scholarly journals Numerical Simulations of Dense Collisional Systems with Extended Distribution of Particle Sizes

1992 ◽  
Vol 152 ◽  
pp. 103-108
Author(s):  
H. Salo
Keyword(s):  
Time Scale ◽  
Local Equilibrium ◽  
Dynamical Evolution ◽  
Simulation Method ◽  
Orbital Evolution ◽  
Momentum Exchange ◽  
Local Equilibrium State ◽  
Radial Evolution ◽  
Self Gravity ◽  
Radial Behaviour

The dynamical evolution of dense planetary rings, such as Saturn's rings, is mainly governed by the mutual impacts between macroscopic icy particles. The local equilibrium state is determined by the energy loss in partially inelastic impacts and the viscous gain of energy from the systematic velocity field. Due to frequent impacts the time-scale for the establishment of local energy equilibrium is very short, as compared to the time-scale for radial evolution, which is determined by viscous spreading, and in some cases also by the angular momentum exchange with external satellites. Therefore, local and radial behaviour can, to a large extent be studied separately. This fact is utilized by the local simulation method (Wisdom and Tremaine, 1988; Salo, 1991), following the orbital evolution in a small co-moving region inside the rings with periodic boundary conditions. Compared to previous simulation methods (Salo, 1987) this enables much higher surface density. With the presently attainable number of particles (up to several thousands), realistic modeling of dense regions is possible, taking simultaneously into account the particle size distribution, rotation of particles, as well as vertical self-gravity. By combining several local simulations with different surface densities, it is possible to deduce the expected radial behaviour as well.

scholarly journals Orbital evolution of Saturn’s satellites due to the interaction between the moons and the massive rings

2020 ◽  
Vol 640 ◽  
pp. L15
Author(s):  
Ayano Nakajima ◽  
Shigeru Ida ◽  
Yota Ishigaki
Keyword(s):  
Orbital Evolution ◽  
The Self ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Saturn’S Satellites ◽  
Orbital Configuration ◽  
Self Gravity ◽  
Spiral Arm ◽  
Orbital Migration

Context. Saturn’s mid-sized moons (satellites) have a puzzling orbital configuration with trapping in mean-motion resonances with every-other pairs (Mimas-Tethys 4:2 and Enceladus-Dione 2:1). To reproduce their current orbital configuration on the basis of a recent model of satellite formation from a hypothetical ancient massive ring, adjacent pairs must pass first-order mean-motion resonances without being trapped. Aims. The trapping could be avoided by fast orbital migration and/or excitation of the satellite’s eccentricity caused by gravitational interactions between the satellites and the rings (the disk), which are still unknown. In our research we investigate the satellite orbital evolution due to interactions with the disk through full N-body simulations. Methods. We performed global high-resolution N-body simulations of a self-gravitating particle disk interacting with a single satellite. We used N ∼ 105 particles for the disk. Gravitational forces of all the particles and their inelastic collisions are taken into account. Results. Dense short-wavelength wake structure is created by the disk self-gravity and a few global spiral arms are induced by the satellite. The self-gravity wakes regulate the orbital evolution of the satellite, which has been considered as a disk spreading mechanism, but not as a driver for the orbital evolution. Conclusions. The self-gravity wake torque to the satellite is so effective that the satellite migration is much faster than was predicted with the spiral arm torque. It provides a possible model to avoid the resonance capture of adjacent satellite pairs and establish the current orbital configuration of Saturn’s mid-sized satellites.

scholarly journals Growth after the streaming instability

2019 ◽  
Vol 624 ◽  
pp. A114 ◽  
Author(s):  
Beibei Liu ◽  
Chris W. Ormel ◽  
Anders Johansen
Keyword(s):  
Dynamical Evolution ◽  
Bimodal Distribution ◽  
Stokes Number ◽  
Volume Density ◽  
Mass Star ◽  
Type I ◽  
Solar Mass ◽  
Streaming Instability ◽  
Two Component ◽  
Self Gravity

Context. Streaming instability is a key mechanism in planet formation, clustering pebbles into planetesimals with the help of self-gravity. It is triggered at a particular disk location where the local volume density of solids exceeds that of the gas. After their formation, planetesimals can grow into protoplanets by feeding from other planetesimals in the birth ring as well as by accreting inwardly drifting pebbles from the outer disk. Aims. We aim to investigate the growth of planetesimals into protoplanets at a single location through streaming instability. For a solar-mass star, we test the conditions under which super-Earths are able to form within the lifetime of the gaseous disk. Methods. We modified the Mercury N-body code to trace the growth and dynamical evolution of a swarm of planetesimals at a distance of 2.7 AU from the star. The code simulates gravitational interactions and collisions among planetesimals, gas drag, type I torque, and pebble accretion. Three distributions of planetesimal sizes were investigated: (i) a mono-dispersed population of 400 km radius planetesimals, (ii) a poly-dispersed population of planetesimals from 200 km up to 1000 km, (iii) a bimodal distribution with a single runaway body and a swarm of smaller, 100 km size planetesimals. Results. The mono-dispersed population of 400 km size planetesimals cannot form protoplanets of a mass greater than that of the Earth. Their eccentricities and inclinations are quickly excited, which suppresses both planetesimal accretion and pebble accretion. Planets can form from the poly-dispersed and bimodal distributions. In these circumstances, it is the two-component nature that damps the random velocity of the large embryo through the dynamical friction of small planetesimals, allowing the embryo to accrete pebbles efficiently when it approaches 10−2 M⊕. Accounting for migration, close-in super-Earth planets form. Super-Earth planets are likely to form when the pebble mass flux is higher, the disk turbulence is lower, or the Stokes number of the pebbles is higher. Conclusions. For the single site planetesimal formation scenario, a two-component mass distribution with a large embryo and small planetesimals promotes planet growth, first by planetesimal accretion and then by pebble accretion of the most massive protoplanet. Planetesimal formation at single locations such as ice lines naturally leads to super-Earth planets by the combined mechanisms of planetesimal accretion and pebble accretion.

scholarly journals On the survivability of planets in young massive clusters and its implication of planet orbital architectures in globular clusters

2019 ◽  
Vol 489 (3) ◽  
pp. 4311-4321 ◽  
Author(s):  
Maxwell X Cai ◽  
S Portegies Zwart ◽  
M B N Kouwenhoven ◽  
Rainer Spurzem
Keyword(s):  
Globular Cluster ◽  
Time Scale ◽  
Globular Clusters ◽  
Semimajor Axis ◽  
Stellar System ◽  
Dynamical Evolution ◽  
The Other ◽  
Crossing Time ◽  
Massive Clusters ◽  
Full Investigation

ABSTRACT As of 2019 August, among the more than 4000 confirmed exoplanets, only one has been detected in a globular cluster (GC) M4. The scarce of exoplanet detections motivates us to employ direct N-body simulations to investigate the dynamical stability of planets in young massive clusters (YMC), which are potentially the progenitors of GCs. In an N = 128 k cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets (a ≥ 20 au) will be ejected within a time-scale of 10 Myr. Interestingly, more than $70{{\ \rm per\ cent}}$ of planets with a < 5 au survive in the 100 Myr simulations. Ignoring planet–planet scattering and tidal damping, the survivability at t Myr as a function of initial semimajor axis a0 in au in such a YMC can be described as fsurv(a0, t) = −0.33log10(a0)(1 − e−0.0482t) + 1. Upon ejection, about $28.8{{\ \rm per\ cent}}$ of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing time-scale. The other FFPs will remain bound to the cluster potential, but the subsequent dynamical evolution of the stellar system can result in the delayed ejection of FFPs from the host cluster. Although a full investigation of planet population in GCs requires extending the simulations to multiGyr, our results suggest that wide-orbit planets and free-floating planets are unlikely to be found in GCs.

scholarly journals Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy

Science ◽  
2019 ◽  
Vol 365 (6456) ◽  
pp. 926-929 ◽  
Author(s):  
Richard E. Zeebe ◽  
Lucas J. Lourens
Keyword(s):  
Solar System ◽  
Time Scale ◽  
Dynamical Evolution ◽  
Resonance Transition ◽  
Fundamental Frequencies ◽  
Thermal Maximum ◽  
Astronomical Time ◽  
Geologic Data

Astronomical calculations reveal the Solar System’s dynamical evolution, including its chaoticity, and represent the backbone of cyclostratigraphy and astrochronology. An absolute, fully calibrated astronomical time scale has hitherto been hampered beyond ~50 million years before the present (Ma) because orbital calculations disagree before that age. Here, we present geologic data and a new astronomical solution (ZB18a) showing exceptional agreement from ~58 to 53 Ma. We provide a new absolute astrochronology up to 58 Ma and a new Paleocene–Eocene boundary age (56.01 ± 0.05 Ma). We show that the Paleocene–Eocene Thermal Maximum (PETM) onset occurred near a 405-thousand-year (kyr) eccentricity maximum, suggesting an orbital trigger. We also provide an independent PETM duration (170 ± 30 kyr) from onset to recovery inflection. Our astronomical solution requires a chaotic resonance transition at ~50 Ma in the Solar System’s fundamental frequencies.

scholarly journals Dynamical evolution of objects on highly elliptical orbits near high-order resonance zones

2014 ◽  
Vol 9 (S310) ◽  
pp. 168-169
Author(s):  
Eduard D. Kuznetsov ◽  
Stanislav O. Kudryavtsev
Keyword(s):  
Dynamical Evolution ◽  
Major Axis ◽  
Orbital Evolution ◽  
High Order ◽  
Semi Major Axis ◽  
Order Resonance ◽  
High Order Resonance ◽  
Elliptical Orbits ◽  
Pass Through

AbstractBoth analytical and numerical results are used to study high-order resonance regions in the vicinity of Molnya-type orbits. Based on data of numerical simulations, long-term orbital evolution are studied for objects in highly elliptical orbits depending on their area-to-mass ratio. The Poynting–Robertson effect causes a secular decrease in the semi-major axis of a spherically symmetrical satellite. Under the Poynting–Robertson effect, objects pass through the regions of high-order resonances. The Poynting–Robertson effect and secular perturbations of the semi-major axis lead to the formation of weak stochastic trajectories.

scholarly journals Thermodynamic aspects of describing the contribution of spontaneous magnetism of electrons to the Hall resistance

2018 ◽  
Vol 185 ◽  
pp. 01017 ◽  
Author(s):  
Vsevolod Okulov ◽  
Evgeny Pamyatnykh
Keyword(s):  
Equilibrium State ◽  
Spontaneous Magnetization ◽  
Local Equilibrium ◽  
Electron System ◽  
Hall Resistance ◽  
Orbital Interaction ◽  
Spin Orbital ◽  
Conduction Current ◽  
Local Equilibrium State ◽  
Current Densities

On the base of the analysis of quantum-statistical description of the magnetization of electron system containing the spontaneous spin polarization contribution there were found the magnetization and conduction current densities in equilibrium state. It has been shown that equilibrium surface conduction current ensures realization of demagnetization effects but in local equilibrium state determines local equilibrium part of the Hall conductivity. As a result one is given the justification of influence of the spontaneous magnetization on galvanomagnetic effects, which is not related to spin-orbital interaction.

scholarly journals Dynamical Behaviour of Asteroids in the 4:1 Resonance

1999 ◽  
Vol 172 ◽  
pp. 377-378 ◽  
Author(s):  
Francisco López-García ◽  
Adrian Brunini
Keyword(s):  
Time Scale ◽  
Initial Conditions ◽  
Major Axis ◽  
Orbital Evolution ◽  
Dynamical Behaviour ◽  
Three Dimensions ◽  
Symplectic Integrators ◽  
Minor Planets ◽  
Semi Major Axis ◽  
Secular Resonance

We study the dynamics of mean motion resonance with Jupiter in the 4:1 gap using only gravitational methods. This mechanism is capable of explaining this Kirkwood gap in an uniform way (see Ferraz-Mello, 1994; Ferraz-Mello et al., 1994; Moons, 1997; Yoshikawa, 1989). We considered the asteroidal motion in two and three dimensions and we carried out our investigations integrating numerically the full equations of motion and taking into account Mars, Jupiter and Saturn as disturbing planets. The orbital evolution of asteroids was obtained considering the elements variation. The numerical investigations were carried out using symplectic integrators. These integrations were stopped when the asteroid had close encouters with Mars or Jupiter, this occurs when the distance between the planet and the asteroid is of the order of 0.01 AU or less, or when the eccentricity increases up to 0.9. We studied real and fictitious asteroids on a time scale of 5 × 107 yr. The initial osculating elements of perturbing planets and their inverse masses were taken from the Ephemerides of Minor Planets (EMP) at the epoch of JD 2450000.5. The initial data corresponding to the real asteroids were also taken from the EMP. The starting elements of fictitious asteroids were, in all analyzed cases, a = acrit = 2.064; AU, i = 2°.5 and e = 0.01 (in the majority of cases). The other initial elements are shown in Table II. We have also studied fictitious asteroids with i = 0°, a = acrit and e = 0.01 (Table I). The present analysis leads to the following results: (1) The motions are unstable. The eccentricity, in the majority of cases, has very large increase. It may grow up to 0.9 in 106 yr. The semi major axis has large variations then, owing to both effects some fictitious asteroids reach the 3:1 resonance while others reach 7:2 resonance in a few million years, they are very chaotic regions. (2) The eccentricities of fictitious asteroids become large by the effect of the secular resonance v6, i.e. when (ϖ − ϖSat) ≅ 0, the rate of this resonance is 26.217”/year with period ~ 4.9 × 104 years (Bretagnon, 1974). (3) The fictitious asteroids studied with a = acrit, e < 0.05 and i < 3° are removed of this gap mainly by the effects of the secular resonances v6 and v16 (see Moons and Morbidelli, 1995; Williams, 1969). (4) There are close encounters with Mars or eventually with the Earth (not considered here) in a time scale of 106 - 107 yr. (5) For certain initial conditions some fictitious asteroids are temporally captured by Mars and in some cases for a long time. (6) If a = acrit,e = 0.3 and the inclination is less than 3°, Mars and asteroid’s perihelion are very close ( ~ 0.06AU ). This situation helps the capture. (7) The (a,e)-plane was used to determine the dynamical behaviour of all asteroids and we found that the 4:1 resonance is very strong. The Lyapunov times are very short.

scholarly journals Building Planets with Dusty Gas

2004 ◽  
Vol 213 ◽  
pp. 231-234
Author(s):  
S. T. Maddison ◽  
R. J. Humble ◽  
J. R. Murray
Keyword(s):  
Solar Nebula ◽  
Numerical Technique ◽  
Dynamical Evolution ◽  
Gas Flows ◽  
Dusty Gas ◽  
Dust Distribution ◽  
Self Gravity ◽  
Gas Medium

We have developed a new numerical technique for simulating dusty-gas flows. Our code incorporates gas hydrodynamics, self-gravity and dust drag to follow the dynamical evolution of a dusty-gas medium. We have incorporated several descriptions for the drag between gas and dust phases and can model flows with submillimetre, centimetre and metre size “dust”. We present calculations run on the APAC1 supercomputer following the evolution of the dust distribution in the pre-solar nebula.

Dynamical evolution of near-Earth objects

2020 ◽  
Author(s):  
Athanasia Toliou ◽  
Mikael Granvik
Keyword(s):  
Semimajor Axis ◽  
Dynamical Evolution ◽  
Orbital Evolution ◽  
Derived Categories ◽  
Asteroid Belt ◽  
The Sun ◽  
Escape Route ◽  
Perihelion Distance ◽  
Main Asteroid Belt ◽  
Near Earth Objects

&lt;p&gt;&lt;span&gt;An apparent discrepancy between the number of observed near-Earth objects (NEOs) with small perihelion distances (q) and the number of objects that models &lt;br /&gt;predict, has led to the conclusion that asteroids get destroyed at non-trivial distances from the Sun. Consequently, there must be a, possibly thermal, &lt;br /&gt;mechanism at play, responsible for breaking up asteroids asteroids in such orbits.&lt;br /&gt;&lt;br /&gt;We studied the dynamical evolution of ficticious NEOs whose perihelion distance reaches below the average disruption distance q_dis=0.076 au, as suggested by &lt;br /&gt;Granvik et al. (2016). To that end, we used the orbital integrations of objects that escaped from the main asteroid belt (Granvik et al. 2017), and entered the &lt;br /&gt;near-Earth region (Granvik et al. 2018). First, we investigated a variety of mechanisms that can lower the perihelion distance of an object to a small-enough &lt;br /&gt;value. In particular, we considered mean-motion resonances with Jupiter, secular resonances with Jupiter and Saturn (v_5 and v_6) and also the Kozai resonance.&lt;br /&gt;&lt;br /&gt;We developed a code that calculates the evolution of the critical argument of all the relevant resonances and identifies librations during the last stages of &lt;br /&gt;an object's orbital evolution, namely, just before q=q_dis. Any subsequent evolution of the object was disregarded, since we considered it disrupted. The &lt;br /&gt;accuracy of our model is ~96%.&lt;br /&gt;&lt;br /&gt;In addition, we measured the dynamical 'lifetimes' of NEOs when they orbit the innermost parts of the inner Solar System. More precisely, we calculated the &lt;br /&gt;total time it takes for the q of each object to go from 0.4 au to q_dis (&amp;#964;_lq). The outer limit of this range was chosen such because it is a) the approximate &lt;br /&gt;semimajor axis of Mercury, and b) an absence of sub-meter-sized boulders with q smaller than this distance has been proposed by Wiegert et al (2020). Combining &lt;br /&gt;this measure with the recorded resonances, we can get a sense of the timescale of each q-lowering mechanism.&lt;br /&gt;&lt;br /&gt;Next, for a more rigorous study of the evolution of the NEOs with q&lt;0.4 au, we divided this region in bins and measured the relevant time they spend at &lt;br /&gt;different distances from the Sun. Together with the total time spent in each bin, we kept track of the number of times that q entered one of the bins. &lt;br /&gt;Finally, we computed the actual time each object spends in each bin during its evolution, i.e., the total time it spends in a specific range in radial &lt;br /&gt;heliocentric distance.&lt;br /&gt;&lt;br /&gt;By following this approach, we derived categories of typical evolutions of NEOs that reach the average disruption distance. In addition, since we have the &lt;br /&gt;information concerning the escape route from the main asteroid belt followed by each NEO, we linked the q-lowering mechanism and the associated orbital &lt;br /&gt;evolutions in the range below the orbit of Mercury, to their source regions and thus were able to draw conclusions abour their physical properties.&lt;/span&gt;&lt;/p&gt;

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