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The optical and infrared colors of L and T dwarfs are sensitive to cloudsedimentation and chemical equilibrium processes in their atmospheres. Thei'-z' vs. J-K color-color diagram provides a window into diverse atmosphericprocesses mainly because different chemical processes govern each color, andcloud opacity largely affects J-K but not i'-z'. Using theoretical atmospheremodels that include for the first time a self-consistent treatment of cloudformation, we present an interpretation of the i'-z' vs. J-K color trends ofknown L and T dwarfs. We find that the i'-z' color is extremely sensitive tochemical equilibrium assumptions: chemical equilibrium models accounting forcloud sedimentation predict redder i'-z' colors--by up to 2 magnitudes--thanmodels that neglect sedimentation. We explore the previously known J-K colortrends where objects first become redder, then bluer with decreasing effectivetemperature. Only models that include sedimentation of condensates are able toreproduce these trends. We find that the exact track of a cooling brown in J-K(and i'-z') is very sensitive to the details of clouds, in particular to theefficiency of sedimentation of condensates in its atmosphere. We also find thatclouds still affect the strength of the J, H, and K band fluxes of even thecoolest T dwarfs. In addition, we predict the locus in the i'-z' vs. J-Kcolor-color diagram of brown dwarfs cooler than yet discovered.Comment: 20 pages, 4 figures, AASTex, accepted by Astrophysical Journal;  replacement version substantially expands discussion of clouds and chemical  processes and adds figure showing model temperature profile

Clouds and Chemistry: Ultracool Dwarf Atmospheric Properties from Optical and Infrared Colors