Initial Mass Segregation Research Articles

Hypervelocity stars from young stellar clusters in the Galactic Centre

The enormous velocities of the so called hypervelocity stars (HVSs) derive, likely, from close interactions with massive black holes, binary stars encounters or supernova explosions. In this paper, we investigate the origin of hypervelocity stars as consequence of the close interaction between the Milky Way central massive black hole and a passing-by young stellar cluster. We found that both single and binary HVSs may be generated in a burst-like event, as the cluster passes near the orbital pericentre. High velocity stars will move close to the initial cluster orbital plane and in the direction of the cluster orbital motion at the pericentre. The binary fraction of these HVS jets depends on the primordial binary fraction in the young cluster. The level of initial mass segregation determines the value of the average mass of the ejected stars. Some binary stars will merge, continuing their travel across and out of the Galaxy as blue stragglers.

Dynamical ejections of massive stars from young star clusters under diverse initial conditions

We study the effects of initial conditions of star clusters and their massive star population on dynamical ejections of massive stars from star clusters up to an age of 3 Myr. We use a large set of direct N-body calculations for moderately massive star clusters (Mecl=$10^{3.5}$ Msun). We vary the initial conditions of the calculations such as the initial half-mass radius of the clusters, initial binary populations for massive stars and initial mass segregation. We find that the initial density is the most influential parameter for the ejection fraction of the massive systems. The clusters with an initial half-mass radius of 0.1 (0.3) pc can eject up to 50% (30%) of their O-star systems on average. Most of the models show that the average ejection fraction decreases with decreasing stellar mass. For clusters efficient at ejecting O stars, the mass function of the ejected stars is top-heavy compared to the given initial mass function (IMF), while the mass function of stars that remain in the cluster becomes slightly steeper (top-light) than the IMF. The top-light mass functions of stars in 3 Myr old clusters in our N-body models agree well with the mean mass function of young intermediate-mass clusters in M31, as reported previously. We show that the multiplicity fraction of the ejected massive stars can be as high as 60%, that massive high-order multiple systems can be dynamically ejected, and that high-order multiples become common especially in the cluster. We also discuss binary populations of the ejected massive systems. When a large kinematic survey of massive field stars becomes available, for instance through Gaia, our results may be used to constrain the birth configuration of massive stars in star clusters. (Abridged)

Possible smoking-gun evidence for initial mass segregation in re-virialized post-gas expulsion globular clusters

We perform a series of direct $N$-body calculations to investigate the effect of residual gas expulsion from the gas-embedded progenitors of present-day globular clusters (GCs) on the stellar mass function (MF). Our models start either tidally filling or underfilling, and either with or without primordial mass segregation. We cover 100 Myr of the evolution of modeled clusters and show that the expulsion of residual gas from initially mass-segregated clusters leads to a significantly shallower slope of the stellar MF in the low- ($m\leq 0.50 M_\odot$) and intermediate-mass ($\simeq 0.50-0.85 M_\odot$) regime. Therefore, the imprint of residual gas expulsion and primordial mass segregation might be visible in the present-day MF. We find that the strength of the external tidal field, as an essential parameter, influences the degree of flattening, such that a primordially mass-segregated tidally-filling cluster with $r_h/r_t\geq 0.1$ shows a strongly depleted MF in the intermediate stellar mass range. Therefore, the shape of the present-day stellar MF in this mass range probes the birth place of clusters in the Galactic environment. We furthermore find that this flattening agrees with the observed correlation between the concentration of a cluster and its MF slope, as found by de Marchi et al.. We show that if the expansion through the residual gas expulsion in primordial mass segregated clusters is the reason for this correlation then GCs most probably formed in strongly fluctuating local tidal fields in the early proto-Milky Way potential, supporting the recent conclusion by Marks \& Kroupa.

DEPENDENCY OF DYNAMICAL EJECTIONS OF O STARS ON THE MASSES OF VERY YOUNG STAR CLUSTERS

Massive stars can be efficiently ejected from their birth star clusters through encounters with other massive stars. We study how the dynamical ejection fraction of O star systems varies with the masses of very young star clusters, , by means of direct N-body calculations. We include diverse initial conditions by varying the half-mass radius, initial mass segregation, initial binary fraction, and orbital parameters of the massive binaries. The results show robustly that the ejection fraction of O star systems exhibits a maximum at a cluster mass of for all models, even though the number of ejected systems increases with cluster mass. We show that lower mass clusters () are the dominant sources for populating the Galactic field with O stars by dynamical ejections, considering the mass function of embedded clusters. About 15% (up to ≈38%, depending on the cluster models) of O stars of which a significant fraction are binaries, and which would have formed in a ≈10 Myr epoch of star formation in a distribution of embedded clusters, will be dynamically ejected to the field. Individual clusters may eject 100% of their original O star content. A large fraction of such O stars have velocities up to only 10 km s−1. Synthesising a young star cluster mass function, it follows, given the stellar-dynamical results presented here, that the observed fractions of field and runaway O stars, and the binary fractions among them, can be well understood theoretically if all O stars form in embedded clusters.

Formation of young massive clusters from turbulent molecular clouds

Abstract Young massive clusters are as young as open clusters but more massive and compact compared with typical open clusters. The formation process of young massive clusters is still unclear, and it is an open question whether the formation process is the same for typical open clusters or not. We perform a series of N-body simulations starting from initial conditions constructed from the results of hydrodynamical simulations of turbulent molecular clouds. In our simulations, both open clusters and young massive clusters form when we assume a density-dependent star-formation efficiency. We find that a local star-formation efficiency higher than 50% is necessary for the formation of young massive clusters, but open clusters form from less dense regions with a local star formation efficiency of < 50%. We confirm that the young massive clusters formed in our simulations have mass, size, and density profile similar to those of observed young massive clusters such as NGC 3603 and Trumpler 14. We also find that these simulated clusters evolve via hierarchical mergers of sub-clusters within a few mega years, as is suggested by recent simulations and observations. Although we do not assume initial mass segregation, we observe that the simulated massive clusters show a shallower slope of the mass function (Γ ∼ −1) in the cluster center compared to that of the entire cluster (Γ ∼ −1.3). These values are consistent with those of some young massive clusters in the Milky Way such as Westerlund 1 and Arches.

EXTENDED MAIN SEQUENCE TURNOFFS IN INTERMEDIATE-AGE STAR CLUSTERS: A CORRELATION BETWEEN TURNOFF WIDTH AND EARLY ESCAPE VELOCITY

We present color-magnitude diagram analysis of deep Hubble Space Telescope imaging of a mass-limited sample of 18 intermediate-age (1 - 2 Gyr old) star clusters in the Magellanic Clouds, including 8 clusters for which new data was obtained. We find that ${\it all}$ star clusters in our sample feature extended main sequence turnoff (eMSTO) regions that are wider than can be accounted for by a simple stellar population (including unresolved binary stars). FWHM widths of the MSTOs indicate age spreads of 200-550 Myr. We evaluate dynamical evolution of clusters with and without initial mass segregation. Our main results are: (1) the fraction of red clump (RC) stars in secondary RCs in eMSTO clusters scales with the fraction of MSTO stars having pseudo-ages $\leq 1.35$ Gyr; (2) the width of the pseudo-age distributions of eMSTO clusters is correlated with their central escape velocity $v_{\rm esc}$, both currently and at an age of 10 Myr. We find that these two results are unlikely to be reproduced by the effects of interactive binary stars or a range of stellar rotation velocities. We therefore argue that the eMSTO phenomenon is mainly caused by extended star formation within the clusters; (3) we find that $v_{\rm esc} \geq 15$ km/s out to ages of at least 100 Myr for ${\it all}$ clusters featuring eMSTOs, while $v_{\rm esc} \leq 12$ km/s at all ages for two lower-mass clusters in the same age range that do ${\it not}$ show eMSTOs. We argue that eMSTOs only occur for clusters whose early escape velocities are higher than the wind velocities of stars that provide material from which second-generation stars can form. The threshold of 12-15 km/s is consistent with wind velocities of intermediate-mass AGB stars in the literature.

NEW CLUES TO THE CAUSE OF EXTENDED MAIN-SEQUENCE TURNOFFS IN INTERMEDIATE-AGE STAR CLUSTERS IN THE MAGELLANIC CLOUDS

We use the Wide Field Camera 3 (WFC3) onboard the Hubble Space Telescope (HST) to obtain deep, high resolution images of two intermediate-age star clusters in the Large Magellanic Cloud of relatively low mass ($\approx$ $10^4$ $M_{\odot}$) and significantly different core radii, namely NGC2209 and NGC2249. For comparison purposes, we also re-analyzed archival HST images of NGC1795 and IC2146, two other relatively low mass star clusters. From the comparison of the observed color-magnitude diagrams with Monte Carlo simulations, we find that the main sequence turnoff (MSTO) regions in NGC2209 and NGC2249 are significantly wider than that derived from simulations of simple stellar populations, while those in NGC1795 and IC2146 are not. We determine the evolution of the clusters' masses and escape velocities from an age of 10 Myr to the present age. We find that the differences among these clusters can be explained by dynamical evolution arguments if the currently extended clusters (NGC2209 and IC2146) experienced stronger levels of initial mass segregation than the currently compact ones (NGC2249 and NGC1795). Under this assumption, we find that NGC2209 and NGC2249 have estimated escape velocities $V_{\rm esc}$ $\geq$ 15 km s$^{-1}$ at an age of 10 Myr, large enough to retain material ejected by slow winds of first-generation stars, while the two clusters that do not feature extended MSTOs have $V_{\rm esc}$ $\leq$ 12 km s$^{-1}$ at that age. These results suggest that the extended MSTO phenomenon can be better explained by a range of stellar ages rather than a range of stellar rotation velocities or interacting binaries.

Structure and mass function of three young open clusters

Using UBVRI CCD data taken from 104-cm Sampurnanand Telescope, ARIES, Nainital, we present the structure, initial mass function and mass segregation of three young age (∼10Myr) open star clusters: NGC 2129, NGC 1502 and King 12. Based on photometric as well as astrometric criteria, the cluster member stars as well as field stars have been identified. We construct luminosity function which is further used to estimate the mass functions by employing theoretical stellar evolutionary isochrones. The entire cluster region mass function (MF) slopes for NGC 2129, NGC 1502 and King 12 are obtained as −2.55±0.14, −2.73±0.36 and −1.94±0.12 respectively. It is found that changes in the MF slope of King 12 are significantly different compared to NGC 2129 and NGC 1502 from inner region to outer region. The MF slope for King 12 is steeper at larger radii. The dynamical relaxation times for all three clusters are found to be less than age of the clusters. This indicates that all these clusters are dynamically relaxed. We show that for NGC 1502 and King 12, passing off of low mass stars from the inner region of the clusters to the halo occurs during the course of evolution.

The evolution of the global stellar mass function of star clusters: an analytic description

The evolution of the global stellar mass function (MF) of star clusters is studied based on a large set of N-body simulations of clusters with a range of initial masses, initial concentrations, in circular or elliptical orbits in different tidal environments. Models with and without initial mass segregation are included. The depletion of low mass stars in initially Roche-volume (tidal) filling clusters starts typically on a time scale of the order of the core collapse time. In clusters that are initially underfilling their Roche-volume it takes longer because the clusters have to expand to their tidal radii before dynamical mass loss becomes important. We introduce the concept of the differential mass function (DMF), which describes the changes with respect to the initial mass function (IMF). We show that the evolution of the DMF can be described by a set of very simple analytic expressions that are valid for a wide range of initial cluster parameters and for different IMFs. The agreement between this description and the models is very good, except for initially Roche-volume underfilling clusters that are severely mass segregated.

THE INITIAL MASS FUNCTION AND THE SURFACE DENSITY PROFILE OF NGC 6231

We have performed new wide-field photometry of the young open cluster NGC 6231 to study the shape of the initial mass function (IMF) and mass segregation. We also investigated the reddening law toward NGC 6231 from optical to mid-infrared color excess ratios, and found that the total-to-selective extinction ratio is Rv = 3.2, which is very close to the normal value. But many early-type stars in the cluster center show large color excess ratios. We derived the surface density profiles of four member groups, and found that they reach the surface density of field stars at about 10', regardless of stellar mass. The IMF of NGC 6231 is derived for the mass range 0.8 -- 45 Msun. The slope of the IMF of NGC 6231 (Gamma = -1.1 +/- 0.1) is slightly shallower than the canonical value, but the difference is marginal. In addition, the mass function varies systematically, and is a strong function of radius - it is is very shallow at the center, and very steep at the outer ring suggesting the cluster is mass segregated. We confirm the mass segregation for the massive stars (m >~ 8 Msun) by a minimum spanning tree analysis. Using a Monte Carlo method, we estimate the total mass of NGC 6231 to be about 2.6 (+/- 0.6) x 10^3 Msun. We constrain the age of NGC 6231 by comparison with evolutionary isochrones. The age of the low-mass stars ranges from 1 to 7 Myr with a slight peak at 3 Myr. However the age of the high mass stars depends on the adopted models and is 3.5 +/- 0.5 Myr from the non- or moderately-rotating models of Brott et al. as well as the non-rotating models of Ekstr\"om et al. But the age is 4.0 -- 7.0 Myr if the rotating models of Ekstr\"om et al. are adopted. This latter age is in excellent agreement with the time scale of ejection of the high mass runaway star HD 153919 from NGC 6231, albeit the younger age cannot be entirely excluded.

The influence of stellar dynamical ejections and collisions on the relation between the maximum stellar and star cluster mass

We perform the largest currently available set of direct N-body calculations of young star cluster models to study the dynamical influence, especially through the ejections of the most massive star in the cluster, on the current relation between the maximum stellar mass and the star cluster mass. We vary several initial parameters such as the initial half-mass radius of the cluster, the initial binary fraction and the degree of initial mass segregation. Two different pairing methods are used to construct massive binaries for more realistic initial conditions of massive binaries. We find that lower mass clusters (⁠⁠) do not shoot out their heaviest star. In the case of massive clusters (⁠⁠), no most massive star escapes the cluster within 3 Myr regardless of the initial conditions if clusters have initial half-mass radii, r0.5, ≥0.8 pc. However, a few of the initially smaller sized clusters (r0.5= 0.3 pc), which have a higher density, eject their most massive star within 3 Myr. If clusters form with a compact size and their massive stars are born in a binary system with a mass ratio biased towards unity, the probability that the mass of the most massive star in the cluster changes due to the ejection of the initially most massive star can be as large as 20 per cent. Stellar collisions increase the maximum stellar mass in a large number of clusters when clusters are relatively dense (⁠ and r0.5= 0.3 pc) and binary rich. Overall, we conclude that dynamical effects hardly influence the observational maximum stellar mass–cluster mass relation.

Limits on initial mass segregation in young clusters

Mass segregation is observed in many star clusters, including several that are less than a few Myr old. Time-scale arguments are frequently used to argue that these clusters must be displaying primordial segregation, because they are too young to be dynamically relaxed. Looking at this argument from the other side, the youth of these clusters and the limited time available to mix spatially distinct populations of stars can provide constraints on the amount of initial segregation that is consistent with current observations. We present n-body experiments testing this idea, and discuss the implications of our results for theories of star formation. For system ages less than a few crossing times, we show that star formation scenarios predicting general primordial mass segregation are inconsistent with observed segregation levels.

The influence of gas expulsion and initial mass segregation on the stellar mass function of globular star clusters

Recently de Marchi, Paresce & Pulone (2007) studied a sample of twenty globular clusters and found that all clusters with high concentrations have steep stellar mass-functions while clusters with low concentration have comparatively shallow mass-functions. No globular clusters were found with a flat mass-function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass-function in the low-mass part. We show that this effect can be explained by residual-gas expulsion from initially mass-segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.

The Influence of Initial Mass Segregation on the Runaway Merging of Stars

We have investigated the effect of initial mass segregation on the runaway merging of stars. The evolution of multimass, dense star clusters was followed by means of direct N-body simulations of up to 131,072 stars. All clusters started from King models with dimensionless central potentials of 3.0 ≤ W0 ≤ 9.0. Initial mass segregation was realized by varying the minimum mass of a certain fraction of stars whose either (1) distances were closest to the cluster center or (2) total energies were lowest. The second case is more favorable to promote the runaway merging of stars by creating a high-mass core of massive, low-energy stars. Initial mass segregation could decrease the central relaxation time and thus help the formation of a high-mass core. However, we found that initial mass segregation does not help the runaway stellar merger to happen if the overall mass density profile is kept constant. This is due to the fact that the collision rate of stars is not increased due to initial mass segregation. Our simulations show that initial mass segregation is not sufficient to allow runaway merging of stars to occur in clusters with central densities typical for star clusters in the Milky Way.

CCD BV survey of 42 open clusters

We present results of a photometric survey whose aim was to derive structural and astrophysical parameters for 42 open clusters. While our sample is definitively not representative of the total open cluster sample in the Galaxy, it does cover a wide range of cluster parameters and is uniform enough to allow for simple statistical considerations. BV wide-field CCD photometry was obtained for open clusters for which photometric, structural, and dynamical evolution parameters were determined. The limiting and core radii were determined by analyzing radial density profiles. The ages, reddenings, and distances were obtained from the solar metallicity isochrone fitting. The mass function was used to study the dynamical state of the systems, mass segregation effect and to estimate the total mass and number of cluster members. This study reports on the first determination of basic parameters for 11 out of 42 observed open clusters. The angular sizes for the majority of the observed clusters appear to be several times larger than the catalogue data indicate. The core and limiting cluster radii are correlated and the latter parameter is 3.2 times larger on average. The limiting radius increases with the cluster's mass, and both the limiting and core radii decrease in the course of dynamical evolution. For dynamically not advanced clusters, the mass function slope is similar to the universal IMF slope. For more evolved systems, the effect of evaporation of low-mass members is clearly visible. The initial mass segregation is present in all the observed young clusters, whereas the dynamical mass segregation appears in clusters older than about log(age)=8. Low-mass stars are deficient in the cores of clusters older than log(age)=8.5 and not younger than one relaxation time.

Mass Segregation and the Initial Mass Function of Super Star Cluster M82‐F

We investigate the initial mass function and mass segregation in super star cluster M82-F with high-resolution Keck NIRSPEC echelle spectroscopy. Cross-correlation with template supergiant spectra provides the velocity dispersion of the cluster, enabling measurement of the kinematic (virial) mass of the cluster when combined with sizes from NICMOS and Advanced Camera for Surveys (ACS) images. We find a mass of 6.6 ± 0.9 × 105 M☉ based on near-IR light and 7.0 ± 1.2 × 105 M☉ based on optical light. Using PSF-fitting photometry, we derive the cluster's light-to-mass (L/M) ratio in both near-IR and optical light and compare to population-synthesis models. The ratios are inconsistent with a normal stellar initial mass function for the adopted age of 40-60 Myr, suggesting a deficiency of low-mass stars within the volume sampled. King model light profile fits to new Hubble Space Telescope ACS images of M82-F, in combination with fits to archival near-IR images, indicate mass segregation in the cluster. As a result, the virial mass represents a lower limit on the mass of the cluster.

Formation of Massive Black Holes in Dense Star Clusters. I. Mass Segregation and Core Collapse

We study the early dynamical evolution of young, dense star clusters using Monte Carlo simulations for systems with up to N~10^7 stars. Rapid mass segregation of massive main-sequence stars and the development of the Spitzer instability can drive these systems to core collapse in a small fraction of the initial half-mass relaxation time. If the core collapse time is less than the lifetime of the massive stars, all stars in the collapsing core may then undergo a runaway collision process leading to the formation of a massive black hole. Here we study in detail the first step in this process, up to the occurrence of core collapse. We have performed about 100 simulations for clusters with a wide variety of initial conditions, varying systematically the cluster density profile, stellar IMF, and number of stars. We also considered the effects of initial mass segregation and stellar evolution mass loss. Our results show that, for clusters with a moderate initial central concentration and any realistic IMF, the ratio of core collapse time to initial half-mass relaxation time is typically ~0.1, in agreement with the value previously found by direct N-body simulations for much smaller systems. Models with even higher central concentration initially, or with initial mass segregation (from star formation) have even shorter core-collapse times. Remarkably, we find that, for all realistic initial conditions, the mass of the collapsing core is always close to ~10^-3 of the total cluster mass, very similar to the observed correlation between central black hole mass and total cluster mass in a variety of environments. We discuss the implications of our results for the formation of intermediate-mass black holes in globular clusters and super star clusters, ultraluminous X-ray sources, and seed black holes in proto-galactic nuclei.

Galactic starburst NGC 3603 from X-rays to radio

While NGC 3603 is often quoted as the most massive visible Giant H ii Region in the Galaxy, there are other similar and even more massive regions now being found towards the inner Galaxy in the near-IR. Nevertheless, NGC 3603 still retains the status of clone to the dense core-object in 30 Dor, R 136 — but 7x closer and 49x less crowded! This paper summarizes the most recent findings concerning NGC 3603's color-magnitude diagram (CMD), initial mass function (IMF), mass segregation and stellar content — including its unusually luminous H-rich WNL members — down to its pre-main-sequence stars near the H-burning limit. Of special relevance are new high-resolution X-ray and radio images as related to merging/colliding winds and three massive proplyd-like objects. NGC 3603 is a somewhat younger, hotter, scaled-down version of typical starbursts found in other galaxies.

Competitive accretion in embedded stellar clusters

We investigate the physics of gas accretion in young stellar clusters. Accretion in clusters is a dynamic phenomenon as both the stars and the gas respond to the same gravitational potential. Accretion rates are highly non-uniform with stars nearer the centre of the cluster, where gas densities are higher, accreting more than others. This competitive accretion naturally results in both initial mass segregation and a spectrum of stellar masses. Accretion in gas-dominated clusters is well modelled using a tidal-lobe radius instead of the commonly used Bondi-Hoyle accretion radius. This works as both the stellar and gas velocities are under the influence of the same gravitational potential and are thus comparable. The low relative velocity that results means that the tidal radius is smaller than the Bondi-Hoyle radius in these systems. In contrast, when the stars dominate the potential and are virialised, the Bondi-Hoyle radius is smaller than the tidal radius and thus Bondi-Hoyle accretion is a better fit to the accretion rates.

N‐Body Simulations of Compact Young Clusters near the Galactic Center

We investigate the dynamical evolution of compact young star clusters (CYCs) near the Galactic center using Aarseth's Nbody6 codes. The relatively small number of stars in the cluster (5000-20,000) makes real-number N-body simulations for these clusters feasible on current workstations. Using Fokker-Planck (F-P) models, Kim, Morris, & Lee made a survey of cluster lifetimes for various initial conditions and have found that clusters with a mass 2 × 104 M☉ evaporate in ~10 Myr. These results were, however, to be confirmed by N-body simulations because some extreme cluster conditions, such as strong tidal forces and a large stellar mass range participating in the dynamical evolution, might violate assumptions made in F-P models. Here we find that, in most cases, the CYC lifetimes of previous F-P calculations are 5%-30% shorter than those from the present N-body simulations. The comparison of projected number density profiles and stellar mass functions between N-body simulations and Hubble Space Telescope/NICMOS observations by Figer and colleagues in 1999 suggests that the current tidal radius of the Arches cluster is ~1.0 pc and that the parameters for the initial conditions of that cluster are as follows: total mass of 2 × 104 M☉ and mass function slope for intermediate to massive stars of 1.75 (the Salpeter function has 2.35). We also find that the lower stellar mass limit, the presence of primordial binaries, the amount of initial mass segregation, and the choice of initial density profile (King or Plummer models) do not significantly affect the dynamical evolution of CYCs.