Oblate Planet Research Articles

The role of Mab as a source for theμring of Uranus

Context. We previously analysed how the solar radiation force combined with the planetary oblateness changes the orbital evolution of a sample of dust particles located at the secondary ring system of Uranus. Both effects combined with the gravitational perturbations of the close satellites lead to the depletion of these dust particles through collisions on the surfaces of these satellites on a timescale of hundreds of years. Aims. In this work we investigate if the impacts of interplanetary dust particles (IDPs) onto Mab’s surface can produce sufficient particles to replenish the μ ring population. Methods. We first analysed through numerical simulations the evolution of a sample of particles ejected from the surface of Mab and computed the lifetime of the grains when the effects of the solar radiation pressure and the planetary oblateness are taken into account. Then we estimated the mass production rate due to the impacts of IDPs following a previously established algorithm, and used this value to determine the time necessary to accumulate an amount of particles comparable with the mass of the μ ring. Results. Based on an estimate of the flux of interplanetary particles and on the surface properties of Mab it is expected that the satellite supplies material to the ring at a rate of ∼ 3g /s. Meanwhile, our numerical model showed that the ejected particles are removed from the system through collisions with the satellite, and the mean lifetime of the grains may vary from 320 to 1500 years, depending on the radius of the particle. Conclusions. The time necessary to accumulate the mass of the μ ring via ejection from Mab is much shorter than the mean lifetime of the particles, and a stationary regime is not reached. If the ring is kept in a steady state, other effects such as the electromagnetic force and/or the existence of additional bodies may play a significant role in the dust balance, but the current lack of information about the environment renders modelling these effects unfeasible.

Survey of Kozai dynamics beyond Neptune

We study the Kozai dynamics affecting the orbital evolution of trans-neptunian objects being captured or not in MMR with Neptune. We provide energy level maps of the type (ω,q) describing the possible orbital paths from Neptune up to semimajor axis of hundreds of AU. The dynamics for non-resonant TNOs with perihelion distances, q, outside Neptune’s orbit, aN, is quite different from the dynamics of TNOs with q<aN, already studied in previous works. While for the last case there are stable equilibrium points at ω=0°, 90°,180° and 270° in a wide range of orbital inclinations, for the former case it appears a family of stable equilibrium points only at a specific value of the orbital inclination, i∼62°, that we call critical inclination. We show this family of equilibrium points is generated by a mechanism analogue to which drives the dynamics of an artificial satellite perturbed by an oblate planet. The planetary system also generates an oscillation in the longitude of the perihelion of the TNOs with i∼46°, being Eris a paradigmatic case. We discuss how the resonant condition with Neptune modify the energy level curves and the location of equilibrium points. The asymmetric librations of resonances of the type 1:N generate a distortion in the energy level curves and in the resulting location of the equilibrium points in the phase space (ω,q). We study the effect on the Kozai dynamics due to the diffusion process in a that occurs in the Scattered Disk. We show that a minimum orbital inclination is required to allow substantial variations in perihelion distances once the object is captured in MMR and that minimum inclination is greater for greater semimajor axis.

Explaining why the uranian satellites have equatorial prograde orbits despite the large planetary obliquity

We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98°.

Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori

The problem of the dynamics of a charged particle orbiting around a rotating magnetic planet is revisited, the goal being twofold. On the one hand the model takes into account, apart from the magnetic and the electric field, the gravitational potential of the planet where the effect of the planetary oblateness is also incorporated. The techniques used in this analysis include averaging with respect to the mean anomaly, reduction to the simplest possible reduced space, study of the possible relative equilibria with the occurring parametric bifurcations and the stability analysis of these equilibria using normal forms. Also, we prove the existence of KAM 3-tori of the original system from the relative equilibria that are elliptic points in the fully-reduced space.

MAPPING CLOUDS AND TERRAIN OF EARTH-LIKE PLANETS FROM PHOTOMETRIC VARIABILITY: DEMONSTRATION WITH PLANETS IN FACE-ON ORBITS

We develop an inversion technique of annual scattered light curves to sketch a two-dimensional albedo map of exoplanets in face-on orbits. As a test-bed for future observations of extrasolar terrestrial planets, we apply this mapping technique to simulated light curves of a mock Earth-twin at a distance of 10 pc in a face-on circular orbit. A primary feature in recovered albedo maps traces the annual mean distribution of clouds. To extract information of other surface types, we attempt to reduce the cloud signal by taking difference of two bands. We find that the inversion of reflectivity difference between 0.8-0.9 and 0.4-0.5 micron bands roughly recover the continental distribution, except for high latitude regions persistently covered with clouds and snow. The inversion of the reflectivity difference across the red edge (0.8-0.9 and 0.6-0.7 micron) emphasizes the vegetation features near the equator. The planetary obliquity and equinox can be estimated simultaneously with the mapping under the presence of clouds. We conclude that the photometric variability of the scattered light will be a powerful means for exploring the habitat of a second Earth.

Transit variability in bow shock-hosting planets

We investigate the formation of bow shocks around exoplanets as a result of the interaction of the planet with the coronal material of the host star, focusing on physical causes that can lead to temporal variations in the shock characteristics. We recently suggested that WASP-12b may host a bow shock around its magnetosphere, similarly to the one observed around the Earth. For WASP12b, the shock is detected in the near-UV transit light curve. Observational follow-up suggests that the near-UV light curve presents temporal variations, which may indicate that the stand-off distance between the shock and the planet is varying. This implies that the size of the planet's magnetosphere is adjusting itself in response to variations in the surrounding ambient medium. We investigate possible causes of shock variations for the known eccentric (e>0.3) transiting planets. We show that, because the distance from the star changes along the orbit of an eccentric planet, the shock characteristics are modulated by orbital phase. We predict time offsets between the beginnings of the near-UV and optical light curves that are, in general, less than the transit duration. Variations in shock characteristics caused in eccentric systems can only be probed if the shock is observed at different orbital phases, which is, in general, not the case for transit observations. However, non-thermal radio emission produced by the interaction of the star and planet should be modulated by orbital phase. We also quantify the response of the shock to variations in the coronal material itself due to, e.g., a non-axisymmetric stellar corona, planetary obliquity, intrinsic variations of the stellar magnetic field. Such variations do not depend on the system eccentricity. We conclude that, for systems where a shock is detectable through transit light curve observations, shock variations should be a common occurrence. (Abridged)

Tidal obliquity evolution of potentially habitable planets

[NASA ADS]

The retrograde orbit of the HAT-P-6b exoplanet

We observed with the SOPHIE spectrograph (OHP, France) the transit of the HAT-P-6b exoplanet across its host star. The resulting stellar radial velocities display the Rossiter-McLaughlin anomaly and reveal a retrograde orbit: the planetary orbital spin and the stellar rotational spin point towards approximately opposite directions. A fit to the anomaly measures a sky-projected angle lambda = 166 +/- 10 degrees between these two spin axes. All seven known retrograde planets are hot jupiters with masses M_p < 3 M_Jup. About two thirds of the planets in this mass range however are prograde and aligned (lambda ~ 0). By contrast, most of the more massive planets (M_p > 4 M_Jup) are prograde but misaligned. Different mechanisms may therefore be responsible for planetary obliquities above and below ~3.5 M_Jup.

Periglacial geomorphology and landscape evolution of the Tempe Terra region, Mars

Abstract A systematic survey was undertaken and an investigation carried out into the geomorphological characteristics of lobate debris aprons in the Tempe Terra region of Mars. Based on the most recent high-resolution (sub 15 m per pixel) imagery and on new topography data, this study endeavoured to raise and discuss questions regarding their formation (emplacement) and modification (deformation sequence), as well as the role of a mantling deposit found at mid-latitude locations on Mars. Furthermore, a model for the formation of debris aprons in the Tempe Terra–Mareotis Fossae settings is proposed. Image survey, in combination with basic morphometric observations within a geomorphological context, provided additional insights into the source, emplacement and modification of hillslope debris material. Our results imply that lobate debris aprons are not mainly relicts of remnant degradation but are substantially composed of mantling material probably deposited episodically in the course of planetary obliquity changes and over a long timespan, as derived erosion rates suggest. Crater-size frequency statistics and the derivation of absolute ages show ages of sub-recent modification and document earlier resurfacing events.

GLOBAL MAPPING OF EARTH-LIKE EXOPLANETS FROM SCATTERED LIGHT CURVES

Scattered lights from terrestrial exoplanets provide valuable information about the planetary surface. Applying the surface reconstruction method proposed by Fujii et al. (2010) to both diurnal and annual variations of the scattered light, we develop a reconstruction method of land distribution with both longitudinal and latitudinal resolutions. We find that one can recover a global map of an idealized Earth-like planet on the following assumptions: 1) cloudless, 2) a face-on circular orbit, 3) known surface types and their reflectance spectra 4) no atmospheric absorption, 5) known rotation rate 6) static map, and 7) no moon. Using the dependence of light curves on the planetary obliquity, we also show that the obliquity can be measured by adopting the chi-square minimization or the extended information criterion. We demonstrate a feasibility of our methodology by applying it to a multi-band photometry of a cloudless model Earth with future space missions such as the occulting ozone observatory (O3). We conclude that future space missions can estimate both the surface distribution and the obliquity at least for cloudless Earth-like planets within 5 pc.

Planet formation: statistics of spin rates and obliquities of extrasolar planets

We develop a simple model of planetary formation, focusing our attention on those planets with masses less than 10 Earth masses and studying particularly the primordial spin parameters of planets resulting from the accretion of planetesimals and produced by the collisions between the embryos. As initial conditions, we adopt the oligarchic growth regime of protoplanets in a disc where several embryos are allowed to form. We take different initial planetary system parameters and for each initial condition, we consider an evolution of 20 millon of years of the system. We perform simulations for 1000 different discs, and from their results we derive the statistical properties of the assembled planets. We have taken special attention to the planetary obliquities and rotation periods, such as the information obtained from the mass and semi major axis diagram, which reflects the process of planetary formation. The distribution of obliquities was found to be isotropic, which means that planets can rotate in direct or indirect sense, regardless of their mass. Our results regarding the primordial rotation periods show that they are dependent on the region where the embryo was formed and evolved. According to our results, most of the planets have rotation periods between 10 and 10000 hours and there are also a large population of planets similar to terrestrial planets in the Solar System.

Planetocentric gravitational sphere of the dominating influence of perturbations from planet oblateness over perturbations from external bodies

The radius of a planetocentric sphere in which the gravitational perturbations caused by the planet oblateness dominate over perturbations caused by external bodies is determined in the paper. Specific features of long-term evolution of orbits of planetary satellites as a function of their average radii (semimajor axes) are considered using as an example two integrable cases in the doubly averaged problem taking into account joint influence of an external body and non-centrality of the planet’s gravitational field. For these cases, descriptions of the diversity of initial conditions leading (or not leading) to a crossing of the satellite orbit with the surface of a planet of finite radius are obtained.

On the mystery of the perennial carbon dioxide cap at the south pole of Mars

A perennial ice cap has long been observed near the south pole of Mars. The surface of this cap is predominantly composed of carbon dioxide ice. The retention of a CO2 ice cap results from the surface energy balance of the latent heat, solar radiation, surface emission, subsurface conduction, and atmospheric sensible heat. While models conventionally treat surface CO2 ice using constant ice albedos and emissivities, such an approach fails to predict the existence of a perennial cap. Here we explore the role of the insolation‐dependent ice albedo, which agrees well with Viking, Mars Global Surveyor, and Mars Express albedo observations. Using a simple parameterization within a general circulation model, in which the albedo of CO2 ice responds linearly to the incident solar insolation, we are able to predict the existence of a perennial CO2 cap at the observed latitude and only in the southern hemisphere. Further experiments with different total CO2 inventories, planetary obliquities, and surface boundary conditions suggest that the location of the residual cap may exchange hemispheres favoring the pole with the highest peak insolation.

EMPIRICAL CONSTRAINTS ON THE OBLATENESS OF AN EXOPLANET

We show that the gas giant exoplanet HD 189733b is less oblate than Saturn, based on Spitzer Space Telescope photometry of seven transits. The observable manifestations of oblatenesswould have been slight anomalies during the ingress and egress phases, as well as variations in the transit depth due to spin precession. Our nondetection of these effects gives the first empirical constraints on the shape of an exoplanet. The results are consistent with the theoretical expectation that the planetary rotation period and orbital period are synchronized, in which case the oblateness would be an order of magnitude smaller than our upper limits. Conversely, if HD 189733b is assumed to be in a synchronous, zero-obliquity state, then the data give an upper bound on the quadrupole moment of the planet (J2 < 0.068 with 95% confidence) that is too weak to constrain the interior structure of the planet. An Appendix describes a fast algorithm for computing the transit light curve of an oblate planet, which was necessary for our analysis.

DETECTING THE WIND-DRIVEN SHAPES OF EXTRASOLAR GIANT PLANETS FROM TRANSIT PHOTOMETRY

Several processes can cause the shape of an extrasolar giant planet's shadow, as viewed in transit, to depart from circular. In addition to rotational effects, cloud formation, non-homogenous haze production and movement, and dynamical effects (winds) could also be important. When such a planet transits its host star as seen from Earth, the asphericity will introduce a deviation in the transit lightcurve relative to the transit of a perfectly spherical (or perfectly oblate) planet. We develop a theoretical framework to interpret planet shapes. We then generate predictions for transiting planet shapes based on a published theoretical dynamical model of HD189733b. Using these shape models we show that planet shapes are unlikely to introduce detectable lightcurve deviations (those >~1e-5 of the host star), but that the shapes may lead to astrophysical sources of systematic error when measuring planetary oblateness, transit time, and impact parameter.

Orbital evolution of theμandνdust ring particles of Uranus

The μ and ν rings of Uranus form a secondary ring-moon system with the satellites Puck, Mab, Portia, and Rosalind. These rings are tenuous and dominated by micrometric particles, which can be strongly disturbed by dissipative forces, such as the solar radiation pressure. In the region of these rings, the solar radiation force and the planetary oblateness change the orbital evolution of these dust particles significantly. In this work, we performed a numerical analysis of the orbital evolution of a sample of particles with radii of 1, 3, 5, and 10 μm under the influence of these perturbations, combined with the gravitational interaction with the close satellites. As expected, the Poynting-Robertson component of the solar radiation force causes the collapse of the orbits on a timescale between 3.1 × 10 5 and 3.6 × 10 6 years, while the radiation pressure causes an increase in the eccentricity of the particles. The inclusion of Uranus’s oblateness prevents a large variation in the eccentricity, confining the particles in the region of the rings. The encounters with the close satellites produce variations in the semimajor axis of the particles, leading them to move inward and outward within the ring region. These particles can either remain within the region of the rings or collide with a neighbouring satellite. The number of collisions depends on the size of both the particles and the satellites, and the radial width of the ring. For the time span analysed, the percentage of particles that collide with a satellite varies from 43% to 94% for the ν ring, and from 12% to 62% for the μ ring. Our study shows that all collisions with Portia and Rosalind have the value of impact velocity comparable to the escape velocity, which could result in the deposition of material onto the surface of the satellite. Collisions between Puck and particles larger than 1 μm also occur at an impact velocity comparable to the value of the escape velocity. The exception is Mab, which is hit by particles with velocities several times larger than the escape velocity. These collisions are energetic enough to eject material and supply material to the μ ring. However, only a few particles (3%) collide with the surface of the satellite Mab at such a velocity.

On the averaging principle for one-frequency systems. An application to satellite motions

This paper is related to our previous works (Morosi and Pizzocchero in J. Phys. A, Math. Gen. 39:3673–3702, 2006; Nonlinear Dyn., 2008), on the error estimate of the averaging technique for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been introduced to obtain precise, fully quantitative estimates on the averaging error. Here, this procedure is applied to the motion of a satellite in a polar orbit around an oblate planet, retaining only the J 2 term in the multipole expansion of the gravitational potential. To exemplify the method, the averaging errors are estimated for the data corresponding to two Earth satellites; for a very large number of orbits, computation of our estimators is much less expensive than the direct numerical solution of the equations of motion.

HABITABLE CLIMATES: THE INFLUENCE OF OBLIQUITY

Extrasolar terrestrial planets with the potential to host life might have large obliquities or be subject to strong obliquity variations. We revisit the habitability of oblique planets with an energy balance climate model (EBM) allowing for dynamical transitions to ice-covered snowball states as a result of ice-albedo feedback. Despite the great simplicity of our EBM, it captures reasonably well the seasonal cycle of global energetic fluxes at Earth's surface. It also performs satisfactorily against a full-physics climate model of a highly oblique Earth-like planet, in an unusual regime of circulation dominated by heat transport from the poles to the equator. Climates on oblique terrestrial planets can violate global radiative balance through much of their seasonal cycle, which limits the usefulness of simple radiative equilibrium arguments. High obliquity planets have severe climates, with large amplitude seasonal variations, but they are not necessarily more prone to global snowball transitions than low obliquity planets. We find that terrestrial planets with massive CO2 atmospheres, typically expected in the outer regions of habitable zones, can also be subject to such dynamical snowball transitions. Some of the snowball climates investigated for CO2-rich atmospheres experience partial atmospheric collapse. Since long-term CO2 atmospheric build-up acts as a climatic thermostat for habitable planets, partial CO2 collapse could limit the habitability of such planets. A terrestrial planet's habitability may thus sensitively depend on its short-term climatic stability.

On the averaging principle for one-frequency systems. Seminorm estimates for the error

We extend some previous results of our work (Morosi and Pizzocchero in J. Phys. A: Math. Gen. 39:3673–3702, 2006) on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use the new approach to get separate error estimates for each action coordinate. An application to rigid body under damping is presented. In a companion paper (Morosi and Pizzocchero, 2006), the same method will be applied to the motion of a satellite around an oblate planet.

The Secular Evolution of a Close Ring‐Satellite System: The Excitation of Spiral Density Waves at a Nearby Gap Edge

The secular perturbations exerted by an inclined satellite orbiting in a gap in a broad planetary ring tends to excite the inclinations of the nearby ring particles, and the ring's self-gravity can allow that disturbance to propagate away in the form of a spiral bending wave. The amplitude of this spiral bending wave is determined, as well as the wavelength, which shrinks as the waves propagate outwards due to the effects of the central planet's oblateness. The excitation of these bending waves also damps the satellite's inclination I. This secular I damping is also compared to the inclination excitation that is due to the satellite's many other vertical resonances in the ring, and the condition for inclination damping is determined. The secular I damping is likely responsible for confining the orbits of Saturn's two known gap-embedded moons, Pan and Daphnis, to the ring plane.