In this work we present a study of the density profiles, as determined from [SII] line ratios, for closed spherical and elliptical shells under different ionizing conditions calculated with a 3-D photoionization code, and for a group of 51 planetary nebulae (PNe)observed in long-slit mode with the Isaac Newton Telescope (INT).In particular, we show how the density profiles change with different ionizing conditions, density gradients from pole to equator and orientations, for elongated elliptical shells. Spherical shells are shown to have flat density profiles independent of thickness of the shell and ionizing condition and we show that elongated ellipsoidal shells, oriented in such a way as to produce a circular morphology do not show this behavior. We then analyze the PNe sample using their density profiles and observed images from the literature and show that many are elongated or open structures producing closed shell like morphologies. We conclude that morphological studies must take into account the orientation of the 3-D structure if a useful classification of PNe is sought and that the [SII] density profile is a helpful diagnostic in this sense.
Introduction
One of the first works to deal with the morphological classification of PNe was that of Curtis (1918). In this work Curtis classified a
sample of PNe in 5 different groups based on their visual appearance.
Since the work of Curtis, many attempts have been made to classify PNe
according to their morphological appearance and correlate this with
their observed and derived properties such as central star
temperature, mass, position in the Galaxy among others
Khromov & Kohoutek (1968) , Balick & Preston (1987), Balick (1987),Balick & Preston (1987), Balick et al. (1997), Icke, Preston & Balick (1989), Masson (1990), Schwars (1993), Zhang & Kwok (1998), Stanghellini (1999), Manchado(2004).
The range of shapes observed up to today has been reproduced by many
theoretical works using arguments such as density enhancements,
magnetic fields, and binary central systems. Despite this,
no complete agreement between models and properties of a given
morphological group has been achieved. One of the main reasons for
this is selection criteria and completeness of studied samples. The
samples are usually limited by available images in few bands such as
Ha, [NII] and [OIII]. Of course they are also limited by
distance, since the further away the object is, the harder it is to
resolve its structure. Even with the modern telescopes, obtaining a
truly complete sample is far from being achieved.
Another limitation rarely discussed on these studies is the fact that
these nebulae are three-dimensional structures in space and therefore
orientation effects will definitely play a role in defining what we
see. It has been shown by Monteiro et al. (2000) and works cited therein, that
an ``hour-glass'' structure can account for many different
morphological shapes when given different orientations. This important
fact has only been recently taken into account in Manchado (2004). In this
work the author shows that as much as 17% of the round (R) PNe in his
sample could be in reality elliptical (E) structures oriented with
their major axis towards the observer. These problems as well as the
others discussed above indicate that drawing conclusions from these
studies is quite complicated.
As discussed above Monteiro et al. (2000) showed that some objects might be
misclassified as closed shells based on their projected morphology
only. In that work NGC 3132 was modeled with an ``hour-glass''
structure oriented in such a way as to have an elliptical projected
morphology. That model proved to be much better in reproducing all the
available observational data for the object, in particular its [SII]
density profile. In this context we propose here to show that the
[SII] density profile can be used as a probe for open structures in
resolved PNe.
In this work we present the [SII] density profile as an additional
tool that can help in achieving a more precise classification scheme
for PNe. To demonstrate this we studied a sample of 51 PNe for which
we obtained long-slit spectroscopy. Using their density profiles and a
grid of three-dimensional photoionization models for different shell
structures we reclassify these observed PNe using their density
profile to decide between open or closed structures.