Radiation Transfer in the Cavity and Shell of Planetary Nebulae

TL;DR

This paper presents an approximate analytical model for radiation transfer in planetary nebulae, fitting observational data to infer cavity sizes and dust distribution characteristics.

Contribution

It introduces a novel analytical approach to model line-averaged radiation transfer in planetary nebulae, accounting for scattering as a perturbation.

Findings

Maximum intensity positions yield cavity radii of ~0.2 times the nebula radius.

Optical depths derived are consistent with observed extinction.

Evidence suggests a clumpy dust distribution in the nebula.

Abstract

We develop an approximate analytical solution for the transfer of line-averaged radiation in the hydrogen recombination lines for the ionized cavity and molecular shell of a spherically symmetric planetary nebula. The scattering problem is treated as a perturbation, using a mean intensity derived from a scattering-free solution. The analytical function was fitted to Halpha and Hbeta data from the planetary nebula NGC6537. The position of the maximum in the intensity profile produced consistent values for the radius of the cavity as a fraction of the radius of the dusty nebula: 0.21 for Halpha and 0.20 for Hbeta. Recovered optical depths were broadly consistent with observed optical extinction in the nebula, but the range of fit parameters in this case is evidence for a clumpy distribution of dust.