To derive the de-projected expansion velocity field and the real gas distribution within the slice of nebula covered by the spectroscopic slit, we will follow the original method described by Sabbadin (1984) and Sabbadin et al. (1985), and recently applied by Sabbadin et al. (2000) to the low excitation PN NGC 40.
The basic consideration is that the position, radial thickness and density of each emitting region in an extended, expanding object can be obtained from the velocity, FWHM and flux, respectively.
In the case of NGC 1501, the limited number of emissions detected and the total absence of stratification effects across the nebula force us to use a linear position-speed relation. Moreover, from the angular extent of the ellipses fitting the "low latitude" nebular regions in Fig. 3, we will adopt = 20", where is the nebular radius in the radial direction at the apparent position of the central star (for details, see Sabbadin, 1984). Finally, an electron temperature of 11500 K and a turbulence of 18 km s-1 (both constant over the nebula) are assumed.
The adoption of other (reasonable) sets of parameters doesn't substantially modify the results here obtained.
Our tomographic analysis of NGC 1501 mainly concerns the electron density; the Ne structure of the nebula at the four position angles is shown in Fig. 5. According to the discussion above, the ) tomographic maps coincide with the Ne ones (but for a scaling factor of 1.1). The same situation occurs for , but in this case the scaling factor is ; in fact, the 5007 Å intensity reported in Table 1 gives (see Aller & Czyzak, 1983 and Aller & Keyes, 1987). Moreover, the ionization structure of NGC 1501 suggests that most oxygen is doubly ionized, so that ; to be noticed that Stanghellini et al. (1994) report for this nebula and .
The only previous Ne determination in NGC 1501 dates back to Aller & Epps (1976), who observed at low spectral resolution a small region centred 20" from the star (in P.A.=125o); they derived , corresponding to Ne=1200 cm-3 (for Te=11500 K). Their direction is intermediate between our P.A.=100o and P.A. =145o; at a distance of 20" from the central star we obtain the following density peaks:
Ne(blue shifted)=900 cm-3 and
Ne(red shifted)=1000 cm-3 in P.A.=100o;
Ne(blue shifted)=700 cm-3 and
Ne(red shifted)=900 cm-3 in P.A.=145o.
Unfortunately, a more detailed comparison appears hazardous, due to the differences in the spectroscopic resolution and reduction procedure, and, in particular, to the presence of small scale density fluctuations within the nebula.
The de-projected expansion velocities of NGC 1501 (directly obtainable from Fig. 5, given the linear position-speed relation used) span in the range 38(2) to 55(2) km s-1. The slowest motions occur in the densest regions at P.A.=10o and P.A.=145o; the combination (high density + low expansion velocity) here observed suggests that the minor axis of the central ellipsoid is projected at P.A.170o (in agreement with the indications given in Sect. 3). The largest expansion velocities [55(2) km s-1] correspond to the high latitude, untilted, hemispheric bubbles at P.A.=100o; in this case, the combination (low density + high velocity) suggests that we are (almost) observing the projection of the major axis of the central figure. Finally, from geometrical considerations, the projection of the intermediate axis can be put at P.A.30o.
Fig. 5 summarizes most of the observational results given in the previous sections, confirming the composite structure of the nebula: NGC 1501 is an ellipsoid of moderate ellipticity, deformed by a pair of large lobes along both the major and intermediate axes and by a number of minor bumps scattered on the whole nebular surface (in a few cases, see for instance the big "ear" in the N-W sector of P.A.=145o, the dimensions of these "minor bumps" appear comparable to those of the lobes related to the axes of the central ellipsoid).
In Fig. 5, the absence of the broad, inwards tail at low latitude is probably due to instrumental limitations: intuitively, our echellograms of an extended PN like NGC 1501 have a "spatial" resolution along the slit which is better than the "spectral" resolution along the dispersion. Due to projection effects, the "low latitude" zones (dominated by the expansion velocity field) have a "spectral" resolution, the "zero-velocity pixel column" has a "spatial" resolution (being unaffected by the expansion velocity field) and the "high latitude" zones an hybrid resolution. Clearly, this gradual variation in resolution conditions the tomographic reconstruction. In other words: we cannot exclude the presence of a low density, inwards tail also at low latitude. Only deep observations at much higher spectral resolution could solve the question.
Having said this, we believe that Fig. 5 adequately reproduces the true matter distribution in NGC 1501, and that the faint, inwards emissions visible at high latitude do represent the trace of the original ellipsoidal structure (note, in particular, the sharp radial profile in the high latitude zone at P.A.=55o and the detached structure in the N-W sector of P.A.=145o, fitting the ellipsoid projection). This implies that some accelerating agent partly swept-up the lower density regions of the triaxial ellipsoid, causing both the extended, hemispheric bubbles and the broad, inwards density tails. The final result of this acceleration is constituted by the spatial structure illustrated in the next section.
© European Southern Observatory (ESO) 2000
Online publication: October 10, 2000