Titan impacts and escape

We report on hydrodynamic calculations of impacts of large (multi-kilometer) objects on Saturn’s moon Titan. We assess escape from Titan, and evaluate the hypothesis that escaping ejecta blackened the leading hemisphere of Iapetus and peppered the surface of Hyperion.We carried out two- and three-dimensional simulations of impactors ranging in size from 4 to 100 km diameter, impact velocities between 7 and 15 km s⁻¹, and impact angles from 0° to 75° from the vertical. We used the ZEUSMP2 hydrocode for the calculations. Simulations were made using three different geometries: three-dimensional Cartesian, two-dimensional axisymmetric spherical polar, and two-dimensional plane polar. Three-dimensional Cartesian geometry calculations were carried out over a limited domain (e.g. 240 km on a side for an impactor of size d_i = 10 km), and the results compared to ones with the same parameters done by Artemieva and Lunine (2005); in general the comparison was good. Being computationally less demanding, two-dimensional calculations were possible for much larger domains, covering global regions of the satellite (from 800 km below Titan’s surface to the exobase altitude 1700 km above the surface). Axisymmetric spherical polar calculations were carried out for vertical impacts. Two-dimensional plane-polar geometry calculations were made for both vertical and oblique impacts. In general, calculations among all three geometries gave consistent results.Our basic result is that the amount of escaping material is less than or approximately equal to the impactor mass even for the most favorable cases. Amounts of escaping material scaled most strongly as a function of velocity, with high-velocity impacts generating the largest amount, as expected. Dependence of the relative amount of escaping mass f_esc = m_esc/M_i on impactor diameter d_i was weak. Oblique impacts (impact angle θ_i > 45°) were more effective than vertical or near-vertical impacts; ratios of m_esc/M_i ∼ 1-2 were found in the simulations.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

Numerical simulations of very large impacts on the Earth

Vertical impacts on the Earth of asteroids 500-3000 km in diameter at 15 km/s have been numerically modelled using the hydrodynamic SOVA code. This code has been modified for the spherical system of coordinates well suited for simulations of very large impacts when the entire Earth is involved in motion. The simulations include cratering process, upward motion of deep mantle layers, fall of ejecta on the Earth, escape of matter to space, and formation of rock vapour atmospheres. The calculations were made for the period preceding disappearance of rock vapour atmospheres caused by radiation several years after the largest impacts. For very large vertical impacts at 15 km/s, escaping masses proved to be negligibly small. Quantities of kinetic, internal, potential, and radiated away energies are obtained as functions of time and space. After the impacts, a global layer of condensed ejecta covers the whole of the Earth's surface and the ejecta energy is sufficient to vaporise an ocean 3 km deep. The mass of rock vapour atmosphere is 10-23% of the impactor mass. This atmosphere has a greater mass than the water atmosphere if impactor is 2000 km in diameter or larger.     

Meridional transport of HCN from SL9 impacts on Jupiter

In July 1994, the Shoemaker-Levy 9 (SL9) impacts introduced hydrogen cyanide (HCN) to Jupiter at a well confined latitude band around −44°, over a range of specific longitudes corresponding to each of the 21 fragments (Bézard et al. 1997, Icarus 125, 94-120). This newcomer to Jupiter's stratosphere traces jovian dynamics. HCN rapidly mixed with longitude, so that observations recorded later than several months after impact witnessed primarily the meridional transport of HCN north and south of the impact latitude band. We report spatially resolved spectroscopy of HCN emission 10 months and 6 years following the impacts. We detect a total mass of HCN in Jupiter's stratosphere of 1.5±0.7×10¹³ g in 1995 and 1.7±0.4×10¹³ g in 2000, comparable to that observed several days following the impacts (Bézard et al. 1997, Icarus 125, 94-120). In 1995, 10 months after impact, HCN spread to −30° and −65° latitude (half column masses), consistent with a horizontal eddy diffusion coefficient of K_yy=2-3×10¹⁰ cm² s⁻¹. Six years following impact HCN is observed in the northern hemisphere, while still being concentrated at 44° south latitude. Our meridional distribution of HCN suggests that mixing occurred rapidly north of the equator, with K_yy=2-5×10¹¹ cm² s⁻¹, consistent with the findings of Moreno et al. (2003, Planet. Space Sci. 51, 591-611) and Lellouch et al. (2002, Icarus 159, 112-131). These inferred eddy diffusion coefficients for Jupiter's stratosphere at 0.1-0.5 mbar generally exceed those that characterize transport on Earth. The low abundance of HCN detected at high latitudes suggests that, like on Earth, polar regions are dynamically isolated from lower latitudes.     

Lunar-forming collisions with pre-impact rotation

Prior models of lunar-forming impacts assume that both the impactor and the target protoearth were not rotating prior to the Moon-forming event. However, planet formation models suggest that such objects would have been rotating rapidly during the late stages of terrestrial accretion. In this paper I explore the effects of pre-impact rotation on impact outcomes through more than 100 hydrodynamical simulations that consider a range of impactor masses, impact angles and impact speeds. Pre-impact rotation, particularly in the target protoearth, can substantially alter collisional outcomes and leads to a more diverse set of final planet-disk systems than seen previously. However, the subset of these impacts that are also lunar-forming candidates—i.e. that produce a sufficiently massive and iron-depleted protolunar disk—have properties similar to those determined for collisions of non-rotating objects [Canup, R.M., Asphaug, E., 2001. Nature 412, 708-712; Canup, R.M., 2004a. Icarus 168, 433-456]. With or without pre-impact rotation, a lunar-forming impact requires an impact angle near 45 degrees, together with a low impact velocity that is not more than 10% larger than the Earth's escape velocity, and produces a disk containing up to about two lunar masses that is composed predominantly of material originating from the impactor. The most significant differences in the successful cases involving pre-impact spin occur for impacts into a retrograde rotating protoearth, which allow for larger impactors (containing up to 20% of Earth's mass) and provide an improved match with the current Earth-Moon system angular momentum compared to prior results. The most difficult state to reconcile with the Moon is that of a rapidly spinning, low-obliquity protoearth before the giant impact, as these cases produce disks that are not massive enough to yield the Moon.     

Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids. II. Effects of initial rotation and spin-down through disruptive collisions

Expanding on our previous N-body simulation of impacts between initially non-rotating rubble-pile objects [Takeda, T., Ohtsuki, K., 2007. Icarus 189, 256-273], we examine effects of initial rotation of targets on mass dispersal and change of spin rates. Numerical results show that the collisional energy needed to disrupt a rubble-pile object is not sensitive to initial rotation of the target, in most of the parameter range studied in our simulations. We find that initial rotation of targets is slowed down through disruptive impacts for a wide range of parameters. The spin-down is caused by escape of high-velocity ejecta and asymmetric re-accumulation of fragments. When these effects are significant, rotation is slowed down even when the angular momentum added by an impactor is in the same direction as the initial rotation of the target. Spin-down is most efficient when the impact occurs in the equatorial plane of the target, because in this case most of the ejected fragments originate from the equatorial region of the target and a significant amount of angular momentum can be easily removed. In the case of impacts from directions inclined relative to the target's equatorial plane, spin-down still occurs with reduced degree, unless impacts occur onto the pole region from the vertical direction. Our results suggest that such spin-down through disruptive impacts may have played an important role in spin evolution of asteroids through collisions in the gravity-dominated regime.     

Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids

We perform N-body simulations of impacts between initially non-rotating rubble-pile asteroids, and investigate mass dispersal and angular momentum transfer during such collisions. We find that the fraction of the dispersed mass (Mdisp) is approximately proportional to , where Qimp is the impact kinetic energy; the power index α is about unity when the impactor is much smaller than the target, and 0.5?α<1 for impacts with a larger impactor. Mdisp is found to be smaller for more dissipative impacts with small values of the restitution coefficient of the constituent particles. We also find that the efficiency of transfer of orbital angular momentum to the rotation of the largest remnant depends on the degree of disruption. In the case of disruptive oblique impacts where the mass of the largest remnant is about half of the target mass, most of the orbital angular momentum is carried away by the escaping fragments and the efficiency becomes very low (<0.05), while the largest remnant acquires a significant amount of spin angular momentum in moderately disruptive impacts. These results suggest that collisions likely played an important role in rotational evolution of small asteroids, in addition to the recoil force of thermal re-radiation.     

Geophysical consequences of planetary-scale impacts into a Mars-like planet

All planetary bodies with old surfaces exhibit planetary-scale impact craters: vast scars caused by the large impacts at the end of Solar System accretion or the late heavy bombardment. Here we investigate the geophysical consequences of planetary-scale impacts into a Mars-like planet, by simulating the events using a smoothed particle hydrodynamics (SPH) model. Our simulations probe impact energies over two orders of magnitude (2 × 10²⁷-6 × 10²⁹ J), impact velocities from the planet’s escape velocity to twice Mars’ orbital velocity (6-50 km/s), and impact angles from head-on to highly oblique (0-75°). The simulation results confirm that for planetary-scale impacts, surface curvature, radial gravity, the large relative size of the impactor to the planet, and the greater penetration of the impactor, contribute to significant differences in the geophysical expression compared to small craters, which can effectively be treated as acting in a half-space. The results show that the excavated crustal cavity size and the total melt production scale similarly for both small and planetary-scale impacts as a function of impact energy. However, in planetary-scale impacts a significant fraction of the melt is sequestered at depth and thus does not contribute to resetting the planetary surface; complete surface resetting is likely only in the most energetic (6 × 10²⁹ J), slow, and head-on impacts simulated. A crater rim is not present for planetary-scale impacts with energies >10²⁹ J and angles ?45°, but rather the ejecta is more uniformly distributed over the planetary surface. Antipodal crustal removal and melting is present for energetic (>10²⁹ J), fast (>6 km/s), and low angle (?45°) impacts. The most massive impactors (with both high impact energy and low velocity) contribute sufficient angular momentum to increase the rotation period of the Mars-sized target to about a day. Impact velocities of >20 km/s result in net mass erosion from the target, for all simulated energies and angles. The hypothesized impact origin of planetary structures may be tested by the presence and distribution of the geochemically-distinct impactor material.     

Simulations of a late lunar-forming impact

Results of about 100 hydrodynamic simulations of potential Moon-forming impacts are presented, focusing on the “late impact” scenario in which the lunar forming impact occurs near the very end of Earth's accretion (Canup and Asphaug, 2001, Nature 412, 708-712). A new equation of state is utilized that includes a treatment of molecular vapor (“M-ANEOS”; Melosh, 2000, in: Proc. Lunar Planet. Sci. Conf. 31st, p. 1903). The sensitivity of impact outcome to collision conditions is assessed, in particular how the mass, angular momentum, composition and origin (target vs. impactor) of the material placed into circumterrestrial orbit vary with impact angle, speed, impactor-to-target mass ratio, and initial thermal state of the colliding objects. The most favorable conditions for producing a sufficiently massive and iron-depleted protolunar disk involve collisions with an impact angle near 45 degrees and an impactor velocity at infinity <4 km/sec. For a total mass and angular momentum near to that of the current Earth-Moon system, such impacts typically place about a lunar mass of material into orbits exterior to the Roche limit, with the orbiting material composed of 10 to 30% vapor by mass. In all cases, the vast majority of the orbiting material originates from the impactor, consistent with previous findings. By mapping the end fate (escaping, orbiting, or in the planet) of each particle and the peak temperature it experiences during the impact onto the figure of the initial objects, it is shown that in the successful collisions, the impactor material that ends up in orbit is primarily that portion of the object that was heated the least, having avoided direct collision with the Earth. Using these and previous results as a guide, a continuous suite of impact conditions intermediate to the “late impact” (Canup and Asphaug, 2001, Nature 412, 708-712) and “early Earth” (Cameron, 2000, in: Canup, R.M., Righter, K. (Eds.), Origin of the Earth and Moon, pp. 133-144; 2001, Meteorit. Planet. Sci. 36, 9-22) scenarios is identified that should also produce iron-poor, ∼lunar-sized satellites and a system angular momentum similar to that of the Earth-Moon system. Among these, those that leave the Earth >95% accreted after the Moon-forming impact are favored here, implying a giant impactor mass between 0.11 and 0.14 Earth masses.     

Scaling of oblique impacts in frictional targets: Implications for crater size and formation mechanisms

Almost every meteorite impact occurs at an oblique angle of incidence, yet the effect of impact angle on crater size or formation mechanism is only poorly understood. This is, in large part, due to the difficulty of inferring impactor properties, such as size, velocity and trajectory, from observations of natural craters, and the expense and complexity of simulating oblique impacts using numerical models. Laboratory oblique impact experiments and previous numerical models have shown that the portion of the projectile’s kinetic energy that is involved in crater excavation decreases significantly with impact angle. However, a thorough quantification of planetary-scale oblique impact cratering does not exist and the effect of impact angle on crater size is not considered by current scaling laws. To address this gap in understanding, we developed iSALE-3D, a three-dimensional multi-rheology hydrocode, which is efficient enough to perform a large number of well-resolved oblique impact simulations within a reasonable time. Here we present the results of a comprehensive numerical study containing more than 200 three-dimensional hydrocode-simulations covering a broad range of projectile sizes, impact angles and friction coefficients. We show that existing scaling laws in principle describe oblique planetary-scale impact events at angles greater than 30° measured from horizontal. The displaced mass of a crater decreases with impact angle in a sinusoidal manner. However, our results indicate that the assumption that crater size scales with the vertical component of the impact velocity does not hold for materials with a friction coefficient significantly lower than 0.7 (sand). We found that increasing coefficients of friction result in smaller craters and a formation process more controlled by impactor momentum than by energy.     

Size-frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families

We investigate the morphology of size-frequency distributions (SFDs) resulting from impacts into 100-km-diameter parent asteroids, represented by a suite of 161 SPH/N-body simulations conducted to study asteroid satellite formation [Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M., 2004. Icarus 170, 243-257]. The spherical basalt projectiles range in diameter from 10 to 46 km (in equally spaced mass increments in logarithmic space, covering six discrete sizes), impact speeds range from 2.5 to 7 km/s (generally in 1 km/s increments), and impact angles range from 15° to 75° (nearly head-on to very oblique) in 15° increments. These modeled SFD morphologies match very well the observed SFDs of many known asteroid families. We use these modeled SFDs to scale to targets both larger and smaller than 100 km in order to gain insights into the circumstances of the impacts that formed these families. Some discrepancies occur for families with parent bodies smaller than a few tens of kilometers in diameter (e.g., 832 Karin), however, so due caution should be used in applying our results to such small families. We find that ∼20 observed main-belt asteroid families are produced by the catastrophic disruption of D>100 km parent bodies. Using these data as constraints, collisional modeling work [Bottke Jr., W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H.F., 2005b. Icarus 179, 63-94] suggests that the threshold specific energy, , needed to eject 50% of the target body's mass is very close to that predicted by Benz and Asphaug [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20].     

Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations

The volume of melt produced in hypervelocity planetary impacts and the size and shape of the melted region are key to understanding the impact histories of solid planetary bodies and the geological effects of impacts on their surfaces and interiors. Prior work of Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) gave the first estimates of impact melt production in geological materials using a modern hydrocode and equation of state. However, computational limits at the time forced use of low resolution, which may have resulted in low melt volumes. Our simulations with 50 times higher resolution provide independent confirmation of the Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) melt volumes in aluminum, iron, dunite, and granite impacts at velocities between 20 and 80 km/s. In ice/ice impacts, we find that melt volumes depend on target temperature and are lower than predicted by Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423). Our melt volumes are directly proportional to impact energy for all materials, over a wide range of impact velocity. We also report new data for melt volume scalings for ice/dunite and iron/dunite impacts and the size and shape of melted region, valuable for interpretation of cratering records and studies of impact-induced differentiation.     

Numerical modeling of asteroid survivability and possible scenarios for the Morokweng crater‐forming impact

The fate of the impactor is an important aspect of the impact‐cratering process. Defining impactor material as surviving if it remains solid (i.e., does not melt or vaporize) during crater formation, previous numerical modeling and experiments have shown that survivability decreases with increasing impact velocity, impact angle (with respect to the horizontal), and target density. Here, we show that in addition to these, impactor survivability depends on the porosity and shape of the impactor. Increasing impactor porosity decreases impactor survivability, while prolate‐shaped (polar axis > equatorial axis) impactors survive impact more so than spherical and oblate‐shaped (polar axis < equatorial axis) impactors. These results are used to produce a relatively simple equation, which can be used to estimate the impactor fraction shocked to a given pressure as a function of these parameters. By applying our findings to the Morokweng crater‐forming impact, we suggest impact scenarios that explain the high meteoritic content and presence of unmolten fossil meteorites within the Morokweng crater. In addition to previous suggestions of a low‐velocity and/or high‐angled impact, this work suggests that an elongated and/or low porosity impactor may also help explain the anomalously high survivability of the Morokweng impactor.     

Velocity distributions of high-velocity ejecta from regolith targets

We measured the velocity distributions of impact ejecta with velocities higher than ∼100 m s⁻¹ (high-velocity ejecta) for impacts at variable impact angle α into unconsolidated targets of small soda-lime glass spheres. Polycarbonate projectiles with mass of 0.49 g were accelerated to ∼250 m s⁻¹ by a single-stage light-gas gun. The impact ejecta are detected by thin aluminum foils placed around the targets. We analyzed the holes on the aluminum foils to derive the total number and volume of ejecta that penetrated the aluminum foils. Using the minimum velocity of the ejecta for penetration, determined experimentally, the velocity distributions of the high-velocity ejecta were obtained at α=15°, 30°, 45°, 60°, and 90°. The velocity distribution of the high-velocity ejecta is shown to depend on impact angle. The quantity of the high-velocity ejecta for vertical impact (α=90°) is considerably lower than derived from a power-law relation for the velocity distribution on the low-velocity ejecta (less than 10 m s⁻¹). On the other hand, in oblique impacts, the quantity of the high-velocity ejecta increases with decreasing impact angle, and becomes comparable to those derived from the power-law relation. We attempt to scale the high-velocity ejecta for oblique impacts to a new scaling law, in which the velocity distribution is scaled by the cube of projectile radius (scaled volume) and a horizontal component of impactor velocity (scaled ejection velocity), respectively. The high-velocity ejecta data shows a good correlation between the scaled volume and the scaled ejection velocity.     

Study of the vertical structure of Saturn's atmosphere using HST/WFPC2 images

We have studied the vertical structure of hazes at six different latitudes (−60°, −50°, −30°, −10°, +30°, and +50°) on Saturn's atmosphere. For that purpose we have compared the results of our forward radiative transfer model to limb-to-limb reflectivity scans at four different wavelengths (230, 275, 673.2, and 893 nm). The images were obtained with the Hubble Space Telescope Wide Field Planetary Camera 2 in September 1997, during fall on Saturn's northern hemisphere. The spatial distribution of particles appears to be very variable with latitude both in the stratosphere and troposphere. For the latitude range +50° to −50°, an atmospheric structure consisting of a stratospheric haze and a tropospheric haze interspersed by clear gas regions has been found adequate to explain the center to limb reflectivities at the different wavelengths. This atmospheric structure has been previously used by Ortiz et al. (1996, Icarus 119, 53-66) and Stam et al. (2001, Icarus 152, 407-422). In this work the top of the tropospheric haze is found to be higher at the southern latitudes than at northern latitudes. This hemispherical asymmetry seems to be related to seasonal effects. Different latitudes experience different amount of solar insolation that can affect the atmospheric structure as the season varies with time. The haze optical thickness is largest (about 30 at 673.2 nm) at latitudes ±50 and −10 degrees, and smallest (about 18) at ±30 degrees. The stratospheric haze is found to be optically thin at all studied latitudes from −50 to +50 degrees being maximum at −10° (τ=0.033). At −60° latitude, where the UV images show a strong darkening compared to other regions on the planet, the cloud structure is remarkably different when compared to the other latitudes. Here, aerosol and gas are found to be uniformly mixed down to the 400 mbar level.     

The opposition and tilt effects of Saturn’s rings from HST observations

The two major factors contributing to the opposition brightening of Saturn’s rings are (i) the intrinsic brightening of particles due to coherent backscattering and/or shadow hiding on their surfaces, and (ii) the reduced interparticle shadowing when the solar phase angle α → 0°. We utilize the extensive set of Hubble Space Telescope observations (Cuzzi, J.N., French, R.G., Dones, L. [2002]. Icarus 158, 199–223) for different elevation angles B and wavelengths λ to disentangle these contributions. We assume that the intrinsic contribution is independent of B, so that any B dependence of the phase curves is due to interparticle shadowing, which must also act similarly for all λ’s. Our study complements that of Poulet et al. (Poulet, F., Cuzzi, J.N., French, R.G., Dones, L. [2002]. Icarus 158, 224), who used a subset of data for a single B ∼ 10°, and the French et al. (French, R.G., Verbiscer, A., Salo, H., McGhee, C.A., Dones, L. [2007b] PASP 119, 623–642) study for the B ∼ 23° data set that included exact opposition. We construct a grid of dynamical/photometric simulation models, with the method of Salo and Karjalainen (Salo and Karjalainen [2003]. Icarus 164, 428–460), and use these simulations to fit the elevation-dependent part of opposition brightening. Eliminating the modeled interparticle component yields the intrinsic contribution to the opposition effect: for the B and A rings it is almost entirely due to coherent backscattering; for the C ring, an intraparticle shadow hiding contribution may also be present.Based on our simulations, the width of the interparticle shadowing effect is roughly proportional to B. This follows from the observation that as B decreases, the scattering is primarily from the rarefied low filling factor upper ring layers, whereas at larger B’s the dense inner parts are visible. Vertical segregation of particle sizes further enhances this effect. The elevation angle dependence of interparticle shadowing also explains most of the B ring tilt effect (the increase of brightness with elevation). From comparison of the magnitude of the tilt effect at different filters, we show that multiple scattering can account for at most a 10% brightness increase as B → 26°, whereas the remaining 20% brightening is due to a variable degree of interparticle shadowing. The negative tilt effect of the middle A ring is well explained by the the same self-gravity wake models that account for the observed A ring azimuthal brightness asymmetry (Salo, H., Karjalainen, R., French, R.G. [2004]. Icarus 170, 70–90; French, R.G., Salo, H., McGhee, C.A., Dones, L. [2007]. Icarus 189, 493–522).     

Voyager color photometry of Saturn's main rings: a correction

We correct a calibration error in our earlier analysis of Voyager color observations of Saturn's main rings at 14° phase angle (Estrada and Cuzzi, 1996, Icarus 122, 251) and present thoroughly revised and reanalyzed radial profiles of the brightness of the main rings in the Voyager green, violet, and ultraviolet filters and the ratios of these brightnesses. These results are consistent with more recent HST results at 6° phase angle, once allowance is made for plausible phase reddening of the rings (Cuzzi et al., 2002, Icarus 158, 199). Unfortunately, the Voyager camera calibration factors are simply not sufficiently well known for a combination of the Voyager and HST data to be used to constrain the phase reddening quantitatively. However, some interesting radial variations in reddening between 6 and 14° phase angles are hinted at. We update a ring-and-satellite color vs albedo plot from Cuzzi and Estrada (1998, Icarus 132, 1) in several ways. The A and B rings are still found to be in a significantly redder part of color-albedo space than Saturn's icy satellites.     

Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune

Raman scattering by H₂ in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ∼20% in a clear atmosphere and ∼10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH₄ bands is mainly Raman scattered is not valid for current estimates of the CH₄ vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ∼6% in the 0.22-0.26 μm range and by ∼13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH₄ absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ∼5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new approximation based on spectral tuning of the effective molecular single scattering albedo provides low errors for zenith angles below 70° in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.     

Impacts of Large Planetesimals on the Early Earth

We considered the impacts of very large cosmic bodies (with radii in the range 100–200 to 1000–2000 km) on the early Earth, whose mass, radius and density distribution are close to the current values. The impacts of such bodies were possible during the first hundreds of million years after the formation of the Earth and the Moon. We present and analyze the results of a numerical simulation of the impact of a planetesimal, the size of which is equal to that of the contemporary Moon (1700 km). In three-dimensional computations, the velocity (15 and 30 km/s) and the angle (45°, 60°, and 90°) of the impact are varied. We determined the mass losses and traced the evolution of the shape of the Earth's surface, taking into account the self-consistent gravitational forces that arise in the ejected and remaining materials in accordance with the real, time-dependent mass distribution. Shock waves reflected from the core are shown to propagate from the impact site deep into the Earth. The core undergoes strong, gradually damped oscillations. Although motions in the Earth's mantle gradually decline, they have enough time to put the Earth in a rotational motion. As a result, a wave travels over the Earth's surface, whose amplitude, in the case of an oblique impact, depends on the direction of the wave propagation. The maximum height of this wave is tremendous—it attains several hundred kilometers. Some portion of the ejected material (up to 40% of the impactor mass) falls back onto Earth under the action of gravity. This portion is equivalent to the layer of a condensed material with a thickness on the order of ten kilometers. The appearance of this hot layer should result in a global melting of near-surface layers, which can limit the age of terrestrial rocks by the time of the impact under consideration. For lesser-sized impactors, say, for impactors with radii of about 160 km, the qualitative picture resembles that described above but the amplitude of disturbances is considerably smaller. This amplitude, however, is sufficient to cause a crustal disruption (if such a crust has already formed) and intense volcanic activity.     

A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions

Collisions are a fundamental process in the creation of asteroid families and in satellite formation. For this reason, understanding the outcome of impacts is fundamental to the accurate modeling of the formation and evolution of such systems. Smoothed-Particle Hydrodynamics/N-body codes have become the techniques of choice to study large-scale impact outcomes, including both the fragmentation of the parent body and the gravitational interactions between fragments. It is now possible to apply this technique to targets with either monolithic or rubble-pile internal structures. In this paper we apply these numerical techniques to rubble-pile targets, extending previous investigations by Durda et al. (Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M. [2004]. Icarus 170, 243–257; Durda, D.D., Bottke, W.F., Nesvorný, D., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C. [2007]. Icarus 186, 498–516). The goals are to study asteroid–satellite formation and the morphology of the size–frequency distributions (SFDs) from 175 impact simulations covering a range of collision speeds, impact angles, and impactor sizes. Our results show that low-energy impacts into rubble-pile and monolithic targets produce different features in the resulting SFDs and that these are potentially diagnostic of the initial conditions for the impact and the internal structure of the parent bodies of asteroid families. In contrast, super-catastrophic events (i.e., high-energy impacts with large specific impact energy) result in SFDs that are similar to each other. We also find that rubble-pile targets are less efficient in producing satellites than their monolithic counterparts. However, some features, such as the secondary-to-primary diameter ratio and the relative separation of components in binary systems, are similar for these two different internal structures of parent bodies.