arXiv subjects

Adrián Rodríguez

Publications and source records attributed to Adrián Rodríguez.

17 recordsLinked to original sources

arXiv2023

Dynamical characterization of the 6/1 mean motion resonance between Quaoar's ring and Weywot

Recently, it has been reported the discovery of a dense ring around the trans-Neptunian object 50000 Quaoar. The ring particles seem to be very close to the 6/1 mean motion resonance with Weywot, the only known satellite in the system. In this work we investigate the dynamical environment in the close vicinity of the 6/1 orbital resonance in the context of the restricted three body problem. We aim to analyze whether, in view of observational constraints, the ring could be effectively evolving in resonant motion with the satellite. Through the technique of dynamical maps we identify and characterize the 6/1 mean motion resonance, finding that the main location of the resonance deviates by only $29$ km from the central part of the ring. This difference lies within the 3$σ$ confidence level, considering the uncertainties in the observational parameters. We also show that the Weywot's eccentricity plays a significant role in the dynamical structure of the 6/1 resonance. The results show that the resonance width is smaller than the estimated ring's width. Under assumption of a ring with eccentricity smaller than 0.05, clumping of test particles appears at the position of the different resonant multiplets, considering the nominal value of Weywot's eccentricity. This is in agreement with observations, which indicate that the estimated resonance width ($\leq$ 10 km) is comparable with the narrow and dense arc of material within Quaoar's ring. Our results may be an indicative that the 6/1 resonance resonance plays a key role in confining the arc ring.

astro-ph.EP↗

arXiv2023

Mapping the structure of the planetary 2:1 mean motion resonance. The TOI-216, K2-24, and HD27894 systems

Mean motion resonances (MMR) are a frequent phenomenon among extrasolar planetary systems. Current observations indicate that many systems have planets that are close to or inside the 2:1 MMR, when the orbital period of one of the planets is twice the other. Analytical models to describe this particular MMR can only be reduced to integrable approximations in a few specific cases. While there are successful approaches to the study of this MMR in the case of very elliptic and/or very inclined orbits using semi-analytical or semi-numerical methods, these may not be enough to completely understand the resonant dynamics. In this work, we propose to apply a well-established numerical method to assess the global portrait of the resonant dynamics, which consists in constructing dynamical maps. Combining these maps with the results from a semi-analytical method, helps to better understand the underlying dynamics of the 2:1 MMR, and to identify the behaviors that can be expected in different regions of the phase space and for different values of the model parameters. We verify that the family of stable resonant equilibria bifurcate from symmetric to asymmetric librations, depending on the mass ratio and eccentricities of the resonant planets pair. This introduces new structures in the phase space, that turns the classical V-shape of the MMR, in the semi-major axis vs. eccentricity space, into a sand clock shape. We construct dynamical maps for three extrasolar planetary systems, TOI-216, HD27894, and K2-24, and discuss their phase space structure and their stability in the light of the orbital fits available in the literature.

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arXiv2023

The orbit of Aegaeon and the 7:6 Mimas-Aegaeon resonance

Aegaeon (S/2008 S 1) is the last satellite discovered by the Cassini spacecraft at the end of the 2000s. Like the satellites Methone and Anthe, it is involved in mean motion resonance with the mid-sized Mimas. In this work, we give a detailed analysis of the current orbit of Aegaeon identifying the resonant, secular and long-term perturbations due to Mimas and the oblateness of Saturn, and the effects of Tethys. For this task, we perform thousands of numerical simulations of full equations of motion of ensembles of small bodies representing clones of Aegaeon. We have mapped the domain of the 7:6 Mimas-Aegaeon resonance in the phase space of the semi-major axis and eccentricity. It displays a large area dominated by regular motions associated with the 7:6 corotation resonance surrounded by chaotic layers. Aegaeon is currently located very close to the periodic orbit of the resonance, which extends up to eccentricities $\sim0.025$ centered at semi-major axis $\sim168,028$ km. We show that the current orbit of Aegaeon has an important forced component in eccentricity due to the 7:6 resonance. The orbital inclination of Aegaeon has a non-negligible forced value due to long-term perturbations of Mimas. These two forced modes explain the complex perturbed orbit of Aegaeon without requiring the co-existence of multiple resonances.

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arXiv2022

Production of hot Jupiter candidates from high-eccentricity mechanisms for different initial planetary mass configurations

Hot Jupiters (HJs) are giant planets with orbital periods of the order of a few days with semimajor axis within $\sim$0.1 au. Several theories have been invoked in order to explain the origin of this type of planets, one of them being the high-eccentricity migration. This migration can occur through different high-eccentricity mechanisms. Our investigation focused on six different kinds of high-eccentricity mechanisms, namely, direct dispersion, coplanar, Kozai-Lidov, secular chaos, E1 and E2 mechanisms. We investigated the efficiency of these mechanisms for the production of HJ candidates in multi-planet systems initially tightly-packed in the semimajor axis, considering a large set of numerical simulations of the exact equations of motion in the context of the N-body problem. In particular, we analyzed the sensitivity of our results to the initial number of planets, the initial semimajor axis of the innermost planetary orbit, the initial configuration of planetary masses, and to the inclusion of general relativity effects. We found that the E1 mechanism is the most efficient in producing HJ candidates both in simulations with and without the contribution of general relativity, followed by the Kozai-Lidov and E2 mechanisms. Our results also revealed that, except for the initial equal planetary mass configuration, the E1 mechanism was notably efficient in the other initial planetary mass configurations considered in this work. Finally, we investigated the production of HJ candidates with prograde, retrograde, and alternating orbits. According to our statistical analysis, the Kozai-Lidov mechanism has the highest probability of significantly exciting the orbital inclinations of the HJ candidates.

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arXiv2022

The current orbit of Atlas (SXV)

With the success of the Cassini-Huygens mission, the dynamic complexity surrounding natural satellites of Saturn began to be elucidated. New ephemeris could be calculated with a higher level of precision, which made it possible to study in detail the resonant phenomena and, in particular, the 54:53 near mean-motion resonance between Prometheus and Atlas. For this task, we have mapped in details the domains of the resonance with dense sets of initial conditions and distinct ranges of parameters. Our initial goal was to identify possible regions in the phase space of Atlas for which some critical angles, associated with the 54:53 mean motion have a stable libration. Our investigations revealed that there is no possibility for the current Atlas orbital configuration to have any regular behavior since it is in a chaotic region located at the boundary of the 54:53 mean-motion resonance phase space. This result is in accordance with previous works (Cooper et al. 2015, Renner et al. 2016). In this work, we generalize such investigations by showing detailed aspects of the Atlas-Prometheus 54:53 mean-motion resonance, like the extension of the chaotic layers, the thin domain of the center of the 54:53 resonance, the proximity of other neighborhood resonances, among other secondary conclusions. In particular, we have also shown that even in the deep interior of the resonance, it is difficult to map periodic motion of the resonant pair for very long time spans.

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arXiv2022

The current orbit of Methone (S/2004 S 1)

The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to interactions with Mimas and the oblateness of the planet. This work is devoted to Methone, which is currently involved in a 15:14 Mean-Motion Resonance with Mimas. We give an in deep study the current orbit of Methone by analyzing and identifying the short, resonant and long-term gravitational perturbations on its orbit. In addition, we perform numerical integrations of full equations of motion of ensembles of close-in small bodies orbiting the non-central field of Saturn. Spectral analyses of the orbits and interpretation of them in dynamical maps allow us to describe the orbit and the dynamics of Methone in view of resonant and long-term dynamics. We show that the current geometric orbit of Methone is aligned with Mimas' due to a forced resonant component in eccentricity, leading to simultaneous oscillations of several critical angles of the expanded disturbing function. Thus, we explain the simultaneous oscillations of four critical arguments associated to the resonance. The mapping of the Mimas-Methone resonance shows that the domains of the 15:14 Mimas-Methone resonance are dominated by regular motions associated to the Corotation resonance located at eccentricities lower than $\sim 0.015$ and osculating semi-major axis in the interval 194,660-194,730 km. Methone is currently located deeply within this site.

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arXiv2021

Past and present dynamics of the circumbinary moons in the Pluto-Charon system

The Pluto-Charon (PC) pair is usually thought of as a binary in the dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motions resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical architecture of the system. Several formation mechanisms for the PC system have been proposed. Our goal is to analyse the past and current orbital dynamics of the satellite system. We study the past and current dynamics of the PC system through a large set of numerical integrations of the exact equations of motion, accounting for the gravitational interactions of the PC binary with the small moons and the tidal evolution, modelled by the constant time lag approach. We construct the stability maps in a pseudo-Jacobian coordinate system. In addition, considering a more realistic model, which accounts for the zonal harmonic $J_2$ of the Pluto's oblateness and the accreting mass of Charon, we investigate the tidal evolution of the whole system. Our results show that, in the chosen reference frame, the current orbits of all satellites are nearly circular, nearly planar and nearly resonant with Charon that can be seen as an indicator of the convergent dissipative migration experimented by the system in the past. We verify that, under the assumption that Charon completes its formation during the tidal expansion, the moons can safely cross the main MMRs, without their motions being strongly excited and consequently ejected. In the more realistic scenario proposed here, the small moons survive the tidal expansion of the PC binary, without having to invoke the hypothesis of the resonant transport. Our results point out that the possibility to find additional small moons in the PC system cannot be ruled out.

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arXiv2021

Dynamical stability in the vicinity of Saturnian small moons. The cases of Aegaeon, Methone, Anthe and Pallene

In this work we analyze the orbital evolution and the dynamical stability in the vicinity of the small Saturnian moons Aegaeon, Methone, Anthe and Pallene. We numerically resolve the exact equations of motions to investigate the orbital motion of thousands of test particles within and near to the domain of the 7/6, 14/15, 10/11 mean motion resonances of Aegaeon, Methone and Anthe with Mimas, respectively. We show that, for massless small moons, the orbits of particles initially restricted to the resonant domains remain stable for at least $10^4$ yr. We also conduct numerical simulations considering Aegaeon, Methone, Anthe and Pallene as massive bodies. The results show that most particles undergo significant perturbations in their orbital motions, ultimately destabilizing in timescales of a few hundreds of years or even less through collisions with the four small moons. In addition, we also simulate the orbital evolution of test particles initially distributed in form of arc around Aegaeon, Methone and Anthe. We show that the initial arcs are dynamically eroded on timescales of hundreds of years, allowing us to constraint the timescales for which gravitational forces operate to remove particles from the observed arcs.

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arXiv2019

Primordial migration of co-orbital satellites as a mechanism for the horseshoe orbit of Janus-Epimetheus

We analyze the orbital motion of two natural satellites initially in co-orbital configuration with a third (guiding) satellite embedded into a circumplanetary gas disc and undergoing tidal interactions with the central planet. By solving the exact equations of motion, including the dissipative effects and the mutual gravitational perturbations, we investigate the configuration of the system soon after the guiding satellite is disrupted when crossing the Roche limit with the central planet during its orbital decay. The application is done for the system composed of Saturn and the two small co-orbital satellites Janus and Epimetheus. We perform a large number of numerical simulations, varying the mass of the hypothetical guiding satellite, Saturn's tidal quality factor and the initial configuration and the masses of the small satellites. Analyzing the orbital configurations of Janus and Epimetheus soon after the disruption of the guiding satellite, we obtain that the mutual horseshoe co-orbital orbits appear as a natural outcome of the numerical simulations.

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arXiv2014

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, including chaotic motions and transient events. We apply our model to some already detected eccentric hot Jupiters and super-Earths in planar configurations. We show that when the relaxation time of the deformation is larger than the orbital period, spin-orbit equilibria arise naturally at half-integers of the mean motion, even for gaseous planets. In the case of super-Earths, these equilibria can be maintained for very low values of eccentricity. Our method can also be used to study planets with complex internal structures and other rheologies.

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arXiv2013

Tidal evolution of close-in exoplanets in co-orbital configurations

In this paper, we study the behavior of a pair of co-orbital planets, both orbiting a central star on the same plane and undergoing tidal interactions. Our goal is to investigate final orbital configurations of the planets, initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting tidal evolution. The study is done in the form of purely numerical simulations of the exact equations of motions accounting for gravitational and tidal forces. The results obtained show that, at least for equal mass planets, the combined effects of the resonant and tidal interactions provoke the orbital instability of the system, often resulting in collision between the planets. We first discuss the case of two hot-super-Earth planets, whose orbital dynamics can be easily understood in the frame of our semi-analytical model of the 1/1 MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.

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arXiv2013

An estimation of distribution algorithm with adaptive Gibbs sampling for unconstrained global optimization

In this paper is proposed a new heuristic approach belonging to the field of evolutionary Estimation of Distribution Algorithms (EDAs). EDAs builds a probability model and a set of solutions is sampled from the model which characterizes the distribution of such solutions. The main framework of the proposed method is an estimation of distribution algorithm, in which an adaptive Gibbs sampling is used to generate new promising solutions and, in combination with a local search strategy, it improves the individual solutions produced in each iteration. The Estimation of Distribution Algorithm with Adaptive Gibbs Sampling we are proposing in this paper is called AGEDA. We experimentally evaluate and compare this algorithm against two deterministic procedures and several stochastic methods in three well known test problems for unconstrained global optimization. It is empirically shown that our heuristic is robust in problems that involve three central aspects that mainly determine the difficulty of global optimization problems, namely high-dimensionality, multi-modality and non-smoothness.

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arXiv2012

Angular momentum exchange during secular migration of two-planet systems

We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or planet-satellite) tidal interactions and interactions of a planet with a gaseous disc. We show that each migration mechanism is characterized by a specific law of orbital angular momentum exchange. Calculating stationary solutions of the conservative secular problem and taking into account the orbital angular momentum leakage, we trace the evolutionary routes followed by the planet pairs during the migration process. This procedure allows us to recover the dynamical history of two-planet systems and constrain parameters of the involved physical processes.

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arXiv2012

Spin-orbit coupling for tidally evolving super-Earths

We investigate the spin behavior of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyze the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behavior by evolving towards synchronization through successive temporary resonant trappings.

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arXiv2011

Tidal decay and orbital circularization in close-in two-planet systems

The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the exact equations of motion through the numerical simulation of the system evolution. In addition to the orbital decay and circularization, we show that the final configuration of the system is affected by the shrink of the inner orbit. Our second approach consist in the analysis of the stationary solutions of mean equations of motion based on a Hamiltonian formalism. We consider the case of a hot super-Earth planet with a more massive outer companion. As a real example, the CoRoT-7 system is analyzed solving the exact and mean equations of motion. The star-planet tidal interaction produces orbital decay and circularization of the orbit of CoRoT-7b. In addition, the long-term tidal evolution is such that the eccentricity of CoRoT-7c is also circularized and a pair of final circular orbits is obtained. A curve in the space of eccentricities can be constructed through the computation of stationary solutions of mean equations including dissipation. The application to CoRoT-7 system shows that the stationary curve agrees with the result of numerical simulations of exact equations. A similar investigation performed in a super-Earth-Jupiter two-planet system shows that the doubly circular state is accelerated when there is a significant orbital migration of the inner planet, in comparison with previous results were migration is neglected.

astro-ph.EP↗

arXiv2011

Modeling the secular evolution of migrating planet pairs

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semi-major axes and the planets move inward/outward the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion is determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

astro-ph.EP↗

arXiv2009

Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited

This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

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