The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

On the infant weight loss of low- to intermediate-mass star clusters

Star clusters are born in a highly compact configuration, typically with radii of less than about 1 pc roughly independently of mass. Since the star formation efficiency is less than 50 per cent by observation and because the residual gas is removed from the embedded cluster, the cluster must expand. In the process of doing so it only retains a fraction f _st of its stars. To date there are no observational constraints for f _st, although N -body calculations by Kroupa, Aarseth & Hurley suggest it to be about 20–30 per cent for Orion-type clusters. Here we use the data compiled by Testi et al., Testi, Palla & Natta and Testi, Palla & Natta for clusters around young Ae/Be stars and by de Wit et al. and de Wit et al. around young O stars and the study of de Zeeuw et al. of OB associations and combine these measurements with the expected number of stars in clusters with primary Ae/Be and O stars, respectively, using the empirical correlation between maximal stellar mass and star cluster mass of Weidner & Kroupa. We find that   f _st < 50  per cent with a decrease to higher cluster masses/more massive primaries. The interpretation would be that cluster formation is very disruptive. It appears that clusters with a birth stellar mass in the range  10–10³ M_⊙  keep at most 50 per cent of their stars.     

A stochastic Monte Carlo approach to model real star cluster evolution – II. Self-consistent models and primordial binaries

The new approach outlined in Paper I to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few per cent of the initial number of stars in the cluster mass). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300 000 equal point-mass stars, plus 30 000 equal-mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. The cluster evolution is about three times slower than found by Gao et al. Other features are rather comparable. At every moment we are able to show the individual distribution of binaries in the cluster.     

Numerical simulations of protostellar encounters — III. Non-coplanar disc–disc encounters

It is expected that an average protostar will undergo at least one impulsive interaction with a neighbouring protostar whilst a large fraction of its mass is still in a massive, extended disc. If protostars are formed individually within a cluster before falling together and interacting, there should be no preferred orientation for such interactions. As star formation within clusters is believed to be coeval, it is probable that, during interactions, both protostars possess massive, extended discs.   We have used an SPH code to carry out a series of simulations of non-coplanar disc–disc interactions. We find that non-coplanar interactions trigger gravitational instabilities in the discs, which may then fragment to form new companions to the existing stars. (This is different from coplanar interactions, in which most of the new companion stars form after material in the discs has been swept up into a shock layer, and this then fragments.) The original stars may also capture each other, leading to the formation of a small- N cluster. If every star undergoes a randomly oriented disc–disc interaction, then the outcome will be the birth of many new stars and substellar objects. Approximately two-thirds of the stars will end up in multiple systems.     

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.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Determination of a temporally and spatially resolved supernova rate from OB stars within 5 kpc

We spatially and temporally resolve the future Supernova (SN) rate in the Solar vicinity and the whole Galaxy by comparing observational parameters of massive stars with theoretical models for estimating age and mass and, hence, the remaining lifetime until the SN explosion. Our SN rate derived in time and space for the future (few Myr) should be the same as in the last few Myr by assuming a constant rate. From BVRIJHK photometry, parallax, spectral type, and luminosity class we compile a Hertzsprung‐Russell diagram (HRD) for 25027 massive stars and derive extinction, and luminosity, then mass, age, and remaining lifetime from evolutionary models. Within 600 pc our sample of SN progenitors and, hence, SN prediction, is complete, and all future SN events of our sample stars take place in 8 % of the area of the sky, whereas 90 % of the events take place in 7 % of the area of the sky. The current SN rate within 600 pc is increased by a factor of 5–6 compared with the Galactic rate. For a distance of 5 kpc our sample is incomplete, nevertheless 90 % of those SN events take place in only 12 % of the area of the projected sky. If the SN rate in the near future is the same as the recent past, there should be unknown young neutron stars concentrated in those areas. Our distribution can be used as input for constraints of gravitational waves detection and for neutron star searches. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The growth and assembly of a massive galaxy at z∼ 2

We study the stellar mass assembly of the Spiderweb galaxy  (MRC 1138−262)  , a massive   z = 2.2  radio galaxy in a protocluster and the probable progenitor of a brightest cluster galaxy. Nearby protocluster galaxies are identified and their properties are determined by fitting stellar population models to their rest-frame ultraviolet to optical spectral energy distributions. We find that within 150 kpc of the radio galaxy the stellar mass is centrally concentrated in the radio galaxy, yet most of the dust-uncorrected, instantaneous star formation occurs in the surrounding low-mass satellite galaxies. We predict that most of the galaxies within 150 kpc of the radio galaxy will merge with the central radio galaxy by   z = 0  , increasing its stellar mass by up to a factor of ≃2. However, it will take several hundred Myr for the first mergers to occur, by which time the large star formation rates are likely to have exhausted the gas reservoirs in the satellite galaxies. The tidal radii of the satellite galaxies are small, suggesting that stars and gas are being stripped and deposited at distances of tens of kpc from the central radio galaxy. These stripped stars may become intracluster stars or form an extended stellar halo around the radio galaxy, such as those observed around cD galaxies in cluster cores.     

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.     

Evidence for cometary bombardment episodes

Evidence is found that large terrestrial impacts tend to cluster in discrete episodes, with characteristic separations 25–30 Myr and durations of about 1–2 Myr. The largest impactors are strongly concentrated within such events, and the Cretaceous–Tertiary extinctions occurred within one of them. The evidence also indicates the presence of a weak periodicity, which might be ∼24, ∼35 or ∼42 Myr depending on which peaks are taken as harmonics. The periodicity is most easily explained as a result of the action of the Galactic tide on the Oort comet cloud. The two longer period solutions are consistent with Galactic density estimates and with the current passage of the Solar system through the plane of the Galaxy. Other episodes may be a result of sporadic encounters with spiral arms, nebulae or stars.     

Predictions of the extent of self-enrichment in oxygen of giant metal-poor H ii regions

In general, H  ii regions do not show clear signs of self-enrichment in products from massive stars  ( M ≥ 8 M_⊙)  . In order to explore why I modelled the contamination with Wolf–Rayet star ejecta of metal-poor  ( Z = 0.001)  H  ii regions, ionized either by a  10⁶ M_⊙  cluster of coeval stars (cluster 1) or by a cluster resulting from continuous star formation at a rate of  1 M_⊙ yr⁻¹  (cluster 2). The clusters have   Z = 0.001  and a Salpeter initial mass function from 0.1 to  120 M_⊙  . Independent one-dimensional constant density simulations of the emission-line spectra of unenriched H  ii regions were computed at the discrete ages 1, 2, 3, 4 and 5 Myr, with the photoionization code cloudy , using as input, radiative and mechanical stellar feedbacks predicted by the evolutionary synthesis code starburst99 . Each H  ii region was placed at the outer radius of the adiabatically expanding superbubble of Mac Low & McCray. For models with thermal and ionization balance time-scales of less than 1 Myr, and with oxygen emission-line ratios in agreement with observations, the volume of the superbubble and the H  ii region was uniformly and instantaneously polluted with stellar ejecta predicted by starburst99 . I obtained a maximum oxygen abundance enhancement of 0.025 dex, with cluster 1, at 4 Myr. It would be unobservable.     

Brown dwarfs and very low‐mass stars: variability in the Pleiades

We present the results of the optical photometric observations of the Pleiades (125 Myr) cluster. The aim of this research is to look for variability, both due to rotation of single stars and the presence of eclipsing binaries. We have used differential photometry and two different methods of statistical analysis of the data.We have found variability in the Pleiades cluster with amplitudes of about 50 mmag and uncertainties of 5 mmag until I=17.9, well within the brown dwarf regime. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of gas loss on the formation of bound stellar clusters

The effect of gas ejection on the structure and binding energy of newly formed stellar clusters is investigated. The star formation efficiency (SFE), necessary for forming a gravitationally bound stellar cluster, is determined.
Two sets of numerical N -body simulations are presented. As a first simplified approach we treat the residual gas as an external potential. The gas expulsion is approximated by reducing the gas mass to zero on a given time-scale, which is treated as a free parameter. In a second set of simulations we use smoothed particle hydrodynamics (SPH) to follow the dynamics of the outflowing residual gas self-consistently. We investigate cases where gas outflow is induced by an outwards propagating shock front and where the whole gas cloud is heated homogeneously, leading to ejection.
If the stars are in virial equilibrium with the gaseous environment initially, bound clusters only form in regions where the local SFE is larger than 50 per cent or where the gas expulsion time-scale is long compared with the dynamical time-scale. A small initial velocity dispersion of the stars leads to a compaction of the cluster during the expulsion phase and reduces the SFE needed to form bound clusters to less than 10 per cent.     

Captured older stars as the reason for apparently prolonged star formation in young star clusters

The existence of older stars within a young star cluster can be interpreted to imply that star formation occurs on time-scales longer than a free-fall time of a pre-cluster cloud core. Here, the idea is explored that these older stars are not related to the star formation process forming the young star cluster but rather that the orbits of older field stars are focused by the collapsing pre-cluster cloud core. Two effects appear: the focusing of stellar orbits leads to an enhancement of the density of field stars in the vicinity of the centre of the young star cluster; and due to the time-dependent potential of the forming cluster some of these stars can get bound gravitationally to the cluster. These stars exhibit similar kinematical properties to the newly formed stars and cannot be distinguished from them on the basis of radial velocity or proper motion surveys. Such contaminations may lead to a wrong apparent star formation history of a young cluster. In the case of the ONC, the theoretical number of gravitationally bound older low-mass field stars agrees with the number of observed older low-mass stars.     

The lithium depletion boundary in NGC 2547 as a test of pre-main-sequence evolutionary models

Intermediate resolution spectroscopy from the European Southern Observatory Very Large Telescope is analysed for 63 photometrically selected low-mass  (0.08–0.30 M_⊙)  candidates of the open cluster NGC 2547. We have confirmed membership for most of these stars using radial velocities, and found that lithium remains undepleted for cluster stars with   I > 17.54 ± 0.14  and   K_s > 14.86 ± 0.12  . From these results, several pre–main-sequence evolutionary models give almost model independent ages of 34–36 Myr, with a precision of 10 per cent. These ages are only slightly larger than the ages of 25–35(±5) Myr obtained using the same models to fit isochrones to higher mass stars descending towards the zero-age main-sequence, both in empirically calibrated and theoretical colour–magnitude diagrams. This agreement between age determinations in different mass ranges is an excellent test of the current generation of low-mass pre–main-sequence stellar models and lends confidence to ages determined with either method between 30 and 120 Myr.     

The role of tidal interactions in star formation

Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in discs are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar discs may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming discs may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper initial mass function (IMF) . Many of the processes discussed here have analogues on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.     

The stellar content of a spiral arm of NGC 4321

The effects of the passage of a spiral arm through the disc of the giant Virgo Sc galaxy NGC 4321 are investigated with Hubble Space Telescope WFPC2 images in two colours. Concentrating on a portion of the southern spiral arm of NGC 4321, we have applied a new program to solve for the star formation histories in the arm and interarm regions separately. The observational uncertainties and the variable crowding across the spiral arm are taken into account using the results of artificial star tests. In the interarm regions the data are consistent with a constant star formation rate for the last 50 Myr while the stars in the arm region show a star formation rate four times larger than in the interarm regions in the last 5 Myr.     

The history of the Solar system's debris disc: observable properties of the Kuiper belt

The Nice model of Gomes et al. suggests that the migration of the giant planets caused a planetesimal clearing event, which led to the late heavy bombardment (LHB) at 880 Myr. Here, we investigate the infrared emission from the Kuiper belt during the history of the Solar system as described by the Nice model. We describe a method for easily converting the results of N -body planetesimal simulations into observational properties (assuming blackbody grains and a single size distribution) and further modify this method to improve its realism (using realistic grain properties and a three-phase size distribution). We compare our results with observed debris discs and evaluate the plausibility of detecting an LHB-like process in extrasolar systems. Recent surveys have shown that 4 per cent of stars exhibit 24 μm excess and 16 per cent exhibit 70 μm excess. We show that the Solar system would have been amongst the brightest of these systems before the LHB at both 24 and 70 μm. We find a significant increase in 24 μm emission during the LHB, which rapidly drops off and becomes undetectable within 30 Myr, whereas the 70 μm emission remains detectable until 360 Myr after the LHB. Comparison with the statistics of debris disc evolution shows that such depletion events must be rare occurring around less than 12 per cent of Sun-like stars and with this level of incidence we would expect approximately one of the 413 Sun-like field stars so far detected to have a 24 μm excess to be currently going through an LHB. We also find that collisional processes are important in the Solar system before the LHB and that parameters for weak Kuiper belt objects are inconsistent with the Nice model interpretation of the LHB.     

Predictions for triple stars with and without a pulsar in star clusters

Though about 80 pulsar binaries have been detected in globular clusters so far, no pulsar has been found in a triple system in which all three objects are of comparable mass. Here, we present predictions for the abundance of such triple systems, and for the most likely characteristics of these systems. Our predictions are based on an extensive set of more than 500 direct simulations of star clusters with primordial binaries, and a number of additional runs containing primordial triples. Our simulations employ a number N _tot of equal-mass stars from   N _tot= 512  to  19 661  and a primordial binary fraction from 0 to 50 per cent. In addition, we validate our results against simulations with   N = 19 661  that include a mass spectrum with a turn-off mass at  0.8 M_⊙  , appropriate to describe the old stellar populations of Galactic globular clusters. Based on our simulations, we expect that typical triple abundances in the core of a dense cluster are two orders of magnitude lower than the binary abundances, which in itself already suggests that we do not have to wait too long for the first comparable-mass triple with a pulsar to be detected.