Pre-mare cratering and early solar system history

An evaluation of the application of the high extralunar flux in pre-mare times to more general problems of early solar system history is attempted by combining the results of dynamic studies with lunar chronological data. There is a twofold to fourfold contrast in the integral impact flux between the Apollo 14 and 16 sites and the older mare surfaces. This is judged insufficient to account for the contrasting lithology between these two sites: basalts and soil breccias in the maria, annealed breccias and impact melts in the highlands. Therefore, these rocks and their ages (3.9-4.0 b.y.) are thought to predate the surfaces in which they are found. Estimation of the flux needed to produce these lithologies, and difficulties associated with extrapolating this further back in lunar history give support to the "cataclysm" hypothesis of Tera, Papanastassiou, and Wasserburg. Dynamical studies permit separate evaluation of the possible sources for both the "normal" flux during the first 600 million years of lunar history and the "peak" that apparently occurred 4.0 billion years ago. The most likely sources for the normal flux are comets from the vicinity of Uranus and Neptune. The most promising source for the peak is tidal disruption by Earth or Venus of a Ceres-size asteroid initially in a Mars-crossing orbit. Alternative possibilities are suggested

Dynamical evidence regarding the relationship between asteroids and meteorites

Meteorites are fragments of small solar system bodies transferring into the vicinity of earth from the inner edge of the asteroid belt. Photometric measurements support an association between Apollo objects and chondritic meteorites. Dynamical arguments indicate that most Apollo objects are devolatilized comet residues, however; petrographic and cosmogonical reasons argue against this conclusion

Accumulation of the planets

In modeling the accumulation of planetesimals into planets, it is appropriate to distinguish between two stages: an early stage, during which approximately 10 km diameter planetesimals accumulate locally to form bodies approximate 10 to the 25th g in mass; and a later stage in which the approximately 10 to the 25th g planetesimals accumulate into the final planets. In the terrestrial planet region, an initial planetesimal swarm corresponding to the critical mass of dust layer gravitational instabilities is considered. In order to better understand the accumulation history of Mercury-sized bodies, 19 Monte-Carlo simulations of terrestrial planet growth were calculated. A Monte Carlo technique was used to investigate the orbital evolution of asteroidal collision debris produced interior to 2.6 AU. It was found that there are two regions primarily responsible for production of Earth-crossing meteoritic material and Apollo objects. The same techniques were extended to include the origin of Earth-approaching asteroidal bodies. It is found that these same two resonant mechanisms predict a steady-state number of Apollo-Amor about 1/2 that estimated based on astronomical observations

Spitzer observations of the Hyades: Circumstellar debris disks at 625 Myr of age

We use the Spitzer Space Telescope to search for infrared excess at 24, 70, and 160 micron due to debris disks around a sample of 45 FGK-type members of the Hyades cluster. We supplement our observations with archival 24 and 70 micron Spitzer data of an additional 22 FGK-type and 11 A-type Hyades members in order to provide robust statistics on the incidence of debris disks at 625 Myr of age an era corresponding to the late heavy bombardment in the Solar System. We find that none of the 67 FGK-type stars in our sample show evidence for a debris disk, while 2 out of the 11 A-type stars do so. This difference in debris disk detection rate is likely to be due to a sensitivity bias in favor of early-type stars. The fractional disk luminosity, L_dust/L*, of the disks around the two A-type stars is ~4.0E-5, a level that is below the sensitivity of our observations toward the FGK-type stars. However, our sensitivity limits for FGK-type stars are able to exclude, at the 2-sigma level, frequencies higher than 12% and 5% of disks with L_dust/L* > 1.0E-4 and L_dust/L* > 5.0E-4, respectively. We also use our sensitivity limits and debris disk models to constrain the maximum mass of dust, as a function of distance from the stars, that could remain undetected around our targets.Comment: 33 pages, 11 figures, accepted by Ap

Forming Jupiter, Saturn, Uranus and Neptune in Few Million Years by Core Accretion

Giant planet formation process is still not completely understood. The current most accepted paradigm, the core instability model, explains several observed properties of the solar system's giant planets but, to date, has faced difficulties to account for a formation time shorter than the observational estimates of protoplanetary disks' lifetimes, especially for the cases of Uranus and Neptune. In the context of this model, and considering a recently proposed primordial solar system orbital structure, we performed numerical calculations of giant planet formation. Our results show that if accreted planetesimals follow a size distribution in which most of the mass lies in 30-100 meter sized bodies, Jupiter, Saturn, Uranus and Neptune may have formed according to the nucleated instability scenario. The formation of each planet occurs within the time constraints and they end up with core masses in good agreement with present estimations.Comment: 11 pages, 3 figures, in press (Icarus

Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure