Abstract
Here we extend the conservation of energy in the framework of the thin layer approximation to the asymmetrical case. Four types of interstellar medium are analysed, in which the density follows an inverse square profile, a power law profile, an exponential profile and a toroidal profile. An analytical solution for the radius as a function of time and the polar angle in spherical coordinates is derived in the case of the inverse square profile. The analytical and numerical results are applied to two supernova remnants: SN 1987A and SN 1006. The back reaction due to the radiative losses is evaluated in the case of the inverse square profile for the surrounding medium. Two models for the image formation are presented, which explain the triple ring visible in SN 1987A and the jet feature of SN 1006.
Highlights
The asymmetries observed in supernovae (SNs) and supernova remnants (SNRs) have been recently investigated by different approaches: on analysing a type Ia SN that exploded around CE 1900 [1] reported that it is asymmetric in the radio region but shows a bipolar morphology in the X region
The following approaches will model the circumstellar medium (CSM) around the point of explosion of the SN which is characterized by a plane, z = 0, which produces an up and down symmetry in the polar angle, r (θ ) = r (π −θ ), and by a polar axis,=x 0=, y 0, which produces a right and left symmetry for the azimuthal angle r (= φ ) r (φ + π)
A geometric section of the above X-map was digitized and rotated in the x-z plane by −45 ̊, see Figure 9; it will be the test for the simulations based on the previous data we can speak of a weak asymmetry for SN 1006
Summary
The asymmetries observed in supernovae (SNs) and supernova remnants (SNRs) have been recently investigated by different approaches: on analysing a type Ia SN that exploded around CE 1900 [1] reported that it is asymmetric in the radio region but shows a bipolar morphology in the X region. The presence of an asymmetric circumstellar medium (CSM) responsible for the lack of narrow lines within the first two days of the explosion for the Type II-P supernova SN 2017gmr was suggested by [6]. The differences in the Si II line widths in type Ia supernovae with an asymmetric CSM were explained by [7]. An asymmetric explosion as seen from different viewing angles was suggested by [8] in order to explain some anomalies in the photospheric velocities.
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