On the rate and on the gravitational wave emission of short and long GRBs

On the ground of the large number of gamma-ray bursts (GRBs) detected with cosmological redshift, we have introduced a new classification of GRBs in seven subclasses, all with binary progenitors originating gravitational waves (GWs). Each binary is composed by a different combination of carbon-oxygen cores (CO$_{\rm core}$), neutron stars (NSs), black holes (BHs) and white dwarfs (WDs). The long bursts, traditionally assumed to originate from a single BH with an ultra-relativistic jetted emission, not expected to emit GWs, have instead been subclassified as (I) X-ray flashes (XRFs), (II) binary-driven hypernovae (BdHNe), and (III) BH-supernovae (BH-SNe). They are framed within the induced gravitational collapse (IGC) paradigm with progenitor a tight binary composed of a CO$_{\rm core}$ and a NS or BH companion. The supernova (SN) explosion of the CO$_{\rm core}$ triggers a hypercritical accretion process onto the companion NS or BH. If the accretion is not sufficient for the NS to reach its critical mass, an XRF occurs, while when the BH is already present or formed by accretion, a BdHN occurs. When these binaries are not disrupted by the mass-loss process, XRFs lead to NS-NS binaries and BdHNe lead to NS-BH ones. The short bursts, originating in NS-NS mergers, are subclassified as (IV) short gamma-ray flashes (S-GRFs) and (V) short GRBs (S-GRBs), the latter when a BH is formed. Two additional families are (VI) ultra-short GRBs (U-GRBs) and (VII) gamma-ray flashes (GRFs), respectively formed in NS-BH and NS-WD mergers. We use the occurrence rate of these subclasses and their GW emission to assess their detectability by Advanced LIGO and Virgo, eLISA, and resonant bars. We also discuss the consequences of our results in view of the recent announcement of the LIGO-Virgo Collaboration of the source GW 170817 as being originated by a NS-NS merger.