New constraints on the presence of debris disks around G 196-3 B and VHS J125601.92-125723.9 b

We obtained deep images of G 196-3 B and VHS J1256-1257 b with the NOrthern Extended Millimeter Array (NOEMA) at 1.3 mm. These data were combined with recently published Atacama Large Millimeter Array (ALMA) and Very Large Array (VLA) data of VHS J1256-1257 b at 0.87 mm and 0.9 cm, respectively. Neither G 196-3 B nor VHS J1256-1257 b were detected in the NOEMA, ALMA and VLA data. At 1.3 mm, we imposed flux upper limits of 0.108 mJy (G 196-3 B) and 0.153 mJy (VHS J1256-1257 b) with a 3-sigma confidence. Using the flux upper limits at the millimeter and radio wavelength regimes, we derived maximum values of 0.016 M$_{\rm Earth}$ and 0.004 M$_{\rm Earth}$ for the mass of any cold dust that might be surrounding G 196-3 B and VHS J1256-1257 b, respectively. We put our results in the context of other deep millimeter observations of free-floating and companion objects with substellar masses smaller than 20 M$_{\rm Jupiter}$ and ages between 1 and a few hundred million years. Only two very young objects are detected out of a few tens concluding, as other groups did before, that the disks around these very low-mass objects must have small masses and possibly reduced sizes. If debris disks around substellar objects scale down in a similar manner as protoplanetary disks do, millimeter observations of moderately young brown dwarfs and planets must be at least two orders of magnitude deeper for being able to detect and characterize their surrounding debris disks.