Estimating Physical Parameters by Means of Radio Continuum Observations: the Case of Planetary Nebulae

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For over four decades, physical parameters such as electron density, total ionized mass, and emission measure from H II regions, have been derived using radio continuum observations applying the formalism by Mezger & Henderson (1967, Astrophysical Journal, 147, 471), which assumes filled sphere, cylinder, and gaussian models. These models are good approximations when applied to H II regions. However, in the case of most of the planetary nebulae (PNe), we must take into account that emission comes mainly from a shell, and not from a filled body. In this work, we have followed the Mezger & Henderson formalism for a spherical shell model in order to derive physical parameters. Our results are compared with those from the filled sphere model. We conclude that physical parameters obtained using the shell model differ from those derived from the filled sphere model, by a factor of (1-α2)3/8 for electron density, (1-α2)3/4 for total ionized mass, and (1-α2)3/2 for emission measure. In all the cases, α is the internal radius of the shell, given in terms of its external radius. If we assume typical values for PNe shell thicknesses, the differences in the physical parameters derived for the two models range from 22% to 32% (electron density), 40% to 54% (ionized mass), and 64% to 78% (emission measure). We have applied the shell model to few PNe observed in radio continuum with the VLA (archive data). We also explore the feasibility for extending this study to other typical PNe morphologies (elliptical, bipolar, etc.).
This work is supported by grants CONACYT 102582 and PAPIIT-UNAM IN109509. SSG thanks CONACYT for her graduate scholarship.

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