Brown dwarf disks are excellent laboratories to test our understanding of disk physics in an extreme parameter regime .
In this paper we investigate a sample of 29 well-characterized brown dwarfs and very low-mass stars , for which Herschel far-infrared fluxes and ( sub ) -mm fluxes are available .
We measured new Herschel PACS fluxes for 11 objects and complement these with ( sub ) -mm data and Herschel fluxes from the literature .
We analyze their spectral energy distributions in comparison with results from radiative transfer modeling .
Fluxes in the far-infrared are strongly affected by the shape and temperature of the disk ( and hence stellar luminosity ) , whereas the ( sub ) -mm fluxes mostly depend on disk mass .
Nevertheless , there is a clear correlation between far-infrared and ( sub ) -mm fluxes .
We argue that the link results from the combination of the stellar mass-luminosity relation and a scaling between disk mass and stellar mass .
We find strong evidence of dust settling to the disk midplane .
The spectral slopes between near- and far-infrared are mostly between -0.5 and -1.2 in our sample , which is comparable to more massive T Tauri stars ; this may imply that the disk shapes are similar as well , although highly flared disks are rare among brown dwarfs .
We find that dust temperatures in the range of 7–15 K , calculated with T \approx 25 ( L / L _ { \odot } ) ^ { 0.25 } K , are appropriate for deriving disk masses from ( sub ) -mm fluxes for these low luminosity objects .
About half of our sample hosts disks with at least one Jupiter mass , confirming that many brown dwarfs harbor sufficient material for the formation of Earth-mass planets in their midst .