The Keck Interferometer Nuller (KIN) was used to survey 25 nearby main sequence stars in the mid-infrared, in order to assess the prevalence of warm circumstellar (exozodiacal) dust around nearby solar-type stars. The KIN measures circumstellar emission by spatially blocking the star but transmitting the circumstellar flux in a region typically 0.1 - 4 AU from the star. We find one significant detection (eta Crv), two marginal detections (gamma Oph and alpha Aql), and 22 clear non-detections. Using a model of our own Solar Systems zodiacal cloud, scaled to the luminosity of each target star, we estimate the equivalent number of target zodis needed to match our observations. Our three zodi detections are eta Crv (1250 +/- 260), gamma Oph (200 +/- 80) and alpha Aql (600 +/- 200), where the uncertainties are 1-sigma. The 22 non-detected targets have an ensemble weighted average consistent with zero, with an average individual uncertainty of 160 zodis (1-sigma). These measurements represent the best limits to date on exozodi levels for a sample of nearby main sequence stars. A statistical analysis of the population of 23 stars not previously known to contain circumstellar dust (excluding eta Crv and gamma Oph) suggests that, if the measurement errors are uncorrelated (for which we provide evidence) and if these 23 stars are representative of a single class with respect to the level of exozodi brightness, the mean exozodi level for the class is <150 zodis (3-sigma upper-limit, corresponding to 99% confidence under the additional assumption that the measurement errors are Gaussian). We also demonstrate that this conclusion is largely independent of the shape and mean level of the (unknown) true underlying exozodi distribution.
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