  We investigate the question of the nature of compact stars, considering they
may be neutron stars or hybrid stars containing a quark core, within the
present constraints given by gravitational waves, radio-astronomy, X-ray
emissions from millisecond pulsars and nuclear physics. A Bayesian framework is
used to combine together all these constraints and to predict tidal
deformabilities and radii for a 1.4~M$_\odot$ compact star. We find that
present gravitation wave and radio-astronomy data favors stiff nucleonic EoS
compatible with nuclear physics and that GW170817 waveform is best described
for binary hybrid stars. Binary neutron stars with soft EoS could however not
be totally excluded. In all cases, these %In addition, this data favor stiff
quark matter, independently of the nuclear EoS, with a low value for the
transition density ($n_\mathrm{tr}\in[0.18,0.35]~\mathrm{fm}^{-3}$). Combining
these results with constraints from X-ray observation supports the existence
$1.4$~M$_\odot$ mass hybrid star, with a radius predicted to be about
$R_{1.4}=12.22(45)$~km.
