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Next: 6.2 Model results Up: 6.1 Model input parameters Previous: 6.1.2 Nebular abundances

6.1.3 Ionizing source

The central ionizing source of SuWt 2 was modelled using different non-local thermodynamic equilibrium (NLTE; Rauch, 2003) model atmospheres listed in Table 6, as they resulted in the best fit of the nebular emission-line fluxes. Initially, we tested a set of blackbody fluxes with the effective temperature ( $ T_{\rm eff}$) ranging from $ 80\,000$ to $ 190\,000$ K, the stellar luminosity compared to that of the Sun ( $ L_{\star}/{\rm L}_{\bigodot}$) ranging from 50-800 and different evolutionary tracks (Blöcker, 1995). A blackbody spectrum provides a rough estimate of the ionizing source required to photoionize the PN SuWt 2. The assumption of a blackbody spectral energy distribution (SED) is not quite correct as indicated by Rauch (2003). The strong differences between a blackbody SED and a stellar atmosphere are mostly noticeable at energies higher than 54 eV (He II ground state). We thus successively used the NLTE Tübingen Model-Atmosphere Fluxes Package4 (TMAF; Rauch, 2003) for hot compact stars. We initially chose the stellar temperature and luminosity (gravity) of the best-fitting blackbody model, and changed them to get the best observed ionization properties of the nebula.

Fig. 9 shows the NTLE model atmosphere fluxes used to reproduce the observed nebular emission-line spectrum by our photoionization models. We first used a hydrogen-rich model atmosphere with an abundance ratio of H:He=8:2 by mass, $ \log g =7$ (cgs), and $ T_{\rm eff}=140\,000$ K (Model 1), corresponding to the final stellar mass of $ M_{\star}=0.605\,{\rm M}_{\bigodot}$ and the zero-age main sequence (ZAMS) mass of $ M_{\rm\textsc{zams}}=3\,{\rm M}_{\bigodot}$, where $ {\rm M}_{\bigodot}$ is the solar mass. However, its post-AGB age ( $ \tau _{\rm post-\textsc {agb}}$) of 7500yr, as shown in Fig. 10 (left-hand panel), is too short to explain the nebula's age. We therefore moved to a hydrogen-deficient model, which includes Wolf-Rayet central stars ([WC]) and the hotter PG 1159 stars. [WC]-type central stars are mostly associated with carbon-rich nebula (Zijlstra et al., 1994). The evolutionary tracks of the VLTP for H-deficient models, as shown in Fig.10 (right-hand panel), imply a surface gravity of $ \log g= 7.2$ for given $ T_{\rm eff}$ and $ L_{\star}$. From the high temperature and high surface gravity, we decided to use `typical' PG 1159 model atmosphere fluxes (He:C:N:O=33:50:2:15) with $ T_{\rm eff}=160\,000$ K and $ L_{\star}/{\rm L}_{\bigodot}=600$ (Model 2), corresponding to the post-AGB age of about $ \tau_{\rm post-\textsc{agb}}=2$5000yr, $ M_{\star}=0.64\,{\rm M}_{\bigodot}$ and $ M_{\rm\textsc{zams}}=3\,{\rm M}_{\bigodot}$. The stellar mass found here is in agreement with the $ 0.7\,{\rm M}_{\bigodot}$ estimate of Exter et al. (2010). Fig.9 compares the two model atmosphere fluxes with a blackbody with $ T_{\rm eff}=160\,000$ K.

Table 6 lists the parameters used for our final simulations in two different NTLE model atmosphere fluxes. The ionization structure of this nebula was best reproduced using these best two models. Each model has different effective temperature, stellar luminosity and abundances (N/H, O/H and Ne/H). The results of our two models are compared in Tables 7-10 to those derived from the observation and empirical analysis.


Table 8: Mean electron temperatures (K) weighted by ionic species for the whole nebula obtained from the photoionization model. For each element the upper row is for Model 1 and the lower row is for Model 2. The bottom lines present the mean electron temperatures and electron densities for the torus (ring) and the oblate spheroid (inside).
  Ion  
Element I II III IV V VI VII  
H 11696 12904            
  11470 12623            
He 11628 12187 13863          
  11405 11944 13567          
C 11494 11922 12644 15061 17155 17236 12840  
  11289 11696 12405 14753 16354 16381 12550  
N 11365 11864 12911 14822 16192 18315 18610  
  11170 11661 12697 14580 15836 17368 17475  
O 11463 11941 12951 14949 15932 17384 20497  
  11283 11739 12744 14736 15797 17559 19806  
Ne 11413 11863 12445 14774 16126 18059 22388  
  11196 11631 12215 14651 16166 18439 20488  
S 11436 11772 12362 14174 15501 16257 18313  
  11239 11557 12133 13958 15204 15884 17281  
Ar 11132 11593 12114 13222 14908 15554 16849  
  10928 11373 11894 13065 14713 15333 16392  
  Torus Spheroid
  $ T_{\rm e}[$OIII$ ]$ $ N_{\rm e}[$SII$ ]$ $ T_{\rm e}[$OIII$ ]$ $ N_{\rm e}[$SII$ ]$
M.1 12187K 105cm$ {}^{-3}$ 15569K 58cm$ {}^{-3}$
M.2 11916K 103cm$ {}^{-3}$ 15070K 58cm$ {}^{-3}$


Table 9: Fractional ionic abundances for SuWt 2 obtained from the photoionization models. For each element the upper row is for the torus (ring) and the lower row is for the oblate spheroid (inside).
    Ion
  Element I II III IV V VI VII
Model 1 H 6.53($ -2$) 9.35($ -1$)          
    3.65($ -3$) 9.96($ -1$)          
  He 1.92($ -2$) 7.08($ -1$) 2.73($ -1$)        
    3.05($ -4$) 1.27($ -1$) 8.73($ -1$)        
  C 5.92($ -3$) 2.94($ -1$) 6.77($ -1$) 2.33($ -2$) 1.86($ -4$) 7.64($ -16$) 1.00($ -20$)
    3.49($ -5$) 1.97($ -2$) 3.97($ -1$) 4.50($ -1$) 1.33($ -1$) 1.09($ -12$) 1.00($ -20$)
  N 7.32($ -3$) 4.95($ -1$) 4.71($ -1$) 2.62($ -2$) 4.18($ -4$) 6.47($ -6$) 2.76($ -17$)
    1.02($ -5$) 1.30($ -2$) 3.65($ -1$) 3.97($ -1$) 1.59($ -1$) 6.69($ -2$) 6.89($ -13$)
  O 6.15($ -2$) 4.98($ -1$) 4.21($ -1$) 1.82($ -2$) 7.09($ -4$) 1.34($ -5$) 7.28($ -8$)
    6.96($ -5$) 1.26($ -2$) 3.31($ -1$) 4.03($ -1$) 1.69($ -1$) 6.00($ -2$) 2.42($ -2$)
  Ne 3.46($ -4$) 6.70($ -2$) 9.10($ -1$) 2.26($ -2$) 3.56($ -4$) 4.25($ -6$) 2.11($ -9$)
    1.39($ -6$) 3.32($ -3$) 3.71($ -1$) 3.51($ -1$) 2.05($ -1$) 6.55($ -2$) 4.49($ -3$)
  S 1.13($ -3$) 1.67($ -1$) 7.75($ -1$) 5.52($ -2$) 1.15($ -3$) 6.20($ -5$) 8.53($ -7$)
    3.18($ -6$) 3.89($ -3$) 1.73($ -1$) 3.53($ -1$) 2.43($ -1$) 1.57($ -1$) 6.91($ -2$)
  Ar 4.19($ -4$) 3.15($ -2$) 7.51($ -1$) 2.10($ -1$) 5.97($ -3$) 1.13($ -3$) 5.81($ -5$)
    1.12($ -7$) 2.33($ -4$) 5.81($ -2$) 2.83($ -1$) 1.85($ -1$) 2.73($ -1$) 2.01($ -1$)
Model 2 H 7.94($ -2$) 9.21($ -1$)          
    4.02($ -3$) 9.96($ -1$)          
  He 2.34($ -2$) 7.25($ -1$) 2.51($ -1$)        
    3.51($ -4$) 1.33($ -1$) 8.67($ -1$)        
  C 7.97($ -3$) 3.23($ -1$) 6.49($ -1$) 1.93($ -2$) 1.29($ -4$) 5.29($ -16$) 1.00($ -20$)
    4.45($ -5$) 2.23($ -2$) 4.13($ -1$) 4.41($ -1$) 1.23($ -1$) 1.00($ -12$) 1.00($ -20$)
  N 1.00($ -2$) 5.44($ -1$) 4.24($ -1$) 2.15($ -2$) 2.62($ -4$) 2.20($ -6$) 9.23($ -18$)
    1.31($ -5$) 1.52($ -2$) 3.84($ -1$) 4.07($ -1$) 1.50($ -1$) 4.40($ -2$) 4.34($ -13$)
  O 7.91($ -2$) 5.29($ -1$) 3.78($ -1$) 1.40($ -2$) 4.27($ -4$) 2.05($ -6$) 6.62($ -11$)
    9.34($ -5$) 1.50($ -2$) 3.60($ -1$) 4.20($ -1$) 1.75($ -1$) 2.97($ -2$) 1.85($ -4$)
  Ne 4.54($ -4$) 7.35($ -2$) 9.09($ -1$) 1.73($ -2$) 1.41($ -4$) 1.94($ -8$) 2.25($ -14$)
    1.75($ -6$) 3.85($ -3$) 4.19($ -1$) 3.86($ -1$) 1.89($ -1$) 1.73($ -3$) 6.89($ -7$)
  S 1.64($ -3$) 1.95($ -1$) 7.58($ -1$) 4.47($ -2$) 7.84($ -4$) 3.39($ -5$) 3.05($ -7$)
    4.23($ -6$) 4.86($ -3$) 1.96($ -1$) 3.61($ -1$) 2.39($ -1$) 1.47($ -1$) 5.16($ -2$)
  Ar 7.22($ -4$) 3.99($ -2$) 7.74($ -1$) 1.81($ -1$) 3.95($ -3$) 5.62($ -4$) 1.60($ -5$)
    1.72($ -7$) 3.22($ -4$) 7.30($ -2$) 3.30($ -1$) 1.96($ -1$) 2.62($ -1$) 1.39($ -1$)


Table 10: Integrated ionic abundance ratios for the entire nebula obtained from the photoionization models.
    Model 1 Model 2
Ionic ratio Empirical Abundance Ionic Fraction Abundance Ionic Fraction
He$ {}^{+}$/H$ {}^{+}$ 4.80($ -2$) 5.308($ -2$) 58.97% 5.419($ -2$) 60.21%
He$ {}^{2+}$/H$ {}^{+}$ 3.60($ -2$) 3.553($ -2$) 39.48% 3.415($ -2$) 37.95%
C$ {}^{+}$/H$ {}^{+}$ - 9.597($ -5$) 23.99% 1.046($ -4$) 26.16%
C$ {}^{2+}$/H$ {}^{+}$ - 2.486($ -4$) 62.14% 2.415($ -4$) 60.38%
N$ {}^{+}$/H$ {}^{+}$ 1.309($ -4$) 9.781($ -5$) 40.09% 1.007($ -4$) 43.58%
N$ {}^{2+}$/H$ {}^{+}$ - 1.095($ -4$) 44.88% 9.670($ -5$) 41.86%
N$ {}^{3+}$/H$ {}^{+}$ - 2.489($ -5$) 10.20% 2.340($ -5$) 10.13%
O$ {}^{+}$/H$ {}^{+}$ 1.597($ -4$) 1.048($ -4$) 40.30% 1.201($ -4$) 42.44%
O$ {}^{2+}$/H$ {}^{+}$ 1.711($ -4$) 1.045($ -4$) 40.20% 1.065($ -4$) 37.64%
O$ {}^{3+}$/H$ {}^{+}$ - 2.526($ -5$) 9.72% 2.776($ -5$) 9.81%
Ne$ {}^{+}$/H$ {}^{+}$ - 6.069($ -6$) 5.47% 6.571($ -6$) 5.92%
Ne$ {}^{2+}$/H$ {}^{+}$ 1.504($ -4$) 8.910($ -5$) 80.27% 9.002($ -5$) 81.10%
Ne$ {}^{3+}$/H$ {}^{+}$ - 1.001($ -5$) 9.02% 1.040($ -5$) 9.37%
S$ {}^{+}$/H$ {}^{+}$$ ^{a}$ 2.041($ -6$) 2.120($ -7$) 13.50% 2.430($ -7$) 15.48%
S$ {}^{2+}$/H$ {}^{+}$ 1.366($ -6$) 1.027($ -6$) 65.44% 1.013($ -6$) 64.55%
S$ {}^{3+}$/H$ {}^{+}$ - 1.841($ -5$) 11.73% 1.755($ -7$) 11.18%
Ar$ {}^{+}$/H$ {}^{+}$ - 3.429($ -8$) 2.54% 4.244($ -8$) 3.14%
Ar$ {}^{2+}$/H$ {}^{+}$ 1.111($ -6$) 8.271($ -7$) 61.26% 8.522($ -7$) 63.13%
Ar$ {}^{3+}$/H$ {}^{+}$ 4.747($ -7$) 3.041($ -7$) 22.52% 2.885($ -7$) 21.37%
Ar$ {}^{4+}$/H$ {}^{+}$ - 5.791($ -8$) 4.29% 5.946($ -8$) 4.40%
Ar$ {}^{5+}$/H$ {}^{+}$ - 7.570($ -8$) 5.61% 7.221($ -8$) 5.35%
$ ^{a}$ Shock excitation largely enhances the S$ {}^{+}$/H$ {}^{+}$ ionic abundance ratio.

next up previous contents
Next: 6.2 Model results Up: 6.1 Model input parameters Previous: 6.1.2 Nebular abundances
Ashkbiz Danehkar
2018-03-26