DENSITY CONTRAST SHELL MODELS FOR THE PLANETARY-NEBULA IC-2165

Since planetary nebulae are spatially extended sources, measurements of individual line fluxes may pertain to different areas of their images. Photoelectric or infrared observations of the strongest lines may embrace the entire image, International Ultraviolet Explorer observations involve an elliptical aperture, 10'' x 23''; while a spectrum scanner or slit spectrograph takes a narrow pencil, typically approximately 2'' x 4'', through a selected portion of the nebula. Therefore, we should be able to use a theoretical model to predict the emission from any one of these traverses, provided that the observers describe accurately the regions they have selected. Thus the present investigation involves not just the calculation of models, hopefully improved by including the best available physics, radiative transfer, charge-exchange and atomic data, etc., but also the development of procedures for predicting the emission from cross sections of arbitrary placement, shape, and size, taken thru the nebular image. Spherically symmetrical shells pose no great difficulty, but most regularly shaped planetary nebulae show a bilateral symmetry. Since the axis of symmetry can be oriented at any angle with respect to the plane of the sky, calculations of the flux from a pencil beam now become more intricate, since a ray may pass through zones of quite different density. Detailed results are presented for the well-observed high-excitation planetary nebula IC 2165, for which observations with different techniques and pencils of varying size have been obtained. By comparing each body of observational data with its appropriate theoretical nebular slice, it is believed that substantially improved chemical compositions are found; model abundances, log N on the scale log N(H) = 12.00, are He = 11.02, C = 8.61, N = 7.90, 0 = 8.30, Ne = 7.70, Si = 6.48; S = 6.45, Cl = 4.95, Ar = 6.00, K = 4.90, Ca = 5.08.