Modeling of the Initial Mass Function Using the Metropolis−Hastings Algorithm
TL;DR: In this article, a stochastic model for the hierarchical fragmentation of a molecular cloud was developed, where the number of fragments, time between successive fragmentation steps, and mass of a fragment were considered as random variables, and fragment masses were generated using the Metropolis-Hastings algorithm.
Abstract: 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.
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TL;DR: In this article, a left truncated beta probability density function was introduced to demonstrate the advantage of introducing a four-parameter initial mass function for the stars and the presence of brown dwarfs.
Abstract: The initial mass function (IMF) for the stars is usually fitted by three straight lines, which means seven parameters. The presence of brown dwarfs (BD) increases to four the straight lines and to nine the parameters. Another common fitting function is the lognormal distribution, which is characterized by two parameters. This paper is devoted to demonstrating the advantage of introducing a left truncated beta probability density function, which is characterized by four parameters. The constant of normalization, the mean, the mode and the distribution function are calculated for the left truncated beta distribution. The normal-beta (NB) distribution which results from convolving independent normally distributed and beta distributed components is also derived. The chisquare test and the K-S test are performed on a first sample of stars and BDs which belongs to the massive young cluster NGC 6611 and on a second sample which represents the star’s masses of the cluster NGC 2362.
16 citations
TL;DR: In this paper, the authors investigated the effect of the evolution of the stellar initial mass function (IMF) with increasing redshift on the formation of massive clusters in star burst galaxies.
Abstract: 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 $\alpha_{2,IGIMF}$ 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. $\beta$). It is found that for z $\sim$ 0 - 2, $\alpha_{2,IGIMF}$ becomes steeper (i.e. bottom heavy), for z $\sim$ 2 - 4, $\alpha_{2,IGIMF}$ becomes flatter (i.e. top heavy ) and from z $\sim$ 4 onwards $\alpha_{2,IGIMF}$ becomes again steeper. The effects are faster for higher values of $\beta$. $\alpha_{2,IGIMF}$ 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.
12 citations
TL;DR: In this article, the authors investigate the evolution of the stellar initial mass function (IMF) and varying indices of β for the integrated galactic initial mass functions, in relation to several measures of star formation rates of galaxies at various redshifts by random simulation.
Abstract: Theoretical as well as observational studies suggest that the stellar initial mass func-tion (IMF) might become top heavy with increasing redshift. Embedded cluster massfunction is a power law having index β, whose value still remains controversial. Inthe present work, we investigate the effect of evolving IMF and varying indices ofβ for the integrated galactic initial mass function, in relation to several measures ofstar formation rates of galaxies at various redshifts by random simulation. The result-ing IGIMF is segmented power law at various redshifts having slopes α 1,IGIMF andα 2,IGIMF with a turnover at a characteristic mass m c ′ . These differ from the stel-lar initial mass functions with slopes α 1,IMF , α 2,IMF , and characteristic masses m c for different values of redshift z, β, minimum and maximum masses of the embeddedclusters.Key words: galaxies:star clusters: general - galaxies:evolution 1 INTRODUCTIONThe form of stellar initial mass function is of considerabledebate in the present era as it describes the nature ofstellar population, the ratio of high mass to low mass starsand influences the dynamical evolution of star clusters aswell as star formation history of the whole galaxy. Usuallyit is derived using observed luminosity function togetherwith an assumed mass-to-light ratio for the stars underconsideration. Generally, IMFs, as suggested by variousauthors, are either of Salpeter type (Salpeter 1955) orconsists of segmented power laws (Scalo 1986; Kroupa 2001;Chabrier 2003) with a turnover at some characteristic massm
10 citations
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...In the work by Chattopadhyay et al. (2011), the authors have considered the random fragmentation of young massive clouds in our Galaxy as well as in external galaxies....
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TL;DR: In this article, the authors presented deep Hubble Space Telescope (HST) NICMOS 2 F160W band observations of the central 56*57" (14pc*14.25pc) region around R136 in the starburst cluster 30 Dor (NGC 2070) located in the Large Magellanic Cloud.
Abstract: We present deep Hubble Space Telescope (HST) NICMOS 2 F160W band observations of the central 56*57" (14pc*14.25pc) region around R136 in the starburst cluster 30 Dor (NGC 2070) located in the Large Magellanic Cloud. Our aim is to derive the stellar Initial Mass Function (IMF) down to ~1 Msun in order to test whether the IMF in a massive metal-poor cluster is similar to that observed in nearby young clusters and the field in our Galaxy. We estimate the mean age of the cluster to be 3 Myr by combining our F160W photometry with previously obtained HST WFPC2 optical F555W and F814W band photometry and comparing the stellar locus in the color-magnitude diagram with main sequence and pre-main sequence isochrones. The color-magnitude diagrams show the presence of differential extinction and possibly an age spread of a few megayears. We convert the magnitudes into masses adopting both a single mean age of 3 Myr isochrone and a constant star formation history from 2 to 4 Myr. We derive the IMF after correcting for incompleteness due to crowding. The faintest stars detected have a mass of 0.5 Msun and the data are more than 50% complete outside a radius of 5 pc down to a mass limit of 1.1 Msun for 3 Myr old objects. We find an IMF of dN/dlog(M) M^(-1.20+-0.2) over the mass range 1.1--20 Msun only slightly shallower than a Salpeter IMF. In particular, we find no strong evidence for a flattening of the IMF down to 1.1 Msun at a distance of 5 pc from the center, in contrast to a flattening at 2 Msun at a radius of 2 pc, reported in a previous optical HST study. We examine several possible reasons for the different results. If the IMF determined here applies to the whole cluster, the cluster would be massive enough to remain bound and evolve into a relatively low-mass globular cluster.
7 citations
Journal Article•
TL;DR: In this paper, the results of numerical N-body calculations which simulate the dynamical evolution of young clusters as they emerge from molecular clouds have been presented, and the combination of these parameters which result in the production of bound stellar groups after the gas not used in star formation is completely dispersed.
Abstract: We present the results of numerical N-body calculations which simulate the dynamical evolution of young clusters as they emerge from molecular clouds. We follow the evolution of initially virialized stellar systems of 50 and, in some cases, 100 stars from the point in time immediately after the stars have formed in a cloud until a time long after all the residual star-forming gas has been dispersed from the system. By varying the star formation efficiency and the gas dispersal time for each model, we determined the combination of these parameters which result in the production of bound stellar groups after the gas not used in star formation is completely dispersed.
7 citations
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TL;DR: In this paper, a double main-sequence turn-off star cluster in the Large Magellanic Cloud (GC 1846) was detected by fitting isochrones, and it was shown that the observed properties of the colour-magnitude diagram can be explained if there are two stellar populations of equivalent metal abundance in NGC1846, differing in age by ≈300 Myr.
Abstract: We report on Hubble Space Telescope/ACS photometry of the rich intermediate-age star cluster NGC 1846 in the Large Magellanic Cloud, which clearly reveals the presence of a double main-sequence turn-off in this object. Despite this, the main-sequence, subgiant branch and red giant branch are all narrow and well defined, and the red clump is compact. We examine the spatial distribution of turn-off stars and demonstrate that all belong to NGC 1846 rather than to any field star population. In addition, the spatial distributions of the two sets of turn-off stars may exhibit different central concentrations and some asymmetries. By fitting isochrones, we show that the properties of the colour-magnitude diagram can be explained if there are two stellar populations of equivalent metal abundance in NGC 1846, differing in age by ≈300 Myr. The absolute ages of the two populations are ∼1.9 and ∼2.2 Gyr, although there may be a systematic error of up to ±0.4 Gyr in these values. The metal abundance inferred from isochrone fitting is [M/H] ≈-0.40, consistent with spectroscopic measurements of [Fe/H]. We propose that the observed properties of NGC 1846 can be explained if this object originated via the tidal capture of two star clusters formed separately in a star cluster group in a single giant molecular cloud. This scenario accounts naturally for the age difference and uniform metallicity of the two member populations, as well as the differences in their spatial distributions.
227 citations
TL;DR: In this paper, the initial mass function (IMF) of one of the most massive Galactic star-forming regions NGC 3603 was determined using very deep, high angular resolution JHKSL' images obtained with NAOS-CONICA at the VLT at ESO.
Abstract: We study the initial mass function (IMF) of one of the most massive Galactic star-forming regions NGC 3603 to answer a fundamental question in current astrophysics: is the IMF universal, or does it vary? Using our very deep, high angular resolution JHKSL' images obtained with NAOS-CONICA at the VLT at ESO, we have successfully revealed the stellar population down to the subsolar mass range in the core of the starburst cluster. The derived IMF of NGC 3603 is reasonably fitted by a single power law with index Γ ~ − 0.74 within a mass range of 0.4-20 M☉, substantially flatter than the Salpeter-like IMF. A strong radial steepening of the IMF is observed mainly in the inner r 30'' field, indicating mass segregation in the cluster center. We estimate the total mass of NGC 3603 to be about 1.0–1.6 × 104 M☉. The derived core density is ≥6 × 104 M☉ pc−3, an order of magnitude larger than, e.g., the Orion Nebula Cluster. The estimate of the half-mass relaxation time for solar-mass stars is about 10-40 Myr, suggesting that the intermediate- and low-mass stars have not yet been affected significantly by the dynamical relaxation in the cluster. The relaxation time for the high-mass stars can be comparable to the age of the cluster. We estimate that the stars residing outside the observed field cannot steepen the IMF significantly, indicating our IMF adequately describes the whole cluster. Analyzing thoroughly the systematic uncertainties in our IMF determination, we conclude that the power-law index of the IMF of NGC 3603 is Γ = − 0.74+ 0.62−0.47. Our result thus supports the hypothesis of a potential top-heavy IMF in massive star-forming clusters and starbursts.
208 citations
TL;DR: In this paper, the authors proposed a method to detect and quantify mass segregation in star clusters by comparing the minimum spanning tree (MST) of massive stars with that of random stars.
Abstract: We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected. We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)' Lambda(MSR) = 8.0 +/- 3.5 (where Lambda(MSR) = 1 is no mass segregation) down to 16M(circle dot), and also that the ONC is mass segregated at a lower level (similar to 2.0 +/- 0.5) down to 5M(circle dot). Below 5M(circle dot) we find no evidence for any further mass segregation in the ONC.
206 citations
196 citations
IBM1
TL;DR: In this article, the initial mass function (IMF) for stars is proposed to result from two distinct physical processes that determine its shape separately in two intervals of mass: random sampling of mass in a fractal cloud gives the power-law portion at intermediate to high mass, and insufficient self-gravity at local temperature and pressure gives the cutoff at low mass.
Abstract: The initial mass function (IMF) for stars is proposed to result from two distinct physical processes that determine its shape separately in two intervals of mass: random sampling of mass in a fractal cloud gives the power-law portion at intermediate to high mass, and insufficient self-gravity at the local temperature and pressure gives the cutoff at low mass. The entire function is modeled numerically, with the assumption that a star's mass is proportional to the mass of the piece of cloud in which it forms. The results typically give an IMF with the Salpeter value for the slope and a flattening at a low mass. There is little sensitivity to parameters at masses greater than the cutoff, although slightly shallower IMFs might be expected in regions with high levels of ionization and turbulence. The low-mass cutoff is essentially the thermal Jeans mass in the star-forming cloud; models with a high value of this mass produce a truncated IMF similar to that proposed for starburst galaxies. The mass of the largest star increases with total stellar mass because of the stochastic nature of the model. The star IMF is steeper than the cloud mass spectrum because of competition for mass and the density dependence of star formation.
182 citations