Two different multivariate clustering techniques, the K-means partitioning method and the Dirichlet process of mixture modeling, have been applied to the BATSE Gamma-ray burst (GRB) catalog, to obtain the optimum number of coherent groups. In the standard paradigm, GRB are classified in only two groups, the long and short bursts. However, for both the clustering techniques, the optimal number of classes was found to be three, a result which is consistent with previous statistical analysis. In this classification, the long bursts are further divided into two groups which are primarily differentiated by their total fluence and duration and hence are named low and high fluence GRB. Analysis of GRB with known red-shifts and spectral parameters suggests that low fluence GRB have nearly constant isotropic energy output of 10 52 ergs while for the high fluence ones, the energy output ranges from 10 52 to 10 54 ergs. It is speculated that the three kinds of GRBs reflect three different origins: mergers of neutron star systems, mergers between white dwarfs and neutron stars, and collapse of massive stars

The fundamental plane of early-type galaxies is a rather tight three-parameter correlation discovered more than twenty years ago. It has resisted a both global and precise physical interpretation despite a consequent number of works, observational, theoretical or using numerical simulations. It appears that its precise properties depend on the population of galaxies in study. Instead of selecting a priori these populations, we propose to objectively construct homologous populations from multivariate analyses. We have undertaken multivariate cluster and cladistic analyses of a sample of 56 low-redshift galaxy clusters containing 699 early-type galaxies, using four parameters: effective radius, velocity dispersion, surface brightness averaged over effective radius, and Mg2 index. All our analyses are consistent with seven groups that define separate regions on the global fundamental plane, not across its thickness. In fact, each group shows its own fundamental plane, which is more loosely defined for less diversified groups. We conclude that the global fundamental plane is not a bent surface, but made of a collection of several groups characterizing several fundamental planes with different thicknesses and orientations in the parameter space. Our diversification scenario probably indicates that the level of diversity is linked to the number and the nature of transforming events and that the fundamental plane is the result of several transforming events. We also show that our classification, not the fundamental planes, is universal within our redshift range (0.007 - 0.053). We find that the three groups with the thinnest fundamental planes presumably formed through dissipative (wet) mergers. In one of them, this(ese) merger(s) must have been quite ancient because of the relatively low metallicity of its galaxies, Two of these groups have subsequently undergone dry mergers to increase their masses. In the k-space, the third one clearly occupies the region where bulges (of lenticular or spiral galaxies) lie and might also have formed through minor mergers and accretions. The two least diversified groups probably did not form by major mergers and must have been strongly affected by interactions, some of the gas in the objects of one of these groups having possibly been swept out. The interpretation, based on specific assembly histories of galaxies of our seven groups, shows that they are truly homologous. They were obtained directly from several observables, thus independently of any a priori classification. The diversification scenario relating these groups does not depend on models or numerical simulations, but is objectively provided by the cladistic analysis. Consequently, our classification is more easily compared to models and numerical simulations, and our work can be readily repeated with additional observables.Comment: Accepted for publication in MNRAS; Monthly Notices of the Royal Astronomical Society (2010

Context. The diversification of galaxies is caused by transforming events such as accretion, interaction, or mergers. These explain the formation and evolution of galaxies, which can now be described by many observables. Multivariate analyses are the obvious tools to tackle the available datasets and understand the differences between different kinds of objects. However, depending on the method used, redundancies, incompatibilities, or subjective choices of the parameters can diminish the usefulness of these analyses. The behaviour of the available parameters should be analysed before any objective reduction in the dimensionality and any subsequent clustering analyses can be undertaken, especially in an evolutionary context. Aims. We study a sample of 424 early-type galaxies described by 25 parameters, 10 of which are Lick indices, to identify the most discriminant parameters and construct an evolutionary classification of these objects. Methods. Four independent statistical methods are used to investigate the discriminant properties of the observables and the partitioning of the 424 galaxies: principal component analysis, K-means cluster analysis, minimum contradiction analysis, and Cladistics. Results. The methods agree in terms of six parameters: central velocity dispersion, disc-to-bulge ratio, effective surface brightness, metallicity, and the line indices NaD and OIII. The partitioning found using these six parameters, when projected onto the fundamental plane, looks very similar to the partitioning obtained previously for a totally different sample and based only on the parameters of the fundamental plane. Two additional groups are identified here, and we are able to provide some more constraints on the assembly history of galaxies within each group thanks to the larger number of parameters. We also identify another "fundamental plane" with the absolute K magnitude, the linear diameter, and the Lick index Hβ. We confirm that the Mg b vs. velocity dispersion correlation is very probably an evolutionary correlation, in addition to several other scaling relations. Finally, combining the results of our two papers, we obtain a classification of galaxies that is based on the transforming processes that are at the origin of the different groups. Conclusions. By taking into account that galaxies are evolving complex objects and using appropriate tools, we are able to derive an explanatory classification of galaxies, based on the physical causes of the diverse properties of galaxies, as opposed to the descriptive classifications that are quite common in astrophysics.

An objective classification of the globular clusters of NGC 5128 has been carried out by using a model-based approach of cluster analysis. The set of observable parameters includes structural parameters, spectroscopically determined Lick indices and radial velocities from the literature. The optimum set of parameters for this type of analysis is selected through a modified technique of Principal Component Analysis, which differs from the classical one in the sense that it takes into consideration the effects of outliers present in the data. Then a mixture model based approach has been used to classify the globular clusters into groups. The efficiency of the techniques used is tested through the comparison of the misclassification probabilities with those obtained using the K-means clustering technique. On the basis of the above classification scheme three coherent groups of globular clusters have been found. We propose that the clusters of one group originated in the original cluster formation event that coincided with the formation of the elliptical galaxy, and that the clusters of the two other groups are of external origin, from tidally stripped dwarf galaxies on random orbits around NGC 5128 for one group, and from an accreted spiral galaxy for the other.

We carry out an objective classification of four samples of spiral galaxies having extended rotation curves beyond the optical radius. A multivariate statistical analysis (viz., principal component analysis [PCA]) shows that about 96% of the total variation is due to two components, one being the combination of absolute blue magnitude and maximum rotational velocity beyond the optical region and the other being the central density of the halo. On the basis of PCA a fundamental plane has been constructed that reduces the scatter in the Tully-Fisher relation up to a maximum of 16%. A multiple stepwise regression analysis of the variation of the overall shape of the rotation curves shows that it is mainly determined by the central surface brightness, while the shape purely in the outer part of the galaxy (beyond the optical radius) is mainly determined by the size of the galactic disk.