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Register a new userThe star cluster mass--galactocentric radius relation: Implications for cluster formation
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Weijia Sun
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Whether or not the initial star cluster mass function is established through a universal, galactocentric-distance-independent stochastic process, on the scales of individual galaxies, remains an unsolved problem. This debate has recently gained new impetus through the publication of a study that concluded that the maximum cluster mass in a given population is not solely determined by size-of-sample effects. Here, we revisit the evidence in favor and against stochastic cluster formation by examining the young ($lesssim$ a few $times 10^8$ yr-old) star cluster mass--galactocentric radius relation in M33, M51, M83, and the Large Magellanic Cloud. To eliminate size-of-sample effects, we first adopt radial bin sizes containing constant numbers of clusters, which we use to quantify the radial distribution of the first- to fifth-ranked most massive clusters using ordinary least-squares fitting. We supplement this analysis with an application of quantile regression, a binless approach to rank-based regression taking an absolute-value-distance penalty. Both methods yield, within the $1sigma$ to $3sigma$ uncertainties, near-zero slopes in the diagnostic plane, largely irrespective of the maximum age or minimum mass imposed on our sample selection, or of the radial bin size adopted. We conclude that, at least in our four well-studied sample galaxies, star cluster formation does not necessarily require an environment-dependent cluster formation scenario, which thus supports the notion of stochastic star cluster formation as the dominant star cluster-formation process within a given galaxy.
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Stars form in spatially and temporarily correlated star formation events (CSFEs) and the dynamical processes within these embedded clusters leave imprints in the stellar populations in galactic fields. Such imprints are correlations in phase space (e.g. gravitationally bound star clusters, tidal streams), in the binary properties of stars and in the present-day stellar mass functions in the surviving clusters. The dynamical processes include expulsion of massive stars from cluster cores, disruption of CSFEs due to residual gas expulsion and energy-equipartition driven evaporation of stars from clusters leading to dark star clusters and cold kinematical streams with epicyclic overdensities. The properties of such phase-space structures in the Milky Way (MW) field depend on the effective gravitational potential of the MW. GAIA data will significantly constrain all of these aspects, and will in particular impact on gravitational dynamics via the properties of cold streams and on star-formation via the constraint on the gas expulsion process through the expanding unbound populations that must be associated with every CSFE.
It is widely accepted that the distribution function of the masses of young star clusters is universal and can be purely interpreted as a probability density distribution function with a constant upper mass limit. As a result of this picture the masses of the most-massive objects are exclusively determined by the size of the sample. Here we show, with very high confidence, that the masses of the most-massive young star clusters in M33 decrease with increasing galactocentric radius in contradiction to the expectations from a model of a randomly sampled constant cluster mass function with a constant upper mass limit. Pure stochastic star formation is thereby ruled out. We use this example to elucidate how naive analysis of data can lead to unphysical conclusions.
Ongoing surveys are in the process of measuring the chemical abundances in large numbers of stars, with the ultimate goal of reconstructing the formation history of the Milky Way using abundances as tracers. However, interpretation of these data requires that we understand the relationship between stellar distributions in chemical and physical space, i.e., how similar in chemical abundance do we expect a pair of stars to be as a function of the distance between their formation sites. We investigate this question by simulating the gravitational collapse of a turbulent molecular cloud extracted from a galaxy-scale simulation, seeded with chemical inhomogeneities with different initial spatial scales. We follow the collapse from galactic scales down to resolutions scales of $approx 10^{-3}$ pc, and find that, during this process, turbulence mixes the metal patterns, reducing the abundance scatter initially present in the gas by an amount that depends on the initial scale of inhomogeneity of each metal field. However, we find that regardless of the initial spatial structure of the metals at the onset of collapse, the final stellar abundances are highly correlated on distances below a few pc, and nearly uncorrelated on larger distances. Consequently, the star formation process defines a natural size scale of $sim 1$ pc for chemically-homogenous star clusters, suggesting that any clusters identified as homogenous in chemical space must have formed within $sim 1$ pc of one another. However, in order to distinguish different star clusters in chemical space, observations across multiple elements will be required, and the elements that are likely to be most efficient at separating distinct clusters in chemical space are those whose correlation length in the ISM is of order tens of pc, comparable to the sizes of individual molecular clouds.
We investigate the star formation rate and its location in the major merger cluster Abell 2465 at $z$ = 0.245. Optical properties of the cluster are described in Paper I. Measurements of the H$alpha$ and infrared dust emission of galaxies in the cluster were made with an interference filter centred on the redshifted line at a wavelength of 817 nm and utilized data from the WISE satellite 12 $mu$m band. Imaging in the Johnson $U$ and $B$ bands was obtained, and along with SDSS $u$ and $r$ was used to study the blue fraction, which appears enhanced, as a further signatures of star formation in the cluster. Star formation rates were calculated using standard calibrations. The total star formation rate normalized by the cluster mass, $Sigma SFR/M_{cl}$ compared to compilations for other clusters indicate that the components of Abell 2465 lie above the mean $z$ and $M_{cl}$ relations, suggestive that interacting galaxy clusters have enhanced star formation. The projected radial distribution of the star forming galaxies does not follow a NFW profile and is relatively flat indicating that fewer star forming galaxies are in the cluster centre. The morphologies of the H$alpha$ sources within $R_{200}$ for the cluster as a whole indicate that many are disturbed or merging, suggesting that a combination of merging or harassment is working.
Recent observations of the dwarf elliptical galaxy Scl-dE1 (Sc22) in the Sculptor group of galaxies revealed an extended globular cluster (Scl-dE1 GC1), which exhibits an extremely large core radius of about 21.2 pc. The authors of the discovery paper speculated on whether this object could reside in its own dark matter halo and/or if it might have formed through the merging of two or more star clusters. In this paper, we present N-body simulations to explore thoroughly this particular formation scenario. We follow the merger of two star clusters within dark matter haloes of a range of masses (as well as in the absence of a dark matter halo). In order to obtain a remnant which resembles the observed extended star cluster, we find that the star formation efficiency has to be quite high (around 33 per cent) and the dark matter halo, if present at all, has to be of very low mass, i.e. raising the mass to light ratio of the object within the body of the stellar distribution by at most a factor of a few. We also find that expansion of a single star cluster following mass loss provides another viable formation path. Finally, we show that future measurements of the velocity dispersion of this system may be able to distinguish between the various scenarios we have explored.
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