## 1. IntroductionThe investigation of Supernova remnants (SNRs) gives important information on the physics of Supernova (SN) explosions, on the properties of the surrounding interstellar medium (ISM) and on shock wave physics. The majority of galactic SNRs are in the adiabatic stage of evolution (Lozinskaya 1992). If the density of the ISM is uniform, their hydrodynamics are well described by the self-similar Sedov solution (Sedov 1959, Shklovskiy 1962). The typical values of plasma temperatures in SNRs are to and, therefore, SNRs radiate mainly in the X-rays. The spectral characteristics of the equilibrium X-ray emission for a plasma typical SNR abundances was calculated by Shapiro & Moore (1976), Raymond & Smith (1977), Shull (1981) and Gaetz & Salpeter (1983). But the real situation is more complicated. In many SNRs, the plasma is in nonequilibrium ionization (NEI). Often there is no thermal equilibrium between the electrons and the ions. The physical conditions in the inner parts of SNR may be modified by electron thermal conductivity (Itoh 1977, Cox & Anderson 1982, Hamilton et al. 1983, Jerius & Teske 1988, Borkowski et al. 1994, Bocchino et al. 1997). There are also other effects which affect the plasma emission in SNR, but their influence is small: resonant scattering, diffusion etc. (Raymond & Brickhouse 1995 and references there). The Sedov solution may also be modified by the presence of small-scale cloudlets in the ISM (Bychkov & Pikelner 1975, McKee & Cowie 1975, Sgro 1975, White & Long 1991). Practically the all above-mentioned investigations assumed
spherical symmetry of SNRs, as the result of their evolution in
Many SNRs with nearly spherical visual shapes have an anisotropic distribution of surface brightness (e.g. Kepler SNR, Cygnus Loop, RCW86 etc.). Therefore, truly spherical SNRs are considerably rarer than believed. Non-spherical SNRs (NSNRs) may be created by an anisotropic SN explosion (e.g. Bisnovatyi-Kogan 1970). Non-spherical shapes of SNRs in the free expansion stage (Fig. 1) should be mainly produced in this way. Another important reason for the non-sphericity of adiabatic SNRs can be a non-uniform density distribution of the ISM or the large-scale magnetic field. In such cases, self-similar solutions cannot be used, while direct numerical calculations of the problem are difficult because of the complications of 3D hydrodynamical modelling SNR evolution multiplies by the complications of nonequilibrium describing of gas element evolution. Therefore, at present only a few simplified models have been built (Tenorio-Tagle et al. 1985, Bodenheimer et al. 1984, Claas et al. 1989, Bocchino et al. 1997). Real possibility to perform an investigation of the evolution of non-spherical SNRs bases on approximate methods for hydrodynamics. The thin-layer (Kompaneets 1960) approximation for the calculation of SNR shape is widely used (Lozinskaja 1992, Bisnovatyi-Kogan & Silich 1995 and references there). But this approximation has low accuracy for the adiabatic stage in a nonuniform medium and does not allow to calculate the behaviour of the gas inside the SNR (Hnatyk 1987, Hnatyk & Petruk 1996). Hnatyk (1987) has shown that for our probleme it is more promising to develop approximate methods under a sector approximation (Laumbach & Probstein 1969), which allows to calculate both the SNR shape and the gas characteristics. In the work of Hnatyk & Petruk (1996) a new approximate analytical method for the complete hydrodynamical description of a point explosion in a medium with an arbitrary regular but smooth density distribution was proposed. It combines the advantages of the two above-mentioned methods and, therefore allows to calculate the hydrodynamical aspects of non-sherical SNR evolution with high enough accuracy in a short computing time. We use this method here, but we limit ourselves to the case of equilibrium emissivity. Non-equilibrium effects will be considered in a further paper. © European Southern Observatory (ESO) 1999 Online publication: March 10, 1999 |