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

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3. SNR shapes in non-uniform media

We now consider the role of the surrounding ISM on the evolution and the X-ray emission of adiabatic SNR on the examples of media with flat exponential and spherically-symmetrical power-law density distributions.

3.1. Shapes of SNRs in a flat exponential medium

The exponential law distribution is frequently encountered in nature, especially in galactic disks. We consider the evolution of the shape of the shock front from a point explosion in a medium with exponential density distribution Eq. (11). The morphological evolution of such SNR are presented in Fig. 4. We can see from this figure the remarkable insensitivity of the visible form of the SNR to the ISM density gradient.

[FIGURE] Fig. 4. a  Profiles of shock front expanding in a exponential medium Eq. (11) (solid lines) and in a uniform medium (dashed lines) for dimensionless times [FORMULA]. The dotted line is the profile fitting by a sphere for [FORMULA]. b  The 3D shape of the same SNR for [FORMULA]. The angle between the symmetry axis of the SNR and the plane of sky is [FORMULA].

The apparent center of the non-spherical SNR does not coincide with real progenitor position. This may be important for localizing a possible compact stellar remnant (pulsar or black hole).

The evolution of some shock characteristics is presented in Fig. 5. The main result is that the average visible morphological characteristics of the non-spherical SNRs are usually close to those for Sedov SNRs with the same initial parameters.

[FIGURE] Fig. 5a and b. Evolution of the shape and characteristics of a shock wave for a point explosion in a flat exponential medium Eq. (11). a : 1 - radius of shock front [FORMULA] in direction [FORMULA] (this equals [FORMULA] for the case a uniform medium); 2 - [FORMULA]; 3 - [FORMULA]; 4 - [FORMULA]; 5 - average visual radius of NSNR in exponential medium. b : 1 - ratio of maximal to minimal diameters of visual shape of shock wave front; 2 - ratio [FORMULA]; 3 - [FORMULA]; 4 - [FORMULA]

3.2. Shapes of SNRs in a power-law medium

Another widely-used density distribution is the power-law one, created by stellar winds, previous SN explosions etc.:

[EQUATION]

We consider the evolution of the shock from a point explosion in a medium with a spherically-symmetrical power-law density distribution when the explosion point is displaced by a distance [FORMULA] from the center of symmetry [FORMULA] (wind source etc.). Therefore the density distribution as a function of the distance r from the explosion point [FORMULA] is:

[EQUATION]

Here [FORMULA] is the initial density in the point of explosion. Hereafter, we take [FORMULA] and [FORMULA].

The shape evolution of the SNR in this density distribution is shown in Fig. 6. It is worthy to note that visible shapes of such SNRs may be elongated transverse to the density gradient.

[FIGURE] Fig. 6a and b. The same as in Fig. 4 for a power law density distribution Eq. (13) for [FORMULA] and [FORMULA] The angle between the symmetry axis of NSNR and the plane of the sky in the right figure equals [FORMULA].

As one can see from Fig. 6b like to the previous case (Fig. 4b), the projection of the SNR on the plane of the sky can cause a spherization of the visible SNR shape. So, even a visible spherical shape of SNR does not guarantee the uniformity of ISM and isotropy of explosion.

3.3. Discussion

From the above results, it follows that:

1. The non-uniformity of the surrounding medium causes asphericity of SNRs. The visible shapes may be elongated not only along (Fig. 4) but also transverse to (Fig. 6) the density gradient, depending on the type of density distribution.

2. SNR may have an apparent shape close to spherical even in cases of essential anisotropy of the real form and essential gradient of density distribution along the surface.

3. The observed anisotropy of the shape is smaller than the real anisotropy as result of projection. The visible shape remains, generally, close to spherical.

4. The non-uniformity of the surrounding medium results in differences of shock characteristics along the SNR surface. If the initial density [FORMULA] varies along the shock surface, the maximal contrasts are expected in the X-ray surface brightness ([FORMULA]), they are smaller for the temperature distribution ([FORMULA]) and minimal in shock and postshock gas velocities ([FORMULA]) (Figs. 4-6).

Therefore to determine the real conditions inside and around SNR, it is necessary to use additional information about SNR. We consider further the X-ray observations as an effective tool for SNR diagnostics.

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© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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