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

Did a stellar fly-by shape the planetary system around Pr 0211 in the cluster M 44?

Out of the $\sim$ 3000 exoplanets detected so far, only fourteen planets are members of open clusters: among them an exoplanet system around Pr 0211 in the cluster M44 which consists of at least two planets with the outer planet moving on a highly eccentric orbit at 5.5 AU. One hypothesis is that a close fly-by of a neighbouring star was responsible for the eccentric orbit. We test this hypothesis. First we determine the type of fly-by that would lead to the observed parameters and then use this result to determine the history of such fly-bys in simulations of the early dynamics in an M44-like environment. We find that although very close fly-bys are required to obtain the observed properties of Pr 0211c, such fly-bys are relatively common due to the high stellar density and longevity of the cluster. Such close fly-bys are most frequent during the first 1-2 Myr after cluster formation, corresponding to a cluster age $\leq$ 3 Myr. During the first 2 to 3 Myr about 6.5% of stars actually experience a fly-by that would lead to such a small system-size as observed for Pr0211 or even smaller. It is unclear whether planets generally form on such short timescales. However, afterwards the close fly-by rate is still 0.2-0.5 Myr$^{-1}$, which means extrapolating this to the age of M44 12%-20% of stars would experience such close fly-bys over this timespan. Our simulations show that the fly-by scenario is a realistic option for the formation of eccentricity orbits of the planets in M44. The occurrence of such events is relatively high leading to the expectation that similar systems are likely common in open clusters in general.Comment: 7 pages, 6 figures, accepted by A&

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&

Strong effect of the cluster environment on the size of protoplanetary discs?

Context. Most stars are born in clusters, thus the protoplanetary discs surrounding the newly formed stars might be influenced by this environment. Isolated star-disc encounters have previously been studied, and it was shown that very close encounters are necessary to completely destroy discs. However, relatively distant encounters are still able to change the disc size considerably. Aims. We quantify the importance of disc-size reduction that is due to stellar encounters in an entire stellar population. Methods. We modelled young, massive clusters of different densities using the code Nbody6 to determine the statistics of stellar encounter parameters. In a second step, we used these parameters to investigate the effect of the environments on the disc size. For this purpose, we performed a numerical experiment with an artificial initial disc size of 105 AU. Results. We quantify to which degree the disc size is more sensitive to the cluster environment than to the disc mass or frequency. We show that in all investigated clusters a large portion of discs is significantly reduced in size. After 5 Myr, the fraction of discs smaller than 1000 AU in ONC-like clusters with an average number density of 60pc$^3$, the fraction of discs smaller than 1000 AU is 65%, while discs smaller than 100 AU make up 15%. These fractions increase to 84% and 39% for discs in denser clusters like IC 348 (500pc$^3$). Even in clusters with a density four times lower than in the ONC (15pc$^3$), about 43% of all discs are reduced to sizes below 1 000 AU and roughly 9% to sizes below 100 AU. Conclusions. For any disc in the ONC that initially was larger than 1 000 AU, the probability to be truncated to smaller disc sizes as a result of stellar encounters is quite high. Thus, among other effects, encounters are important in shaping discs and potentially forming planetary systems in stellar clusters.Comment: accepted for publication in 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

Sizes of protoplanetary discs after star-disc encounters

Most stars do not form in isolation, but as part of a star cluster or association. These young stars are initially surrounded by protoplanetary discs. In these cluster environments tidal interactions with other cluster members can alter the disc properties. Besides the disc frequency, its mass, angular momentum, and energy, in particular the disc's size is prone to being changed by a passing star. So far the change in disc size was only investigated for a small number of very specific encounters. Several studies investigated the effect of the cluster environment on the sizes of planetary systems, like our own solar system, based on a generalisation of information from this limited sample. We performed numerical simulations covering the wide parameter space typical for young star clusters, to test the validity of this approach. Here the sizes of discs after encounters are presented, based on a size definition which is comparable to that one used in observational studies. We find that, except for encounters between equal-mass stars, the usually applied estimates are insufficient. They tend to severely overestimate the remaining disc size. We show that the disc size after an encounter can be described by a relatively simple dependence on the periastron distance and the mass ratio of the encounter partners. This knowledge allows, for example, to pin down the types of encounter possibly responsible for the structure of today's solar system.Comment: 7 pages, 4 figures, + 2 pages Online material, accepted by A&

Outer solar system possibly shaped by a stellar fly-by

The planets of our solar system formed from a gas-dust disk. However, there are some properties of the solar system that are peculiar in this context. First, the cumulative mass of all objects beyond Neptune (TNOs) is only a fraction of what one would expect. Second, unlike the planets themselves, the TNOs do not orbit on coplanar, circular orbits around the Sun, but move mostly on inclined, eccentric orbits and are distributed in a complex way. This implies that some process restructured the outer solar system after its formation. However, some of TNOs, referred to as Sednoids, move outside the zone of influence of the planets. Thus external forces must have played an important part in the restructuring of the outer solar system. The study presented here shows that a close fly-by of a neighbouring star can simultaneously lead to the observed lower mass density outside 30 AU and excite the TNOs onto eccentric, inclined orbits, including the family of Sednoids. In the past it was estimated that such close fly-bys are rare during the relevant development stage. However, our numerical simulations show that such a scenario is much more likely than previously anticipated. A fly-by also naturally explains the puzzling fact that Neptune has a higher mass than Uranus. Our simulations suggest that many additional Sednoids at high inclinations still await discovery, perhaps including bodies like the postulated planet X.Comment: 16 pages, 7 figures, accepted by Ap

How star cluster evolution shapes protoplanetary disc sizes

The majority of stars form from cold, collapsing Giant Molecular Clouds (GMCs), which not only yield single stars, but groups of a few up to many hundreds of thousands of stars. The gas and dust which was not transformed into stars is expelled at the end of the star formation process. Stellar groups react very differently to this mass removal, depending on their virial state and on the fraction of gas which is transformed into stars, called star-formation efficiency (SFE). In one type of group, called associations, the SFE is rather low (=< 0.3$) and the gas removal leaves the stellar members (largely) unbound. On the other hand, if the SFE is higher, observations and theory find that the stellar accumulations largely remain bound and can survive many billions of years in this state, which makes them stellar clusters. These two types of stellar groups evolve on very distinct tracks concerning their density, size, and mass. It is probable that most - if not all - stars are initially surrounded by a protoplanetary disc, the formation site of planets. In the last decades - and especially since the launch of Kepler in 2009 - observations were able to find more than 3700 planets orbiting other stars. Many of these extrasolar planets (exoplanets) are part of planetary systems, which differ significantly from our own solar system. External processes in the stellar birth environments like gravitational interactions between the cluster members (fly-bys) and external photoevaporation are possible reasons for these differences. The strength of such processes is directly connected to the dynamical and density evolution of the environments. Simulations of different associations and clusters were performed and the influence of fly-bys on protoplanetary discs was investigated. In associations, the most fly-bys happen in the phase, where they are still embedded in their natal gas. After gas expulsion, most members of the associations become unbound and thus the effect of stellar fly-bys becomes less important. In systems comparable to the Orion Nebular Cluster (ONC), the discs in the simulations are cut down to a few hundreds of AU, which fits observational findings very well. By contrast, stellar clusters, like for example the Arches, retain their high stellar density even after gas expulsion. In such dense clusters, fly-bys play an important role in shaping disc properties at later evolutionary stages as well, cutting down discs to much smaller sizes of ~20AU. For a long time, such very dense systems were considered to be too hostile to yield, for example, a planetary system like our own solar system. However, under the assumption that the steep drop in mass density at 30AU in our solar system was caused by a fly-by, the results presented in this thesis show that the solar system was most probably part of a very massive association, like for example NGC6611, or a stellar cluster, like Arches

Cradle(s) of the Sun

The Sun likely formed as part of a group of stars. A close stellar flyby by one of the solar siblings is probably responsible for the sharp outer edge in the solar system`s mass distribution. The frequency of such close flybys can be used to determine the likely type of birth environment of the solar system. Young stellar groups develop very quickly, expanding significantly within just a few Myr. Here we model this strong dynamical development of young stellar groups and determine the resulting close flyby history. We find that solar system equivalents are predominantly produced in areas with stellar densities in the range 5 $\times$ 10$^4$pc$^{-3}$$20 000$M_{sun}$) and intermediate-mass mass, compact clusters ($M_c <$3000$M_{sun}$). Current day counterparts would be the association NGC 2244 and the M44 cluster, respectively. In these two types of stellar groups, close flybys take place at a sufficiently high rate, while not being too destructive either. A final decision between these two remaining options will require incorporation of constraints from cosmo-chemical studies