Planetary nebulae (PN) often have weird shapes, due to an inhomogeneous interstellar medium. We investigated the propagation of the shock wave that forms a PN. The form of the shock wave depends on...Show morePlanetary nebulae (PN) often have weird shapes, due to an inhomogeneous interstellar medium. We investigated the propagation of the shock wave that forms a PN. The form of the shock wave depends on the initial density distribution. The equation that describes the shock propagation is a first order non-linear partial differential equation. We found a analytic solution for the equation after a certain assumptions for some basic functions and made estimations for more complex density functions. We also made a model that used toroidal coordinates and one in three dimensions. The toroidal model resembles the Red Rectangle nebula. We also inverted the two-dimensional equation with some assumptions to derive the initial density function from a known shock wave. We used a numerical model to compute the density profile for eleven known planetary nebula. This leads to a qualitative classification into the ellipsoidal, disk and and irregular nebula. Inserting some test shock waves into this equation shows the existence of a extraordinary clover like shape in the density function.Show less
