thesis - IRS, The Infrared Spectrograph

132 CHAPTER 6: Physical Conditions in PDRs around Planetary Nebulaederived because the Hβ flux is unknown.Knowing the H 2 column density (N(H 2 )) and the distance to the object the mass of themolecular hydrogen (M(H 2 )) can be determined using;M(H 2 ) = 2 m H π(d θ 2 )2 N(H 2 ) (6.7)where m H is the mass of the hydrogen nuclei, d being the distance to the nebulae and θ thenebular diameter (see Table 6.2). Note that this estimate of the molecular hydrogen mass isheavily weighted towards warm molecular hydrogen associated with the PDR.The atomic, ionized and H 2 masses are given in Table 6.10. These mass estimates arecomplemented by molecular masses derived from low J CO observations (Huggins et al.1996). These latter mass estimates are much better probes of the cold molecular gas massassociated with these PNe. Since they sometimes adopted distances that are different fromour values, we have scaled their masses to our assumed distances. They also adopted a COabundanceof 3×10 −4 . We have scaled these to the carbon abundance on the oxygen-richPNe (since the carbon should be in CO), and to the oxygen abundance for the carbon-richPNe (since all the oxygen should be in CO). Table 6.10 shows that the overall mass budget isin general dominated by the atomic mass. However, for NGC 3918 and NGC 6543 the ionizedmass is larger than the atomic mass by a factor ∼4. This is interesting since it implies thatnot in all nebulae the atomic mass is larger than the ionized mass, as is often assumed. Thederived H 2 mass is in principle representative of the warm molecular region in the PDR (sinceit is rotationally and vibrationally excited) and not of the total molecular mass. This can beseen in NGC 7027 where the H 2 mass is clearly smaller than the molecular mass. However,in NGC 6302 the differences is very small. Since for Hb 5 no molecular mass is available, forthe discussion in the next section, we have assumed that the H 2 mass is representative of themolecular mass for that nebula. This is probably a lower limit but as we shall see later evena molecular mass double of that assumed does not compromise our conclusions. The largeatomic mass in NGC 6302 contrast with that found by Liu et al. (2001) (0.7 M ⊙ ).6.11 General discussionAn interpretation of the evolution of the different mass components (ionized, molecular andatomic) in the nebulae is given in this section. For that purpose, ratios of masses (to avoiduncertainties in the distances) have been plotted against the nebular radius in Fig 6.10. Thisradius can be roughly related to the age of the nebula where older nebulae have larger radiusthan young nebulae. Due to the different morphologies in PNe and in order to be consistent,the nebular radius used is that of the main ionized component in the nebula. In many cases theemission from the ionized material is coming from a spherical shell even in PNe with bipolaror complex morphology. These radii have been derived from the diameters labeled in the lastcolumn of Table 6.10 and have been taken from Cahn et al. (1992), except, BD+30 3639 andNGC 6302 (Acker et al. 1992, from optical and radio images, respectively), and NGC 3918from Corradi et al. (1999).Unfortunately, the conclusions drawn below are impacted by the small sample of objectsand the strong bipolar geometries exhibited by some of the sources. In addition to the small