First observations of warm and cold methanol in Class 0/I proto-brown dwarfs

We present results from the first molecular line survey to search for the fundamental complex organic molecule, methanol (CH$_{3}$OH), in 14 Class 0/I proto-brown dwarfs (proto-BDs). IRAM 30-m observations over the frequency range of 92-116 GHz and 213-280 GHz have revealed emission in 14 CH$_{3}$OH transition lines, at upper state energy level, E$_{upper}\sim$7-49 K, and critical densities, $n_{crit}$ of 10$^{5}$ to 10$^{9}$ cm$^{-3}$. The most commonly detected lines are at E$_{upper} <$ 20 K, while 11 proto-BDs also show emission in the higher excitation lines at E$_{upper}\sim$21-49 K and $n_{crit}\sim$10$^{5}$ to 10$^{8}$ cm$^{-3}$. In comparison with the brown dwarf formation models, the high excitation lines likely probe the warm ($\sim$25-50 K) corino region at $\sim$10-50 au in the proto-BDs, while the low-excitation lines trace the cold ($<$ 20 K) gas at $\sim$50-150 au. The column density for the cold component is an order of magnitude higher than the warm component. The CH$_{3}$OH ortho-to-para ratios range between $\sim$0.3-2.3. The volume-averaged CH$_{3}$OH column densities show a rise with decreasing bolometric luminosity among the proto-BDs, with the median column density higher by a factor of $\sim$3 compared to low-mass protostars. Emission in high-excitation (E$_{upper}>$ 25 K) CH$_{3}$OH lines together with the model predictions suggest that a warm corino is present in $\sim$78\% of the proto-BDs in our sample. The remaining show evidence of only the cold component, possibly due to the absence of a strong, high-velocity jet that can stir up the warm gas around it.