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.     

Tidal dissipation in the solid cores of the major planets

If the orbital resonances in the Jovian and Saturnian satellite systems are the result of orbital evolution due to tidal dissipation then the present rates of energy dissipation ($\text{E}\text{dot}$) are >2 × 10²⁰ ergs sec^?1 (Jupiter) and ?2 × 10¹⁶ ergs sec^?1 (Saturn). These values of $\text{E}\text{dot}$ can be accounted for if the planets have rocky cores with volumes equal to those suggested by current models of the interiors and if the material of these cores is both solid and imperfectly elastic (Q_e ～ 34). The calculated values of Q_e are not strongly dependent on either the rigidity of the core or the densities of the core and the mantle. Thus, these quantities need not be known precisely. It may be significant that approximately the same value of Q_e is needed for all the major planets (Jupiter, Saturn, and Uranus) even though the values of $\text{E}\text{dot}$ for these planets differ by a factor greater than 10⁴.     

Calculations of the accretion and evolution of giant planets: The effects of solid cores

The evolution of the giant planets is calculated under the general hypothesis that the solid cores formed first, by accretion of small particles, and that these cores later gravitationally attracted their gaseous envelopes from the solar nebula. The evolution passes through the following phases. (1) Planetesimals accrete to form a core of rocky and icy material. (2) When the core mass has grown to a few tenths of an Earth mass, a gaseous envelope in hydrostatic equilibrium begins to form around the core. (3) The core and envelope continue to grow until the “critical” core mass is reached, beyond which point the envelope increases in mass much more rapidly than the core. (4) The envelope mass increases quickly to its present value and prodices a relatively high luminosity, derived from gravitational contraction. (5) Accretion of both core and envelope terminates, and the planet contracts and cools to its present state on a time scale of 5 × 10⁹ years. Evolutionary calculations of phases (2) through (5) are presented, based on solutions of the time-dependent stellar structure equations in spherical symmetry. The physical considerations that determine the critical core mass are discussed; its value is found to depend strongly on the core accretion rate but only weakly on surface boundary conditions. Evolutionary tracks up to the present state are presented for objects of Uranus and Saturn mass.     

Aeronomy of extra-solar giant planets at small orbital distances

One-dimensional aeronomical calculations of the atmospheric structure of extra-solar giant planets in orbits with semi-major axes from 0.01 to 0.1 AU show that the thermospheres are heated to over 10,000 K by the EUV flux from the central star. The high temperatures cause the atmosphere to escape rapidly, implying that the upper thermosphere is cooled primarily by adiabatic expansion. The lower thermosphere is cooled primarily by radiative emissions from H⁺₃, created by photoionization of H₂ and subsequent ion chemistry. Thermal decomposition of H₂ causes an abrupt change in the composition, from molecular to atomic, near the base of the thermosphere. The composition of the upper thermosphere is determined by the balance between photoionization, advection, and H⁺ recombination. Molecular diffusion and thermal conduction are of minor importance, in part because of large atmospheric scale heights. The energy-limited atmospheric escape rate is approximately proportional to the stellar EUV flux. Although escape rates are large, the atmospheres are stable over time scales of billions of years.     

Evolution of the obliquities of the giant planets in encounters during migration

Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461] have proposed that the current orbital architecture of the outer Solar System could have been established if it was initially compact and Jupiter and Saturn crossed the 2:1 orbital resonance by divergent migration. The crossing led to close encounters among the giant planets, but the orbital eccentricities and inclinations were damped to their current values by interactions with planetesimals. Brunini [Brunini, A., 2006. Nature 440, 1163-1165] has presented widely publicized numerical results showing that the close encounters led to the current obliquities of the giant planets. We present a simple analytic argument which shows that the change in the spin direction of a planet relative to an inertial frame during an encounter between the planets is very small and that the change in the obliquity (which is measured from the orbit normal) is due to the change in the orbital inclination. Since the inclinations are damped by planetesimal interactions on timescales much shorter than the timescales on which the spins precess due to the torques from the Sun, especially for Uranus and Neptune, the obliquities should return to small values if they are small before the encounters. We have performed simulations using the symplectic integrator SyMBA, modified to include spin evolution due to the torques from the Sun and mutual planetary interactions. Our numerical results are consistent with the analytic argument for no significant remnant obliquities.     

On the existence of small comets and their interactions with planets

Arguments are presented for a substantial, unexplored population of comets with radii less than 1 km. Known examples confirm this population and extrapolation of any plausible size-distribution function indicates large numbers. However, their accurate numbers, orbital characteristics, and physical properties are unknown. Thus, even though the small comets may be the most frequent cometary bodies impacting the planets, a quantitative evaluation is not currently possible. We advocate an optimized, dedicated search program to characterize this population.Laboratory for Atmospheric and Space Physics, University of Colorado at BoulderLaboratory for Atmospheric and Space Physics, University of Colorado at BoulderLaboratory for Atmospheric and Space Physics, University of Colorado at Boulder     

On the existence of small comets and their interactions with planets

Arguments are presented for a substantial, unexplored population of comets with radii less than 1 km. Known examples confirm this population and extrapolation of any plausible size-distribution function indicates large numbers. However, their accurate numbers, orbital characteristics, and physical properties are unknown. Thus, even though the small comets may be the most frequent cometary bodies impacting the planets, a quantitative evaluation is not currently possible. We advocate an optimized, dedicated search program to characterize this population.     

Computer simulation of regolith vertical structure and exposure age of small satellites of planets

The simulation has shown that the regolith layers several hundred meters thick can be formed on the small satellites of planets of Phobos and Deimos type providing that almost all the material lost at meteorite impacts return to the satellite. The existence of a global layer on Deimos that filled the craters for the depth of about 5 m can be explained by the crater presence of diameter of about 4 km and the age of less than 350 Myr on its hemisphere almost unstudied. Dust belts with dust concentration by 3 orders greater than round the Earth can exist in the region of satellite orbits.     

Crystallization of magmatic iron meteorites: The role of mixing in the molten core

Abstract— The IIIAB group is the largest of the magmatic iron meteorite groups and consequently is commonly used to test models of asteroid core crystallization. Simple fractional crystallization calculations appear to reproduce the general shape of the elemental trends observed in the IIIAB group when these trends are plotted vs. Ni, as is traditionally done. However, when the elemental trends are examined vs. another element (such as Ge vs. Ir), simple fractional crystallization fails to match a significant portion of the trend, specifically meteorites formed during the final stages of crystallization. Our simple mixing model, which attempts to account for the possibility of inhomogeneities in the molten metallic core, is able to reproduce the entire IIIAB trend observed. This model is a variant of simple fractional crystallization and involves mixing between a zone of liquid involved in the crystallization process and a second zone too far from the crystallizing solid to be actively involved in crystallization. This model does not suggest one unique solution for the method by which an asteroidal core crystallizes; rather it demonstrates that including the effects of mixing in the molten core can account for the observed IIIAB elemental trends, particularly the late-stage crystallizing members, which other models have difficulty explaining.     

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 10⁹ years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 10³ to 5 × 10⁴ AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 10⁵ AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 10⁴ < a < 3 × 10⁴ AU. The orbital planes of the comets with initial $\text{a ≧ 3 × 10}{}^4\text{AU}$ acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 10⁴AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiter's orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 10¹⁰ and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.     

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.     

Deuterium enrichment in giant planets

Recently published laboratory measurements of the isotopic exchange rate constant k⁻(T) between CD₄ and H₂ are used to calculate f(z)—the isotopic enrichment factor between CH₄ and H₂—at every level in the outer atmosphere of the giant planets. The variation of f(z) with local vertical velocity, temperature and pressure has been calculated under the assumption that atmospheres are convective and uncertainties have been calculated by error propagation. Considering only the random errors—mainly the uncertainty on k⁻(T)—the f values in the observable upper atmospheres of giant planets (i.e. at z = 0, P = 1 bar) are: f(0) = 1.25 ± 0.05, 1.38 ± 0.06, 1.68 ± 0.09, and 1.61 ± 0.08 for Jupiter, Saturn, Uranus, and Neptune, respectively. Additional systematic errors due to the uncertainty in calculating the vertical velocity in the framework of the mixing length Prandtl theory lead to an overall uncertainty on f(0) of ±0.12, ±0.15, ±0.23, and ±0.21 for each planet, respectively. The D/H ratios in H₂ derived from the measured CH₃D/CH₄ ratios in the upper atmosphere of the four giant planets are then recalculated. Uranus and Neptune seem to be enriched in deuterium with respect to the protosolar nebula but depleted relative to the Standard Mean Oceanic Water on the Earth (SMOW). However calculations based on current interior models of Neptune suggest that ices which formed the core of the planet had a D/H ratio of the order of the SMOW. The deuterium abundance in proto-Uranian ices remains uncertain. The case where water is a major constituent of the fluid envelope of Neptune is discussed. It is shown that the D/H ratio of the planet would then be higher than the value measured in hydrogen. Even in this case, the D/H ratio in proto-Neptunian ices is less than the recently revised value in P/Halley and less than the value measured in water of the Semarkona meteorite. These results suggest that the ices which formed the core of Neptune did not have an interstellar origin. Similarly, the comparison of the most recent determination of the D/H ratio in the atmosphere of Titan with the value of D/H in P/Halley suggests that this atmosphere was not formed by infalling comets but more likely from grains embedded in the sub-nebula of Saturn.     

Transits of extrasolar planets

In this paper, we consider the physical properties and characteristic features of extrasolar planets and planetary systems, those, for which the passage of low-orbit giant planets across the stellar disk (transits) are observed. The paper is mostly a review. The peculiarities of the search for transits are briefly considered. The main attention in this paper is given to the difference in the physical properties of low-orbit giant planets. A comparison of the data obtained during the transits of “hot Jupiters” points to the probable existence of several distinct subtypes of low-orbit extrasolar planets. “Hot Jupiters” of low density (HD 209458b), “hot Jupiters” with massive cores composed of heavy elements (HD 149026b), and “very hot Jupiters” (HD 189733b) are bodies that probably fall into different categories of exoplanets. Dissipation of the atmospheres of low-orbit giant planets estimated from the experimental data is compared with the calculated Jeans atmospheric losses. For “hot Jupiters”, the expected Jeans mass losses due to atmospheric escape on a cosmogonic time scale hardly exceed a few percent. Low-orbit giant planets should have a strong magnetic field. Since the orbital velocity of “hot Jupiters” is close to the magnetosonic velocity (or can even exceed it), the moving planet should actively interact with the “stellar wind” plasma. The possession of a magnetic field by extrasolar planets and the effects of their interaction with plasma can be used to search for extrasolar planets.     

Detecting planets in planetary nebulae

We examine the possibility of detecting signatures of surviving Uranus/Neptune-like planets inside planetary nebulae. Planets that are not too close to the stars (orbital separation larger than ∼5 au) are likely to survive the entire evolution of the star. As the star turns into a planetary nebula, it has a fast wind and strong ionizing radiation. The interaction of the radiation and wind with a planet may lead to the formation of a compact condensation or tail inside the planetary nebula, which emits strongly in H α , but not in [O  iii ]. The position of the condensation (or tail) will change over a time-scale of ∼10 yr. Such condensations might be detected with currently existing telescopes.     

Discovery of pulsar planets

In this paper I recount the events which have led to the discovery of the first planets beyond the Solar System. The two planets circling an old neutron star, the 6.2 ms pulsar PSR B1257+12, were discovered in 1991 with the 1000 ft Arecibo radio telescope. The pulsar itself was detected by a large, all-sky survey conducted during the telescope maintenance period in early 1990. The subsequent timing observations have shown that the only plausible explanation of the variability of pulse arrival times of PSR B1257+12 was the existence of at least two terrestrial-mass planets around it. The third, Moon-mass planet in the system was detected in 1994, along with the measurement of perturbations resulting from a near 3:2 mean motion resonance between the two more massive bodies, which has provided the confirmation of a planetary origin of the observed variations of pulse arrival times. Further observations and analyses have resulted in an unambiguous measurement of orbital inclinations and masses of the planets in 2003. The measured approximate coplanarity of the orbits along with the inner solar system – like dynamical properties of the pulsar planets strongly suggest their origin in a protoplanetary disk, just like in the case of planets around normal stars. The existence of such a system predicts that rocky, Earth-mass planets should be common around various kinds of stars.     

Observations of minor planets

The PDS 2020 GM-microdensitometer of the University of Münster has been used to determine 115 positions of minor planets observed with the astrograph and the double refractor of Hoher List Observatory.     

Expected planets in globular clusters

We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity   I _e ≡ M _p[ a (1 − e )]²  is considered;   M _p, a   and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I _e , with a low-populated gap near   I _e ∼ 0.3 M _J au²  , where M _J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I _e , with a tail to low values of I _e . Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung–Russell diagram of some globular clusters, and in forming low-mass white dwarfs.     

Magnetically enhanced coagulation of very small iron grains

Laboratory experiments, in which very small (approximately 20 nm) grains are produced in the presence of a magnetic field on the order of 100 Gauss in a low-pressure hydrogen atmosphere, have demonstrated that such smokes can become permanently magnetized. We show that magnetization results in an enormous enhancement in the coagulation efficiency of such materials even in the absence of external magnetic fields. Small iron grains should have been produced in the solar nebula by thermal processing of preexisting interstellar grains. If such processing occurred via high-energy electromagnetic events then the resultant magnetized grains could have triggered the formation of centimeter- to meter-sized protoplanetessimals by acting as "nets" capable of sweeping up nonconductive silicates suspended in the gas. It is possible that the presence of conductive fractal aggregates observed in modern-day protostellar disks could be explained by the enhanced coagulation efficiency of very small magnetized iron particles.