Abstract
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 ${\mathrm{M}}_{\ensuremath{\bigodot}}$ compact star. We find that present gravitation wave and radioastronomy data favor stiff nucleonic equation of state (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 data favor stiff quark matter, independently of the nuclear EoS, with a low value for the transition density (${n}_{\mathrm{tr}}\ensuremath{\in}[0.18,0.35]\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$). Combining these results with constraints from x-ray observation supports the existence $1.4\phantom{\rule{4pt}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ mass hybrid star, with a radius predicted to be about ${R}_{1.4}=12.22(45)\phantom{\rule{0.16em}{0ex}}\mathrm{km}$.