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.     

Hierarchical star formation: stars and stellar clusters in the Gould Belt

We perform a study of the spatial and kinematical distribution of young open clusters in the solar neighbourhood, discerning between bound clusters and transient stellar condensations within our sample. Then, we discriminate between Gould Belt (GB) and local Galactic disc (LGD) members, using our previous estimate of the structural parameters of both systems obtained from a sample of O-B6 Hipparcos stars. Single membership probabilities of the clusters are also calculated in the separation process. Using this classified sample, we analyse the spatial structure and the kinematic behaviour of the cluster system in the GB. The two star formation regions that dominate and give the GB its characteristic-inclined shape show a striking difference in their content of star clusters: while Ori OB1 is richly populated by open clusters, not a single one can be found within the boundaries of Sco OB2. This is mirrored in the velocity space, translating again into an abundance of clusters in the region of the kinematic space populated by the members of Ori OB1, and a marginal number of them associated with Sco OB2. We interpret all these differences by characterizing the Orion region as a cluster complex typically surrounded by a stellar halo, and the Sco-Cen region as an OB association in the outskirts of the complex. In the light of these results, we study the nature of the GB with respect to the optical segment of the Orion Arm, and we propose that the different content of star clusters, the different heights over the Galactic plane and the different residual velocities of Ori OB1 and Sco OB2 can be explained in terms of their relative position to the density maximum of the Local Arm in the solar neighbourhood. Although morphologically intriguing, the GB appears to be the result of our local and biased view of a larger star cluster complex in the Local Arm, that could be explained by the internal dynamics of the Galactic disc.     

Mass segregation in young stellar clusters

We investigate the evolutionary effect of dynamical mass segregation in young stellar clusters. Dynamical mass segregation acts on a time-scale of order the relaxation time of a cluster. Although some degree of mass segregation occurs earlier, the position of massive stars in rich young clusters generally reflects the cluster's initial conditions. In particular, the positions of the massive stars in the Trapezium cluster in Orion cannot be due to dynamical mass segregation, but indicate that they formed in, or near, the centre of the cluster. Implications of this for cluster formation and for the formation of high-mass stars are discussed.     

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 which results means that R _tidal< R _BH in these systems. In contrast, when the stars dominate the potential and are virialized, R _BH< R _tidal and Bondi–Hoyle accretion is a better fit to the accretion rates.     

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 formation of higher order hierarchical systems in star clusters

We simulate open clusters containing up to 182 stars initially in the form of singles, binaries and triples. Due to the high interaction rate a large number of stable quadruples, quintuples, sextuples and higher order hierarchies form during the course of the simulations. For our choice of initial conditions, the formation rate of quadruple systems after about 2 Myr is roughly constant with time at ∼0.008 per cluster per Myr. The formation rates of quintuple and sextuple systems are about half and one-quarter, respectively, of the quadruple formation rate, and both rates are also approximately constant with time. We present reaction channels and relative probabilities for the formation of persistent systems containing up to six stars. The reaction networks for the formation and destruction of quintuple and sextuple systems can become quite complicated, although the branching ratios remain largely unchanged during the course of the cluster evolution. The total number of quadruples is about a factor of 3 smaller than observed in the solar neighbourhood.     

Brown dwarf populations in open clusters

We present the results of multiple simulations of open clusters, modelling the dynamics of a population of brown dwarf members. We consider the effects of a large range of primordial binary populations, including the possibilities of having brown dwarf members contained within a binary system. We also examine the effects of various cluster diameters and masses. Our examination of a population of wide binary systems containing brown dwarfs, reveals evidence for exchange reactions whereby the brown dwarf is ejected from the system and replaced by a heavier main-sequence star. We find that there exists the possibility of hiding a large fraction of the brown dwarfs contained within the primordial binary population. We conclude that it is probable that the majority of brown dwarfs are contained within primordial binary systems which then hides a large proportion of them from detection.     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

On the formation of massive stars

We present a model for the formation of massive ( M ≳10 M⊙) stars through accretion-induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate-mass stars that have formed through accretion on to low-mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.     

Triggered planet formation in young stellar clusters

Conventional planet formation models via coagulation of planetesimals require timescales in the range of several 10 or even 100 Myr in the outer regions of a protoplanetary disk. But according to observational data, the lifetime of a protoplanetary disk is limited to about 6 Myr. Therefore the existence of Uranus and Neptune poses a problem. Planet formation via gravitational instability may be a solution for this discrepancy. We present a parameter study of the possibility of gravitationally triggered disk instability. Using a restricted N‐body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1 M_⊙ can probably induce gravitational instabilities in the pre‐planetary solar disk for prograde passages with minimum separations below 80‐170 AU. Inclined and retrograde encounters lead to similar results but require slightly closer passages. Such encounter distances are quite likely in young moderately massive star clusters. The induced gravitational instabilities may lead to enhanced planetesimal formation in the outer regions of the protoplanetary disk, and could therefore be relevant for the formation of Uranus and Neptune. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Binary formation with different metallicities: dependence on initial conditions

The fragmentation process in collapsing clouds with various metallicities is studied using three-dimensional nested-grid hydrodynamics. Initial clouds are specified by three parameters: cloud metallicity, initial rotation energy and initial cloud shape. For different combinations of these parameters, we calculate 480 models in total and study cloud evolution, fragmentation conditions, orbital separation and binary frequency. For the cloud to fragment during collapse, the initial angular momentum must be higher than a threshold value, which decreases with decreasing metallicity. Although the exact fragmentation conditions depend also on the initial cloud shape, this dependence is only modest. Our results indicate a higher binary frequency in lower metallicity gas. In particular, with the same median rotation parameter as in the solar neighbourhood, a majority of stars are born as members of binary/multiple systems for  <10⁻⁴ Z_⊙  . With initial mass  <0.1 M_⊙  , if fragments are ejected in embryo from the host clouds by multibody interaction, they evolve to substellar-mass objects. This provides a formation channel for low-mass stars in zero- or low-metallicity environments.