We describe the creation of a model of the main asteroid belt whose purpose is to describe the main-belt asteroid size frequency distribution and simulate the number of main-belt asteroids and their fluxes at visual through midinfrared ($0.3-70 m) wavelengths in any area of sky for an arbitrary date. This model is based on a population of $1:9 ; 10 6 asteroids obtained from the complete known asteroid sample, plus extrapolation of the size-frequency distributions of 15 asteroid dynamical families and three background populations, to a diameter limit of 1 km. The model is compared with data and other models, example applications are given, planned refinements and extensions to the model are presented, and some implications of the resulting size frequency distribution are discussed. Key words: infrared: solar system -minor planets, asteroids -solar system: general
INTRODUCTIONIt is now over 200 years since the discovery of the first asteroid. Yet it is only recently that the question, how many mainbelt asteroids are there with diameters greater than N ? can be answered, with an uncertainty better than about a factor of 3, for values of N greater than 1 km. The answer to this question is of more than academic interest, for as numerous studies have demonstrated, the asteroid size distribution is important because it provides constraints on models of the original size distribution of the planetesimals formed in the inner solar system and their subsequent evolution (see, e.g., Davis et al. 1989Davis et al. , 2002. It is also a key datum in modeling the numerical size of the population of near-Earth asteroids, accounting for their evolution from the main belt into Earth-orbit-crossing orbits (Michel 1999;Morbidelli et al. 2002), and for providing fundamental data for addressing the asteroid-meteorite connection, zodiacal dust models, and studies of asteroid collisional evolution (e.g., such recent studies as those by Durda & Dermott 1997, Reach 1997, and Durda et al. 1998, including impact probabilities in the main belt ( Dell'Oro et al. 2001).The limitation of all studies dependent on knowledge of the asteroid size-frequency distribution (SFD) is that, except for the largest (i.e., diameters greater than between about 7 and 20 km, depending on the heliocentric distance, to which size the population is essentially complete), the main-belt asteroid (MBA) SFD is poorly known. For example, recent estimates of the number of MBAs with diameters larger than 1 km range from $3 ; 10 5 (Evans et al. 1998) to $2 ; 10 6 (this paper). During 1998 a preliminary version of the Supplemental IRAS Minor Planet Survey's (SIMPS; results for asteroids numbered through 8603 was used to update the asteroid database portion of the US Air Force's Celestial Background Scene Descriptor (CBSD;1 Kennealy et al. 1993). The following year a preliminary version of the model presented here was submitted to the US Air Force for inclusion in the CBSD (Tedesco 2000). The present work is an extension of that described therein. The model presente...