  The discovery of epsilon Indi Ba, Bb, a binary brown dwarf system very close
to the Sun, makes possible a concerted campaign to characterise the physical
parameters of two T dwarfs. Recent observations suggest substellar atmospheric
and evolutionary models may be inconsistent with observations, but there have
been few conclusive tests to date. We therefore aim to characterise these
benchmark brown dwarfs to place constraints on such models. We have obtained
high angular resolution optical, near-infrared, and thermal-infrared imaging
and medium-resolution (up to R~5000) spectroscopy of epsilon Indi Ba, Bb with
the ESO VLT and present VRIzJHKL'M' broad-band photometry and 0.63--5.1 micron
spectroscopy of the individual components. Furthermore, we use deep AO-imaging
to place upper limits on the (model-dependent) mass of any further system
members. We derive luminosities of log L/L_sun = -4.699+/-0.017 and
-5.232+/-0.020 for epsilon Indi Ba, Bb, respectively, and using the dynamical
system mass and COND03 evolutionary models predict a system age of 3.7--4.3
Gyr, in excess of previous estimates and recent predictions from observations
of these brown dwarfs. Moreover, the effective temperatures of 1352--1385 K and
976--1011 K predicted from the COND03 evolutionary models, for epsilon Indi Ba
and Bb respectively, are in disagreement with those derived from the comparison
of our data with the BT-Settl atmospheric models where we find effective
temperatures of 1300--1340 K and 880--940 K, for epsilon Indi Ba and Bb
respectively, with surface gravities of log g=5.25 and 5.50. Finally, we show
that spectroscopically determined effective temperatures and surface gravities
for ultra-cool dwarfs can lead to underestimated masses even where precise
luminosity constraints are available.
