We carry out N-body simulations to examine the effects of dynamical interactions on planetary systems in young open star clusters. We explore how the planetary populations in these star clusters evolve, and how this evolution depends on the initial amount of substructure, the virial ratio, the cluster mass and density, and the initial semi-major axis of the planetary systems. The fraction of planetary systems that remains intact as a cluster member, f_BPS, is generally well-described by the functional form f_BPS = f₀(1 + [a/a₀]^c)⁻¹, where (1 − f₀) is the fraction of stars that escapes from the cluster, a₀ the critical semi-major axis for survival, and c a measure for the width of the transition region. The effect of the initial amount of substructure over time t can be quantified as f_BPS = A(t) + B(D), where A(t) decreases nearly linearly with time, and B(D) decreases when the clusters are initially more substructured. Provided that the orbital separation of planetary systems is smaller than the critical value a₀, those in clusters with a higher initial stellar density (but identical mass) have a larger probability of escaping the cluster intact. These results help us to obtain a better understanding of the difference between the observed fractions of exoplanets-hosting stars in star clusters and in the Galactic field. It also allows us to make predictions about the free-floating planet population over time in different stellar environments.

Instabilities in planetary systems can result in the ejection of planets from their host system, resulting in free-floating planets (FFPs). If this occurs in a star cluster, the FFP may remain bound to the star cluster for some time and interact with the other cluster members until it is ejected. Here, we use N-body simulations to characterize close star–planet and planet–planet encounters and the dynamical fate of the FFP population in star clusters containing 500–2000 single or binary star members. We find that FFPs ejected from their planetary system at low velocities typically leave the star cluster 40 per cent earlier than their host stars, and experience tens of close (<1000 au) encounters with other stars and planets before they escape. The fraction of FFPs that experiences a close encounter depends on both the stellar density and the initial velocity distribution of the FFPs. Approximately half of the close encounters occur within the first 30 Myr, and only 10 per cent occur after 100 Myr. The periastron velocity distribution for all encounters is well described by a modified Maxwell–Bolzmann distribution, and the periastron distance distribution is linear over almost the entire range of distances considered, and flattens off for very close encounters due to strong gravitational focusing. Close encounters with FFPs can perturb existing planetary systems and their debris structures, and they can result in re-capture of FFPs. In addition, these FFP populations may be observed in young star clusters in imaging surveys; a comparison between observations and dynamical predictions may provide clues to the early phases of stellar and planetary dynamics in star clusters.

The statistical results of transiting planets show that there are two peaks, around 1.5 and 2.0, in the distribution of orbital period ratios. A large number of planet pairs are found near the exact location of mean motion resonances (MMRs). In this work, we find that the depletion and structures of the gas disk play crucial roles in driving planet pairs out of the exact location of MMRs. Under such a scenario, planet pairs are trapped into exact MMRs during orbital migration first and keep migrating at the same pace. The eccentricities can be excited. Due to the existence of a gas disk, eccentricities can be damped, leading to a change in orbital period, which will make planet pairs depart from the exact location of MMRs. With depletion timescales larger than 1 Myr, near-MMR configurations are formed easily. Planet pairs have higher possibilities of escaping from MMRs with a higher disk aspect ratio. Additionally, with a weaker corotation torque, planet pairs can depart farther from the exact location of MMRs. The final location of the innermost planets in the systems are directly related to the transition radius from the optically thick region to the outer optically thin disk. While the transition radius is smaller than 0.2 au at the late stage of the star evolution process, the period of the inner planets can reach around 10 days. Our formation scenario is a possible mechanism for explaining the formation of near-MMR configurations with the innermost planet farther than 0.1 au.

The orbital distribution of the S-star cluster surrounding the supermassive black hole in the center of the Milky Way is analyzed. A tight dependence of the pericenter distance r _p on orbital eccentricity e _⋆ is found, log ( r p ) ∼ ( 1 − e ⋆ ) , which cannot be explained simply by a random distribution of semimajor axis and eccentricities. No stars are found in the region with high e _⋆ and large log ( r p ) or in the region with low e _⋆ and small log ( r p ) . Although the sample is still small, the G-clouds show a very similar distribution. The likelihood P ( log ( r p ) , ( 1 − e ⋆ ) ) to determine the orbital parameters of S-stars is determined. P is very small for stars with large e _⋆ and large log ( r p ) . S-stars might exist in this region. To determine their orbital parameters, one however needs observations over a longer time period. On the other hand, if stars would exist in the region of low log ( r p ) and small e _⋆, their orbital parameters should by now have been determined. That this region is unpopulated therefore indicates that no S-stars exist with these orbital characteristics, providing constraints for their formation. We call this region, defined by log ( r p / AU ) < 1.57 + 2.6 ( 1 − e ⋆ ) , the zone of avoidance. Finally, it is shown that the observed frequency of eccentricities and pericenter distances is consistent with a random sampling of log ( r p ) and e _⋆ if one takes into account the fact that no stars exist in the zone of avoidance and that orbital parameters cannot yet be determined for stars with large r _p and large e _⋆.

Chondritic meteorites, or chondrites, contain some of the oldest and most primitive solids in our solar system. They record the physical conditions at the early phase of the solar nebula evolution and planet formation. Chondrites are mainly composed of chondrules, which are millimeter-sized silicate spheroids. To form the chondrules we see today, chondrule precursors need to be heated to temperatures above 1600 K and cooled down rapidly on timescales of minutes to hours. Considering ordinary chondrites make up about 10% of meteorites found on Earth, chondrule heating events should be common in the early solar system. One of the most promising mechanisms for chondrule heating is the passage through bow shocks of highly eccentric planetesimals in the protoplanetary disk. This mechanism explains many features in the thermal histories of chondrules, such as the ambient temperature, the peak temperature, and the cooling rate. However, theoretical models so far have difficulties producing a large number of planetesimals with high eccentricities, which is needed to form chondrules efficiently. In this paper, we investigate a scenario in which the orbits of planetesimals are influenced by both Jupiter and a depleting protoplanetary disk. As the disk mass decreases with time, the location of the Jovian secular resonance moves from the outer to the inner disk. This phenomenon is called the sweeping secular resonance. We propose that this mechanism, illustrated in Figure 1, can explain chondrule formation, by exciting the planetesimals in the asteroid belt region to high eccentricity orbits. We study the orbital evolution of planetesimals in the disk using semi-analytic models and numerical simulations. We investigate the dependence of eccentricity excitation on the planetesimal's size as well as the physical environment, and calculate the probability for chondrule formation. We find that 50-2000 km planetesimals can obtain eccentricities larger than 0.6, as shown in Figure 2, and lead to effective chondrule heating. Most chondrules form in high-velocity shocks, in low-density gas, and in the inner disk. Figure 3 shows that the age spread of chondrule is comparable to the depletion timescale of the disk, which is directly linked to the timescale for the secular resonance to pass through the asteroid belt region. The fraction of chondrule precursors that become chondrules is about 4-9% between 1.5-3 AU, consistent with observational constraints. Our model suggests that the depletion timescale for the protoplanetary disk around the Sun is comparable to the age spread of chondrules at around 1 Myr; and that Jupiter formed before chondrules, no more than 0.7 Myr after the formation of the CAIs. Reference: Gong M., Zheng X., Lin D.~N.~C., Silsbee K., Baruteau C., Mao S., 2019, ApJ, 883, 164 .

The inner parsec of the supermassive black hole (SMBH) in the center of the Milky Way, Sgr A^★, contains a cluster of several hundred young, massive stars. Their complex, highly structured kinematics poses an intriguing conundrum on their origin within the strong tidal field close to the SMBH. It has been suggested that the encounter of a gas cloud with the SMBH could produce a fast rotating disk of coeval, massive stars. This result however differs strongly from the observed multi-component orbital distribution. We demonstrate that star-star scattering within the disk can only weakly change their orbits and cannot explain the observations, even if one includes the dispersal of an additional gaseous disk component. Including however the gravitational interaction with a putative intermediate-mass companion (IMC) of Sgr A$^\star$, possibly an intermediate mass black hole, naturally scatters the stars into their current kinematic configuration on timescales consistent with their stellar ages.