Accretion of the gaseous envelope of Jupiter around a 5-10 Earth-mass core

New numerical simulations of the formation and evolution of Jupiter are presented. The formation model assumes that first a solid core of several M_⊕ accretes from the planetesimals in the protoplanetary disk, and then the core captures a massive gaseous envelope from the protoplanetary disk. Earlier studies of the core accretion-gas capture model [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62-85] demonstrated that it was possible for Jupiter to accrete with a solid core of 10-30 M_⊕ in a total formation time comparable to the observed lifetime of protoplanetary disks. Recent interior models of Jupiter and Saturn that agree with all observational constraints suggest that Jupiter's core mass is 0-11 M_⊕ and Saturn's is 9-22 M_⊕ [Saumon, G., Guillot, T., 2004. Astrophys. J. 609, 1170-1180]. We have computed simulations of the growth of Jupiter using various values for the opacity produced by grains in the protoplanet's atmosphere and for the initial planetesimal surface density, σinit,Z, in the protoplanetary disk. We also explore the implications of halting the solid accretion at selected core mass values during the protoplanet's growth. Halting planetesimal accretion at low core mass simulates the presence of a competing embryo, and decreasing the atmospheric opacity due to grains emulates the settling and coagulation of grains within the protoplanet's atmosphere. We examine the effects of adjusting these parameters to determine whether or not gas runaway can occur for small mass cores on a reasonable timescale. We compute four series of simulations with the latest version of our code, which contains updated equation of state and opacity tables as well as other improvements. Each series consists of a run without a cutoff in planetesimal accretion, plus up to three runs with a cutoff at a particular core mass. The first series of runs is computed with an atmospheric opacity due to grains (hereafter referred to as ‘grain opacity’) that is 2% of the interstellar value and . Cutoff runs are computed for core masses of 10, 5, and 3 M_⊕. The second series of Jupiter models is computed with the grain opacity at the full interstellar value and . Cutoff runs are computed for core masses of 10 and 5 M_⊕. The third series of runs is computed with the grain opacity at 2% of the interstellar value and . One cutoff run is computed with a core mass of 5 M_⊕. The final series consists of one run, without a cutoff, which is computed with a temperature dependent grain opacity (i.e., 2% of the interstellar value for ramping up to the full interstellar value for ) and . Our results demonstrate that reducing grain opacities results in formation times less than half of those for models computed with full interstellar grain opacity values. The reduction of opacity due to grains in the upper portion of the envelope with has the largest effect on the lowering of the formation time. If the accretion of planetesimals is not cut off prior to the accretion of gas, then decreasing the surface density of planetesimals lowers the final core mass of the protoplanet, but increases the formation timescale considerably. Finally, a core mass cutoff results in a reduction of the time needed for a protoplanet to evolve to the stage of runaway gas accretion, provided the cutoff mass is sufficiently large. The overall results indicate that, with reasonable parameters, it is possible that Jupiter formed at 5 AU via the core accretion process in 1 Myr with a core of 10 M_⊕ or in 5 Myr with a core of 5 M_⊕.     

Optical and thermal infrared observations of six near-Earth asteroids in 2002

We present thermal infrared photometry and spectrophotometry of six Near-Earth Asteroids (NEAs) using the 3.8 m United Kingdom Infrared Telescope (UKIRT) together with quasi-simultaneous optical observations of five NEAs taken at the 1.0 m Jacobus Kapteyn Telescope (JKT). For Asteroid (6455) 1992 HE we derive a rotational period P=2.736±0.002 h, and an absolute visual magnitude H=14.32±0.24. For Asteroid 2002 HK₁₂ we derive . The Standard Thermal Model (STM), the Fast Rotating Model (FRM) and the Near-Earth Asteroid Thermal Model (NEATM) have been fitted to the measured fluxes to derive albedos and effective diameters. The derived geometric albedos and effective diameters are (6455) 1992 HE: pv=0.26±0.08, Deff=3.55±0.5 km; 1999 HF₁: pv=0.18±0.07, ; 2000 ED₁₀₄: pv=0.18±0.05, Deff=1.21±0.2 km; 2002 HK₁₂: , Deff=0.62±0.2 km; 2002 NX₁₈: pv=0.031±0.009, Deff=2.24±0.3 km; 2002 QE₁₅: , Deff=1.94±0.4 km. The limitations of using the NEATM to observe NEAs at high phase angles are discussed.     

The capture of interstellar dust: the Lorentz force case

The capture of arbitrarily shaped interstellar dust in the Solar System is investigated. Electromagnetic radiation and gravitational forces of the Sun and Lorentz force generated by interplanetary magnetic field are considered. The capture conditions appear to be very sensitive to the particle shape. Non-spherical particles as well as their spherical equivalents are captured only when they are moving initially in the vicinity of ecliptic plane. Capture of non-charged non-spherical dust typically occurs in the region , where R_Sun is solar radius and impact parameter b is defined as the smallest distance between the particle and the Sun if no forces existed. In contrast, charged particles are typically captured at b>150 R_Sun. The total amount of captured non-spherical sub-micron particles differs significantly from the corresponding amount of spherical dust grains. However, both amounts are comparable in the micron-sized range. It is shown that a certain mass of captured non-spherical particles may survive in the Solar System, while captured spherical ones hit the Sun or sublimate in its vicinity. Only a negligible amount of spherical particles can survive. Consideration of solar wind within around of yields that 20% of the captured non-spherical particles of the effective radius survive; the corresponding percentage for particles of the radius is 7%. The total mass of the surviving charged particles is about two orders of magnitude larger than the mass of the surviving non-charged particles. As a result, the sub-micron-sized particles are candidates to contribute to the density increase of the circumsolar dust cloud.     

A ballistics analysis of the Deep Impact ejecta plume: Determining Comet Tempel 1's gravity, mass, and density

In July of 2005, the Deep Impact mission collided a 366 kg impactor with the nucleus of Comet 9P/Tempel 1, at a closing speed of 10.2 km s⁻¹. In this work, we develop a first-order, three-dimensional, forward model of the ejecta plume behavior resulting from this cratering event, and then adjust the model parameters to match the flyby-spacecraft observations of the actual ejecta plume, image by image. This modeling exercise indicates Deep Impact to have been a reasonably “well-behaved” oblique impact, in which the impactor-spacecraft apparently struck a small, westward-facing slope of roughly 1/3-1/2 the size of the final crater produced (determined from initial ejecta plume geometry), and possessing an effective strength of not more than . The resulting ejecta plume followed well-established scaling relationships for cratering in a medium-to-high porosity target, consistent with a transient crater of not more than 85-140 m diameter, formed in not more than 250-550 s, for the case of (gravity-dominated cratering); and not less than 22-26 m diameter, formed in not less than 1-3 s, for the case of (strength-dominated cratering). At , an upper limit to the total ejected mass of 1.8×¹⁰⁷ kg (1.5-2.2×¹⁰⁷ kg) is consistent with measurements made via long-range remote sensing, after taking into account that 90% of this mass would have stayed close to the surface and then landed within 45 min of the impact. However, at , a lower limit to the total ejected mass of 2.3×¹⁰⁵ kg (1.5-2.9×¹⁰⁵ kg) is also consistent with these measurements. The expansion rate of the ejecta plume imaged during the look-back phase of observations leads to an estimate of the comet's mean surface gravity of (0.17-0.90 mm s⁻²), which corresponds to a comet mass of mt=4.5×¹⁰¹³ kg (2.3-12.0×¹⁰¹³ kg) and a bulk density of (200-1000 kg m⁻³), where the large high-end error is due to uncertainties in the magnitude of coma gas pressure effects on the ejecta particles in flight.     

Modeling crater populations on Venus and Titan

We describe a model for crater populations on planets and satellites with dense atmospheres, like those of Venus and Titan. The model takes into account ablation (or mass shedding), pancaking, and fragmentation. Fragmentation is assumed to occur due to the hydrodynamic instabilities promoted by the impactors’ deceleration in the atmosphere. Fragments that survive to hit the ground make craters or groups thereof. Crater sizes are estimated using standard laws in the gravity regime, modified to take into account impactor disruption. We use Monte Carlo methods to pick parameters from appropriate distributions of impactor mass, zenith angle, and velocity. Good fits to the Venus crater populations (including multiple crater fields) can be found with reasonable values of model parameters. An important aspect of the model is that it reproduces the dearth of small craters on Venus: this is due to a cutoff on crater formation we impose, when the expected crater would be smaller than the (dispersed) object that would make it. Hydrodynamic effects alone (ablation, pancaking, fragmentation) due to the passage of impactors through the atmosphere are insufficient to explain the lack of small craters. In our favored model, the observed number of craters (940) is produced by ∼5500 impactors with masses , yielding an age of (1-σ uncertainty) for the venusian surface. This figure does not take into account any uncertainties in crater scaling and impactor population characteristics, which probably increase the uncertainty to a factor of two in age.We apply the model with the same parameter values to Titan to predict crater populations under differing assumptions of impactor populations that reflect present conditions. We assume that the impactors (comets) are made of 50% porous ice. Predicted crater production rates are ≈190 craters . The smallest craters on Titan are predicted to be in diameter, and ≈5 crater fields are expected. If the impactors are composed of solid ice (density ), crater production rates increase by ≈70% and the smallest crater is predicted to be in diameter. We give cratering rates for denser comets and atmospheres 0.1 and 10 times as thick as Titan's current atmosphere. We also explicitly address leading-trailing hemisphere asymmetries that might be seen if Titan's rotation rate were strictly synchronous over astronomical timescales: if that is the case, the ratio of crater production on the leading hemisphere to that on the trailing hemisphere is ≈4:1.     

The Cassini Campaign observations of the Jupiter aurora by the Ultraviolet Imaging Spectrograph and the Space Telescope Imaging Spectrograph

We have analyzed the Cassini Ultraviolet Imaging Spectrometer (UVIS) observations of the Jupiter aurora with an auroral atmosphere two-stream electron transport code. The observations of Jupiter by UVIS took place during the Cassini Campaign. The Cassini Campaign included support spectral and imaging observations by the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS). A major result for the UVIS observations was the identification of a large color variation between the far ultraviolet (FUV: 1100-1700 Å) and extreme ultraviolet (EUV: 800-1100 Å) spectral regions. This change probably occurs because of a large variation in the ratio of the soft electron flux (10-3000 eV) responsible for the EUV aurora to the hard electron flux (∼15-22 keV) responsible for the FUV aurora. On the basis of this result a new color ratio for integrated intensities for EUV and FUV was defined (4πI1550-1620 Å/4πI1030-1150 Å) which varied by approximately a factor of 6. The FUV color ratio (4πI1550-1620 Å/4πI1230-1300 Å) was more stable with a variation of less than 50% for the observations studied. The medium resolution (0.9 Å FWHM, G140M grating) FUV observations (1295-1345 Å and 1495-1540 Å) by STIS on 13 January 2001, on the other hand, were analyzed by a spectral modeling technique using a recently developed high-spectral resolution model for the electron-excited H₂ rotational lines. The STIS FUV data were analyzed with a model that considered the Lyman band spectrum (B ) as composed of an allowed direct excitation component (X ) and an optically forbidden component (X followed by the cascade transition ). The medium-resolution spectral regions for the Jupiter aurora were carefully chosen to emphasize the cascade component. The ratio of the two components is a direct measurement of the mean secondary electron energy of the aurora. The mean secondary electron energy of the aurora varies between 50 and 200 eV for the polar cap, limb and auroral oval observations. We examine a long time base of Galileo Ultraviolet Spectrometer color ratios from the standard mission (1996-1998) and compare them to Cassini UVIS, HST, and International Ultraviolet Explorer (IUE) observations.     

R-band light curve of Comet 9P/Tempel 1 during the Deep Impact event

We present high-speed CCD photometry of Comet 9P/Tempel 1 during the Deep Impact event on 2005 July 4 UT. Approximately 2 h and 50 min of R-band data were acquired at Mount Laguna Observatory with a temporal resolution of 5.5 s. The flux increased by 9% in the first minute after impact. This was followed by a more gradual two-part linear rise, with a change in slope at 9.2 min post-impact, at which time the rate of brightening increased from ∼ to ∼. An analysis of the light curve obtained with the guide camera on the United Kingdom Infrared Telescope and yields very similar results. These findings are mildly in disagreement with the 3-part linear rise found by Fernández et al. (2007) in that we do not find any evidence for a change at 4 min post-impact. We interpret the linear rise phase as due to solar illumination of the edge of an expanding optically thick dust ejecta plume. After approximately 20 min, the light curves begin to flatten out, perhaps coincident with the start of the transition to becoming optically thin. In the large apertures (>10^″) the light curve continues to gradually rise until the end of the observations. In smaller apertures, the light curves reach a peak at approximately 50 min, then decrease back towards the pre-impact flux level. The drop in flux in the smaller apertures may be caused by the ejecta expanding beyond the edge of the photometric aperture, and if so, we can use this timescale to infer an expansion velocity of ∼, consistent with previous published estimates.     

Calculation of the enrichment of the giant planet envelopes during the “late heavy bombardment”

The giant planets of our solar system possess envelopes consisting mainly of hydrogen and helium but are also significantly enriched in heavier elements relatively to our Sun. In order to better constrain how these heavy elements have been delivered, we quantify the amount accreted during the so-called “late heavy bombardment”, at a time when planets were fully formed and planetesimals could not sink deep into the planets. On the basis of the “Nice model”, we obtain accreted masses (in terrestrial units) equal to for Jupiter, and for Saturn. For the two other giant planets, the results are found to depend mostly on whether they switched position during the instability phase. For Uranus, the accreted mass is with an inversion and without an inversion. Neptune accretes in models in which it is initially closer to the Sun than Uranus, and otherwise. With well-mixed envelopes, this corresponds to an increase in the enrichment over the solar value of 0.033±0.001 and 0.074±0.007 for Jupiter and Saturn, respectively. For the two other planets, we find the enrichments to be 2.1±1.4 (w/ inversion) or 1.2±0.7 (w/o inversion) for Uranus, and 2.0±1.2 (w/ inversion) or 2.7±1.6 (w/o inversion) for Neptune. This is clearly insufficient to explain the inferred enrichments of ∼4 for Jupiter, ∼7 for Saturn and ∼45 for Uranus and Neptune.     

The fate of ejecta from Hyperion

Ejecta from Saturn's moon Hyperion are subject to powerful perturbations from nearby Titan, which control their ultimate fate. We have performed numerical integrations to simulate a simplified system consisting of Saturn (including optical flattening as well as dynamical oblateness), its main ring system (treated as a massless flat annulus), the moons Tethys, Dione, Titan, Hyperion, and Iapetus, and the Sun (treated simply as a massive satellite). At several different points in Hyperion's orbit, 1050 massless particles, more or less evenly distributed over latitude and longitude, were ejected radially outward from 1 km above Hyperion's mean radius at speeds 10% faster than escape speed from Hyperion. Most of these particles were removed within the first few thousand years, but ∼3% of them survived the entire 100,000-year duration of the simulations. Ejecta from Hyperion are much more widely scattered than previously thought, and can cross the orbits of all of Saturn's satellites. About 9% of all the particles escaped from the saturnian system, but Titan accreted ∼78% of the total, while Hyperion reaccreted only ∼5%. This low efficiency of reaccretion may help to account for Hyperion's small size and rugged shape. Only ∼1% of all the particles hit other satellites, and another ∼1% impacted Saturn itself, while ∼3% of them struck its main rings. The high proportion of impacts into Saturn's rings is surprising; these collisions show a broad decline in impact speed with time, suggesting that Hyperion ejecta gradually spread inwards. Additional simulations were used to investigate the dependence of ejecta evolution on launch speed, the mass of Hyperion, and the presence of the Sun. In general, the wide distribution of ejecta from Hyperion suggests that it does contribute to “Population II” craters on the inner satellites of Saturn. Ejecta which escape from a satellite into temporary orbit about its planet, but later reimpact into the same moon or another one produce “poltorary” impacts, intermediate in character between primary and secondary impacts. It may be possible to distinguish poltorary craters from primary and secondary craters on the basis of morphology.     

On the collisional disruption of porous icy targets simulating Kuiper belt objects

We present results from 27 impact experiments using porous (porosity ranging from 0.39 to 0.54) ice targets and solid ice projectiles at impact speeds ranging from 90 to 155 m/s. These targets were designed to simulate Kuiper Belt Objects (KBOs) in structure. We measured a specific energy for shattering, , of 2.1×¹⁰⁵ erg/g for those snowball targets hit by intact ice projectiles; this is of the same order as that measured for solid ice targets. The fragment mass distribution follows a power law, although the exponent is not simply related to the largest fragment size as assumed by fragmentation models. We provide the first measurement of the three-dimensional mass-velocity distribution for disrupted ice targets and find that fragment speeds range from ∼2 to ∼20 m/s. The fraction of collisional kinetic energy that is partitioned into ejecta speeds is between 1 and 15% (although it should be noted that the lower limit is more reliable than the upper).     

Thermal infrared and optical observations of four near-Earth asteroids

We present thermal infrared photometry and spectrophotometry of four near-Earth asteroids (NEAs), namely (433) Eros, (66063) 1998 RO₁, (137032) 1998 UO₁, and (138258) 2000 GD₂, using the United Kingdom Infrared Telescope (UKIRT) in 2002. For two objects, i.e. (433) Eros and (137032) 1998 UO₁, quasi-simultaneous optical observations were also obtained, using the Jacobus Kapteyn Telescope (JKT). For (127032) 1998 UO₁, we obtain a rotation period P=3.0±0.1 h and an absolute visual magnitude HV=16.7±0.4. The Standard Thermal Model (STM), Fast Rotating Model (FRM) and near-Earth asteroid Thermal Model (NEATM) have been fitted to the IR fluxes to determine effective diameters Deff, geometric albedos pv, and beaming parameters η. The derived values are (433) Eros: Deff=23.3±3.5 km (at lightcurve maximum), pv=0.24±0.07, η=0.95±0.19; (66063) 1998 RO₁: , ; (137032) 1998 UO₁: Deff<1.13 km, pv>0.29; (138258) 2000 GD₂: Deff=0.27±0.04 km, , η=0.74±0.15. (66063) 1998 RO₁ is a binary asteroid from lightcurve characteristics [Pravec, P., and 56 colleagues, 2006. Icarus 181, 63-93] and we estimate the effective diameter of the primary (Dp) and secondary (Ds) components: and . The diameter and albedo of (138258) 2000 GD₂ are consistent with the trend of decreasing diameter for S- and Q-type asteroids found by Delbó et al. [Delbó, M., Harris, A.W., Binzel, R.P., Pravec, P., Davies, J.K., 2003. Icarus 166, 116-130]. A possible trend of increasing beaming parameter with diameter for small (less than about 3 km) S- and Q-type asteroids is found.     

Submillimeter Wave Astronomy Satellite observations of Comet 9P/Tempel 1 and Deep Impact

On 4 July 2005 at 5:52 UT the Deep Impact mission successfully completed its goal to hit the nucleus of 9P/Tempel 1 with an impactor, forming a crater on the nucleus and ejecting material into the coma of the comet. NASA's Submillimeter Wave Astronomy Satellite (SWAS) observed the ₁₁₀-₁₀₁ ortho-water ground-state rotational transition in Comet 9P/Tempel 1 before, during, and after the impact. No excess emission from the impact was detected by SWAS and we derive an upper limit of 1.8×¹⁰⁷ kg on the water ice evaporated by the impact. However, the water production rate of the comet showed large natural variations of more than a factor of three during the weeks before and after the impact. Episodes of increased activity with alternated with periods with low outgassing (). We estimate that 9P/Tempel 1 vaporized a total of N∼4.5×¹⁰³⁴ water molecules (∼1.3×¹⁰⁹ kg) during June-September 2005. Our observations indicate that only a small fraction of the nucleus of Tempel 1 appears to be covered with active areas. Water vapor is expected to emanate predominantly from topographic features periodically facing the Sun as the comet rotates. We calculate that appreciable asymmetries of these features could lead to a spin-down or spin-up of the nucleus at observable rates.     

Parametric analysis of modeled ion escape from Mars

We develop a parametric fit to the results of a detailed magnetohydrodynamic (MHD) study of the response of ion escape rates (O⁺, and ) to strongly varied solar forcing factors, as a way to efficiently extend the MHD results to different conditions. We then use this to develop a second, evolutionary model of solar forced ion escape. We treat the escape fluxes of ion species at Mars as proportional to the product of power laws of four factors - that of the EUV flux R_euv, the solar wind particle density R_ρ, its velocity (squared) R_v², and the interplanetary magnetic field pressure R_B², where forcing factors are expressed in units of the current epoch-averaged values. Our parametric model is: , where ?(i) is the escape flux of ion i. We base our study on the results of just six provided MHD model runs employing large forcing factor variations, and thus construct a successful, first-order parametric model of the MHD program. We perform a five-dimensional least squares fit of this power law model to the MHD results to derive the flux normalizations and the indices of the solar forcing factors. For O⁺, we obtain the values, 1.73 × 10²⁴ s⁻¹, 0.782, 0.251, 0.382, and 0.214, for ?₀, α, β, γ, and δ, respectively. For , the corresponding values are 1.68 × 10²⁴ s⁻¹, −0.393, 0.798, 0.967, and 0.533. For , they are 8.66 × 10²² s⁻¹, −0.427, 1.083, 1.214, and 0.690. The fit reproduces the MHD results to an average error of about 5%, suggesting that the power laws are broadly representative of the MHD model results. Our analysis of the MHD model shows that by itself an increase in R_EUV enhances O⁺ loss, but suppresses the escape of and , whereas increases in solar wind (i.e., in , and R_B², with R_euv constant) favors the escape of heavier ions more than light ions. The ratios of escaping ions detectable at Mars today can be predicted by this parametric fit as a function of the solar forcing factors. We also use the parametric model to compute escape rates over martian history. This second parametric model expresses ion escape functions of one variable (per ion), ?(i) = ?₀(i)(t/t₀)^−ξ(i). The ξ(i) are linear combinations of the epoch-averaged ion escape sensitivities, which are seen to increase with ion mass. We integrate the and oxygen ion escape rates over time, and find that in the last 3.85 Gyr, Mars would have lost about mbars of , and of water (from O⁺ and ) from ion escape.     

A sensitive search for nitric oxide in the lower atmospheres of Venus and Mars: Detection on Venus and upper limit for Mars

High-resolution spectra of Venus and Mars at the NO fundamental band at 5.3 μm with resolving power ν/δν=76,000 were acquired using the TEXES spectrograph at NASA IRTF on Mauna Kea, Hawaii. The observed spectrum of Venus covered three NO lines of the P-branch. One of the lines is strongly contaminated, and the other two lines reveal NO in the lower atmosphere at a detection level of 9 sigma. A simple photochemical model for NO and N at 50-112 km was coupled with a radiative transfer code to simulate the observed equivalent widths of the NO and some CO₂ lines. The derived NO mixing ratio is 5.5±1.5 ppb below 60 km and its flux is . Predissociation of NO at the (0-0) 191 nm and (1-0) 183 nm bands of the δ-system and the reaction with N are the only important loss processes for NO in the lower atmosphere of Venus. The photochemical impact of the measured NO abundance is significant and should be taken into account in photochemical modeling of the Venus atmosphere. Lightning is the only known source of NO in the lower atmosphere of Venus, and the detection of NO is a convincing and independent proof of lightning on Venus. The required flux of NO is corrected for the production of NO and N by the cosmic ray ionization and corresponds to the lightning energy deposition of . For a flash energy on Venus similar to that on the Earth (∼¹⁰⁹ J), the global flashing rate is ∼90 s⁻¹ and ∼6 km⁻² y⁻¹ which is in reasonable agreement with the existing optical observations. The observed spectrum of Mars covered three NO lines of the R-branch. Two of these lines are contaminated by CO₂ lines, and the line at 1900.076 cm⁻¹ is clean and shows some excess over the continuum. Some photochemical reactions may result in a significant excitation of NO (v=1) in the lowest 20 km on Mars. However, quenching of NO (v=1) by CO₂ is very effective below 40 km. Excitation of NO (v=1) in the collisions with atomic oxygen is weak because of the low temperature in the martian atmosphere, and we do not see any explanation of a possible emission of NO at 5.3 μm. Therefore the data are treated as the lack of absorption with a 2 sigma upper limit of 1.7 ppb to the NO abundance in the lower atmosphere of Mars. This limit is above the predictions of photochemical models by a factor of 3.     

Low-speed impacts between rubble piles modeled as collections of polyhedra, 2

We present the results of additional calculations involving the collisions of km-scale rubble piles. In new work, we used the Open Dynamics Engine (ODE), an open-source library for the simulation of rigid-body dynamics that incorporates a sophisticated collision-detection and resolution routine. We found that using ODE resulted in a speed-up of approximately a factor of 30 compared with previous code. In this paper we report on the results of almost 1200 separate runs, the bulk of which were carried out with 1000-2000 elements. We carried out calculations with three different combinations of the coefficients of friction η and (normal) restitution ?: low (η=0,?=0.8), medium (η=0,?=0.5), and high (η=0.5,?=0.5) dissipation.For target objects of ∼1 km in radius, we found reduced critical disruption energy values in head-on collisions from 2 to 100 J kg⁻¹ depending on dissipation and impactor/target mass ratio. Monodisperse objects disrupted somewhat more easily than power-law objects in general. For oblique collisions of equal-mass objects, mildly off-center collisions (b/b₀=0.5) seemed to be as efficient or possibly more efficient at collisional disruption as head-on collisions. More oblique collisions were less efficient and the most oblique collisions we tried (b/b₀=0.866) required up to ∼200 J kg⁻¹ for high-dissipation power-law objects. For calculations with smaller numbers of elements (total impactor or 200 elements) we found that collisions were more efficient for smaller numbers of more massive elements, with values as low as for low-dissipation cases. We also analyzed our results in terms of the relations proposed by Stewart and Leinhardt [Stewart, S.T., Leinhardt, Z.M., 2009. Astrophys. J. 691, L133-L137] where where Q_R is the impact kinetic energy per unit total mass m_i+m_T. Although there is a significant amount of scatter, our results generally bear out the suggested relation.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

On the population, physical decay and orbital distribution of Jupiter family comets: Numerical simulations

We study the Jupiter family comet (JFC) population assumed to come from the Scattered Disk and transferred to the Jupiter’s zone through gravitational interactions with the Jovian planets. We shall define as JFCs those with orbital periods and Tisserand parameters in the range 2<T?3.1, while those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods ) will be called ‘non-JFCs’. We performed a series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical-physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. With the dynamical model, we obtain a poor match between the computed distributions of orbital elements and the observed ones. However with the inclusion of physical effects in the complete model we are able to obtain good fits to observations. The best fits are attained with four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is less when the frequency is high and vice versa. The mean lifetime of JFCs with radii and is found to be of about 150-200 revolutions (∼. The total population of JFCs with radii within Jupiter’s zone is found to be of 450±50. Yet, the population of non-JFCs with radii in Jupiter-crossing orbits may be ∼4 times greater, thus leading to a whole population of JFCs + non-JFCs of ∼2250±250. Most of these comets have perihelia close to Jupiter’s orbit. On the other hand, very few non-JFCs reach the Earth’s vicinity (perihelion distances ) which gives additional support to the idea that JFCs and Halley-type comets have different dynamical origins. Our model allows us to define the zones of the orbital element space in which we would expect to find a large number of JFCs. This is the first time, to our knowledge, that a physico-dynamical model is presented that includes sublimation and different splitting laws. Our work helps to understand the role played by these erosion effects in the distribution of the orbital elements and lifetimes of JFCs.