Scaling for the intensity of radiation in spherical and aspherical planetary nebulae

TL;DR

This paper develops a comprehensive model for the intensity of radiation in spherical and aspherical planetary nebulae, combining shell expansion, particle diffusion, and line-of-sight integration, and applies it to specific nebulae.

Contribution

It introduces a unified framework that models radiation intensity considering physical processes and geometries in planetary nebulae, including diffusion and line-of-sight effects.

Findings

Model successfully applied to A39, Ring nebula, and MyCn 18.

Provides insights into the physical processes shaping nebulae images.

Enhances understanding of radiation distribution in complex nebular structures.

Abstract

The image of planetary nebulae is made by three different physical processes. The first process is the expansion of the shell that can be modeled by the canonical laws of motion in the spherical case and by the momentum conservation when gradients of density are present in the interstellar medium. The second process is the diffusion of particles that radiate from the advancing layer. The 3D diffusion from a sphere as well as the 1D diffusion with drift are analyzed. The third process is the composition of the image through an integral operation along the line of sight. The developed framework is applied to A39, to the Ring nebula and to the etched hourglass nebula MyCn 18.