A stochastic model has been developed for the hierarchical fragmentation of a molecular cloud. Here, the number of fragments, time between successive fragmentation steps, and mass of a fragment are considered as random variables, and fragment masses are generated using the Metropolis-Hastings algorithm. The resulting mass spectra, computed at different projected distances and taking opacity into consideration, show a signature of mass segregation. The critical mass, mass spectrum, and mass segregation are consistent with the observations of young massive clusters in our Galaxy as well as in external galaxies. © 2011. The American Astronomical Society. All rights reserved.

TANUKA CHATTOPADHYAYKANJILAL

Applied Mathematics

Asis Kumar Chattopadhyay

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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

Modeling of the Initial Mass Function Using the Metropolis−Hastings Algorithm

Astrophysical Journal

A stochastic model has been developed to study the hierarchical fragmentation process of young massive clusters in external galaxies considering close binary components along with individual ones. Stellar masses for individual ones have been generated from truncated Pareto distribution and stellar masses for close binary components have been generated from a truncated Bi-variate Gumbel Exponential distribution. The above distribution is identified by fitting the observed bi-variate distribution of masses of eclipsing binary stars computed from the light curves catalogued in the package Binary Maker 3.0. The resulting mass spectra computed at different projected distances, show signature of mass segregation. Degree of mass segregation becomes reduced due to the inclusion of binary fraction. This might be due to the reduction of massive stars and inclusion of less massive stars rather than inclusion of single massive stars and the effect of line of sight length projected to an observer. © 2016, Springer Science+Business Media Dordrecht.

Astrophysics and Space Science

Influence of binary fraction on the fragmentation of young massive clustersâ€”a Monte Carlo simulation

Theoretical and indirect observational evidence suggests that the stellar initial mass function (IMF) increases with redshift. On the other hand, star formation rates (SFRs) may be as high as 100 M yr-1 in starburst galaxies. These may lead to the formation of massive clusters, hence massive stars, making the integrated galactic stellar initial mass function (IGIMF) top-heavy (i.e., the proportion of massive stars is higher than that of less massive stars). We investigate the joint effect of evolving the IMF and several measures of SFRs in dependence on the galaxywide IMF. The resulting IGIMFs have slopes α2,IGIMF in the high-mass regime, which is highly dependent on the minimum mass of the embedded cluster (Mecl,min), SFR, and mass-spectrum indices of embedded clusters (β). It is found that for z∼0-2, α2,IGIMF becomes steeper (i.e., bottom-heavy), for z∼2-4, α2,IGIMF becomes flatter (i.e., top-heavy ), and from z∼ 4 onward, α2,IGIMF again becomes steeper. The effects are faster for higher values of β. a2,IGIMF is also for higher values of Mecl,min. All of these effects may be attributable to the joint effect of increasing the temperature of the ambient medium as well as varying the SFR with increasing redshift.

COSMIC HISTORY of the INTEGRATED GALACTIC STELLAR INITIAL MASS FUNCTION: A SIMULATION STUDY

Monte Carlo simulation study is carried out for the investigation of the nature of initial mass function in molecular clouds of various masses in which effect of time has been taken into account. The number of fragments, the fractional masses of the fragments at any stage in the hierarchy of fragmentation and the fractional mass of the parent cloud consumed in the fragmentation process are considered as random numbers. The distribution of the number of fragments is time dependent which is generated from Poisson process and that of the fractional masses is assumed to be Gaussian. The resulting mass spectrum, at the end of fragmentation is a power law and a substantial amount of cloud mass is found to be in the brown dwarf regime. The results are discussed and compared with observations.

Systems Analysis Modelling Simulation

Random fragmentation of molecular cloud and initial mass function - A Monte Carlo simulation study

Opacity limited fragmentation is considered for a spherically-collapsing isothermal molecular cloud in a low temperature range where molecular hydrogen and grains are the only cooling and opacity sources. The minimum Jeans mass of a fragment is calculated for different values of the parameters. The form of the initial mass function (IMF) is derived for low-mass protostellar fragments for different values of the parameters. They are discussed and compared with observations. A rough estimate of the cloud mass contained in the brown-dwarf regime is given. © 1992 Kluwer Academic Publishers.

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