Eccentricity Oscillations Research Articles

ECCENTRICITY GROWTH AND ORBIT FLIP IN NEAR-COPLANAR HIERARCHICAL THREE-BODY SYSTEMS

The dynamical evolution of a hierarchical three body system is well characterized by the eccentric Kozai-Lidov mechanism, where the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40-140 degree) can produce long timescale modulations that drives the eccentricity to extremely large value and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ~180 degree, rolling over its major axis. The ~180 degree flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exo-planetary systems. In addition, we also show that this mechanism has the potential to enhance the tidal disruption or collision rates for different systems.

ORBITAL DYNAMICS OF MULTI-PLANET SYSTEMS WITH ECCENTRICITY DIVERSITY

Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based on the radial velocity residuals. We show that the two known planets in each system exchange angular momentum through secular oscillations of their eccentricities. We calculate the amplitude and timescale for these eccentricity oscillations and associated periastron precession. We further demonstrate the effect of mutual orbital inclinations on the amplitude of high-frequency eccentricity oscillations. Finally, we discuss the implications of these oscillations in the context of possible origin scenarios for unequal eccentricities.

Rapid eccentricity oscillations and the mergers of compact objects in hierarchical triples

Kozai-Lidov (KL) oscillations can accelerate compact object mergers via gravitational wave (GW) radiation by driving the inner binaries of hierarchical triples to high eccentricities. We perform direct three-body integrations of high mass ratio compact object triple systems using Fewbody including post-Newtonian terms. We find that the inner binary undergoes rapid eccentricity oscillations (REOs) on the timescale of the outer orbital period which drive it to higher eccentricities than secular theory would otherwise predict, resulting in substantially reduced merger times. For a uniform distribution of tertiary eccentricity ($e_2$), ~40% of systems merge within ~1-2 eccentric KL timescales whereas secular theory predicts that only ~20% of such systems merge that rapidly. This discrepancy becomes especially pronounced at low $e_2$, with secular theory overpredicting the merger time by many orders of magnitude. We show that a non-negligible fraction of systems have eccentricity > 0.8 when they merge, in contrast to predictions from secular theory. Our results are applicable to high mass ratio triple systems containing black holes or neutron stars. In objects in which tidal effects are important, such as white dwarfs, stars, and planets, REOs can reduce the tidal circularization timescale by an order of magnitude and bring the components of the inner binary into closer orbits than would be possible in the secular approximation.

FORMING CIRCUMBINARY PLANETS: N -BODY SIMULATIONS OF KEPLER-34

Observations of circumbinary planets orbiting very close to the central stars have shown that planet formation may occur in a very hostile environment, where the gravitational pull from the binary should be very strong on the primordial protoplanetary disk. Elevated impact velocities and orbit crossings from eccentricity oscillations are the primary contributors towards high energy, potentially destructive collisions that inhibit the growth of aspiring planets. In this work, we conduct high resolution, inter-particle gravity enabled N-body simulations to investigate the feasibility of planetesimal growth in the Kepler-34 system. We improve upon previous work by including planetesimal disk self-gravity and an extensive collision model to accurately handle inter-planetesimal interactions. We find that super-catastrophic erosion events are the dominant mechanism up to and including the orbital radius of Kepler-34(AB)b, making in-situ growth unlikely. It is more plausible that Kepler-34(AB)b migrated from a region beyond 1.5 AU. Based on the conclusions that we have made for Kepler-34 it seems likely that all of the currently known circumbinary planets have also migrated significantly from their formation location with the possible exception of Kepler-47(AB)c.

Greatly enhanced eccentricity oscillations in quadruple systems composed of two binaries: implications for stars, planets and transients

We study the orbital evolution of hierarchical quadruple systems composed of two binaries on a long mutual orbit, where each binary acts as a Kozai–Lidov (KL) perturber on the other. We find that the coupling between the two binaries qualitatively changes the behaviour of their KL cycles. The binaries can experience coherent eccentricity oscillations as well as excursions to very high eccentricity that occur over a much larger fraction of the parameter space than in triple systems. For a ratio of outer to inner semimajor axes of 10–20, about 30–50 per cent of equal-mass quadruples reach eccentricity 1 − e < 10−3 in one of the binaries. This is about 4–12 times more than for triples with equivalent parameters. Orbital ‘flips’ and collisions without previous tidal interaction are similarly enhanced in quadruples relative to triples. We argue that the frequency of evolutionary paths influenced by KL cycles is comparable in the triple and quadruple populations even though field quadruples are a factor of ∼5 less frequent than triples. Additionally, quadruples might be a non-negligible source of triples and provide fundamentally new evolutionary outcomes involving close binaries, mergers, collisions and associated transients, which occur without any fine tuning of parameters. Finally, we study the perturbations to a planetary orbit due to a distant binary and we find that the fraction of orbital flips is a factor of 3–4 higher than for the corresponding triple system given our fiducial parameters with implications for hot Jupiters and star–planet collisions.

Chaotic dust dynamics and implications for the hemispherical color asymmetries of the Uranian satellites

Dust grains generated by the Uranian irregular satellites will undergo chaotic large-amplitude eccentricity oscillations under the simultaneous action of radiation forces and the highly misaligned quadrupole potentials of the oblate planet and distant Sun. From a suite of orbital histories, we estimate collision probabilities of dust particles with the regular satellites and argue that this process may explain the observed hemispherical color asymmetries of the outermost four regular satellites of Uranus.

PLUTINO DETECTION BIASES, INCLUDING THE KOZAI RESONANCE

Because of their proximity within the transneptunian region, the plutinos (objects in the 3:2 mean-motion resonance with Neptune) are numerous in flux-limited catalogs, and well-studied theoretically. We perform detailed modelling of the on-sky detection biases for plutinos, with special attention to those that are simultaneously in the Kozai resonance. In addition to the normal 3:2 resonant argument libration, Kozai plutinos also show periodic oscillations in eccentricity and inclination, coupled to the argument of perihelion (omega) oscillation. Due to the mean-motion resonance, plutinos avoid coming to pericenter near Neptune's current position in the ecliptic plane. Because Kozai plutinos are restricted to certain values of omega, perihelion always occurs out of the ecliptic plane, biasing ecliptic surveys against finding these objects. The observed Kozai plutino fraction (fkoz) has been measured by several surveys, finding values between 8% and 25%, while the true fkoz has been predicted to be between 10% and 30% by different giant planet migration simulations. We show that the observed fkoz varies widely depending on the ecliptic latitude and longitude of the survey, so debiasing to find the true ratio is complex. Even a survey that covers most or all of the sky will detect an apparent Kozai fraction that is different from the true fkoz. We present a map of the on-sky plutino Kozai fraction that would be detected by all-sky flux-limited surveys. This will be especially important for the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS) and Large Synoptic Survey Telescope (LSST) projects, which may detect large numbers of plutinos as they sweep the sky. The Kozai fraction and the distribution of the orbital elements of Kozai plutinos may be a diagnostic of giant planet migration; future migration simulations should provide details on their resonant Kozai populations.

DYNAMICAL INSTABILITIES IN HIGH-OBLIQUITY SYSTEMS

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68.875 degrees. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. We find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this is occurs because radiation pressure modifies the equilibrium Laplace plane.

Debris disks as signposts of terrestrial planet formation

Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We simulate planetary system evolution around Sun-like stars from initial conditions that comprise: an inner disk of planetesimals and planetary embryos, three giant planets at Jupiter-Saturn distances, and a massive outer planetesimal disk. We then calculate dust production rates and debris disk SEDs assuming that each planetesimal particle represents an ensemble of smaller bodies in collisional equilibrium. We predict a strong correlation between the presence of terrestrial planets and debris disks, mediated by the giant planets. Strong giant planet instabilities destroy all rocky material - including fully-formed terrestrial planets if the instabilities occur late - along with the icy planetesimals. Stable or weakly unstable systems allow terrestrial planets to accrete and significant dust to be produced in their outer regions. Stars older than ~100 Myr with bright cold dust emission (at ~70 microns) signpost the dynamically calm environments conducive to efficient terrestrial accretion. We predict that while the typical eccentricities of terrestrial planets are small, there should exist a novel class of terrestrial planet system whose single planet undergoes large amplitude oscillations in eccentricity and inclination. By scaling to the observed semimajor axis distribution of giant exoplanets, we estimate that terrestrial exoplanets in the same systems should be a few times more abundant at 0.5 AU than giant or terrestrial exoplanets at 1 AU. Finally, we discuss the Solar System, which appears to be unusual in combining a rich terrestrial planet system with a low dust content.

GENERALIZED MILANKOVITCH CYCLES AND LONG-TERM CLIMATIC HABITABILITY

Although the Earth's orbit is never far from circular, terrestrial planets around other stars might experience substantial changes in eccentricity that could lead to climate changes, including possible "phase transitions" such as the snowball transition (or its opposite). There is evidence that Earth has gone through at least one globally frozen, "snowball" state in the last billion years, which it is thought to have exited after several million years because global ice-cover shut off the carbonate-silicate cycle, thereby allowing greenhouse gases to build up to sufficient concentration to melt the ice. Due to the positive feedback caused by the high albedo of snow and ice, susceptibility to falling into snowball states might be a generic feature of water-rich planets with the capacity to host life. This paper has two main thrusts. First, we revisit one-dimensional energy balance climate models as tools for probing possible climates of exoplanets, investigate the dimensional scaling of such models, and introduce a simple algorithm to treat the melting of the ice layer on a globally-frozen planet. We show that if a terrestrial planet undergoes Milankovitch-like oscillations of eccentricity that are of great enough magnitude, it could melt out of a snowball state. Second, we examine the kinds of variations of eccentricity that a terrestrial planet might experience due to the gravitational influence of a giant companion. We show that a giant planet on a sufficiently eccentric orbit can excite extreme eccentricity oscillations in the orbit of a habitable terrestrial planet. More generally, these two results demonstrate that the longterm habitability (and astronomical observables) of a terrestrial planet can depend on the detailed architecture of the planetary system in which it resides.

TIDAL BREAKUP OF BINARY STARS AT THE GALACTIC CENTER AND ITS CONSEQUENCES

The tidal breakup of binary star systems by the supermassive black hole (SMBH) in the center of the galaxy has been suggested as the source of both the observed sample of hypervelocity stars (HVSs) in the halo of the Galaxy and the S-stars that remain in tight orbits around Sgr A*. Here, we use a post-Newtonian N-body code to study the dynamics of main-sequence binaries on highly elliptical bound orbits whose periapses lie close to the SMBH, determining the properties of ejected and bound stars as well as collision products. Unlike previous studies, we follow binaries that remain bound for several revolutions around the SMBH, finding that in the case of relatively large periapses and highly inclined binaries the Kozai resonance can lead to large periodic oscillations in the internal binary eccentricity and inclination. Collisions and mergers of the binary elements are found to increase significantly for multiple orbits around the SMBH, while HVSs are primarily produced during a binary's first passage. This process can lead to stellar coalescence and eventually serve as an important source of young stars at the galactic center.

Induced Kozai Migration and Formation of Close-in Planets in Binaries

AbstractMany recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20%, and presumably a larger fraction, of the known extrasolar planetary systems are associated with one or more stellar companions. These stellar companions normally exist at large distances from the planetary systems (typical projected binary separations are 102–104AU) and are often faint (ranging from F to T spectral types). Yet, secular cyclic angular momentum exchange with these distant stellar companions can significantly alter the orbital configuration of the planets around the primaries. One of the most interesting and fairly common outcomes seen in numerical simulations is the opening of a large mutual inclination angle between the planetary orbits, forced by differential nodal precessions caused by the binary companion. The growth of the mutual inclination angle between planetary orbits induces additional large-amplitude eccentricity oscillations of the inner planet due to the quadrupole gravitational perturbation by the outer planet. This eccentricity oscillation may eventually result in the orbital decay of the inner planet through tidal friction, as previously proposed as Kozai migration or Kozai cycles with tidal friction (KCTF). This orbital decay mechanism induced by the binary perturbation and subsequent tidal dissipation may stand as an alternative formation channel for close-in extrasolar planets.

Three Disk Oscillation Modes of Rotating Magnetized Neutron Stars

We discuss three specific modes of accretion disks around rotating magnetized neutron stars which may explain the separations of the kilohertz quasi-periodic oscillations (QPOs) seen in low-mass X-ray binaries. The existence of these modes requires that there be a maximum in the angular velocity of the accreting material, and that the fluid be in stable, nearly circular motion near this maximum rather than moving rapidly toward the star or out of the disk plane into funnel flows. It is currently not known whether these conditions occur, but we are exploring this with 3D magnetohydrodynamic simulations and will report the results elsewhere. The first mode is a corotation mode which is radially trapped in the vicinity of the maximum of the disk rotation rate and is unstable. The second mode, relevant to relatively slowly rotating stars, is a magnetically driven eccentric (m = 1) oscillation of the disk excited at a Lindblad radius in the vicinity of the maximum of the disk rotation. The third mode, relevant to rapidly rotating stars, is a magnetically coupled eccentric (m = 1) and an axisymmetric (m = 0) radial disk perturbation which has an inner Lindblad radius also in the vicinity of the maximum of the disk rotation. We suggest that the first mode is associated with the upper QPO frequency νu, the second with the lower QPO frequency νl = νu - ν*, and the third with the lower QPO frequency νl = νu - ν*/2, where ν* is the star's rotation rate.

Planet dispersal in binary systems during transient multiple star phases

Aims. If a significant fraction of binary star systems spent some time as inclined triple systems, either during their formation process or as the outcome of several close dynamical encounters in a crowded stellar environemnt, then the number of planets in binaries would be significantly lower than around single stars. The stellar chaotic phase preceding the instability of the triple system and the wide oscillations in eccentricity and inclination of the companion star due to the high mutual inclination between the companion and the singleton would quickly eject planets orbiting the binary in S-type orbits. Methods. We perform numerical simulations of the dynamical evolution of hierarchical triple star systems with planets hosted around the primary star of the inner binary. Different values of mutual inclination, binary separation and singleton initial semimajor axis are explored in a statistical way. Results. We find that a significant mutual inclination i m between the singleton and the binary is a key factor for instability of the planetary system. When i m is larger than ~$40^{\circ}$ the fraction of planets in the binary surviving the chaotic phase of the triple declines dramatically. The combination of eccentricity and inclination oscillations of the binary companion induced by the secular perturbations of the singleton and the sequence of close encounters preceding the ejection of one star fully destabilize a planetary system extending beyond 1 AU from the star. For i m around $90^{\circ}$ the percentage of surviving planets is lower than 20% for all binaries with a semimajor axis smaller than 200 AU. Conclusions. The frequency of planets in binaries with low separation may be strongly reduced by the residence of the pair in the past in a temporary inclined hierarchical triple.

The superorbital variability and triple nature of the X-ray source 4U 1820-303

We perform a comprehensive analysis of the superorbital modulation in the ultracompact X-ray source 4U 1820‐303, consisting of a white dwarf accreting on to a neutron star. Based on RXTE data, we measure the fractional amplitude of the source superorbital variability (with a ∼170-d quasi-period) in the folded and averaged light curves, and find it to be by a factor of ∼2. As proposed before, the superorbital variability can be explained by oscillations of the binary eccentricity. We now present detailed calculations of the eccentricity-dependent flow through the inner Lagrangian point, and find a maximum of the eccentricity of � 0.004 is sufficient to explain the observed fractional amplitude. We then study hierarchical triple models yielding the required quasi-periodic eccentricity oscillations through the Kozai process. We find the resulting theoretical light curves to match well the observed ones. We constrain the ratio of the semimajor axes of the outer and inner systems, the component masses and the inclination angle between the inner and outer orbits. Last but not least, we discover a remarkable and puzzling synchronization between the observed period of the superorbital variability (equal to the period of the eccentricity oscillations in our model) and the period of the general-relativistic periastron precession of the binary.

Kozai resonance model for Sagittarius A* stellar orbits

AbstractWe study a possibility of tidal disruptions of stars orbiting a supermassive black hole due to eccentricity oscillations driven by Kozai's mechanism. We apply the model to conditions relevant for the Galactic Centre where we consider two different sources of the perturbation to the central potential, which trigger the resonance mechanism. Firstly, it is a disc of young massive stars orbiting Sgr A* atr≳ 0.08 pc, and, secondly, a molecular circumnuclear disc. Each of the two possibilities appears to be capable of exciting eccentricities to values sufficient for the tidal disruption of ∼100 stars from the nuclear stellar cluster on a time-scale of 0.1–10 Myrs. Tidally disrupted stars may cause periods of increased accretion activity of Sgr A*.

High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets is their high orbital eccentricities. Observations have shown that at least 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism, because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e=0.1-0.6).

The Kozai Mechanism and the Evolution of Binary Supermassive Black Holes

We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the outer black hole on the inner binary produces eccentricity oscillations through the Kozai mechanism, and this can substantially reduce the gravitational wave merger time of the inner binary. We numerically calculate the merger time for a wide range of initial conditions and black hole mass ratios, including the effects of octupole interactions in the triple as well as general relativistic periastron precession in the inner binary. The semimajor axes and the mutual inclination of the inner and outer binaries are the most important factors affecting the merger time. We find that for a random distribution of inclination angles and approximately equal mass black holes, it is possible to reduce the merger time of a near circular inner binary by more than a factor of 10 in over 50% of all cases. We estimate that a typical exterior quadrupole moment from surrounding matter in the galaxy may also be sufficient to excite eccentricity oscillations in supermassive black hole binaries and to accelerate black hole mergers.

Techniques for blade tip clearance measurements with capacitiveprobes

This article presents a proven but advantageous concept for bladetip clearance evaluation in turbomachinery. The system is based on heavy dutyprobes and a high frequency (HF) and amplifying electronic unit followed by asignal processing unit. Measurements are taken under high temperature andother severe conditions such as ionization. Every single blade can beobserved. The signals are digitally filtered and linearized in real time. Theelectronic set-up is highly integrated. Miniaturized versions of theelectronic units exist. The small and robust units can be used in turboengines in flight. With several probes at different angles in one radial planefurther information is available. Shaft eccentricity or blade oscillations canbe calculated.

Cyclostratigraphy of a carbonate platform as a tool for high-precision correlation

Mesozoic Carbonate Platforms of Southern Italy are thick (>3000 m) and well-stratified bodies, uplifted by the Late Tertiary–Quaternary deformation of the Northern Gondwanian Continental Margin. They formed mostly in the shallow ramp, open to restricted lagoon and peritidal/supratidal settings, and show a prevailingly cyclic organization, consisting of m-scale shallowing upward units. We think that this cyclicity is demonstrably controlled by the Earth's orbital perturbations (individual cycle duration, hierarchical organization, numerical analysis of their sedimentological and petrophysical features). The genetic mechanisms of the cyclicity have a climatic dictator (allocyclicity), that is coupled with eustatic oscillations evidenced by features related to subaerial exposure, ranging from microkarst to more mature karst and paleosoils. Exposure features are widespread at the top of the cycles, even when these units are formed by only subtidal deposits, suggesting eustatic control. This paper presents a study of three sections of the Aptian in the Campania region of Southern Italy. Here, a total of ≅250 m has been studied at a cm scale. Sections include Serra Sbregavitelli (Central Matese Mountains, ≅160 m, Upper Aptian–Lower Albian); Monte Faito (Sorrento Peninsula, ≅55 m, Upper Aptian–Lower Albian); and Monte Tobenna (Picentini Mountains, ≅35 m, Upper Aptian), the latter two outcropping ≅100 km SSE of the former. The three sections have a hierarchical organization composed of elementary cycles in turn grouped in bundles and superbundles, that have been related respectively to the Earth's short and long orbital eccentricity oscillation, while the elementary cycles mostly appear to correspond to the precession or to a combination of precession and obliquity periodicities. In these successions, the stratal pattern shows a dominant aggradational configuration. The thickness of the cycles and their groups appears environmentally controlled, the thicker cycles being those formed in more open marine settings and vice versa. If analysed in terms of sequence stratigraphy, we may recognize in the superbundles a transgressive and a highstand system tract that, together with maximum flooding surfaces and sequence boundaries, was used to develop chronostratigraphic diagrams and to identify cycle omissions at the bundle and superbundle level. The number and amplitude of omissions in the successions appear proportional to the environmental conditions: the more restricted the water circulation in their original depositional sites, the more prone they were to cycle omissions. The sections of Monte Tobenna and Monte Faito were punctuated by omissions (one of them at the superbundle level), while in Serra Sbregavitelli, we recognize a smaller number of gaps, not reaching the superbundle level. Lower-frequency oscillations (800–2000 k.y.) are also evident and suggest a long-term eustatic oscillation of the same periodicity during the lower Cretaceous. Based on the hierarchical organization of the cyclic successions analysed and taking into account the recognized omissions, we have correlated the Serra Sbregavitelli Section (SSS) with the two distant sections of Monte Tobenna (corresponding to the lower SSS) and of Monte Faito (corresponding to the upper SSS). Using appropriate biostratigraphic markers, a correlation appears possible at the scale of bundles of cycles (≅100 k.y.) and sometimes also at the elementary cycle level (≤50 k.y.).