Comparison of chaos detection methods in the circular restricted three‐body problem

In this study, a sample of orbits is considered in the framework of the planar circular restricted three‐body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two‐body system with a rotating central body (e.g. Earth‐Moon system) within the Projective Unified Field Theory

In this treatise the well‐known 2‐body problem with a rotating central body is systematically reinvestigated on the basis of the Projective Unified Field Theory (PUFT) under the following aspects (including the special case of the Newton mechanics): First, equation of motion with abstract additional terms being appropriate for the interpretation of the various effects under discussion: tidal friction effect as well as non‐tidal effects (e.g. rebound effect as temporal variation of the moment of inertia of the rotating body, general‐relativistic Lense‐Thirring effect, new scalaric effects of cosmological origin, being an outcome of the scalarity phenomenon of matter (PUFT). Second, numerical evaluation of the theory. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The MultiDark Database: Release of the Bolshoi and MultiDark cosmological simulations

We present the online MultiDark Database – a Virtual Observatory‐oriented, relational database for hosting various cos‐mological simulations. The data is accessible via an SQL (Structured Query Language) query interface, which also allows users to directly pose scientific questions, as shown in a number of examples in this paper. Further examples for the usage of the database are given in its extensive online documentation. The database is based on the same technology as the Millennium Database, a fact that will greatly facilitate the usage of both suites of cosmological simulations. The first release of the MultiDark Database hosts two 8.6 billion particle cosmological N‐body simulations: the Bolshoi (250 h^–1 Mpc simulation box, 1 h^–1 kpc resolution) and MultiDark Run1 simulation (MDR1, or BigBolshoi, 1000 h^–1 Mpc simulation box, 7 h^–1 kpc resolution). The extraction methods for halos/subhalos from the raw simulation data, and how this data is structured in the database are explained in this paper. With the first data release, users get full access to halo/subhalo catalogs, various profiles of the halos at redshifts z = 0–15, and raw dark matter data for one time‐step of the Bolshoi and four time‐steps of the MultiDark simulation. Later releases will also include galaxy mock catalogs and additional merger trees for both simulations as well as new large volume simulations with high resolution. This project is further proof of the viability to store and present complex data using relational database technology. We encourage other simulators to publish their results in a similar manner. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High‐resolution simulations and visualization of protoplanetary disks: structure of the flow in the vicinity of a massive planet

A problem of mass flow in the immediate vicinity of a planet embedded in a protoplanetary disk is studied numerically in two dimensions. Large differences in temporal and spatial scales involved suggest that a specialized discretization method for solution of hydrodynamical equations may offer great savings in computational resources, and can make extensive parameter studies feasible. Preliminary results obtained with help of Adaptive Mesh Refinement technique and high‐order explicit Eulerian solver are presented. This combination of numerical techniques appears to be an excellent tool which allows for direct simulations of mass flow in vicinity of the accretor at moderate computational cost. The present communication is focused on the structure of the outer part of the circumplanetary disk. We employ the multifluid option to the hydrodynamical solver to prove that the circumplanetary disk is composed of the gas transfered into it from the edges of the gap.     

The evolution of chaos in active galaxy models with an oblate or a prolate dark halo component

The evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale‐length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of the orbit of Interball‐1

We investigated the motion of the Earth's artificial satellite Interball‐1 by using a method suitable for the computation of large eccentricity orbits. Though the measured and the computed orbital elements differ from each other within the measured error bound, we found a slight tendency for secular decreasing in the semi‐major axis, caused probably by electromagnetic drag. We analysed the dominant role of the Moon in the variations of the orbital eccentricity, leading to zero perigee height and the end of the lifetime of the satellite. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of a planet in the HD 41004 binary system

The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M_⊙ and 0.4 M_⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 M_J) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 M_J planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new model of angular momentum transfer from the rotating central body of a two‐body system to the orbital motion of the system

In a previous paper we treated within the framework of our Projective Unified Field Theory (Schmutzer 2004, 2005a) the 2‐body system (e.g. Earth‐Moon system) with a rotating central body in a rather abstract manner. Here a concrete model of the transfer of angular momentum from the rotating central body to the orbital motion of the whole 2‐body system is presented, where particularly the transfer is caused by the inhomogeneous gravitational force of the Moon acting on the oceanic waters of the Earth, being modeled by a spherical shell around the solid Earth. The theory is numerically tested. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Roche volume filling and the dissolution of open star clusters

From direct N‐body simulations we find that the dynamical evolution of star clusters is strongly influenced by the Roche volume filling factor. We present a parameter study of the dissolution of open star clusters with different Roche volume filling factors and different particle numbers. We study both Roche volume underfilling and overfilling models and compare with the Roche volume filling case. We find that in the Roche volume overfilling limit of our simulations two‐body relaxation is no longer the dominant dissolution mechanism but the changing cluster potential. We call this mechanism “mass‐loss driven dissolution” in contrast to “two‐body relaxation driven dissolution” which occurs in the Roche volume underfilling regime. We have measured scaling exponents of the dissolution time with the two‐body relaxation time. In this experimental study we find a decreasing scaling exponent with increasing Roche volume filling factor. The evolution of the escaper number in the Roche volume overfilling limit can be described by a log‐logistic differential equation. We report the finding of a resonance condition which may play a role for the evolution of star clusters and may be calibrated by the main periodic orbit in the large island of retrograde quasiperiodic orbits in the Poincaré surfaces of section. We also report on the existence of a stability curve which may be of relevance with respect to the structure of star clusters. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Velocity dispersion in N‐body simulations of CDM models

This work reports on a study of the spatially coarse‐grained velocity dispersion in cosmological N‐body simulations (OCDM and ΛCDM models) as a function of time (redshifts z = 0–4) and of the coarsening length (0.6–20 h⁻¹ Mpc). The main result is the discovery of a polytropic relationship ℐ₁ ∝ ϱ^2–η between the velocity‐dispersion kinetic energy density of the coarsening cells, ℐ₁, and their mass density, ϱ. The exponent η, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction η_virial = 0. This relationship supports the “polytropic assumption” which has been employed in theoretical models for the growth of cosmological structure by gravitational instability. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inferring the emission regions for different kinds of gamma‐ray bursts

Using a theoretical model describing pulse shapes, we have clarified the relations between the observed pulses and their corresponding timescales, such as the angular spreading time, the dynamic time as well as the cooling time. We find that the angular spreading timescale caused by curvature effect of fireball surface only contributes to the falling part of the observed pulses, while the dynamic one in the co‐moving frame of the shell merely contributes to the rising portion of pulses provided the radiative time is negligible. In addition, the pulses resulted from the pure radiative cooling time of relativistic electrons exhibit properties of fast rise and slow decay (a quasi‐FRED) profile together with smooth peaks. Besides, we interpret the phenomena of wider pulses tending to be more asymmetric to be a consequence of the difference in emission regions. Meanwhile, we find the intrinsic emission time is decided by the ratios of lorentz factors and radii of the shells between short and long bursts. Based on the analysis of asymmetry, our results suggest that the long GRB pulses may occur in the regions with larger radius, while the short bursts could locate at the smaller distance from central engine. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (ln Λ). We determine the accurate value of this parameter using the direct N -body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that  ln Λ= 6.6 ± 0.6  for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, ln Λ is smaller, with a value of the logarithm argument Λ inversely proportional to the object size.     

Study of the atmospheric refraction in a single-mode instrument – application to AMBER/VLTI

This paper presents a study of the atmospheric refraction and its effect on the light coupling efficiency in an instrument using single-mode optical fibres. We show the analytical approach which allowed us to assess the need to correct the refraction in J and H bands while observing with an 8-m Unit Telescope. We then developed numerical simulations to go further in calculations. The hypotheses on the instrumental characteristics are those of AMBER (Astronomical Multi BEam combineR), the near-infrared focal beam combiner of the Very Large Telescope Interferometric mode, but most of the conclusions can be generalized to other single-mode instruments. We used the software package caos to take into account the atmospheric turbulence effect after correction by the European Southern Observatory system Multi-Application Curvature Adaptive Optics. The optomechanical study and design of the system correcting the atmospheric refraction on AMBER is then detailed. We showed that the atmospheric refraction becomes predominant over the atmospheric turbulence for some zenith angles z and spectral conditions: for z larger than 30° in J band for example. The study of the optical system showed that it allows to achieve the required instrumental performance in terms of throughput in J and H bands. First observations in J band of a bright star, α Cir star, at more than 30° from zenith clearly showed the gain to control the atmospheric refraction in a single-mode instrument, and validated the operating law.     

GJ 581 update: Additional evidence for a Super‐Earth in the habitable zone

We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super‐Earth‐mass planet in the star's Habitable Zone. We were able to reproduce their reported χ²_ν and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N‐body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6σ detection of e = 0.32 for the eccentricity of GJ 581e is manifestly incompatible with the system's dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the χ²_ν and demonstrates the need for including non‐Keplerian orbital precession when modeling this system. We find that a four‐planet model with all of the planets on circular or nearly circular orbits provides both an excellent self‐consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4‐planet all‐circular‐orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240‐point HARPS data set, when analyzed in its entirety, and modeled with fully self‐consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a false alarm probability of <4% and is consistent with a planet of minimum mass 2.2 M_⊕, orbiting squarely in the star's habitable zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)