We have analyzed a broad-band optical and near-infrared spectrum of FU Tau A, a presumed young brown dwarf in the Taurus star forming region that has intrigued both theorists and observers by its over-luminosity in the HR diagram with respect to standard pre-main sequence evolutionary models. The new data, obtained with the X-Shooter spectrograph at the Very Large Telescope, include an unprecedented wealth of information on stellar parameters and simultaneously observed accretion and outflow indicators for FU Tau A. We present the first measurements of gravity (log g = 3.5 +- 0.5), radial velocity (RV = 22.5 +- 2.9 km/s), rotational velocity (v sin(i) = 20 +- 5 km/s) and lithium equivalent width (W_Li = 430 +- 20 mAA) for FUTau A. From the rotational velocity and the published period we infer a disk inclination of i ~ 50^deg. The lithium content is much lower than theoretically expected for such a young very low mass object, adding another puzzling feature to this objects properties. We determine the mass accretion rate of FU Tau A from comparison of the luminosities of 24 emission lines to empirical calibrations from the literature and find a mean of log (dM/dt)_acc [M_sun/yr] = -9.9 +- 0.2. The accretion rate determined independently from modeling of the excess emission in the Balmer and Paschen continua is consistent with this value. The corresponding accretion luminosity is too small to make a significant contribution to the bolometric luminosity. The existence of an outflow in FU Tau A is demonstrated through the first detection of forbidden emission lines from which we obtain an estimate for the mass loss rate, log (dM/dt)_out [M_sun/yr] < -10.4. The mass outflow and inflow rates can be combined to yield (dM/dt)_out / (dM/dt)_acc ~ 0.3, a value that is in agreement with jet launching models.
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