A Tenth Order Symplectic Runge–Kutta–Nyström Method

A tenth order explicit symmetric and in consequence symplectic Runge–Kutta–Nyström method is presented here. We derive the order conditions needed and solve them for the parameters of the method. Numerical results indicate the superiority of the new method compared to the other high order symplectic methods appeared in the literature until now.     

Behaviour of a new type of Runge–Kutta methods when integrating satellite orbits

Recently, González, Martín and Farto have developed new numerical methods (RKGM methods) of Runge–Kutta type and fixed step size for the numerical integration of perturbed oscillators. Moreover, it seems natural to study the behaviour of these new methods for the accurate integration of orbital problems after the application of linearizing transformation, such us KS or BF due to the fact that in these variables, the structure of the problem is of the form of perturbed oscillators, for which the methods constructed are indicated. In this paper, we check the efficiency of these new methods when integrating the satellite problem. The RKGM methods show a very good behaviour when they compete with other, classical and special, methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solving Kepler’s equation using implicit functions

A new approach to solve Kepler’s equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower bounds initialize a two-step procedure involving the solution of two implicit functions. These two implicit functions, which are non-rational (polynomial) Bézier functions, can be linear or quadratic, depending on the derivatives of the initial bound values. These are new initial bounds that have been compared and proven more accurate than Serafin’s bounds. The procedure reaches machine error accuracy with no more that one quadratic and one linear iterations, experienced in the “tough range”, where the eccentricity is close to one and the mean anomaly to zero. The proposed method is particularly suitable for space-based applications with limited computational capability.     

Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites.     

Luminosity–colour relations for red clump stars

We calibrated the absolute magnitudes M _V , M _J , $M_{K_{s}}$ and M _g of red clump stars in terms of colours. M _V and M _g are strongly dependent on colour, while the dependence of M _J and $M_{K_{s}}$ on colour is rather weak. The calibration of the absolute magnitudes M _V and $M_{K_{s}}$ is tested on 101 RC stars in the field SA 141. The Galactic model parameters estimated with this sample are in good agreement with earlier studies.     

Period–Luminosity Relationship for δ Scuti Stars Revisited

The Gaia DR3 parallax approach was used to estimate the absolute parameters of 2375 δ Scuti stars from the ASAS catalog.The selected stars have a variety of observational characteristics,with a higher than 80% probability of being δ Scuti stars.We have displayed all the stars in the Hertzsprung-Russell diagram along with the δ Scuti instability strip,the Zero Age Main Sequence and the Terminal Age Main Sequence.Then,we determined which fundamental and overtone modes each star belongs to using pu...     

Nonlinear ion acoustic waveforms for Kadomstev–Petviashvili equation

The reductive perturbation method has been employed to derive the Kadomstev–Petviashvili equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation is applied in obtaining a series of solutions of the Kadomstev–Petviashvili equation. Numerical studies have been made using plasma parameters reveals different waveforms such as bell-shaped solitary pulses, rational pulses and others with singularity at finite points which called blowup solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere plasma.     

Periodicities in Solar Flare Index for Cycles 21 – 23 Revisited

The periodic analyses of solar flare data have been carried out by different authors for about three decades. Controversial results appear as depending on the analysis techniques and investigated time periods. Considering that different authors applied different methods to different data sets, it seems necessary to reanalyze the periodicity of solar flare index with a unified method. In this study we used two new methods to investigate the periodic behavior of solar flare index data, first for individual cycles 21, 22 and 23, and then for all of them. We used i) the multi taper method with red- and white-noise approximations, and ii) the Morlet wavelet transform for periodicity analysis. Apart from the solar rotation periodicity of about 27 days which is of obvious significance and is found in all examined cycles with at least a 90% significance level, we obtained the following prominent periods: 152 days for cycle 21, 73 days for cycle 22, and 62 days for cycle 23. Finally, we compare our results with the ones previously found. We emphasize the fact that a lesser number of periodicities is found in the range of low frequencies (long periods) while the higher frequencies show a greater number of periodicities. This result might be useful for better predictions of the solar cycles.     

A Simon–Weiss model for supergranule flows and their cross-correlations

Supergranule revolution rate and lifetime can be measured by cross-correlating pairs of Doppler-velocity maps that have been filtered (by Hathaway's method) to remove other flows. As a conceptual framework for that analysis, this exploratory paper develops an idealized, phenomenological model of supergranule flows. Assumptions made about supergranule cells on the Sun's photosphere include: random location in space and time, and horizontal flows with circular symmetry and having a Simon–Weiss velocity function. Each supergranule is stable for a time, dies, and after a while, a daughter is born at a nearby position determined by a random walk. The effect on the cross-correlations of changing projection onto the line-of-sight as the Sun rotates is analyzed. The total cross-correlation for strips of constant latitude depends on two generic, slowly-varying projection functions. Effects of differential rotation and time-evolution are also considered. GONG observations of June 1994 show systematic variations in the width and shape of correlation peaks with latitude; our model suggests that projection effects alone can account for these without invoking any intrinsic variations of the supergranules.     

Study and Classification of SDSS Spectra for Byurakan–Iras Galaxies

The sample of Byurakan–IRAS galaxies (BIG) has been created based on optical identifications of IRAS Point Source Catalog (PSC) at high galactic latitudes. As a result, 1178 galaxies have been identified. 172 of them have been observed spectroscopically with Byurakan Astrophysical Observatory (BAO, Armenia) 2.6 m, Special Astrophysical Observatory (SAO, Russia) 6m and Observatoire de Haute Provence (OHP, France) 1.93 m telescopes. Later on, spectra were obtained for more 83 BIG objects in Sloan Digital Sky Survey (SDSS). We have extracted and studied these spectra, classified them and measured spectral features. Diagnostic diagrams have been built to distinguish starbursts (SB), LINERs and Seyfert galaxies. Cross-correlations weremade for these objects with multiwavelength (MW) catalogues and their physical properties were studied. Among these 83 objects, 55 HII, 8 Seyfert galaxies, 2 LINERs, 4 other AGN, 6 composite spectrum objects, and 8 other emission-line galaxies have been revealed. Three of these objects are Ultra-Luminous InfraRed Galaxies (ULIRG).     

A GPU accelerated Barnes–Hut tree code for FLASH4

We present a GPU accelerated CUDA-C implementation of the Barnes Hut (BH) tree code for calculating the gravitational potential on octree adaptive meshes. The tree code algorithm is implemented within the FLASH4 adaptive mesh refinement (AMR) code framework and therefore fully MPI parallel. We describe the algorithm and present test results that demonstrate its accuracy and performance in comparison to the algorithms available in the current FLASH4 version. We use a MacLaurin spheroid to test the accuracy of our new implementation and use spherical, collapsing cloud cores with effective AMR to carry out performance tests also in comparison with previous gravity solvers. Depending on the setup and the GPU/CPU ratio, we find a speedup for the gravity unit of at least a factor of 3 and up to 60 in comparison to the gravity solvers implemented in the FLASH4 code. We find an overall speedup factor for full simulations of at least factor 1.6 up to a factor of 10.     

A model of neutron-star–white-dwarf collision for fast radio bursts

Fast radio bursts (FRBs) with unknown origin emit a huge luminosity (about 1 Jy at 1 GHz) with a duration of milliseconds or less at extragalactic distances estimated from their large dispersion measure (DM). We propose herein a scenario for a collision between a neutron star (NS) and a white dwarf (WD) as the progenitor of the FRBs by considering the burst duration scaling to the collision time and the radio luminosity proportional to the kinetic energy of the collision. The relations among the observed flux density, pulse width, and the DM are derived from the model and compared with the statistical results from the observed FRBs. Although the sample is quite small, we tentatively report a nearly inverse-square correlation between the observed peak flux density and the DM excess, which is an consequence of the assumption that the DM excess (i.e. that not due to our Galaxy) is dominated by the intergalactic medium. We also tentatively note a correlation among the duration of the FRB and the DM excess (possibly interpreted as due to the broadening of the signal in the intergalactic medium) and a correlation among the duration of the FRB and the flux density (shorter burst should be brighter), both roughly in agreement with the proposed model.     

Updated results of a search for main-belt comets using the Canada–France–Hawaii Telescope Legacy Survey

The results of a search for main-belt comets using Canada–France–Hawaii Telescope Legacy Survey data are updated. The remaining observations in the Very Wide segment of data, taken in the g’ or r’ filters, are visually inspected for cometary activity. The number of main-belt objects in the original and new data sets are 11,438 and 13,802, respectively, giving a total number of 25,240. This is the largest, and least biased, search for main-belt comets to date. One object is observed to show cometary activity, and a new upper limit for strongly active main-belt comets is derived to be 40 ± 18.     

Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.     

“Anti-glitches” in the Quark–Nova model for AXPs I

In the Quark–Nova model, Anomalous X-ray Pulsars (AXPs) are quark stars surrounded by a degenerate iron-rich Keplerian ring (a few stellar radii away). AXP bursts are caused by accretion of chunks from the inner edge of the ring following magnetic field penetration. For bright bursts, the inner disk is prone to radiation induced warping which can tilt it into counter-rotation (i.e. retrograde). For AXP 1E2259+586, the 2002 burst satisfies the condition for the formation of a retrograde inner ring. We hypothesize the 2002 burst reversed the inner ring setting the scene for the 2012 outburst and “anti-glitch” when the retrograde inner ring was suddenly accreted leading to the basic observed properties of the 2012 event.     

Infrared photometry for variable stars of selected types in 1978–1999

We present and discuss IR observations for 35 stars of different variability types averaged over many years. These include about twenty symbiotic stars, four W Ser stars and one Algol, six Miras, etc.