Code Development to Model Collisional and Dynamical Evolution of the Main Asteroid Belt, 15-9360

Principal Investigator
William F. Bottke

Inclusive Dates: 10/10/02 - 02/10/03

Background - The geologic history of asteroid 433 Eros, the target of NASA's recent Near-Earth Asteroid Rendezvous (NEAR) mission, is poorly understood at this time. For example, NEAR images show that Eros has a surprising paucity of small (diameter D < 200 m) craters and is covered by numerous boulders that show relatively few signs of degradation. These results are considered mysterious because high resolution images of the Moon taken during the Apollo era show the opposite: numerous small craters and relatively few boulders (most which are heavily eroded). Two solutions for this quandary have been offered: a crater erasure mechanism is at work in the low-gravity environment of Eros, and/or the production population in the main belt is severely depleted in small asteroids.

To determine which scenario is correct, or whether both mechanisms are partially responsible, we need to understand the size-frequency distribution of projectiles in the main belt and near-Earth object (NEO) populations. Unfortunately, this information does not yet exist. This fundamental gap in our knowledge is also impeding on-going studies of 951 Gaspra, 243 Ida, and 253 Mathilde, other asteroids observed by spacecraft. For these reasons, we believe that deriving the size-frequency distribution of the main belt and NEO populations is an essential component of the NASA research program.

To deal with this vital issue, we proposed an ambitious, but achievable, numerical modeling effort to simultaneously track how the main asteroid belt and NEO size-frequency distributions evolve in response to both collisional processes (e.g., cratering, catastrophic disruption) and various dynamical removal mechanisms (e.g., resonances, Yarkovsky thermal forces, Poynting-Robertson drag). Because material drained from the main belt becomes part of the steady-state NEO population, we can use NEO observations and terrestrial/lunar impact data to constrain the main belt population over size ranges where main belt data are currently unavailable. It is our intention to use this integrated "one-dimensional" model to predict the nature of the main belt and NEO size distributions from several different tens of micrometers to asteroid 1 Ceres.

Approach - To test our scenario and create proof of concept runs, we chose to significantly modify the self-consistent 1-D collisional evolution model provided by collaborator D. Durda (called CoDDEM). CoDDEM was developed, tested, and applied with NASA funding to examine the collisional evolution of small bodies in the solar system. The most significant modification to CoDDEM was the inclusion of dynamical removal mechanisms such as Poynting-Robertson drag, the Yarkovsky effect, resonances, and so on. Because the importance of these mechanisms for real asteroid sizes, shapes, and thermal properties is only vaguely known at this time, we treated the net fraction of main belt asteroids lost over each set of logarithmic size bins over time as a size-dependant function called F(D). Hence, F(D) is a mass loss "look-up" table for CoDDEM. At each timestep, CoDDEM removes the appropriate number of objects from each bin according to F(D). The F(D) function, like the asteroid break-up law and fragmentation functions, is considered a free parameter. Using trial-and-error, we used CoDDEM runs to constrain their values over a wide range of asteroid diameters. With these code improvements (involving several hundred new lines of code), CoDEEM can now conduct the first realistic simulations of depletion and evolution of main belt and NEO material.

Accomplishments - The coding changes to CoDDEM have been fully implemented, and several preliminary runs were attempted. An on-going effort was also undertaken to better understand model constraints and determine reasonable confidence limits. To accomplish this, we tracked down papers, talked to experts in various fields, reinterpreted and, in some cases, remodeled existing data, and then determined how these constraints should be incorporated into CoDDEM. This work, while time-consuming and not particularly flashy, was absolutely necessary to get the best possible results.

Our new results, a description of the code modifications undertaken as a result of this project, and a thorough list of model constraints were included in a proposal to NASA's Discovery Data Analysis program. This proposal was funded in October 2003.

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