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Terrestrial Planet Formation Around Individual Stars Within Binary Star Systems

We calculate herein the late stages of terrestrial planet accumulation around a solar type star that has a binary companion with semimajor axis larger than the terrestrial planet region. We perform more than one hundred simulations to survey binary parameter space and to account for sensitive dependence on initial conditions in these dynamical systems. As expected, sufficiently wide binaries leave the planet formation process largely unaffected. As a rough approximation, binary stars with periastron $q_B > 10$ AU have minimal effect on terrestrial planet formation within $\sim 2$ AU of the primary, whereas binary stars with $q_B \la$ 5 AU restrict terrestrial planet formation to within $\sim$ 1 AU of the primary star. Given the observed distribution of binary orbital elements for solar type primaries, we estimate that about 40 -- 50 percent of the binary population is wide enough to allow terrestrial planet formation to take place unimpeded. The large number of simulations allows for us to determine the distribution of results -- the distribution of plausible terrestrial planet systems -- for effectively equivalent starting conditions. We present (rough) distributions for the number of planets, their masses, and their orbital elements.