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, the disc's size is particularly prone to being changed by a passing star. So far the change in disc size has only been 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 of young star clusters, to test the validity of this approach. Here the sizes of discs after encounters are presented, based on a size definition that is comparable to the 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 us, for example, to pin down the types of encounter possibly responsible for the structure of today's solar system.
To what degree the cluster environment influences the sizes of protoplanetary disks surrounding young stars is still an open question. This is particularly true for the short-lived clusters typical for the solar neighborhood, in which the stellar density and therefore the influence of the cluster environment change considerably over the first 10 Myr. In previous studies,the effect of the gas on the cluster dynamics has oftenbeen neglected;this is remedied here. Using the code NBody6++,we study the stellar dynamics in different developmental phases-embedded, expulsion, and expansion-including the gas, and quantify the effect of fly-bys on the disksize. We concentrate on massive clusters (M cl 10 3 -6 * 10 4 M 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, disks in sparser clusters are initially less affected, but because these clusters expand moreslowly,13% of disks are truncated after gas expulsion. For ONC-like clusters, we find that disks larger than 500 au are usuallyaffected by the environment, which corresponds to the observation that 200 ausized disks are common. For NGC 6611-like clusters, disksizes are cut-down on average to roughly 100 au. A testable hypothesis would be that the disks in the center of NGC 6611 should be on average ≈20 au and therefore considerably smaller than those in the ONC.
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 10 5 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 ρ cluster ∼ 60 pc −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 (ρ cluster ∼ 500 pc −3 ). Even in clusters with a density four times lower than in the ONC (ρ cluster ∼ 15 pc −3 ), about 43% of all discs are reduced to sizes below 1000 AU and roughly 9% to sizes below 100 AU. Conclusions. For any disc in the ONC that initially was larger than 1000 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.
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.
Stars mostly form in groups consisting of a few dozen to several ten thousand members. For 30 years, theoretical models provide a basic concept of how such star clusters form and develop: they originate from the gas and dust of collapsing molecular clouds. The conversion from gas to stars being incomplete, the left over gas is expelled, leading to cluster expansion and stars becoming unbound. Observationally, a direct confirmation of this process has proved elusive, which is attributed to the diversity of the properties of forming clusters. Here we take into account that the true cluster masses and sizes are masked, initially by the surface density of the background and later by the still present unbound stars. Based on the recent observational finding that in a given star-forming region the star formation efficiency depends on the local density of the gas, we use an analytical approach combined with N-body simulations, to reveal evolutionary tracks for young massive clusters covering the first 10 Myr. Just like the Hertzsprung-Russell diagram is a measure for the evolution of stars, these tracks provide equivalent information for clusters. Like stars, massive clusters form and develop faster than their lower-mass counterparts, explaining why so few massive cluster progenitors are found.
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