Accretion in $\mathsf{\rho}$ Ophiuchus brown dwarfs: infrared hydrogen line ratios

Context. Mass accretion rate determinations are fundamental for an understanding of the evolution of pre-main sequence star circumstellar disks. Aims. Magnetospheric accretion models are used to derive values of the mass accretion rates in objects of very different properties, from brown dwarfs to intermediate-mass stars; we test the validity of these models in the brown dwarf regime, where the stellar mass and luminosity, as well as the mass accretion rate, are much lower than in T Tauri stars. Methods. We have measured nearly simultaneously two infrared hydrogen lines, Pa β  and Br$_\gamma$, in a sample of 16 objects in the star-forming region ρ -Oph. The sample includes 7 very low mass objects and brown dwarfs and 9 T Tauri stars. Results. Brown dwarfs where both lines are detected have a ratio Pa β /Br$_\gamma$of ~2. Larger values, $\ga$3.5, are only found among the T Tauri stars. The low line ratios in brown dwarfs indicate that the lines cannot originate in the column of gas accreting from the disk onto the star along the magnetic field lines, and we suggest that they form instead in the shocked photosphere, heated to temperatures of ~3500 K. If so, in analogy to veiling estimates in T Tauri stars, the hydrogen infrared line fluxes may provide a reliable measure of the accretion rate in brown dwarfs.