Secular Evolution of Hierarchical Planetary Systems

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha<0.1 and reasonably accurate even for systems with alpha as large as 1/3, provided that alpha is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661 system is the first extrasolar planetary system found to have w_1-w_2 librating about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of both e_j in the HD 12661 system are consistent with the analytic results on systems with lambda \approx lambda_{crit}. The HD 12661 system with the best- fit orbital parameters and sin i = 1 is affected by the close proximity to the 11:2 commensurability, but small changes in the outer orbital period can result in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in Ap

Current-induced synchronized switching of magnetization

We investigate current-induced magnetization switching for a multilayer structure that allows a reduced switching current while maintaining high thermal stability of the magnetization. The structure consists of a perpendicular polarizer, a perpendicular free-layer, and an additional free-layer having in-plane magnetization. When the current runs perpendicular to the structure, the in-plane free-layer undergoes a precession and supplies an internal rf field to the perpendicular free-layer, resulting in a reduced switching current for one current polarity. For the other polarity, the in-plane free-layer almost saturates perpendicular to the plane and acts as another perpendicular polarizer, which also reduces the switching current.Comment: 18 pages, 4 figure

Quantum discord amplification induced by quantum phase transition via a cavity-Bose-Einstein-condensate system

We propose a theoretical scheme to realize a sensitive amplification of quantum discord (QD) between two atomic qubits via a cavity-Bose-Einstein condensate (BEC) system which was used to firstly realize the Dicke quantum phase transition (QPT) [Nature 464, 1301 (2010)]. It is shown that the influence of the cavity-BEC system upon the two qubits is equivalent to a phase decoherence environment. It is found that QPT in the cavity-BEC system is the physical mechanism of the sensitive QD amplification.Comment: 5 pages, 3 figure

Complete Tidal Evolution of Pluto-Charon

Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto's tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis $a \approx 4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function $Q \propto$ 1/frequency and $Q=$ constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient $C_{22}$ of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic $J_2$ can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum - including temporary capture into spin-orbit resonances as Charon's spin decreases and damped librations about the same.Comment: 36 pages, including 18 figures; accepted for publication in Icaru

A Primordial Origin of the Laplace Relation Among the Galilean Satellites

Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive volcanism on Io, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2 n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st

Laser spectroscopic studies of the pure rotational U_0(0) and W_0(0) transitions of solid parahydrogen

High resolution spectrum of multipole-induced transitions of solid parahydrogen was recorded using diode and difference frequency laser spectroscopy. The J=4<--0 pure rotational U_0(0) transition observed in the diode spectrum agrees well in frequency with the value reported by Balasubramanian et al. [Phys. Rev. Lett. 47, 1277 (1981)] but we observed a spectral width smaller by about a factor of 4. The J=6<--0 W_0(0) transition was observed to be exceedingly sharp, with a width of ~70 MHz, using a difference frequency spectrometer with tone-burst modulation. This transition is composed of three components with varying relative intensity depending upon the direction of polarization of laser radiation. These components were interpreted as the splitting of the M levels in the J=6 state due to crystal field interactions. In addition, a new broad feature was found at 2452.4 cm^(−1) in the low resolution Fourier-transform infrared (FTIR) spectrum of solid hydrogen and was assigned to be the phonon branch W_R(0) transition of the W_0(0) line. The selection rules, crystal field splitting of J=4 and J=6 rotons, and the measured linewidth based on these observations are discussed

The analytical discussion on strong gravitaional lensing for a gravitational source with a f(R)f(R) global monopole

Here the gravitational lensing in strong field limit of a Schwarzschild black hole with a solid deficit angle owing to global monopole within the context of the $f(R)$ gravity theory is investigated. We obtain the expressions of deflection angle and time delay in the forms of elliptic integrals and discuss the asymptotic behaviour of the elliptic integrals to find the explicit formulae of angle and time difference in the strong field limit. We show that the deflection angle and the time delay between multiple images are related not only to the monopole but also to the $f(R)$ correction $\psi_{0}$ by taking the cosmological boundary into account. Some observables such as the minimum impact parameter, the angular separation, the relative magnification and the compacted angular position have been estimated as well. It is intriguing that the tiny modification on the standard general relativity will make the remarkable deviation on the angle and the time lag, offering a significant way to explore some possible distinct signatures of the topological soliton and the correction of the Einstein general relativity.Comment: 11 pages, 5 figures. arXiv admin note: text overlap with arXiv:1004.342