The Lissajous transformation IV. Delaunay and Lissajous variables

Relations are established between the Delaunay variables defined over a phase space E in four dimensions and the Lissajous variables defined over a four-dimensional phase space F when the latter is mapped onto E by a parabolic canonical transformation.     

The Lissajous transformation II. Normalization

Normalization of a perturbed elliptic oscillator, when executed in Lissajous variables, amounts to averaging over the elliptic anomaly. The reduced Lissajous variables constitute a system of cylindrical coordinates over the orbital spheres of constant energy, but the pole-like singularities are removed by reverting to the subjacent Hopf coordinates. The two-parameter coupling that is a polynomial of degree four admitting the symmetries of the square is studied in detail. It is shown that the normalized elliptic oscillator in that case behaves everywhere in the parameter plane like a rigid body in free rotation about a fixed point, and that it passes through butterfly bifurcations wherever its phase flow admits non isolated equilibria.     

Integrability of the Yang-Mills Hamiltonian system

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.     

On the measure of the structure around the last kam torus before and after its break-up

We review theorems for proving non-integrability of Hamiltonian dynamical systems, which are based on properties of the variational equations in real or complex time or on the destruction of the resonant tori of an integrable system under a perturbation.     

A re-analysis of the 1971 Beta Scorpii occultation by Jupiter: study of temperature fluctuations and detection of wave activity

Data from the 13 May 1971 β Scorpii occultation by the southern polar region of Jupiter (Vapillon et al., 1973, Astron. Astrophys. 29, 135-149) are re-analyzed with current methods. We correct the previous results for an inacurrate background estimation and calculate new temperature profiles, that are now consistent with the results of other observers of this occultation, as well as with the current knowledge of the jovian atmosphere. The characteristics of the profiles of temperature gradient and the spectral behavior of the temperature fluctuations are found to be similar to the results of previous investigations of planetary atmospheres and in agreement with the presence of atmospheric propagating gravity waves in the jovian atmosphere. We use a wavelet analysis of the temperature profiles to identify the dominant modes of wave activity and compare the reconstructed temperature fluctuations to model-generated gravity waves.     

Motion On the Sphere: Integrability and Families of Orbits

We study the problem of the motion of a unit mass on the unit sphere and examine the relation between integrability and certain monoparametric families of orbits. In particular we show that if the potential is compatible with a family of meridians, it is integrable with an integral linear in the velocities, while a family of parallels guarantees integrability with an integral quadratic in the velocities.     

Direct detection and characterization of extrasolar planets: The Mariotti space interferometer

Space infrared nulling interferometry has been identified as one of the most promising techniques for direct detection of Earthlike extrasolar planets and spectroscopic analysis of their atmospheres in the near future. After a review of various nulling interferometer schemes, we introduce the concept of internal modulation. As an illustration, we describe a two-dimensional array of telescopes that provides full internal modulation capabilities: the Mariotti space interferometer. It consists of six free-flying telescopes positioned on the sides of an equilateral triangle and grouped into three nulling interferometers. Their nulled outputs are suitably phase-shifted with respect to each other, coherently recombined, and detected. The phase shifts applied between the nullers are periodically changed, providing signal modulation at a frequency that can be selected to minimize instrumental and background noise. The frequency upper limit is set by the read-out noise of the detectors, and turns out to be ¹⁰⁻¹-¹⁰⁻² Hz for currently available Si:As BIB devices. This “fast” signal modulation allows much better monitoring of the background and detector drifts than when one relies solely on the external modulation provided by the slow rotation of the whole interferometer (at typical frequencies of 3×¹⁰⁻⁴-3×¹⁰⁻⁵ Hz). Mariotti internal modulation, also known as “phase chopping,” thus appears as a major step toward the feasibility of the Darwin and TPF space missions.     

The collisional and dynamical evolution of the main-belt and NEA size distributions

The size distribution of main belt of asteroids is determined primarily by collisional processes. Large asteroids break up and form smaller asteroids in a collisional cascade, with the outcome controlled by the strength-size relationship for asteroids. In addition to collisional processes, the non-collisional removal of asteroids from the main belt (and their insertion into the near-Earth asteroid (NEA) population) is critical, and involves several effects: strong resonances increase the orbital eccentricity of asteroids and cause them to enter the inner planet region; chaotic diffusion by numerous weak resonances causes a slow leak of asteroids into the Mars- and Earth-crossing populations; and the Yarkovsky effect, a radiation force on asteroids, is the primary process that drives asteroids into these resonant escape routes. Yarkovsky drift is size-dependent and can modify the main-belt size distribution. The NEA size distribution is primarily determined by its source, the main-belt population, and by the size-dependent processes that deliver bodies from the main belt. All of these effects are simulated in a numerical collisional evolution model that incorporates removal by non-collisional processes. We test our model against a wide range of observational constraints, such as the observed main-belt and NEA size distributions, the number of asteroid families, the preserved basaltic crust of Vesta and its large south-pole impact basin, the cosmic ray exposure ages of meteorites, and the cratering records on asteroids. We find a strength-size relationship for main-belt asteroids and non-collisional removal rates from the main belt such that our model fits these constraints as best as possible within the parameter space we explore. Our results are consistent with other independent estimates of strength and removal rates.     

Development of potential ecological niches in impact-induced hydrothermal systems: The small-to-medium size impacts

Effect of meteorite impact on the biological evolution is usually considered by its catastrophic consequences. However, the impacts can create opportunity for other organisms and the structures themselves can serve as suitable ecological niches (oases) for life. In this contribution we present results of modeling of an impact-induced hydrothermal (IHT) system in a small-to-medium sized impact crater, where the development of zones habitable for primitive hydrothermal thermophilic and hypethermophilic microorganisms was studied. The impact and geothermal modeling was verified against the 4-km diameter Kärdla complex structure, Hiiumaa Island, Estonia. If there is an sufficient amount of water present in the target (e.g., sea cover, groundwater or permafrost resources) then the differential temperature fields created by the impact initiate a hydrothermal circulation system within the crater. The results of transient fluid flow and heat transfer simulations in Kärdla suggest that immediately after impact the temperatures in the central area, which contains the most hydrothermal alteration, were well above the boiling point. However, due to efficient heat loss at the groundwater vaporization front, the vapor-dominated area disappears within a few decades. In the central uplift area, the conditions favorable for thermophilic microorganisms (temperatures <100 °C) were reached in 500–1000 years after the impact. The overall cooling to ambient temperatures in the deeper parts of the central uplift lasted for thousands of years. In the crater depression and rim area the initial temperatures, suggested by the impact modeling, were much lower—from 150 °C to ambient temperatures, except locally in fracture zones and suevite pockets. Our data suggest that in small-to-medium size impact craters with insignificant melting, the suitable conditions for hydrothermal microbial communities are established shortly (tens to few hundreds of years as maximum) after the impact in most parts of the crater. In the central uplift area the microbial colonization is inhibited for about a thousand years. However, this is the area, which afterwards retains the optimum temperatures (45–120 °C) needed for hydrothermal microorganisms for the longest period. Geochemical and mineralogical data suggest, in general, neutral pH 7(±1) fluid of the IHT system, which is, when compared to volcanic hydrotherms, richer in dissolved oxygen and poor in reduced compounds. This suggests the preference for sulfur-reducing microorganisms in the possible impact-induced hydrothermal communities.     

Simulations of high-latitude spots on Jupiter: Constraints on vortex strength and the deep wind

We combine high-resolution observations of the dynamical behavior of small vortices (diameters ?5000 km) located at latitude 60°N on Jupiter with forward modeling, using the EPIC atmospheric model, to address two open questions: the dependence of the zonal winds with depth, and the strength of vortices that are too small to apply cloud tracking to their internal structure. The observed drift rates of the vortices can only be reproduced in the model when the zonal winds increase slightly with depth below the cloud tops, with a vertical shear that is less than was measured at 7°N at the southern rim of a 5-μm hotspot by the Galileo Probe Doppler Wind Experiment (DWE). This supports the idea that Jupiter's vertical shear may vary significantly with latitude. Our simulations suggest that the morphology of the mergers between vortices mainly depends on their maximum tangential velocities, the best results occurring when the tangential velocity is close to the velocity difference of the alternating jets constraining the zone in which the vortices are embedded. We use this correlation, together with the high-resolution data available for the White Ovals, to derive an empirical relationship between the maximum tangential velocity of a jovian vortex and its size, normalized by the strength and size of the encompassing shear zone. The Great Red Spot stands out as a significant anomaly to this relationship, but interestingly it is becoming less so with time.     

The jovian anticyclone BA: II. Circulation and interaction with the zonal jets

In this second part of our study of the large jovian anticyclone BA we present detailed measurements of its internal circulation and numerical models of its interaction with the zonal jets and nearby cyclonic regions. We characterized the flow using high-resolution observations obtained by the Cassini spacecraft in December 2000 (9 months after the genesis of BA as a result of the merger of two large White Ovals), by the ACS camera onboard HST in January 2005 and April 2006 and by the New Horizons spacecraft in February 2007. Cloud motions were derived from high-resolution images using an automatic correlator that provides a large sampling of the motions in images separated by short time intervals (30 min-2 h). The internal wind structure did not change when the oval changed its color reddening in late 2005-early 2006 and all four datasets from 2000 to 2007 consistently show a similar wind regime: an asymmetric intense anticyclonic vortex with faster winds in its Southern portion with mean speeds of 110 m/s and peak velocities of 135 m/s. These speeds are slightly higher than those measured in the three White Ovals predecessors of BA by the Voyagers [Mitchell, J.L., Beebe, R.F., Ingersoll, A.P., Garneau, G.W., 1981. J. Geophys. Res. 86, 8751-8757] and Galileo [Vasavada, A.R., and 13 colleagues, 1998. Icarus 135, 265-275] but not as much as it has been recently reported [Simon-Miller, A.A., Chanover, N.J., Orton, G.S., Sussman, M., Tsavaris, I.G., Karkoschka, E., 2006. Icarus 185, 558-562; Cheng, A.F., and 14 colleagues, 2008. Astronom. J. 135, 2446-2452]. The asymmetry of the velocities in the vortex is a consequence of the interaction of BA with the zonal circulation and emerges as a natural result in high-resolution simulations of the vortex dynamics using the EPIC model.     

Astrometric detection of binary companions and planets: Acceleration of proper motion

Apparent acceleration of proper motion is one of the observable manifestations of orbital motion in binary stars. Owing to the increasing accuracy of astrometric measurements, it may also be a method to detect binarity of stars. This paper presents some analytical expressions for the effects of binary motion on proper motions when the orbital period is at least several times the span of observations. We estimate orbit dimensions and distances at which low‐mass companions and planets may be detected around main‐sequence stars, using preliminary estimates of precision for the AMEX, GAIA and SIM space missions.     

The 10 October 1999 HIP 9369 occultation by the northern polar region of Jupiter: ingress and egress lightcurves analysis

The occultation of bright star HIP9369 by the northern polar region of Jupiter was observed from four locations in North and South America, providing four data sets for ingress and egress. The inversion of the eight occultation lightcurves provides temperature profiles at different latitudes ranging from 55°N to 73.2°N. We estimate the errors on the profiles due to the uncertainties of the inversion method and compare the value of the temperature at the deepest level probed (∼ 50 μbar) with previous observations. The shape of the temperature gradient profile is found similar to previous investigations of planetary atmospheres with propagating and breaking gravity waves. We analyze the small scale structures in both lightcurves and temperature profiles using the continuous wavelet transform. The calculated power spectra of localized fluctuations in the temperature profiles show slopes close to −3 for all eight profiles. We also isolate and reconstruct the three-dimensional geometry of a single wave mode with vertical and horizontal wavelengths of respectively 3 and 70 km. The identified wave is consistent with the gravity wave regime, with a horizontal phase speed nearly parallel to the planetary meridian. Nevertheless, the dissipation of the corresponding wave in Jupiter’s stratosphere should preclude its detection at the observed levels and an acoustic wave cannot be ruled out.     

Orbital evolution of the Gefion and Adeona asteroid families: close encounters with massive asteroids and the Yarkovsky effect

Asteroid families are groupings of minor planets identified by clustering in their proper orbital elements; these objects have spectral signatures consistent with an origin in the break-up of a common parent body. From the current values of proper semimajor axes a of family members one might hope to estimate the ejection velocities with which the fragments left the putative break-up event (assuming that the pieces were ejected isotropically). However, the ejection velocities so inferred are consistently higher than N-body and hydro-code simulations, as well as laboratory experiments, suggest. To explain this discrepancy between today’s orbital distribution of asteroid family members and their supposed launch velocities, we study whether asteroid family members might have been ejected from the collision at low speeds and then slowly drifted to their current positions, via one or more dynamical processes. Studies show that the proper a of asteroid family members can be altered by two mechanisms: (i) close encounters with massive asteroids, and (ii) the Yarkovsky non-gravitational effect. Because the Yarkovsky effect for kilometer-sized bodies decreases with asteroid diameter D, it is unlikely to have appreciably moved large asteroids (say those with D > 15 km) over the typical family age (1-2 Gyr).For this reason, we numerically studied the mobility of family members produced by close encounters with main-belt, non-family asteroids that were thought massive enough to significantly change their orbits over long timescales. Our goal was to learn the degree to which perturbations might modify the proper a values of all family members, including those too large to be influenced by the Yarkovsky effect. Our initial simulations demonstrated immediately that very few asteroids were massive enough to significantly alter relative orbits among family members. Thus, to maximize gravitational perturbations in our 500-Myr integrations, we investigated the effect of close encounters on two families, Gefion and Adeona, that have high encounter probabilities with 1 Ceres, by far the largest asteroid in the main belt. Our results show that members of these families spreads in a of less than 5% since their formation. Thus gravitational interactions cannot account for the large inferred escape velocities.The effect of close encounters with massive asteroids is, however, not entirely negligible. For about 10% of the simulated bodies, close encounters increased the “inferred” ejection velocities from sub-100 m/s to values greater than 100 m/s, beyond what hydro-code and N-body simulations suggest are the maximum possible initial ejection velocity for members of Adeona and Gefion with D > 15 km. Thus this mechanism of mobility may be responsible for the unusually high inferred ejection speeds of a few of the largest members of these two families.To understand the orbital evolution of the entire family, including smaller members, we also performed simulations to account for the drift of smaller asteroids caused by the Yarkovsky effect. Our two sets of simulations suggest that the two families we investigated are relatively young compared to larger families like Koronis and Themis, which have estimated ages of about 2 Byr. The Adeona and Gefion families seems to be no more than 600 and 850 Myr old, respectively.     

On the potential of transit surveys in star clusters: impact of correlated noise and radial velocity follow-up

We present an extension of the formalism recently proposed by Pepper and Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity (RV) follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high -mass end which, when considered jointly with the RV requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide-field surveys may detect hot Neptunes whose RV signal can be measured with present-day instrumentation in very nearby (<100 pc) clusters.     

Microscale simulations of Venus’ convective adjustment and mixing near the surface: Thermal and material transport processes

Heat and material transport processes caused by convective adjustment and mixing are important in modeling of Venus’ atmosphere. In the present study, microscale atmospheric simulations near the venusian surface were conducted using a Weather Research and Forecasting model to elucidate the thermal and material transport processes of convective adjustment and mixing. When convective adjustment occurs, the heat and passive tracer are rapidly mixed into the upper stable layer with convective penetration. The convective adjustment produces large eddy diffusions of heat and passive tracer, which may explain the large eddy diffusions estimated in the radiative-convective equilibrium model.For values of surface heat flux Q greater than a threshold (=0.064 K m s⁻¹ in the present study), the convectively mixed layer with high eddy diffusion coefficients grows with time. In contrast, the mixed layer decays with time for Q values smaller than the threshold. The thermal structure near the surface is controlled not only by extremely long-term radiative processes, but also by microscale dynamics with time scales of several hours. A mixed layer with high eddy diffusion coefficients may be maintained or grow with time if the surface heat flux is high in the volcanic hotspot and adjacent areas.     

The high-pressure phase relation of the MgSO4-H2O system and its implication for the internal structure of Ganymede

We have determined the phase relation of the MgSO₄-H₂O binary system using an externally heated diamond anvil cell in the compositional range of 0-30 wt.% MgSO₄, and under temperature and pressure conditions from 298 to 500 K and up to 4.5 GPa. Using our experimental results, we were able to estimate the composition of the ice mantle of the large icy satellites of Jupiter, such as Ganymede.In our experiments, we identified the following phases in the MgSO₄-H₂O system up to 4 GPa at 298 K: Ices VI and VII, magnesium heptahydrate, MgSO₄·7H₂O, and a liquid phase. The present phase relations suggest that there may be a deep internal ocean down to a depth about 800 km in the interior of Ganymede.     

Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars

At present, approximately 1500 asteroids are known to evolve inside or sticked to the exterior 1:2 resonance with Mars at a ? 2.418 AU, being (142) Polana the largest member of this group. The effect of the forced secular modes superposed to the resonance gives rise to a complex dynamical evolution. Chaotic diffusion, collisions, close encounters with massive asteroids and mainly orbital migration due to the Yarkovsky effect generate continuous captures to and losses from the resonance, with a fraction of asteroids remaining captured over long time scales and generating a concentration in the semimajor axis distribution that exceeds by 20% the population of background asteroids. The Yarkovsky effect induces different dynamics according to the asteroid size, producing an excess of small asteroids inside the resonance. The evolution in the resonance generates a signature on the orbits, mainly in eccentricity, that depends on the time the asteroid remains captured inside the resonance and on the magnitude of the Yarkovsky effect. The greater the asteroids, the larger the time they remain captured in the resonance, allowing greater diffusion in eccentricity and inclination. The resonance generates a discontinuity and mixing in the space of proper elements producing misidentification of dynamical family members, mainly for Vesta and Nysa-Polana families. The half-life of resonant asteroids large enough for not being affected by the Yarkovsky effect is about 1 Gyr. From the point of view of taxonomic classes, the resonant population does not differ from the background population and the excess of small asteroids is confirmed.     

The impact of martian mesoscale winds on surface temperature and on the determination of thermal inertia

Radiative control of surface temperature is a key characteristic of the martian environment and its low-density atmosphere. Here we show through meteorological modeling that surface temperature can be far from radiative equilibrium over numerous sloping terrains on Mars, where nighttime mesoscale katabatic winds impact the surface energy budget. Katabatic circulations induce both adiabatic atmospheric heating and enhancement of downward sensible heat flux, which then becomes comparable to radiative flux and acts to warm the ground. Through this mechanism, surface temperature can increase up to 20 K. One consequence is that warm signatures of surface temperature over slopes, observed through infrared spectrometry, cannot be systematically associated with contrasts of intrinsic soil thermal inertia. Apparent thermal inertia maps retrieved thus far possibly contain wind-induced structures. Another consequence is that surface temperature observations close to sloping terrains could allow the validation of model predictions for martian katabatic winds, provided contrasts in intrinsic thermal inertia can be ruled out. The thermal impact of winds is mostly discussed in this paper in the particular cases of Olympus Mons/Lycus Sulci and Terra Meridiani but is generally significant over any sloped terrains in low thermal inertia areas. It is even general enough to apply under daytime conditions, thereby providing a possible explanation for observed afternoon surface cooling, and to ice-covered terrains, thereby providing new insights on how winds could have shaped the present surface of Mars.     

The radio environment of the 21 Centimeter Array:RFI detection and mitigation

Detection and mitigation of radio frequency interference(RFI) is the first and also the key step for data processing in radio observations, especially for ongoing low frequency radio experiments towards the detection of the cosmic dawn and epoch of reionization(Eo R). In this paper we demonstrate the technique and efficiency of RFI identification and mitigation for the 21 Centimeter Array(21CMA), a radio interferometer dedicated to the statistical measurement of Eo R. For terrestrial, man-made RFI, we concentrate mainly on a statistical approach by identifying and then excising non-Gaussian signatures, in the sense that the extremely weak cosmic signal is actually buried under thermal and therefore Gaussian noise. We also introduce the so-called visibility correlation coefficient instead of conventional visibility, which allows a further suppression of rapidly time-varying RFI. Finally, we briefly discuss removals of the sky RFI, the leakage of sidelobes from off-field strong radio sources with time-invariant power and a featureless spectrum. It turns out that state of the art technique should allow us to detect and mitigate RFI to a satisfactory level in present low frequency interferometer observations such as those acquired with the 21 CMA, and the accuracy and efficiency can be greatly improved with the employment of low-cost, high-speed computing facilities for data acquisition and processing.