%0 Journal Article %T A radio-continuum and photoionization-model study of the two planetary nebulae in the Sagittarius dwarf galaxy %A G. Dudziak %A D. Pequignot %A A. A. Zijlstra %A J. R. Walsh %J Physics %D 2000 %I arXiv %X Radio continuum observations at 1.4, 4.8 and 8.6 GHz of the two Planetary Nebulae (PNe) in the Sagittarius dwarf galaxy reveal the elongated shape of Wray 16-423 and the extreme compactness of He 2-436. He 2-436 is confirmed as subject to local dust extinction. Photoionization models for both PNe are obtained from two different codes, allowing theoretical uncertainties to be assessed. Wray 16-423, excited by a star of Teff 1.07x10^5K, is an ellipsoidal, matter-bounded nebula, except for a denser sector. He 2-436, excited by a 7x10^4K star, includes two radiation-bounded shells, with the inner one possibly corresponding to a transitory event. Both stars are on the same (H-burning) evolutionary track of initial mass (1.2+/-0.1) Msun and may be twins, with the PN ejection of Wray 16-423 having occured ~1500 years before He 2-436. The PN abundances re-inforce the common origin of the parent stars, indicating almost identical depletions with respect to solar for O, Ne, Mg, S, Cl, Ar, and K (-0.55+/-0.07 dex), large identical overabundances for He and strong overabundances for carbon, particularly in He2-436. Excess nitrogen makes Wray 16-423 nearly a Type I PN. These PNe provide a means to calibrate both metallicity and age of the Sagittarius stellar population, and they confirm that the youngest, most metal-rich population has an age of 5Gyr and a metallicity of [Fe/H]=-0.55, in agreement with the slope of the red giant branch. (Abridged abstract) %U http://arxiv.org/abs/astro-ph/0009054v1