Encounter Distances Research Articles

The Alpha-proton Differential Flow in the Alfvénic Young Solar Wind: from Sub-Alfvénic to Super-Alfvénic

Data obtained from Parker Solar Probe (PSP) since 2021 April have shown the first in situ observation of the solar corona, where the solar wind is formed and accelerated. Here, we investigate the alpha-proton differential flow and its characteristics across the critical Alfvén surface (CAS) using data from PSP during encounters 8–10 and 12–13. We first show the positive correlation between the alpha-proton differential velocity and the bulk solar wind speed at PSP encounter distances. Then we explore how the characteristics of the differential flow vary across the CAS and how they are affected by Alfvénic fluctuations including switchbacks. We find that the differential velocity below the CAS is generally smaller than that above the CAS, and the local Alfvén speed well limits the differential speed both above and below the CAS. The deviations from the alignment between the differential velocity and the local magnetic field vector are accompanied by large-amplitude Alfvénic fluctuations and decreases in the differential speed. Moreover, we observe that V α p increases from M A < 1 to M A ≃ 2 and then starts to decrease, which suggests that alphas may remain preferentially accelerated well above the CAS. Our results also reveal that in the sub-Alfvénic solar wind both protons and alphas show a strong correlation between their velocity fluctuations and magnetic field fluctuations, with a weaker correlation for alphas. By contrast, in the super-Alfvénic regime the correlation remains high for protons, but is reduced for alphas.

An Improved VO Method for Collision Avoidance of Ships in Open Sea

In order to effectively deal with collisions in various encounter situations in open water environments, a ship collision avoidance model was established, and multiple constraints were introduced into the velocity obstacle method, a method to determine the ship domain by calculating the safe distance of approach was proposed. At the same time, the ship collision avoidance model based on the ship domain is analyzed, and the relative velocity set of the collision cone is obtained by solving the common tangent line within the ellipse. The timing of starting collision avoidance is determined by calculating the ship collision risk, and a method for ending collision avoidance is proposed. Finally, by comparing the simulation experiments of the improved algorithm with those of the traditional algorithm and the actual ship experiment results of manual ship maneuvering, it is shown that the method can effectively avoid collisions based on safe encounter distances that comply with navigation experience in different encounter situations. At the same time, it has better performance in collision avoidance behavior. It has certain feasibility and practical applicability.

Modelling whale-vessel encounters: the role of speed in mitigating collisions with humpback whales (Megaptera novaeangliae)

Increasing whale populations and vessel traffic worldwide has led to an increase in reported whale-vessel collisions. This paper reports on factors that affect the rate of whale-vessel collisions in the four-island region of Maui, Hawai’i. More specifically, it aims at quantifying the probability of a whale-vessel collision with varying vessel speeds using encounter distances as a proxy. A change point model was used to identify a speed threshold of 12.5kts (6.4m/s), which showed a significant change in the relationship between speed and mean sighting distance. A 3.4-fold decrease in close encounters with humpback whales was observed when vessels travelled at speeds of 12.5kts (6.4m/s) or less. Furthermore, results indicate that lone adult whales and calves are the most likely to be involved in a collision. A speed limit of 12.5kts (6.4m/s) is warranted in areas and/or during seasons where a high density of whales occurs. This limit aligns with a reduction in lethal vessel strikes with speed from previous studies which found a significant increase in the likelihood of mortality when vessel speed exceeds 12kts.

Stars That Approach within One Parsec of the Sun: New and More Accurate Encounters Identified in Gaia Data Release 3

Close encounters of stars to the Sun could affect life on Earth through gravitational perturbations of comets in the Oort cloud or exposure to ionizing radiation. By integrating orbits through the Galactic potential, I identify which of 33 million stars in Gaia DR3 with complete phase space information come close to the Sun. 61 stars formally approach within 1 pc, although there is high confidence in only 42 (two thirds) of these, the rest being spurious measurements or (in) binary systems. Most of the stars will encounter within the past or future 6 Myr; earlier/later encounters are less common due to the magnitude limit of the Gaia radial velocities (RVs). Several close encountering stars are identified for the first time, and the encounter times, distances, and velocities of previously known close encounters are determined more precisely on account of the significantly improved precision of Gaia DR3 over earlier releases. The K7 dwarf Gl 710 remains the closest known encounter, with an estimated (median) encounter distance of 0.0636 pc (90% confidence interval 0.0595–0.0678 pc) to take place in 1.3 Myr. The new second closest encounter took place 2.8 Myr ago: this was the G3 dwarf HD 7977, now 76 pc away, which approached within less than 0.05 pc of the Sun with a probability of one third. The apparent close encounter of the white dwarf UPM J0812-3529 is probably spurious due to an incorrect RV in Gaia DR3.

Inferring Vortex and Dust Devil Statistics from InSight

Abstract The InSight mission has operated on the surface of Mars for nearly two Earth years, returning detections of the first marsquakes. The lander also deployed a meteorological instrument package and cameras to monitor local surface activity. These instruments have detected boundary layer phenomena, including small-scale vortices. These vortices register as short-lived, negative pressure excursions and closely resemble those that could generate dust devils. Although our analysis shows that InSight encountered more than 900 vortices and collected more than 1000 images of the Martian surface, no active dust devils were imaged. In spite of the lack of dust devil detections, we can leverage the vortex detections and InSight’s daily wind speed measurements to learn about the boundary layer processes that create dust devils. We discuss our analysis of InSight’s meteorological data to assess the statistics of vortex and dust devil activity. We also infer encounter distances for the vortices and, therefrom, the maximum vortex wind speeds. Surveying the available imagery, we place upper limits on what fraction of vortices carry dust (i.e., how many are bona fide dust devils) and estimate threshold wind speeds for dust lifting. Comparing our results to detections of dust devil tracks seen in space-based observations of the InSight landing site, we can also infer thresholds and frequency of track formation by vortices. Comparing vortex encounters and parameters with advective wind speeds, we find evidence that high wind speeds at InSight may have suppressed the formation of dust devils, explaining the lack of imaged dust devils.

The effect of planetary flybys on singly synchronous binary asteroids

The evolution of binary asteroid dynamics are not fully understood. The method of formation is widely accepted as spin-up and fission due to the YORP effect, but it is unclear why systems exist at a variety of energy levels. Binary asteroids are observed in states ranging from relaxed, synchronous equilibriums to chaotic dynamics. Previous planetary encounters may have an effect on the dynamic configuration of binary asteroids. We develop a model for the spherical restricted full three-body problem to simulate a binary asteroid perturbed by a planetary flyby, as well as a method of obtaining initial conditions for a relaxed, singly synchronous binary asteroid system. These are used in a numeric analysis employing a modified version of the General Use Binary Asteroid Simulator, where Monte Carlo simulations are leveraged to investigate how a range of Earth encounters affect the dynamic evolution of a generic binary asteroid system in a singly synchronous equilibrium. The results show that planetary flybys can disrupt the synchronous equilibrium, with the effects dropping off at far encounter distances and fast flyby speeds. After the impulsive perturbation of a planetary flyby, the binary asteroid spin-orbit coupling can prevent the system from settling into a new equilibrium, forcing the system to go through the energy dissipation process to re-equilibrate. It is therefore possible that planetary encounters may have a part in creating chaotic binary asteroid systems from previously relaxed equilibrated systems.

Capture of satellites during planetary encounters

Context.Single-binary scattering may lead to an exchange where the single object captures a component of the binary, forming a new binary. This has been well studied in encounters between a star–planet pair and a single star.Aims.Here we explore the application of the exchange mechanism to a planet–satellite pair and another planet in the gravitational potential of a central star. As a case study, we focus on encounters between a satellite-bearing object and Neptune. We investigate whether Neptune can capture satellites from that object and if the captured satellites have orbits analogous to the Neptunian moons Triton and Nereid.Methods.UsingN-body simulations, we study the capture probability at different encounter distances. Post-capture, we use a simple analytical argument to estimate how the captured orbits evolve under collisional and tidal effects.Results.We find that the average capture probability reaches ~10% if Neptune penetrates the donor planet’s satellite system. Most moons grabbed by Neptune acquire highly eccentric orbits. Post-capture, around half of those captured, especially those on tight orbits, can be circularised, either by tides only or by collisions+tides, turning into Triton-like objects. Captures further out, on the other hand, stay on wide and eccentric orbits like that of Nereid. Both moon types can be captured in the same encounter and they have wide distributions in orbital inclination. Therefore, Triton naturally has a ~50% chance of being retrograde.Conclusions.A similar process potentially applies to an exoplanetary system, and our model predicts that exomoons can jump from one planet to another during planetary scattering. Specifically, there should be two distinct populations of captured moons: one on close-in circular orbits and the other on far-out eccentric orbits. The two populations may have highly inclined prograde or retrograde orbits.

Behavioural responses of southern mountain caribou to helicopter and skiing activities

Helicopter- and snowcat-supported backcountry skiing is a unique industry that is widespread throughout southern mountain caribou habitat in British Columbia. We analyzed standardized caribou encounter data collected by operators under an agreement between the BC government and Helicat Canada. Average reported encounter rates were low for helicopters (0.6%) and skiing groups (0.1%); however, encounters were likely underreported due to factors that affect caribou sightability. Although helicopters encountered caribou more frequently than skiing groups, caribou were detected from helicopters at greater distances than by skiers. We used Bayesian network models to assess the independent contribution of different factors to the behavioural response of caribou to encounters. Encounter distance was the most important factor in both helicopter and skiing models. Larger groups of caribou responded strongly to skiers but not to helicopters, although the independent effect of this factor was small in both models. Larger helicopters elicited stronger reactions from caribou than smaller machines and was responsible for 25% of the modelled variation in caribou response. Encounters with helicopters at distances of 100–500m had a 78% probability of eliciting a concerned-to-very-alarmedresponse from caribou, while skiers at a similar distance had a 60% probability of eliciting the same response. The probability of concerned-to-very-alarmed responses dropped to &lt;20% at encounter distances of &gt;1000 m. These results indicate that initial encounter distance is the key variable to manage risk to caribou of helicopter and skiing encounters. Ongoing feedback on the effectiveness of management practices is critical to ensure the continued viability of industries operating in caribou habitat.

Plausible Home Stars of the Interstellar Object ‘Oumuamua Found in Gaia DR2

Abstract The first detected interstellar object, ‘Oumuamua, which passed within 0.25 au of the Sun on 2017 September 9, was presumably ejected from a stellar system. We use its newly determined non-Keplerian trajectory together with the reconstructed Galactic orbits of 7 million stars from Gaia DR2 to identify past close encounters. Such an “encounter” could reveal the home system from which ‘Oumuamua was ejected. The closest encounter, at 0.60 pc (0.53–0.67 pc, 90% confidence interval), was with the M2.5 dwarf HIP 3757 at a relative velocity of 24.7 , 1 Myr ago. A more distant encounter (1.6 pc) but with a lower encounter (ejection) velocity of 10.7 was with the G5 dwarf HD 292249, 3.8 Myr ago. Two more stars have encounter distances and velocities intermediate to these. The encounter parameters are similar across six different non-gravitational trajectories for ‘Oumuamua. The ejection of ‘Oumuamua by scattering from a giant planet in one of the systems is plausible, but requires a rather unlikely configuration to achieve the high velocities found. A binary star system is more likely to produce the observed velocities. None of the four home candidates have published exoplanets or are known to be binaries. Given that the 7 million stars in Gaia DR2 with 6D phase space information is just a small fraction of all stars for which we can eventually reconstruct orbits, it is a priori unlikely that our current search would find ‘Oumuamua’s home star system. As ‘Oumuamua is expected to pass within 1 pc of about 20 stars and brown dwarfs every Myr, the plausibility of a home system also depends on an appropriate (low) encounter velocity.

New stellar encounters discovered in the second Gaia data release

Passing stars may play an important role in the evolution of our solar system. We search for close stellar encounters to the Sun among all 7.2 million stars in Gaia DR2 that have six-dimensional phase space data. We characterize encounters by integrating their orbits through a Galactic potential and propagating the correlated uncertainties via a Monte Carlo resampling. After filtering to remove spurious data, we find 694 stars that have median (over uncertainties) closest encounter distances within 5 pc, all occurring within 15 Myr from now. 26 of these have at least a 50% chance of coming closer than 1 pc (and 7 within 0.5 pc), all but one of which are newly discovered here. We confirm some and refute several other previously-identified encounters, confirming suspicions about their data. The closest encounter in the sample is Gl 710, which has a 95% probability of coming closer than 0.08 pc (17 000 AU). Taking mass estimates obtained from Gaia astrometry and multiband photometry for essentially all encounters, we find that Gl 710 also has the largest impulse on the Oort cloud. Using a Galaxy model, we compute the completeness of the Gaia DR2 encountering sample as a function of perihelion time and distance. Only 15% of encounters within 5 pc occurring within ±5 Myr of now have been identified, mostly due to the lack of radial velocities for faint and/or cool stars. Accounting for the incompleteness, we infer the present rate of encounters within 1 pc to be 19.7 ± 2.2 per Myr, a quantity expected to scale quadratically with the encounter distance out to at least several pc. Spuriously large parallaxes in our sample from imperfect filtering would tend to inflate both the number of encounters found and this inferred rate. The magnitude of this effect is hard to quantify.

Flight Load Assessment for Light Aircraft Landing Trajectories in Windy Atmosphere and Near Wind Farms

This work focuses on the wake encounter problem occurring when a light, or very light, aircraft flies through or nearby a wind turbine wake. The dependency of the aircraft normal load factor on the distance from the turbine rotor in various flight and environmental conditions is quantified. For this research, a framework of software applications has been developed for generating and controlling a population of flight simulation scenarios in presence of assigned wind and turbulence fields. The JSBSim flight dynamics model makes use of several autopilot systems for simulating a realistic pilot behavior during navigation. The wind distribution, calculated with OpenFOAM, is a separate input for the dynamic model and is considered frozen during each flight simulation. The aircraft normal load factor during wake encounters is monitored at different distances from the rotor, aircraft speeds, rates of descent and crossing angles. Based on these figures, some preliminary guidelines and recommendations on safe encounter distances are provided for general aviation aircraft, with considerations on pilot comfort and flight safety. These are needed, for instance, when an accident risk assessment study is required for flight in proximity of aeolic parks. A link to the GitHub code repository is provided.

Application of potential assessment of risk (PARK) model in Korea waterways

Korean coastal waterways are potentially the most dangerous zones for marine accidents owing to a high volume of traffic, irregular traffic patterns of fishing vessels, frequent ship encounters, and narrowness of navigable area because of offshore construction and port enlargement construction. However, there are only few marine traffic assessment models that can be referenced from other countries, and none of them contain a risk assessment model suitable for the situation regarding Korean waterways. Therefore, it is necessary to develop a quantitative assessment of marine traffic environments based on ship navigator’s consciousness. To develop a new, suitable assessment model for marine traffic, the internal and external elements of vessels, based on a questionnaire survey and simulation experiment, are considered. The ship’s internal static parameters, vessel type, length, and width, as well as mariner’s experience, license, and rank on board are determined for the risk value. Furthermore, the external dynamic elements are calculated by the results of the questionnaire, which addresses the ship’s encounter situations and distances. Through this potential assessment of risk model, we used function as navigation equipment onboard to prevent a collision accident, applied it as a solution of a Vessel Traffic System (VTS) decision-making support system, and used the vessel evacuation route to recover the vessel’s normal situation from an emergency.

Close encounters of the stellar kind

Stars which pass close to the Sun can perturb the Oort cloud, injecting comets into the inner solar system where they may collide with the Earth. Using van Leeuwen's re-reduction of the Hipparcos data complemented by the original Hipparcos and Tycho-2 catalogues, along with recent radial velocity surveys, I integrate the orbits of over 50 000 stars through the Galaxy to look for close encounters. The search uses a Monte Carlo simulation over the covariance of the data in order to properly characterize the uncertainties in the times, distances, and speeds of the encounters. I show that modelling stellar encounters by assuming instead a linear relative motion produces, for many encounters, inaccurate and biased results. I find 42, 14, and 4 stars which have encounter distances below 2, 1, and 0.5 pc respectively, although some of these stars have questionable data. Of the 14 stars coming within 1 pc, 5 were found by at least one of three previous studies (which found a total of 7 coming within 1 pc). The closest encounter appears to be Hip 85605, a K or M star, which has a 90% probability of coming between 0.04 and 0.20 pc between 240 and 470 kyr from now (90% Bayesian confidence interval). However, its astrometry may be incorrect, in which case the closest encounter found is the K7 dwarf GL 710, which has a 90% probability of coming within 0.10-0.44 pc in about 1.3 Myr. A larger perturbation may have been caused by gamma Microscopii, a G6 giant with a mass of about 2.5 Msol, which came within 0.35-1.34 pc (90% confidence interval) around 3.8 Myr ago.

Response distances of wild forest reindeer (Rangifer tarandus fennicus Lönnb.) and semi-domestic reindeer (R. t. tarandus L.) to direct provocation by a human on foot/snowshoes

The objective of the study was to examine response distances of wild forest reindeer (Rangifer tarandus fennicus Lönnb.) and semi-domestic reindeer (R. t. tarandus L.) in Finland and Norway to direct provocation by a human on foot/snowshoes in 5 areas and in 15 reindeer herding cooperatives during different seasons in 2010-12. There were no significant differences in mean herd size or in sight, alert, flight and closest response distances of wild forest reindeer in the Kuhmo and Suomenselkä areas. The encounter distance in wild forest reindeer was significantly (P&lt; 0.005) longer than in semi-domestic reindeer in Finland and in Finnmark, Norway, and it increased with the group size. The sight and the alert distances in wild forest reindeer were significantly (P&lt; 0.001) longer than in semi-domestic reindeer. In addition, the flight distance for wild forest reindeer (mean 192 m) was significantly (P&lt; 0.001) and almost three times longer than in semi-domestic reindeer in Finland (mean 68 m). The closest mean distance was in wild forest reindeer 191m (range 100-320 m) but only 44 m (range 2-110 m) in semi-domestic reindeer (P&lt; 0.001). The sight, alert, flight and closest response distances were slightly longer in Norwegian than in Finnish semi-domestic reindeer. However, these distances were significantly (P&lt;0.005) longer in Pohjois-Salla (no supplementary feeding) than in other Finnish reindeer herding cooperatives and at the Kaamanen experimental station. The mean flight distance of reindeer in Pohjois-Salla was 115 m but only 65 m in other cooperatives (P&lt; 0.001). The closest distance of semi-domestic reindeer in Pohjois-Salla (mean 105 m) was more than 2.5 times longer than in other reindeer herding cooperatives (mean 40 m). The mean sight, alert and flight distances in wild forest reindeer in autumn and winter were significantly longer (P&lt;0.005) than in semi-domestic reindeer in Finland. However, during summer these distances in wild forest reindeer herds with young calves were significantly longer (P&lt;0.005). The mean herd size of Finnish semi-domestic reindeer was almost the same in different seasons, but in wild forest reindeer it was slightly bigger during winter and spring and smaller during summer and autumn, only 7-23 reindeer. The mean encounter and sight distances in semi-domestic reindeer were significantly longer (P&lt;0.005) in winter, but the mean alert and flight distances were almost the same in winter and summer and slightly longer than during other seasons. The results suggest that the supplementary feeding practice during winter may likely cause a reduction in flight distances in semi-domestic reindeer.

DISKS AROUND BROWN DWARFS IN THE EJECTION SCENARIO. I. DISK COLLISIONS IN TRIPLE SYSTEMS

We investigate the fate of disks around brown dwarfs in the ejection scenario and the implications on their observable properties. For that purpose, a parameter study of close triple approaches leading to escape is carried out where the ejected body is surrounded by a low-mass disk. We analyze the recircularized radial surface density profile of the post-encounter disk in dependence of the minimum two-body distances between the escaper and the perturbing bodies. Our results show that the general appearance of the disks is rather similar to disks after two-body encounters in as much as there is also an exponential drop in surface density for the outer disk regions as well as an enhancement of surface density for the innermost region relative to the initial disk profile. However, the disks after close triple approaches are mostly less massive, have generally flatter recircularized surface density disk profiles, and have radii that are similar or larger compared to disks after two-body encounters. From our results, we construct a simple scale-free model only depending on the minimum encounter distances of the two perturbers. Such a model is especially useful for statistical studies of disk collisions in triple systems that must cover a large range of encounter distances.

A Bayesian approach for understanding the role of ship speed in whale–ship encounters

Mandatory or voluntary reductions in ship speed are a common management strategy for reducing deleterious encounters between large ships and large whales. This has produced strong resistance from shipping and marine transportation entities, in part because very few studies have empirically demonstrated whether or to what degree ship speed influences ship-whale encounters. Here we present the results of four years of humpback whale sightings made by observers aboard cruise ships in Alaska, representing 380 cruises and 891 ship-whale encounters. Encounters occurred at distances from 21 m to 1000 m (x = 567 m) with 61 encounters (7%) occurring between 200 m and 100 m, and 19 encounters (2%) within 100 m. Encounters were spatially aggregated and highly variable across all ship speeds. Nevertheless a Bayesian change-point model found that the relationship between whale distance and ship speed changed at 11.8 knots (6.1 m/s) with whales encountering ships, on average, 114 m closer when ship speeds were above 11.8 knots. Binning encounter distances by 1-knot speed increments revealed a clear decrease in encounter distance with increasing ship speed over the range of 7-17 knots (3.6-8.7 m/s). Our results are the first to demonstrate that speed influences the encounter distance between large ships and large whales. Assuming that the closer ships come to whales the more likely they are to be struck, our results suggest that reduced ship speed may be an effective management action in reducing the probability of a collision.

DYNAMICAL EVOLUTION OF YOUNG EMBEDDED CLUSTERS: A PARAMETER SPACE SURVEY

This paper investigates the dynamical evolution of embedded stellar clusters from the protocluster stage, through the embedded star-forming phase, and out to ages of 10 Myr -- after the gas has been removed from the cluster. The relevant dynamical properties of young stellar clusters are explored over a wide range of possible star formation environments using N-body simulations. Many realizations of equivalent initial conditions are used to produce robust statistical descriptions of cluster evolution including the cluster bound fraction, radial probability distributions, as well as the distributions of close encounter distances and velocities. These cluster properties are presented as a function of parameters describing the initial configuration of the cluster, including the initial cluster membership N, initial stellar velocities, cluster radii, star formation efficiency, embedding gas dispersal time, and the degree of primordial mass segregation. The results of this parameter space survey, which includes about 25,000 simulations, provide a statistical description of cluster evolution as a function of the initial conditions. We also present a compilation of the FUV radiation fields provided by these same cluster environments. The output distributions from this study can be combined with other calculations, such as disk photoevaporation models and planetary scattering cross sections, to ascertain the effects of the cluster environment on the processes involved in planet formation.

Star cluster disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N-body simulations of cluster-GMC encounters and excellent agreement is found. The fractional mass loss from the cluster is 0.25 times the fractional energy gain. This is because 75% of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We derive an expression for the cluster disruption time (t_dis) based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. The disruption time depends on the cluster mass (M_c) and half-mass radius (r_h) as t_dis=2.0 S (M_c/10^4 M_sun)(3.75 pc/r_h)^3 Gyr, with S=1 for the solar neighbourhood and inversely proportional to the GMC density. The observed shallow relation between cluster radius and mass gives t_dis a power-law dependence on the mass with index 0.7, similar to that found from observations and from simulations of clusters dissolving in tidal fields (0.62). The constant of 2.0 Gyr is about a factor of 3.5 shorter than found from earlier simulations of clusters dissolving under the combined effect of galactic tidal field and stellar evolution. It is somewhat higher than the observationally determined value of 1.3 Gyr. It suggests, however, that the combined effect of tidal field and encounters with GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC encounters can also explain the (very) short disruption time that was observed for star clusters in the central region of M51, since there rho_n is an order of magnitude higher than in the solar neighbourhood.

Triggered planet formation in young stellar clusters

AbstractConventional planet formation models via coagulation of planetesimals require timescales in the range of several 10 or even 100 Myr in the outer regions of a protoplanetary disk. But according to observational data, the lifetime of a protoplanetary disk is limited to about 6 Myr. Therefore the existence of Uranus and Neptune poses a problem. Planet formation via gravitational instability may be a solution for this discrepancy. We present a parameter study of the possibility of gravitationally triggered disk instability. Using a restricted N‐body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1 M⊙ can probably induce gravitational instabilities in the pre‐planetary solar disk for prograde passages with minimum separations below 80‐170 AU. Inclined and retrograde encounters lead to similar results but require slightly closer passages. Such encounter distances are quite likely in young moderately massive star clusters. The induced gravitational instabilities may lead to enhanced planetesimal formation in the outer regions of the protoplanetary disk, and could therefore be relevant for the formation of Uranus and Neptune. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Induced planet formation in stellar clusters: a parameter study of star-disc encounters

We present a parameter study of the possibility of tidally triggered disk instability. Using a restricted N-body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1 M ⊙ can probably induce gravitational instabilities in the pre-planetary solar disk for prograde passages with minimum separations below 80–170 AU for isothermal or adiabatic disks. Inclined and retrograde encounters lead to similar results but require slightly closer passages. Such encounter distances are quite likely in young moderately massive star clusters (Scally & Clarke 2001; Bonnell et al. 2001). The induced gravitational instabilities may lead to enhanced planetesimal formation in the outer regions of the protoplanetary disk, and could therefore be relevant for the existence of Uranus and Neptune, whose formation timescale of about 100 Myr (Wuchterl et al. 2000) is inconsistent with the disk lifetimes of about a few Myr according to observational data by Haisch et al. (2001). The relatively small gas/solid ratio in Uranus and Neptune can be matched if the perturbing fly-by occurred after early gas depletion of the solar system, i.e. when the solar system was older than about 5 Myr. We also confirm earlier results by Heller (1993) that the observed 7 degree tilt of the solar equatorial plane relative to the ecliptic plane could be the consequence of such a close encounter.