratio is .
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 . Corresponding NSNR characteristics are . 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 and for exponential NSNR:
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
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 . We may see that surface brightness contrast in this range is essentially smaller then in the wider range where line emission dominates. So, for (Fig. 11) the maximal surface brightness contrast is for and is only for . A contrast of surface brightness in range is mainly caused by the contrast of the surrounding medium density distribution (), but in range it weakly depends on density contrast () (Hnatyk & Petruk 1996).
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.
We will summarize the results presented in this section.
© European Southern Observatory (ESO) 1999
Online publication: March 10, 1999