## 4. Integrated characteristics of the X-ray radiation from non-spherical SNRsSNRs are powerful sources of X-ray radiation, therefore X-ray observations of SNR give unique information about physical conditions inside the remnants. We calculate here the X-ray luminosities in the energy ranges () and () as well as the spectral index at ## 4.1. Plasma X-ray emissivity under ionization equilibrium conditionWe assume the cosmic abundance (Allen 1973). The X-ray continuum energy emissivity per unit energy interval is (in ) where is the photon energy in keV , is the plasma temperature in , is the electron number density. The approximation for total Gaunt factor as the sum of Gaunt factors for free-free free-bound and two-photon processes was taken from Mewe et al. (1986): This approximation represents the continuum losses to an accuracy of for and of for . For calculation of continuum and line emission of plasma in the different energy ranges, we have approximated the Raymond & Smith (1977) data for plasma emissivity (in ) for as follows: (accurate to for ); for as follows: (accurate to for ); for as follows: (accurate to for ). The total continuum flux at
photon energy and luminosity
of the entire SNR can be calculated
by integrating over the remnant volume ## 4.2. Evolution of the total X-ray emission from aspherical SNRsIt is well-known that the Sedov (1959) solution for SNR
characteristics in a uniform medium is determined by three parameters,
e.g., the energy of the explosion
the initial number density and time
If the SN explodes in a non-uniform medium, we have an additional
fourth parameter which characterises the non-uniform density
distribution. In our cases, it is the scale height It is naturally to expect, that in cases of NSNR considered, the
total X-ray luminosity as well as
spectral index will strongly depend
on non-uniformity characteristics, such as scale height We show in Fig. 7 the evolution of X-ray luminosity for range
and spectral index
at
for SNR in an exponential medium.
It is easy to see that both X-ray characteristics of NSNR evolve
analogously to the Sedov case and similarity increases with decreasing
surrounding medium density gradient (with increasing
We have calculated a grid of NSNR models (Tables 1-4) which confirms that this analogy in evolution is an intrinsic property of NSNR X-ray radiation. In fact, it may be seen from Tables 1-4 that for a wide range of number density at the point of explosion the X-ray luminosity of adiabatic NSNR evolving in a medium with strong enough density gradient () in different energy ranges are not far from the X-ray luminosity of SNR in a uniform density medium with the same initial model parameters. The differences increase with age of the SNR and with decreasing . But even for old NSNR (e.g., ) in a low density medium (), the maximal difference is about (for ). The differences in spectral index of adiabatic NSNR do not exceed . Table 1 shows that luminosity in range is close to the Sedov case also. These last two facts reveal the similarity of total spectra of Sedov SNR and non-spherical ones.
We suppose that the behavior of integral X-ray characteristics of
NSNR in other cases of smooth continuous density distribution of
surrounding medium will be similar considered above, since X-ray
emission mainly depends on the emission measure
but both mass of swepted up gas
where with and The temperature determined from the observed spectrum will be connected with as in the Sedov case (Itoh 1977). This characteristic temperature may be used to estimate the parameters of the whole remnant, such as mass, volume, etc.
The results of calculations show that integral X-ray
characteristics weakly depend on the surrounding medium density
gradient (e.g.,
## 4.3. DiscussionFrom Fig. 7 and Tables 1-6 follows a remarkable fact of proximity of total fluxes and spectrum shapes of SNRs in uniform and non-uniform media even in case of considerable anisotropy of adiabatic NSNR. The reason of this phenomenon is mutual compensation of emission deficit from low density regions of NSNR and enhanced emission from high density regions. This explains the strange circumstance that integral X-ray characteristics of the majority of SNRs with evident asymetry in shape and/or surface brightness distribution are described with sufficient accuracy by the Sedov model of SN explosion in a uniform medium. For more correct modelling of physical conditions inside and outside the SNR, it is necessary to analyze the characteristics of X-ray emission distributed over the SNR surface. © European Southern Observatory (ESO) 1999 Online publication: March 10, 1999 |