Table 6 lists the observed and predicted nebular emission line fluxes. Column 4 presents the observed, dereddened intensities of PB8 from García-Rojas et al. (2009), relative to the intrinsic dereddened H flux, on a scale where (H). The ratios of predicted over observed values from the model MC1 are presented in Column 6. Columns 7-9 present the ratios of predicted over observed values for the normal component, the metal-rich component, and the entire nebula (normal+metal-rich) from the best-fitting model MC2. The same values obtained from the model MC3 are given in Columns 10-12. The majority of the CEL intensities predicted by model MC1 are in reasonable agreement with the observations. However, there are some large discrepancies between the prediction of model MC1 and the observations for ORLs. From the model MC2, it can be seen that the ORL discrepancy between model and observations can be explained by recombination processes of colder metal-rich inclusions embedded in the global H-rich environments.
As seen in Table 6, the NII 6584 and OIII 5007 line intensities predicted by the models MC1 and MC2 are in excellent agreement with the observations. As both the models MC2 and MC3 have exactly the same density distribution and chemical abundances, we can see how dust grains introduce a percent increase in the NII 6584 line, which means that nitrogen abundance could be overestimated in some dusty nebulae. The HI line intensities as well as the majority of the HeI line intensities are in reasonable agreement with the observations, discrepancies within 20 percent, apart from the HeI 3889, 5875 and 7065 (around 30 percent). This could be due to high uncertainties of the recombination coefficients of the HeI lines below 5000K (see Porter et al., 2013; Porter et al., 2012). The [OII]7319 and 7330 doublets are underestimated by around 50 percent in the model MC1. Recombination processes can largely contribute to the observed fluxes of these lines, which can be estimated by the empirical equation given by Liu et al. (2000) (see equation 2).
There are discrepancies between the predicted intensities of SII and SIII lines and the observed values. While the intensities of the SII lines are predicted to be about 10-20 percent lower than the observations, the intensity of the SIII 6312 line is calculated to be almost twice more than the observed value. Adjusting the sulfur abundance cannot help reproduce SIII lines, so these discrepancies could be related to either the atomic data or the physical conditions. The predicted intensities of SII lines were calculated using S collision strengths from Ramsbottom et al. (1996) incorporated into the CHIANTI database (V 7.0), which is currently used in MOCASSIN. Recently, new S collision strengths were calculated by Tayal & Zatsarinny (2010), which ignored the effect of coupling to the continuum in their calculations, so their results were estimated to be accurate to about 30 percent or better. We note that the emissivities of SII 6716,6731 lines calculated by the proEQUIB IDL Library 3, which includes an IDL implementation of the Fortran program EQUIB (Howarth et al., 2016; Howarth & Adams, 1981), show that the collision strengths by Tayal & Zatsarinny (2010) make them about 8 percent lower at the given physical conditions. The predicted SIII line intensities are perhaps much more uncertain, as there seem to be some errors in the atomic data, as mentioned by Grieve et al. (2014). For example, the emissivity of SIII 18.68m line calculated using the collision strengths from Tayal & Gupta (1999) is about 40 percent higher than the calculation made with Hudson et al. (2012) or Grieve et al. (2014). This issue might be related to the long-standing problem of the sulfur anomaly in PNe (see reviews by Henry et al., 2012).
The predicted intensities of the ArIII 7136,7751 lines are in agreement with the observations, discrepancies within 20 percent, however, the IR fine-structure ArIII 8.99 m line is predicted to be about 80 percent higher. We used Ar collision strengths from Galavis et al. (1995) used by the CHIANTI database (V 7.0). There is another set for Ar collision strengths (Munoz Burgos et al., 2009) whose predictions are significantly different and need to be examined carefully. We notice that the emissivities of ArIII 7136,7751 lines predicted by proEQUIB with the collision strengths from Munoz Burgos et al. (2009) show a discrepancy of about 9 percent in comparison to those calculated with Galavis et al. (1995), whereas there is a 30 percent difference in the ArIII 8.99 m emissivity calculated with the different atomic data.
The predicted NeII 12.82 m and NeIII 3869,3967 line intensities do not show high discrepancies (less than 20 percent), nevertheless, the calculated intensities of NeII 15.55,36.02 m lines have discrepancies about 26 and 57 percent. The predicted ClIII 5518,5538 lines are in agreement with the observations, discrepancies less than 25 percent.
Although the [OIII] 4363 auroral line is perfectly matched by the model MC3 and discrepancies remain less than 10 percent in the model MC2, there is a notable discrepancy in the [NII] 5755 auroral line. This could be due to excitation by continuum fluorescence and/or recombination process. Bautista (1999) found that the [NI] 5198,5200 lines are efficiently affected by fluorescence excitation in many objects, while [OI] lines were found to be sensitive to fluorescence in colder regions (K) or very high radiation fields. Nevertheless, this PN is not known to be surrounded by a photo-dissociation region (PDR) that is responsible for the fluorescence excitation. We notice that García-Rojas et al. (2009) observed the brightest part of the nebula, and excluded the central star contamination and the surrounding potential PDR. Moreover, the absences of the [O I] 6300,6364 lines emitted by neutral O ion and the [N I] 5198,5200 lines emitted by neutral N ion in the spectrum presented by García-Rojas et al. (2009) exclude any possibilities of the fluorescence contamination. Hence, there is no strong evidence for any possible fluorescence contributions to the observed fluxes. Alternatively, the recombination contribution to [NII] auroral lines may have some implications, which can be estimated for low-density uniform nebular media (see e.g. Liu et al., 2000).
The recombination contribution to the [NII] 5755 line and the [OII] 7320,7330 doublet can be estimated as follows (Liu et al., 2000):
The intensities of the ORLs predicted by the model MC2 and MC3, both bi-abundance models, can be compared to the observed values in Table 6. Figure 6 compares the predicted over observed flux ratio for the model MC3, and shows the relative contributions of the normal and the metal-rich components to each emission-line flux. The agreement between the ORL intensities predicted by the two latter models and the observations is better than those derived from the first model (MC1). The majority of the OII lines with strong intensities are in reasonable agreement with the observations, with discrepancies below 40 percent, except for 4649.13, 3749.48, 4075.86, 4132.80 and 4153.30. The well-measured NII 5666.64, 5676.02 and 5679.56 lines are in good agreement with the observations, and discrepancies are less than 30 percent. There are some discrepancies in some OII ORLs (e.g. 4416.97, 4121.46, 4906.81) and NII ORLs (e.g. 4601.48, 4613.87, 5931.78), which have weak intensities and higher uncertainties (20-30 percent). However, as seen in Figure 6, the model MC3 has significant improvements in predicting the O II and N II lines having intensities stronger then other ORLs. Particularly, the bi-abundance models MC2 and MC3 provide better predictions for the O II ORLs from the V1 multiplet and the N II ORLs from the V3 multiplet, which have the reliable atomic data. Comparing Figure 6 with Fig. 15 in Yuan et al. (2011) demonstrates that our bi-abundance models of PB8, similar to the photoionization model of NGC6153, better predict the observed intensities of the N II and O II ORLs. The models also reproduce the C II ORLs with discrepancies about 10 percent, except the CII 6578 line. The CII 4267.2 line is stronger than the other C II lines, and it is not blended with any nearby OII ORLs. The CII 6578 line may be blended with nearby lines, so its measured line strength may be uncertainty.