Hints for Small Disks around Very Low-Mass Stars and Brown Dwarfs
  The properties of disks around brown dwarfs and very-low mass stars
(hereafter VLMOs) provide important boundary conditions on the process of
planet formation and inform us about the numbers and masses of planets than can
form in this regime. We use the Herschel Space Observatory PACS spectrometer to
measure the continuum and [OI] 63um line emission towards 11 VLMOs with known
disks in the Taurus and Chamaeleon I star-forming regions. We fit radiative
transfer models to the spectral energy distributions of these sources.
Additionally, we carry out a grid of radiative transfer models run in a regime
that connects the luminosity of our sources with brighter T~Tauri stars. We
find VLMO disks with sizes [1.3--78] au, smaller than typical T~Tauri disks,
fit well the spectral energy distributions assuming disk geometry and dust
properties are stellar-mass independent. Reducing the disk size increases the
disk temperature and we show that VLMOs do not follow previously derived disk
temperature-stellar luminosity relationships if the disk outer radius scales
with stellar mass. Only 2 out of 11 sources are detected in [OI] despite a
better sensitivity than was achieved for T Tauri stars, suggesting that VLMO
disks are underluminous. Using thermochemical models we show that smaller disks
can lead to the unexpected [OI] non-detections in our sample. The disk outer
radius is an important factor in determining the gas and dust observables.
Hence, spatially resolved observations with ALMA -- to establish if and how
disk radii scale with stellar mass -- should be pursued further.
