Exciting Mutual Inclination in Planetary Systems with a Distant Stellar Companion: The Case of Kepler-108

We study the excitation of mutual inclination between planetary orbits by a novel secular-orbital resonance in multi-planet systems perturbed by binary companions, which we call “ivection.” The ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously studied evection resonance. Capture into an ivection resonance requires encountering the resonance with slowly increasing nodal precession rate, and it can excite the mutual inclination of the planets without affecting their eccentricities. We discuss the possible outcomes of ivection resonance capture, and we use simulations to illustrate that it is a promising mechanism for producing the mutual inclination in systems where planets have significant mutual inclination but modest eccentricity, such as Kepler-108. We also find an apparent deficit of multi-planet systems that would have a nodal precession period comparable to the binary orbital period, suggesting that ivection resonance may inhibit formation of or destablize multi-planet systems with an external binary companion.

Probing the parameters of a Schwarzschild black hole surrounded by quintessence and cloud of strings through four standard astrophysical tests

In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime’s parameters in the context of the observational data, which results in about $$\sim 10^{-9}$$ ∼ 10 - 9 for the cloud of strings parameter, and $$\sim 10^{-20}$$ ∼ 10 - 20 m$$^{-1}$$ - 1 for that of quintessence. The response of the black hole to the gravitational perturbations is also discussed.

On the stability of planetary orbits in binary star systems I. The S-type orbits

Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planet with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. (Astron. Astrophys. 434:355, 2005). For planets of negligible mass, we estimate the critical semi-major axis $a_{c}$ a c as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert (Astron. J. 117:621, 1999). However we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.

James Croll, celestial mechanics and climate change

ABSTRACT James Croll was a pioneer in studies of the impact of the slowly changing orbital dynamics of the Earth on climate change. His book Climate and Time in their Geological Relations (1875) was far ahead of its time in seeking correlations between climate change, the occurrence of ice ages and perturbations to the Earth's orbit about the Sun. The astronomical cycles he discovered are now called ‘Milankovitch Cycles’ after the Serbian scientist whose research was first published in the Handbuch der Klimatologie in 1930. The celestial mechanical and astronomical background to Croll's research is the focus of this essay. The development of the understanding of the impact of perturbations of the elliptical planetary orbits by other bodies in the solar system paralleled new mathematical techniques, many of which were developed in association with celestial mechanical problems. The central contributions of many of the major mathematicians of the late 18th and 19th Centuries, including Euler, Lagrange, Laplace and Le Verrier, are highlighted. Although Croll's contributions faded from view for several generations, his pioneering insights have now been demonstrated to have been basically correct.

Neural Systems Under Change of Scale

We derive a theoretical construct that allows for the characterisation of both scalable and scale free systems within the dynamic causal modelling (DCM) framework. We define a dynamical system to be “scalable” if the same equation of motion continues to apply as the system changes in size. As an example of such a system, we simulate planetary orbits varying in size and show that our proposed methodology can be used to recover Kepler’s third law from the timeseries. In contrast, a “scale free” system is one in which there is no characteristic length scale, meaning that images of such a system are statistically unchanged at different levels of magnification. As an example of such a system, we use calcium imaging collected in murine cortex and show that the dynamical critical exponent, as defined in renormalization group theory, can be estimated in an empirical biological setting. We find that a task-relevant region of the cortex is associated with higher dynamical critical exponents in task vs. spontaneous states and vice versa for a task-irrelevant region.

Binary Gravitational Perturbations and Their Influence on the Habitability of Circumstellar Planets

In order to assess the habitability of planets in binary star systems, not only astrophysical considerations regarding stellar and atmospheric conditions are needed, but orbital dynamics and the architecture of the system also play an important role. Due to the strong gravitational perturbations caused by the presence of the second star, the study of planetary orbits in double star systems requires special attention. In this context, we show the important role of the main gravitational perturbations (resonances) and review our recently developed methods which allow a quick determination of locations of secular resonances (SRs) in binary stars for circumstellar planetary motion where a giant planet has to move exterior to the habitable zone (HZ). These methods provide the basis for our online-tool ShaDoS which allows a quick check of circumstellar HZs regarding secular perturbations. It is important to know the locations of SRs since they can push a dynamically quiet HZ into a high-eccentricity state which will change the conditions for habitability significantly. Applications of SHaDoS to the wide binary star HD106515 AB and the tight system HD41004 AB reveal a quiet HZ for both systems. However, the study of these systems indicates only for the tight binary star a possible change of the HZ's dynamical state if the orbital parameters change due to new observational data.