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The study has calculated the grid of photoionization models for the homogeneous planetary nebulae in the Milky Way galaxy with the dust grain along the evolutionary tracks of their central stars. Based on these calculations, the age dependencies of the electron temperature of doubly-ionized oxygen atoms (O III) were obtained. For nebulae with low-mass progenitor stars (up to ≈1.5М☉), these age dependencies contain domains with an almost constant temperature. However, this temperature is sensitive to the masses of both the progenitor star and the nebular envelope. Thus, the behavior of the electron temperature obtained for the doubly-ionized oxygen ionization zone can be used to determine the masses mentioned above. Here we test our assumptions in the case of the Milky Way homogeneous planetary nebulae. As a result, a method for the determination of the masses of a planetary nebula envelope as well as its progenitor star using the value of the electron temperature within the doubly-ionized oxygen ionization zone is proposed. This method consists of two steps. At the first step, for a given planetary nebula we define the ratio of the emission line intensities of ionized sulfur atoms I[SII]λ 6716/I[SII]λ 6731. This ratio is sensitive to the age of the nebula, which allows us to obtain the limit on its age. At the second step, based on the temperature diagnostic ratio λ 4363AA/(λ 4959AA + λ 5007AA) between the emission line intensities of the doubly-ionized oxygen in the planetary nebula envelope, the value of the electron temperature is determined. Taking into account the limit on the age of the planetary nebula mentioned above, the obtained result is compared with the age dependencies of the averaged electron temperature within the nebular gas for different masses of the progenitor star and the planetary nebula envelope. Matching this value with a specific curve within the respective age range allows us to determine the masses of both the progenitor star and the planetary nebula envelope. This procedure is verified for two cases of the electron temperature determination: using the method of crossing of $n_{\rm e}-T_{\rm e}$ dependences obtained for various diagnostic ratios between emission lines as well as the popular two-zones Pagel's method (the so-called $T_{\rm e}$-method), that is based on diagnostic ratios between auroral and nebular emission lines of the doubly-ionized oxygen. As a result, using this method the mass of a progenitor star is determined with some accuracy. However, the mass of a planetary nebula envelope is determined within the accuracy of ±0.1 М. [ABSTRACT FROM AUTHOR]

The study has established the electron density and temperature, ionic and elemental abundances, optical thickness at the ionization potentials of H0 , He0 and He+ in nebular envelopes of the symbiotic novae V1016 Cyg and НМ Sge. Also, the temperature of the central stars and their radii as well as other characteristics of these objects were obtained. The photoionization and optimal photoionization models of the envelopes of V1016 Cyg and НМ Sge were calculated using required input data (gas density distribution, spectrum of the ionizing source as well as chemical abundances) obtained previously by diagnostic methods. In particular, the optimal photoionization models were found using a three-stage approach developed by us previously to model the planetary nebulae envelopes. As a result, the chemical abundances and physical parameters of these objects were determined in a more correct way than before. A similarity between radial density distributions and ionization potentials of ions was detected. Such similarity, if it is detected also in other compact nebular environments, can open a new approach to the determination of the gas density distribution along the sight line. Also, it was shown that the character of the radial density distribution within these objects is similar to that seen in some planetary nebulae. It was demonstrated that the electron temperature radial distribution in such kind of nebular objects is sensitive to the boundary between He++ and He+ ionization zones. The compactness of such nebular objects in most cases allows using only spectroscopical methods to determine their internal structure. Therefore, to calculate more detailed models of V1016 Cyg and HM Sge, with deviation from spherical symmetry, it is necessary to obtain the spectroscopic observational data of these objects with a high signal-to-noise ratio over a wide wavelength range (e. g., λ3500 ˚A–λ7500 ˚A). [ABSTRACT FROM AUTHOR]