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Journal of Physical Studies 20(4), Article 4901 [13 pages] (2016)
DOI: https://doi.org/10.30970/jps.20.4901 METHOD FOR DETAILED CALCULATION OF THE DIFFUSE IONIZING RADIATION IN NEBULAR ENVIRONMENTSO. S. Buhajenko, B. Ya. Melekh
Astrophysics Department, Ivan Franko National University of Lviv, |
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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. \par 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. \par 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$_\beta$ line (and, correspondingly, an increase of the intensities of emission lines relative to the H$_\beta$ 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 $\sim 17$\%). It can be explained by a longer mean free path of DIR photons in the nebular environment with a lower density.
PACS number(s): 98.58.Hf, 98.58.Li, 98.58.Ca