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Constraints on Long-Period Planets from an L' and M band Survey of Nearby Sun-Like Stars: Modeling Results

We have carried out an L' and M band Adaptive Optics (AO) extrasolar planet imaging survey of 54 nearby, sunlike stars using the Clio camera at the MMT. Our survey concentrates more strongly than all others to date on very nearby F, G, and K stars, in that we have prioritized proximity higher than youth. Our survey is also the first to include extensive observations in the M band, which supplemented the primary L' observations. These longer wavelength bands are most useful for very nearby systems in which low temperature planets with red IR colors (i.e. H - L', H - M) could be detected. The survey detected no planets, but set interesting limits on planets and brown dwarfs in the star systems we investigated. We have interpreted our null result by means of extensive Monte Carlo simulations, and constrained the distributions of extrasolar planets in mass $M$ and semimajor axis $a$. If planets are distributed according to a power law with $dN \propto M^α a^β dM da$, normalized to be consistent with radial velocity statistics, we find that a distribution with $α= -1.1$ and $β= -0.46$, truncated at 110 AU, is ruled out at the 90% confidence level. These particular values of $α$ and $β$ are significant because they represent the most planet-rich case consistent with current statistics from radial velocity observations. With 90% confidence no more than 8.1% of stars like those in our survey have systems with three widely spaced, massive planets like the A-star HR 8799. Our observations show that giant planets in long-period orbits around sun-like stars are rare, confirming the results of shorter-wavelength surveys, and increasing the robustness of the conclusion.