The subparsec proximity around the Sgr A(star) supermassive black hole (SMBH) in the center of the Milky Way contains an inner cluster of eccentric S-stars with randomly oriented orbits, a midway-disk of clockwise-rotating stars (CWSs), and a surrounding population of off-the-disk stars (ODSs). Despite their diverse kinematic properties, all three populations appear to be massive (WR/O/B types) and have similarly limited life span tau(star) similar to 6-15 Myr. Several scenarios, including star formation induced by SMBH's close encounters with one or more gas clouds as well as impulsive close scattering by a putative intermediate-mass companion (IMC) of Sgr A(star) possible an intermediate-mass black hole, have been proposed to explain the origin and dynamical evolution of S-stars, CWSs, ODSs, as well as hyper-velocity stars in the Galaxy. However, their coexistence and the origin of a recently discovered zone of avoidance in S-stars' eccentricity-pericentric-distance distribution remain enigmatic. Here, we construct a unified model to comprehensively take into account these stars' interaction with each other, their single natal disk, and an independent IMC. We show their disparate present-day orbits would only be concurrently attainable, within their multi-Myr age, under the combined influence of IMC's secular perturbation and these stars' resonant relaxation in a depleting gaseous-disk environment.

Secular perturbations from binary stars and distant massive planets can drive cold planets onto nearly parabolic orbits with pericenter passages extremely close to their host stars. Meanwhile, short-period super-Earths are frequently observed around nearby stars. Gravitational scattering between these two distinct populations can lead to substantial orbital energy exchange, liberating some intruders from the gravitational confinement of their host systems. This process offers a robust formation channel for a subset of the abundant free-floating planet population. It may also significantly perturb the original orbits of close-in planets, induce collisional trajectories between close-in planets and their host stars, and disrupt the dynamical evolution of cold planets toward close stellar encounters.

Tidal disruption event (TDE) rates in active galactic nuclei (AGNs) consistently exceed predictions from two-body relaxation, particularly in post-starburst and green valley galaxies. We explain this excess with a new mechanism: a sweeping secular resonance driven by an intermediate-mass companion (IMC) and a depleting gaseous disk. As the disk mass declines, a resonance between stellar and IMC orbital precession sweeps through the nuclear cluster, exciting stellar eccentricities to near unity on orbital timescales far faster than gravitational relaxation. Our analytical framework, validated by N-body simulations (REBOUND), shows this mechanism requires IMC-to-SMBH mass ratios of q >= 10-3, disk mass ratio p >= 10-3, and few megayear-scale disk depletion. It is highly effective for coorbiting IMCs but negligible for counterorbiting ones. The TDE rate peaks at 10-3-10-2 per galaxy per year for a depletion timescale tau dep similar to 10 Myr. Even lower-mass IMCs can produce significant enhancements with compact, long-lived disks. Our model naturally explains elevated AGN TDE rates and implies that a high TDE incidence is a potential tracer of hidden parsec-scale IMCs, offering testable predictions for future AGN monitoring.

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.

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.

There is a population of stars with velocities in excess of 500 km s −1 relative to the Galactic center. Many, perhaps most, of these hypervelocity stars (HVSs) are B stars similar to the disk and S stars in a nuclear cluster around a supermassive black hole (SMBH) near Sgr A ⋆ . In Paper I of this series, we showed that the eccentricity of the stars emerged from a hypothetical disk around the SMBH that can be rapidly excited by the secular perturbation of its intermediate-mass companion (IMC), and we suggested IRS 13E as a potential candidate for the IMC. Here we show that this process leads to an influx of stars on parabolic orbits to the proximity of Sgr A ⋆ on a secular timescale of a few megayears. This timescale is much shorter than the diffusion timescale into the lost cone through either the classical or the resonant relaxation. Precession of the highly eccentric stars’ longitude of periastron, relative to that of the IMC, brings them to its proximity within a few megayears. The IMC’s gravitational perturbation scatters a fraction of the stars from nearly parabolic to hyperbolic orbits with respect to the SMBH. Their follow-up close encounters with the SMBH induce them to escape with hypervelocity. This scenario is a variant of the hypothesis proposed by Hills based on the anticipated breakup of some progenitor binary stars in the proximity of the SMBH, and its main objective is to account for the limited life span of the known HVSs. We generalize our previous numerical simulations of this process with a much wider range of orbital configurations. We demonstrate the robustness and evaluate the efficiency of this channel of HVS formation. From these numerical simulations, we infer observable kinematic properties for the HVSs.

There is a dense group of OB and Wolf-Rayet stars within a fraction of a parsec from the super-massive black hole (SMBH) at the Galactic Center. These stars appear to be coeval and relatively massive. A subgroup of these stars orbits on the same plane. If they emerged with low to modest eccentricity orbits from a common gaseous disk around the central super-massive black hole, their inferred lifespan would not be sufficiently long to account for the excitation of their high orbital eccentricity through dynamical relaxation. Here we analyze the secular perturbation on Galactic Center stars by an intermediate-mass companion (IMC) as a potential mechanism to account for these young disk stars' high eccentricity. This IMC may be either an intermediate-mass black hole (IMBH) or a compact cluster such as IRS-13E. If its orbital angular momentum vector is anti-parallel to that of the disk stars, this perturbation would be effective in exciting the eccentricity of stars with orbital precession rates which resonate with IMC's precession rate. If it orbits around the SMBH in the same direction as the disk stars, the eccentricity of the young stars can still be highly excited by the IMC during the depletion of their natal disk, possible associated with the launch of the Fermi bubble. In this scenario, IMC's precession rate decreases and its secular resonance sweeps through the proximity of the young stars. We carry out numerical simulations with various inclination angles between the orbits of IMC and the disk stars and show this secular interaction is a robust mechanism to excite the eccentricity and inclination of some disk stars.

The Juno mission1 has provided an accurate determination of Jupiter’s gravitational field2, which has been used to obtain information about the planet’s composition and internal structure. Several models of Jupiter’s structure that fit the probe’s data suggest that the planet has a diluted core, with a total heavy-element mass ranging from ten to a few tens of Earth masses (about 5 to 15 per cent of the Jovian mass), and that heavy elements (elements other than hydrogen and helium) are distributed within a region extending to nearly half of Jupiter’s radius3,4. Planet-formation models indicate that most heavy elements are accreted during the early stages of a planet's formation to create a relatively compact core5–7 and that almost no solids are accreted during subsequent runaway gas accretion8–10. Jupiter’s diluted core, combined with its possible high heavy-element enrichment, thus challenges standard planet-formation theory. A possible explanation is erosion of the initially compact heavy-element core, but the efficiency of such erosion is uncertain and depends on both the immiscibility of heavy materials in metallic hydrogen and on convective mixing as the planet evolves11,12. Another mechanism that can explain this structure is planetesimal enrichment and vaporization13–15 during the formation process, although relevant models typically cannot produce an extended diluted core. Here we show that a sufficiently energetic head-on collision (giant impact) between a large planetary embryo and the proto-Jupiter could have shattered its primordial compact core and mixed the heavy elements with the inner envelope. Models of such a scenario lead to an internal structure that is consistent with a diluted core, persisting over billions of years. We suggest that collisions were common in the young Solar system and that a similar event may have also occurred for Saturn, contributing to the structural differences between Jupiter and Saturn16–18. An energetic head-on collision between a large impactor and the proto-Jupiter with a primordial compact core could have mixed the heavy elements within the deep interior, leading to a ‘diluted’ core for Jupiter.

Chondrules are silicate spheroids found in meteorites, and they serve as important fossil records of the early solar system. In order to form chondrules, chondrule precursors must be heated to temperatures much higher than the typical conditions in the current asteroid belt. One proposed mechanism for chondrule heating is the passage through bow shocks of highly eccentric planetesimals in the protoplanetary disk in the early solar system. However, it is difficult for planetesimals to gain and maintain such high eccentricities. In this paper, we present a new scenario in which planetesimals in the asteroid belt region are excited to high eccentricities by the Jovian sweeping secular resonance in a depleting disk, leading to efficient formation of chondrules. 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 the probability for chondrule formation. We find that 50–2000 km planetesimals can obtain eccentricities larger than 0.6 and cause effective chondrule heating. Most chondrules form in high-velocity shocks, in low-density gas, and in the inner disk. The fraction of chondrule precursors that become chondrules is about 4%–9% between 1.5 and 3 au. Our model implies that the disk depletion timescale is τ dep ≈ 1 Myr, comparable to the age spread of chondrules, and that Jupiter formed before chondrules, no more than 0.7 Myr after the formation of calcium aluminum inclusions.

The distribution of heavy elements is anomalously low in the asteroid main belt region compared with elsewhere in the solar system. Observational surveys also indicate a deficit in the number of small ($ \le 50$~km size) asteroids that is two orders of magnitude lower than what is expected from the single power-law distribution that results from a collisional coagulation and fragmentation equilibrium. Here, we consider the possibility that a major fraction of the original asteroid population may have been cleared out by Jupiter's secular resonance, as it swept through the main asteroid belt during the depletion of the solar nebula. This effect leads to the excitation of the asteroids' orbital eccentricities. Concurrently, hydrodynamic drag and planet-disk tidal interaction effectively damp the eccentricities of sub-100 km-size and of super-lunar-size planetesimals, respectively. These combined effects lead to the asteroids' orbital decay and clearing from the present-day main belt region ($\sim 2.1-3.3$~AU). The intermediate-size (50 to several hundreds of kilometers) planetesimals therefore preferentially remain as main belt asteroids near their birthplaces, with modest asymptotic eccentricities. The smaller asteroids are the fragments of subsequent disruptive collisions at later times as suggested by the present-day asteroid families. This scenario provides a natural explanation for both the observed low surface density and the size distribution of asteroids in the main belt. It also offers an explanation for the confined spatial extent of the terrestrial planet building blocks without the requirement of extensive migration of Jupiter.

Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent “lone-planet” scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. With a series of numerical simulations, we show that the gravitational potential of the natal disk induces the planet to precess. At the locations where its precession frequency matches the precession frequency the planet imposes on the residual planetesimals, their eccentricity is excited by its resonant perturbation. Due to the hydrodynamic drag by the residual disk gas, the planetesimals undergo orbital decay as their excited eccentricities are effectively damped. During the depletion of the disk gas, the planet’s secular resonance propagates inward and clears a wide gap over an extended region of the disk. Although some residual intermediate-size planetesimals may remain in the gap, their surface density is too low to either produce super-Earths or lead to sufficiently frequent disruptive collisions to generate any observable dusty signatures. The main advantage of this lone-planet sweeping-secular-resonance model over the previous multiple gas giant tidal truncation scenario is the relaxed requirement on the number of gas giants. The observationally inferred upper mass limit can also be satisfied provided the hypothetical planet has a significant eccentricity. A significant fraction of solar or more massive stars bear gas giant planets with significant eccentricities. If these planets acquired their present-day kinematic properties prior to the depletion of their natal disks, their sweeping secular resonance would effectively impede the retention of neighboring planets and planetesimals over a wide range of orbital semimajor axes.

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.

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, fbps, is generally well-described by the functional form fbps=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 can be quantified as fbps=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.