Showing papers on "Mass segregation published in 2006"

Star formation through gravitational collapse and competitive accretion

Abstract: Competitive accretion, a process to explain the origin of the initial mass function (IMF), occurs when stars in a common gravitational potential accrete from a distributed gaseous component. Stars located near the centre of the potential benefit from the gravitational attraction of the full potential and accrete at much higher rates than do isolated stars. We show that concerns recently raised on the efficiency of competitive accretion are incorrect as they use globally averaged properties which are inappropriate for the detailed physics of a forming stellar cluster. A full treatment requires a realistic treatment of the cluster potential, the distribution of turbulent velocities and gas densities. Accreting gas does not travel at the global virial velocity of the system due to the velocity-sizescale relation inherent in turbulent gas and due to the lower velocity dispersion of small-N clusters in which much of the accretion occurs. Accretion occurs due to the effect of the local potential in funnelling gas down to the centre. Stars located in the gas-rich centres of such systems initially accrete from low relative velocity gas attaining larger masses before needing to accrete the higher velocity gas. Stars not in the centres of such potentials, or that enter the cluster later when the velocity dispersion is higher, do not accrete significantly and thus retain their low masses. In competitive accretion, most stars do not continue to accrete significantly such that their masses are set from the fragmentation process. It is the few stars which continue to accrete that become higher-mass stars. Competitive accretion is therefore likely to be responsible for the formation of higher-mass stars and can explain the mass distribution, mass segregation and binary frequency of these stars. Global kinematics of competitive accretion models include large-scale mass infall, with mean inflow velocities of the order of ≈0.5 km s -1 at scales of 0.5 pc, but infalling signatures are likely to be confused by the large tangential velocities and the velocity dispersion present. Finally, we discuss potential limitations of competitive accretion and conclude that competitive accretion is currently the most likely model for the origin of the high-mass end of the IMF.

Equilibrium Star Cluster Formation

Abstract: We argue that rich star clusters take at least several local dynamical times to form and so are quasi-equilibrium structures during their assembly. Observations supporting this conclusion include morphologies of star-forming clumps, momentum flux of protostellar outflows from forming clusters, age spreads of stars in the Orion Nebula cluster (ONC) and other clusters, and the age of a dynamical ejection event from the ONC. We show that these long formation timescales are consistent with the expected star formation rate in turbulent gas, as recently evaluated by Krumholz & McKee. Finally, we discuss the implications of these timescales for star formation efficiencies, the disruption of gas by stellar feedback, mass segregation of stars, and the longevity of turbulence in molecular clumps.

The Effect of Mass Segregation on Gravitational Wave Sources near Massive Black Holes

Abstract: Gravitational waves (GWs) from the inspiral of compact remnants (CRs) into massive black holes (MBHs) will be observable to cosmological distances. While a CR spirals in, two-body scattering by field stars may cause it to fall into the central MBH before reaching a short-period orbit that would give an observable signal. As a result, only CRs very near (~0.01 pc) the MBH can spiral in successfully. In a multimass stellar population, the heaviest objects sink to the center, where they are more likely to slowly spiral into the MBH without being swallowed prematurely. We study how mass segregation modifies the stellar distribution and the rate of GW events. We find that the inspiral rate per galaxy is 30 Gyr-1 for white dwarfs, 6 Gyr-1 for neutron stars, and 250 Gyr-1 for 10 M? stellar black holes (SBHs). The high rate for SBHs is due to their extremely steep density profile, nBH(r) r-2. The GW detection rate will be dominated by SBHs.

Runaway collisions in young star clusters - II. Numerical results

Abstract: We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, M-BH greater than or similar to 100M(circle dot)) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (M-* similar or equal to 30-120M(circle dot)) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence ( MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, 'sticky-sphere' mergers or using realistic prescriptions derived from 3D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (similar or equal to 3 Myr), we obtain the growth of a single very massive star (VMS, M-* similar or equal to 400-4000M(circle dot)) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma(v) similar to 1000 km s(-1), does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma(v) > 300 km s(-1), collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to greater than or similar to 1000M(circle dot) in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. In the vast majority of cases, we find that the time between successive collisions becomes much shorter than the thermal time-scale of the VMS. Therefore, our assumption that all stars return quickly to the MS after a collision must eventually break down for the runaway product, and the stellar evolution of the VMS becomes very uncertain. For the same reason, the final fate of the VMS, including its possible collapse to an IMBH, remains unclear.

The radial distribution of blue straggler stars and the nature of their progenitors

Abstract: The origin of blue straggler stars (BSS) in globular clusters (GCs) is still not fully understood: they can form from stellar collisions, or through mass transfer in isolated, primordial binaries (PBs). In this paper we use the radial distribution of BSS observed in four GCs (M3, 47 Tuc, NGC 6752 and ω Cen) to investigate which formation process prevails. We find that both channels co-exist in all the considered GCs. The fraction of mass-transfer (collisional) BSS with respect to the total number of BSS is around ∼0.4‐0.5 (∼0.5‐0.6) in M3, 47 Tuc and NGC 6752. The case of ω Cen is peculiar with an underproduction of collisional BSS. The relative lack of collisional BSS in ω Cen can be understood if mass segregation has not yet driven to the core a sizeable number of PBs, which dominate stellar collisions through threeand four-body processes. The spatial distribution of BSS provides strong hints to their origin: the BSS in the cluster outskirts form almost exclusively from mass transfer in PBs, whereas the BSS found close to the cluster core most likely have a collisional origin.

The Secrets of the Nearest Starburst Cluster. II. The Present-Day Mass Function in NGC 3603

Abstract: Based on deep Very Large Telescope Infrared Spectrometer and Array Camera JHK photometry, we have derived the present-day mass function (MF) of the central starburst cluster NGC 3603 YC (Young Cluster) in the giant H II region NGC 3603. The effects of field contamination, individual reddening, and a possible binary contribution are investigated. The MF slopes resulting from the different methods are compared and lead to a surprisingly consistent cluster MF with a slope of ? = -0.9 ? 0.15. Analyzing different radial annuli around the cluster core, no significant change in the slope of the MF is observed. However, mass segregation in the cluster is evidenced by the increasing depletion of the high-mass tail of the stellar mass distribution with increasing radius. We discuss the indications of mass segregation with respect to the changes observed in the binned and cumulative stellar MFs and argue that the cumulative function, as well as the fraction of high- to low-mass stars, provides better indicators for mass segregation than the MF slope alone. Finally, the observed MF and starburst morphology of NGC 3603 YC are discussed in the context of massive local star-forming regions such as the Galactic center Arches cluster, R136/30 Dor in the LMC, and the Orion Trapezium cluster, all providing resolved templates for extragalactic star formation. Despite the similarity in the observed MF slopes, dynamical considerations suggest that the starburst clusters do not form gravitationally bound systems over a Hubble time. Both the environment (gravitational potential of the Milky Way) and the concentration of stars in the cluster core determine the dynamical stability of a dense star cluster, such that the long-term evolution of a starburst is not exclusively determined by the stellar evolution of its members, as frequently assumed for globular cluster systems.

Mass functions and structure of the young open cluster NGC 6611

Abstract: We use J, H and K S 2MASS photometry to study colour-magnitude (CMDs) and colour-colour diagrams, structure and mass distribution in the ionizing open cluster NGC 661 1. Reddening variation throughout the cluster region is taken into account followed by field-star decontamination of the CMDs. Decontamination is also applied to derive the density profile and luminosity functions in the core, halo and overall (whole cluster) regions. The field-star deconlamination showed that the lower limit of the main sequence (MS) occurs at 5 M ○. . Based on the fraction of K S excess stars in the colour-colour diagram we estimate an age of 1.3 ± 0.3 Myr which is consislent with the presence of a large number of premain sequence (PMS) stars. The distance from the Sun was estimated from known O V stars in the cluster area and the turn-on stars connecting the PMS and MS, resulting in d ○. = 1.8 ± 0.5 kpc. The radial density distribution including MS and PMS stars is fitted by a King profile with a core radius R core = 0.70 ± 0.08 pc. The cluster density profile merges into the background at a limiting radius R lim = 6.5 ± 0.5 pc. From the field-star subtracted luminosity functions we derive the mass functions (MFs) in the form Φ(m) m -(1+x) . In the halo and through the whole cluster the MFs have slopes X = 1.52 ± 0.13 and X = 1.45 ± 0.12, respectively, thus slightly sleeper than Salpeter's IMF. In the core the MF is flat, X = 0.62 ± 0.16, indicating some degree of mass segregation since the cluster age is a factor ∼2 larger than the relaxation time. Because of the very young age of NGC 6611, part of this effect appears to be related to the molecular cloud-fragmentation process itself. We detect 362 ± 120 PMS stars. The total observed mass including detected MS (in the range 5-85 M ○. ) and PMS stars amounts to ∼1600 M ○. , thus more massive than the Trapezium cluster. Compared to older open clusters of different masses, the overall NGC 6611 fits in the relations involving structural and dynamical parameters. However, the cure is atypical in the sense that it looks like an old/dynamically evolved core. Again, part of this effect must he linked to formation processes.

Detection rate estimates of gravity waves emitted during parabolic encounters of stellar black holes in globular clusters

Abstract: The rapid advance of gravitational wave (GW) detector facilities makes it very important to estimate the event rates of possible detection candidates. We consider an additional possibility of GW bursts produced during parabolic encounters (PEs) of stellar-mass compact objects in globular clusters (GCs). We estimate the rate of successful detections for specific detectors: the initial Laser Interferometric Gravitational-Wave Observatory (InLIGO), the French-Italian gravitational wave antenna VIRGO, the near-future Advanced-LIGO (AdLIGO), the space-based Laser Interferometric Space Antenna (LISA), and the Next Generation LISA (NGLISA). Simple GC models are constructed to account for the compact object mass function, mass segregation, number density distribution, and velocity distribution. We both calculate encounters classically and account for general relativistic corrections by extrapolating the results for infinite mass ratios. We also include the cosmological redshift of waveforms and event rates. We find that typical PEs with masses m1 = m2 = 40 M? are detectable with matched filtering over a signal-to-noise ratio S/N = 5 within a distance dL ~ 200 Mpc for InLIGO and VIRGO, z = 1 for AdLIGO, 0.4 Mpc for LISA, and 1 Gpc for NGLISA. We estimate single data stream detection rates of 5.5 ? 10-5 yr-1 for InLIGO, 7.2 ? 10-5 yr-1 for VIRGO, 0.063 yr-1 for AdLIGO, 2.9 ? 10-6 yr-1 for LISA, and 1.0 yr-1 for NGLISA, for reasonably conservative assumptions. These estimates are subject to uncertainties in the GC parameters, most importantly the total number and mass distribution of BHs in the cluster core. In reasonably optimistic cases, we get 1 detection for AdLIGO per year. We expect that a coincident analysis using multiple detectors and accounting for GW recoil capture significantly increases the detection rates. The regular detection of GWs during PEs would provide a unique observational probe for constraining the stellar BH mass function of dense clusters.

The radial distribution of blue straggler stars and the nature of their progenitors

Abstract: The origin of blue straggler stars (BSS) in globular clusters (GCs) is still not fully understood: they can form from stellar collisions, or through mass transfer in isolated, primordial binaries (PBs). In this paper we use the radial distribution of BSS observed in four GCs (M3, 47Tuc, NGC6752 and omega Cen) to investigate which formation process prevails. We find that both channels co-exist in all the considered GCs. The fraction of mass-transfer (collisional) BSS with respect to the total number of BSS is around ~0.4-0.5 (~0.5-0.6) in M3, 47Tuc, and NGC6752. The case of omega Cen is peculiar with an underproduction of collisional BSS. The relative lack of collisional BSS in omega Cen can be understood if mass segregation has not yet driven to the core a sizeable number of PBs, which dominate stellar collisions through three- and four-body processes. The spatial distribution of BSS provides strong hints to their origin: the BSS in the cluster outskirts form almost exclusively from mass transfer in PBs, whereas the BSS found close to the cluster core most likely have a collisional origin.

Runaway collisions in young star clusters – I. Methods and tests

Abstract: We present the methods and preparatory work for our study of the collisional runaway scenario to form a very massive star (VMS, M∗ > 400 M� ) at the centre of a young, compact stellar cluster. In the first phase of the process, a very dense central core of massive stars (M∗ � 30‐120 M � ) forms through mass segregation and gravothermal collapse. This leads to a collisional stage, likely to result in the formation of a VMS (itself a possible progenitor for an intermediate-mass black hole) through a runaway sequence of mergers between the massive stars. In this paper, we present the runaway scenario in a general astrophysical context. We then explain the numerical method used to investigate it. Our approach is based on a Monte Carlo code to simulate the stellar dynamics of spherical star clusters, using a very large number of particles (a few 10 5 to several 10 6 ). Finally, we report on test computations carried out to ensure that our implementation of the important physics is sound. In a second paper, we present results from more than 100 cluster simulations realized to determine the conditions leading to the collisional formation of a VMS and the characteristics of the runaway sequences.

On the mass of dense star clusters in starburst galaxies from spectrophotometry

Abstract: The mass of unresolved young star clusters derived from spectrophotometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar initial mass function (IMF), the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter η. When we compute η for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cut-off mass of 25.5 M� . We also monitor the rise of colour gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the Large Magellanic Cloud cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate derived for the cluster population is then underestimated by from 20 to 50 per cent.

On the Mass of Dense Star Clusters in Starburst Galaxies from Spectro-Photometry

Abstract: The mass of unresolved young star clusters derived from spectro-photometric data may well be off by a factor of 2 or more once the migration of massive stars driven by mass segregation is accounted for. We quantify this effect for a large set of cluster parameters, including variations in the stellar IMF, the intrinsic cluster mass, and mean mass density. Gas-dynamical models coupled with the Cambridge stellar evolution tracks allow us to derive a scheme to recover the real cluster mass given measured half-light radius, one-dimensional velocity dispersion and age. We monitor the evolution with time of the ratio of real to apparent mass through the parameter eta. When we compute eta for rich star clusters, we find non-monotonic evolution in time when the IMF stretches beyond a critical cutoff mass of 25.5 solar mass. We also monitor the rise of color gradients between the inner and outer volume of clusters: we find trends in time of the stellar IMF power indices overlapping well with those derived for the LMC cluster NGC 1818 at an age of 30 Myr. We argue that the core region of massive Antennae clusters should have suffered from much segregation despite their low ages. We apply these results to a cluster mass function, and find that the peak of the mass distribution would appear to observers shifted to lower masses by as much as 0.2 dex. The star formation rate (SFR) derived for the cluster population is then underestimated by from 20 to 50 per cent.

Dynamics of compact object clusters: a post‐Newtonian study

Abstract: Compact object clusters are likely to exist in the centres of some galaxies because of mass segregation. The high densities and velocities reached in them need a better understanding. The formation of binaries and their subsequent merging by gravitational radiation emission are important to the evolution of such clusters. We address the evolution of such a system in a relativistic regime. The recurrent mergers at high velocities create an object with a mass much larger than the average. For this purpose we modified the direct NBODY6++ code to include post-Newtonian effects on the force during two-body encounters. We adjusted the equations of motion to include for the first time the effects of both periastron shift and energy loss by emission of gravitational waves, and so to study the eventual decay and merger of radiating binaries. The method employed allows us to give here an accurate post-Newtonian description of the formation of a runaway compact object by successive mergers with surrounding particles, as well as the distribution of characteristic eccentricities in the events. This study should be envisaged as a first step towards a detailed, accurate study of possible gravitational wave sources, thanks to the combination of the direct NBODY numerical tool with the implementation of post-Newtonian terms.

Dynamics of compact objects clusters: A post-Newtonian study

Abstract: Compact object clusters are likely to exist in the centre of some galaxies because of mass segregation. The high densities and velocities reached in them deserves a better understanding. The formation of binaries and their subsequent merging by gravitational radiation emission is important to the evolution of such clusters. We address the evolution of such a system in a relativistic regime. The recurrent mergers at high velocities create an object with a mass much larger than the average. For this aim we modified the direct {\sc Nbody6}++ code to include post-Newtonian effects to the force during two-body encounters. We adjusted the equations of motion to include for the first time the effects of both periastron shift and energy loss by emission of gravitational waves and so to study the eventual decay and merger of radiating binaries. The method employed allows us to give here an accurate post-Newtonian description of the formation of a run-away compact object by successive mergers with surrounding particles, as well as the distribution of characteristic eccentricities in the events. This study should be envisaged as a first step towards a detailed, accurate study of possible gravitational waves sources thanks to the combination of the direct {\sc Nbody} numerical tool with the implementation of post-Newtonian terms on it.

Detection of Ks-excess stars in the 14 Myr open cluster NGC 4755

Abstract: Aims. We derive the structure, distribution of MS and PMS stars and dynamical state of the young open cluster NGC4755. We explore the possibility that, at the cluster age, some MS and PMS stars still present infrared excesses related to dust envelopes and proto-planetary discs. Methods. J, H and K, 2MASS photometry is used to build CMD and colour-colour diagrams, radial density profiles, luminosity and mass functions. Field-star decontamination is applied to uncover the cluster's intrinsic CMD morphology and detect candidate PMS stars. Proper motions from UCAC2 are used to determine cluster membership. Results. The radial density profile follows King's law with a core radius R core = 0.7 ± 0.1 pc and a limiting radius R lim = 6.9 ± 0.1 pc. The cluster age derived from Padova isochrones is 14 ± 2 Myr. Field-star decontamination reveals a low-MS limit at ≈1.4 M ⊙ . The core MF (Χ = 0.94 ± 0.16) is flatter than the halo's (Χ = 1.58 ± 0.11). NGC4755 contains ∼285 candidate PMS stars of age ∼1-15 Myr, and a few evolved stars. The mass locked up in PMS, MS and evolved stars amounts to ∼1150 M ⊙ . Proper motions show that /;,-excess MS and PMS stars are cluster members. K s -excess fractions in PMS and MS stars are 5.4 ± 2.1% and 3.9 ± 1.5% respectively, consistent with the cluster age. The core is deficient in PMS stars, as compared with MS ones. NGC 4755 hosts binaries in the halo but they are scarce in the core. Conclusions. Compared to open clusters in different dynamical states studied with similar methods, NGC 4755 fits relations involving structural and dynamical parameters in the expected locus for its age and mass. On the other hand, the flatter core MF probably originates from primordial processes related to parent molecular cloud fragmentation and mass segregation over ∼14 Myr. Star formation in NGC4755 began ≈ 14 Myr ago and proceeded for about the same length of time. Detection of K s -excess emission in member MS stars suggests that some circumstellar dust discs survived for ∼10 7 yr, occurring both in some MS and PMS stars for the age and spread observed in NGC 4755.

Population analysis of open clusters: radii and mass segregation

Abstract: Aims. Based on our well-determined sample of open clusters in the all-sky catalogue ASCC-2.5 we derive new linear sizes of some 600 clusters, and investigate the effect of mass segregation of stars in open clusters. Methods. Using statistical methods, we study the distribution of linear sizes as a function of spatial position and cluster age. We also examine statistically the distribution of stars of different masses within clusters as a function of the cluster age. Results. No significant dependence of the cluster size on location in the Galaxy is detected for younger clusters (<200 Myr), whereas older clusters inside the solar orbit turned out to be, on average. smaller than outside. Also, small old clusters are preferentially found close to the Galactic plane, whereas larger ones more frequently live farther away from the plane and at larger Galactocentric distances. For clusters with (V - M V ) < 10.5, a clear dependence of the apparent radius on age has been detected: the cluster radii decrease by a factor of about 2 from an age of 10 Myr to an age of 1 Gyr. A detailed analysis shows that this observed effect can be explained by mass segregation and does not necessarily reflect a real decrease of cluster radii. We found evidence for the latter for the majority of clusters older than 30 Myr. Among the youngest clusters (between 5 and 30 Myr), there are some clusters with a significant grade of mass segregation, whereas some others show no segregation at all. At a cluster age between 50 and 100 Myr, the distribution of stars of different masses becomes more regular over cluster area. In older clusters the evolution of the massive stars is the most prominent effect we observe.

Exploring the lower mass function in the young open cluster ic 4665

Abstract: We present a study of the young (30-100 Myr) open cluster IC 4665 with the aim to determine the shape of the mass function well into the brown dwarf regime. We photometrically select 691 low-mass stellar and 94 brown dwarf candidate members over an area of 3.82 square degrees centred on the cluster. K-band follow-up photometry and Two-Micron All-Sky Survey data allow a first filtering of contaminant objects from our catalogues. A second filtering is performed for the brightest stars using proper motion data provided by the Tycho-2 and UCAC2 public catalogues. Contamination by the field population for the lowest mass objects is estimated using same latitude control fields. We fit observed surface densities of various cluster populations with King profiles and find a consistent tidal radius of 1.0°. The presence of possible mass segregation is discussed. In most respects investigated, IC 4665 is similar to other young open clusters at this age: (1) a power law fit to the mass function between 1 and 0.04 M ⊙ results in best fit for a slope of -0.6; (2) a cusp in the mass function is noticed at about the substellar boundary with respect to the power law description, the interpretation of which is discussed; (3) a fraction between 10-19% for BDs with M ≥ 0.03 M ⊙ to total members; (4) a best-fit lognormal function to the full mass distribution shows an average member mass of 0.32 M ⊙ , if IC 4665 has an age of 50 Myr.

Methods for improving open cluster fundamental parameters applied to M 52 and NGC 3960

Abstract: Aims. We derive accurate parameters related to the CMD, structure and dynamical state of M 52 and NGC 3960, whose fields are affected by differential reddening. Previous works estimated their ages in the ranges 35-135 Myr and 0.5-1.0 Gyr, respectively. Methods. J, H and K, 2MASS photometry with errors <0.2 mag is used to build CMDs, radial density profiles, luminosity and mass functions, and correct for differential reddening. Field-star decontamination is applied to uncover the cluster's intrinsic CMD morphology, and colour-magnitude filters are used to isolate stars with high probability of being cluster members. Results. The differential-reddening corrected radial density profile of M52 follows King's law with core and limiting radii of R core = 0.91 ± 0.14 pc and R lim = 8.0 ± 1.0 pc. NGC 3960 presents an excess of the stellar density over King's profile (R core = 0.62 ± 0.11 pc and R lim = 6.0 ± 0.8 pc) at the center. The tidal radii of M52 and NGC 3960 are R tidal = 13.1 ± 2.2 pc and R tidal = 10.7 ± 3.7 pc. Cluster ages of M52 and NGC 3960 derived with Padova isochrones are constrained to 60 ± 10 Myr and 1.1 ± 0.1 Gyr. In M 52 the core MF (Χ core = 0.89 ± 0.12) is flatter than the halo's (Χ halo = 1.65 ± 0.12). In NGC 3960 they are Χ core = -0.74 ± 0.35 and Χ halo = 1.26 ± 0.26. The mass locked up in MS/evolved stars in M52 is ∼1200 M ⊙ , and the total mass (extrapolated to 0.08 M ⊙ ) is ∼3800 M ⊙ . The total mass in NGC 3960 is ∼ 1300 M ⊙ . Conclusions. Compared to open clusters in different dynamical states studied with similar methods, the core and overall parameters of M 52 are consistent with an open cluster more massive than 1000 M ⊙ and ∼60 Myr old, with some mass segregation in the inner region. The core of NGC 3960 is in an advanced dynamical state with strong mass segregation in the core/halo region, while the somewhat flat overall MF (Χ ≈ 1.07) suggests low-mass star evaporation. The excess stellar density in the core may suggest post-core collapse. The dynamical evolution of NGC 3960 may have been accelerated by the tidal Galactic field, since it lies ≈0.5 kpc inside the Solar circle.

The photometric evolution of dissolving star clusters I: First predictions

Abstract: We calculated the broad-band photometric evolution of unresolved star clusters, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: (a) the evolution of massive stars; (b) early tidal effects reduce the mass function independently of the stellar mass; (c) after mass segregation has completed, tidal effects preferentially remove the lowest-mass stars from the cluster. Results: (1) During the first ~40% of the lifetime of a cluster the cluster simply gets fainter due to the loss of stars by tidal effects. (2) Between ~40 and ~80% of its lifetime the cluster gets bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used (0.15 -- 0.5 dex). (3) After ~80% of the total lifetime of a cluster it will rapidly get redder. This is because stars at the low-mass end of the main sequence, which are preferentially lost, are bluer than the AGB stars that dominate the light at long wavelengths, resulting in an age overestimate. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour-colour diagrams as clusters without mass segregation. Therefore it will be difficult to distinguish this effect from that due to the cluster age for unresolved clusters, unless the total lifetime of the clusters can be estimated. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the SFHs. (6) The preferential loss of low-mass stars might explain the presence of old (~13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2 - 5 Gyr). [Abridged]

The photometric evolution of dissolving star clusters I. First predictions

Abstract: The broad-band photometric evolution of unresolved star clusters is calculated in a simplified way, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: (a) the evolution of the massive stars reduces their number; (b) tidal effects before cluster-wide mass segregation reduce the mass function homogeneously, i.e. independently of the stellar mass; (c) after mass segregation has finished, tidal effects preferentially remove the lowest-mass stars from the cluster. These effects result in a narrowing of the stellar mass range. These effects are described quantitatively, following the results of N-body simulations, and are taken into account in the calculation of the photometric history, based on the galev cluster evolution models for solar metallicity and a Salpeter mass function. We find the following results: (1) During the first ∼40% of the lifetime of a cluster its colour evolution is adequately described by the standard galev models (without mass segregation) but the cluster becomes fainter due to the loss of stars by tidal effects. (2) Between ∼40 and ∼80% of its lifetime (independent of the total lifetime), the cluster becomes bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used. (3) After ∼80% of the total lifetime of a cluster it will rapidly become redder. This will result in an overestimate of the age of clusters if standard cluster evolution models are used. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour–colour diagrams as clusters without mass segregation. Only if the total lifetime of clusters can be estimated can the colours be used to give reliable age estimates. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the star formation histories of galaxies if they are derived from clusters that have a total lifetime of less than about 30 Gyr. (6) The preferential loss of low-mass stars might explain the presence of old (∼13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2–5 Gyr), if the expected total lifetime of these clusters is between 16 and 32 Gyr.

Methods for improving open cluster fundamental parameters applied to M 52 and NGC 3960

Abstract: We derive accurate parameters related to the CMD, structure and dynamical state of M52 and NGC3960, whose fields are affected by differential reddening. Compared to open clusters in different dynamical states studied with similar methods, the core and overall parameters of M52 are consistent with an open cluster more massive than 1000Mo and ~60Myr old, with some mass segregation in the inner region. The core of NGC3960 is in an advanced dynamical state with strong mass segregation in the core/halo region, while the somewhat flat overall MF (x~1.07) suggests low-mass star evaporation. The excess stellar density in the core may suggest post-core collapse. The dynamical evolution of NGC3960 may have been accelerated by the tidal Galactic field, since it lies \~0.5kpc inside the Solar circle.

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

Abstract: We present N-body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using NBODY6, which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.

Capture Formed Binaries via Encounters with Massive Protostars

Abstract: Most massive stars are found in the center of dense clusters, and have a companion fraction much higher than their lower mass siblings; the massive stars of the Trapezium core in Orion have ~ 1.5 companions each. This high multiplicity could be a consequence of formation via a capture scenario, or it could be due to fragmentation of the cores that form the massive stars. During stellar formation circumstellar disks appear to be nearly ubiquitous. Their large radii compared to stellar sizes increase the interaction radius significantly, suggesting that disk interactions with neighboring stars could assist in capturing binary companions. This mechanism has been studied for stars of approximately solar mass and found to be inefficient. In this paper we present simulations of interactions between a 22 Msun star-disk system and less massive impactors, to study the disk-assisted capture formation of binaries in a regime suited to massive stars. The formation of binaries by capture is found to be much more efficient for massive capturers. We discuss the effects of a mass dependent velocity dispersion and mass segregation on the capture rates, and consider the long term survival of the resultant binaries in a dense cluster.

The young star cluster NGC 2362 : low-mass population and initial mass function from a Chandra X-ray observation

Abstract: Context. We study the stellar population of the very young cluster NGC 2362, using a deep Chandra ACIS-I X-ray observation. This cluster, only 5 Myr old, has already cleared most of its inter- and circumstellar dust, and with its small and uniform reddening offers a unique opportunity of studying its pre-main-sequence stellar population with minimal disturbance from a dense interstellar medium. Aims. Our main purposes are to select cluster members down to low masses and to study their properties as a population (spatial properties, initial mass function, and coronal properties). Methods. We compare existing deep optical photometry and H α data with new X-ray data. We use combined optical and X-ray criteria to select cluster members. Results. We detect 387 X-ray sources down to $\log L_{\rm X} = 29.0$ (erg/s), and identify most of them (308) with star-like objects. The majority (88%) of optically identified X-ray sources are found to be very good candidate low-mass pre-main-sequence stars, with minimal field-object contamination. This increases the known cluster census by a substantial amount at low masses, with respect to previous optical/IR studies. The fraction of stars with active accretion is found to be in the range 5–9%. We find a significantly wider spatial distribution for low-mass stars than for massive stars (mass segregation). We find only a small spread around the low-mass cluster sequence in the HR diagram, indicating that star formation lasted only about 1–2 Myr. We have derived the cluster initial mass function, which appears to flatten (on the low-mass side) at higher masses with respect to other very young clusters. The quiescent X-ray emission of low-mass cluster stars is found to be rather strictly correlated with the stellar bolometric luminosity: the small spread in this correlation puts an upper bound on the amplitude of X-ray variability on time scales longer than one day (e.g., activity cycles) in such young coronal sources. We find significant X-ray spectral differences between low-mass stars brighter and fainter than $\log L_{\rm X} \sim 30.3$ (erg/s), respectively, with X-ray brighter stars showing hotter components ($kT \sim 2$ keV), absent in fainter stars.

Star formation through gravitational collapse and competitive accretion

Abstract: Competitive accretion, a process to explain the origin of the IMF, occurs when stars in a common gravitational potential accrete from a distributed gaseous component. We show that concerns recently raised on the efficiency of competitive accretion are incorrect as they use globally averaged properties which are inappropriate for the detailed physics of a forming stellar cluster. A full treatment requires a realistic treatment of the cluster potential, the distribution of turbulent velocities and gas densities. Accreting gas does not travel at the global virial velocity of the system due to the velocity-sizescale relation inherent in turbulent gas and due to the lower velocity dispersion of small-N clusters in which much of the accretion occurs. Stars located in the gas-rich centres of such systems initially accrete from low relative velocity gas attaining larger masses before needing to accrete the higher velocity gas. Stars not in the centres of such potentials, or that enter the cluster later when the velocity dispersion is higher, do not accrete significantly and thus retain their low-masses. In competitive accretion, most stars do not continue to accrete significantly such that their masses are set from the fragmentation process. It is the few stars which continue to accrete that become higher-mass stars. Competitive accretion is therefore likely to be responsible for the formation of higher-mass stars and can explain the mass distribution, mass segregation and binary frequency of these stars. Global kinematics of competitive accretion models include large-scale mass infall, with mean inflow velocities of order 0.5 km/s at scales of 0.5 pc, but infall signatures are likely to be confused by the large tangential velocities and the velocity dispersion present.

Mass segregation in rich LMC clusters from modelling of deep HST colour–magnitude diagrams

Abstract: Aims. We used the deep colour–magnitude diagrams (CMDs) of five rich LMC clusters (NGC 1805, NGC 1818, NGC 1831, NGC 1868, and Hodge 14) observed with HST/WFPC2 to derive their present day mass function (PDMF) and its variation with position within the cluster. Methods. The PDMF was parameterized as a power law in the available main-sequence mass range of each cluster, typically 0.9 < m/M� < 2.5; its slope was determined at different positions spanning from the very centre out to several core radii. The CMDs in the central regions of the clusters were carefully studied earlier, resulting in accurate age, metallicity, distance modulus, and reddening values. The slope α (where Salpeter is 2.35) was determined in annuli by following two distinct methods: 1) a power law fit to the PDMF obtained from the systemic luminosity function (LF); 2) a statistical comparison between observed and model CMDs. In the second case, α is a free input parameter in the CMD modelling process where we incorporate photometric errors and the effect of binarity as a fraction of unresolved binaries (fbin = 100%) with random pairing of masses from the same PDMF. Results. In all clusters, significant mass segregation is found from the positional dependence of the PDMF slope: α < 1. 8f or R ≤ 1.0 Rcore and α ∼ Salpeter inside R = 2 ∼ 3 Rcore (except for Hodge 14, where α ∼ Salpeter for R ∼ 4 Rcore). The results are robust in the sense that they hold true for both methods used. The CMD method reveals that unresolved binaries flatten the PDMF obtained form the systemic LF, but this effect is smaller than the uncertainties in the α determination. For each cluster we estimated dynamical ages inside the core and for the entire system. In both cases we found a trend in the sense that older clusters have flatter PDMF, consistent with a dynamical mass segregation and stellar evaporation.

Willman 1 - A Galactic Satellite at 40 kpc With Multiple Stellar Tails

Abstract: SDSSJ1049+5103, commonly known as Willman 1, is an extremely low-luminosity Milky Way companion whose properties are intermediate between those of globular clusters and dwarf spheroidals. In this paper, we use deep photometry to show that this object is old and moderately metal-poor, has a distance of 38 +/- 7 kpc, has an M_V of -2.5 mag, and has a half-light radius of 21 +/- 7 pc, consistent with previous estimates. The spatial distribution of Willman 1's main sequence stars shows 1) its total spatial extent exceeds its tidal radius for a range of assumptions about its total mass and its orbit and 2) the presence of prominent multi-directional stellar tails. The tidal interactions causing these tail features may explain the large physical size of Willman 1 relative to low-luminosity globular clusters. It is the most distant Galactic object yet known to display prominent tails, and is the only distant satellite to display multi-directional tails. Although we cannot at present determine the cause of this unusual morphology, preliminary comparisons between the morphology of Willman 1 and published simulations suggest that it may be near the apocenter of its orbit, or that it may have interacted with another halo object. We find a significant difference between the luminosity functions of stars in the center and in the tails of Willman 1, strongly suggesting mass segregation much like that seen in Palomar 5. Although Willman 1 has more pronounced tidal tails than most confirmed Milky Way dwarf galaxies, because of its very low stellar mass we cannot at present rule out the possibility that it has a dark matter halo. (Abridged)

XMM-Newton X-ray and optical observations of the globular clusters M 55 and NGC 3201

Abstract: We have observed two low concentration Galactic globular clusters with the X-ray observatory XMM-Newton. We detect 47 faint X-ray sources in the direction of M 55 and 62 in the field of view of NGC 3201 . Using the statistical Log N - Log S relationship of extragalactic sources derived from XMM-Newton Lockman Hole observations, to estimate the background source population, we estimate that very few of the sources ($1.5\pm1.0$) in the field of view of M 55 actually belong to the cluster. These sources are located in the centre of the cluster as we expect if the cluster has undergone mass segregation. NGC 3201 has approximately 15 related sources, which are centrally located but are not constrained to lie within the half mass radius. The sources belonging to this cluster can lie up to 5 core radii from the centre of the cluster which could imply that this cluster has been perturbed. Using X-ray (and optical, in the case of M 55 ) colours, spectral and timing analysis (where possible) and comparing these observations to previous X-ray observations, we find evidence for sources in each cluster that could be cataclysmic variables, active binaries, millisecond pulsars and possible evidence for a quiescent low mass X-ray binary with a neutron star primary, even though we do not expect any such objects in either of the clusters, due to their low central concentrations. The majority of the other sources are background sources, such as AGN.

Membership and Segregation Effects in the Young Open Cluster NGC 6530

Abstract: From photographic plate data of Shanghai Astronomical Observatory with a time baseline of 87 years, proper motions and membership probabilities of 364 stars in the open cluster NGC 6530 region are reduced. On the basis of membership determination, luminosity function and segregation effect of the cluster are discussed with details. Spatial mass segregation is obviously present in NGC 6530 while there is no clear evidence for a velocity-mass (or velocity-luminosity) dependence. The observed spatial mass segregation for NGC 6530 might be due to a combination of initial conditions and relaxation process.