Global contraction of planetary bodies due to despinning: Application to Mercury and Iapetus

We extend previous work on the global tectonic patterns generated by despinning with a self-consistent treatment of the isotropic despinning contraction that has been ignored. We provide simple analytic approximations that quantify the effect of the isotropic despinning contraction on the global shape and tectonic pattern. The isotropic despinning contraction of Mercury is ∼93 m (T/1 day)⁻², where T is the initial rotation period. If we take into account both the isotropic contraction and the degree-2 deformations associated with despinning, the preponderance of compressional tectonic features on Mercury’s surface requires an additional isotropic contraction ?1 km (T/1 day)⁻², presumably due to cooling of the interior and growth of the solid inner core. The isotropic despinning contraction of Iapetus is ∼9 m (T/16 h)⁻², and it is not sensitive to the presence of a core or the thickness of the elastic lithosphere. The tectonic pattern expected for despinning, including the isotropic contraction, does not explain Iapetus’ ridge. Furthermore, the ridge remains unexplained with the addition of any isotropic compressional stresses, including those generating by cooling.     

East-west faults due to planetary contraction

Contraction, expansion and despinning have been common in the past evolution of Solar System bodies. These processes deform the lithosphere until it breaks along faults. Their characteristic tectonic patterns have thus been sought for on all planets and large satellites with an ancient surface. While the search for despinning tectonics has not been conclusive, there is good observational evidence on several bodies for the global faulting pattern associated with contraction or expansion, though the pattern is seldom isotropic as predicted. The cause of the non-random orientation of the faults has been attributed either to regional stresses or to the combined action of contraction/expansion with another deformation (despinning, tidal deformation, reorientation). Another cause of the mismatch may be the neglect of the lithospheric thinning at the equator or at the poles due either to latitudinal variation in solar insolation or to localized tidal dissipation. Using thin elastic shells with variable thickness, I show that the equatorial thinning of the lithosphere transforms the homogeneous and isotropic fault pattern caused by contraction/expansion into a pattern of faults striking east-west, preferably formed in the equatorial region. By contrast, lithospheric thickness variations only weakly affect the despinning faulting pattern consisting of equatorial strike-slip faults and polar normal faults. If contraction is added to despinning, the despinning pattern first shifts to thrust faults striking north-south and then to thrust faults striking east-west. If the lithosphere is thinner at the poles, the tectonic pattern caused by contraction/expansion consists of faults striking north/south. I start by predicting the main characteristics of the stress pattern with symmetry arguments. I further prove that the solutions for contraction and despinning are dual if the inverse elastic thickness is limited to harmonic degree two, making it easy to determine fault orientation for combined contraction and despinning. I give two methods for solving the equations of elasticity, one numerical and the other semi-analytical. The latter method yields explicit formulas for stresses as expansions in Legendre polynomials about the solution for constant shell thickness. Though I only discuss the cases of a lithosphere thinner at the equator or at the poles, the method is applicable for any latitudinal variation of the lithospheric thickness. On Iapetus, contraction or expansion on a lithosphere thinner at the equator explains the location and orientation of the equatorial ridge. On Mercury, the combination of contraction and despinning makes possible the existence of zonal provinces of thrust faults differing in orientation (north-south or east-west), which may be relevant to the orientation of lobate scarps.     

Global tectonics of a despun planet

Mercury, the Moon, and many large satellites of the major planets have been tidally despun from an initially faster rotation. These bodies probably possessed equatorial bulges which relaxed as they lost their spin. An analysis of the stresses induced in an elastic shell by the relaxation of an equatorial bulge indicates that differential stresses may reach a few kilobars and that the tectonic pattern developed depends mainly upon the shell thickness. In every model studied the azimuthal stress σ_?? is larger (more compressive) than the meridional stress σθθ. For a thin elastic shell (thickness less than one-twentieth of the planet's radius) the zone from the equator to 48° latitude is characterized by strike-slip faulting. Poleward of this, normal faults and graben trending east-west are expected. Thicker elastic shells acquire an equatorial belt of thrust faults with east-west throw and rough north-south trends. These tectonic styles may be modified by a small (0.05-0.1%) radial expansion or contraction. Expansion shifts the polar normal faulting province toward the equator, while contraction shifts the equatorial provinces poleward. These patterns are not substantially altered by plastic yielding of the shell, although the equatorial thrust fault province is suppressed by strike-slip faulting until strike-slip faults occur poleward of 64.8° latitude. We conclude that there are many tectonic patterns consistent with despinning and radial contraction or expansion, but they must all be consistent with σ_?? > σθθ. These results also indicate that the polar regions of a despun planet are of particular interest in deciding whether a given lineament system is due to stresses induced by the relaxation of the planet's equatorial bulge.     

The velocity dispersion in Saturn's rings

The surface of Mercury exhibits a global tectonic system consisting of an ancient set of NE and NW trending lineaments and a younger set of planimetrically arcuate escarpments interpreted as thrust or high-angle reverse faults. The trends, distribution, and age relations of these tectonic features can be explained by a combination of tidal despinning and global contraction of the planet. In our model, early tidal despinning resulted in conjugate shear fractures trending roughly N60°E and N60°W which were subsequently modified by a variety of surface processes to produce the presently visible set of lineaments. Continued despinning plus global contraction produced thrust faults with roughly north-south trends. Final contraction may have postdated despinning and produced randomly oriented thrust faults. All of these events predated the formation of Caloris basin, because basin-associated deposits blanket both lineaments and arcuate thrust faults.     

Despinning plus global contraction and the orientation of lobate scarps on Mercury: Predictions for MESSENGER

Observations by the Mariner 10 spacecraft suggest that the lobate scarps on Mercury, which have been interpreted to record at most 1-2 km of radial contraction of the planet after the end of the Late Heavy Bombardment, possess a global, preferred N-S orientation but lack a strong latitudinal dependence on their surface expression. Here, we reexamine the idea that a decrease in the planetary rotation rate (despinning) coupled with global contraction of at least 3-5.5 km prior to the end of Late Heavy Bombardment resulted in global N-S oriented thrust faults. The surface expression of these faults is assumed to have been erased by the end of the Late Heavy Bombardment, and the faults were subsequently reactivated by later global contraction, producing generally N-S oriented thrust faults from an isotropic stress field. We use the estimate of >3-5.5 km contraction prior to ∼4 Ga as an additional constraint to thermomechanical simulations of the evolution of Mercury, finding that a wide range of models are consistent with this observation. The fact that a wide range of states are consistent with the contraction of Mercury prior to the end of Late Heavy Bombardment but only a restricted set of states are consistent with the at most 1-2 km of subsequent contraction bolsters the idea that there may be hidden strain on Mercury, features unseen by Mariner 10 but likely visible to the MESSENGER spacecraft.     

A co-accretional model of satellite formation

Numerical calculation of a simple accretion model including the effects of tidal friction indicate that coformation is tenable only if the planet's Q is less than about 10³. The parameter which most strongly affects the final mass ratio of the pair is the time at which the secondary embryo is introduced. Our model yields the proper Moon-Earth mass ratio if the Moon embryo is introduced when the Earth is only about $\text{1}\text{10}$ of its final mass. The lunar orbit remains at about 10 Earth radii throughout most of the growth.This model of satellite formation overcomes two difficulties of the “circumterrestrial cloud” model of Ruskol (1960, 1963, 1972): (1) The difficulty of accumulating a mass as great as the entire Moon before gravitational instability reduces the cloud to a small number of moonlets is removed. (2) The differences between terrestrial and outer planet satellite systems is easily understood in terms of the differences in Q between these planets. The high Q of the outer planets does not allow a satellite embryo to survive a significant portion of the accretion process, thus only small bodies which formed very late in the accumulation of the planet remain as satellites. The low Q of the terrestrial planets allows satellite embryos of these planets to survive during accretion, thus massive satellites such as the Earth's Moon are expected. The present lack of such satellites of the other terrestrial planets may be the result of tidal evolution, either infall following primary despinning (Burns, 1973) or escape due to increase in orbit eccentricity.     

Tectonics on Iapetus: Despinning, respinning, or something completely different?

Saturn’s moon Iapetus is unique in that it has apparently despun while retaining a substantial equatorial bulge. Stresses arising from such a non-hydrostatic shape should in principle cause surface deformation (tectonics). As part of a search for such a tectonic signature, lineaments (linear surface features) on Iapetus were mapped on both its bright and dark hemispheres. Lineament orientations were then compared to model stress patterns predicted for spin-down from a rotation period of 16.5 h (or less) to its present synchronous period, and for a range of lithospheric thicknesses. Many lineaments are straight segments of crater rimwalls, which may be faults or joints reactivated during complex crater collapse. Most striking are several large troughs on the bright, trailing hemisphere. These troughs appear to be extensional and are distinctive on that hemisphere, because the interior floors and walls of the troughs contain dark material. Globally, no specific evidence of strike slip or thrust offsets are seen, but this could be due to the age and degraded nature of any such features. We find that observed lineament orientations do not correlate with predicted patterns due to despinning on either hemisphere (the equatorial ridge was specifically excluded from this analysis, and is considered separately). Modest evidence for preferred orientations ±40° from north could be construed as consistent with respinning, which is not necessarily far-fetched. Assuming the rigidity of unfractured ice, predicted maximum lithospheric differential stresses from despinning range from ∼1 MPa to ∼160 MPa for the elastic spheroid and thin lithosphere limits, respectively (although it is only for thicker elastic lithospheres that we expect a nonhydrostatic state to be maintained over geologic time against lithospheric failure). The tectonic signature of despinning may have been obscured over time because the surface of Iapetus is very ancient, Iapetus’ thick lithosphere may have inhibited the full tectonic expression of despinning, or both. Several prominent lineaments strike E–W, and are thus parallel to the equatorial ridge (though not physically close to it), but a tectonic or volcanic origin for the ridge is highly problematic.     

Geologic evolution and cratering history of Mercury

Among the terrestrial planets, Mercury is the smallest and has the highest bulk density. Mercury exhibits a lunar-like surface, shaped by impact basins and craters. Rapid cooling and contraction as well as tidal despinning have resulted in a large inventory of tectonic scarps and faults visible on the surface. With plans for new orbiter missions to this intriguing planet taking shape, this paper presents a summary of our current knowledge on Mercury's geology and cratering history. On the basis of improved data on asteroid populations and crater scaling, we updated the time stratigraphic sequence for the planet and made new estimates for the time of formation of impact basins such as Tolstoj and Caloris, which generally are now thought to be younger than in previous estimates. In order to advance our understanding of the geology of the planet, imaging experiments on future missions must fill the gap in the global coverage left by the Mariner spacecraft, and increase the global multispectral spatial resolution to at least 100 m/pixel. Locally, the image resolution must reach approx. 10 m/pixel. Also, stereo topographic models with global and local resolutions of 200 and 20 m, respectively, are required.     

The chronology of Mercury's geological and geophysical evolution: The vulcanoid hypothesis

Previous discussions of Mercury's evolution have assumed that its cratering chronology is tied to that of the Moon, i.e., with Caloris forming about 3.9 Gyr ago as part of a late heavy bombardment that affected all of the terrestrial planets. That assumption requires that Mercury's core formed very early, because associated expansion features are not visible, and must have been erased before the cratering flux declined. Moreover, the modest amount of global shrinkage inferred from visible compressional features on Mercury's surface implies that the core is either largely molten at present, or had largely solidified before the end of the bombardment. The former interpretation requires a significant volatile content or implausibly large internal heat sources, while the latter raises questions about how to generate the planet's magnetic field. We have investigated whether constraints on Mercury's chronology could be relaxed by effects of a Mercury-specific bombarding population of planetesimals interior to its orbit, encountering the planet only occasionally due to secular perturbations. Such “vulcanoids” could have been a significant source of early cratering. However, those in orbits that can cross Mercury's are depleted by mutual collisions in ⪅1 Gyr, and can provide at most a modest extension of the period of heavy bombardment. Further inside Mercury's orbit, lower collisional velocities might allow survival of vulcanoids to the present. We report on a search for such bodies and on observational limits to such a population. We also review evidence that Mercury's intercrater plains are of volcanic origin and mainly predate Caloris, and that scarp formation (and global contraction) mainly postdates Caloris and has continued to recent times. If global lineaments are the product of tidal despinning, they constrain core formation to the first half of the planet's lifetime. While some questions and inconsistencies remain, the preponderance of evidence suggests that Mercury differentiated early, and at least half of its core volume is presently molten, probably due to a significant content of some light element such as sulfur.     

The internal activity and thermal evolution of Earth-like planets

We model the internal thermal evolution of planets with Earth-like composition and masses ranging from 0.1 to 10 Earth masses over a period of 10 billion years. We also characterize the internal activity of the planets by the velocity of putative tectonic plates, the rate at which mantle material is processed through melting zones, and the time taken to process one mantle mass. The more massive the planet the larger its processing rate (?), which scales approximately as ?∝M0.8-1.0. The processing times for all the planets increase with time as they cool and become less active. As would be expected, the surface heat flow scales with planet mass. All planets have similar declines in mantle temperature except for the largest, in which pressure effects cause a larger decline. The larger planets have higher mantle temperatures over all times. The less massive the planet, the larger the decrease in core temperature with time. The core heat flow is also found to decrease more rapidly for smaller planet masses. Finally, rough predictions are made for the time required to generate an atmosphere from estimates of the time to degas water and carbon dioxide in mantle melting zones. The degassing times depend strongly on the initial temperature of the planet, but for the temperatures used in our model all the planets degas within ∼32 Ma after their formation.     

Consequences of tidal interaction between disks and orbiting protoplanets for the evolution of multi-planet systems with architecture resembling that of Kepler 444

We study orbital evolution of multi-planet systems with masses in the terrestrial planet regime induced through tidal interaction with a protoplanetary disk assuming that this is the dominant mechanism for producing orbital migration and circularization. We develop a simple analytic model for a system that maintains consecutive pairs in resonance while undergoing orbital circularization and migration. This model enables migration times for each planet to be estimated once planet masses, circularization times and the migration time for the innermost planet are specified. We applied it to a system with the current architecture of Kepler 444 adopting a simple protoplanetary disk model and planet masses that yield migration times inversely proportional to the planet mass, as expected if they result from torques due to tidal interaction with the protoplanetary disk. Furthermore the evolution time for the system as a whole is comparable to current protoplanetary disk lifetimes. In addition we have performed a number of numerical simulations with input data obtained from this model. These indicate that although the analytic model is inexact, relatively small corrections to the estimated migration rates yield systems for which period ratios vary by a minimal extent. Because of relatively large deviations from exact resonance in the observed system of up to 2 %, the migration times obtained in this way indicate only weak convergent migration such that a system for which the planets did not interact would contract by only \({\sim }1\,\%\) although undergoing significant inward migration as a whole. We have also performed additional simulations to investigate conditions under which the system could undergo significant convergent migration before reaching its final state. These indicate that migration times have to be significantly shorter and resonances between planet pairs significantly closer during such an evolutionary phase. Relative migration rates would then have to decrease allowing period ratios to increase to become more distant from resonances as the system approached its final state in the inner regions of the protoplanetary disk.     

Planetary dynamics in the system α Centauri: The stability diagrams

The stability of the motion of a hypothetical planet in the binary system ?? Cen A?CB has been investigated. The analysis has been performed within the framework of a planar (restricted and full) three-body problem for the case of prograde orbits. Based on a representative set of initial data, we have obtained the Lyapunov spectra of the motion of a triple system with a single planet. Chaotic domains have been identified in the pericenter distance-eccentricity plane of initial conditions for the planet through a statistical analysis of the data obtained. We have studied the correspondence of these chaotic domains to the domains of initial conditions that lead to the planet??s encounter with one of the binary??s stars or to the escape of the planet from the system. We show that the stability criterion based on the maximum Lyapunov exponent gives a more clear-cut boundary of the instability domains than does the encounterescape criterion at the same integration time. The typical Lyapunov time of chaotic motion is ??500 yr for unstable outer orbits and ??60 yr for unstable inner ones. The domain of chaos expands significantly as the initial orbital eccentricity of the planet increases. The chaos-order boundary has a fractal structure due to the presence of orbital resonances.     

On the Radii of Close-in Giant Planets

The recent discovery that the close-in extrasolar giant planet HD 209458b transits its star has provided a first-of-its-kind measurement of the planet's radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet tau Bootis b. Including the effects of stellar irradiation, we estimate the general behavior of radius/age trajectories for such planets and interpret the large measured radii of HD 209458b and tau Boo b in that context. We find that HD 209458b must be a hydrogen-rich gas giant. Furthermore, the large radius of a close-in gas giant is not due to the thermal expansion of its atmosphere but to the high residual entropy that remains throughout its bulk by dint of its early proximity to a luminous primary. The large stellar flux does not inflate the planet but retards its otherwise inexorable contraction from a more extended configuration at birth. This implies either that such a planet was formed near its current orbital distance or that it migrated in from larger distances (>/=0.5 AU), no later than a few times 107 yr of birth.     

Young Jupiters are faint: new models of the early evolution of giant planets

Here we show preliminary calculations of the cooling and contraction of a 2 M_J planet. These calculations, which are being extended to 1–10 M_J, differ from other published “cooling tracks” in that they include a core accretion‐gas capture formation scenario, the leading theory for the formation of gas giant planets.We find that the initial post‐accretionary intrinsic luminosity of the planet is ∼3 times less than previously published models which use arbitrary initial conditions. These differences last a few tens of millions of years. Young giant planets are intrinsically fainter than has been previously appreciated. We also discuss how uncertainties in atmospheric chemistry and the duration of the formation time of giant planets lead to challenges in deriving planetary physical properties from comparison with tabulated model values. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the homeostasis and bistability on a Gaian planet

Geochemical disequilibrium of Earth's atmosphere is a sign of life. The fact that Earth's atmosphere is just right for life led Lovelock to propose the Gaia hypothesis: life itself regulates the environment on planetary scale in order to maintain habitability. This hypothesis is supported by the so-called Daisyworld parable, which illustrates a possible mechanism for such a self regulation. Here we revisit Daisyworld and challenge some of its conclusions from a closer examination of the model. We find that even within this simple, conceptual model of a Gaian planet there are regimes where climate is less homeostatic than on a dead planet. Furthermore, in other regimes, bistability between two climate states is found to exist due to the presence of life. This indicates that even if the Gaian stability might describe life in some planetary conditions, it need not be generic to all inhabited planets.     

A calculation of Saturn's gravitational contraction history

A calculation has been made of the gravitational contraction of a homogeneous, quasi-equilibrium Saturn model of solar composition. The calculations begin at a time when the planet's radius is ten times larger than its present size, and the subsequent gravitational contraction is followed for 4.5 × 10⁹ years. For the first million years of evolution, the Saturn model contracts rapidly like a pre-main sequence star and has a much higher luminosity and effective temperature than at present. Later stages of contraction occur more slowly and are analogous to the cooling phase of a degenerate white dwarf star.Examination of the interior structure of the models indicates the presence of a metallic hydrogen region near the center of the planet. Differences in the size of this region for Jupiter and Saturn may, in part, be responsible for Saturn having a weaker magnetic field. While the interior temperatures are much too high for the fluids in the molecular and metallic regions to become solids by the current epoch, the temperature in the outer portion of the metallic zone falls below Stevenson's [Phys. Rev. J. (1975)] phase separation curve for helium after 1.2 billion years of evolution. This would lead to a sinking of helium from the outer to the inner portion of the metallic region, as described by Salpeter [Astrophys. J.181, L83–L86 (1973)].At the current epoch, the radius of the model is about 9% larger, while its excess luminosity is comparable to the observed value of Rieke [Icarus26, 37–44 (1975)], as refined by Wright [Harvard College Obs. Preprint No. 480 (1976)]. This behavior of the Saturn model may be compared to the good agreement with both Jupiter's observed radius and excess luminosity shown by an analogous model of Jupiter [Graboske et al., Astrophys. J.199, 255–264 (1975)]. The discrepancy in radius of our Saturn model may be due to errors in the equations of state and/or our neglect of a rocky core. However, arguments are presented which indicate that helium separation may cause an expansion of the model and thus lead to an even bigger discrepancy in radius. Improvement in the radius may also foster a somewhat larger predicted luminosity. At least part and perhaps most of Saturn's excess luminosity is due to the loss of internal thermal energy that was built up during the early rapid contraction, with a minor contribution coming from Saturn's present rate of contraction. These two sources dominate Jupiter's excess luminosity. If helium separation makes an important contribution to Saturn's excess luminosity, then planetwide segregation is required.Finally, because Saturn's early high luminosity was about an order of magnitude smaller than Jupiter's, water-ice satellites may have been able to form closer to Saturn to Jupiter.     

Metastability of Liquid Water on Mars

A simple model of local heat transport on Mars demonstrates that transient melting of ice may occur in depressions and gullies nearly anywhere on the planet where thin ice is illuminated by normal-incidence insolation. An experiment has been performed to confirm the model of evaporation rate at low pressure. Reduction of radiative cooling due to gully geometry is shown to be important. Since appropriate meteorological, topographic, and optical conditions may occur on slopes nearly anywhere on the planet, hydrological features such as gullies would likely form only where such ice might accumulate, notably in sheltered locations at high latitudes. It is suggested that cold-trapping of winter condensation could concentrate a sufficient amount of ice to allow seasonal melting in gullies.     

Nebular drag and capture into spin-orbit resonance

The majority of planetary satellites whose spin period is known are observed to be in synchronous spin-orbit resonance. The commonly accepted explanation for this observation is that it is due to the effects of tidal evolution. However, cosmogonic theories state that the formation of planetary and satellite systems occurs within a primordial solar nebula and circumplanetary nebulae, respectively. In this paper the influence of nebular drag on the capture into spin-orbit resonance is analysed. The results show that the torques generated are important for these resonances in a wide range of cases. Using the protojovian nebula model by Lunine and Stevenson (1982), conservative estimates of the despinning time scales for the Galilean satellites are computed. In comparison the despinning time scale from tidal effects are several orders of magnitude larger.on leave of absence from Departamento de Matemática, Faculdade de Engenharia de Guaratinguetá, UNESP, CP 205, 12500-000, Guaratinguetá, SP, Brazil     

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of hot Jupiters

In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t _ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P _obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P _obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P _orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters.     

The effects of metallicity and grain growth and settling on the early evolution of gaseous protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large (∼1 AU) and internal temperatures are low (<2000 K). The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of isolated, non-accreting planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.