Embedded Cluster Mass Function Research Articles

The influence of a top-heavy integrated galactic IMF and dust on the chemical evolution of high-redshift starbursts

ABSTRACT We study the effects of the integrated galactic initial mass function (IGIMF) and dust evolution on the abundance patterns of high redshift starburst galaxies. In our chemical models, the rapid collapse of gas clouds triggers an intense and rapid star formation episode, which lasts until the onset of a galactic wind, powered by the thermal energy injected by stellar winds and supernova explosions. Our models follow the evolution of several chemical elements (C, N, α-elements, and Fe) both in the gas and dust phases. We test different values of β, the slope of the embedded cluster mass function for the IGIMF, where lower β values imply a more top-heavy initial mass function (IMF). The computed abundances are compared to high-quality abundance measurements obtained in lensed galaxies and from composite spectra in large samples of star-forming galaxies in the redshift range 2 ≲ z ≲ 3. The adoption of the IGIMF causes a sensible increase of the rate of star formation with respect to a standard Salpeter IMF, with a strong impact on chemical evolution. We find that in order to reproduce the observed abundance patterns in these galaxies, either we need a very top-heavy IGIMF (β < 2) or large amounts of dust. In particular, if dust is important, the IGIMF should have β ≥ 2, which means an IMF slightly more top-heavy than the Salpeter one. The evolution of the dust mass with time for galaxies of different mass and IMF is also computed, highlighting that the dust amount increases with a top-heavier IGIMF.

On the primordial specific frequency of globular clusters in dwarf and giant elliptical galaxies

Globular clusters (GC) are important objects for tracing the early evolution of a galaxy. We study the relation between the properties of globular cluster systems - as quantified by the GC specific frequency (SN) - and the properties of their host galaxies. In order to understand the origin of the relation between the GC specific frequency (SN) and galaxy mass, we devise a theoretical model for the specific frequency (SN,th). GC erosion is considered to be an important aspect for shaping this relation, since observations show that galaxies with low densities have a higher SN, while high density galaxies have a small SN. We construct a model based on the hypothesis that star-formation is clustered and depends on the minimum embedded star cluster mass (Mecl,min), the slope of the power-law embedded cluster mass function (beta) and the relation between the star formation rate (SFR) and the maximum star cluster mass (Mecl,max). We find an agreement between the primordial value of the specific frequency (SNi) and our model for beta between 1.5 and 2.5 with Mecl,min <10^4 Msun.

Simulating radiative feedback and star cluster formation in GMCs – II. Mass dependence of cloud destruction and cluster properties

The process of radiative feedback in Giant Molecular Clouds (GMCs) is an important mechanism for limiting star cluster formation through the heating and ionization of the surrounding gas. We explore the degree to which radiative feedback affects early ($\lesssim$5 Myr) cluster formation in GMCs having masses that range from 10$^{4-6}$ M$_{\odot}$ using the FLASH code. The inclusion of radiative feedback lowers the efficiency of cluster formation by 20-50\% relative to hydrodynamic simulations. Two models in particular --- 5$\times$10$^4$ and 10$^5$ M$_{\odot}$ --- show the largest suppression of the cluster formation efficiency, corresponding to a factor of $\sim$2. For these clouds only, the internal energy, a measure of the energy injected by radiative feedback, exceeds the gravitational potential for a significant amount of time. We find a clear relation between the maximum cluster mass, M$_{cl,max}$, formed in a GMC of mass M$_{GMC}$; M$_{cl,max}\propto$ M$_{GMC}^{0.81}$. This scaling result suggests that young globular clusters at the necessary scale of $10^6 M_{\odot}$ form within host GMCs of masses near $\sim 5 \times 10^7 M_{\odot}$. We compare simulated cluster mass distributions to the observed embedded cluster mass function ($dlog(N)/dlog(M) \propto M^{\beta}$ where $\beta$ = -1) and find good agreement ($\beta$ = -0.99$\pm$0.14) only for simulations including radiative feedback, indicating this process is important in controlling the growth of young clusters. However, the high star formation efficiencies, which range from 16-21\%, and high star formation rates compared to locally observed regions suggest other feedback mechanisms are also important during the formation and growth of stellar clusters.

On the origin of the Schechter-like mass function of young star clusters in disc galaxies

The mass function of freshly formed star clusters is empirically often described as a power law. However the cluster mass function of populations of young clusters over the scale of a galaxy has been found to be described by a Schechter-function. Here we address this apparent discrepancy. We assume that in an annulus of an isolated self- regulated radially-exponential axially-symmetric disk galaxy, the local mass function of very young (embedded) clusters is a power law with an upper mass limit which depends on the local star formation rate density. Radial integration of this mass function yields a galaxy-wide embedded cluster mass function. This integrated embedded cluster mass function has a Schechter-type form, which results from the addition of many low mass clusters forming at all galactocentric distances and rarer massive clusters only forming close to the center of the galaxy.

Distribution of star formation rates during the rapid assembly of NGC 1399 as deduced from its globular cluster system

Ultra-compact dwarf galaxies (UCDs) share many properties with globular clusters (GCs) and are found in similar environments. A large sample of UCDs and GCs around NGC 1399, the central giant elliptical of the Fornax galaxy cluster, is used to infer their formation history and also that of NGC 1399. We assumed that all GCs and UCDs in our sample are star clusters (SCs) and used them as tracers of past star formation activities. After correcting our GC/UCD sample for mass loss, we interpreted their overall mass function to be a superposition of SC populations that formed coevally during different times. The SC masses of each population were distributed according to the embedded cluster mass function (ECMF), a pure power law with the slope $-\beta$ and a stellar upper mass limit, $M_{\mathrm{max}}$, which depended on the star formation rate (SFR). We decomposed the observed GC/UCD mass function into individual SC populations and converted $M_{\mathrm{max}}$ of each SC population to an SFR. The overall distribution of SFRs reveals how the GC/UCD sample formed. Considering the age of the GCs/UCDs and the present stellar mass of NGC 1399, we found that the formation of the GCs/UCDs can be well explained for $\beta<2.3$. This agrees very well with the observation in young SCs where $\beta\approx2.0$ is usually found. Even if taking into account that some of the most massive objects might not be genuine SCs and applying different corrections for the mass loss, the outcome is not influenced much. We found peak SFRs between approximately 300 and 3000 $M_{\odot}\mathrm{yr}^{-1}$, which matches the SFRs observed in massive high-$z$ sub-mm galaxies and an SFR estimate inferred from NGC 1399 based on "downsizing", i.e. more massive galaxies must have formed over shorter times. Our results suggest that NGC 1399 and its GC/UCD system formed in an early, short, and intense starburst.

Mass distributions of star clusters for different star formation histories in a galaxy cluster environment

Clusters of galaxies usually contain rich populations of globular clusters (GCs). We investigate how different star formation histories (SFHs) shape the final mass distribution of star clusters. We assume that every star cluster population forms during a formation epoch of length dt at a constant star-formation rate (SFR). The mass distribution of such a population is described by the embedded cluster mass function (ECMF), which is a pure power law extending to an upper limit M_max. Since the SFR determines M_max, the ECMF implicitly depends on the SFR. Starting with different SFHs, each SFH is divided into formation epochs of length dt at different SFRs. The requested mass function arises from the superposition of the star clusters of all formation epochs. An improved optimal sampling technique is introduced that allows generating number and mass distributions, both of which accurately agree with the ECMF. Moreover, for each SFH the distribution function of all involved SFRs, F(SFR), is computed. For monotonically decreasing SFHs, F(SFR) always follows a power law. With F(SFR), we develope the theory of the integrated galactic embedded cluster mass function (IGECMF). It describes the distribution function of birth stellar masses of star clusters that accumulated over a formation episode much longer than dt. The IGECMF indeed reproduces the mass distribution of star clusters created according to the superposition principle. Interestingly, all considered SFHs lead to a turn-down with increasing star cluster mass in their respective IGECMFs. In the past, a turn-down at the high-mass end has been observed for GC systems in different galaxy clusters and in the cluster initial mass function. This behavior can be explained naturally if the observed star cluster ensembles are superpositions of several individual star cluster populations that formed at different times at different SFRs.

From a star cluster ensemble to its formation history

AbstractThe present-day sample of ultra-compact dwarf galaxies (UCDs) and globular clusters (GCs) around NGC 1399 is interpreted to be composed of individual star cluster (SC) populations. It is assumed that such an SC population forms at a constant star-formation rate (SFR), and its mass distribution is described by the embedded cluster mass function (ECMF) up to the upper limit Mmax. The GCs and UCDs probably formed in interactions of the progenitor galaxies during the assembly of the central Fornax galaxy cluster which is why we use them as tracers of those events. After some corrections, the overall GC/UCD mass function is decomposed into separate SC populations, each described by an ECMF. Mmax of each ECMF is converted to an SFR according to the SFR-Mmax relation, revealing the SFRs reached during the assembly of galaxies in the central Fornax galaxy cluster.

The galaxy-wide initial mass function of dwarf late-type to massive early-type galaxies

Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs > 10 Msol yr^-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk- and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index beta of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.

The mass function and dynamical mass of young star clusters: why their initial crossing-time matters crucially

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.

ULTRACOMPACT EMBEDDED CLUSTERS IN THE GALACTIC PLANE

We have identified a previously unrecognized population of very compact, embedded low-mass Galactic stellar clusters. These tight (r$ \approx $0.14 pc) groupings appear as bright singular objects at the few arcsec resolution of the Spitzer Space Telescope at 8 and 24 $\mu$m but become resolved in the sub-arcsecond UKIDSS images. They average six stars per cluster surrounded by diffuse infrared emission and coincide with 100 -- 300 M$_{\sun}$ clumps of molecular material within a larger molecular cloud. The magnitudes of the brightest stars are consistent with mid- to early-B stars anchoring $\sim$80 M$_{\sun}$ star clusters. Their evolutionary descendants are likely to be Herbig Ae/Be pre-main sequence clusters. These ultra-compact embedded clusters (UCECs) may fill part of the low-mass void in the embedded cluster mass function. We provide an initial catalog of 18 UCECs drawn from infrared Galactic Plane surveys.

Top-heavy integrated galactic stellar initial mass functions in starbursts

Star formation rates (SFR) larger than 1000 Msun/ yr are observed in extreme star bursts. This leads to the formation of star clusters with masses > 10^6 Msun in which crowding of the pre-stellar cores may lead to a change of the stellar initial mass function (IMF). Indeed, the large mass-to-light ratios of ultra-compact dwarf galaxies and recent results on globular clusters suggest the IMF to become top-heavy with increasing star-forming density. We explore the implications of top-heavy IMFs in these very massive and compact systems for the integrated galactic initial mass function (IGIMF), which is the galaxy-wide IMF, in dependence of the star-formation rate of galaxies. The resulting IGIMFs can have slopes, alpha_3, for stars more massive than about 1 Msun between 1.5 and the Salpeter slope of 2.3 for an embedded cluster mass function (ECMF) slope (beta) of 2.0, but only if the ECMF has no low-mass clusters in galaxies with major starbursts. Alternatively, beta would have to decrease with increasing SFR >10 Msun/ yr such that galaxies with major starbursts have a top-heavy ECMF. The resulting IGIMFs are within the range of observationally deduced IMF variations with redshift.

Effects of the integrated galactic IMF on the chemical evolution of the solar neighbourhood

The initial mass function determines the fraction of stars of different intial mass born per stellar generation. In this paper, we test the effects of the integrated galactic initial mass function (IGIMF) on the chemical evolution of the solar neighbourhood. The IGIMF (Weidner & Kroupa 2005) is computed from the combination of the stellar intial mass function (IMF), i.e. the mass function of single star clusters, and the embedded cluster mass function, i.e. a power law with index beta. By taking into account also the fact that the maximum achievable stellar mass is a function of the total mass of the cluster, the IGIMF becomes a time-varying IMF which depends on the star formation rate. We applied this formalism to a chemical evolution model for the solar neighbourhood and compared the results obtained by assuming three possible values for beta with the results obtained by means of a standard, well-tested, constant IMF. In general, a lower absolute value of beta implies a flatter IGIMF, hence a larger number of massive stars and larger metal ejection rates. This translates into higher type Ia and II supernova rates, higher mass ejection rates from massive stars and a larger amount of gas available for star formation, coupled with lower present-day stellar mass densities. (abridged) We also discuss the importance of the present day stellar mass function (PDMF) in providing a way to disentangle among various assumptions for beta. Our results indicate that the model adopting the IGIMF computed with beta ~2 should be considered the best since it allows us to reproduce the observed PDMF and to account for most of the chemical evolution constraints considered in this work.

IMF variations in dwarf galaxies

Dwarf galaxies tend to have a large spread in metal abundances and overall lower metallicites than large Spiral or Elliptical ones. Here we propose that if all stars are formed from an invariant canonical IMF within each star cluster which are distributed according to an embedded cluster mass function (ECMF), then the integrated stellar IMF over the whole galaxy (the integrated galaxial IMF, IGIMF) must be steeper than the canonical IMFs within the clusters, and additionally they must depended on the stellar mass of the galaxy. In particular, dwarf galaxies and low-surface brightness galaxies show steeper galaxial IMFs which vary strongly with the star-formation rate. The resulting number of Supernovae II per low-mass star, and the chemical enrichment history of these galaxies therefore vary substantially depending on the galaxy assembly history.