Cellinoid Shape Model for Asteroids

The ellipsoid shape model plays an important role in physical research on asteroids. However, its symmetric structure cannot practically simulate real asteroids. This article applies a general shape model, named the cellinoid, instead of the ellipsoid model to simulate the asymmetric shape of asteroids. The cellinoid shape model consists of eight octants of ellipsoids having different semi-axes, with the constraint that adjacent octants must have two equal semi-axes in common. Totally, the shape of the cellinoid model is controlled by six parameters, not three as in the case of the shape of the ellipsoid. Using this shape model, the brightness of asteroids observed from the Earth can be fitted numerically by the surface triangularization of the cellinoid. The Levenberg–Marquardt algorithm is also employed here to solve a nonlinear minimization problem. Owing to the asymmetric shape of the cellinoid, the physical parameters of asteroids, such as the rotation period and pole orientation, can be fitted more accurately than in the case of the ellipsoid model. Finally, this is confirmed numerically by applying the shape to both synthetic light curves and real light curves of asteroids. Additionally, the center of mass and moment of inertia of the cellinoid are analyzed explicitly.     

Seismic probing of outer regions of the Sun

The inverse scattering problem for reconstruction of the structure of reflecting potential from the observed frequency dependence of the phase shift of reflected acoustic waves is considered. The linearized formulation of the ill-posed inverse problem is used, which is solved using a perturbation technique. The potential perturbation of the standard model as a combination of five B-splines leads to a constructive solution of the discrepancy problem between the observational and theoretical frequencies of the 5-min oscillations. The discrepancy is reduced by an order of magnitude. The corresponding change of the shape of the reflecting potential is interpreted as a requirement of a general increase of convection efficiency in the standard solar model. In this way, the agreement of the oscillation frequencies of high degree is also improved.     

A contraction model for the flattening and equatorial ridge of Iapetus

Others have explained the excess flattening of Iapetus by a model in which the moon formed at a high spin rate, achieved isostatic equilibrium by very rapid interior heating caused by short-lived radioactive isotopes (SLRI), and subsequently cooled, locking in the excess flattening with respect to an equilibrium shape at its present spin rate. Here we propose an alternate model that does not require an unusually high initial spin rate or the SLRI. The initial formation of Iapetus results in a slightly oblate spheroid with porosity >10%. Radioactive heating by long-lived isotopes warms the interior to about 200 K, at which point it becomes ductile and the interior compacts by 10%, while the 120 km-thick exterior shell remains strong. The shell must deform to match the reduced volume of the ductile interior, and we propose that this deformation occurs along the equator, perhaps focused by a thinner equatorial shell. The final shape of the collapsed sphere matches the observed shape of Iapetus today, described as an oblate ellipse, except along the equator where strain concentration forms a broad ridge. To maintain this non-equilibrium shape, the thickness of the shell must exceed 120 km. Testing the equatorial focusing hypothesis will require a model that includes non-linear processes to account for the finite yield strength of the thick lithosphere. Nevertheless, we show that the stress in the lithosphere generated by the contraction of the interior is about 3 times greater than the stress needed to deform the lithosphere, so some type of lithospheric deformation is expected.     

Tailoring triaxial N-body models via a novel made-to-measure method

The made-to-measure N -body method slowly adapts the particle weights of an N -body model, whilst integrating the trajectories in an assumed static potential, until some constraints are satisfied, such as optimal fits to observational data. I propose a novel technique for this adaption procedure, which overcomes several limitations and shortcomings of the original method. The capability of the new technique is demonstrated by generating realistic N -body equilibrium models for dark matter haloes with prescribed density profile, triaxial shape and slowly outwardly growing radial velocity anisotropy.     

Stability of Surface Motion on a Rotating Ellipsoid

The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid.     

On the relation between orbital structure and observed bar morphology

We investigate the morphological relation between the orbits of the central family of periodic orbits ( x ₁ family) and the bar itself using models of test particles moving in a barred potential. We show that different bar morphologies may have as a backbone the same set of x ₁ periodic orbits. We point out that by populating initially axisymmetric stellar discs exponentially with test particles in circular, or almost circular motion, we may end up with a response bar which reveals a shape different in crucial details from that of the individual stable x ₁ orbits. For example, a bar model in which the x ₁ orbits are pure ellipses may have a much more complicated response morphology. This depends on the particular invariant curves around x ₁, which are populated in each model.     

Observation Plan for Refining Shape Model of (6) HEBE

As the number of observatories located on the surface of Earth is increasing largely in decades more and more photometric data of asteroids is observed to make the research about their various physical and chemical characteristics. Compared with hundreds of thousands of asteroids found up to now, rare hundreds of three-dimensional shape models of asteroids have been built from the tremendous photometric data with incessant observations, i.e. lightcurves. For some specific asteroid already with many observed lightcurves, the unceasing observation is not too much valuable, nevertheless an additional lightcurve observed in a request viewing aspect can refine the shape model and other related parameters. This article taking the asteroid (6) HEBE for example, attempts to introduce a method to make the observation plan by combining the request of the shape model and the orbital limitation of asteroids. Through analyzing the distribution of lightcurves of (6) HEBE, small cabins without any lightcurve data are found, which can be filled by new observations at some specified dates when the positions of Asteroid, Sun, Earth are limited as the request geometry.     

A two-dimensional model for a solar prominence: Effect of an external magnetic field

Using analytical approximations we study the effects of different external magnetic configurations on the half-width, mass, and internal magnetic structure of a quiescent solar prominence, modelled as a thin vertical sheet of cool plasma. Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant- force-free field. This model allows us to obtain the half-width and mass of the prominence for different values of the external field, pressure and shear angle. Secondly, the effects of these external magnetic configurations on a two-dimensional model proposed by Ballester and Priest (1987) are studied. The main effects are a change of the half-width with height, an increase of the mass, a decrease of the magnetic field strength with height and a change in the shape of the magnetic field lines.     

Integrable models of galactic discs with double nuclei

We introduce a new class of 2D mass models, whose potentials are of Stäckel form in elliptic coordinates. Our model galaxies have two separate strong cusps that form double nuclei. The potential and surface density distributions are locally axisymmetric near the nuclei and become highly non-axisymmetric outside the nucleus. The surface density diverges toward the cuspy nuclei with the law     Our model is sustained by four general types of regular orbits: butterfly , nucleophilic banana , horseshoe and aligned loop orbits. Horseshoes and nucleophilic bananas support the existence of cuspy regions. Butterflies and aligned loops control the non-axisymmetric shape of outer regions. Without any need for central black holes, our distributed mass models resemble the nuclei of M31 and NGC 4486B. It is also shown that the self-gravity of the stellar disc can prevent the double nucleus to collapse.     

Model Radiants of the Geminid Meteor Shower

This paper describes the final stage of the study of the Geminid meteoroid stream formation and evolution using the nested polynomials method reported by Ryabova (in: Warmbein (ed.) Meteoroids 2001, Proc. of the Internat. Conf., Kiruna, Sweden, 6–10 August 2001; MNRAS 375:1371–1380, 2007). In the previous work we discussed possibility to calibrate the model using the shape of the model activity profiles and configuration of orbital parameters. Here we show that the radiant structure also could be utilized for this purpose, since the model radiant structure has a very specific pattern. Model area of radiation does not have a “classical” prolate linear shape, and the configuration of activity centers has a “V” shape. During one night of simulated observations several activity centers could be observed. The model produced maps of the velocity distribution in the radiant area.     

Evidence of Magnetic Helicity in Emerging Flux and Associated Flare

The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multiwavelength analysis of an M1.6 flare occurring in the NOAA active region 10365 on 27 May 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the “tongue” shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues indicates the emergence of a flux tube with a right-hand twist (i.e., positive magnetic helicity). The flare signatures in the chromosphere are ribbons observed in Hα by the MSDP spectrograph in the Meudon solar tower and in 1600 Å by TRACE. These ribbons have a J shape and are shifted along the inversion line. The pattern of these ribbons suggests that the flare was triggered by magnetic reconnection at coronal heights below a twisted flux tube of positive helicity, corresponding to that of the observed emergence. It is the first time that such a consistency between the signatures of the emerging flux through the photosphere and flare ribbons has been clearly identified in observations. Another type of ribbons observed during the flare at the periphery of the active region by the MSDP and SOHO/EIT is related to the existence of a null point, which is found high in the corona in a potential field extrapolation. We discuss the interpretation of these secondary brightenings in terms of the “breakout” model and in terms of plasma compression/heating within large-scale separatrices.     

On the depths and shapes of the freshest kilometer-scale simple craters on the lunar maria: A new crater shape model

Recent work on the shapes of small, simple impact craters on the Moon has shown that the parabolic ideal does not well represent the vast majority of these craters. They are hyperbolic in shape and usually resemble a cone more than a parabola. A parabolic shape also does not fit the most commonly held archetype for simple craters in general (Linné), which is also hyperbolic. In addition, Linné itself may not be the best model for fresh simple craters, in terms of cross-sectional shape, although shape data to compare it to have heretofore been lacking. Here, the “free shadowfront method” for determining the shapes of simple craters is used to measure 64 fresh simple craters on five lunar maria to test both assumptions. Laser altimetry cross sections, available for many of the craters measured herein, are used to complement and spot-check the shadow measurement results, and thereby demonstrate the efficacy of the free shadowfront method. A new shape model is established, and two craters that better fit this model than Linné are identified. These are located at 24.45° N/328.12° E and 31.35° N/296.46° E and have diameters of 1.40 and 2.73 km, respectively. An apparent dichotomy between fresh simple craters smaller than 2.5 km and those larger than this is observed. Flat floors are found to be ubiquitous among the larger craters, but rare and small in extent in smaller ones. A slide in one crater which appears to be an incipient flat floor suggests a major mode of formation for these flat floors.     

The inflationary Kantowski-Sachs cosmological model in general relativity

In this paper, we have investigated the inflationary Kantowski-Sachs cosmological model in the presence of mass less scalar field with a flat potential. To get an inflationary solution, we have considered a flat region of a constant potential V. Some physical and kinematical properties of the model are studied.     

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project  (72 ± 8 km s⁻¹ Mpc⁻¹)  . Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, for example, neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the cold dark matter paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal haloes and use an Markov Chain Monte Carlo method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.     

Behaviour of ion velocity distributions for a simple collision model

For application to studies of the high latitude ionosphere, we have calculated ion velocity distributions for a weekly-ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV m^?1. This shape persists for 1–2 hr after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fileds. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.     

Study of photometric phase curve: assuming a cellinoid ellipsoid shape for asteroid(106) Dione

We carried out new photometric observations of asteroid(106) Dione at three apparitions(2004, 2012 and 2015) to understand its basic physical properties. Based on a new brightness model,new photometric observational data and published data of(106) Dione were analyzed to characterize the morphology of Dione's photometric phase curve. In this brightness model, a cellinoid ellipsoid shape and three-parameter(H, G_1, G_2) magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of(106) Dione by considering an asymmetric shape of an asteroid, but also can be applied to more asteroids, especially those without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo(MCMC) method, Dione's absolute magnitude of H = 7.66_(-0.03)~(+0.03) mag, and phase function parameters G_1= 0.682_(-0.077)~(+0.077) and G_2= 0.081_(-0.042)~(+0.042) were obtained. Simultaneously, Dione's simplistic shape, orientation of pole and rotation period were also determined preliminarily.     

The Shape of the Solar Limb: Models and Observations

In this paper we compare observed, empirical, and modelled solar limb profiles and discuss their potential use to derive physical properties of the solar atmosphere. The PHOENIX, SolMod3D, and COSI radiative transfer codes as well as VAL-C models are used to calculate the solar limb shape under different assumptions. The main properties of each model are shown. The predicted limb shape as a function of wavelength for different features on the solar disk, such as quiet Sun, sunspots, and faculae, is investigated. These models provide overall consistent limb shapes with some discrepancies that are discussed here in terms of differences in solar atmosphere models, opacities, and the algorithms used to derive the solar limb profile. Our analysis confirms that the most common property of all models is limb shapes that are much steeper than what is observed, or predicted by the available empirical models. Furthermore, we have investigated the role of the Fraunhofer lines within the spectral domain used for the solar limb measurements. Our results show that the presence of the Fraunhofer lines significantly displaces the limb inflection point from its position estimated assuming only the photospheric continuum. The PICARD satellite, launched on 15 June 2010, will provide measurements of the limb shape at several wavelengths. This work shows that the precision of these measurements allows for discrimination among the available models.     

An interpretation of the decay characteristics of solar hard X-ray bursts

A simple trap model of solar hard X-ray bursts is discussed in which nonthermal electrons trapped in a magnetic bottle precipitate into the lower chromosphere through the resonant scattering by whistlers. In such a model, the X-ray spectra produced from trapped and precipitating electrons have different spectral shape, and both of the spectra will initially soften with time, provided the precipitation dominates over collisional degradation.     

Shapes of the saturnian icy satellites and their significance

The sizes and shapes of six icy saturnian satellites have been measured from Cassini Imaging Science Subsystem (ISS) data, employing limb coordinates and stereogrammetric control points. Mimas, Enceladus, Tethys, Dione and Rhea are well described by triaxial ellipsoids; Iapetus is best represented by an oblate spheroid. All satellites appear to have approached relaxed, equilibrium shapes at some point in their evolution, but all support at least 300 m of global-wavelength topography. The shape of Enceladus is most consistent with a homogeneous interior. If Enceladus is differentiated, its shape and apparent relaxation require either lateral inhomogeneities in an icy mantle and/or an irregularly shaped core. Iapetus supports a fossil bulge of over 30 km, and provides a benchmark for impact modification of shapes after global relaxation. Satellites such as Mimas that have smoother limbs than Iapetus, and are expected to have higher impact rates, must have relaxed after the shape of Iapetus was frozen.     

Origin and flatness of ponds on asteroid 433 Eros

NEAR‐Shoemaker Multi‐Spectral Imager data reveal several hundred “ponds” on 433 Eros: smooth deposits that sharply embay the bounding depressions in which they lie, and whose spectra appear blue relative to that of the surrounding terrain. We investigate the topography of these ponds on Eros using a new shape model derived from stereophotoclinometric analysis, and validated against altimetry from the NEAR Laser Rangefinder, to constrain the mode of pond formation from three existing models. We update the locations of 55 pond candidates identified in images registered to the new shape model. We classify the flatness of these features according to the behavior of the first and second derivatives of the topography. We find that less than half of pond candidates have clearly flat floors. Based on the pond topography, we favor an external origin for the ponds' deposits. We suggest that fine dust may be transported into bounding depressions by electrostatic levitation, but may adhere to slopes, and that seismic shaking may not be sufficient to bring the deposits to an equipotential surface. Disaggregation of a central boulder should result in an obvious break in slope, such a variation is only observed in roughly half the pond candidates.