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Galactic globular clusters contain two main groups of stars, the pristine or 1P stars, and the polluted or 2P stars. The pristine-star fraction in clusters, $F_{1P}$, is a decreasing function of the cluster present-day mass, $m_{prst}$. Paper~I has introduced a model mapping the region of the $(m_{prst},F_{1P})$ space occupied by clusters, with the cluster mass threshold for 2P-star formation a key building-block. We now expand this model to the pristine-star fraction in dependence of the pristine- and polluted-population masses. Milone et al.(2020) found that $F_{1P}$ anticorrelates more tightly with the polluted-population present-day mass, $m_{2P,prst}$, than with the cluster total mass, $m_{prst}$. In contrast, $F_{1P}$ anticorrelates poorly with the pristine-population current mass, $m_{1P,prst}$. We show the loose anticorrelation between $F_{1P}$ and $m_{1P,prst}$ to result from a roughly constant pristine-population mass among clusters as they start their long-term evolution in the Galactic tidal field. As for the tight anticorrelation between $m_{2P,prst}$ and $F_{1P}$, it stems from the initially shallow relation between $m_{2P}$ and $F_{1P}$ (Fig.4). Clusters of the Large and Small Magellanic Clouds (LMC and SMC, respectively) appear to behave unexpectedly with respect to each other. For a given $F_{1P}$, LMC clusters are more massive than SMC clusters despite their enduring a stronger tidal field (Fig.6). This is opposite to how the Galactic outer- and inner-halo clusters behave (bottom panels of Figs 1-3). The explanation may lie in cluster formation conditions. Finally, we wonder whether the single-population clusters NGC~419 and Rup~106 formed as multiple-populations clusters., Comment: 16 pages, 6 figures, accepted in ApJ

The phenomenon of multiple stellar populations is exacerbated in massive globular clusters, with the fraction of first-population (1P) stars a decreasing function of the cluster present-day mass. We decipher this relation in far greater detail than has been done so far. We assume (i) a fixed stellar mass threshold for the formation of second-population (2P) stars, (ii) a power-law scaling $F_{1P} \propto m_{ecl}^{-1}$ between the mass $m_{ecl}$ of newly-formed clusters and their 1P-star fraction $F_{1P}$, and (iii) a constant $F_{1P}$ over time. The $F_{1P}(m_{ecl})$ relation is then evolved up to an age of 12Gyr for tidal field strengths representative of the entire Galactic halo. The 12Gyr-old model tracks cover extremely well the present-day distribution of Galactic globular clusters in (mass,$F_{1P}$) space. The distribution is curtailed on its top-right side by the scarcity of clusters at large Galactocentric distances, and on its bottom-left side by the initial scarcity of very high-mass clusters, and dynamical friction. Given their distinct dissolution rates, "inner" and "outer" model clusters are offset from each other, as observed. The locus of Magellanic Clouds clusters in (mass,$F_{1P}$) space is as expected for intermediate-age clusters evolving in a gentle tidal field. Given the assumed constancy of $F_{1P}$, we conclude that 2P-stars do not necessarily form centrally-concentrated. We infer a minimum mass of $4 \cdot 10^5~M_{\odot}$ for multiple-populations clusters at secular evolution onset. This high-mass threshold severely limits the amount of 2P-stars lost from evolving clusters, thereby fitting the low 2P-star fraction of the Galactic halo field., Comment: accepted for publication in the Astrophysical Journal, 29 pages, 12 figures

The presence of a volume density gradient in molecular clumps allow them to raise their star formation rate compared to what they would experience were their gas uniform in density. This higher star formation rate yields in turn a higher value for the star formation efficiency per freefall time that we measure. The measured star formation efficiency per freefall time $\epsilon_{\rm ff, meas}$ of clumps is therefore plagued by a degeneracy, as two factors contribute to it: one is the density gradient of the clump gas, the other is the intrinsic star formation efficiency per freefall time $\epsilon_{\rm ff, int}$ with which the clump would form stars should there be no gas density gradient. This paper presents a method allowing one to recover the intrinsic efficiency of a centrally-concentrated clump. It hinges on the relation between the surface densities in stars and gas measured locally from clump center to clump edge. Knowledge of the initial density profile of the clump gas is not required. A step-by-step description of the method is provided as a tool in hand for observers. Once $\epsilon_{\rm ff, int}$ has been estimated, it can be compared with its measured, clump-averaged, counterpart $\epsilon_{\rm ff, meas}$ to quantify the impact that the initial gas density profile of a clump has had on its star formation history., Comment: 11 pages, 6 figures, accepted for publication in ApJ

Star-forming regions presenting a density gradient experience a higher star formation rate than if they were of uniform density. We refer to the ratio between the star formation rate of a spherical centrally-concentrated gas clump and the star formation rate that this clump would experience if it were of uniform density as the magnification factor $\zeta$. We map $\zeta$ as a function of clump mass, radius, initial volume density profile and star formation time-span. For clumps with a steep density profile (i.e. power-law slope ranging from $-3$ to $-4$, as observed in some high-density regions of Galactic molecular clouds), we find the star formation rate to be at least an order of magnitude higher than its top-hat equivalent. This implies that such clumps experience faster and more efficient star formation than expected based on their mean free-fall time. This also implies that measurements of the star formation efficiency per free-fall time of clumps based on their global properties, namely, mass, mean volume density and star formation rate, present wide fluctuations. These reflect the diversity in the density profile of star-forming clumps, not necessarily variations in the physics of star formation. Steep density profiles inside star-cluster progenitors may be instrumental in the formation of multiple stellar populations, such as those routinely observed in old globular clusters., Comment: 10 pages, 7 figures, accepted for publication in ApJ

We study the evolution of star clusters in the Galactic tidal field starting from their birth in molecular clumps. Our model clusters form according to the local-density-driven cluster formation model in which the stellar density profile is steeper than that of gas. As a result, clusters resist the gas expulsion better than predicted by earlier models. We vary the impact of the Galactic tidal field {\lambda}, considering different Galactocentric distances (3-18 kpc), as well as different cluster sizes. Our model clusters survive the gas expulsion independent of {\lambda}. We investigated the relation between the cluster mass at the onset of secular evolution and their dissolution time. The model clusters formed with a high star-formation efficiency (SFE) follow a tight mass-dependent dissolution relation, in agreement with previous theoretical studies. However, the low-SFE models present a shallower mass-dependent relation than high-SFE clusters, and most dissolve before reaching 1 Gyr (cluster teenage mortality)., Comment: 4 pages, 2 figures. Submitted for publication in the Proceedings of IAU Symposium 351

We have studied the long-term evolution of star clusters of the solar neighborhood, starting from their birth in gaseous clumps until their complete dissolution in the Galactic tidal field. We have combined the "local-density-driven cluster formation model" of Parmentier & Pfalzner (2013) with direct N-body simulations of clusters following instantaneous gas expulsion. We have studied the relation between cluster dissolution time, $t_{dis}$, and cluster "initial" mass, $M_{init}$, defined as the cluster {mass at the end of the dynamical response to gas expulsion (i.e. violent relaxation), when the cluster age is 20-30 Myr}. We consider the "initial" mass to be consistent with other works which neglect violent relaxation. The model clusters formed with a high star formation efficiency (SFE -- i.e. gas mass fraction converted into stars) follow a tight mass-dependent relation, in agreement with previous theoretical studies. However, the low-SFE models present a large scatter in both the "initial" mass and the dissolution time, and a shallower mass-dependent relation than high-SFE clusters. Both groups differ in their structural properties on the average. Combining two populations of clusters, high- and low-SFE ones, with domination of the latter, yields a cluster dissolution time for the solar neighborhood in agreement with that inferred from observations, without any additional destructive processes such as giant molecular cloud encounters. An apparent mass-independent relation may emerge for our low-SFE clusters when we neglect low-mass clusters (as expected for extra-galactic observations), although more simulations are needed to investigate this aspect., Comment: Acceped for publication in Astrophysical Journal (ApJ), 17 pages, 9 figures

We study the effect of the instantaneous gas expulsion on star clusters wherein the residual gas has a density profile shallower than that of the embedded cluster. This is expected if star formation proceeds with a given SFE per free-fall time in a centrally-concentrated molecular clump. We perform direct N-body simulations whose initial conditions are generated by the program "mkhalo" "falcON" adapted for our models. Our model clusters initially have a Plummer profile and are in virial equilibrium with the gravitational potential of the cluster-forming clump. The residual gas contribution is computed based on the model of Parmentier&Pfalzner(2013). Our simulations include mass loss by stellar evolution and the tidal field of the Galaxy. We find that a star cluster with a minimum global SFE of 15% is able to survive instantaneous gas expulsion and to produce a bound cluster. Its violent relaxation lasts no longer than 20 Myr, independently of its global SFE and initial stellar mass. At the end of violent relaxation the bound fractions of surviving clusters with the same global SFEs are similar regardless of their initial stellar mass. Their subsequent lifetime in the gravitational field of the Galaxy depends on their bound stellar masses. We therefore conclude that the critical SFE needed to produce a bound cluster is 15%, which is twice smaller than earlier estimates of 33%. Thus we have improved the survival likelihood of young clusters after instantaneous gas expulsion. Those can now survive instantaneous gas expulsion with global SFEs as low as those observed for embedded clusters of Solar Neighbourhood (15-30%). This is the consequence of the star cluster having a density profile steeper than that of the residual gas. However, in terms of the effective SFE, measured by the virial ratio of the cluster at gas expulsion, our results are in agreement with previous studies., Comment: Accepted for publication in Astronomy&Astrophysics, 13 pages, 10 figures

We model the star formation relation of molecular clumps in dependence of their dense-gas mass when their volume density profile is that of an isothermal sphere, i.e. $\rho_{clump}(r) \propto r^{-2}$. Dense gas is defined as gas whose volume density is higher than a threshold $\rho_{th}=700\,M_{\odot}.pc^{-3}$, i.e. HCN(1-0)-mapped gas. We divide the clump into two regions: a dense inner region (where $\rho_{clump}(r) \geq \rho_{th}$), and low-density outskirts (where $\rho_{clump}(r) < \rho_{th}$). We find that the total star formation rate of clumps scales linearly with the mass of their dense inner region, even when more than half of the clump star formation activity takes place in the low-density outskirts. We therefore emphasize that a linear star formation relation does not necessarily imply that star formation takes place exclusively in the gas whose mass is given by the star formation relation. The linearity of the star formation relation is strengthened when we account for the mass of dense fragments (e.g. cores, fibers) seeding star formation in the low-density outskirts, and which our adopted clump density profile $\rho_{clump}(r)$ does not resolve. We also find that the star formation relation is significantly tighter when considering the dense gas than when considering all the clump gas, as observed for molecular clouds of the Galactic plane. When the clumps have no low-density outskirts (i.e. they consist of dense gas only), the star formation relation becomes superlinear and progressively wider., Comment: 9 pages, 7 figures, accepted for publication in the Astrophysical Journal

We explore the pitfalls which affect the comparison of the star-formation (SF) relation for nearby molecular clouds with that for distant compact molecular clumps. We show that both relations behave differently in the ($\Sigma_{gas}$, $\Sigma_{SFR}$) space, where $\Sigma_{gas}$ and $\Sigma_{SFR}$ are, respectively, the gas and SF rate surface densities, even when the physics of star formation is the same. This is because the SF relation of nearby clouds relates gas and star surface densities measured locally, that is, within a given interval of gas surface density, or at a given protostar location. We refer to such measurements as local measurements, and the corresponding SF relation as the local relation. In contrast, the stellar content of a distant molecular clump remains unresolved. Only the mean SF rate can be obtained from e.g. the clump infrared luminosity. One clump therefore provides one single point to the ($\Sigma_{gas}$, $\Sigma_{SFR}$) space, that is, its mean gas surface density and SF rate surface density. We refer to this SF relation as a global relation since it builds on the global properties of molecular clumps. Its definition therefore requires an ensemble of cluster-forming clumps. We show that, although the local and global relations have different slopes, this per se cannot be taken as evidence for a change in the physics of SF with gas surface density. It therefore appears that great caution should be taken when physically interpreting a composite SF relation, that is, a relation combining together local and global measurements., Comment: 12 pages, 7 figures; accepted for publication in The Astrophysical Journal

It has recently been suggested that high-density clusters have stellar age distributions narrower than that of the Orion Nebula Cluster, indicating a possible trend of narrower age distributions for denser clusters. We show this effect to likely arise from star formation being faster in gas with a higher density. We model the star formation history of molecular clumps in equilibrium by associating a star formation efficiency (SFE) per free-fall time, \eff, to their volume density profile. Our model predicts a steady decline of the star formation rate (SFR), which we quantify with its half-life time, namely, the time needed for the SFR to drop to half its initial value. Given the uncertainties affecting the SFE per free-fall time, we consider two distinct values: 0.1 and 0.01. For isothermal spheres, \eff=0.1 leads to a half-life time of order the clump free-fall time, \tff. Therefore, the age distributions of stars formed in high-density clumps have smaller full-widths at half-maximum than those of stars formed in low-density clumps. When \eff=0.01, the half-life time is 10 times longer. We explore what happens if the star formation duration is shorter than 10\tff, that is, if the half-life time of the SFR cannot be defined. There, we build on the invariance of the shape of the young cluster mass function to show that an anti-correlation between clump density and star formation duration is expected. Therefore, regardless of whether the star formation duration is longer than the SFR half-life time, denser molecular clumps yield narrower star age distributions in clusters. Published densities and stellar age spreads of young clusters actually suggest that the time-scale for star formation is of order 1-4\tff. We conclude that there is no need to invoke the existence of multiple cluster formation mechanisms to explain the observed range of stellar age spreads in clusters., Comment: 14 pages, 11 figures, 2 tables, accepted for publication in The Astrophysical Journal

A positive power-law trend between the local surface densities of molecular gas, $\Sigma_{gas}$, and young stellar objects, $\Sigma_{\star}$, in molecular clouds of the Solar Neighbourhood has been identified by Gutermuth et al. How it relates to the properties of embedded clusters, in particular to the recently established radius-density relation, has so far not been investigated. In this paper, we model the development of the stellar component of molecular clumps as a function of time and initial local volume density so as to provide a coherent framework able to explain both the molecular-cloud and embedded-cluster relations quoted above. To do so, we associate the observed volume density gradient of molecular clumps to a density-dependent free-fall time. The molecular clump star formation history is obtained by applying a constant SFE per free-fall time, $\eff$. For volume density profiles typical of observed molecular clumps (i.e. power-law slope $\simeq -1.7$), our model gives a star-gas surface-density relation $\Sigma_{\star} \propto \Sigma_{gas}^2$, in very good agreement with the Gutermuth et al relation. Taking the case of a molecular clump of mass $M_0 \simeq 10^4 Msun$ and radius $R \simeq 6 pc$ experiencing star formation during 2 Myr, we derive what SFE per free-fall time matches best the normalizations of the observed and predicted ($\Sigma_{\star}$, $\Sigma_{gas}$) relations. We find $\eff \simeq 0.1$. We show that the observed growth of embedded clusters, embodied by their radius-density relation, corresponds to a surface density threshold being applied to developing star-forming regions. The consequences of our model in terms of cluster survivability after residual star-forming gas expulsion are that due to the locally high SFE in the inner part of star-forming regions, global SFE as low as 10% can lead to the formation of bound gas-free star clusters., Comment: 16 pages, 15 figures, Astronomy & Astrophysics, in press

We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-dependent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {\it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours., Comment: 14 pages, 10 figures, accepted for publication in MNRAS

The Large Magellanic Cloud is one of the nearest galaxies to us and is one of only few galaxies where the star formation history can be determined from studying resolved stellar populations. We have compiled a new catalogue of ages, luminosities and masses of LMC star clusters and used it to determine the age distribution and dissolution rate of LMC star clusters. We find that the frequency of massive clusters with masses M>5000 Msun is almost constant between 10 and 200 Myr, showing that the influence of residual gas expulsion is limited to the first 10 Myr of cluster evolution or clusters less massive than 5000 Msun. Comparing the cluster frequency in that interval with the absolute star formation rate, we find that about 15% of all stars in the LMC were formed in long-lived star clusters that survive for more than 10 Myr. We also find that the mass function of LMC clusters younger than 1 Gyr can be fitted by a power-law mass function with slope \alpha=-2.3, while older clusters follow a significantly shallower slope and interpret this is a sign of the ongoing dissolution of low-mass clusters. Our data shows that for ages older than 200 Myr, about 90% of all clusters are lost per dex of lifetime. The implied cluster dissolution rate is significantly faster than that based on analytic estimates and N-body simulations. Our cluster age data finally shows evidence for a burst in cluster formation about 1 Gyr ago, but little evidence for bursts at other ages., Comment: 18 pages, 6 figures, MNRAS in press

To understand how systems of star clusters have reached their presently observed properties constitutes a powerful probe into the physics of cluster formation, without needing to resort to high spatial resolution observations of individual cluster-forming regions (CFRg) in distant galaxies. In this contribution I focus on the mass-radius relation of CFRgs, how it can be uncovered by studying the gas expulsion phase of forming star clusters, and what the implications are. I demonstrate that, through the tidal field impact upon exposed star clusters, the CFRg mass-radius relation rules cluster infant weight-loss in dependence of cluster mass. The observational constraint of a time-invariant slope for the power-law young cluster mass function is robustly satisfied by CFRgs with a constant mean volume density. In contrast, a constant mean surface density would be conducive to the preferential destruction of high-mass clusters. A purely dynamical line-of-reasoning leads therefore to a conclusion consistent with star formation a process driven by a volume density threshold. Developing this concept further, properties of molecular clumps and CFRgs naturally get dissociated. This allows to understand: (i) why the star cluster mass function is steeper than the molecular cloud (clump) mass function; (ii) the presence of a massive star formation limit in the mass-size space of molecular structures., Comment: 12 pages, 3 figures of 2 panels each, to appear in proceedings of "Star Clusters and Associations: A RIA Workshop on GAIA", Granada, 23-27 May 2011

We aim at understanding the massive star formation (MSF) limit $m(r) = 870 M_{\odot} (r/pc)^{1.33}$ in the mass-size space of molecular structures recently proposed by Kauffmann & Pillai (2010). As a first step, we build on the hypothesis of a volume density threshold for overall star formation and the model of Parmentier (2011) to establish the mass-radius relations of molecular clumps containing given masses of star-forming gas. Specifically, we relate the mass $m_{clump}$, radius $r_{clump}$ and density profile slope $-p$ of molecular clumps which contain a mass $m_{th}$ of gas denser than a volume density threshold $\rho_{th}$. In a second step, we use the relation between the mass of embedded-clusters and the mass of their most-massive star to estimate the minimum mass of star-forming gas needed to form a $10\,M_{\odot}$ star. Assuming a star formation efficiency of $SFE \simeq 0.30$, this gives $m_{th,crit} \simeq 150 M_{\odot}$. In a third step, we demonstrate that, for sensible choices of the clump density index ($p \simeq 1.7$) and of the cluster formation density threshold ($n_{th} \simeq 10^4\,cm^{-3}$), the line of constant $m_{th,crit} \simeq 150 M_{\odot}$ in the mass-radius space of molecular structures equates with the MSF limit for spatial scales larger than 0.3\,pc. Hence, the observationally inferred MSF limit of Kauffmann & Pillai is consistent with a threshold in star-forming gas mass beyond which the star-forming gas reservoir is large enough to allow the formation of massive stars. For radii smaller than 0.3\,pc, the MSF limit is shown to be consistent with the formation of a $10\,M_{\odot}$ star out of its individual pre-stellar core of density threshold $n_{th} \simeq 10^5\,cm^{-3}$. The inferred density thresholds for the formation of star clusters and individual stars within star clusters match those previously suggested in the literature., Comment: 8 pages, 5 figs, accepted for publication in MNRAS

The mass function of molecular clouds and clumps is shallower than the mass function of young star clusters, gas-embedded and gas-free alike, as their respective mass function indices are $\beta_0 \simeq 1.7$ and $\beta_\star \simeq 2$. We demonstrate that such a difference can arise from different mass-radius relations for the embedded-clusters and the molecular clouds (clumps) hosting them. In particular, the formation of star clusters with a constant mean {\it volume} density in the central regions of molecular clouds of constant mean {\it surface} density steepens the mass function from clouds to embedded-clusters. This model is observationally supported since the mean surface density of molecular clouds is approximately constant, while there is a growing body of evidence, in both Galactic and extragalactic environments, that efficient star-formation requires a hydrogen molecule number density threshold of $n_{th} \simeq 10^{4-5}\,cm^{-3}$. In the framework of the same model, the radius distribution steepens from clouds (clumps) to embedded-clusters, which contributes to explaining observed cluster radius distributions. [Abridged], Comment: 15 pages, 12 figures, accepted to MNRAS

We highlight how the mass-radius relation of cluster-forming cores combined with an external tidal field can influence infant weight-loss and disruption likelihood of clusters after gas expulsion. Specifically, we study how the relation between the bound fraction of stars staying in clusters at the end of violent relaxation and the cluster-forming core mass is affected by the slope and normalization of the core mass-radius relation. Assuming mass-independent star formation efficiency and gas-expulsion time-scale $\tau_{GExp}/\tau_{cross}$ and a given external tidal field, it is found that constant surface density cores and constant radius cores have the potential to lead to the preferential removal of high- and low-mass clusters, respectively. In contrast, constant volume density cores result in mass-independent cluster infant weight-loss, as suggested by observations. Our modelling includes predictions about the evolution of high-mass cluster-forming cores, a regime not yet covered by the observations. An overview of various issues directly affected by the nature of the core mass-radius relation is presented (e.g. cluster mass function, galaxy star formation histories, globular cluster self-enrichment). Finally, we emphasize that observational mass-radius data-sets of dense gas regions must be handled with caution as they may be the imprint of the molecular tracer used to map them, rather than reflecting cluster formation conditions. [Abridged], Comment: 14 pages, 7 figures, accepted to MNRAS

Violent relaxation -- the protocluster dynamical response to the expulsion of its residual star forming gas -- is a short albeit crucial episode in the evolution of star clusters and star cluster systems. Because it is heavily driven by cluster formation and environmental conditions, it is a potentially highly rewarding phase in terms of probing star formation and galaxy evolution. In this contribution I review how cluster formation and environmental conditions affect the shape of the young cluster mass function and the relation between the present star formation rate of galaxies and the mass of their young most massive cluster., Comment: 8 pages, 5 figures. Invited talk. To appear in the proceedings of IAU Symp. 266 (Star clusters, Rio de Janeiro, Brazil, August 2009), eds. R. de Grijs and J. Lepine

We investigate the ratio between the half-mass radii r_h of Galactic globular clusters and their Jacobi radii r_J given by the potential of the Milky Way and show that clusters with galactocentric distances R_{GC}>8 kpc fall into two distinct groups: one group of compact, tidally-underfilling clusters with r_h/r_J<0.05 and another group of tidally filling clusters which have 0.1 < r_h/r_J<0.3. We find no correlation between the membership of a particular cluster to one of these groups and its membership in the old or younger halo population. Based on the relaxation times and orbits of the clusters, we argue that compact clusters and most clusters in the inner Milky Way were born compact with half-mass radii r_h < 1 pc. Some of the tidally-filling clusters might have formed compact as well, but the majority likely formed with large half-mass radii. Galactic globular clusters therefore show a similar dichotomy as was recently found for globular clusters in dwarf galaxies and for young star clusters in the Milky Way. It seems likely that some of the tidally-filling clusters are evolving along the main sequence line of clusters recently discovered by Kuepper et al. (2008) and are in the process of dissolution., Comment: 8 pages, 4 figures, MNRAS in press

Violent relaxation -- the protocluster dynamical response to the expulsion of its leftover star forming gas -- is a short albeit crucial episode in the evolution of star clusters and star cluster systems. In this contribution, I survey how it influences the cluster age distribution, the cluster mass function and the ratio between the cluster mass and the stellar mass. I highlight the promising potential that the study of this phase holds in terms of deciphering star cluster formation and galaxy evolution, and (some of) the issues which are to be dealt with before achieving this goal., Comment: Highlight Talk at JENAM2008 Symposium "Star Clusters - Witnesses of Cosmic History"; to appear in "Reviews in Modern Astronomy" of the Astronomische Gesellschaft, S.Roeser (ed), vol.21, Wiley-VCH, in press (15 pages, 5 figs)

We use Monte-Carlo simulations, combined with homogeneously determined age and mass distributions based on multi-wavelength photometry, to constrain the cluster formation history and the rate of bound cluster disruption in the Large Magellanic Cloud (LMC) cluster system. We evolve synthetic star cluster systems formed with a power-law initial cluster mass function (ICMF) of spectral index $\alpha =-2$ assuming different cluster disruption time-scales. For each of these disruption time-scales we derive the corresponding cluster formation rate (CFR) required to reproduce the observed cluster age distribution. We then compare, in a Poissonian $\chi^2$ sense, model mass distributions and model two-dimensional distributions in log(mass) vs. log(age) space of the detected surviving clusters to the observations. Because of the bright detection limit ($M_V^{\rm lim} \simeq -4.7$ mag) above which the observed cluster sample is complete, one cannot constrain the characteristic disruption time-scale for a $10^4$ M$_\odot$ cluster, $t_4^{\rm dis}$ (where the disruption time-scale depends on cluster mass as $t_{\rm dis} = t_4^{\rm dis} (M_{\rm cl} / 10^4 {\rm M}_\odot)^0.62$), to better than $t_4^{\rm dis} \ge 1$ Gyr. We conclude that the CFR has increased from 0.3 clusters Myr$^{-1}$ 5 Gyr ago, to a present rate of $(20-30)$ clusters Myr$^{-1}$. For older ages the derived CFR depends sensitively on our assumption of the underlying CMF shape. If we assume a universal Gaussian ICMF, then the CFR has increased steadily over a Hubble time from $\sim 1$ cluster Gyr$^{-1}$ 15 Gyr ago to its present value. If the ICMF has always been a power law with a slope close to $\alpha=-2$, the CFR exhibits a minimum some 5 Gyr ago, which we tentatively identify with the well-known age gap in the LMC's cluster age distribution., Comment: 20 pages, accepted for publication in MNRAS

We review the long-term survival chances of young massive star clusters (YMCs), hallmarks of intense starburst episodes often associated with violent galaxy interactions. We address the key question as to whether at least some of these YMCs can be considered proto-globular clusters (GCs), in which case these would be expected to evolve into counterparts of the ubiquitous old GCs believed to be among the oldest galactic building blocks. In the absence of significant external perturbations, the key factor determining a cluster's long-term survival chances is the shape of its stellar initial mass function (IMF). It is, however, not straightforward to assess the IMF shape in unresolved extragalactic YMCs. We discuss in detail the promise of using high-resolution spectroscopy to make progress towards this goal, as well as the numerous pitfalls associated with this approach. We also discuss the latest progress in worldwide efforts to better understand the evolution of entire cluster systems, the disruption processes they are affected by, and whether we can use recently gained insights to determine the nature of at least some of the YMCs observed in extragalactic starbursts as proto-GCs. We conclude that there is an increasing body of evidence that GC formation appears to be continuing until today; their long-term evolution crucially depends on their environmental conditions, however., Comment: invited refereed review article; ChJA&A, in press; 33 pages LaTeX (2 postscript figures); requires chjaa.cls style file

[Abridged] Evidence favouring a Gaussian initial globular cluster mass function has accumulated over recent years. We show that an approximately Gaussian mass function is naturally generated from a power-law mass distribution of protoglobular clouds by expulsion from the protocluster of star forming gas due to supernova activity, provided that the power-law mass distribution shows a lower-mass limit. As a result of gas loss, the gravitational potential of the protocluster gets weaker and only a fraction of the newly formed stars is retained. The mass fraction of bound stars ranges from zero to unity, depending on the local star formation efficiency $\epsilon$. Assuming that $\epsilon$ is independent of the protoglobular cloud mass, we investigate how such variations affect the mapping of a protoglobular cloud mass function to the resulting globular cluster initial mass function. A truncated power-law cloud mass spectrum generates bell-shaped cluster initial mass functions, with a turnover location mostly sensitive to the lower limit of the cloud mass range. We also show that a Gaussian mass function for the protoglobular clouds with a mean ${\rm log}m_G \simeq 6.1-6.2$ and a standard deviation $\sigma \lesssim 0.4$ provides results very similar to those resulting from a truncated power-law cloud mass spectrum, that is, the distribution function of masses of protoglobular clouds influences only weakly the shape of the resulting globular star cluster initial mass function. The gas removal process and the protoglobular cloud mass-scale dominate the relevant physics. Moreover, gas removal during star formation in massive clouds is likely the prime cause of the predominance of field stars in the Galactic halo., Comment: 24 pages, accepted for publication in MNRAS

We present new constraints on the initial mass spectrum of the Galactic Old Halo globular clusters. This has remained poorly-known so far, as both an initial power-law mass spectrum and an initial lognormal mass function could have evolved into the presently observed globular cluster mass distribution, making the initial contribution of now lost low-mass objects ill-determined. Our approach consists in comparing the evolution with time of both the radial mass density profile and the number density profile of the globular cluster system. Using the analytical expression established by Vesperini & Heggie for the temporal evolution of the mass of a globular cluster on a circular orbit in a stable Galactic potential, we evolve the mass and number density profiles of many putative globular cluster systems, each starting with different initial cluster mass spectrum and initial cluster space-density. We then compare the modelled profiles with those of the Old Halo cluster system in order to investigate which system(s) provide(s) the best consistency with the data. (abridged), Comment: 12 pages, MNRAS accepted

We investigate what may be the origin of the presently observed spatial distribution of the mass of the Galactic Old Halo globular cluster system. We propose its radial mass density profile to be a relic of the distribution of the cold baryonic material in the protoGalaxy. Assuming that this one arises from the profile of the whole protoGalaxy minus the contribution of the dark matter (and a small contribution of the hot gas by which the protoglobular clouds were bound), we show that the mass distributions around the Galactic centre of this cold gas and of the Old Halo agree satisfactorily. In order to demonstrate our hypothesis even more conclusively, we simulate the evolution with time, up to an age of 15 Gyr, of a putative globular cluster system whose initial mass distribution in the Galactic halo follows the profile of the cold protogalactic gas. We show that beyond a galactocentric distance of order 2 to 3 kpc, the initial shape of such a mass density profile is preserved in spite of the complete destruction of some globular clusters and the partial evaporation of some others. This result is almost independent of the choice of the initial mass function for the globular clusters, which is still ill-determined. The shape of these evolved cluster system mass density profiles also agree with the presently observed profile of the Old Halo globular cluster system, thus strengthening our hypothesis. Our result might suggest that the flattening shown by the Old Halo mass density profile at short distance from the Galactic centre is, at least partly, of primordial origin., Comment: 10 pages, accepted in MNRAS

We explore the self-enrichment hypothesis for globular cluster formation with respect to the star formation aspect. Following this scenario, the massive stars of a first stellar generation chemically enrich the globular progenitor cloud up to Galactic halo metallicities and sweep it into an expanding spherical shell of gas. This paper investigates the ability of this swept proto-globular cloud to become gravitationally unstable and, therefore, to seed the formation of second generation stars which may later on form a globular cluster. We use a simple model based on a linear perturbation theory for transverse motions in a shell of gas to demonstrate that the pressures by which the progenitor clouds are bound and the supernova numbers required to achieve Galactic halo metallicities support the successful development of the shell transverse collapse. Interestingly, the two parameters controling the metallicity achieved through self-enrichment, namely the number of supernovae and the external pressure, also rule the surface density of the shell and thus its ability to undergo a transverse collapse. Such a supernova-induced origin for the globular cluster stars opens therefore the way to the understanding of the halo metallicity distributions. This model is also able to explain the lower limit of the halo globular cluster metallicity., Comment: 16 pages, 16 figures, MNRAS accepted