Formation and Evolution of Planetary Systems in Presence of Highly Inclined Stellar Perturbers

The presence of highly eccentric extrasolar planets in binary stellar systems suggests that the Kozai effect has played an important role in shaping their dynamical architectures. However, the formation of planets in inclined binary systems poses a considerable theoretical challenge, as orbital excitation due to the Kozai resonance implies destructive, high-velocity collisions among planetesimals. To resolve the apparent difficulties posed by Kozai resonance, we seek to identify the primary physical processes responsible for inhibiting the action of Kozai cycles in protoplanetary disks. Subsequently, we seek to understand how newly-formed planetary systems transition to their observed, Kozai-dominated dynamical states. We find that theoretical difficulties in planet formation arising from the presence of a distant companion star, posed by the Kozai effect and other secular perturbations, can be overcome by a proper account of gravitational interactions within the protoplanetary disk. In particular, fast apsidal recession induced by disk self-gravity tends to erase the Kozai effect, and ensure that the disk's unwarped, rigid structure is maintained. Subsequently, once a planetary system has formed, the Kozai effect can continue to be wiped out as a result of apsidal precession, arising from planet-planet interactions. However, if such a system undergoes a dynamical instability, its architecture may change in such a way that the Kozai effect becomes operative. The results presented here suggest that planetary formation in highly inclined binary systems is not stalled by perturbations, arising from the stellar companion. Consequently, planet formation in binary stars is probably no different from that around single stars on a qualitative level. Furthermore, it is likely that systems where the Kozai effect operates, underwent a transient phase of dynamical instability in the past.Comment: 9 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Reconstructing the size distribution of the primordial Main Belt

In this work we aim to constrain the slope of the size distribution of main-belt asteroids, at their primordial state. To do so we turn out attention to the part of the main asteroid belt between 2.82 and 2.96~AU, the so-called "pristine zone", which has a low number density of asteroids and few, well separated asteroid families. Exploiting these unique characteristics, and using a modified version of the hierarchical clustering method we are able to remove the majority of asteroid family members from the region. The remaining, background asteroids should be of primordial origin, as the strong 5/2 and 7/3 mean-motion resonances with Jupiter inhibit transfer of asteroids to and from the neighboring regions. The size-frequency distribution of asteroids in the size range $17<D(\rm{km})<70$ has a slope $q\simeq-1$. Using Monte-Carlo methods, we are able to simulate, and compensate for the collisional and dynamical evolution of the asteroid population, and get an upper bound for its size distribution slope $q=-1.43$. In addition, applying the same 'family extraction' method to the neighboring regions, i.e. the middle and outer belts, and comparing the size distributions of the respective background populations, we find statistical evidence that no large asteroid families of primordial origin had formed in the middle or pristine zones

Kozai resonance in extrasolar systems

Aims. We study the possibility that extrasolar two-planet systems, similar to the ones that are observed, can be in a stable Kozairesonant state, assuming a mutual inclination of the orbital planes of order Imut - 40-60°. Methods. Five known multi-planet systems that are not in mean motion resonance were selected, according to defined criteria, as "possible prototypes" (v Andromedae, HD 12661, HD 169830, HD 741.56, HD 1.55358). We performed a parametric study, integrating several sets of orbits of the two planets, obtained by varying the (unknown) inclination of their orbital planes and their nodal longitudes, thus changing the values of their masses and mutual inclination. We also take into account the reported observational errors on the orbital elements. These numerical results are characterized using analytical secular theory and frequency analysis. Surface of section techniques are also used to distinguish between stable and chaotic motions. Results. Frequency analysis offers a reliable way of identifying the Kozai resonance in a general reference frame, where the argument of the pericenter of the inner planet does not necessarily librate around ±90° as in the frame of the Laplace plane, through the non-coupling of the eccentricities of the two planets. We find that four of the five selected systems (v Andromedae, HD 12661, HD 169830 and HD 741.56) could in principle be in Kozai resonance, as their eccentricities and apsidal orientations are such that the system, enters in the stability region of the Kozai resonance in 20-70% of the cases, provided that their mutual inclination is at least 45°. Thus, a large fraction of the observed multi-planet systems has observed orbital characteristics that are consistent with stable, Kozai-type, motion in 3D. Unstable sets of orbits are also found, due to the chaos that develops around the stability islands of the Kozai resonance. A variety of physical mechanisms that could generate the necessary large mutual, inclinations are discussed, including (a) planet formation; (b) type II migration and resonant interactions during the gas-dominated phase; (c) planetesimal-driven migration and resonance crossing during the gas-free era; (d) multi-planet scattering, caused by the presence of an additional planet.</p

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable DV cost. We simulated the dynamics over 120-200 years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90deg, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed ~40years, mainly around three specific inclination values: 46deg, 56deg, and 68deg; a result compatible with our understanding of MEO secular dynamics. For DV <= 300 m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with e<0.3), reentry times from GNSS altitudes exceed ~70 years, while low-cost (DV ~= 5-35 m/s) graveyard orbits, stable for at lest 200 years, are found for eccentricities up to e~0.018. This investigation was carried out in the framework of the EC-funded "ReDSHIFT" project.Comment: 39 pages, 23 figure

Constructing the secular architecture of the solar system I: The giant planets

Using numerical simulations, we show that smooth migration of the giant planets through a planetesimal disk leads to an orbital architecture that is inconsistent with the current one: the resulting eccentricities and inclinations of their orbits are too small. The crossing of mutual mean motion resonances by the planets would excite their orbital eccentricities but not their orbital inclinations. Moreover, the amplitudes of the eigenmodes characterising the current secular evolution of the eccentricities of Jupiter and Saturn would not be reproduced correctly; only one eigenmode is excited by resonance-crossing. We show that, at the very least, encounters between Saturn and one of the ice giants (Uranus or Neptune) need to have occurred, in order to reproduce the current secular properties of the giant planets, in particular the amplitude of the two strongest eigenmodes in the eccentricities of Jupiter and Saturn.Comment: Astronomy & Astrophysics (2009) in pres

Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture

We study the orbital evolution of the 4 giant planets of our solar system in a gas disk. Our investigation extends the previous works by Masset and Snellgrove (2001) and Morbidelli and Crida (2007, MC07), which focussed on the dynamics of the Jupiter-Saturn system. The only systems that we found to reach a steady state are those in which the planets are locked in a quadruple mean motion resonance (i.e. each planet is in resonance with its neighbor). In total we found 6 such configurations. For the gas disk parameters found in MC07, these configurations are characterized by a negligible migration rate. After the disappearance of the gas, and in absence of planetesimals, only two of these six configurations (the least compact ones) are stable for a time of hundreds of millions of years or more. The others become unstable on a timescale of a few My. Our preliminary simulations show that, when a planetesimal disk is added beyond the orbit of the outermost planet, the planets can evolve from the most stable of these configurations to their current orbits in a fashion qualitatively similar to that described in Tsiganis et al. (2005).Comment: The Astronomical Journal (17/07/2007) in pres

Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune

We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to ~35 AU to the Kuiper belt without excessive inclination excitation. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of ~27 AU and an eccentricity of ~0.3, and that subsequently Neptune's eccentricity damped in ~1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level