Orbital Stability of Planet-hosting Triple-star Systems according to Hill: Applications to Alpha Centauri and 16 Cygni

In this study we investigate aspects of orbital stability for the Alpha Centauri and 16 Cygni systems. They are planet-hosting triple star systems of highly hierarchic nature. For each system, orbital stability of the outlying stellar component and the observed exoplanet(s) are explored through assessing Hill stability. Orbital stability is identified for all components, including the observed system planets.

Exomoon indicators in high-precision transit light curves

Context. While the Solar System contains about 20 times more moons than planets, no moon has been confirmed around any of the thousands of extrasolar planets discovered so far. Considering the large computational load required for the statistical vetting of exomoon candidates in a star–planet–moon framework, tools for an uncomplicated identification of the most promising exomoon candidates could be beneficial to streamline follow-up studies. Aims. Here we study three exomoon indicators that emerge if well-established planet-only models are fitted to a planet–moon transit light curve: transit timing variations (TTVs), transit duration variations (TDVs), and apparent planetary transit radius variations (TRVs). We re-evaluate under realistic conditions the previously proposed exomoon signatures in the TTV and TDV series. Methods. We simulated light curves of a transiting exoplanet with a single moon, taking into account stellar limb darkening, orbital inclinations, planet–moon occultations, and noise from both stellar granulation and instrumental effects. These model light curves were then fitted with a planet-only transit model whilst pretending there were no moon, and we explored the resulting TTV, TDV, and TRV series for evidence of the moon. Results. The previously described ellipse in the TTV-TDV diagram of an exoplanet with a moon emerges only for high-density moons. However, low-density moons distort the sinusoidal shapes of the TTV and the TDV series due to their photometric contribution to the combined planet–moon transit. Sufficiently large moons can nevertheless produce periodic apparent TRVs of their host planets that could be observable. We find that Kepler and PLATO have similar performances in detecting the exomoon-induced TRV effect around simulated bright (mV = 8) stars. Although these stars are rare in the Kepler sample, they will be abundant in the PLATO sample. Moreover, PLATO’s higher cadence yields a stronger TTV signal. We detect substantial TRVs of the Saturn-sized planet Kepler-856 b although an exomoon could only ensure Hill stability in a very narrow orbital range. Conclusions. The periodogram of the sequence of transit radius measurements can indicate the presence of a moon. The TTV and TDV series of exoplanets with moons could be more complex than previously assumed. We propose that TRVs could be a more promising means to identify exomoons in large exoplanet surveys.

Parametric Resonance Analysis of a Submerged Floating Pipeline Considering Uncertainties

The submerged floating pipeline is floating at a certain ocean depth with tethers anchored to the seabed. This novel concept of pipeline can be a promising solution for challenging seabed conditions. Because the pipeline is floating at the mid-deep water and does not interact directly with the seabed, there is no need to do any seabed intervention work and wave forces on the pipeline can also be ignored. But the dynamic response of this type of pipeline under strong currents poses several challenges for design of floating pipeline. This work investigates the parametric resonance of submerged floating pipeline between two floating structures. The parametric resonance can lead to the huge motions and fatigue damage of the pipeline. Thus, it is essential to investigate the parametric resonance of the submerged floating pipeline system under combined parametric and vortex excitations considering uncertainties. Hill’s equation of dynamic responses of the pipeline are derived and hill stability diagrams are used to analyses the corresponding motion stability. The effect of the significant uncertain factors on the probability of the parametric stability is investigated using the metamodel method. According to analyses, some effective measures are given to the designers to avoid the parametric instability for the submerged floating pipeline design.

Hill stability in the AMD framework

In a two-planet system, a topological boundary that is created by Sundman (1912, Acta Math., 36, 105) inequality can forbid close encounters between the two planets for an infinite time. A system is said to be Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extrasolar planet dynamics. However, the coplanar and circular orbit approximation is often used. In this paper, we explain how the Hill stability can be understood in the framework of angular momentum deficit (AMD). In the secular approximation, AMD allows us to discriminate between a priori stable systems and systems for which a more in-depth dynamical analysis is required. We show that the general Hill stability criterion can be expressed as a function of only semimajor axes, masses, and total AMD of the system. The proposed criterion is only expanded in the planets-to-star mass ratio ε and not in the semimajor axis ratio, eccentricities, nor the mutual inclination. Moreover, the expansion in ε remains excellent up to values of about 10−3 even for two planets with very different mass values. We performed numerical simulations in order to highlight the sharp change of behavior between Hill stable and Hill unstable systems. We show that Hill stable systems tend to be very regular, whereas Hill unstable systems often lead to rapid planet collisions. We also note that Hill stability does not provide protection from the ejection of the outer planet.