Quaternions and the rotation of a rigid body

The orientation of an arbitrary rigid body is specified in terms of a quaternion based upon a set of four Euler parameters. A corresponding set of four generalized angular momentum variables is derived (another quaternion) and then used to replace the usual three-component angular velocity vector to specify the rate by which the orientation of the body with respect to an inertial frame changes. The use of these two quaternions, coordinates and conjugate moments, naturally leads to a formulation of rigid-body rotational dynamics in terms of a system of eight coupled first-order differential equations involving the four Euler parameters and the four conjugate momenta. The equations are formally simple, easy to handle and free of singularities. Furthermore, integration is fast, since only arithmetic operations are involved.     

The final state of charged collapsing core and its optical appearance

We discuss the optical appearance of a charged collapsing stellar core. In the case Q < M , the collapse leads to the formation of a black hole and the phenomenon will be qualitatively similar to the uncharged case, that is, an exponentially increasing redshift and an exponentially decreasing intensity but the time-constant may be very much greater. In the case Q >M, if the collapse ends in a singularity, then infinite redshift and vanishing of light will be seen optically within a finite time. But the formation of singularity does not seem to be a real possibility. More probably, a steady, vibrating configuration will form, which will show very large redshift if Q is close to M.     

The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem

In a previous note we have shown that the KS-transformation, introduced by Kustaanheimo and Stiefel into Celestial Mechanics for the regularization of the Kepler problem, may be formulated in terms of hypercomplex numbers as the product of a quaternion and its anti-involute, thus representing a particular morphism of the real algebra of quaternions-having for image the physical configuration space of the Kepler problem. In the present note we show, first, that this formulation allows a straight derivation of the Hopf fibering of the sphere S³ (characterized by unit quaternions) having the base space given by the sphere S² (characterized by unit vectors), and secondly that the KS-transformation allows the quantization of the symplectic manifold S² in the sense of Souriau, the associated quantum manifold S³ having a contact structure given by the bilinear relation characteristic of the KS-theory. Furthermore, after presenting a natural extension of the hypercomplex KS-transformation to the full phase space of the Kepler problem, we show that this extension allows the quantization of the manifold of Kepler orbits of fixed negative energy (manifold diffeomorphic to the symplectic product S²×S²). The energy levels satisfy a well known quantum integrality condition and the associated quantum manifold is diffeomorphic to the product manifold S³×S³ quotiented by a suitable equivalence relation.Research supported by the Consiglio Nazionale delle Ricerche of Italy, Gruppo per la Fisica-Matematica.     

Leveraging data lineage to infer logical relationships between astronomical catalogs

A novel method to infer logical relationships between sets is presented. These sets can be any collection of elements, for example astronomical catalogs of celestial objects. The method does not require the contents of the sets to be known explicitly. It combines incomplete knowledge about the relationships between sets to infer a priori unknown relationships. Relationships between sets are represented by sets of Boolean hypercubes. This leads to deductive reasoning by application of logical operators to these sets of hypercubes. A pseudo code for an efficient implementation is described. The method is used in the Astro-WISE information system to infer relationships between catalogs of astronomical objects. These catalogs can be very large and, more importantly, their contents do not have to be available at all times. Science products are stored in Astro-WISE with references to other science products from which they are derived, or their dependencies. This creates a full data lineage that links every science product all the way back to the raw data. Catalogs are created in a way that maximizes knowledge about their relationship with their dependencies. The presented algorithm is used to determine which objects a catalog represents by leveraging this information.     

HH 111 STIS Observations and their Analysis using Analytical and Numerical Models

The internal structure of stellar jets arising from young stellar objects is characterized by a series of `knots' or condensations which have highly supersonic proper motions. These structures, we believe, are the result of a variable ejection from the source, which leads to the formation of internal working surfaces or small bowshock within the jet beam. In this paper we present a long-slit spectrum of Herbig-Haro object HH 111 obtained with STIS and an interpretation of this observation in terms of an ejection velocity variability model.     

The equal area law of asymptotically AdS black holes in extended phase space

According to Maxwell’s equal area law we study the “real” phase diagram of the charged AdS black hole and the Kerr-AdS black hole. In the extended phase space constructed by treating the cosmological constant as pressure, the two kinds of AdS black hole display themselves like van der Waals system. Under the critical temperature T _c , there exists a regime where the condition of stable equilibrium will be violated. We employ the equal area law to find an isobar which is the real two phase coexistence line. As a byproduct we find a simple method to derive the critical value of the thermodynamic quantities.     

Étude du choc de deux petites masses en présence d'un troisième corps de masse prépondérante

The analytical study of the evolution in the rectilinear problem of three bodies, leads us to consider the collision between two bodies,M ₂ andM ₃, in the presence of the third body,M ₁. This problem, which seems to be difficult to approach in the general case, can be partly solved if the masses ofM ₂ andM ₃ are equal and can be neglected in regard toM ₁. In this particular case of the general problem, the mechanical study of a collision betweenM ₂ andM ₃, leads to two distinct types of collisions: ‘instantaneous collisions’, and ‘collisions with repetition’, according to the value of a parameter which depends on the position and the speed of the binaryM ₂ M ₃, relative toM ₁, in the collision. In the first type, the collision exchanges the speeds ofM ₂ andM ₃, while in the second type, there is a series of collisions succeeding each other.     

Minimal spanning tree algorithm for γ-ray source detection in sparse photon images: cluster parameters and selection strategies

The minimal spanning tree (MST) algorithm is a graph-theoretical cluster-finding method. We previously applied it to γ-ray bidimensional images, showing that it is quite sensitive in finding faint sources. Possible sources are associated with the regions where the photon arrival directions clusterize. MST selects clusters starting from a particular “tree” connecting all the point of the image and performing a cut based on the angular distance between photons, with a number of events higher than a given threshold. In this paper, we show how a further filtering, based on some parameters linked to the cluster properties, can be applied to reduce spurious detections. We find that the most efficient parameter for this secondary selection is the magnitude M of a cluster, defined as the product of its number of events by its clustering degree. We test the sensitivity of the method by means of simulated and real Fermi-Large Area Telescope (LAT) fields. Our results show that $\sqrt{M}$ is strongly correlated with other statistical significance parameters, derived from a wavelet based algorithm and maximum likelihood (ML) analysis, and that it can be used as a good estimator of statistical significance of MST detections. We apply the method to a 2-year LAT image at energies higher than 3 GeV, and we show the presence of new clusters, likely associated with BL Lac objects.     

A software package for evaluating the performance of a star sensor operation

We have developed a low-cost off-the-shelf component star sensor (StarSense) for use in minisatellites and CubeSats to determine the attitude of a satellite in orbit. StarSense is an imaging camera with a limiting magnitude of 6.5, which extracts information from star patterns it records in the images. The star sensor implements a centroiding algorithm to find centroids of the stars in the image, a Geometric Voting algorithm for star pattern identification, and a QUEST algorithm for attitude quaternion calculation. Here, we describe the software package to evaluate the performance of these algorithms as a star sensor single operating system. We simulate the ideal case where sky background and instrument errors are omitted, and a more realistic case where noise and camera parameters are added to the simulated images. We evaluate such performance parameters of the algorithms as attitude accuracy, calculation time, required memory, star catalog size, sky coverage, etc., and estimate the errors introduced by each algorithm. This software package is written for use in MATLAB. The testing is parametrized for different hardware parameters, such as the focal length of the imaging setup, the field of view (FOV) of the camera, angle measurement accuracy, distortion effects, etc., and therefore, can be applied to evaluate the performance of such algorithms in any star sensor. For its hardware implementation on our StarSense, we are currently porting the codes in form of functions written in C. This is done keeping in view its easy implementation on any star sensor electronics hardware.     

Self-consistent Modelling of the interstellar medium

The dynamical evolution of hot optically thin plasmas in the ISMcrucially depends on the heating and cooling processes. It isessential to realize that all physical processes that contributeoperate on different time scales. In particular detailedbalancing is often violated since the statistically inverseprocess of e.g. collisional ionization is recombination of an ionwith two electrons, which as a three-body collision is usuallydominated by radiative recombination, causing a departure fromcollisional ionization equilibrium. On top of these differences inatomic time scales, hot plasmas are often in a dynamical state,thereby introducing another time scale, which canbe the shortest one.The non-equilibrium effects will be illustrated and discussed inthe case of galactic outflows. It will be shown, that spectralanalyses of X-ray data of edge-on galaxies show a clear signaturein the form of ‘multi-temperature’ halos, which can mostnaturally be explained by the ‘freezing-in’ of highly ionizedspecies in the outflow, which contribute to the overall spectrumby delayed recombination. This naturally leads to anon-equilibrium cooling function, which modifies the dynamics,which in turn changes the plasma densities and thermal energybudget, thus feeding back on the ionization structure. Thereforeself-consistent modelling is needed.     

Can Cassini detect a subsurface ocean in Titan from gravity measurements?

Recent models of Titan's interior predict that the satellite contains an ocean of water and ammonia under an icy layer. Direct evidence for the presence of an ocean can be provided on the Cassini mission only by radio science determination of Titan Love number k₂. Simulations that use the five flybys T11, T22 T33, T45, and T68 (the latter two belonging to the extended mission) lead to the result that in the elastic case, where the Love number is real, k₂ will be determined with a one-sigma accuracy of 0.1. In the viscoelastic case, where k₂ is complex, the real and imaginary parts of k₂ will be determined with one sigma accuracies of 0.138 and 0.115, respectively. Ocean and oceanless models that include a viscoelastic rheology are built. In the viscoelastic case, there is a 93% probability to correctly predict the presence or absence of an ocean; this probability improves to 97% in the elastic case.     

Equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag

We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.     

Variable Chaplygin gas cosmologies in f(R,T) gravity with particle creation

A flat FLRW (Friedmann–Lemaitre–Robertson–Walker) cosmological model with perfect fluid comprising of variable Chaplygin gas (VCG) has been studied in the context of f(R, T) gravity with particle creation. The solutions of the modified field equations are obtained through three different considered form of scale factors. The effective pressure is negative throughout the evolution of universe, which leads to accelerated expansion of the universe. In addition to that we have also discussed the importance of particle creation pressure on the cosmological parameters, energy conditions and state-finder diagnostic parameters. It is noticed that the time evolution of source function yields almost constant particle production at late times.     

Introducing the CTA concept

The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.     

Model for the onset of a magnetospheric substorm

In view of observations which show that a substorm often begins in a small local time sector, a model is assumed in which the neutral sheet current is diverted around a small region we call a bubble. The simplest assumption is that of a linear variation of current with distance from the centre of the bubble in the x-direction in a SM coordinate system, with the diverted current being channelled within narrow paths of width δ_y on the dawn and dusk sides of the bubble. This assumption leads to vector potential integrals that can be evaluated analytically. The addition of this current loop into the magnetotail results in a magnetic field structure where new neutral lines of X- and 0-type can be observed; these are connected to each other as a continuous neutral ring in the xy equatorial plane. The magnetic and electric field components around the neutral regions are calculated, and the time dependent evolution of the neutral ring is studied. Comparison with some published satellite observations shows good agreement. Taking typical values for the various quantities on the basis of actual observations within the magnetotail, we show that the induced electric field is at least comparable to the average cross-tail electrostatic field, and it may well be one or two orders of magnitude greater. The response of the plasma to the induction field is discussed qualitatively. It is concluded that field aligned currents may be produced due to inertial forces of the expanding disturbance. Interpretation of the ground based precipitation patterns of energized particles during auroral breakup is given.     

The secular acceleratons in Gylden's problem

In a two body-problem, any type of variation in time of the Keplerian parameter μ (product of the constant of gravitationG by the reduced massm) causes a mean secular acceleration in the mean anomaly, but leaves the mean argument of perigee stationary. All asymptotic estimates for mean marginal rates of variation in the osculating elements, that Vinti established in the case whenG is inversely proportional to the time, are now extended to the most general kind of Gylden systems, and made into exact relations. The role of a Gylden system in explaining the marginal acceleration in the moon's mean motion is clarified. In addition, separable Gylden systems are classified from a physical standpoint by the integrals that they admit.     

Detection of Quasi-Periodic Pulsations in Solar EUV Time Series

Quasi-periodic pulsations (QPPs) are intrinsically connected to the mechanism of solar flares. They are regularly observed in the impulsive phase of flares since the 1970s. In the past years, the studies of QPPs regained interest with the advent of a new generation of soft X-ray/extreme ultraviolet radiometers that pave the way for statistical surveys. Since the amplitude of QPPs in these wavelengths is rather small, detecting them implies that the overall trend of the time series needs to be removed before applying any Fourier or wavelet transform. This detrending process is known to produce artificial detection of periods that must then be distinguished from real ones. In this paper, we propose a set of criteria to help identify real periods and discard artifacts. We apply these criteria to data taken by the Extreme Ultraviolet Variability Experiment (EVE)/ESP onboard the Solar Dynamics Observatory (SDO) and the Large Yield Radiometer (LYRA) onboard the PRoject for On-Board Autonomy 2 (PROBA2) to search for QPPs in flares stronger than M5.0 that occurred during Solar Cycle 24.