Extrasolar planets and the rotation and axisymmetric mass-loss of evolved stars

I examine the implications of the recently found extrasolar planets on the planet-induced axisymmetric mass-loss model for the formation of elliptical planetary nebulae (PNe). This model attributes the low departure from spherical mass-loss of upper asymptotic giant branch (AGB) stars to envelope rotation which results from deposition of orbital angular momentum of the planets. Since about half of all PNe are elliptical, i.e., have low equatorial to polar density contrast, it was predicted that about 50 per cent of all Sun-like stars have Jupiter-like planets around them, i.e., a mass about equal to that of Jupiter, M _J, or more massive. In the light of the new findings that only 5 per cent of Sun-like stars have such planets, and a newly proposed mechanism for axisymmetric mass-loss, the cool magnetic spots model, I revise this prediction. I predict that indeed ∼50 per cent of PN progenitors do have close planets around them, but the planets can have much lower masses, as low as ∼0.01 M _J, in order to spin-up the envelopes of AGB stars efficiently. To support this claim, I follow the angular momentum evolution of single stars with main-sequence mass in the range of 1.3–2.4 M_⊙ , as they evolve to the post-AGB phase. I find that single stars rotate much too slowly to possess any significant non-spherical mass-loss as they reach the upper AGB. It seems, therefore, that planets, in some cases even Earth-like planets, are sufficient to spin-up the envelope of these AGB stars for them to form elliptical PNe. The prediction that on average several such planets orbit each star, as in the Solar system, still holds.     

Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets

Since 20 years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star–planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from \(0.6~M_\odot \) to \(1.2~M_\odot \)) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in Celestial Mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions.     

Achromatic interfero-coronagraph with variable rotation shearing for studying extrasolar planets

Direct observation of exoplanets will make it possible to clarify many principal questions connected both with extrasolar planets and planetary systems and to measure atmospheric spectra of the planets. Obtaining an exoplanet image not distorted by the light from a star is at the cutting edge of present-day optical technologies owing to the combination of tremendous brightness contrasts and small angular distances between the planet and star. To observe the exo-Earth, it is necessary to weaken the brightness of the parent star image by 9–10 orders of magnitude (in the optical and near-IR ranges). To compensate the influence of the atmosphere, ground-based (e.g., 8–10 m) telescopes intended for observing exoplanets are equipped with adaptive optics systems, the spatial and temporal resolutions of which are not yet sufficient. A meter-class space telescope equipped with a star coronagraph will make it possible to observe the nearest exoplanets. In this paper, an improved tool for star coronagraphy is considered, namely, the achromatic interferometric coronagraph with a variable rotational shear. It is fabricated according to the optical scheme of the common path interferometer for studying extrasolar planets by direct observations. Theoretical and experimental estimations for the main characteristics of the scheme were carried out. Laboratory experimental measurements were carried out on a coronagraph model.     

The effects of rotation rate on deep convection in giant planets with small solid cores

We study how the pattern of thermal convection and differential rotation in the interior of a giant gaseous planet is affected by the presence of a small solid core as a function of the planetary rotation rate. We show, using 2D anelastic, hydrodynamic simulations, that the presence of a small solid core results in significantly different flow structure relative to that of a fully convective interior only if there is little or no planetary rotation.     

Climatic change on the terrestrial planets

In this paper, we review the observational data on climatic change for the terrestrial planets, discuss the basic factors that influence climate, and examine the manner in which these factors may have been responsible for some of the known changes. Emphasis is placed on trying to understand the similarities and differences in both the basic factors and their climatic impacts on Venus, the Earth, and Mars. Climatic changes have occurred on the Earth over a broad spectrum of time scales that range from the elevated temperatures of Pre-Cambrian times (～10⁹ years ago), through the alternating glacial and interglacial epochs of the last few million years, to the small but significant decadal and centurial variations of the recent past. Evidence for climatic change on Mars is given by certain channel features, which suggest an early to intermediate aged epoch of warmer and wetter climate, and by layered polar deposits, which imply more recent periodic climate variations. No evidence for climatic change on Venus exists as yet, but comparison of its present climate state with that of outer terrestrial planets offers important clues on some of the mechanisms affecting climate. The important determinants of climate for a terrestrial planet include the Sun's output, astronomical perturbations of its orbital and axial characteristics, the gaseous and particulate content of its atmosphere, its land surface, volatile reservoirs, and its interior. All these factors appear to have played major roles in causing climatic changes on the terrestrial planets. Despite a lower solar luminosity in the past, the Earth and Mars have had warmer periods in their early history. In both cases, a more reducing atmosphere may have been the responsible agent through an enhanced greenhouse effect. In this paper, we present detailed calculations of the effect of atmospheric pressure and composition on the temperature state of Mars. We find that the higher temperature period is easier to explain with a reducing atmosphere than with the current fully oxidizing one. Both the very high surface temperature and massive atmosphere of Venus may be the result of the solar flux being a factor of two higher at its orbit than at the Earth's orbit. This difference may have led to a runaway greenhouse effect on Venus, i.e., the emplacement of volatiles entirely in the atmosphere rather than mostly in surface reservoirs. But if Venus formed with relatively little or no water, it may have always had an oxidizing atmosphere. In this case, a lower solar luminosity would have led to a moderate surface temperature in Venus' early history. Quasi-periodic variations in orbital eccentricity and axial obliquity may have contributed to the alternation between Pleistocene glacial and interglacial periods in the case of the Earth and to the formation of the layered polar deposits in the case of Mars. In this paper, we postulate that two mechanisms, acting jointly, account for the creation of the laminated terrain of Mars: dust particles serve as nucleation centers for the condensation of water vapor and carbon dioxide. The combined dust-H₂O-CO₂ particle is much larger and so has a much higher terminal velocity than either a dust-H₂O or a plain dust particle. As a result, dust and water ice are preferentially deposited in the polar regions. In addition, we postulate that the obliquity variations are key drivers of the periodic layering because of their impact on both atmospheric pressure and polar surface temperature, which, in turn, influence the amounts of dust and water ice in the atmosphere. But eccentricity and precessional changes probably also play important roles in creating the polar layers. The drifting of continents on the Earth has caused substantial climatic changes on individual continents and may have helped to set the stage for the Pleistocene ice ages through a positioning of the continents near the poles. While continental drift apparently has not occurred on Mars, tectonic distortions of its lithosphere may, in some circumstances, cause an alteration in the mean value of that planet's obliquity, which would significantly impact its climate. Atmospheric aerosols can influemce climate through their radiative effects. In the case of the Earth, volcanic aerosols appear to have contributed to past climatic changes, while consideration needs to be given to the future impact of man-generated aerosols. In the case of Mars, the atmospheric temperature structure and thereby atmospheric dynamics are greatly altered by suspended dust particles. The sulfuric acid clouds of Venus play a major role in its heat balance. Cometary impacts may have added substantial quantities of water vapor and sulfur gases to Venus' atmosphere and thus have indirectly affected its cloud properties. Calculations presented in this paper indicate substantial changes in surface temperature accompany these compositional changes.     

Masses for free-floating planets and dwarf planets

The mass and distance functions of free-floating planets(FFPs) would give major insights into the formation and evolution of planetary systems, including any systematic differences between those in the disk and bulge. We show that the only way to measure the mass and distance of individual FFPs over a broad range of distances is to observe them simultaneously from two observatories separated by D ～ O(0.01 au)(to measure their microlens parallax π_E) and to focus on the finite-source point-lens(FSPL) events(which yield the Einstein radius θ_E). By combining the existing KMTNet 3-telescope observatory with a 0.3 m 4 deg~2 telescope at L2, of order 130 such measurements could be made over four years, down to about M ～ 6 M_⊕for bulge FFPs and M ～ 0.7 M_⊕for disk FFPs. The same experiment would return masses and distances for many bound planetary systems. A more ambitious experiment, with two 0.5 m satellites(one at L2 and the other nearer Earth) and similar camera layout but in the infrared, could measure masses and distances of sub-Moon mass objects, and thereby probe(and distinguish between) genuine sub-Moon FFPs and sub-Moon "dwarf planets" in exo-Kuiper Belts and exo-Oort Clouds.     

Formation of the terrestrial planets

The early phases of formation in the inner solar system were dominated by collisions and short-range dynamical interactions among planetesimals. But the later phases, which account for most of the differences among planets, are unsure because the dynamics are more subtle. Jupiter's influence became more important, leading to drastic clearing out of the asteroid belt and the stunting of Mars's growth. Further in, the effect of Jupiter-- both directly and indirectly, through ejection of mass in the outer solar system-- was probably to speed up the process without greatly affecting the outcome. The great variety in bulk properties of the terrestrial bodies indicate a terminal phase of great collisions, so that the outcome is the result of small-N statistics. Mercury, 65 percent iron, appears to be a residual core from a high-velocity collision. All planets appear to require a late phase of high energy impacts to erode their atmospheres: including the Earth, to remove CO₂ so that its ocean could form by condensation of water.Consistent with this model is that the largest collision, about 0.2 Earth masses, was into the proto-Earth, although the only property that appears to require it is the great lack of iron in the Moon. The other large differences between the Earth and Venus, angular momentum (spin plus satellite) and inert gas abundances, must arise from origin circumstances, but neither require nor forbid the giant impact. Venus's higher ratio of light to heavy inert gases argues for it receiving a large icy impactor, about 10^–6 Earth masses from far out, requiring some improbable dynamics to get a low enough approach velocity. Core formation in both planets probably started rather early during accretion.Some geochemical evidences argue for the Moon coming from the Earth's mantle, but are inconclusive. Large scale melting of the mantle by the giant impact would plausibly have led to stratification. But the "lock-up" at the end of turbulent mantle convection is a trade-off between rates: crystallization of constituents of small density difference versus overall freezing. Also, factors such as differences in melting temperatures and densities, melt compressibilities, and phase transitions may have had homogenizing effects in the subsequent mantle convection.     

Deep jets on gas-giant planets

Three-dimensional numerical simulations of the atmospheric flow on giant planets using the primitive equations show that shallow thermal forcing confined to pressures near the cloud tops can produce deep zonal winds from the tropopause all the way down to the bottom of the atmosphere. These deep winds can attain speeds comparable to the zonal jet speeds within the shallow, forced layer; they are pumped by Coriolis acceleration acting on a deep meridional circulation driven by the shallow-layer eddies. In the forced layer, the flow reaches an approximate steady state where east-west eddy accelerations balance Coriolis accelerations acting on the meridional flow. Under Jupiter-like conditions, our simulations produce 25 to 30 zonal jets, similar to the number of jets observed on Jupiter and Saturn. The simulated jet widths correspond to the Rhines scale; this suggests that, despite the three-dimensional nature of the dynamics, the baroclinic eddies energize a quasi-two-dimensional inverse cascade modified by the β effect (where β is the gradient of the Coriolis parameter). In agreement with Jupiter, the jets can violate the barotropic and Charney-Stern stability criteria, achieving curvatures ^∂2u/∂y² of the zonal wind u with northward distance y up to 2β. The simulations exhibit a tendency toward neutral stability with respect to Arnol'd's second stability theorem in the upper troposphere, as has been suggested for Jupiter, although deviations from neutrality exist. When the temperature varies strongly with latitude near the equator, our simulations can also reproduce the stable equatorial superrotation with wind speeds greater than . Diagnostics show that barotropic eddies at low latitudes drive the equatorial superrotation. The simulations also broadly explain the distribution of jet-pumping eddies observed on Jupiter and Saturn. While idealized, these simulations therefore capture many aspects of the cloud-level flows on Jupiter and Saturn.     

Formation of the giant planets

Observational constraints on interior models of the giant planets indicate that these planets were all much hotter when they formed and they all have rock and/or ice cores of ten to thirty earth masses. These cores are probably soluble in the envelopes above, especially in Jupiter and Saturn, and are therefore likely to be primordial. They persist despite the continual upward mixing by thermally driven convection throughout the age of the solar system, because of the inefficiency of double-diffusive convection. Thus, these planets most probably formed by the hydrodynamic collapse of a gaseous envelope onto a core rather than by direct instability of the gaseous solar nebula. Recent calculations by Mizuno (1980, Prog. Theor. Phys.64, 544) show that this formation mechanism may explain the similarity of giant planet core masses. Problems remain however, and no current model is entirely satisfactory in explaining the properties of the giant planets and simultaneously satisfying the terrestrial planet constraints. Satellite systematics and protoplanetary disk nebulae are also discussed and related to formation conditions.     

A hypothesis on the Oort clouds of planets

Although, we have no quantitative arguments to prove, but we have good reasoning to believe that the Oort clouds existed surrounding the planets. The short period comets, Apollo-Amor-Toro-asteroids and such other objects may be the relics of the Oort clouds that had existed surrounding the planets long ago.     

Unbound planets

Current protostellar theory has determined a lower limit to the mass of a pre-stellar gas cloud fragment of ~0.01 M. This suggests that isolated interstellar bodies in the mass range ~10 M_-710_-2 M must have originated within a planetary system. Two possible mechanisms whereby planets are lost from their parental systems to interstellar space are discussed and the abundance and distribution of such unbound planets within the Galaxy is examined. It is found that, except within the central regions of the Galaxy, unbound planets are expected to be scarce. In the solar neighbourhood for instance, the number density ratio of unbound planets to stars is estimated to range between extremes of ~4 × 10^–4–3 × 10^–2 with a most probable value of ~6 x 10^–3. The faint possibility that the hypothetical Planet X might be of extra-solar origin is also discussed.     

Excitation of the oxygen nightglow on the terrestrial planets

A scheme of excitation, quenching, and energy transfer processes in the oxygen nightglow on the Earth, Venus, and Mars has been developed based on the observed nightglow intensities and vertical profiles, measured reaction rate coefficients, and photochemical models of the nighttime atmospheres of the Venus and Mars. The scheme involves improved radiative lifetimes of some band systems, calculated yields of the seven electronic states of O₂ in termolecular association, and rate coefficients of seven processes of electronic quenching of the Herzberg states of O₂, which are evaluated by fitting to the nightglow observations. Electronic quenching of the vibrationally excited Herzberg states by O₂ and N₂ in the Earth's nightglow is a quarter of total collisional removal of the O₂(A, A′) states and a dominant branch for the O₂(c) state. The scheme supports the conclusion by Steadman and Thrush (1994) that the green line is excited by energy transfer from the O₂(A³Σ_u⁺, v≥6) molecules, and the inferred rate coefficient of this transfer is 1.5×10⁻¹¹ cm³ s⁻¹. The O₂ bands at 762 nm and 1.27 μm are excited directly, by quenching of the Herzberg states, and by energy transfer from the O₂(⁵Π_g) state. Quenching of the O₂ band at 762 nm excites the band at 1.27 μm as well. Effective yield of the O₂(a¹Δ_g) state in termolecular association on Venus and Mars is ∼0.7. Quantitative assessments of all these processes have been made. A possible reaction of O₂(c¹Σ_u⁻)+CO is a very minor branch of recombination of CO₂ on Venus and Mars. Night airglow on Mars is calculated for typical conditions of the nighttime atmosphere. The calculated vertical intensity of the O₂ band at 1.27 μm is 13 kR, far below the recently reported detections.     

Structure of the terrestrial planets

Recent reviews (cf. Runcorn, 1968; or Cook, 1972, 1975) on the structure of the planets omit reference to the phase-change hypothesis for the nature of the terrestrial core, despite that numerous prior predictions of the theory based on this hypothesis have subsequently been borne out as correct. These reviews also ignore the existence of theoretical calculations of the internal structure of Venus which can be computed with high accuracy by use of the terrestrial seismic data. Several examples of numerous mistakes committed in these reviews are pointed out.     

Models of the giant planets

Models of the giant planets were constructed based on the assumption that the hydrogen to helium ratio is solar in these planets. This assumption, together with arguments about the condensation sequence in the primitive solar nebula, yields models with a central core of rock and possibly ice surrounded by an envelope of hydrogen, helium, methane, ammonia, and water. These last three volatiles may be individually enhanced due to condensation at the period of core formation. Jupiter was found to have a core of about 40 earth masses and a water enhancement in the atmosphere of about 7.5 times the solar value. Saturn was found to have a core of 20 earth masses and a water enhancement in the atmosphere of about 25 times the solar value. Rock plus ice constitute 75–85% of the mass of Uranus and Neptune. Temperatures in the interiors of these planets are probably above the melting points, if there is an adiabatic relation throughout the interiors. Some aspects of the sensitivities of these results to uncertainties in rotational flattening are discussed.     

Direct perturbations of the planets on the Moon's motion

The aim of the present paper is to present the theoretical background of a method to compute the planetary perturbations on the Moon's motion. We formulate an algorithm based upon the Lie transform method and well-suited to the particular problem at hand.This algorithm is being implemented using Henrard's Semi-Analytical Lunar Ephemeris (SALE) as solution of the Main Problem and Bretagnon's planetary theory. The accuracy of the solution is intended to be about 0".001 for terms of period up to 2000 years.To illustrate the interest of our approach, we comment on some preliminary results obtained about the direct perturbations due to Venus on the Moon's longitude. The final results will be the subject of another paper.     

Comments on the paper by Y. Kubo: ‘A core-mantle interaction in the rotation of the earth’

A recently-published paper, concerning the effects of core-mantle coupling on the Earth's precession and nutation, is critically appraised in the light of previously-published work in astronomy and geophysics.     

The formation and habitability of terrestrial planets in the presence of close-in giant planets

‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.     

Love numbers of the giant planets

We calculate the Love numbers k_n for n = 2 to 10, and determine the “gravitational noise” from tides. The new values k₂ for Jupiter, Saturn, and Uranus yield new estimates for the planetary dissipation functions: $\text{Q}{}_{\mathrm{<mtext>J</mtext>}}\text{? 2.5 × 10}{}^4$, $\text{Q}{}_{\mathrm{<mtext>S</mtext>}}\text{? 1.4 × 10}{}^4\text{, Q}{}_{\mathrm{<mtext>U</mtext>}}\text{? 5 × 10}{}^3$.