3-D modelling of the collimated bipolar outflows of compact planetary nebulae with WR-type central stars

Abstract: We present high-resolution, long-slit spectroscopic observations of five compact ($\leq$ 10 arcsec) planetary nebulae located close to the galactic bulge region and for which no high spatial resolution images are available. The data have been drawn from the San Pedro M\'artir kinematic catalogue of galactic planetary nebulae (L\'opez et al. 2012). The central star in four of these objects (M 1-32, M 2-20, M 2-31 and M 3-15) is of WR-type and the fifth object (M 2-42) has a wels type nucleus. These observations reveal the presence in all of them of a dense and thick equatorial torus-like component and high-speed, collimated, bipolar outflows. The code SHAPE is used to investigate the main morpho-kinematic characteristics and reproduce the 3-D structure of these objects assuming a cylindrical velocity field for the bipolar outflows and a homologous expansion law for the torus/ring component. The deprojected expansion velocities of the bipolar outflows are found to be in the range of 65 to 200 km $\rm{s^{-1}}$, whereas the torus/ring component shows much slower expansion velocities, in the range of 15 to 25 km $\rm{s^{-1}}$. It is found that these planetary nebulae have very similar structural components and the differences in their emission line spectra derive mostly from their different projections on the sky. The relation of their morpho-kinematic characteristics with the WR-type nuclei deserves further investigation.