Mark Gieles

Binary Interaction Dominates the Evolution of Massive Stars

Star Partners Stars more massive than eight times the mass of the Sun are rare and short-lived, yet they are fundamentally important because they produce all the heavy elements in the universe, such as iron, silicon, and calcium. Sana et al. (p. 444) examined the properties of a sample of ∼70 massive stars in six stellar clusters located nearby in our galaxy. Over half of the stars in the sample belong to a binary system and, during the course of their lifetimes, most of the stars in these binaries will interact with one another, either by merging or exchanging mass. Binary interaction may thus affect the evolution of the majority of massive stars. Analysis of a sample of massive stars in our Galaxy implies that most will interact with a nearby companion. The presence of a nearby companion alters the evolution of massive stars in binary systems, leading to phenomena such as stellar mergers, x-ray binaries, and gamma-ray bursts. Unambiguous constraints on the fraction of massive stars affected by binary interaction were lacking. We simultaneously measured all relevant binary characteristics in a sample of Galactic massive O stars and quantified the frequency and nature of binary interactions. More than 70% of all massive stars will exchange mass with a companion, leading to a binary merger in one-third of the cases. These numbers greatly exceed previous estimates and imply that binary interaction dominates the evolution of massive stars, with implications for populations of massive stars and their supernovae.

Young massive star clusters

Young massive clusters (YMCs) are dense aggregates of young stars that form the fundamental building blocks of galaxies. Several examples exist in the Milky Way Galaxy and the Local Group, but they are particularly abundant in starburst and interacting galaxies. The few YMCs that are close enough to resolve are of prime interest for studying the stellar mass function and the ecological interplay between stellar evolution and stellar dynamics. The distant unresolved clusters may be effectively used to study the star-cluster mass function, and they provide excellent constraints on the formation mechanisms of young cluster populations. YMCs are expected to be the nurseries for many unusual objects, including a wide range of exotic stars and binaries. So far only a few such objects have been found in YMCs, although their older cousins, the globular clusters, are unusually rich in stellar exotica. In this review, we focus on star clusters younger than ∼100 Myr, more than a few current crossing times old, and m...

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 VLT-FLAMES Tarantula Survey VIII. Multiplicity properties of the O-type star population

Context. The Tarantula Nebula in the Large Magellanic Cloud is our closest view of a starburst region and is the ideal environment to investigate important questions regarding the formation, evolution and final fate of the most massive stars. Aims. We analyze the multiplicity properties of the massive O-type star population observed through multi-epoch spectroscopy in the framework of the VLT-FLAMES Tarantula Survey. With 360 O-type stars, this is the largest homogeneous sample of massive stars analyzed to date. Methods. We use multi-epoch spectroscopy and variability analysis to identify spectroscopic binaries. We also use a Monte-Carlo method to correct for observational biases. By modeling simultaneously the observed binary fraction, the distributions of the amplitudes of the radial velocity variations and the distribution of the time scales of these variations, we constrain the intrinsic current binary fraction and period and mass-ratio distributions. Results. We observe a spectroscopic binary fraction of 0.35 ± 0.03, which corresponds to the fraction of objects displaying statistically significant radial velocity variations with an amplitude of at least 20 km s-1. We compute the intrinsic binary fraction to be 0.51 ± 0.04. We adopt power-laws to describe the intrinsic period and mass-ratio distributions: f(log 10P/d) ~ (log 10P/d)π (with log 10P/d in the range 0.15−3.5) and f(q) ~ qκ with 0.1 ≤ q = M2/M1 ≤ 1.0. The power-law indexes that best reproduce the observed quantities are π = −0.45 ± 0.30 and κ = −1.0 ± 0.4. The period distribution that we obtain thus favours shorter period systems compared to an Opik law (π = 0). The mass ratio distribution is slightly skewed towards low mass ratio systems but remains incompatible with a random sampling of a classical mass function (κ = −2.35). The binary fraction seems mostly uniform across the field of view and independent of the spectral types and luminosity classes. The binary fraction in the outer region of the field of view (r > 7.8′, i.e. ≈117 pc) and among the O9.7 I/II objects are however significantly lower than expected from statistical fluctuations. The observed and intrinsic binary fractions are also lower for the faintest objects in our sample (Ks > 15.5 mag), which results from observational effects and the fact that our O star sample is not magnitude-limited but is defined by a spectral-type cutoff. We also conclude that magnitude-limited investigations are biased towards larger binary fractions. Conclusions. Using the multiplicity properties of the O stars in the Tarantula region and simple evolutionary considerations, we estimate that over 50% of the current O star population will exchange mass with its companion within a binary system. This shows that binary interaction is greatly affecting the evolution and fate of massive stars, and must be taken into account to correctly interpret unresolved populations of massive stars.

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 disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N-body simulations of cluster-GMC encounters, where the GMC is represented by a moving analytical potential. Excellent agreement is found between the simulations and the analytical work for fractional energy gains of Delta E/vertical bar E-0 vertical bar < 10, where vertical bar E-0 vertical bar is the initial total cluster energy. The fractional mass loss from the cluster scales with the fractional energy gain as (Delta M/M-0) = f(Delta E/vertical bar E-0 vertical bar), where f similar or equal to 0.25. This is because a fraction 1 - f of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We therefore suggest that the disruption time of clusters, t(dis), is best defined as the time needed to bring the cluster mass to zero, instead of the time needed to inject the initial cluster energy. We derive an expression for t(dis) based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. Assuming spatially homogeneous distributions of clusters and GMCs with a relative velocity dispersion of sigma(cn), we find that clusters lose most of their mass in relatively close encounters with high relative velocities (similar to 2 sigma(cn)). The disruption time depends on the cluster mass (M-c) and half-mass radius (r(h)) as t(dis) = 2.0 S(M-c/10(4) M-circle dot)(3.75 pc/r(h))(3) Gyr, with S equivalent to 1 for the solar neighbourhood and S scales with the surface density of individual GMCs (Sigma(n)) and the global GMC density (rho(n)) as S proportional to (Sigma(n)rho(n))(-1). Combined with the observed relation between r(h) and M-c, that is, r(h) proportional to M-c(lambda), t(dis) depends on M-c as t(dis)proportional to M-c(gamma). The index gamma is then defined as gamma= 1 - 3 lambda. The observed shallow relation between cluster radius and mass (e.g. lambda similar or equal to 0.1), makes the value of the index gamma = 0.7 similar to that found from observations and from simulations of clusters dissolving in tidal fields (gamma similar or equal to 0.62). The constant of 2.0 Gyr, which is the disruption time of a 10(4) M circle dot cluster in the solar neighbourhood, is about a factor of 3.5 shorter than that found from earlier simulations of clusters dissolving under the combined effect of Galactic tidal field and stellar evolution. It is somewhat higher than the observationally determined value of 1.3 Gyr. It suggests, however, that the combined effect of tidal field and encounters with GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC encounters can also explain the (very) short disruption time that was observed for star clusters in the central region of M51, since there rho(n) is an order of magnitude higher than that in the solar neighbourhood.

Hierarchical star formation in M51: Star/cluster complexes

We report on a study of young star cluster complexes in the spiral galaxy M 51. Recent studies have confirmed that star clusters do not form in isolation, but instead tend to form in larger groupings or complexes. We use HST broad and narrow band images (from both WFPC2 and ACS), along with BIMA-CO observations to study the properties and investigate the origin of these complexes. We find that the complexes are all young (<10 Myr), have sizes between ∼85 and ∼240 pc, and have masses between 3–30 × 10 4 M� . Unlike that found for isolated young star clusters, we find a strong correlation between the complex mass and radius, namely M ∝ R 2.33±0.19 . This is similar to that found for giant molecular clouds (GMCs). By comparing the mass-radius relation of GMCs in M 51 to that of the complexes we can estimate the star formation efficiency within the complexes, although this value is heavily dependent on the assumed CO-to-H2 conversion factor. The complexes studied here have the same surface density distribution as individual young star clusters and GMCs. If star formation within the complexes is proportional to the gas density at that point, then the shared mass-radius relation of GMCs and complexes is a natural consequence of their shared density profiles. We briefly discuss possibilities for the lack of a mass-radius relation for young star clusters. We note that many of the complexes show evidence of merging of star clusters in their centres, suggesting that larger star clusters can be produced through the build up of smaller clusters.

Disruption time scales of star clusters in different galaxies

The observed average lifetime of the population of star clusters in the Solar Neighbourhood, the Small Magellanic Cloud and in selected regions of M 51 and M 33 is compared with simple theoretical predictions and with the results of N-body simulations. The empirically derived lifetimes (or disruption times) of star clusters depend on their initial mass as tdis emp ∝ Mcl 0.60 in all four galaxies. N-body simulations have shown that the predicted disruption time of clusters in a tidal field scales as tdis pred ∝ t 0.75 rh t 0.25 cr ,w heretrh is the initial half-mass relaxation time and tcr is the crossing time for a cluster in equilibrium. We show that this can be approximated accurately by tdis pred ∝ M 0.62 cl for clusters in the mass range of about 10 3 to 10 6 M � ,i n excellent agreement with the observations. Observations of clusters in different extragalactic environments show that tdis also depends on the ambient density in the galaxies where the clusters reside. Linear analysis predicts that the disruption time will depend on the ambient density of the cluster environment as tdis ∝ ρ −1/2 amb . This relation is consistent with N-body simulations. The empirically derived disruption times of clusters in the Solar Neighbourhood, in the SMC and in M 33 agree with these predictions. The best fitting expression for the disruption time is tdis = Cenv(Mcl/10 4 M� ) 0.62 (ρamb/Mpc −3 ) −0.5 where Mcl is the initial mass of the cluster and Cenv � 300−800 Myr. The disruption times of star clusters in M 51 within 1−5 kpc from the nucleus, is shorter than predicted by about an order of magnitude. This discrepancy might be due to the strong tidal field variations in M 51, caused by the strong density contrast between the spiral arms and interarm regions, or to the disruptive forces from giant molecular clouds.

The luminosity function of young star clusters: implications for the maximum mass and luminosity of clusters

We introduce a method to relate a possible truncation of the star cluster mass function at the high mass end to the shape of the cluster luminosity function (LF). We compare the observed LFs of five galaxies containing young star clusters with synthetic cluster population models with varying initial conditions. The LF of the SMC, the LMC and NGC 5236 are characterized by a power-law behavior N dL ∝ L−α dL, with a mean exponent of α = 2.0 ± 0.2. This can be explained by a cluster population formed with a constant cluster formation rate, in which the maximum cluster mass per logarithmic age bin is determined by the size-of-sample effect and therefore increases with log (age/yr). The LFs of NGC 6946 and M51 are better described by a double power-law distribution or a Schechter function. When a cluster population has a mass function that is truncated below the limit given by the size-of-sample effect, the total LF shows a bend at the magnitude of the maximum mass, with the age of the oldest cluster in the population, typically a few Gyr due to disruption. For NGC 6946 and M51 this suggests a maximum mass of Mmax = 0.5−1 × 106 M , although the bend is only a 1–2 σ detection. Faint-ward of the bend the LF has the same slope as the underlying initial cluster mass function and bright-ward of the bend it is steeper. This behavior can be well explained by our population model. We compare our results with the only other galaxy for which a bend in the LF has been observed, the “Antennae” galaxies (NGC 4038/4039). There the bend occurs brighter than in NGC 6946 and M51, corresponding to a maximum cluster mass of Mmax = 1.3−2.5 × 106 M . Hence, if the maximum cluster mass has a physical limit, then it can vary between different galaxies. The fact that we only observe this bend in the LF in the “Antennae” galaxies, NGC 6946 and M51 is because there are enough clusters available to reach the limit. In other galaxies there might be a physical limit as well, but the number of clusters formed or observed is so low, that the LF is not sampled up to the luminosity of the bend. The LF can then be approximated with a single power-law distribution, with an index similar to the initial mass function index.