3.1 The ionizing spectrum

The H-deficient non-LTE model atmosphere (Todt et al., 2010), which was calculated using the PoWR models for expanding atmospheres (Gräfener et al., 2002; Hamann & Gräfener, 2004), was used as an ionizing source in our photoionization models. The PoWR models were constructed by solving the non-LTE radiative transfer equation of an expanding stellar atmosphere under the assumptions of spherical symmetry and chemical homogeneity. The PoWR model used was calculated for the stellar surface abundances H:He:C:N:O = 40:55:1.3:2:1.3 (by mass), the stellar temperature $T_{\rm eff}$=52kK, the stellar luminosity $L_{\star}=6000{\rm L}_{\odot}$, the transformed radius $\log R_{\rm t}=1.43$R ${}_{\odot}$ and the wind terminal velocity $V_{\infty}=1000$ kms$^{-1}$, which well matches the dereddened stellar spectra from FUSE, IUE and MIKE, as well as 2MASS JHK bands (Todt et al., 2010). We see that the nebular $[$OIII$]$ $\lambda$5007 line flux relative to the H$\beta$ flux is well reproduced with an effective temperature of $T_{\rm eff}=52$kK in our photoionization models. The stellar luminosity of $L_{\star}=6000{\rm L}_{\odot}$ adopted by Todt et al. (2010) is related to a remnant core with a typical mass of $0.6M_{\odot}$ (e.g. Miller Bertolami & Althaus, 2007; Schönberner et al., 2005a). The distance was also varied in order to reproduce the nebular emission-line fluxes, under the constraints of our adopted stellar parameters and spherical density distribution. The best results for the photoionization models were obtained at a distance of 4.9 kpc.

Figure 3 compares the non-LTE model atmosphere flux of PB 8 with a blackbody flux at the same temperature. At energies higher than 54 eV (HeII ground state), there is a significant difference between the non-LTE model atmosphere and blackbody flux. As discussed by Rauch (2003), a blackbody is not an accurate representation of the ionizing flux. The H-deficient non-LTE model atmosphere has a major departure from the solar model atmosphere at higher energies due to the small opacity from hydrogen. In our photoionization models, we theretofore used an non-LTE model atmosphere as the ionizing source to provide the best fit to the nebular spectrum. However, the difference may not be largely noticeable in our model as high-excitation lines (e.g. HeII) are not observed.