Early evolution of the birth cluster of the solar system

The solar system was most likely born in a star cluster containing at least 1000 stars. It is highly probable that this cluster environment influenced various properties of the solar system like its chemical composition, size and the orbital parameters of some of its constituting bodies. In the Milky Way, clusters with more than 2000 stars only form in two types - starburst clusters and leaky clusters - each following a unique temporal development in the mass-radius plane. The aim is here to determine the encounter probability in the range relevant to solar system formation for starburst or leaky cluster environments as a function of cluster age. N-body methods are used to investigate the cluster dynamics and the effect of gravitational interactions between cluster members on young solar-type stars surrounded by discs. Using the now available knowledge of the cluster density at a given cluster age it is demonstrated that in starburst clusters the central densities over the first 5Myr are so high (initially > 10^5 Msun pc^{-3}) that hardly any discs with solar system building potential would survive this phase. This makes a starburst clusters an unlikely environment for the formation of our solar system. Instead it is highly probable that the solar system formed in a leaky cluster (often classified as OB association). It is demonstrated that an encounter determining the characteristic properties existing in our solar systems most likely happened very early on (< 2Myr) in its formation history and that after 5Myr the likelihood of a solar-type star experiencing such an encounter in a leaky cluster is negligible even if it was still part of the bound remnant. This explains why the solar system could develop and maintain its high circularity later in its development.Comment: 11 pages, 7 figures, accepted by A&

Quasi-binarity of massive stars in young dense clusters - the case of the ONC

Observations indicate that in young stellar clusters the binary fraction for massive stars is higher than for solar mass stars. For the Orion Nebula Cluster (ONC) there is a binary frequency of ~ 50% for solar-mass stars compared to 70-100% for the massive O- and B-stars. We explore the reasons for this discrepancy and come up with two possible answers: a) a primordially higher binarity of massive stars could be inherent to the star formation process or b) the primordial binary rate might be the same for solar-mass and massive stars, but the higher capture cross section of the massive stars possibly leads to the formation of additional massive binaries in the early cluster development. Here we investigate the likelihood of the latter using the ONC as an example. N-body simulations are performed to track the capture events in an ONC-like cluster. We find that whereas low-mass stars rarely form bound systems through capture, the dynamics of the massive stars - especially in the first 0.5 Myrs - is dominated by a rapid succession of ``transient binary or multiple systems''. In observations the transient nature of these systems would not be apparent, so that they would be rated as binaries. At 1-2 Myrs, the supposed age of the ONC, the ``transient'' massive systems become increasingly stable, lasting on average several 10^6 yrs. Despite the ONC being so young, the observed binary frequency for massive stars -- unlike that of solar-mass stars -- is not identical to the primordial binary frequency but is increased by at least 10-15% through dynamical interaction processes. This value might be increased to at least 20-25% by taking disc effects into account. The primordial binary frequency could well be the same for massive and solar mass stars because the observed difference can be explained by capture processes alone.Comment: 9 pages, 7 figures. accepted by A&

Reaction of Massive Clusters to Gas Expulsion - The cluster density dependence

The expulsion of the unconverted gas at the end of the star formation process potentially leads to the expansion of the just formed stellar cluster and membership loss. The degree of expansion and mass loss depends largely on the star formation efficiency and scales with the mass and size of the stellar group as long as stellar interactions can be neglected. We investigate under which circumstances stellar interactions between cluster members become so important that the fraction of bound stars after gas expulsion is significantly altered. The Nbody6 code is used to simulate the cluster dynamics after gas expulsion for different SFEs. Concentrating on the most massive clusters observed in the Milky Way, we test to what extend the results depend on the model, i.e. stellar mass distribution, stellar density profile etc., and the cluster parameters, such as cluster density and size.We find that stellar interactions are responsible for up to 20% mass loss in the most compact massive clusters in the Milky Way, making ejections the prime mass loss process in such systems. Even in the loosely bound OB associations stellar interactions are responsible for at least ~5% mass loss. The main reason why the importance of encounters for massive clusters has been largely overlooked is the often used approach of a single-mass representation instead of a realistic distribution for the stellar masses. The density-dependence of the encounter-induced mass loss is shallower than expected because of the increasing importance of few-body interactions in dense clusters compared to sparse clusters where 2-body encounters dominate.Comment: 9 pages, 6 figures, A&A accepte

Cluster dynamics largely shapes protoplanetary disc sizes

It is still on open question to what degree the cluster environment influences the sizes of protoplanetary discs surrounding young stars. Particularly so for the short-lived clusters typical for the solar neighbourhood in which the stellar density and therefore the influence of the cluster environment changes considerably over the first 10 Myr. In previous studies often the effect of the gas on the cluster dynamics has been neglected, this is remedied here. Using the code NBody6++ we study the stellar dynamics in different developmental phases - embedded, expulsion, expansion - including the gas and quantify the effect of fly-bys on the disc size. We concentrate on massive clusters ($M_{\text{cl}} \geq 10^3 - 6 \cdot 10^4 M_{\text{Sun}}$), which are representative for clusters like the Orion Nebula Cluster (ONC) or NGC 6611. We find that not only the stellar density but also the duration of the embedded phase matters. The densest clusters react fastest to the gas expulsion and drop quickly in density, here 98% of relevant encounters happen before gas expulsion. By contrast, discs in sparser clusters are initially less affected but as they expand slower 13% of discs are truncated after gas expulsion. For ONC-like clusters we find that usually discs larger than 500 AU are affected by the environment, which corresponds to the observation that 200 AU-sized discs are common. For NGC 6611-like clusters disc sizes are cut-down on average to roughly 100 AU. A testable hypothesis would be that the discs in the centre of NGC 6611 should be on average ~20 AU and therefore considerably smaller than in the ONC.Comment: Accepted for publication in Ap

How do disks and planetary systems in high-mass open clusters differ from those around field stars?

Only star clusters that are sufficiently compact and massive survive largely unharmed beyond 10 Myr. However, their compactness means a high stellar density which can lead to strong gravitational interactions between the stars. As young stars are often initially surrounded by protoplanetary disks and later on potentially by planetary systems, the question arises to what degree these strong gravitational interactions influence planet formation and the properties of planetary systems. Here, we perform simulations of the evolution of compact high-mass clusters like Trumpler 14 and Westerlund 2 from the embedded to the gas-free phase and study the influence of stellar interactions. We concentrate on the development of the mean disk size in these environments. Our simulations show that in high-mass open clusters $80-90\%$ of all disks/planetary systems should be smaller than 50 AU just due to the strong stellar interactions in these environments. Already in the initial phases, 3-4 close fly-bys lead to typical disk sizes within the range of 18-27 AU. Afterwards, the disk sizes are altered only to a small extent. Our findings agree with the recent observation that the disk sizes in the once dense environment of the Upper Scorpio OB association, NGC~2362, and h/$\chi$Persei are at least three times smaller in size than, for example, in Taurus. We conclude that the observed planetary systems in high-mass open clusters should also be on average smaller than those found around field stars; in particular, planets on wide orbits are expected to be extremely rare in such environments.Comment: 20 pages, 9 figures, accepted for publication in Ap

Local-Density Driven Clustered Star Formation

A positive power-law trend between the local surface densities of molecular gas, $\Sigma_{gas}$, and young stellar objects, $\Sigma_{\star}$, in molecular clouds of the Solar Neighbourhood has been identified by Gutermuth et al. How it relates to the properties of embedded clusters, in particular to the recently established radius-density relation, has so far not been investigated. In this paper, we model the development of the stellar component of molecular clumps as a function of time and initial local volume density so as to provide a coherent framework able to explain both the molecular-cloud and embedded-cluster relations quoted above. To do so, we associate the observed volume density gradient of molecular clumps to a density-dependent free-fall time. The molecular clump star formation history is obtained by applying a constant SFE per free-fall time, \eff. For volume density profiles typical of observed molecular clumps (i.e. power-law slope $\simeq -1.7$), our model gives a star-gas surface-density relation $\Sigma_{\star} \propto \Sigma_{gas}^2$, in very good agreement with the Gutermuth et al relation. Taking the case of a molecular clump of mass $M_0 \simeq 10^4 Msun$ and radius $R \simeq 6 pc$ experiencing star formation during 2 Myr, we derive what SFE per free-fall time matches best the normalizations of the observed and predicted ($\Sigma_{\star}$, $\Sigma_{gas}$) relations. We find \eff \simeq 0.1. We show that the observed growth of embedded clusters, embodied by their radius-density relation, corresponds to a surface density threshold being applied to developing star-forming regions. The consequences of our model in terms of cluster survivability after residual star-forming gas expulsion are that due to the locally high SFE in the inner part of star-forming regions, global SFE as low as 10% can lead to the formation of bound gas-free star clusters.Comment: 16 pages, 15 figures, Astronomy & Astrophysics, in pres

Does the mass distribution in discs influence encounter-induced losses in young star clusters?

One mechanism for the external destruction of protoplanetary discs in young dense clusters is tidal disruption during the flyby of another cluster member. The degree of mass loss in such an encounter depends, among other parameters, on the distribution of the material within the disc. Previous work showed that this is especially so in encounters that truncate large parts of the outer disc. The expectation is that the number of completely destroyed discs in a cluster depends also on the mass distribution within the discs. Here we test this hypothesis by determining the influence of encounters on the disc fraction and average disc mass in clusters of various stellar densities for different mass distributions in the discs. This is done by performing Nbody6 simulation of a variety of cluster environments, where we track the encounter dynamics and determine the mass loss due to these encounters for different disc-mass distributions. We find that although the disc mass distribution has a significant impact on the disc losses for specific star-disc encounters, the overall disc frequency generally remains rather unaffected. The reason is that in single encounters the dependence on the mass distribution is strongest if both stars have very different masses. Such encounters are rather infrequent in sparse clusters. In dense clusters such encounters are more common, however, here the disc frequency is largely determined by encounters between low-mass stars such that the overall disc frequency does not change significantly. For tidal disruption the disc destruction in clusters is fairly independent of the actual distribution of the material in the disc. The all determining factor remains the cluster density.Comment: 7pages, 4 figures, accepted by A&

The expansion of massive young star clusters - observation meets theory

Most stars form as part of a star cluster. The most massive clusters in the Milky Way exist in two groups - loose and compact clusters - with significantly different sizes at the end of the star formation process. After their formation both types of clusters expand up to a factor 10-20 within the first 20 Myr. Gas expulsion at the end of the star formation process is usually regarded as only possible process that can lead to such an expansion.We investigate the effect of gas expulsion by a direct comparison between numerical models and observed clusters concentrating on clusters with masses >10^3 M(sun). For these clusters the initial conditions before gas expulsion, the characteristic cluster development, its dependence on cluster mass, and the star formation efficiency (SFE) are investigated. We perform N-body simulations of the cluster expansion process after gas expulsion and compare the results with observations. We find that the expansion processes of the observed loose and compact massive clusters are driven by completely different physical processes. As expected the expansion of loose massive clusters is largely driven by the gas loss due to the low SFE of ~30%. One new revelation is that all the observed massive clusters of this group seem to have a very similar size of 1-3 pc at the onset of expansion. It is demonstrated that compact clusters have a much higher effective SFE of 60-70% and are as a result much less affected by gas expulsion. Their expansion is mainly driven by stellar ejections caused by interactions between the cluster members. The reason why ejections are so efficient in driving cluster expansion is that they occur dominantly from the cluster centre and over an extended period of time. Thus during the first 10 Myr the internal dynamics of loose and compact clusters differ fundamentally.Comment: 10 pages, 9 figures, accepted by A&

From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We approximate such events as subset of the restricted three-body problem by considering only perturbations of non-interacting low-mass objects initially on circular Keplerian orbits. In this paper we present a new parametrisation of the initial conditions of this problem. Under certain conditions the initial positions of the low-mass objects can be specified largely independent of the initial position of the perturber. Exploiting additionally the known scalings of the problem reduces the parameter space of initial conditions for one specific perturbation to two dimensions. To this two-dimensional initial condition space we have related the final properties of the perturbed trajectories of the low-mass objects from our numerical simulations. That way, maps showing the effect of the perturbation on the low-mass objects have been created, which provide a new view on the perturbation process. Comparing the maps for different mass-ratios reveals that the perturbations by low- and high-mass perturbers are dominated by different physical processes. The equal-mass case is a complicated mixture of the other two cases. Since the final properties of trajectories with similar initial conditions are usually also similar, the results of the limited number of integrated trajectories can be generalised to the full presented parameter space by interpolation. Since our results are also unique within the accuracy strived for, they constitute general numerical solutions for this subset of the restricted three-body problem. As such, they can be used to predict the evolution of real physical problems by simple transformations like scaling and without further simulations. (...)Comment: 11 pages, 8 figures, + 2 pages appendix, published by A&A; This version includes the Corrigendum (DOI: 10.1051/0004-6361/201526068e) and changes from the editing proces

Which young clusters/associations are we missing today?

Currently clusters/associations of stars are mainly detected as surface density enhancements relative to the background field. While clusters form, their surface density increases. It likely decreases again at the end of the star formation process when the system expands as a consequence of gas expulsion. Therefore the surface density of a single cluster can change considerably in young clusters/associations during the first 20 Myr of their development. We investigate the effect of the gas expulsion on the detectability of clusters/associations typical for the solar neighborhood, where the star formation efficiency is <35%. The main focus will be laid on the dependence on the initial cluster mass. Nbody methods are used to determine the cluster/association dynamics after gas expulsion. We find that, even for low background densities, only clusters/associations with initial central surface densities exceeding a few 5000 M(sun)/pc2 will be detected as clusters at ages ~5 Myr. Even the Orion Nebula cluster, one of the most massive nearby clusters, would only be categorized as a small co-moving group with current methods after 5 Myr of development. This means that cluster expansion leads to a selection effect - at ages of <1-2 Myr the full range of clusters/associations is observed whereas at ages > 4 Myr only the most massive clusters are identified, while systems with initially M_c < 3 000 M(sun) are missing. The temporal development of stellar properties is usually determined by observing clusters of different ages. The potentially strong inhomogeneity of the cluster sample makes this methods highly questionable. However, GAIA could provide the means to rectify this situation as it will be able to detect lower mass clusters.Comment: 8 pages, 4 figures, accepted by A&