A review of Titan’s atmospheric phenomena

Saturn’s satellite Titan is a particularly interesting body in our solar system. It is the only satellite with a dense atmosphere, which is primarily made of nitrogen and methane. It harbours an intricate photochemistry, that populates the atmosphere with aerosols, but that should deplete irreversibly the methane. The observation that methane is not depleted led to the study of Titan’s methane cycle, starting with its atmospheric part. The features that inhabit Titan’s atmosphere can last for timescales varying from year to day. For instance, the reversal of the north–south asymmetry is linked to the 16-year seasonal cycle. Diurnal phenomena have also been observed, like a stratospheric haze enhancement or a possible tropospheric drizzle. Furthermore, clouds have been reported on Titan since 1993. From these first detections and up to now, with the recent inputs from the Cassini–Huygens mission, clouds have displayed a large range of shapes, altitudes, and natures, from the flocky tropospheric clouds at the south pole to the stratiform ones in the northern stratosphere. It is still difficult to compose a clear picture of the physical processes governing these phenomena, even though of lot of different means of observation (spectroscopy, imaging) are available now. We propose here an overview of the phenomena reported between 1993 and 2008 in the low atmosphere of Titan, with indications on the location, altitude, and their characteristics in order to give a perspective of our up-to-date understanding of Titan’s meteorological manifestations. We shall focus mainly on direct imaging observations, from both space- and ground-based facilities. All of these observations, published in more than 30 different refereed papers to date, allow us to build a precise chronology of Titan’s atmospheric changes (including the north–south asymmetry, diurnal and seasonal effects, etc). Since the interpretation is at an early stage, we only briefly mention some of the current theories regarding the features’ nature.     

LAPLACE: A mission to Europa and the Jupiter System for ESA’s Cosmic Vision Programme

The exploration of the Jovian System and its fascinating satellite Europa is one of the priorities presented in ESA’s “Cosmic Vision” strategic document. The Jovian System indeed displays many facets. It is a small planetary system in its own right, built-up out of the mixture of gas and icy material that was present in the external region of the solar nebula. Through a complex history of accretion, internal differentiation and dynamic interaction, a very unique satellite system formed, in which three of the four Galilean satellites are locked in the so-called Laplace resonance. The energy and angular momentum they exchange among themselves and with Jupiter contribute to various degrees to the internal heating sources of the satellites. Unique among these satellites, Europa is believed to shelter an ocean between its geodynamically active icy crust and its silicate mantle, one where the main conditions for habitability may be fulfilled. For this very reason, Europa is one of the best candidates for the search for life in our Solar System. So, is Europa really habitable, representing a “habitable zone” in the Jupiter system? To answer this specific question, we need a dedicated mission to Europa. But to understand in a more generic way the habitability conditions around giant planets, we need to go beyond Europa itself and address two more general questions at the scale of the Jupiter system: to what extent is its possible habitability related to the initial conditions and formation scenario of the Jovian satellites? To what extent is it due to the way the Jupiter system works? ESA’s Cosmic Vision programme offers an ideal and timely framework to address these three key questions. Building on the in-depth reconnaissance of the Jupiter System by Galileo (and the Voyager, Ulysses, Cassini and New Horizons fly-by’s) and on the anticipated accomplishments of NASA’s JUNO mission, it is now time to design and fly a new mission which will focus on these three major questions. LAPLACE, as we propose to call it, will deploy in the Jovian system a triad of orbiting platforms to perform coordinated observations of its main components: Europa, our priority target, the Jovian satellites, Jupiter’s magnetosphere and its atmosphere and interior. LAPLACE will consolidate Europe’s role and visibility in the exploration of the Solar System and will foster the development of technologies for the exploration of deep space in Europe. Its multi-platform and multi-target architecture, combined with its broadly multidisciplinary scientific dimension, will provide an outstanding opportunity to build a broad international collaboration with all interested nations and space agencies. Team members: full list available at . Full list of LAPLACE proposal members at .     

Regularization of the circular restricted three-body problem using ‘similar’ coordinate systems

The regularization of a new problem, namely the three-body problem, using ‘similar’ coordinate system is proposed. For this purpose we use the relation of ‘similarity’, which has been introduced as an equivalence relation in a previous paper (see Roman in Astrophys. Space Sci. doi:, 2011). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function, we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered in the more massive and the less massive star of the binary system. The ‘similar’ polar angle’s definition is introduced, in order to analyze the regularization’s geometrical transformation. The effect of Levi-Civita’s transformation is described in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically, for the Earth-Moon binary system.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

Mass density of the upper atmosphere derived from Starlette’s Precise Orbit Determination with Satellite Laser Ranging

The atmospheric mass density of the upper atmosphere from the spherical Starlette satellite’s Precise Orbit Determination is first derived with Satellite Laser Ranging measurements at 815 to 1115 km during strong solar and geomagnetic activities. Starlette’s orbit is determined using the improved orbit determination techniques combining optimum parameters with a precise empirical drag application to a gravity field. MSIS-86 and NRLMSISE-00 atmospheric density models are compared with the Starlette drag-derived atmospheric density of the upper atmosphere. It is found that the variation in the Starlette’s drag coefficient above 800 km corresponds well with the level of geomagnetic activity. This represents that the satellite orbit is mainly perturbed by the Joule heating from geomagnetic activity at the upper atmosphere. This result concludes that MSIS empirical models strongly underestimate the mass density of the upper atmosphere as compared to the Starlette drag-derived atmospheric density during the geomagnetic storms. We suggest that the atmospheric density models should be analyzed with higher altitude acceleration data for a better understanding of long-term solar and geomagnetic effects.     

Long-term perturbations due to a disturbing body in elliptic inclined orbit

In the current study, a double-averaged analytical model including the action of the perturbing body’s inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body’s inclination, and illustrate that the lunar obliquity with the value 6.68^∘ is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.     

PHOKA experiment: Description of the equipment and first results

The CORONAS-PHOTON Russian satellite intended to study the Sun was successfully launched into orbit on January 30, 2009. Scientific equipment of the satellite includes the PHOKA radiometer of soft X-ray and extreme UV radiation. The PHOKA instrument is intended to measure the absolute flux of solar electromagnetic radiation in the spectral windows of 0.5–7 nm, 0.5–11 nm, 27–37 nm, and 116–125 nm. When leaving and entering the Earth’s shadow, the instrument aboard the spacecraft measures absorption of radiation by various layers of the Earth’s atmosphere. Before the launch, photodiodes of the instrument had been calibrated using a synchrotron radiation source. In-flight stability of sensitivity of main channels is controlled using calibration channels. The paper describes the PHOKA instrument and presents its capabilities and main characteristics, as well as some results of its operation in orbit.     

A New Version of the Neutron Monitor Based Anisotropic GLE Model: Application to GLE60

In this work we present a cosmic ray model that couples primary solar cosmic rays at the top of the Earth’s atmosphere with the secondary ones detected at ground level by neutron monitors during Ground-Level Enhancements (GLEs). The Neutron Monitor Based Anisotropic GLE Pure Power Law (NMBANGLE PPOLA) model constitutes a new version of the already existing NMBANGLE model, differing in the solar cosmic ray spectrum assumed. The total output of the model is a multi-dimensional GLE picture that reveals part of the characteristics of the big solar proton events recorded at ground level. We apply both versions of the model to the GLE of 15 April 2001 (GLE60) and compare the results.     

Influence of geomagnetic field on the motion of low satellites

The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1 satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis.     

On the relationship of cosmic ray intensity with solar,interplanetary, and geophysical parameters

The flux rate of cosmic rays incident on the Earth’s upper atmosphere is modulated by the solar wind and the Earth’s magnetic field. The amount of solar wind is not constant due to changes in solar activity in each solar cycle, and hence the level of cosmic ray modulation varies with solar activity. In this context, we have investigated the variability and the relationship of cosmic ray intensity with solar, interplanetary, and geophysical parameters from January 1982 through December 2008. Simultaneous observations have been made to quantify the exact relationship between the cosmic ray intensity and those parameters during the solar maxima and minima, respectively. It is found that the stronger the interplanetary magnetic field, solar wind plasma velocity, and solar wind plasma temperature, the weaker the cosmic ray intensity. Hence, the lowest cosmic ray intensity has good correlations with simultaneous solar parameters, while the highest cosmic ray intensity does not. Our results show that higher solar activity is responsible for a higher geomagnetic effect and vice versa.     

Bicentennial decrease of the solar constant leads to the Earth’s unbalanced heat budget and deep climate cooling

Long-wave energy emitted by the Earth-atmosphere into space is characterized by changes in power over time that always lag behind the changes in power of the absorbed solar radiation due to slow variation in enthalpy of the Earth-atmosphere system. Long-term variation of the solar energy radiation absorbed by the Earth remains uncompensated by the energy radiated into space over the interval of time that is determined by the thermal inertia. The basic state of the climate system is when the debit and credit sides in the Earth’s global annual mean energy budget (including the air and water envelopes) are almost always unbalanced. The annual mean balance of the heat budget of the Earth-atmosphere over a long time period will reliably define the behavior and magnitude of the energy excess accumulated by the Earth or energy deficit to allow us to determine adequately and to predict beforehand the trend and amplitude of the forthcoming climate change using the prognosis of variations in the total solar irradiance (solar constant). The decrease in solar constant has been observed since the early 1990s. The Earth as a planet will have a negative balance in the energy budget in the future as well, because the Sun is entering the decline phase of the bicentennial luminosity changes. This will lead to a drop in temperature in approximately 2014. The increase in albedo and decrease in greenhouse gas concentration in the atmosphere will result in the additional decrease in absorbed portion of the solar energy and reduced greenhouse effect. The additional drop in temperature exceeding the effect of decreased solar constant can occur as a result of successive feedback effects. A deep bicentennial minimum in solar constant is to be anticipated in 2042 ± 11 and the 19th Little Ice Age (for the last 7500 years) may occur in 2055 ± 11.     

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.     

A New Way that Planets Can Affect the Sun

We derive a perturbation inside a rotating star that occurs when the star is accelerated by orbiting bodies. If a fluid element has rotational and orbital components of angular momentum with respect to the inertially fixed point of a planetary system that are of opposite sign, then the element may have potential energy that could be released by a suitable flow. We demonstrate the energy with a very simple model in which two fluid elements of equal mass exchange positions, calling to mind a turbulent field or natural convection. The exchange releases potential energy that, with a minor exception, is available only in the hemisphere facing the barycenter of the planetary system. We calculate its strength and spatial distribution for the strongest case (“vertical”) and for weaker horizontal cases whose motions are all perpendicular to gravity. The vertical cases can raise the kinetic energy of a few well positioned convecting elements in the Sun’s envelope by a factor ≤7. This is the first physical mechanism by which planets can have a nontrivial effect on internal solar motions. Occasional small mass exchanges near the solar center and in a recently proposed mixed shell centered at 0.16R _s would carry fresh fuel to deeper levels. This would cause stars like the Sun with appropriate planetary systems to burn somewhat more brightly and have shorter lifetimes than identical stars without planets. The helioseismic sound speed and the long record of sunspot activity offer several bits of evidence that the effect may have been active in the Sun’s core, its envelope, and in some vertically stable layers. Additional proof will require direct evidence from helioseismology or from transient waves on the solar surface.     

DuneXpress

The DuneXpress observatory will characterize interstellar and interplanetary dust in-situ, in order to provide crucial information not achievable with remote sensing astronomical methods. Galactic interstellar dust constitutes the solid phase of matter from which stars and planetary systems form. Interplanetary dust, from comets and asteroids, represents remnant material from bodies at different stages of early solar system evolution. Thus, studies of interstellar and interplanetary dust with DuneXpress in Earth orbit will provide a comparison between the composition of the interstellar medium and primitive planetary objects. Hence DuneXpress will provide insights into the physical conditions during planetary system formation. This comparison of interstellar and interplanetary dust addresses directly themes of highest priority in astrophysics and solar system science, which are described in ESA’s Cosmic Vision. The discoveries of interstellar dust in the outer and inner solar system during the last decade suggest an innovative approach to the characterization of cosmic dust. DuneXpress establishes the next logical step beyond NASA’s Stardust mission, with four major advancements in cosmic dust research: (1) analysis of the elemental and isotopic composition of individual interstellar grains passing through the solar system, (2) determination of the size distribution of interstellar dust at 1 AU from 10^− 14 to 10^− 9 g, (3) characterization of the interstellar dust flow through the planetary system, (4) establish the interrelation of interplanetary dust with comets and asteroids. Additionally, in supporting the dust science objectives, DuneXpress will characterize dust charging in the solar wind and in the Earth’s magnetotail. The science payload consists of two dust telescopes of a total of 0.1 m² sensitive area, three dust cameras totaling 0.4 m² sensitive area, and a nano-dust detector. The dust telescopes measure high-resolution mass spectra of both positive and negative ions released upon impact of dust particles. The dust cameras employ different detection methods and are optimized for (1) large area impact detection and trajectory analysis of submicron sized and larger dust grains, (2) the determination of physical properties, such as flux, mass, speed, and electrical charge. A nano-dust detector searches for nanometer-sized dust particles in interplanetary space. A plasma monitor supports the dust charge measurements, thereby, providing additional information on the dust particles. About 1,000 grains are expected to be recorded by this payload every year, with 20% of these grains providing elemental composition. During the mission submicron to micron-sized interstellar grains are expected to be recorded in statistically significant numbers. DuneXpress will open a new window to dusty universe that will provide unprecedented information on cosmic dust and on the objects from which it is derived.     

Fast magnetic reconnection with Cowling’s conductivity

The aim of the present paper is to explore the mechanism of fast Sweet–Parker’s magnetic reconnection with the Cowling’s conductivity. Cowling derived the resistivity of plasma with three components: electrons, ions and neutral particles in magnetic field theoretically after Spitzer. The resistivity is much larger than the Spitzer’s. According to the idea of partially ionized plasmas ejected into the corona as the trigger of flares, we adopt Cowling’s Conductivity to Sweet–Parker’s reconnection model in this paper. The result shows that the reconnection rate can be improved a lot in solar corona and approaches the timescale of solar flare in the absence of anomalous resistivity.     

Secular Variation of Earth's Rotation: Inferred from the Chinese Ancient Shoushi Calendar (Ad 1281)

The Shoushi calendar (epoch of AD 1281, Yuan dynasty) is famous and very accurate in ancient China. It has evolved perfect and complete theoretical models of solar system objects, such as solar and lunar motions during that period. Almost every part of this work corresponds to the modern astronomical yearbooks. Compiled by native Chinese astronomers, it sums up through their studies many real observing results. The mathematical methods were adopted in this calendar before the foundation of Newton’s mechanical system. It is presented in this paper that the indirect system is also very useful to recover the real observing historical material. By selecting these calculating results, we may sum up the integral data of the secular variation of the Earth’s rotation from 1000 BC to AD 1500. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.     

Position and velocity perturbations for the determination of geopotential from space geodetic measurements

Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting (LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values, our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic measurements for the determination of geopotential.     

The degree of anisotropy of cosmic ray electrons of solar origin

Data obtained by the Explorer 34 satellite regarding the degree of anisotropy of ≳ 70 keV electrons of solar origin are reported. It is shown that the anisotropies are initially field aligned, and that they decay to ≲ 10% in a time of the order of 1 hr. The decays of the concurrent ionic and electronic anisotropies for one well observed event are in good agreement with the diffusive propagation model of Fisk and Axford. The data suggest parallel diffusion coefficients for both ions and electrons that are rigidity independent. From considerations of a long lived electron event, it is shown that the electronic fluxes exhibit ‘equilibrium’ anositropies at late times. These are interpreted as indicating that convective removal at the solar wind velocity is the dominant mechanism whereby solar cosmic ray electrons (∼- 70 keV) leave the solar system. They also indicate that there is a positive density gradient at late times in a solar electron event. The data suggest that this was established prior to the establishment of a similar gradient for the cosmic ray ions. This research was supported by the National Aeronautics and Space Administration under contracts NASr-198 and NAS5-9075. The research in India was supported by funds from the Department of Atomic Energy, Government of India and funds from the grant NAS-1492 from the National Academy of Sciences, U.S.A. Support in data analysis was also provided by Air Force Cambridge Research Laboratories, and by the Australian Research Grants Committee.