  We have obtained new images and high-resolution (R ~ 22400) near-infrared
(1.2400-1.2575 micron) spectra of each component of the brown dwarf binary GJ
569Bab using the Adaptive Optics facility of the Keck II telescope and the
NIRSPEC spectrometer. These data have allowed us to improve the determination
of the astrometric orbit and to measure radial velocities of the components. We
have used the astrometric and spectroscopic measurements to derive the
dynamical mass of each brown dwarf and the systemic velocity of the pair by
means of a chi^2 fitting technique. From various considerations, the mass of
each component is likely in the range 0.034-0.070 Msol (GJ 569Bb) and
0.055-0.087 Msol (GJ 569Ba). This implies that the mass ratio, q, of the binary
is greater than 0.4, being the most likely value q = 0.75-0.85. Adopting 0.072
Msol as the most conservative location of the substellar limit for solar
metallicity, our analysis confirms GJ 569Bb as the first genuine brown dwarf
known without any theoretical assumption. We have compared the dynamical masses
of GJ 569Ba and Bb, and their effective temperatures and luminosities, to the
predictions of state-of-the-art theoretical evolutionary isochrones, finding
that models exhibit good performance in the regime of high substellar masses if
the binary is about a few hundred million years old. However, the surface
gravities of GJ 569Ba (M8.5V) and Bb (M9V) derived from our spectral analysis
(the observed data have been compared to the latest synthetic spectra) appear
to be smaller than the values provided by the evolutionary models.
