Bayesian posterior classification of planetary nebulae according to the Peimbert types^*

¹ Observatório Nacional, Rua General José Cristino 77, 20921-400 Rio de Janeiro, RJ, Brazil e-mail: quireza@on.br
² Observatório do Valongo, Universidade Federal do Rio de Janeiro, Lad. Pedro Antônio 43, 20080-090 Rio de Janeiro RJ, Brazil e-mail: helio@ov.ufrj.br
³ Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, 05508-900, São Paulo, SP, Brazil e-mail: maciel@astro.iag.usp.br

Received: 14 June 2007
Accepted: 30 August 2007

Abstract

Context.Galactic planetary nebulae are observed with a wide variety of kinematic properties, spatial distribution, chemical composition and morphologies, comprising members of the dominant stellar populations of our Galaxy. Due to their broad astrophysical interest, a proper characterization of these populations is of major importance.

Aims.In this paper we present a re-analysis of the criteria used to characterize the Peimbert classes I, IIa, IIb, III and IV, through a statistical study of a large sample of planetary nebulae previously classified according to these groups. In the original classification, it is usual to find planetary nebulae that cannot be associated with a single type; these most likely have dubious classifications into two or three types. Statistical methods can greatly contribute in providing a better characterization of planetary nebulae groups.

Methods.We use the Bayes Theorem to calculate the posterior probabilities for an object to be member of each of the types I, IIa, IIb, III and IV. This calculation is particularly important for planetary nebulae that are ambiguously classified in the traditional method. The posterior probabilities are defined from the probability density function of classificatory parameters of a well-defined sample, composed only by planetary nebulae unambiguously fitted into the Peimbert types. Because the probabilities depend on the available observational data, they are conditional probabilities, and, as new observational data are added to the sample, the classification of the nebula can be improved, to take into account this new information.

Results.This method differs from the original classificatory scheme, because it provides a quantitative result of the representativity of the object within its group. Also, through the use of marginal distributions it is possible to extend the Peimbert classification even to those objects for which only a few classificatory parameters are known.

Conclusions.We found that ambiguities in the classification of planetary nebulae into the Peimbert types, should be associated to difficulties in defining sharp boundaries for the progenitor star mass for each of these types. Those can be at least partially explained by real overlaps of some of the parameters that characterize the different stellar populations. Those results suggest the need of a larger number of classificatory parameters for a reliable physical classification of planetary nebulae.