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

Since planetary nebulae are spatially extended sources, measurements o f individual line fluxes may pertain to different areas of their image s. Photoelectric or infrared observations of the strongest lines may e mbrace the entire image, International Ultraviolet Explorer observatio ns involve an elliptical aperture, 10'' x 23''; while a spectrum scann er or slit spectrograph takes a narrow pencil, typically approximately 2'' x 4'', through a selected portion of the nebula. Therefore, we sh ould be able to use a theoretical model to predict the emission from a ny one of these traverses, provided that the observers describe accura tely the regions they have selected. Thus the present investigation in volves not just the calculation of models, hopefully improved by inclu ding the best available physics, radiative transfer, charge-exchange a nd atomic data, etc., but also the development of procedures for predi cting 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 th e flux from a pencil beam now become more intricate, since a ray may p ass through zones of quite different density. Detailed results are pre sented for the well-observed high-excitation planetary nebula IC 2165, for which observations with different techniques and pencils of varyi ng size have been obtained. By comparing each body of observational da ta with its appropriate theoretical nebular slice, it is believed that substantially improved chemical compositions are found; model abundan ces, 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.