4. Expansion velocities
The velocity fields resulting from fitting the [OIII ] lines are given in Table 2. We represent the velocity field of the model by two numbers: is the mass-weighted average velocity and is the difference between the velocities at the outer and inner radius.
Table 2. The expansion velocities and derived data concerning the nebulae and the central stars. Remarks: `wels' indicates a weak emission line star. Two nebulae are situated in the Sagittarius Dwarf galaxy and two objects may be halo PN.
The expansion velocity is defined in the same way as in Paper II, i.e. it is a mean value of the velocity field weighted by the mass distribution. This definition gives an average velocity which is more representative for the full nebula than using an unweighted value which would be more biased to the inner region. A separate column lists the expansion velocity as estimated from the observed profiles. For PNe with a [WC]-type nucleus we can expect strong turbulent motions which are beyond present analysis; these objects are marked in the last column.
Almost all nebulae show indications of the presence of a velocity gradient. The few objects with constant expansion velocity () show small expansion when broadening dominates. (One exception is PN G 001.7-04.6 with km s-1 but in this case we model only the line core.) For two objects is very small and may not be representative for the full nebula. We are probably missing some kinematical component not visible in [OIII ] lines.
The observed lines with the calculated profiles superposed are presented in Fig. 3 and Fig. 4. Many observed profiles show extended wings indicating high velocity outflows not modelled by us. We believe that this corresponds to the situation discussed earlier and shown in Fig. 2. For M 3-32 (009.4-09.8), the long-slit spectrum reveals a bipolar nature, which is confirmed by the radio image (Zijlstra et al. 1989). The effect is not very pronounced and we kept this PN in our sample, but the spherically symmetric model should be treated with caution.
Almost all models are ionization bounded. If the line ratios could be adequately reproduced with an ionization-bounded model, this model was accepted. Only if no good fit could be obtained did we attempt to fit density-bounded models. In our sample only PC 13 (351.9+09.0), appears density bounded since otherwise its very weak [NII ] 6584 Å line cannot be reproduced.
Table 3 and Fig. 5 present the velocities and line profiles for several PNe which were observed but for which the line profiles are too asymmetric for modelling. (In the case of 351.6-06.2, the velocities show a large gradient along the slit indicating a bipolar outflow. The spectrum shown in Fig. 5 appears symmetric only because it is summed over the slit.) These objects are not included in Fig. 6 since the values may not be a good representation for strongly aspherical nebulae. The non-symmetric, possibly bipolar objects show on average larger outflow velocities than the objects in Table 2.
Table 3. The expansion velocities estimated from half width at half maximum of the asymmetric [OIII ] line profiles
Fig. 6 presents the histogram of the expansion velocities, in bins of 5 km s-1. Separately shown are the mass-weighted average velocities from the models (continuous line) and the HWHM values (dashed line). The model velocities peak between 20 and 30 km s-1 but the distribution shows a long wing towards smaller velocities. The HWHM velocities have a maximum at smaller values of about 15-20 km s-1. This difference can be easily understood, because the [OIII ] emission comes from layers where OIII is the dominant ionization stage and the photoionization calculations show that this is always the inner nebular region. The models correct for this effect, defining as a global parameter of the nebula. We calculated the mean values which are respectively: km s-1, km s-1. The mean ionized mass is 0.16 .
4.2. Comparison with other expansion velocity data
The largest data set for expansion velocities of Galactic PNe is the catalog of Weinberger (1989) which is included in the ESO-Strasbourg Catalog of Galactic PNe (CGPN: Acker et al. 1992). The available data include measurements both in the [OIII ] and [NII ] lines, although for many objects only [OIII ] has been measured. Sabbadin (1984) presented a previous catalogue of expansion velocities of 165 PNe, mostly based on [OIII ] line profiles. Dopita et al. (1985 and 1988) present [OIII ] expansion velocities for PNe in the SMC and the LMC respectively. Because they are relatively faint, few measurements of Bulge PN have so far been made.
The expansion velocities in Sabbadin's catalogue were derived in a variety of ways, but mostly from line splitting. Weinberger also primarily uses line splitting, but lists more values for [NII ] and H. Note that both catalogues present twice the expansion velocity. Observations were typically taken at a resolution of 10-20 km s-1.
Because of the way of measuring the expansion velocity, these values cannot be readily be compared with ours. For [OIII ], the published values may have been underestimated (see Fig. 1). Some measured velocities were reduced to correct for the presence of velocity gradients (e.g. Bianchi 1992). The MCs values of Dopita et al. are based on half width at ten per cent of the maximum. Table 1 shows that such a definition overestimates the velocity, but in the case of a velocity gradient their velocity is biased towards the outermost velocity and would be much larger than our mass-weighted average velocity.
4.3. Radius versus expansion velocity
Several papers have noticed a correlation between nebular radius and expansion velocity (e.g. Robinson et al. 1982, Sabbadin 1984, Bianchi 1992). These relations were based on [OIII ] expansion velocities, and used statistical distances. Chu et al. (1984) show that when instead of the [OIII ] line the [OII ] is used, only a very weak correlation remains for the most compact nebulae. Compact nebulae tend to have cooler central stars, and their [OIII ] emission arises from near the inner radius. The internal velocity gradient causes these velocities to be artificially low.
Fig. 7 shows our data: the only relation which seems to exist is that at small radii, a number of Bulge PN have very low expansion velocities, which are absent at larger nebulae. However, other Bulge PNe at the same radii do show large velocities. Among the disk PNe, there are no objects at small radii and low velocities. The sample is too small to judge whether this difference between the populations is real.
For very large, nearby PNe, the expansion velocities are known to decrease with radius. However, this strongly depends on the height above the Galactic plane: Hippelein & Weinberger (1990) show that for PNe larger than 0.25 pc radius, the mean expansion velocity is 10 km s-1 in the plane but 35 km s-1 at . The decrease in expansion velocity therefore seems related to deceleration by the ISM. In the Bulge, where the ISM is relatively unimportant, one would expect little deceleration. Interestingly, no Bulge PN larger than 0.2 pc is known. This may be related to a lack of ISM, so that the ionized mass does not increase beyond of the order of 0.2 . This would cause large PNe to quickly diminish in brightness.
4.4. Evidence for acceleration
The expansion velocity field of a planetary nebula arises from the original AGB wind, accelerated by interacting winds and ionization. The kinetic energy in the expansion can thus be seen as the original kinetic energy of the AGB wind, plus the amount deposited by the fast wind from the PN core. The original AGB wind has a near-constant velocity with radius; the gradient in the PN velocity field is caused by the interacting winds and the ionization (Schönberner & Steffen 1999, 2000).
The original AGB outflow velocity can be estimated if the luminosity and metallicity of the star is known. Habing et al. (1994) show that where is the dust-to-gas ratio. For mass-loss rates above the velocities are almost independent of mass-loss rates. We have calculated for the PNe with known metallicity (using the O/H in Table 2). We assumed that a star with solar metallicity (O/H=8.93) has an AGB outflow velocity of 15 km s-1. Fig. 8 plots against . All but one object are expanding faster than their original AGB wind, typically by a factor of 2. This is direct evidence for the acceleration processes even for the most compact objects (in contrast to the result of Gussie & Taylor 1994). There is little evidence that depends on the original AGB velocity: most of the memory of this wind is lost in the ionized region of a PN. We note that the single object with a very low abundance in our sample also has a low which could be a residual effect of its very low predicted . However, confirmation would require a much larger sample.
© European Southern Observatory (ESO) 2000
Online publication: June 20, 2000