The physics and modes of star cluster formation: simulations

We review progress in numerical simulations of star cluster formation. These simulations involve the bottom-up assembly of clusters through hierarchical mergers, which produces a fractal stellar distribution at young (~0.5 Myr) ages. The resulting clusters are predicted to be mildly aspherical and highly mass-segregated, except in the immediate aftermath of mergers. The upper initial mass function within individual clusters is generally somewhat flatter than for the aggregate population. Recent work has begun to clarify the factors that control the mean stellar mass in a star-forming cloud and also the efficiency of star formation. The former is sensitive to the thermal properties of the gas while the latter depends both on the magnetic field and the initial degree of gravitational boundedness of the natal cloud. Unmagnetized clouds that are initially bound undergo rapid collapse, which is difficult to reverse by ionization feedback or stellar winds.Comment: 21 pages, 10 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 3 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil

A highly abnormal massive star mass function in the Orion Nebula cluster and the dynamical decay of trapezia systems

The ONC appears to be unusual on two grounds: The observed constellation of the OB stars of the entire Orion Nebula cluster and its Trapezium at its centre implies a time-scale problem given the age of the Trapezium, and an IMF problem for the whole OB star population in the ONC. Given the estimated crossing time of the Trapezium, it ought to have totally dynamically decayed by now. Furthermore, by combining the lower limit of the ONC mass with a standard IMF it emerges that the ONC should have formed at least about 40 stars heavier than 5 M_sun while only ten are observed. Using N-body experiments we (i) confirm the expected instability of the trapezium and (ii) show that beginning with a compact OB-star configuration of about 40 stars the number of observed OB stars after 1 Myr within 1 pc radius and a compact trapezium configuration can both be reproduced. These two empirical constraints thus support our estimate of 40 initial OB stars in the cluster. Interestingly, a more-evolved version of the ONC resembles the Upper Scorpius OB association. The N-body experiments are performed with the new C-code CATENA by integrating the equations of motion using the chain-multiple-regularisation method. In addition, we present a new numerical formulation of the initial mass function.Comment: Accepted by MNRAS, 11 pages, 5 figure

Constraints on the star formation histories of galaxies in the Local Cosmological Volume

IB is supported by an Alexander von Humboldt postdoctoral research fellowship. PK acknowledges support from the Grant Agency of the Czech Republic under grant number 20-21855S. This work benefited from the International Space Science Institute (ISSI/ISSI-BJ) in Bern and Beijing, thanks to the funding of the team ‘Chemical abundances in the ISM: the litmus test of stellar IMF variations in galaxies across cosmic time’ (Donatella Romano and Zhi-Yu Zhang).The majority of galaxies with current star formation rates (SFRs), SFRo≥10−3M⊙yr−1⁠, in the Local Cosmological Volume, where observations should be reliable, have the property that their observed SFRo is larger than their average SFR. This is in tension with the evolution of galaxies described by delayed-τ models, according to which the opposite would be expected. The tension is apparent in that local galaxies imply the star formation time-scale τ ≈ 6.7 Gyr, much longer than the 3.5–4.5 Gyr obtained using an empirically determined main sequence at several redshifts. Using models where the SFR is a power law in time of the form ∝(t − t1)η for t1 = 1.8 Gyr (with no stars forming prior to t1) implies that η = 0.18 ± 0.03. This suggested near-constancy of a galaxy’s SFR over time raises non-trivial problems for the evolution and formation time of galaxies, but is broadly consistent with the observed decreasing main sequence with increasing age of the Universe.Publisher PDFPeer reviewe

Top-heavy integrated galactic stellar initial mass functions (IGIMFs) 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.Comment: Accepted for publication in MNRAS, reference adde

On the degree of stochastic asymmetry in the tidal tails of star clusters

Context: Tidal tails of star clusters are commonly understood to be populated symmetrically. Recently, the analysis of Gaia data revealed large asymmetries between the leading and trailing tidal tail arms of the four open star clusters Hyades, Praesepe, Coma Berenices and NGC 752. Aims: As the evaporation of stars from star clusters into the tidal tails is a stochastic process, the degree of stochastic asymmetry is quantified in this work. Methods: For each star cluster 1000 configurations of test particles are integrated in the combined potential of a Plummer sphere and the Galactic tidal field over the life time of the particular star cluster. For each of the four star clusters the distribution function of the stochastic asymmetry is determined and compared with the observed asymmetry. Results: The probabilities for a stochastic origin of the observed asymmetry of the four star clusters are: Praesepe ~1.7 sigma, Coma Berenices ~2.4 sigma, Hyades ~6.7 sigma, NGC 752 ~1.6 sigma. Conclusions: In the case of Praesepe, Coma Berenices and NGC 752 the observed asymmetry can be interpreted as a stochastic evaporation event. However, for the formation of the asymmetric tidal tails of the Hyades additional dynamical processes beyond a pure statistical evaporation effect are required.Comment: accepted for publication by A&

Properties of hierarchically forming star clusters

We undertake a systematic analysis of the early (< 0.5 Myr) evolution of clustering and the stellar initial mass function in turbulent fragmentation simulations. These large scale simulations for the first time offer the opportunity for a statistical analysis of IMF variations and correlations between stellar properties and cluster richness. The typical evolutionary scenario involves star formation in small-n clusters which then progressively merge; the first stars to form are seeds of massive stars and achieve a headstart in mass acquisition. These massive seeds end up in the cores of clusters and a large fraction of new stars of lower mass is formed in the outer parts of the clusters. The resulting clusters are therefore mass segregated at an age of 0.5 Myr, although the signature of mass segregation is weakened during mergers. We find that the resulting IMF has a smaller exponent (alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters are truncated at masses only somewhat larger than the most massive stars (which depends on the richness of the cluster) and an universal upper mass limit of 150 Msun is ruled out. We also find that the simulations show signs of the IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars is suppressed in the integrated IMF compared to the IMF in individual clusters. We identify clusters through the use of a minimum spanning tree algorithm which allows easy comparison between observational survey data and the predictions of turbulent fragmentation models. In particular we present quantitative predictions regarding properties such as cluster morphology, degree of mass segregation, upper slope of the IMF and the relation between cluster richness and maximum stellar mass. [abridged]Comment: 21 Pages, 25 Figure

Massive runaway stars in the Small Magellanic Cloud

Using archival Spitzer Space Telescope data, we identified for the first time a dozen runaway OB stars in the Small Magellanic Cloud (SMC) through the detection of their bow shocks. The geometry of detected bow shocks allows us to infer the direction of motion of the associated stars and to determine their possible parent clusters and associations. One of the identified runaway stars, AzV 471, was already known as a high-velocity star on the basis of its high peculiar radial velocity, which is offset by ~40 km/s from the local systemic velocity. We discuss implications of our findings for the problem of the origin of field OB stars. Several of the bow shock-producing stars are found in the confines of associations, suggesting that these may be "alien" stars contributing to the age spread observed for some young stellar systems. We also report the discovery of a kidney-shaped nebula attached to the early WN-type star SMC-WR3 (AzV 60a). We interpreted this nebula as an interstellar structure created owing to the interaction between the stellar wind and the ambient interstellar medium.Comment: Accepted by A&

Massive runaway stars in the Large Magellanic Cloud

The origin of massive field stars in the Large Magellanic Cloud (LMC) has long been an enigma. The recent measurements of large offsets (~100 km/s) between the heliocentric radial velocities of some very massive (O2-type) field stars and the systemic LMC velocity provides a possible explanation of this enigma and suggests that the field stars are runaway stars ejected from their birth places at the very beginning of their parent cluster's dynamical evolution. A straightforward way to prove this explanation is to measure the proper motions of the field stars and to show that they are moving away from one of the nearby star clusters or OB associations. This approach however is complicated by the large distance to the LMC, which makes accurate proper motion measurements difficult. We use an alternative approach for solving the problem, based on the search for bow shocks produced by runaway stars. The geometry of detected bow shocks would allow us to infer the direction of stellar motion and thereby to determine their possible parent clusters. In this paper we present the results of a search for bow shocks around six massive field stars which were suggested in the literature as candidate runaway stars. Using archival (Spitzer Space Telescope) data, we found a bow shock associated with one of our program stars, the O2 V((f*)) star BI 237, which is the first-ever detection of bow shocks in the LMC. Orientation of the bow shock suggests that BI 237 was ejected from the OB association LH 82 (located at ~120 pc in projection from the star). A by-product of our search is the detection of bow shocks generated by four OB stars in the field of the LMC and an arc-like structure attached to the candidate luminous blue variable R81 (HD 269128). The geometry of two of these bow shocks is consistent with the possibility that their associated stars were ejected from the 30 Doradus star forming complex.Comment: 5 pages, 7 figures, accepted for publication in A&

Maximum stellar mass versus cluster membership number revisited

We have made a new compilation of observations of maximum stellar mass versus cluster membership number from the literature, which we analyse for consistency with the predictions of a simple random drawing hypothesis for stellar mass selection in clusters. Previously, Weidner and Kroupa have suggested that the maximum stellar mass is lower, in low mass clusters, than would be expected on the basis of random drawing, and have pointed out that this could have important implications for steepening the integrated initial mass function of the Galaxy (the IGIMF) at high masses. Our compilation demonstrates how the observed distribution in the plane of maximum stellar mass versus membership number is affected by the method of target selection; in particular, rather low n clusters with large maximum stellar masses are abundant in observational datasets that specifically seek clusters in the environs of high mass stars. Although we do not consider our compilation to be either complete or unbiased, we discuss the method by which such data should be statistically analysed. Our very provisional conclusion is that the data is not indicating any striking deviation from the expectations of random drawing.Comment: 7 pages, 3 Figures; accepted by MNRAS; Reference added