We report the complete photometric results from our Herschel study which is the first comprehensive program to search for far-infrared emission from cold dust around young brown dwarfs. We surveyed 50 fields containing 51 known or suspected brown dwarfs and very low mass stars that have evidence of circumstellar disks based on Spitzer photometry and/or spectroscopy. The objects with known spectral types range from M3 to M9.5. Four of the candidates were subsequently identified as extragalactic objects. Of the remaining 47 we have successfully detected 36 at 70micron and 14 at 160micron with S/N greater than 3, as well as several additional possible detections with low S/N. The objects exhibit a range of [24]--[70] micron colors suggesting a range in mass and/or structure of the outer disk. We present modeling of the spectral energy distributions of the sample and discuss trends visible in the data. Using two Monte Carlo radiative transfer codes we investigate disk masses and geometry. We find a very wide range in modeled total disk masses from less than 1e-6 solar masses up to 1e-3 solar masses with a median disk mass of order 3e-5 solar masses, suggesting that the median ratio of disk mass to central object mass may be lower than for T Tauri stars. The disk scale heights and flaring angles, however, cover a range consistent with those seen around T Tauri stars. The host clouds in which the young brown dwarfs and low-mass stars are located span a range in estimated age from ~1-3 Myr to ~10 Myr and represent a variety of star-forming environments. No obvious dependence on cloud location or age is seen in the disk properties, though the statistical significance of this conclusion is not strong.
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