5. Further discussion
5.1. Nebular mass
The nebular mass can be calculated in the usual way, assuming it to be a homogeneous sphere. The result is only approximate, not only because of this assumption, but also because it is difficult to accurately measure the nebular flux for low surface brightness objects. The results are given in column 6 of Table 5. The nebular masses span a large range. The mass of NGC 1360, 0.3 M , is about the average mass expected for PN, while that for A36 is about a factor of 5 lower. The mass of PHL 932, although uncertain, is about 2 orders of magnitude lower than the average PN. It is not an extreme value, however. Several other PN have similar values (see Table 9 of Pottasch, 1996). The lowest nebular mass is that of HW 5 with a mass of 5 10-4 M .
Table 5. Nebular mass and age
The two other PN with spectroscopic surface gravities and distances from VLA expansion as discussed above, have also been listed in Table 5 for comparison. Their masses are less than the average PN value, but in these two cases, a considerable amount of neutral material could exist outside the ionized nebula. This is not likely for PHL 932, A36 or NGC 1360, since the low Zanstra temperatures computed indicate that ionizing radiation is escaping from the nebula.
5.2. Position in the HR diagram
Since the distance is known, the luminosity can be calculated rather simply. The stellar radius can be calculated from Eq. (1), since
Note that the core mass no longer enters. The stellar temperature used is that given in Table 3. Since in PHL 932 and A36 this temperature has only been determined from the spectroscopic H analysis in which a substantially too low log g was found, the actual effective temperature could be higher, perhaps by as much as 30-40%.
The resultant positions in the HR diagram are shown in Fig. 1. The theoretical curves are those calculated by Schönberner and colleagues, and are taken from Blocker (1995). Also shown in the figure are lines of constant age, which are marked in units of 103 years. In addition to the central stars of the 3 nebulae under discussion in this paper, the 2 central stars mentioned earlier, of the PN NGC 3242 and NGC 6210 are also plotted using the distances of Hajian et al., 1995 (the other parameters are those listed in Pottasch, 1997). Further, the effect of increasing the effective temperature by 30% for A36 and PHL 932 is shown. The kinetic age (in units of 103 years) is shown for each nebula.
As can be seen from Fig. 1, the points for all of the central stars fall close to the tracks corresponding to the lowest core mass. However, there is a tendency for the kinetic age to be substantially lower than the theoretical age. This is most obvious for PHL 932 and NGC 3242. Only for the case of the central star of NGC 1360 is there reasonable agreement between the two ages.
© European Southern Observatory (ESO) 1998
Online publication: November 24, 1997