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 ≈ 25 (L/L ⊙ ) 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.

Super-massive black holes (SMBHs) with M • ∼ 10 9 M at z > 6 likely originate from massive seed black holes (BHs). We investigate the consequences of seeding SMBHs with direct collapse BHs (DCBHs) (M • = 10 4−6 M ) on proto-galactic disc growth. We show that even in the absence of direct feedback effects, the growth of seed BHs reduces the development of gravitational instabilities in host galaxy discs, suppressing star formation and confining stars to a narrow ring in the disc and leading to galaxies at z ∼ 6 which lie above the local BH-stellar mass relation. The relative magnitude of cosmic and BH accretion rates governs the evolution of the BH-stellar mass relation. For typical DCBH formation epochs, z i ∼ 10, we find star formation is inhibited in haloes growing at the average rate predicted by ΛCDM which host BHs capable of reaching M • ∼ 10 9 M by z 6. Slower growing BHs cause a delay in the onset of star formation; a M • ∼ 10 6 M seed growing at 0.25 times the Eddington limit will delay star formation by ∼ 100 Myr. This delay is reduced by a factor of ∼ 10 if the halo growth rate is increased by ∼ 0.6 σ. Our results suggest that SMBHs seeded by DCBHs and their host galaxies form in separate progenitor haloes. In the absence of subsequent mergers, higher than average cosmic accretion or earlier seed formation (z i ∼ 20) are required to place the evolving BH on the local BH-stellar mass relation by z = 6.

Super-massive black holes (SMBHs) observed to have masses of M • ∼ 10 9 M at z 6, < 1 Gyr after the Big Bang, are thought to have been seeded by massive black holes which formed before growing concurrently with the formation of their host galaxies. We model analytically the idealised growth of seed black holes, fed through gas inflow from growing proto-galaxy discs. The inflow depends on the disc gravitational stability and thus varies with black hole and disc mass. We find that for a typical host halo, the efficiency of angular momentum transport, as parametrised by the disc viscosity, is the limiting factor in determining the inflow rate and the black hole accretion rate. For our fiducial case we find an upper black hole mass estimate of M • ∼ 1.8 × 10 7 M at z = 6. Only in the extreme case of ∼ 10 16 M haloes at z = 6 produces SMBH masses of ∼ 10 9 M . However, the number density of such haloes is many orders of magnitude below the estimated 1 Gpc −3 of SMBHs at z = 6, indicating that viscosity driven accretion is too inefficient to feed the growth of seeds into M • ∼ 10 9 M SMBHs by z ∼ 6. We demonstrate that major mergers are capable of resolving the apparent discrepancy in black hole mass at z = 6, with some dependence on the exact choice of orbital parameters of the merger.1 UV photons with energies of 11.2 − 13.6 eV capable of dissociating H 2 molecules, though hereafter also used to loosely refer to photons with energies > 0.76 eV, capable of causing the photodetachment of H − .