5 Photoionization modelling

The 3-D photoionization code MOCASSIN (version 2.02.67; Ercolano et al., 2005; Ercolano et al., 2008; Ercolano et al., 2003b) was used to study the best-fitting model for Abell48. The code has been used to model a number of PNe, for example NGC 3918 (Ercolano et al., 2003a), NGC 7009 (Gonçalves et al., 2006), NGC 6302 (Wright et al., 2011), and SuWt 2 (Danehkar et al., 2013). The modelling procedure consists of defining the density distribution and elemental abundances of the nebula, as well as assigning the ionizing spectrum of the CS. This code uses a Monte Carlo method to solve self-consistently the 3-D radiative transfer of the stellar radiation field in a gaseous nebula with the defined density distribution and chemical abundances. It produces the emission-line spectrum, the thermal structure and the ionization structure of the nebula. It allows us to determine the stellar characteristics and the nebula parameters. The atomic data sets used for the calculation are energy levels, collision strengths and transition probabilities from the CHIANTI data base (version 5.2; Landi et al., 2006), hydrogen and helium free-bound coefficients of Ercolano & Storey (2006), and opacities from Verner et al. (1993) and Verner & Yakovlev (1995).

The best-fitting model was obtained through an iterative process, involving the comparison of the predicted H$ \beta $ luminosity $ L_{{\rm H}\beta}$(ergs$ {}^{-1}$), the flux intensities of some important lines, relative to H$ \beta $ (such as $ [$III$ ]$ $ \lambda $5007 and $ [$II$ ]$ $ \lambda $6584), with those measured from the observations. The free parameters included distance and nebular parameters. We initially used the stellar luminosity ( $ L_{\star}=6000$L $ _{\bigodot}$) and effective temperature ( $ T_{\rm eff}=70$kK) found by Todt et al. (2013). However, we slightly adjusted the stellar luminosity to match the observed line flux of $ [$III$ ]$ emission line. Moreover, we adopted the nebular density and abundances derived from empirical analysis in Section 4, but they have been gradually adjusted until the observed nebular emission-line spectrum was reproduced by the model. The best-fitting $ L_{{\rm H}\beta}$ depends upon the distance and nebula density. The plasma diagnostics yields $ N_{\rm e} = 750$-1000cm$ ^{-3}$, which can be an indicator of the density range. Based on the kinematic analysis, the distance must be less than 2 kpc, but more than 1.5 kpc due to the large interstellar extinction. We matched the predicted H$ \beta $ luminosity $ L({\rm H}\beta)$ with the value derived from the observation by adjusting the distance and nebular density. Then, we adjusted abundances to get the best emission-line spectrum.

Ashkbiz Danehkar