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 Physics , 2012, DOI: 10.1088/0004-637X/750/1/43 Abstract: Neptune's dynamical history shaped the current orbits of Kuiper belt objects (KBOs), leaving clues to the planet's orbital evolution. In the "classical" region, a population of dynamically "hot" high-inclination KBOs overlies a flat "cold" population with distinct physical properties. Simulations of qualitatively different histories for Neptune -including smooth migration on a circular orbit or scattering by other planets to a high eccentricity - have not simultaneously produced both populations. We explore a general Kuiper belt assembly model that forms hot classical KBOs interior to Neptune and delivers them to the classical region, where the cold population forms in situ. First, we present evidence that the cold population is confined to eccentricities well below the limit dictated by long-term survival. Therefore Neptune must deliver hot KBOs into the long-term survival region without excessively exciting the eccentricities of the cold population. Imposing this constraint, we explore the parameter space of Neptune's eccentricity and eccentricity damping, migration, and apsidal precession. We rule out much of parameter space, except where Neptune is scattered to a moderately eccentric orbit (e > 0.15) and subsequently migrates a distance Delta aN=1-6 AU. Neptune's moderate eccentricity must either damp quickly or be accompanied by fast apsidal precession. We find that Neptune's high eccentricity alone does not generate a chaotic sea in the classical region. Chaos can result from Neptune's interactions with Uranus, exciting the cold KBOs and placing additional constraints. Finally, we discuss how to interpret our constraints in the context of the full, complex dynamical history of the solar system.
 Physics , 2009, DOI: 10.1111/j.1365-2966.2009.15243.x Abstract: We present the results of detailed dynamical simulations of the effect of the migration of the four giant planets on both the transport of pre-formed Neptune Trojans, and the capture of new Trojans from a trans-Neptunian disk. We find that scenarios involving the slow migration of Neptune over a large distance (50Myr to migrate from 18.1AU to its current location) provide the best match to the properties of the known Trojans. Scenarios with faster migration (5Myr), and those in which Neptune migrates from 23.1AU to its current location, fail to adequately reproduce the current day Trojan population. Scenarios which avoid disruptive perturbation events between Uranus and Neptune fail to yield any significant excitation of pre-formed Trojans (transported with efficiencies between 30 and 98% whilst maintaining the dynamically cold nature of these objects). Conversely, scenarios with periods of strong Uranus-Neptune perturbation lead to the almost complete loss of such pre-formed objects. In these cases, a small fraction (~0.15%) of these escaped objects are later recaptured as Trojans prior to the end of migration, with a wide range of eccentricities (<0.35) and inclinations (<40 deg). In all scenarios (including those with such disruptive interaction between Uranus and Neptune) the capture of objects from the trans-Neptunian disk (through which Neptune migrates) is achieved with efficiencies between ~0.1 and ~1%. The captured Trojans display a wide range of inclinations (<40 deg for slow migration, and <20 deg for rapid migration) and eccentricities (<0.35), and we conclude that, given the vast amount of material which undoubtedly formed beyond the orbit of Neptune, such captured objects may be sufficient to explain the entire Neptune Trojan population. (Shortened version)
 Physics , 2009, DOI: 10.1016/j.icarus.2009.06.008 Abstract: We explore conventional Neptune migration model with one additional planet of mass at 0.1-2.0 Me. This planet inhabited in the 3:2 mean motion resonance with Neptune during planet migration epoch, and then escaped from the Kuiper belt when Jovian planets parked near the present orbits. Adding this extra planet and assuming the primordial disk truncated at about 45 AU in the conventional Neptune migration model, it is able to explain the complex structure of the observed Kuiper belt better than the usual Neptune migration model did in several respects. However, numerical experiments imply that this model is a low-probability event. In addition to the low probability, two features produced by this model may be inconsistent with the observations. They are small number of low-inclination particles in the classical belt, and the production of a remnant population with near-circular and low-inclination orbit within a = 50-52 AU. According to our present study, including one extra planet in the conventional Neptune migration model as the scenario we explored here may be unsuitable because of the low probability, and the two drawbacks mentioned above, although this model can explain better several features which is hard to produce by the conventional Neptune migration model. The issues of low-probability event and the lack of low-inclination KBOs in the classical belt are interesting and may be studied further under a more realistic consideration.
 Physics , 2003, DOI: 10.1016/j.icarus.2003.09.021 Abstract: We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. The single greatest episode of loss ejects nearly 75% of existing Neptune Trojans and occurs just prior to Neptune reaching its final orbit.
 Physics , 2011, DOI: 10.1088/0004-637X/746/2/171 Abstract: The current dynamical structure of the Kuiper belt was shaped by the orbital evolution of the giant planets, especially Neptune, during the era following planet formation, when the giant planets may have undergone planet-planet scattering and/or planetesimal-driven migration. Numerical simulations of this process, while reproducing many properties of the belt, fail to generate the high inclinations and eccentricities observed for some objects while maintaining the observed dynamically "cold" population. We present the first of a three-part parameter study of how different dynamical histories of Neptune sculpt the planetesimal disk. Here we identify which dynamical histories allow an in situ planetesimal disk to remain dynamically cold, becoming today's cold Kuiper belt population. We find that if Neptune undergoes a period of elevated eccentricity and/or inclination, it secularly excites the eccentricities and inclinations of the planetesimal disk. We demonstrate that there are several well-defined regimes for this secular excitation, depending on the relative timescales of Neptune's migration, the damping of Neptune's orbital inclination and/or eccentricity, and the secular evolution of the planetesimals. We model this secular excitation analytically in each regime, allowing for a thorough exploration of parameter space. Neptune's eccentricity and inclination can remain high for a limited amount of time without disrupting the cold classical belt. In the regime of slow damping and slow migration, if Neptune is located (for example) at 20 AU, then its eccentricity must stay below 0.18 and its inclination below 6{\deg}.
 Physics , 2014, DOI: 10.1051/0004-6361/201322041 Abstract: Through a semi-analytic approach of the Kozai resonance inside an MMR, we show phase diagrams (e,{\omega}) that suggest the possibility of a scattered particle, after being captured in an MMR with Neptune, to become a detached object. We ran several numerical integrations with thousands of particles perturbed by the four major planets, and there are cases with and without Neptune's residual migration. These were developed to check the semi-analytic approach and to better understand the dynamical mechanisms that produce the detached objects close to an MMR. The numerical simulations with and without a residual migration for Neptune stress the importance of a particular resonance mode, which we name the hibernating mode, on the formation of fossilized detached objects close to MMRs. When considering Neptune's residual migration we are able to show the formation of detached orbits. These objects are fossilized and cannot be trapped in the MMRs again. We find a ratio of the number of fossilized objects with moderate perihelion distance (35 < q < 40 au) to the number of objects with high perihelion distance (q > 40 au) as 3.0/1 for objects close to the 2:5, and 1.7/1 for objects close to the 1:3 resonance. We estimate that the two fossilized population have a total mass between 0.1 and 0.3 Pluto's mass.
 Physics , 1999, DOI: 10.1086/300891 Abstract: The existence of the Oort Comet Cloud, the Kuiper Belt, and plausible inefficiencies in planetary core formation, all suggest that there was once a residual planetesimal disk of mass 10-100 Earth-masses in the vicinity of the giant planets following their formation. Since removal of this disk requires an exchange of orbital energy and angular momentum with the planets, significant planetary migration can ensue. The planet migration phenomenon is examined numerically by evolving the orbits of the giant planets while they are embedded in a planetesimal disk having a mass of M_d=10 to 200 Earth-masses. We find that Saturn, Uranus, and Neptune evolve radially outwards as they scatter the planetesimals, while Jupiter's orbit shrinks as it ejects mass. Higher-mass disks result in more rapid and extensive planet migration. If orbit expansion and resonance trapping by Neptune is invoked to explain the eccentricities of Pluto and its cohort of Kuiper Belt Objects at Neptune's 3:2 mean-motion resonance, then our simulations suggest that a disk mass of order M_d~50 Earth-masses is required to expand Neptune's orbit by ~7 AU in order to pump up Plutino eccentricities to e~0.3. Such planet migration implies that the initial Solar System was more compact in the past, with the Jupiter-Neptune separation having been smaller by about 30%. The planetesimal disk is also the source of the Oort Cloud of comets. Using the results of our simulations together with a simple treatment of Oort Cloud dynamics, we estimate that ~12 Earth-masses of disk material was initially deposited in the Oort Cloud, of which ~4 Earth-masses will persist over the age of the Solar System. The majority of these comets originated from the Saturn-Neptune region of the solar nebula.
 Sergei Nayakshin Physics , 2015, Abstract: I argue that feedback is as important to formation of planets as it is to formation of stars and galaxies. Energy released by massive solid cores puffs up pre-collapse gas giant planets, making them vulnerable to tidal disruptions by their host stars. I find that feedback is the ultimate reason for some of the most robust properties of the observed exoplanet populations: the rarity of gas giants at all separations from $\sim 0.1$ to $\sim 100$~AU, the abundance of $\sim 10 M_\oplus$ cores but dearth of planets more massive than $\sim 20 M_\oplus$. Feedback effects can also explain (i) rapid assembly of massive cores at large separations as needed for Uranus, Neptune and the suspected HL Tau planets; (ii) the small core in Jupiter yet large cores in Uranus and Neptune; (iii) the existence of rare "metal monster" planets such as CoRoT-20b, a gas giant made of heavy elements by up to $\sim 50$\%.
 Physics , 2010, DOI: 10.1111/j.1365-2966.2010.16381.x Abstract: In this work, we investigate the dynamical stability of pre-formed Neptune Trojans under the gravitational influence of the four giant planets in compact planetary architectures, over 10 Myr. In our modelling, the initial orbital locations of Uranus and Neptune (aN) were varied to produce systems in which those planets moved on non-resonant orbits, or in which they lay in their mutual 1:2, 2:3 and 3:4 mean-motion resonances (MMRs). In total, 420 simulations were carried out, examining 42 different architectures, with a total of 840000 particles across all runs. In the non-resonant cases, the Trojans suffered only moderate levels of dynamical erosion, with the most compact systems (those with aN less than or equal 18 AU) losing around 50% of their Trojans by the end of the integrations. In the 2:3 and 3:4 MMR scenarios, however, dynamical erosion was much higher with depletion rates typically greater than 66% and total depletion in the most compact systems. The 1:2 resonant scenarios featured disruption on levels intermediate between the non-resonant cases and other resonant scenarios, with depletion rates of the order of tens of percent. Overall, the great majority of plausible pre-migration planetary architectures resulted in severe levels of depletion of the Neptunian Trojan clouds. In particular, if Uranus and Neptune formed near their mutual 2:3 or 3:4 MMR and at heliocentric distances within 18 AU (as favoured by recent studies), we found that the great majority of pre-formed Trojans would have been lost prior to Neptune's migration. This strengthens the case for the great bulk of the current Neptunian Trojan population having been captured during that migration.
 Physics , 2009, DOI: 10.1051/0004-6361:200810774 Abstract: Precise radial-velocity measurements with the HARPS spectrograph reveal the presence of two planets orbiting the solar-type star HD45364. The companion masses are 0.187 Mjup and 0.658 Mjup, with semi-major axes of 0.681 AU and 0.897 AU, and eccentricities of 0.168 and 0.097, respectively. A dynamical analysis of the system further shows a 3:2 mean motion resonance between the two planets, which prevents close encounters and ensures the stability of the system over 5 Gyr. This is the first time that such a resonant configuration has been observed for extra-solar planets, although there is an analogue in our Solar System formed by Neptune and Pluto. This singular planetary system may provide important constraints on planetary formation and migration scenarios.
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