Orbital stability of S-type circumbinary planets

Nowadays, more than 4,000 exoplanets have been discovered, including a hundred of circumbinary planets. In the following work, the orbital variations of 67 S-type circumbinary planets have been studied. Their orbital evolutions for a thousand years are simulated using the REBOUND package. The published physical and orbital parameters of the systems are used to computed the systems’ orbital instability limits: Roche limit and Hill’s sphere. From 67 systems, there are two unstable circumbinary systems: Kepler-420 and GJ 86. Kepler-420 Ab orbit passes into the system’s Roche limit due to its high orbital eccentricity. For GJ 86 Ab, the planet orbits outside its Hill’s sphere. The instability of GJ 86 Ab might be caused by an inaccurate measurement of GJ 86 A physical parameters. Using the GJ 86 A mass obtained from Farihi et al., the planet orbits in the stable orbit zone.

Discovery of primitive CO2-bearing fluid in an aqueously altered carbonaceous chondrite

Water is abundant as solid ice in the solar system and plays important roles in its evolution. Water is preserved in carbonaceous chondrites as hydroxyl and/or H2O molecules in hydrous minerals, but has not been found as liquid. To uncover such liquid, we performed synchrotron-based x-ray computed nanotomography and transmission electron microscopy with a cryo-stage of the aqueously altered carbonaceous chondrite Sutter’s Mill. We discovered CO2-bearing fluid (CO2/H2O > ~0.15) in a nanosized inclusion incorporated into a calcite crystal, appearing as CO2 ice and/or CO2 hydrate at 173 K. This is direct evidence of dynamic evolution of the solar system, requiring the Sutter’s Mill’s parent body to have formed outside the CO2 snow line and later transportation to the inner solar system because of Jupiter’s orbital instability.

Orbital stability of solitary waves for the generalized long-short wave resonance equations with a cubic-quintic strong nonlinear term

In this paper, we investigate the orbital stability of solitary waves for the following generalized long-short wave resonance equations of Hamiltonian form: $$ \textstyle\begin{cases} iu_{t}+u_{{xx}}=\alpha uv+\gamma \vert u \vert ^{2}u+\delta \vert u \vert ^{4}u, \\ v_{t}+\beta \vert u \vert ^{2}_{x}=0. \end{cases} $$ { i u t + u x x = α u v + γ | u | 2 u + δ | u | 4 u , v t + β | u | x 2 = 0 . We first obtain explicit exact solitary waves for Eqs. (0.1). Second, by applying the extended version of the classical orbital stability theory presented by Grillakis et al., the approach proposed by Bona et al., and spectral analysis, we obtain general results to judge orbital stability of solitary waves. We finally discuss the explicit expression of $\det (d^{\prime \prime })$ det ( d ″ ) in three cases and provide specific orbital stability results for solitary waves. Especially, we can get the results obtained by Guo and Chen with parameters $\alpha =1$ α = 1 , $\beta =-1$ β = − 1 , and $\delta =0$ δ = 0 . Moreover, we can obtain the orbital stability of solitary waves for the classical long-short wave equation with $\gamma =\delta =0$ γ = δ = 0 and the orbital instability results for the nonlinear Schrödinger equation with $\beta =0$ β = 0 .

Orbital Instability of Chaotic Laser Diode with Optical Injection and Electronically Applied Chaotic Signal

We numerically studied the chaotic dynamics of a laser diode (LD) system with optical injection, where a chaotic signal, which is generated by an LD with optical feedback, is applied to the drive current of the master LD. To quantify the orbital instability of the slave LD, the Lyapunov exponent was calculated as a function of the optical injection ratio between the master and slave LDs and the optical feedback ratio of the applied signal. We found that the Lyapunov exponent was increased and the orbital instability was enhanced by applying a chaotic signal when the inherent system without the applied signal was in a “window”. Next, we investigated the orbital instability of the slave LD in terms of statistical and dynamical quantities of the applied chaotic signal. The maximal value of the Lyapunov exponent for a certain range of the injection ratio was calculated and we showed that a chaotic pulsation is suitable for enhancing the orbital instability of the LD system. We then investigated chaos synchronization between the LDs. It is concluded that the orbital instability of an LD with optical injection can be enhanced by applying chaotic pulsation without chaos synchronization.

Tidal evolution of circumbinary systems with arbitrary eccentricities: applications for Kepler systems

We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are computed, regardless of their size. We derive analytical expressions for the variational equations governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numerical simulations with arbitrary eccentricities very well, as well as reducing to our previous results in the low-eccentric case. Our model is then applied to the well-characterised Kepler circumbinary systems by analysing the tidal timescales and unveiling the tidal flow around each different system. In all cases we find that the spins reach stationary values much faster than the characteristic timescale of the orbital evolution, indicating that all Kepler circumbinary planets are expected to be in a sub-synchronous state. On the other hand, all systems are located in a tidal flow leading to outward migration; thus the proximity of the planets to the orbital instability limit may have been even greater in the past. Additionally, Kepler systems may have suffered a significant tidally induced eccentricity damping, which may be related to their proximity to the capture eccentricity. To help understand the predictions of our model, we also offer a simple geometrical interpretation of our results.

A record of the final phase of giant planet migration fossilized in the asteroid belt’s orbital structure

ABSTRACT The asteroid belt is characterized by an extreme low total mass of material on dynamically excited orbits. The Nice model explains many peculiar qualities of the Solar system, including the belt’s excited state, by invoking an orbital instability between the outer planets. However, previous studies of the Nice model’s effect on the belt’s structure struggle to reproduce the innermost asteroids’ orbital inclination distribution. Here, we show how the final phase of giant planet migration sculpts the asteroid belt, in particular its inclination distribution. As interactions with leftover planetesimals cause Saturn to move away from Jupiter, its rate of orbital precession slows as the two planets’ mutual interactions weaken. When the planets approach their modern separation, where Jupiter completes just short of five orbits for every two of Saturn’s, Jupiter’s eccentric forcing on Saturn strengthens. We use numerical simulations to show that the absence of asteroids with orbits that precess between 24 and 28 arcsec yr−1 is related to the inclination problem. As Saturn’s precession speeds back up, high-inclination asteroids are excited on to planet crossing orbits and removed from the inner main belt. Through this process, the asteroid belt’s orbital structure is reshaped, leading to markedly improved simulation outcomes.

Photosynthesis on exoplanets and exomoons from reflected light

Photosynthesis offers a convenient means of sustaining biospheres. We quantify the constraints for photosynthesis to be functional on the permanent nightside of tidally locked rocky exoplanets via reflected light from their exomoons. We show that the exomoons must be at least half the size of Earth's moon in order for conventional oxygenic photosynthesis to operate. This scenario of photosynthesis is unlikely for exoplanets around late-type M-dwarfs due to the low likelihood of large exomoons and their orbital instability over long timescales. Subsequently, we investigate the prospects for photosynthesis on habitable exomoons via reflected light from the giant planets that they orbit. Our analysis indicates that such photosynthetic biospheres are potentially sustainable on these moons except those around late-type M-dwarfs. We conclude our analysis by delineating certain physiological and biochemical features of photosynthesis and other carbon fixation pathways, and the likelihood of their evolution on habitable planets and moons.

Capillary-gravity water waves with vorticity : steady wind-driven waves and waves with a submerged dipole

In this thesis, we study two mathematical problems on water waves in the setting of the incompressible Euler equations with vorticity, gravity, and surface tension. We investigate the existence of small-amplitude steady wind-driven water waves in finite depth, using the Crandall Rabinowitz theorem. As part of the result, elliptic equations with transmission and Wentzell boundary conditons are also examined, and Schauder type estimates on classical solutions are established. The second chapter considers the existence and instability of solitary water waves with a nite dipole in in nite depth. We construct waves of this type using an Implicit Function Theorem argument. Then we establish orbital instability. This is proved using a modi cation of the classical Grillaks Shatash Strauss method.