Although morphological classification of dwarf galaxies into early and late types can account for some of their origin and characteristics, this does not aid the study of their formation mechanism. Thus an objective classification using principal component analysis together with K means cluster analysis of these dwarf galaxies and their globular clusters (GCs) is carried out to overcome this problem. It is found that the classification of dwarf galaxies in the local volume is irrespective of their morphological indices. The more massive (MV0 &lt; -13.7) galaxies evolve through self-enrichment and harbor dynamically less evolved younger GCs, whereas fainter galaxies (M V0 &gt; -13.7) are influenced by their environment in the star formation process.

TANUKA CHATTOPADHYAYKANJILAL

Applied Mathematics

M SHARINA

P KARMAKAR

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Astrophysical Journal

A model is proposed for the formation of gas-rich dwarf irregular galaxies and gas-poor, rotating dwarf elliptical galaxies following the interaction between two giant galaxies as a function of space density. The formation of dwarf galaxies is considered to depend on a random variable, the tidal index Θ, an environmental parameter defined by Karachentsev et al. (2004), such that for Θ&lt;0 the formation of dwarf irregular galaxy is assured whereas for Θ&gt;0 the formation of dwarf ellipticals is preferred. It is found that for particular ranges of the interactive parameters the model predictions are in good agreement with the observed number density of the different galaxy types as a function of space density in four clusters of galaxies. This supports the fact that galaxy interactions do not all necessarily give rise to the formation of either dwarf irregulars or dwarf ellipticals. It is also shown that the formation of dwarf irregulars at high densities is much lower than that of dwarf ellipticals, and that the formation of the latter reaches a maximum at a particular space density, unlike the former. This suggests that at high densities many dwarf irregulars are stripped of their gaseous envelopes to become dwarf elliptical. © 2014 Elsevier B.V. All rights reserved.

New Astronomy

Formation of dwarf ellipticals and dwarf irregular galaxies by interaction of giant galaxies under environmental influence

An objective classification of 147 globular clusters (GCs) in the inner region of the giant elliptical galaxy M87 is carried out with the help of two methods of multivariate analysis. First, independent component analysis (ICA) is used to determine a set of independent variables that are linear combinations of various observed parameters (mostly Lick indices) of the GCs. Next, K-means cluster analysis (CA) is applied on the independent components (ICs), to find the optimum number of homogeneous groups having an underlying structure. The properties of the four groups of GCs thus uncovered are used to explain the formation mechanism of the host galaxy. It is suggested that M87 formed in two successive phases. First a monolithic collapse, which gave rise to an inner group of metal-rich clusters with little systematic rotation and an outer group of metal-poor clusters in eccentric orbits. In a second phase, the galaxy accreted low-mass satellites in a dissipationless fashion, from the gas of which the two other groups of GCs formed. Evidence is given for a blue stellar population in the more metal rich clusters, which we interpret by Helium enrichment. Finally, it is found that the clusters of M87 differ in some of their chemical properties (NaD, TiO1, light-element abundances) from GCs in our Galaxy and M31. © 2015 Astronomical Society of Australia.

Publications of the Astronomical Society of Australia

Multivariate Analysis of the Globular Clusters in M87

A multivariate classification has been performed for a large sample of dynamically hot stellar systems comprising globular clusters to giant ellipticals, in quest of the formation theory of ultra compact dwarf galaxies (UCDs). For this K means cluster analysis is carried out together with the optimum criterion (Sugar et al., 2003) with respect to three parameters, logarithm of stellar mass, logarithm of effective radius and stellar mass to light ratio. The present data set has been taken from Misgeld and Hilker (2011). We found five groups MK1-MK5. These are predominated by giant ellipticals (gEs), faint dwarf ellipticals (dEs), globular clusters (GCs), massive compact objects (UCDs and nuclei of dE,Ns) and bright dwarf ellipticals respectively. Almost all UCDs are found either in MK3 or MK4. The fraction is roughly 50%-50% between MK3 and MK4. Comparable fraction of UCDs share properties either with normal GCs or with nuclei of dE,N. This adds a quantitative constraint to the long discussed hypothesis that UCDs may be formed either as massive globular clusters or have an origin similar to nuclei of dwarf galaxies. We finally find that for our clustering test in mass-size-stellar M/L ratios, ultra faint dwarf galaxies are attributed to globular cluster group (MK3) and not to the dwarf galaxy group (MK2). This highlights that there is no clear cut morphological distinction between extended star clusters and ultra faint dwarfs. These groups are highly consistent with the groups found in a previous classification for a smaller sample and completely different set of parameters. © 2012 Elsevier B.V. All rights reserved.

Multivariate study of dynamically hot stellar systems: Clues to the origin of ultra compact and ultra faint dwarfs

Springer Series in Astrostatistics

Astrostatistical Challenges for the New Astronomy

The proper interpretation of horizontal branch (HB) morphology is crucial to the understanding of the formation history of stellar populations. In the present study a multivariate analysis is used (principal component analysis) for the selection of appropriate HB morphology parameter, which, in our case, is the logarithm of effective temperature extent of the HB (log T effHB). Then this parameter is expressed in terms of the most significant observed independent parameters of Galactic globular clusters (GGCs) separately for coherent groups, obtained in a previous work, through a stepwise multiple regression technique. It is found that, metallicity ([Fe/H]), central surface brightness (μv), and core radius (rc ) are the significant parameters to explain most of the variations in HB morphology (multiple R 2 0.86) for GGC elonging to the bulge/disk while metallicity ([Fe/H]) and absolute magnitude (Mv ) are responsible for GGC belonging to the inner halo (multiple R 2 0.52). The robustness is tested by taking 1000 bootstrap samples. A cluster analysis is performed for the red giant branch (RGB) stars of the GGC belonging to Galactic inner halo (Cluster 2). A multi-episodic star formation is preferred for RGB stars of GGC belonging to this group. It supports the asymptotic giant branch (AGB) model in three episodes instead of two as suggested by Carretta etal. for halo GGC while AGB model is suggested to be revisited for bulge/disk GGC. © 2009 The American Astronomical Society. All rights reserved.

Horizontal branch morphology of globular clusters: A multivariate statistical analysis

An objective classification of the globular clusters (GCs) 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 GCs 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 GCs 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. © 2009. The American Astronomical Society. All rights reserved.

Study of NGC 5128 globular clusters under multivariate statistical paradigm

Aims. To find an objective classification of the globular clusters in our Galaxy, M 31, and LMC. Methods. A new method of Cluster Analysis (CA)was carried out and the set of parameters for this method was selected through an objective process, Principal Component Analysis (PCA). Robustness of the classification was established using bootstrap samples. Results. In every case they exhibit multi-population structure instead of bimodality as is found in many spirals and giant elliptical galaxies. The kinematics of MW and M 31 GCs are examined in support of these sub-populations in the cluster system. It is found that for MW and M 31 GCs a disc, inner halo, and outer halo populations of GCs are more likely to exist than only the disc and halo populations of GCs in MW as concluded by Zinn (1985, ApJ, 293, 424). This supports the existence of three populations more firmly explained by Zinn (1993, Globular Cluster-Galaxy Connection, 38) and Mackey &amp; Gilmore (2004, MNRAS, 355, 504) whereas only two populations are found for LMC GCs. The new multivariate analysis increases the importance of the inclusion of many parameters while at the same time it eliminates less significant parameters and helps to enunciate a unique theory of galaxy formation.

Astronomy & Astrophysics

Globular clusters of the Local Group – statistical classification

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. © 2006. The American Astronomical Society, All rights reserved.

Journal	Astrophysical Journal
Publisher	Institute of Physics Publishing
ISSN	0004-637X
Open Access	Yes