Seven young star clusters in the inner region of the Small Magellanic Cloud

We present CCD photometry in the Washington system C and T ₁ passbands down to   T ₁∼ 22  in the fields of L35, L45, L49, L50, L62, L63 and L85, seven poorly studied star clusters in the inner region of the Small Magellanic Cloud (SMC). We measured T ₁ magnitudes and   C − T ₁  colours for a total of 114 826 stars distributed throughout cluster areas of 13.7 × 13.7 arcmin² each. Cluster radii were estimated from star counts distributed throughout the entire observed fields. The seven clusters are generally characterized by a relatively small angular size and by a high field star contamination. We performed an in-depth analysis of the field star contamination of the colour–magnitude diagrams (CMDs), and statistically cleaned the cluster CMDs. Based on the best fits of isochrones computed by the Padova group to the  ( T ₁,  C − T ₁)  CMDs, we derive ages for the sample, assuming Z = 0.004, finding ages between 25 Myr and 1.2 Gyr. We then examined different relationships between positions in the SMC, age and metallicity of a larger sample of clusters including our previous work whose ages and metallicities are on the same scale used in this paper. We confirm previous results in the sense that the further a cluster is from the centre of the galaxy, the older and more metal poor it is, with some dispersion; although clusters associated with the Magellanic Bridge clearly do not obey the general trend. The number of clusters within ∼ 2° of the SMC centre appears to have increased substantially after ∼2.5 Gyr ago, hinting at a burst.     

Constraining the LMC cluster age gap: Washington photometry of NGC 2155 and SL 896 (LW 480)

We carried out Washington system photometry of the intermediate-age Large Magellanic Cloud (LMC) star clusters NGC 2155 and SL 896 (LW 480). We derive ages and metallicities from the T ₁ versus     colour–magnitude diagrams (CMDs). For the first time an age has been obtained for SL 896,     . For NGC 2155 we derive     . The two clusters basically define the lower age limit of the LMC age gap. In particular, NGC 2155 is confirmed as the oldest intermediate-age LMC cluster so far studied. The derived metallicities are     and     for NGC 2155 and SL 896, respectively. We also studied the CMDs of the surrounding fields, which have a dominant turn-off comparable to that of the clusters themselves, and similar metallicity, showing that one is dealing with an intermediate-age disc where clusters and field stars have the same origin. We inserted the present clusters in the LMC and Small Magellanic Cloud (SMC) age–metallicity relations, using a set of homogeneous determinations with the same method as in our previous studies, now totalling 15 LMC clusters and four SMC clusters, together with some additional values from the literature. The LMC and SMC age–metallicity relations appear to be remarkably complementary, since the SMC was actively star-forming during the LMC quiescent age gap epoch.     

BVI CCD photometry of the distant open star clusters Berkeley 81, Berkeley 99, NGC 6603 and NGC 7044

We present CCD observations for the distant northern open star clusters Berkeley 81, Berkeley 99, NGC 6603 and NGC 7044 in B V I photometric passbands. A total of 9 900 stars have been observed in fields of about 6 × 6 arcmin² of the sky around the clusters. Colour–magnitude diagrams in V , ( B  −  V ) and V , ( V  −  I ) have been generated down to V  = 22 mag and, for the first time, such diagrams have been produced for the clusters Berkeley 81 and Berkeley 99. The data serve as a base for the study of mass functions and for comparison with theoretical models. Analysis of the radial distribution of stellar surface density indicates that the radius values for Berkeley 81, Berkeley 99, NGC 6603 and NGC 7044 are 2.7, 2.8, 2.8 and 2.2 arcmin respectively. By fitting the latest convective core overshooting isochrones to the colour–magnitude diagram and using its morphological features, reddenings, distances and ages of the star clusters have been determined. Broad but well-defined main sequences with stellar evolutionary effects in the brighter stars are clearly visible in colour–magnitude diagrams of all the clusters under study. Some blue stragglers along with well-developed giant branches and red giant clumps are also clearly seen in all of them. The clusters studied here are located at a distance of ∼ 3 kpc, except for Berkeley 99 which is located at a distance of 4.9 kpc. Their linear sizes lie between 3.8 and 8.0 pc; E ( B  −  V ) values range from 0.3 to 1.0 mag, while their ages are between 0.5 and 3.2 Gyr. Thus the star clusters studied here are of intermediate and high age but are compact and distant objects.     

On the origin of double main-sequence turn-offs in star clusters of the Magellanic Clouds

Recent observational studies of intermediate-age star clusters (SCs) in the Large Magellanic Cloud (LMC) have reported that a significant number of these objects show double main-sequence turn-offs (DMSTOs) in their colour-magnitude diagrams (CMDs). One plausible explanation for the origin of these DMSTOs is that the SCs are composed of two different stellar populations with age differences of ∼300 Myr. Based on analytical methods and numerical simulations, we explore a new scenario in which SCs interact and merge with star-forming giant molecular clouds (GMCs) to form new composite SCs with two distinct component populations. In this new scenario, the possible age differences between the two different stellar populations responsible for the DMSTOs are due largely to secondary star formation within GMCs interacting and merging with already-existing SCs in the LMC disc. The total gas masses being converted into new stars (i.e. the second generation of stars) during GMC-SC interaction and merging can be comparable to or larger than the masses of the original SCs (i.e. the first generation of stars) in this scenario. Our simulations show that the spatial distributions of new stars in composite SCs formed from GMC-SC merging are more compact than those of stars initially in the SCs. We discuss both advantages and disadvantages of the new scenario in explaining fundamental properties of SCs with DMSTOs in the LMC and in the Small Magellanic Cloud (SMC). We also discuss the merits of various alternative scenarios for the origin of the DMSTOs.     

Be phenomenon in open clusters: results from a survey of emission-line stars in young open clusters

Emission-line stars in young open clusters are identified to study their properties, as a function of age, spectral type and evolutionary state. 207 open star clusters were observed using the slitless spectroscopy method and 157 emission stars were identified in 42 clusters. We have found 54 new emission-line stars in 24 open clusters, out of which 19 clusters are found to house emission stars for the first time. About 20 per cent clusters harbour emission stars. The fraction of clusters housing emission stars is maximum in both the 0–10 and 20–30 Myr age bin (∼40 per cent each). Most of the emission stars in our survey belong to Classical Be class (∼92 per cent) while a few are Herbig Be stars (∼6 per cent) and Herbig Ae stars (∼2 per cent). The youngest clusters to have Classical Be stars are IC 1590, NGC 637 and 1624 (all 4 Myr old) while NGC 6756 (125–150 Myr) is the oldest cluster to have Classical Be stars. The Classical Be stars are located all along the main sequence (MS) in the optical colour–magnitude diagrams (CMDs) of clusters of all ages, which indicates that the Be phenomenon is unlikely due to core contraction near the turn-off. The distribution of Classical Be stars as a function of spectral type shows peaks at B1–B2 and B6–B7 spectral types. The Be star fraction [N(Be)/N(B+Be)] is found to be less than 10 per cent for most of the clusters and NGC 2345 is found to have the largest fraction (∼26 per cent). Our results indicate there could be two mechanisms responsible for the Classical Be phenomenon. Some are born Classical Be stars (fast rotators), as indicated by their presence in clusters younger than 10 Myr. Some stars evolve to Classical Be stars, within the MS lifetime, as indicated by the enhancement in the fraction of clusters with Classical Be stars in the 20–30 Myr age bin.     

Clues about the star formation history of the M31 disc from WFPC2 photometry

Over the past several years, the Hubble Space Telescope ( HST ) has acquired many broad-band images of various regions in the M31 disc. I have obtained 27 such fields from the HST data archive in order to produce colour–magnitude diagrams (CMDs) of the stellar populations contained within these areas of the disc. I have attempted to reproduce these CMDs using theoretical stellar evolution models in conjunction with statistical tools for determining the star formation history that best fits the observations. The wide range of extinction values within any given field makes the data difficult to reproduce accurately; nevertheless, I have managed to find star formation histories that roughly reproduce the data. These statistically determined star formation histories reveal that, like the disc of the Galaxy, the disc of M31 contains very few old metal-poor stars. The histories also suggest that the star formation rate of the disc as a whole has been low over the past ∼1 Gyr.     

Numerical methods of star formation history measurement and applications to seven dwarf spheroidals

A comprehensive study of the measurement of star formation histories from colour–magnitude diagrams (CMDs) is presented, with an emphasis on a variety of subtle issues involved in the generation of model CMDs and maximum likelihood solution. Among these are the need for a complete sampling of the synthetic CMD, the use of proper statistics for dealing with Poisson-distributed data (and a demonstration of why χ ² must not be used), measuring full uncertainties in all reported parameters, quantifying the goodness-of-fit, and questions of binning the CMD and incorporating outside information. Several example star formation history measurements are given. Two examples involve synthetic data, in which the input and recovered parameters can be compared to locate possible flaws in the methodology (none were apparent) and measure the accuracy with which ages, metallicities and star formation rates can be recovered. Solutions of the histories of seven Galactic dwarf spheroidal companions (Carina, Draco, Leo I, Leo II, Sagittarius, Sculptor and Ursa Minor) illustrate the ability to measure star formation histories given a variety of conditions – numbers of stars, complexity of star formation history and amount of foreground contamination. Significant measurements of ancient >8 Gyr star formation are made in all seven galaxies. Sculptor, Draco and Ursa Minor appear entirely ancient, while the other systems show varying amounts of younger stars.     

The period–luminosity relation for type II Cepheids in globular clusters

We report the result of our near-infrared observations ( JHK _s) for type II Cepheids (including possible RV Tau stars) in galactic globular clusters. We detected variations of 46 variables in 26 clusters (10 new discoveries in seven clusters) and present their light curves. Their periods range from 1.2 d to over 80 d. They show a well-defined period–luminosity relation at each wavelength. Two type II Cepheids in NGC 6441 also obey the relation if we assume the horizontal branch stars in NGC 6441 are as bright as those in metal-poor globular clusters in spite of the high metallicity of the cluster. This result supports the high luminosity which has been suggested for the RR Lyr variables in this cluster. The period–luminosity relation can be reproduced using the pulsation equation     assuming that all the stars have the same mass. Cluster RR Lyr variables were found to lie on an extrapolation of the period–luminosity relation. These results provide important constraints on the parameters of the variable stars.
Using Two Micron All-Sky Survey (2MASS) data, we show that the type II Cepheids in the Large Magellanic Cloud (LMC) fit our period–luminosity relation within the expected scatter at the shorter periods. However, at long periods (   P > 40  d, i.e. in the RV Tau star range) the LMC field variables are brighter by about one magnitude than those of similar periods in galactic globular clusters. The long-period cluster stars also differ from both these LMC stars and galactic field RV Tau stars in a colour–colour diagram. The reasons for these differences are discussed.     

Chromospheric activity in the late A- and early F-type stars of open clusters – II. Pleiades and Alpha Persei

We report observations of the He  i λ 5876 (D3) line in the late A- and early F-type stars in the Pleiades and Alpha Persei star clusters used to determine chromospheric activity levels. This represents the first sample of young stars in this temperature range with chromospheric activity measurements. We find the same average activity level in the young early F stars as in Hyades-age stars and field stars. In addition, the young star sample shows the same large star-to-star variation in activity as seen in the older stars. Thus, as a whole, chromospheric activity in this photospheric temperature range remains the same over nearly a factor of 100 in stellar age (50 Myr to 3 Gyr), in striking contrast to the behaviour of later-type stars. In the five late A stars we find three certain detections of D3 and one likely detection. This includes the bluest star yet observed with a chromospheric D3 line, Pleiades star HII 1362 at ( B − V )₀=0.22, making it one of the earliest stars with an observed chromosphere. The late A stars have D3 equivalent widths comparable to the weakest early F stars. However, when comparing D3 measurements in the young late A stars with older late A stars, we find evidence for a slight decrease in activity with age based on the large number of non-detections in the older stars. We find an apparently linear relationship between the activity upper limit and B − V over our entire range of B − V . Extrapolated blueward, this relationship predicts that the chromospheric D3 line would disappear for all stars at B − V ≈0.13.     

New spectroscopic classifications of 35 chemically peculiar candidate stars

The chemically peculiar (CP) stars of the upper main sequence are perfect tracers for several astrophysical processes. Their study especially in open clusters further helps to establish their evolutionary status. The latter is most important to understand the origin and evolution of the CP phenomenon, i.e. the connection between diffusion and a stellar magnetic field. There are two important topics, we cover with this paper. First of all, we investigate the reliability of the CCD Δa photometry for fainter objects in open clusters. The latter method is able to detect CP stars very efficiently, but still a spectroscopic verification is needed to verify the photometric candidates. On the other hand, already published spectral classifications on the basis of photographic plates and prism technology have tobe tested with modern instruments. Classification resolution spectroscopy is presented for thirty five bona‐fide CP candidates. Twenty six of them are located within the boundaries of fourteen open clusters, for which we also investigated their membership probabilities. Apart from five objects, they seem tobe members of the respective clusters. The objects were classified in the framework of a refined Morgan‐Keenan system with the extension of well established CP star spectra. We confirm the CP nature of all but one target. The results of Δa photometry and the spectral classifications are in excellent agreement. For the cluster members we find a continuous sequence of CP stars from 10 to 850 Myr, the whole range of investigated cluster ages (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Disentangling the Galaxy at low Galactic latitudes

We have used the field stars from the open cluster survey BOCCE (Bologna Open Clusters Chemical Evolution), to study three low-latitude fields imaged with the Canada–France–Hawaii telescope (CFHT), with the aim of better understanding the Galactic structure in those directions. Because of the deep and accurate photometry in these fields, they provide a powerful discriminant among Galactic structure models. In the present paper we discuss if a canonical star count model, expressed in terms of thin and thick disc radial scales, thick disc normalization and reddening distribution, can explain the observed colour–magnitude diagrams (CMDs). Disc and thick disc are described with double exponentials, the spheroid is represented with a De Vaucouleurs density law. In order to assess the fitting quality of a particular set of parameters, the colour distribution and luminosity function of synthetic photometry is compared to that of target stars selected from the blue sequence of the observed CMDs. Through a Kolmogorov–Smirnov test, we find that the classical decomposition halo-thin/thick disc is sufficient to reproduce the observations – no additional population is strictly necessary. In terms of solutions common to all three fields, we have found a thick disc scalelength that is equal to (or slightly longer than) the thin disc scale.     

Identifying star clusters in a field: A comparison of different algorithms

Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four algorithms that have been developed to identify clusters as stellar density enhancements in a field, namely stellar density maps from star counts, the nearest neighbour method and the Voronoi tessellation, and the separation of minimum spanning trees. These methods are tested and compared to each other by applying them to artificial clusters of different sizes and morphologies. While distinct centrally concentrated clusters are detected by all methods, clusters with low overdensity or highly hierarchical structure are only reliably detected by methods with inherent smoothing (star counts and nearest neighbour method). Furthermore, the algorithms differ strongly in computation time and additional parameters they provide. Therefore, the method to choose primarily depends on the size and character of the investigated area and the purpose of the study (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The spatial evolution of stellar structures in the Large Magellanic Cloud

We present an analysis of the spatial distribution of various stellar populations within the Large Magellanic Cloud (LMC). We combine mid-infrared selected young stellar objects, optically selected samples with mean ages between ∼9 and ∼1000 Myr and existing stellar cluster catalogues to investigate how stellar structures form and evolve within the LMC. For the analysis we use Fractured Minimum Spanning Trees, the statistical Q parameter and the two-point correlation function. Restricting our analysis to young massive (OB) stars, we confirm our results obtained for M33, namely that the luminosity function of the groups is well described by a power law with index −2, and that there is no characteristic length-scale of star-forming regions. We find that stars in the LMC are born with a large amount of substructure, consistent with a two-dimensional fractal distribution with dimension     and evolve towards a uniform distribution on a time-scale of ∼175 Myr. This is comparable to the crossing time of the galaxy, and we suggest that stellar structure, regardless of spatial scale, will be eliminated in a crossing time. This may explain the smooth distribution of stars in massive/dense young clusters in the Galaxy, while other, less massive, clusters still display large amounts of structure at similar ages. By comparing the stellar and star cluster distributions and evolving time-scales, we show that infant mortality of clusters (or 'popping clusters') has a negligible influence on the galactic structure. Finally, we quantify the influence of the elongation, differential extinction and contamination of a population on the measured Q value.     

The stellar composition of the star formation region CMa R1 – I. Results from new photometric and spectroscopic classifications

A new photometric and spectroscopic survey of the star formation region (SFR) CMa R1 is described. In a sample of 165 stars brighter than 13th mag, 88 stars were found to be probable members of the SFR. They are defined as early-type stars with E ( B − V )0.16 mag, which corresponds to a distance of about 1 kpc. 74 of the probable members are B stars. 19 stars are possibly associated with an IRAS point source. We derive a most probable distance of 1050±150 pc to the association. It appears that about 80 candidate members are pre-main-sequence stars with ages lower than 6 million years, while the main sequence extends over 6.0–7.6 mag, which is consistent with star formation starting about 8 million years ago and continuing until at least half a million years ago. Two bright B stars in the association (GU CMa and FZ CMa) seem to be much older and probably do not originate from the same star formation episode. The star formation efficiency appears to increase roughly monotonically with time up to half a million years ago. From our data, we conclude that only a minor fraction of the stars has been created through the scenario suggested by Herbst & Assousa, in which the members of CMa R1 form by compression of ambient material by a supernova shock wave. An extensive search for candidate members with H α emission did not reveal new Herbig Ae/Be candidates, so that the number of stars in this class seems to be limited to four: Z CMa, LkH α 218, LkH α 220 and possibly HD 53367.     

Monte Carlo simulations of star clusters – III. A million-body star cluster

A revision of Stodółkiewicz's Monte Carlo code is used to simulate the evolution of million-body star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The evolution of N -body systems influenced by the tidal field of a parent galaxy and by stellar evolution is presented. All models consist of 1 000 000 stars. The process of energy generation is realized by means of appropriately modified versions of Spitzer's and Mikkola's formulae for the interaction cross-section between binaries and field stars and binaries themselves. The results presented are in good agreement with theoretical expectations and the results of other methods. During the evolution, the initial mass function (IMF) changes significantly. The local mass function around the half-mass radius closely resembles the actual global mass function. At the late stages of evolution, the mass of the evolved stars inside the core can be as high as 97 per cent of the total mass in this region. For the whole system, the evolved stars can compose up to 75 per cent of the total mass. The evolution of cluster anisotropy strongly depends on initial cluster concentration, IMF and the strength of the tidal field. The results presented are the first step in the direction of simulating the evolution of real globular clusters by means of the Monte Carlo method.     

Hot stars in old stellar populations: a continuing need for intermediate ages

We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r ^−1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k ⁻⁴  and   P ∝ k ^−3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10⁻¹⁴ g cm⁻³)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.     

Multiwaveband studies of the hard ROSAT SMC transient 1WGA J0053.8−7226: a new X-ray pulsar

We report on two optical candidates for the counterpart to an X-ray source in the Small Magellanic Cloud , 1WGA J0053.8−7226, identified as a serendipitous X-ray source from the ROSAT Position Sensitive Proportional Counter (PSPC) archive, and also observed by the Einstein Imaging Proportional Counter . Its X-ray properties, namely the hard X-ray spectrum, flux variability and column density, indicate a hard, transient source, with a luminosity of ∼     XTE and ASCA observations have confirmed the source to be an X-ray pulsar, with a 46-s spin period. Our optical observations reveal two possible candidates within the error circle. Both exhibit strong H α and weaker H β emission. The optical colours indicate that both objects are Be-type stars. The Be nature of the stars implies that the counterpart is most likely a Be/X-ray binary system. Subsequent infrared (IR) photometry ( JHK ) of one of the objects shows that the source varies by at least 0.5 mag, while the     measured nearly simultaneously with the UBVRI and spectroscopic observations indicate an IR excess of ∼0.3 mag.     

The dynamical evolution of stellar superclusters

Recent images taken with the Hubble Space Telescope ( HST ) of the interacting disc galaxies NGC 4038/4039 (the Antennae) reveal clusters of many dozens and possibly hundreds of young compact massive star clusters within projected regions spanning about 100 to 500 pc. It is shown here that a large fraction of the individual star clusters merge within a few tens to a hundred Myr. Bound stellar systems with radii of a few hundred parsecs, masses ≲ 10⁹ M⊙ and relaxation times of 10¹¹ − 10¹² yr may form from these. These spheroidal dwarf galaxies contain old stars from the pre-merger galaxy and much younger stars formed in the massive star clusters, and possibly from later gas accretion events. The possibility that star formation in the outer regions of gas-rich tidal tails may also lead to superclusters is raised. The mass-to-light ratio of these objects is small, because they contain an insignificant amount of dark matter. After many hundred Myr such systems may resemble dwarf spheroidal satellite galaxies with large apparent mass-to-light ratios, if tidal shaping is important.     

A search for luminous Be stars

As Be stars are restricted to luminosity classes III‐V, but early B‐type stars are believed to evolve into supergiants, it is to be expected that the Be phenomenon disappears at some point in the evolution of a moderately massive star, before it reaches the supergiant phase. As a first stage in an attempt to determine the physical reasons of this cessation, a search of the literature has provided a number of candidates to be Be stars with luminosity classes Ib or II. Spectroscopy has been obtained for candidates in a number of open clusters and associations, as well as several other bright stars in those clusters. Among the objects observed, HD 207329 is the best candidate to be a high‐luminosity Be star, as it appears like a fast‐rotating supergiant with double‐peaked emission lines. The lines of HD 229059, in Berkeley 87, also appear morphologically similar to those of Be stars, but there are reasons to suspect that this object is an interacting binary. At slightly lower luminosities, LS I +56°92 (B4 II) and HD 333452 (O9 II), also appear as intrinsically luminous Be stars. Two Be stars in NGC 6913, HD 229221 and HD 229239, appear to have rather higher intrinsic magnitudes than their spectral type (B0.2 III in both cases) would indicate, being as luminous as luminosity class II objects in the same cluster. HD 344863, in NGC 6823, is also a rather early Be star of moderately high luminosity. The search shows that, though high‐luminosity Be stars do exist, they are scarce and, perhaps surprisingly, tend to have early spectral types. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hyperfast pulsars as the remnants of massive stars ejected from young star clusters

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of  ∼1100 km s⁻¹  , which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis, we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole (IMBH) and (iii) a single stars and a hard binary IMBH. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of  10⁶– 10⁷ stars pc⁻³  . Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.