The chaotic rotation of Hyperion

A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the ½ and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and ½ states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional motions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. At this point Hyperion becomes attitude unstable and begins to tumble. Capture from the chaotic state into the synchronous or ½ state is impossible since they are also attitude unstable. The 3/2 state does not exist. Capture into the stable 2 state is possible, but improbable. It is expected that Hyperion will be found tumbling chaotically.     

A numerical study of the rotational behavior of the white dwarf in DQ Herculis, II: the turn-over scenario

The optical pulsations in DQ Her are universally believed to be due to emission from the magnetic poles of the white dwarf. However, there is no way for a pulsation to be seen if the magnetic axis and the spin axis are aligned; whether the optical pulsation is seen directly from the magnetic poles or as a result of re-processing this beam from sides in an accretion disc, the magnetic and spin axes must be offset. This fact explains why the `oblique rotator' model has been adopted as a standard model for the DQ Her primary. In a recent paper, we have computed several axisymmetric models simulating the DQ Her white dwarf before its `turn-over' (where the term `turn-over' describes the process by which the magnetic axis gets inclining relative to the spin axis at a gradually increasing angle, the so-called `turn-over angle'). For such models, we have found that the moment of inertia along the rotation axis, I ₃₃, is less than the moment(s) of inertia along the two other principal axes, I ₁₁=I ₂₂. The situation I ₁₁>I ₃₃ is known as `dynamical asymmetry', and can cause a spontaneous turn-over of the magnetic axis with respect to the rotation axis . Consequently, the DQ Her white dwarf is either an oblique rotator undergoing its turn-over phase, or it is already qalmostequal a `perpendicular rotator', i.e., its turn-over angle is almost equal to 90^°. Assuming the first case, we study numerically the so-called `turn-over scenario', that is, a scenario on rotational evolution in which the turn-over phase is taken into account. We give emphasis on computations concerning the spin-down time rate of the DQ Her white dwarf due to turn-over (not to be confused with its spin-uptime rate due to accretion) for several possible values of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

A numerical study of the rotational behavior of the white dwarf in DQ Herculis

It is well-known that the optical pulsations in DQ Her are due to emission from the magnetic poles of the white dwarf. As the white dwarf spins on its axis, the magnetic poles sweep into and out of the line of sight due to the fact that the magnetic axis and the spin axis are not aligned, that is, the DQ Her white dwarf is an `oblique rotator'. So, a central question is if an initially axisymmetric model simulating the DQ Her white dwarf before its `turn-over' (where the term `turn-over' describes the process by which the magnetic axis gets inclining relative to the spin axis at a progressively increasing angle, the so-called `turn-over angle') is indeed susceptible to turn-over. For the puprose of resolving this problem, we compute several axisymmetric models of the DQ Her white dwarf. Our results show that, for both the rotation periods proposed on the basis of the observational evidence regarding the optical pulsations of DQ Her (i.e.,71 s or 142 s), the moment of inertia along the rotation axis is less than the corresponding moment of inertia along the remaining two principal axes of the axisymmetric configuration, I ₃₃ > I ₁₁(=I ₂₂). This is because toroidal magnetic field (tending to derive prolate equidensity surfaces) dominates over rotation (tending, in turn, to derive oblate equidensity surfaces), mainly in the interior of the star. The situation I ₁₁ < I ₃₃ is known as `dynamical asymmetry', and can cause a turn-over of the magnetic symmetry axis with respect to the rotation axis, eventually deriving a nonaxisymmetric configuration corresponding to the so-called `perpendicular rotator' with turn-over angle almost equal to 90^°. In this view, our results explain why the DQ Her white dwarf is now an oblique rotator. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nucleus properties of Comet 67P/Churyumov-Gerasimenko estimated from non-gravitational force modeling

By considering model comet nuclei with a wide range of sizes, prolate ellipsoidal shapes, spin axis orientations, and surface activity patterns, constraints have been placed on the nucleus properties of the primary Rosetta target, Comet 67P/Churyumov-Gerasimenko. This is done by requiring that the model bodies simultaneously reproduce the empirical nucleus rotational lightcurve, the water production rate as function of time, and non-gravitational changes (per apparition) of the orbital period (ΔP), longitude of perihelion (Δ?), and longitude of the ascending node (ΔΩ). Two different thermophysical models are used in order to calculate the water production rate and non-gravitational force vector due to nucleus outgassing of the model objects. By requiring that the nominal water production rate measurements are reproduced as well as possible, we find that the semi-major axis of the nucleus is close to 2.5 km, the nucleus axis ratio is approximately 1.4, while the spin axis argument is either 60°±15° or 240°±15°. The spin axis obliquity can only be preliminarily constrained, indicating retrograde rotation for the first argument value, and prograde rotation for the second suggested spin axis argument. A nucleus bulk density in the range 100-370 kg m⁻³ is found for the nominal ΔP, while an upper limit of 500 kg m⁻³ can be placed if the uncertainty in ΔP is considered. Both considered thermophysical models yield the same spin axis, size, shape, and density estimates. Alternatively, if calculated water production rates within an envelope around the measured data are considered, it is no longer possible to constrain the size, shape, and spin axis orientation of the nucleus, but an upper limit on the nucleus bulk density of 600 kg m⁻³ is suggested.     

Third order effect of rotation on stellar oscillations of a <Emphasis Type="Italic">β</Emphasis>-Cephei star

Here the effect of rotation up to third order in the angular velocity of a star on the p, f and g modes is investigated. To do this, the third-order perturbation formalism presented by Soufi et al. (Astron. Astrophys. 334:911, 1998) and revised by Karami (Chin. J. Astron. Astrophys. 8:285, 2008), was used. I quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating β-Cephei star with 12 M _⊙. For an equatorial velocity of 90 km s⁻¹, it is found that the second- and third-order corrections for (l,m)=(5,−4), for instance, are of order of 0.07% of the frequency for radial order n=−3 and reaches up to 0.6% for n=−20.     

Particle Dynamics in a Maxwell’s Ring-Type Configuration with a Radiating Central Primary

Maxwell’s ring-type configuration (i.e. an N-body model where the ν = Ν − 1 bodies have equal masses and are located at the vertices of a regular ν-gon while the N-th body with a different mass is located at the center of mass of the system) has attracted special attention during the last 15 years and many aspects of it have been studied by considering Newtonian and post-Newtonian potentials (Mioc and Stavinschi 1998, 1999), homographic solutions (Arribas et al. 2007) and relative equilibrium solutions (Elmabsout 1996), etc. An equally interesting problem, known as the ring problem of (N + 1) bodies, deals with the dynamics of a small body in the combined force field produced by such a configuration. This is the problem we are dealing with in the present paper and our aim is to investigate the variations in the dynamics of the small body in the case that the central primary is also a radiating source and therefore acts on the particle with both gravitation and radiation. Based on the general outlines of Radzievskii’s model, we study the permitted and the existing trapping regions of the particle, its equilibrium locations and their parametric variations as well as the existence of focal points in the zero-velocity diagrams. The distribution of the characteristic curves of families of planar symmetric periodic orbits and their stability for various values of the radiation coefficient of the central body is additionally investigated.     

The general equilibria of a spinning satellite in a circular orbit

Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body.     

Dark energy model in anisotropic Bianchi type-III space-time with variable EoS parameter

A new dark energy model in anisotropic Bianchi type-III space-time with variable equation of state (EoS) parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion θ in the model is proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i}. The EoS parameter ω is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003) and SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004). It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.     

A model of the gravitational field of Amalthea

Utilizing the topographic model of Jovian moon Amalthea (Stooke, 1994) and supposing that its mass density is constant we derived its basic geometrical and dynamical characteristics. For calculations the harmonic model of topography of the degree and order 18 was selected. The model appears to fit the entire surface to a mean accuracy of a few hundred meters, except in the regions localized around longitudes 0° and 180°. On the basis of the harmonic expansion of the topography we estimated the volume (V = 2.43 ± 0.02 km³) and the mean radius of topographyr ₀ = (79.7 ± 0.2) km. Generalized moments of inertia up to the order 2, principal moments of inertia and orientation of the principal axes with respect to the original reference frame were also calculated. The results show that although Amalthea has extremely irregular shape it may be treated dynamically as an almost symmetric body (B C). Finally, the set of the Stokes coefficients up to the degree and order 9 was evaluated. The results are verified by direct numerical integration.     

The kinematical mechanism for the perturbation of the rotational axis in the rotation of the elastic Earth

Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation. First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation, A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation of the figure axis.     

The secular variation of pulsar magnetic dipole moments

The time dependences of the inertia tensor and of a dissipative torque caused by the nonleptonic weak interaction have been investigated for a certain class of pulsars with no solid core. Early in the life of the pulsar, the angular velocity vector is predicted to move with respect to fixed body axes in such a way that it becomes perpendicular to the magnetic dipole moment. During this motion, the solid outer shell suffers plastic deformation so that the dipole moment becomes approximately collinear with a principal axis. After 10⁴ or 10⁵ yr, the dissipative torque is negligibly small compared with the electromagnetic torque, the Euler equations are those for a simple rigid body, and alignment of spin and dipole moment occurs. If the dipole moment discussed by Lyneet al. (1975) is interpreted as being equal to the component perpendicular to the spin, its secular decay is a natural property of this model and is not a consequence of field decay through electrical resistivity.     

Are There Rings Around the Sun?

The Theory of Alfven drag (Drell et al. in J Geophys Res 70: 3131–3145 1965; Anselmo and Farinella in Icarus, 58, 182–185 1983) is applied here to show that the existence of a possible solar ring structure at a radial distance of 0.02 AU (~4R _⊙ , R _⊙  = radius of the sun) predicted by earlier authors (Brecher et al. in Nature 282, 50–52 1979; Rawal in Bull. Astr. Soc. India 6, 92–95 1978, Moon Planets 24, 407–414 1981, Moon Planets 31, 175–182 1984, J Astrophys Astr 10, 257–259 1989) may not survive Alfven drag produced during even moderate solar magnetic storms which take place from time to time through the age of the sun, but a possible solar ring structure at a radial distance of 0.13 AU (~27R _⊙ ) (Brecher et al. in Nature 282, 50–52 1979; Rawal in Bull. Astr. Soc. India 6, 92–95 1978, Moon Planets 24, 407–414 1981, Moon Planets 31, 175–182 1984, J Astrophys Astr 10, 257–259 1989) may survive intense Alfven drag produced during even strong magnetic storms of magnetic field value up to 1,000 G.     

Influence of a second satellite on the rotational dynamics of an oblate moon

The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined. A simplified model, assuming the axis of rotation perpendicular to the (Keplerian) orbit plane, is derived. The differences between the two models, i.e. in the absence and presence of the second satellite, are investigated via bifurcation diagrams and by evolving compact sets of initial conditions in the phase space. It turns out that the presence of another satellite causes some trajectories, that were regular in its absence, to become chaotic. Moreover, the highly structured picture revealed by the bifurcation diagrams in dependence on the eccentricity of the oblate body’s orbit is destroyed when the gravitational influence is included, and the periodicities and critical curves are destroyed as well. For demonstrative purposes, focus is laid on parameters of the Saturn–Titan–Hyperion system, and on oblate satellites on low-eccentric orbits, i.e. \(e\approx 0.005\).     

Distribution of Impact Locations and Velocities of Earth Meteorites on the Moon

Following the analytical work of Armstrong et al. (Icarus 160:183–196, 2002), we detail an expanded N-body calculation of the direct transfer of terrestrial material to the Moon during a giant impact. By simulating 1.4 million particles over a range of launch velocities and ejecta angles, we have derived a map of the impact velocities, impact angles, and probable impact sites on the moon over the last 4 billion years. The maps indicate that the impacts with the highest vertical impact speeds are concentrated on the leading edge, with lower velocity/higher-angle impacts more numerous on the Moon’s trailing edge. While this enhanced simulation indicates the estimated globally averaged direct transfer fraction reported in Armstrong et al. (Icarus 160:183–196, 2002) is overestimated by a factor of 3–6, local concentrations can reach or exceed the previously published estimate. The most favorable location for large quantities of low velocity terrestrial material is 50 W, 85 S, with 8.4 times more impacts per square kilometer than the lunar surface average. This translates to 300–500 kg km⁻², compared to 200 kg km⁻² from the previous estimate. The maps also indicate a significant amount of material impacting elsewhere in the polar regions, especially near the South Pole-Aiken basin, a likely target for sample return in the near future. The magnitudes of the impact speeds cluster near 3 km/s, but there is a bimodal distribution in impact angles, leading to 43% of impacts with very low (<1 km/s) vertical impact speeds. This, combined with the enhanced surface density of meteorites in specific regions, increases the likelihood of weakly shocked terrestrial material being identified and recovered on the Moon.     

Generalized YORP evolution: Onset of tumbling and new asymptotic states

Asteroids have a wide range of rotation states. While the majority spin a few times to several times each day in principal axis rotation, a small number spin so slowly that they have somehow managed to enter into a tumbling rotation state. Here we investigate whether the Yarkovsky-Radzievskii-O'Keefe-Paddack (YORP) thermal radiation effect could have produced these unusual spin states. To do this, we developed a Lie-Poisson integrator of the orbital and rotational motion of a model asteroid. Solar torques, YORP, and internal energy dissipation were included in our model. Using this code, we found that YORP can no longer drive the spin rates of bodies toward values infinitely close to zero. Instead, bodies losing too much rotation angular momentum fall into chaotic tumbling rotation states where the spin axis wanders randomly for some interval of time. Eventually, our model asteroids reach rotation states that approach regular motion of the spin axis in the body frame. An analytical model designed to describe this behavior does a good job of predicting how and when the onset of tumbling motion should take place. The question of whether a given asteroid will fall into a tumbling rotation state depends on the efficiency of its internal energy dissipation and on the precise way YORP modifies the spin rates of small bodies.     

Relation Between the 3D-Geometry of the Coronal Wave and Associated CME During the 26 April 2008 Event

We study the kinematical characteristics and 3D geometry of a large-scale coronal wave that occurred in association with the 26 April 2008 flare-CME event. The wave was observed with the EUVI instruments aboard both STEREO spacecraft (STEREO-A and STEREO-B) with a mean speed of ∼ 240 km s⁻¹. The wave is more pronounced in the eastern propagation direction, and is thus, better observable in STEREO-B images. From STEREO-B observations we derive two separate initiation centers for the wave, and their locations fit with the coronal dimming regions. Assuming a simple geometry of the wave we reconstruct its 3D nature from combined STEREO-A and STEREO-B observations. We find that the wave structure is asymmetric with an inclination toward East. The associated CME has a deprojected speed of ∼ 750±50 km s⁻¹, and it shows a non-radial outward motion toward the East with respect to the underlying source region location. Applying the forward fitting model developed by Thernisien, Howard, and Vourlidas (Astrophys. J. 652, 763, 2006), we derive the CME flux rope position on the solar surface to be close to the dimming regions. We conclude that the expanding flanks of the CME most likely drive and shape the coronal wave.     

The fate of ejecta from Hyperion

Ejecta from Saturn's moon Hyperion are subject to powerful perturbations from nearby Titan, which control their ultimate fate. We have performed numerical integrations to simulate a simplified system consisting of Saturn (including optical flattening as well as dynamical oblateness), its main ring system (treated as a massless flat annulus), the moons Tethys, Dione, Titan, Hyperion, and Iapetus, and the Sun (treated simply as a massive satellite). At several different points in Hyperion's orbit, 1050 massless particles, more or less evenly distributed over latitude and longitude, were ejected radially outward from 1 km above Hyperion's mean radius at speeds 10% faster than escape speed from Hyperion. Most of these particles were removed within the first few thousand years, but ∼3% of them survived the entire 100,000-year duration of the simulations. Ejecta from Hyperion are much more widely scattered than previously thought, and can cross the orbits of all of Saturn's satellites. About 9% of all the particles escaped from the saturnian system, but Titan accreted ∼78% of the total, while Hyperion reaccreted only ∼5%. This low efficiency of reaccretion may help to account for Hyperion's small size and rugged shape. Only ∼1% of all the particles hit other satellites, and another ∼1% impacted Saturn itself, while ∼3% of them struck its main rings. The high proportion of impacts into Saturn's rings is surprising; these collisions show a broad decline in impact speed with time, suggesting that Hyperion ejecta gradually spread inwards. Additional simulations were used to investigate the dependence of ejecta evolution on launch speed, the mass of Hyperion, and the presence of the Sun. In general, the wide distribution of ejecta from Hyperion suggests that it does contribute to “Population II” craters on the inner satellites of Saturn. Ejecta which escape from a satellite into temporary orbit about its planet, but later reimpact into the same moon or another one produce “poltorary” impacts, intermediate in character between primary and secondary impacts. It may be possible to distinguish poltorary craters from primary and secondary craters on the basis of morphology.     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Topography and geology of Hyperion

I have mapped the Saturnian satellite Hyperion using Voyager 2 images obtained in 1981 and a shape model derived from the results of Thomas et al. (1995). The results are presented in tabular and graphic form, including detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 270, 201 and 336 km. The volume is estimated to be 9.5 ± 2.0 × 10⁶ km³. Geological interpretations were augmented by the use of super-resolution image composites. The surface is heavily cratered. A system of scarps and an isolated mountain are interpreted as the rim and central peak of an impact crater with a diameter similar to the mean diameter of the satellite itself, the largest crater with recognizable impact morphology in relation to the size of the body yet observed in the solar system. The crater density dates that impact, not the formation of Hyperion. Grooves are identified in several images, and form part of a zone of fracturing radial to a prominent crater.University of Western Ontario