Dynamics of Two Planets in the 2/1 Mean-Motion Resonance

The dynamics of two planets near a first-order mean-motion resonance is modeled in the domain of the general three-body planar problem. The system studied is the pair Uranus-Neptune (2/1 resonance). The phase space of the resonance and near-resonance regions is studied by means of surfaces of section and spectral analysis techniques. After a thorough investigation of the topology of the phase space, we find that several regimes of motion are possible for the Uranus-Neptune system, and the regions of transition between the regimes of motion are the seats of chaotic motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Normalization and the detection of integrability: The generalized Van Der Waals potential

Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits.     

Imaging planets around nearby white dwarfs

We suggest that Jovian planets will survive the late stages of stellar evolution, and that white dwarfs will retain planetary systems in wide orbits (≳5 au). Utilizing evolutionary models for Jovian planets, we show that infrared imaging with 8-m class telescopes of suitable nearby white dwarfs should allow us to resolve and detect companions ≳3 M _JUP. Detection of massive planetary companions to nearby white dwarfs would prove that such objects can survive the final stages of stellar evolution, place constraints on the frequency of main-sequence stars with planetary systems dynamically similar to our own and allow direct spectroscopic investigation of their composition and structure.     

Limits on the 2.2-μm contrast ratio of the close-orbiting planet HD 189733b

We obtained 238 spectra of the close-orbiting extrasolar giant planet HD 189733b with resolution   R ∼ 15 000  during one night of observations with the Near-Infrared High-Resolution Spectrograph (NIRSPEC), at the Keck II Telescope. We have searched for planetary absorption signatures in the  2.0–2.4 μm  region where H₂O and CO are expected to be the dominant atmospheric opacities. We employ a phase-dependent orbital model and tomographic techniques to search for the planetary absorption signatures in the combined stellar and planetary spectra. Because potential absorption signatures are hidden in the noise of each single exposure, we use a model list of lines to apply a spectral deconvolution. The resulting mean profile possesses a signal-to-noise ratio (S/N) that is 20 times greater than that found in individual lines. Our spectral time series thus yields spectral signatures with a mean S/N = 2720. We are unable to detect a planetary signature at a contrast ratio of  log₁₀( F _p/ F _*) =−3.40  , with 63.8 per cent confidence. Our findings are not consistent with model predictions which nevertheless give a good fit to mid-infrared observations of HD 189733b. The 1σ result is a factor of 1.7 times less than the predicted 2.185-μm planet/star flux ratio of  log₁₀( F _p/ F _*) ∼−3.16  .     

3.8-μm photometry during the secondary eclipse of the extrasolar planet HD 209458b

We report infrared photometry of the extrasolar planet HD 209458b during the time of secondary eclipse (planet passing behind the star). Observations were acquired during two secondary eclipses at the NASA Infrared Telescope Facility (IRTF) in 2003 September. We used a circular variable filter (1.5 per cent bandpass) centred at 3.8 μm to isolate the predicted flux peak of the planet at this wavelength. Residual telluric absorption and instrument variations were removed by offsetting the telescope to nearby bright comparison stars at a high temporal cadence. Our results give a secondary eclipse depth of 0.0013 ± 0.0011, not yet sufficient precision to detect the eclipse, whose expected depth is  ∼0.002 –0.003  . We here elucidate the current observational limitations to this technique, and discuss the approach needed to achieve detections of hot Jupiter secondary eclipses at 3.8 μm from the ground.     

Strong bursts and diffusion in avalanching systems

The connection between avalanche dynamics and space physics has been studied for several years. In that context we recently suggested an avalanche model which explains the phenomena of reconnection. In this work the model is generalized to include the influence of an extremely strong perturbation, reflecting the effect of plasma storms originating from the sun. In addition, we allow for diffusion processes and show that the behavior changes with the onset of diffusion processes, rendering it quasi-periodic, along with the supression of small-size avalanches.     

Modelling rainfall/watertable relations using linear response functions

Linear system theory can be used to model and predict watertable responses to precipitation inputs in an artificially drained field. The response function is mathematically equivalent to the Unit Hydrograph concept familiar to hydrologists. This paper shows that it is possible to derive such response functions, and comments on the problems encountered in their derivation. Response functions for two contrasted sites are presented, and the possibilities for their use discussed.     

一种无线数据传输接口及控制装置

本文介绍一种无线数据传接口及控制装置。装置中采用计算机软件实现串—并、并—串变换及频率调制、其硬件成本低廉,工作可靠,可用于速率为50、300、600或1200bps的数传通信。     

Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above.