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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]

The approximate methods to calculate the diffuse ionizing radiation (DIR) fluxes during the calculation of the photoionization model (PhM) of the nebular environment are frequently used with the purpose of increasing the calculation speed of modern photoionization codes as well as for the simplification of their calculation algorithms. The most popular is the so-called Outward Only method. But the precision requirements to PhM codes increase too. Thus, the task arises on the estimation of the errors due to the use of approximate methods for the DIR calculation. We developed the algorithm for a detailed DIR calculation during photoionization modelling of the nebular objects based on the solution of the DIR transfer equation along various directions from the outer edges of nebula to the volume we are modelling. To accelerate the numerical integration over the angles the optimization procedure based on the search for the optimal integration steps was developed. To implement a detailed method for the DIR calculation the DiffRaY procedure was developed. To calculate the DIR fluxes the DiffRaY uses the emissivities map (in Ly-continuum as well as in the emission lines) obtained from the results of the photoionization modelling code. Therefore, it is not necessary to modify the core of the code for photoionization modelling during its upgrade by our DiffRaY procedure for the DIR calculation. That allows us to increase the speed of calculations as well as to avoid the mistakes which could arise during modifications in the core of code for photoinization modelling. We upgraded G. Ferland's code Cloudy 08.00 by our DiffRaY procedure. Using this code the spherically symmetrical PhMs of planetary nebulae (PNe) as well as the HII regions with a constant density distribution over their volumes were calculated. Also, we calculated PhMs of these objects using the Outward Only approximation for the DIR calculation. The comparative analysis of such PhMs has shown that the models calculated using a detailed method for DIR (DM-DIR) fluxes determination have a slightly lesser volume of the ionizing gas than those calculated in the Outward Only approximation (OOA-DIR). It caused a decrease in the radiation fluxes in the H^ line (and, correspondingly, an increase of the intensities of emission lines relative to the H^ one) in the DM-DIR models as compared with the OOA-DIR ones. The deviations of the OOA-DIR models from the DM-DIR ones depend also on the density of the nebular environment. Therefore, the PhMs of PNe calculated using DM-DIR and OOA-DIR methods have shown much fewer differences (2-6%) in relative intensities than in the case of PhMs of HII regions (up to ~ 17%). It can be explained by a longer mean free path of DIR photons in the nebular environment with a lower density. [ABSTRACT FROM AUTHOR]

Samuil Kaplan (1921-1978) was a productive and famous astrophysicist. He was affiliated with a number of scientific centers in different cities of the former Soviet Union. During the earliest 13 years of his career, namely in 1948-1961, he worked at the Lviv University in Ukraine. In the present paper, the Lviv period of his life and scientific activity is described on the basis of archival materials and his published studies. Kaplan arrived in Lviv in June 1948, the same month when he obtained the degree of the Candidate of Science. He was a head of the astrophysics sector at the Astronomical Observatory of the University, a professor of the department for theoretical physics, as well as the founder and head of a station for optical observations of artificial satellites of the Earth. He was active in the organization of an astronomical observatory outside the city. During the years in Lviv, Kaplan wrote more than 80 articles and 3 monographs in 9 areas. At that time, his focus was on the stability of circular orbits in the Schwarzschild field, on the white dwarf theory, on space gas dynamics, on cosmic plasma physics and turbulence, on the acceleration of cosmic rays, on the physics of interstellar medium, on the physics and evolution of stars, on cosmology and gravitation, and on the optical observations of the Earth's artificial satellites. Some of his findings are fundamental to the development of theory in those fields as well as of observational techniques. The paper presents a complete bibliography of Kaplan's works published during the Lviv period and reviews his respective scientific achievements in the light of the current state of research in those areas. [ABSTRACT FROM AUTHOR]