Abstract
In this paper we derive some first order differential equations which model the classical and the relativistic thin layer approximations in the presence of a circumstellar medium with a density which is decreasing in the distance z from the equatorial plane. The circumstellar medium is assumed to follow a density profile with z of hyperbolic type, power law type, exponential type or Gaussian type. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by Pad´e approximants. The initial conditions are chosen in order to model the temporal evolution of SN 1987A over 23 years. The free parameters of the theory are found by maximizing the observational reliability which is based on an observed section of SN 1987A.
Highlights
The theories of the expansion of supernovae (SN) in the circumstellar medium (CSM) are usually built in a spherical framework
A possible classification for the asymmetries firstly identifies the center of the explosion and defines the radius in the equatorial plane, Req, the radius in the downward direction, Rdown, and the radius in the upward direction, Rup, see Zaninetti (2000)
The above classification allows introducing a symmetry: Rdown=Rup means that the expansion from the equatorial plane along the two opposite polar directions is the same
Summary
The theories of the expansion of supernovae (SN) in the circumstellar medium (CSM) are usually built in a spherical framework. The above classification allows introducing a symmetry: Rdown=Rup means that the expansion from the equatorial plane along the two opposite polar directions is the same. We present some maximum observed velocities in SNs: the maximum velocity for Si II λ6355 vary in [15000,25000] km s−1 according to Figure 13 in Silverman et al (2015) or in [13000,24000] km s−1 according to Figure 4 in Zhao et al (2015). These high observed velocities demand a relativistic treatment of the theory.
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