N. Bastian

A Universal Stellar Initial Mass Function? A Critical Look at Variations

Whether the stellar initial mass function (IMF) is universal or is instead sensitive to environmental conditions is of critical importance: The IMF influences most observable properties of stellar populations and thus galaxies, and detecting variations in the IMF could provide deep insights into the star formation process. This review critically examines reports of IMF variations, with a view toward whether other explanations are sufficient given the evidence. Studies of the field, young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a universal system IMF: a power law of Salpeter index (Γ = 1.35) above a few solar masses, and a log normal or shallower power law (Γ ∼ 0–0.25) for lower mass stars. The shape and universality of the substellar IMF is still under investigation. Observations of resolved stellar populations and the integrated properties of most galaxies are also consistent with a universal IMF, suggesting no gross variations over much of cosm...

Gas expulsion and the destruction of massive young clusters

We examine the luminosity and dynamical mass estimates for young massive stellar clusters. For many young (<50 Myr) clusters, the luminosity and dynamical mass estimates differ by a significant amount. We explain this as being due to many young clusters being out of virial equilibrium (which is assumed in dynamical mass estimates) because the clusters are undergoing violent relaxation after expelling gas not used in star formation. We show that, if we assume that luminous mass estimates are correct (for a standard initial mass function), at least 50 per cent of young clusters for which dynamical masses are known are likely to be destroyed within a few tens of Myr of their formation. Even clusters which will retain a bound core may lose a large fraction of their stellar mass. We also show that the core radius and other structural parameters change significantly during the violent relaxation that follows gas expulsion and that they should be considered instantaneous values only, not necessarily reflecting the final state of the cluster. In particular we note that the increasing core radii observed in young LMC/SMC clusters can be well explained as an effect of rapid gas loss.

An analytical description of the disruption of star clusters in tidal fields with an application to Galactic open clusters

We present a simple analytical description of the disruption of star clusters in a tidal field. The cluster disruption time, defined as tdis = {dln M/dt} −1 , depends on the mass M of the cluster as tdis = t0(M/M� ) γ with γ = 0.62 for clusters in a tidal field, as shown by empirical studies of cluster samples in different galaxies and by N-body simulations. Using this simple description we derive an analytic expression for the way in which the mass of a cluster decreases with time due to stellar evolution and disruption. The result agrees very well with those of detailed N-body simulations for clusters in the tidal field of our galaxy. The analytic expression can be used to predict the mass and age histograms of surviving clusters for any cluster initial mass function and any cluster formation history. The method is applied to explain the age distribution of the open clusters in the solar neighbourhood within 600 pc, based on a new cluster sample that appears to be unbiased within a distance of about 1 kpc. From a comparison between the observed and predicted age distributions in the age range between 10 Myr to 3 Gyr we find the following results: (1) The disruption time of a 10 4 Mcluster in the solar neighbourhood is about 1.3 ± 0.5 Gyr. This is a factor of 5 shorter than that derived from N-body simulations of clusters in the tidal field of the galaxy. Possible reasons for this discrepancy are discussed. (2) The present star formation rate in bound clusters within 600 pc of the Sun is 5.9 ± 0.8 × 10 2 MMyr −1 , which corresponds to a surface star formation rate of bound clusters of 5.2 ± 0.7 × 10 −10 Myr −1 pc −2 . (3) The age distribution of open clusters shows a bump between 0.26 and 0.6 Gyr when the cluster formation rate was 2.5 times higher than before and after. (4) The present star formation rate in bound clusters is about half that derived from the study of embedded clusters. The difference suggests that about half of the clusters in the solar neighbourhood become unbound within about 10 Myr. (5) The most massive clusters within 600 pc had an initial mass of about 3 × 10 4 M� . This is in agreement with the statistically expected value based on a cluster initial mass function with a slope of −2, even if the physical upper mass limit for cluster formation is as high as 10 6 M� .

The spatial distribution of star formation in the solar neighbourhood: do all stars form in dense clusters?

We present a global study of low mass, young stellar object (YSO) surface densities (�) in nearby (< 500 pc) star forming regions based on a comprehensive collection of Spitzer Space Telescope surveys. We show that the distribution of YSO surface densities in the solar neighbourhood is a smooth distribution, being adequately described by a lognormal function from a few to 10 3 YSOs per pc 2 , with a peak at � 22 stars pc

Early disc accretion as the origin of abundance anomalies in globular clusters

Globular clusters (GCs), once thought to be well approximated as simple stellar populations (i.e. all stars having the same age and chemical abundance), are now known to host a variety of anomalies, such as multiple discrete (or spreads in) populations in colour–magnitude diagrams and abundance variations in light elements (e.g. Na, O, Al). Multiple models have been put forward to explain the observed anomalies, although all have serious shortcomings (e.g. requiring a non-standard initial mass function of stars and GCs to have been initially 10–100 times more massive than observed today). These models also do not agree with observations of massive stellar clusters forming today, which do not display significant age spreads nor have gas/dust within the cluster. Here we present a model for the formation of GCs, where low-mass pre-main-sequence stars accrete enriched material released from interacting massive binary and rapidly rotating stars on to their circumstellar discs, and ultimately on to the young stars. As was shown in previous studies, the accreted material matches the unusual abundances and patterns observed in GCs. The proposed model does not require multiple generations of star formation, conforms to the known properties of massive clusters forming today and solves the ‘mass budget problem’ without requiring GCs to have been significantly more massive at birth. Potential caveats to the model as well as model predictions are discussed.

The Star Cluster Population of M51: II. Age distribution and relations among the derived parameters

We use archival Hubble Space Telescope observations of broad-band images from the ultraviolet (F255W- filter) through the near infrared (NICMOS F160W-filter) to study the star cluster population of the interacting spiral galaxy M51. We obtain age, mass, extinction, and effective radius estimates for 1152 star clusters in a region of � 7.3 × 8.1 kpc centered on the nucleus and extending into the outer spiral arms. In this paper we present the data set and exploit it to determine the age distribution and relationships among the fundamental parameters (i.e. age, mass, effective radius). We show the critical dependence of the age distribution on the sample selection, and confirm that using a constant mass cut-off, above which the sample is complete for the entire age range of interest, is essential. In particular, in this sample we are complete only for masses above 5×10 4 M⊙ for the last 1 Gyr. Using this dataset we find: i) that the cluster formation rate seems to have had a large increase � 50-70 Myr ago, which is coincident with the suggested second passage of its companion, NGC 5195, ii) a large number of extremely young (< 10 Myr) star clusters, which we interpret as a population of unbound clusters of which a large majority will disrupt within the next �10 Myr, and iii) that the distribution of cluster sizes can be well approximated by a power-law with exponent, � = 2.2 ± 0.2, which is very similar to that of Galactic globular clusters, indicating that cluster disruption is largely independent of cluster radius. In addition, we have used this dataset to search for correlations among the derived parameters. In particular, we do not find any strong trends between the age and mass, mass and effective radius, nor between the galactocentric distance and effective radius. There is, however, a strong correlation between the age of a cluster and its extinction, with younger clusters being more heavily reddened than older clusters.We present the age and mass distribution of star clusters in M51. The structural parameters are found by fitting cluster evolution models to the spectral energy distribution consisting of 8 HST-WFPC2 pass bands. There is evidence for a burst of cluster formation at the moment of the second encounter with the companion NGC5195 (50-100 Myr ago) and a hint for an earlier burst (400-500 Myr ago). The cluster IMF has a power law slope of -2.1. The disruption time of clusters is extremely short (< 100 Myr for a 10^4 Msun cluster).

Star cluster formation and evolution in nearby starburst galaxies — II. Initial conditions

We use the ages, masses and metallicities of the rich young star cluster systems in the nearby starburst galaxies NGC 3310 and NGC 6745 to derive their cluster formation histories and subsequent evolution. We further expand our analysis of the systematic uncertainties involved in the use of broad-band observations to derive these parameters (Paper I) by examining the effects of a priori assumptions on the individual cluster metallicities. The age (and metallicity) distributions of both the clusters in the circumnuclear ring in NGC 3310 and of those outside the ring are statistically indistinguishable, but there is a clear and significant excess of higher-mass clusters in the ring compared to the non-ring cluster sample; it is likely that the physical conditions in the starburst ring may be conducive for the formation of higher-mass star clusters, on average, than in the relatively more quiescent environment of the main galactic disc. For the NGC 6745 cluster system we derive a median age of � 10 Myr. NGC 6745 contains a significant population of high-mass “super star clusters”, with masses in the range 6.5 . log(Mcl/M⊙) . 8.0. This detection supports the scenario that such objects form preferentially in the extreme environments of interacting galaxies. The age of the cluster populations in both NGC 3310 and NGC 6745 is significantly lower than their respective characteristic cluster disruption time-scales, respectively log(t dis /yr) = 8.05 and 7.75, for 10 4 M⊙ clusters. This allows us to obtain an independent estimate of the initial cluster mass function slope, � = 2.04(±0.23) +0.13 −0.43 for NGC 3310, and 1.96(±0.15) ± 0.19 for NGC 6745, respectively, for masses Mcl & 10 5 M⊙ and Mcl & 4 × 10 5 M⊙. These mass function slopes are consistent with those of other

On the star formation rate – brightest cluster relation: estimating the peak star formation rate in post-merger galaxies

We further the recent discussion on the relation between the star formation rate (SFR) of a galaxy and the luminosity of its brightest star cluster (SFR versus M V brightest ). We first show that the observed trend of SFR versus M V brightest is due to the brightest cluster in a galaxy being preferentially young (≤15 Myr - for a constant SFR) and hence a good tracer of the current SFR, although we give notable exceptions to this rule. Archival Hubble Space Telescope (HST) imaging of high-SFR galaxies, as well as additional galaxies/clusters from the literature, is used to further confirm the observed trend. Using a series of Monte Carlo simulations, we show that a pure power-law mass function with index a = 2 is ruled out by the current data. Instead, we find that a Schechter function (i.e. a power law with an exponential truncation at the high-mass end) provides an excellent fit to the data. Additionally, these simulations show that bound cluster formation (in M ⊙ yr -1 ) represents only ∼8±3 per cent of the total star formation within a galaxy, independent of the SFR. From this, we conclude that there is only a single mode of cluster formation which operates over at least 6 orders of magnitude in the SFR. We provide a simple model of star/cluster formation feedback within dwarf galaxies (and star-forming complexes within spirals) which highlights the strong impact that a massive cluster can have on its surroundings. Using this relation, we can extrapolate backwards in time in order to estimate the peak SFR of major merger galaxies, such as NGC 7252,1316 and 3610. The derived SFRs for these galaxies are between a few hundred and a few thousand solar masses per year. The inferred far-infrared luminosity of the galaxies, from the extrapolated SFR, places them well within the range of ultraluminous infrared galaxies (ULIRGs) and for NGC 7252 within the hyperluminous infrared galaxy (HLIRG) regime. Thus, we provide evidence that these post-merger galaxies passed through a ULIRG/HLIRG phase and are now evolving passively. Using the current and extrapolated past SFR of NGC 34, we infer that the ULIRG phase of this galaxy has lasted for at least 150 Myr.

Clusters in the inner spiral arms of M 51: The cluster IMF and the formation history

We present the results of an analysis of the HST-WFPC2 observations of the interacting galaxy M51. From the observations in 5 broadband filters (UBVRI) and two narrowband filters (Hα and (OIII)) we study the cluster population in a region of 3.2 ×3.2 kpc 2 in the inner spiral arms of M51, at a distance of about 1 to 3 kpc from the nucleus. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by means of a comparison between the observed spectral energy distribution and the predictions from cluster synthesis models for instantaneous star formation and solar metallicity. The lack of (OIII) emission in even the youngest clusters with strong Hα emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 M� . The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, much more severe than can be expected on the basis of evolutionary fading of the clusters. This indicates that cluster dispersion is occurring on a timescale of 10 Myr or longer. The cluster initial mass function has been derived from clusters younger than 10 Myr by a linear regression fit of the cumulative mass distribution. This results in an exponent α = −dlogN(M)/dlog (M) = 2.1 ± 0.3 in the range of 2.5 × 10 3 2 × 10 4 M� . In the restricted range of 2.5 × 10 3 < M < 2 × 10 4 Mwe find α = 2.0 ± 0.05. This exponent is very similar to the value derived for clusters in the interacting Antennae galaxies, and to the exponent of the mass distribution of the giant molecular clouds in our Galaxy. To study the possible effects of the interaction of M51 with its companion NGC 5195 about 400 Myr ago, which triggered a huge starburst in the nucleus, we determined the cluster formation rate as a function of time for clusters with an initial mass larger than 10 4 M� . There is no evidence for a peak in the cluster formation rate at around 200 to 400 Myr ago within 2 σ accuracy, i.e. within a factor two. The formation rate of the detected clusters decreases strongly with age by about a factor 10 2 between 10 Myr and 1 Gyr. For clusters older than about 150 Myr this is due to the evolutionary fading of the clusters below the detection limit. For clusters younger than 100 Myr this is due to the dispersion of the clusters, unless one assumes that the cluster formation rate has been steadily increasing with time from 1 Gyr ago to the present time.

The NGC 404 Nucleus: Star Cluster and Possible Intermediate-mass Black Hole

We examine the nuclear morphology, kinematics, and stellar populations in nearby S0 galaxy NGC 404 using a combination of adaptive optics assisted near-IR integral-field spectroscopy, optical spectroscopy, and Hubble Space Telescope imaging. These observations enable study of the NGC 404 nucleus at a level of detail possible only in the nearest galaxies. The surface brightness profile suggests the presence of three components: a bulge, a nuclear star cluster (NSC), and a central light excess within the cluster at radii < 3 pc. These components have distinct kinematics with modest rotation seen in the NSC and counter-rotation seen in the central excess. Molecular hydrogen emission traces a disk with rotation nearly orthogonal to that of the stars. The stellar populations of the three components are also distinct, with half of the mass of the NSC having ages of ~1 Gyr (perhaps resulting from a galaxy merger), while the bulge is dominated by much older stars. Dynamical modeling of the stellar kinematics gives a total NSC mass of 1.1 × 107 M ☉. Dynamical detection of a possible intermediate-mass black hole (BH) is hindered by uncertainties in the central stellar mass profile. Assuming a constant mass-to-light ratio, the stellar dynamical modeling suggests a BH mass of <1 × 105 M ☉, while the molecular hydrogen gas kinematics are best fitted by a BH with a mass of 4.5+3.5 –2.0 × 105 M ☉. Unresolved and possibly variable dust emission in the near-infrared and active galactic nucleus-like molecular hydrogen emission-line ratios do suggest the presence of an accreting BH in this nearby LINER galaxy.