The relation between the ADF and the ionized nebular mass in PNe

Abstract: In this work we analyze the proposed relation between ADFs and ionized masses in planetary nebulae. For this, we have collected from the literature the ADFs and other parameters such as heliocentric distances, H$\beta$ luminosities, logarithmic reddening correction at H$\beta$, c(H$\beta$), electron densities and others and we calculated the ionized mass for a sample of 132 PNe, 27 of which possess a binary central star (14 are close binaries). In addition the distribution of these objects in the Galaxy is analyzed. The ionized masses were calculated considering two different electron densities, the one provided by the [S II] density sensitive lines ratio and the one provided by the [Cl III] lines ratio. No relation was found between ionized masses and ADFs for this sample, although it is confirmed than the PNe with the largest ADFs correspond in general to objects with a close binary central star, although it is important to say that about 20 percent of these objects have an ADF larger than 5 but smaller than 10. Therefore a PN having a close binary central star does not necessarily exhibit an extremely large ADF. We also have searched for possible relations between the ADFs and the stellar atmospheres, divided in H-rich and H-poor stars. No particular relation was found. Interestingly, several PNe with a [WR] H-poor CSPN present an ADF larger than 10, but so far they have not been reported as having a binary central star.