The dynamics of planetary nebulae in the Galaxy: evidence for a third integral

Abstract

We present a dynamical analysis of 673 galactic Planetary Nebulae, using a two-integral axisymmetric model with a Kuzmin-Kutuzov Stäckel potential. The method fits the kinematics to the projected moments of a distribution function, by means of Quadratic Programming. The 2.2 $μ$m COBE brightness map has been used after correction for the interstellar extinction as a projected star counts map in the modeling, because it constitutes a galactic distribution view of evolved red populations which are considered to be the progenitors of PNe. The model we have obtained provides a 2-integral distribution function for the COBE 2.2 $μ$m map, and thus {\it a fortiori} a deprojection of it, which allows moreover the identification of all the major Galactic components. We derive the density laws for them. The projected velocity dispersions are not well fitted though, especially in the disk, which points at the likely presence of a third integral. If this result can be confirmed by additional data, this would mean that for the first time the presence and importance of a third integral on a global scale is demonstrated.