  The population of high energy and very high energy gamma-ray sources,
detected with EGRET and the new generation of ground-based Cherenkov
telescopes, conforms a reduced but physically important sample. Most of these
sources are extragalactic (e.g., blazars), while among the galactic ones there
are pulsars and SN remnants. The microquasar LS 5039, previously proposed to be
associated with an EGRET source by Paredes et al. (2000), has recently been
detected at TeV energies, confirming that microquasars should be regarded as a
class of high energy gamma-ray sources. To model and understand how the
energetic photons are produced and escape from LS 5039 it is crucial to unveil
the nature of the compact object, which remains unknown. Here we present new
intermediate-dispersion spectroscopy of this source which, combined with values
reported in the literature, provides an orbital period of 3.90603+/-0.00017 d,
a mass function f(M)=0.0053+/-0.0009 M_sun, and an eccentricity e=0.35+/-0.04.
Atmosphere model fitting to the spectrum of the optical companion, together
with our new distance estimate of d=2.5+/-0.1 kpc, yields R_opt=9.3+0.7-0.6
R_sun, log (L_opt/L_sun)=5.26+/-0.06, and M_opt=22.9+3.4-2.9 M_sun. These,
combined with our dynamical solution and the assumption of
pseudo-synchronization, yield an inclination i=24.9+/-2.8 degree and a compact
object mass M_X=3.7+1.3-1.0 M_sun. This is above neutron star masses for most
of the standard equations of state and, therefore, we propose that the compact
object in LS 5039 is a black hole. We finally discuss about the implications of
our orbital solution and new parameters of the binary system on the CNO
products, the accretion/ejection energetic balance, the SN explosion scenario,
and the behaviour of the TeV emission with the new orbital period.
