MAMA: An Algebraic Map for the Secular Dynamics of Planetesimals in Tight Binary Systems

We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system (TBS). The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disk. The gas disk is assumed eccentric with a constant precession rate. Gravitational interactions between the planetesimals are ignored. All bodies are assumed coplanar. A comparison with full N-body simulations shows that the map is of the order of 100 times faster, while preserving all the main characteristics of the full system. In a second part of the work, we apply MAMA to the \gamma-Cephei, searching for friendly scenarios that may explain the formation of the giant planet detected in this system. For low-mass protoplanetary disks, we find that a low-eccentricity static disk aligned with the binary yields impact velocities between planetesimals below the disruption threshold. All other scenarios appear hostile to planetary formation

The Resonance Overlap and Hill Stability Criteria Revisited

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances which does not allow for a simple global expression for stability. We propose that, for a given perturbing mass $m_1$ and initial eccentricity $e$, there are actually two critical values of the semimajor axis. All values $a a_{\rm unstable}$ are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity, and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte

The stability in the most external region of the Oort Cloud: The evolution of the ejected comets

In this paper, we present a study about the dynamical effects of the Galaxy on the external region of the Oort Cloud. The aims of this paper are: i) to determine an outer limit for the Oort Cloud; and ii) to analyse the dynamical behaviour of the most external objects of the Cloud and how they are ejected from the Solar System. This is undertaken by following the temporal evolution of massless test particles in the Galactic environment of the solar neighbourhood. Here we show that the effect of the perturbations from the Galactic tide in the particles is similar to that find for the evolution of wide binary stars population. Moreover, in the Oort Cloud we found a dynamical structure around 10 5 au conformed by objects unbound of the Sun. This structure allows us to define a transition region of stability and an outer boundary for the Oort Cloud, and it is also in agreement with previous results about the disruption of wide binary stars.Comment: Accepted for publishing in MNRAS. 13 pages, 9 figures, 2 table

A new scenario for the origin of the 3/2 resonant system HD 45364

We revise the model for the origin of the HD 45364 exoplanetary system proposed by Rein et al. (2010, A&A, 510, A4), which is currently known to host two planets close to the 3/2 mean-motion resonance (MMR). We show that due to the high surface density of the protoplanetary disk needed for type III migration, this model can only lead to planets in a quasi-resonant regime of motion and thus is not consistent with the resonant configuration obtained by Correia et al. (2009, A&A, 496, 521). Although both resonant and quasi-resonant solutions are statistically indistinguishable with respect to radial velocity measurements, their distinct dynamical behavior is intriguing. We used the semi-analytical model to confirm the quantitative difference between two configurations. To form a system that evolves inside the 3/2 resonance, we developed a different model. Our scenario includes an interaction between different (but slower) planetary migration types, planet growth, and gap formation in the protoplanetary disk. The evolutionary path was chosen due to a detailed analysis of the phase space structure in the vicinity of the 3/2 MMR that employed dynamical mapping techniques. The outcomes of our simulations are able to very closely reproduce the 3/2 resonant dynamics obtained from the best fit presented by Correia et al. In addition, by varying the strength of the eccentricity damping, we can also simulate the quasi-resonant configuration similar to that reported in Rein et al. We furthermore show that our scenario is reliable with respect to the physical parameters involved in the resonance-trapping process. However, our scenario can only be confirmed with additional radial velocities measurements.Fil: Correa Otto, J. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Michtchenko, T. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina

A new insight into the Galactic potential: a simple secular model for the evolution of binary systems in the solar neighbourhood

Context. Among the main effects that the Milky Way exerts in binary systems, the Galactic tide is the only one that is not probabilistic and can be deduced from a potential. Therefore, it is possible to perform an analysis of the global structure of the phase space of binary systems in the solar neighbourhood using the Galactic potential. Aims. The aim of this work is to obtain a simple model to study the collisionless dynamical evolution of generic wide binaries systems in the solar neighbourhood. Methods. Through an averaging process, we reduced the three-dimensional potential of the Galaxy to a secular one-degree of freedom model. The accuracy of this model was tested by comparing its predictions with numerical simulations of the exact equations of motion of a two-body problem disturbed by the Galaxy. Results. Using the one-degree of freedom model, we developed a detailed dynamical study, finding that the secular Galactic tide period changes as a function of the separation of the pair, which also gives a dynamical explanation for the arbitrary classification between wide and tight binaries. Moreover, the secular phase space for a generic gravitationally bound pair is similar to the dynamical structure of a Lidov-Kozai resonance, but surprisingly this structure is independent of the masses and semimajor axis of the binary system. Thus, the Galactic potential is able to excite the initially circular orbit of binary systems to high values of eccentricity, which has important implications for studies of binary star systems (with and without exoplanets), comets, and Oort cloud objects.Facultad de Ciencias Astronómicas y Geofísica

Formation and evolution of the two 4/3 resonant giants planets in HD 200946

It has been suggested that HD 200964 is the first exoplanetary system with two Jovian planets evolving in the 4/3 mean- motion resonance. Previous scenarios to simulate the formation of two giant planets in the stable 4/3 resonance configuration have failed. Moreover, the orbital parameters available in the literature point out an unstable configuration of the planetary pair. The purpose of this paper is i) to determine the orbits of the planets from the RV measurements and update the value of the stellar mass (1.57 M), ii) to analyse the stability of the planetary evolution in the vicinity and inside the 4/3 MMR, and iii) to elaborate a possible scenario for the formation of systems in the 4/3 MMR. The results of the formation simulations are able to very closely reproduce the 4/3 resonant dynamics of the best-fit config- uration obtained in this paper. Moreover, the confidence interval of the fit matches well with the very narrow stable region of the 4/3 mean-motion resonance. The formation process of the HD 200964 system is very sensitive to the planetary masses and protoplanetary disk parameters. Only a thin, flat disk allows the embryo-sized planets to reach the 4/3 resonant configuration. The stable evolution of the resonant planets is also sensitive to the mass of the central star, because of overlapping high-order resonances inside the 4/3 resonance. Regardless of the very narrow domain of stable motion, the confidence interval of our fit closely matches the stability area

Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei

The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for Gamma-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for Gamma-Cephei may affect the dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies around 50 % for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.Comment: 11 pages, 9 figure

Mapping the ν⊙\nu_\odot Secular Resonance for Retrograde Irregular Satellites

Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $\nu_\odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to the secular angle $\theta = \varpi - \varpi_\odot$, where $\varpi$ is the longitude of pericenter of the satellite and $\varpi_\odot$ corresponds to the (fixed) planetocentric orbit of the Sun. Our study is performed in the restricted three-body problem, where the satellites are considered as massless particles around a massive planet and perturbed by the Sun. Depending on the initial conditions, the resonance presents a diversity of possible resonant modes, including librations of $\theta$ around zero (as found for Sinope and Pasiphae) or 180 degrees, as well as asymmetric librations (e.g. Narvi). Symmetric modes are present in all giant planets, although each regime appears restricted to certain values of the satellite inclination. Asymmetric solutions, on the other hand, seem absent around Neptune due to its almost circular heliocentric orbit. Simulating the effects of a smooth orbital migration on the satellite, we find that the resonance lock is preserved as long as the induced change in semimajor axis is much slower compared to the period of the resonant angle (adiabatic limit). However, the librational mode may vary during the process, switching between symmetric and asymmetric oscillations. Finally, we present a simple scaling transformation that allows to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.Comment: 11 pages, 13 figure

Dynamics of Planetesimals due to Gas Drag from an Eccentric Precessing Disk

We analyze the dynamics of individual kilometer-size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non-linear gas drag stemming from an eccentric gas disk with a finite precession rate. We consider several precession rates and eccentricities for the gas, and compare the results with a static disk in circular orbit. The disk precession introduces three main differences with respect to the classical static case: (i) The equilibrium secular solutions generated by the gas drag are no longer fixed points in the averaged system, but limit cycles with frequency equal to the precession rate of the gas. The amplitude of the cycle is inversely dependent on the body size, reaching negligible values for $\sim 50$ km size planetesimals. (ii) The maximum final eccentricity attainable by small bodies is restricted to the interval between the gas eccentricity and the forced eccentricity, and apsidal alignment is no longer guaranteed for planetesimals strongly coupled with the gas. (iii) The characteristic timescales of orbital decay and secular evolution decrease significantly with increasing precession rates, with values up to two orders of magnitude smaller than for static disks. Finally, we apply this analysis to the $\gamma$-Cephei system and estimate impact velocities for different size bodies and values of the gas eccentricity. For high disk eccentricities, we find that the disk precession decreases the velocity dispersion between different size planetesimals, thus contributing to accretional collisions in the outer parts of the disk. The opposite occurs for almost circular gas disks, where precession generates an increase in the relative velocities.Comment: 11 pages, 9 figures. Accepted in MNRA

Spectral domain optical coherence tomography in patients after successful management of postoperative endophthalmitis following cataract surgery by pars plana vitrectomy.

BACKGROUND: Acute severe postoperative endophthalmitis may lead to severe vision loss. The aim of this study was the analysis of macular microstructure imaged by spectral domain optical coherence tomography in patients after pars plana vitrectomy due to postcataract endophthalmitis. METHODS: A cross sectional study was carried out in 17 patients who had cataract surgery in both eyes and underwent unilateral pars plana vitrectomy due to postcataract endophthalmitis. Postoperative best corrected visual acuity was determined in both eyes. Evaluation of macular thickness, macular volume, peripapillary retinal nerve fiber layer thickness and choroidal thickness using enhanced depth imaging technique was performed by spectral domain optical coherence tomography. The measurements obtained in the operated eye were compared to the fellow eye by Wilcoxon matched pair test. Correlation test was performed by Spearman rank order. RESULTS: A mean postoperative best corrected visual acuity of 63 +/- 30 ETDRS letters versus 75 +/- 21 letters was achieved in the study and fellow eyes, respectively, after a mean of 5.3 +/- 4.5 months (p = 0.1). The mean macular thickness was 320.6 +/- 28.8 mum SD in the study eyes compared to 318.4 +/- 18.8 mum in the fellow eyes (p = 0.767). No differences were noted in macular volume (p = 0.97) and in peripapillary retinal nerve fiber layer thickness (p = 0.31). Choroidal thickness was significantly lower in the study eyes compared to the fellow eyes (p = 0.018). Epiretinal membrane was found in 7 eyes after endophthalmitis, while in the fellow eyes only in 3 cases (p = 0.13, Fisher's exact test). CONCLUSION: Choroidal thickness decreased significantly after endophthalmitis, but there was no functional correlation with the changes in choroidal microstructure. The development of epiretinal membranes may be associated with either vitrectomy or endophthalmitis in the history. Absence of other significant structural and morphological findings shows that successful treatment may guarantee good clinical results even in long term after this severe postoperative complication