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We have sub-classified short and long-duration gamma-ray bursts (GRBs) into seven families according to the binary nature of their progenitors. Short GRBs are produced in mergers of neutron-star binaries (NS-NS) or neutron star-black hole binaries (NS-BH). Long GRBs are produced via the induced gravitational collapse (IGC) scenario occurring in a tight binary system composed of a carbon-oxygen core (COcore) and a NS companion. The COcore explodes as type Ic supernova (SN) leading to a hypercritical accretion process onto the NS: if the accretion is sufficiently high the NS reaches the critical mass and collapses forming a BH, otherwise a massive NS is formed. Therefore long GRBs can lead either to NS-BH or to NS-NS binaries depending on the entity of the accretion. We discuss for the above compact-object binaries: 1) the role of the NS structure and the nuclear equation of state; 2) the occurrence rates obtained from X and gamma-rays observations; 3) the predicted annual number of detections by the Advanced LIGO interferometer of their gravitational-wave emission

The binary progenitors of short and long GRBs and their gravitational-wave emission