Formation of the resonant system HD 60532

Among multi-planet planetary systems there are a large fraction of resonant systems. Studying the dynamics and formation of these systems can provide valuable informations on processes taking place in protoplanetary disks where the planets are thought have been formed. The recently discovered resonant system HD 60532 is the only confirmed case, in which the central star hosts a pair of giant planets in 3:1 mean motion resonance. We intend to provide a physical scenario for the formation of HD 60532, which is consistent with the orbital solutions derived from the radial velocity measurements. Observations indicate that the system is in an antisymmetric configuration, while previous theoretical investigations indicate an asymmetric equilibrium state. The paper aims at answering this discrepancy as well. We performed two-dimensional hydrodynamical simulations of thin disks with an embedded pair of massive planets. Additionally, migration and resonant capture are studied by gravitational N-body simulations that apply properly parametrized non-conservative forces. Our simulations suggest that the capture into the 3:1 mean motion resonance takes place only for higher planetary masses, thus favouring orbital solutions having relatively smaller inclination i=20 degrees. The system formed by numerical simulations qualitatively show the same behaviour as HD 60532. We also find that the presence of an inner disk (between the inner planet and the star) plays a very important role in determining the final configurations of resonant planetary systems. Its damping effect on the inner planet's eccentricity is responsible for the observed antisymmetric state of HD 60532.Comment: 7 pages, 7 figures, Accepted for publication in Astronomy & Astrophysic

Cooperative Dynamics of an Artificial Stochastic Resonant System

We have investigated cooperative dynamics of an artificial stochastic resonant system, which is a recurrent ring connection of neuron-like signal transducers (NST) based on stochastic resonance (SR), using electronic circuit experiments. The ring showed quasi-periodic, tunable oscillation driven by only noise. An oscillation coherently amplified by noise demonstrated that SR may lead to unusual oscillation features. Furthermore, we found that the ring showed synchronized oscillation in a chain network composed of multiple rings. Our results suggest that basic functions (oscillation and synchronization) that may be used in the central pattern generator of biological system are induced by collective integration of the NST element.Comment: 13 pages, 4 figure

Stability and Formation of the Resonant System HD 73526

Based on radial velocity measurements it has been found recently that the two giant planets detected around the star HD 73526 are in 2:1 resonance. However, as our numerical integration shows, the derived orbital data for this system result in chaotic behavior of the giant planets, which is uncommon among the resonant extrasolar planetary systems. We intend to present regular (non-chaotic) orbital solutions for the giant planets in the system HD 73526 and offer formation scenarios based on combining planetary migration and sudden perturbative effects such as planet-planet scattering or rapid dispersal of the protoplanetary disk. A comparison with the already studied resonant system HD 128311, exhibiting similar behavior, is also done. The new sets of orbital solutions have been derived by the Systemic Console (www.oklo.org). The stability of these solutions has been investigated by the Relative Lyapunov indicator, while the migration and scattering effects are studied by gravitational N-body simulations applying non-conservative forces as well. Additionally, hydrodynamic simulations of embedded planets in protoplanetary disks are performed to follow the capture into resonance. For the system HD 73526 we demonstrate that the observational radial velocity data are consistent with a coplanar planetary system engaged in a stable 2:1 resonance exhibiting apsidal corotation. We have shown that, similarly to the system HD 128311, the present dynamical state of HD 73526 could be the result of a mixed evolutionary process melting together planetary migration and a perturbative event.Comment: 12 pages, 14 figures, accepted in A&A, v2: technical change

Suppression of growth by multiplicative white noise in a parametric resonant system

The author studied the growth of the amplitude in a Mathieu-like equation with multiplicative white noise. The approximate value of the exponent at the extremum on parametric resonance regions was obtained theoretically by introducing the width of time interval, and the exponents were calculated numerically by solving the stochastic differential equations by a symplectic numerical method. The Mathieu-like equation contains a parameter $\alpha$ that is determined by the intensity of noise and the strength of the coupling between the variable and the noise. The value of $\alpha$ was restricted not to be negative without loss of generality. It was shown that the exponent decreases with $\alpha$, reaches a minimum and increases after that. It was also found that the exponent as a function of $\alpha$ has only one minimum at $\alpha \neq 0$ on parametric resonance regions of $\alpha = 0$. This minimum value is obtained theoretically and numerically. The existence of the minimum at $\alpha \neq 0$ indicates the suppression of the growth by multiplicative white noise.Comment: The title and the description in the manuscript are change

Resonant dynamics and the instability of anti-de Sitter spacetime

We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing instability of AdS under arbitrarily small perturbations.Comment: 5 pages, 7 figure

A nonrelativistic limit for AdS perturbations

The familiar $c\rightarrow \infty$ nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schroedinger equation, and the Einstein-massive-scalar system without a cosmological constant to the Schroedinger-Newton (SN) equation. In this paper, motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is affected by the presence of a negative cosmological constant $\Lambda$. Assuming for consistency that the product $\Lambda c^2$ tends to a negative constant as $c\rightarrow \infty$, we show that the corresponding nonrelativistic limit is given by the SN system with an external harmonic potential which we call the Schrodinger-Newton-Hooke (SNH) system. We then derive the resonant approximation which captures the dynamics of small amplitude spherically symmetric solutions of the SNH system. This resonant system turns out to be much simpler than its general-relativistic version, which makes it amenable to analytic methods. Specifically, in four spatial dimensions, we show that the resonant system possesses a three-dimensional invariant subspace on which the dynamics is completely integrable and hence can be solved analytically. The evolution of the two-lowest-mode initial data (an extensively studied case for the original general-relativistic system), in particular, is described by this family of solutions.Comment: v3: slightly expanded published versio