arXiv subjects

Asis Kumar Chattopadhyay

Publications and source records attributed to Asis Kumar Chattopadhyay.

15 recordsLinked to original sources

arXiv2022

Clustering of eclipsing binary light curves through functional principal component analysis

In this paper, we revisit the problem of clustering 1318 new variable stars found in the Milky way. Our recent work distinguishes these stars based on their light curves which are univariate series of brightness from the stars observed at discrete time points. This work proposes a new approach to look at these discrete series as continuous curves over time by transforming them into functional data. Then, functional principal component analysis is performed using these functional light curves. Clustering based on the significant functional principal components reveals two distinct groups of eclipsing binaries with consistency and superiority compared to our previous results. This method is established as a new powerful light curve-based classifier, where implementation of a simple clustering algorithm is effective enough to uncover the true clusters based merely on the first few relevant functional principal components. Simultaneously we discard the noise from the data study involving the higher order functional principal components. Thus the suggested method is very useful for clustering big light curve data sets which is also verified by our simulation study.

stat.AP↗

arXiv2021

Investigation of the Effect of Bars on the Properties of Spiral Galaxies: A Multivariate Statistical Study

Subjective classification of spiral galaxies is not sufficient for studying the effect of bars on their physical characteristics. In reality the problem is to comprehend the complex correlations in a multivariate parametric space. Multivariate tools are the best ones for understanding this complex correlation. In this work an objective classification of a large set (26,089) of spiral galaxies was compiled as a value added galaxy catalogue from sdss DR 15 virtual data archive. Initially for dimensionality reduction, Independent Component Analysis is performed to determine a set of Independent Components that are linear combinations of 48 observed features (namely ionised lines, Lick indices, photometric and morphological properties). Subsequently a K-means cluster analysis is carried out on the basis of the 14 best chosen Independent Components to obtain 12 distinct homogeneous groups of spiral galaxies. Amongst these, 3 groups are the oldest ones (1.6 Gyr - 5.9 Gyr), while 5 groups fall in the medium aged category (1.4 Gyr - 1.6 Gyr), 2 groups consist of only unbarred spirals, 1 group is the youngest one and the remaining one is an outlier. In many groups there are clear indication of recurrent bar formation phenomena which is consistent with few previous simulation works. In order to study the robustness a second method of clustering by Gaussian Mixture Modeling Method (GMMBC) is applied.

astro-ph.GA↗

arXiv2020

Exploration about the origin of galactic and extragalactic star clusters through simulated H-R diagrams

The present work explores the origin of the formation of star clusters in our Galaxy and in Small Magellanic Cloud (SMC) through simulated H-R diagrams and compare those with observed star clusters. The simulation study produces synthetic H-R diagrams by Markov Chain Monte Carlo (MCMC) technique using star formation history (SFH), luminosity function (LF), abundance of heavy metal (Z) and a big library of isochrones as basic inputs and compares them with observed H-R diagrams of various star clusters. The distance based comparison between those two diagrams is carried out through two dimensional matching of points in Color-Magnitude Diagram (CMD) after optimal choice of bin size and appropriate distance function. It is found that a poor medium of heavy elements (Z = 0.0004), Gaia LF along with mixture of multiple Gaussian distributions of SFH may be the origin of formation of globular clusters (GCs). On the contrary, enriched medium (Z = 0.019) is favoured with Gaia LF along with double power law (i.e. unimodal) SFH. For SMC clusters, the choice of exponential LF and exponential SFH is a proper combination for poor medium whereas Gaia LF with Beta type SFH is preferred in an enriched medium for the formation of star clusters.

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arXiv2020

Unsupervised classification of eclipsing binary light curves through k-medoids clustering

This paper proposes k-medoids clustering method to reveal the distinct groups of 1,318 variable stars in the Galaxy based on their light curves, where each light curve represents the graph of brightness of the star against time. To overcome the deficiencies of subjective traditional classification, we separate the stars more scientifically according to their geometrical configuration and show that our approach outperforms the existing classification schemes in astronomy. It results in two optimum groups of eclipsing binaries corresponding to bright, massive systems and fainter, less massive systems.

astro-ph.SR↗

arXiv2017

Two phase formation of massive elliptical galaxies : study through cross-correlation including spatial effect

Formation mechanism of present day population of elliptical galaxies have been revisited in the context of hierarchical cosmological models accompanied by accretion and minor mergers through cross correlation function including spatial effect. The present work investigates the formation and evolution of several components of nearby massive early type galaxies (ETGs) through cross-correlation in the spatial coordinates, right ascension and declination (RA, DEC) and mass-size parameter space with high redshift $(0.5\leq z\leq2.7)$ ETGs. It is found that innermost components of nearby ETGs are highly correlated with ETGs in the redshift range $(2\leq z\leq2.7)$ known as 'red nuggets'. The intermediate and outermost parts have moderate correlations with ETGs in the redshift range $(0.5\leq z\leq0.75)$. The quantitative measures are highly consistent with the two phase formation scenario of massive nearby early type galaxies as suggested by various authors and resolves the conflict raised in a previous work suggesting other possibilities for the formation of outermost part of nearby massive ETGs. The improvement is expected to be due to inclusion of spatial effects in addition to other linear parameters.

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arXiv2017

Clustering of Gamma-Ray bursts through kernel principal component analysis

We consider the problem related to clustering of gamma-ray bursts (from "BATSE" catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets.

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arXiv2015

Multivariate Approaches to Classification in Extragalactic Astronomy

Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still largely in use, together with numerous mono-or bivariate classifications most often made by eye. However, a classification must be driven by the data, and sophisticated multivariate statistical tools are used more and more often. In this paper we review these different approaches in order to situate them in the general context of unsupervised and supervised learning. We insist on the astrophysical outcomes of these studies to show that multivariate analyses provide an obvious path toward a renewal of our classification of galaxies and are invaluable tools to investigate the physics and evolution of galaxies.

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arXiv2015

Cosmic history of integrated galactic stellar initial mass function : a simulation study

Theoretical and indirect observational evidences suggest that stellar initial mass function (IMF) increases with redshift. On the other hand star formation rates (SFR) may be as high as 100 $M_{\odot}$ yr$^{-1}$ in star burst galaxies. These may lead to formation of massive clusters hence massive stars to make the integrated galactic stellar initial mass function (IGIMF) top heavy (i.e. proportion of massive stars is higher than less massive stars). We investigate the joint effect of evolving IMF and several measures of SFR in dependence of galaxy wide IMF. The resulting IGIMF have slopes $α_{2,IGIMF}$ in the high mass regime, which is highly dependent on the minimum mass of the embedded cluster ($M_{ecl,min}$), star formation rates and mass spectrum indices of embedded clusters (viz. $β$). It is found that for z $\sim$ 0 - 2, $α_{2,IGIMF}$ becomes steeper (i.e. bottom heavy), for z $\sim$ 2 - 4, $α_{2,IGIMF}$ becomes flatter (i.e. top heavy ) and from z $\sim$ 4 onwards $α_{2,IGIMF}$ becomes again steeper. The effects are faster for higher values of $β$. $α_{2,IGIMF}$ is flatter also for higher values of $M_{ecl,min}$. All these effects might be counted for the joint effect of increasing temperature of the ambient medium as well as varying SFR with increasing redshift.

astro-ph.GA↗

arXiv2014

Use of spatial cross correlation function to study formation mechanism of massive elliptical galaxies

Spatial clustering nature of galaxies have been studied previously through auto correlation function. The same type of cross correlation function has been used to investigate parametric clustering nature of galaxies e.g. with respect to masses and sizes of galaxies. Here formation and evolution of several components of nearby massive early type galaxies have been envisaged through cross correlations, in the mass-size parametric plane, with high redshift early type galaxies (hereafter ETG).It is found that the inner most components of nearby ETGs have significant correlation with ETGs in the highest redshift range called red nuggets whereas intermediate components are highly correlated with ETGs in the redshift range with z value greater than 0.5 and less than 0.75. The outer most part has no correlation in any range, suggesting a scenario through in situ accretion. The above formation scenario is consistent with the previous results obtained for NGC5128 (Chattopadhyay et al. (2009), Chattopadhyay et al. (2013)) and to some extent for nearby elliptical galaxies (Huang et al. (2013)) after considering a sample of ETGs at high redshift with stellar masses greater than or equal to 108.73 M-Sun. So the present work indicates a three phase formation of massive nearby elliptical galaxies instead of two as discussed in previous works.

stat.AP↗

arXiv2013

Clustering large number of extragalactic spectra of galaxies and quasars through canopies

Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike classi cation, in clustering one has to rst decide the optimum number of clusters and then assign the objects into different clusters. Solution of such problems for a large number of high dimensional data points is quite complicated and most of the existing algorithms will not perform properly. In the present work a new clustering technique applicable to large data set has been used to cluster the spectra of 702248 galaxies and quasars having 1540 points in wavelength range imposed by the instrument. The proposed technique has successfully discovered ve clusters from this 702248X1540 data matrix.

astro-ph.CO↗

arXiv2012

A six-parameter space to describe galaxy diversification

Galaxy diversification proceeds by transforming events like accretion, interaction or mergers. These explain the formation and evolution of galaxies that can now be described with many observables. Multivariate analyses are the obvious tools to tackle the 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 void the usefulness of such analyses. The behaviour of the available parameters should be analysed before an objective reduction of dimensionality and subsequent clustering analyses can be undertaken, especially in an evolutionary context. We study a sample of 424 early-type galaxies described by 25 parameters, ten of which are Lick indices, to identify the most structuring parameters and determine an evolutionary classification of these objects. 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. (abridged)

astro-ph.CO↗

arXiv2012

Uncovering the formation of ultra-compact dwarf galaxies by multivariate statistical analysis

We present a statistical analysis of the properties of a large sample of dynamically hot old stellar systems, from globular clusters to giant ellipticals, which was performed in order to investigate the origin of ultra-compact dwarf galaxies. The data were mostly drawn from Forbes et al. (2008). We recalculated some of the effective radii, computed mean surface brightnesses and mass-to-light-ratios, estimated ages and metallicities. We completed the sample with globular clusters of M31. We used a multivariate statistical technique (K-Means clustering), together with a new algorithm (Gap Statistics) for finding the optimum number of homogeneous sub-groups in the sample, using a total of six parameters (absolute magnitude, effective radius, virial mass-to-light ratio, stellar mass-to-light ratio and metallicity). We found six groups. FK1 and FK5 are composed of high- and low-mass elliptical galaxies respectively. FK3 and FK6 are composed of high-metallicity and low-metallicity objects, respectively, and both include globular clusters and ultra-compact dwarf galaxies. Two very small groups, FK2 and FK4, are composed of Local Group dwarf spheroidals. Our groups differ in their mean masses and virial mass-to-light ratios. The relations between these two parameters are also different for the various groups. The probability density distributions of metallicity for the four groups of galaxies is similar to that of the globular clusters and UCDs. The brightest low-metallicity globular clusters and ultra-compact dwarf galaxies tend to follow the mass-metallicity relation like elliptical galaxies. The objects of FK3 are more metal-rich per unit effective luminosity density than high-mass ellipticals.

astro-ph.CO↗

arXiv2010

Structures in the fundamental plane of early-type galaxies

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.

astro-ph.CO↗

arXiv2009

Study of NGC 5128 Globular Clusters Under Multivariate Statistical Paradigm

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.

astro-ph.CO↗

arXiv2007

Statistical Evidence for Three classes of Gamma-ray Bursts

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.

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