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 classified GRBs in seven subclasses, all with binary progenitors originating gravitational waves (GWs). Each binary is composed by combinations 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 BH with an ultra-relativistic jetted emission, not emitting GWs, have 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 CO$_{\rm core}$-NS/BH binary. The supernova (SN) explosion of the CO$_{\rm core}$ triggers an accretion process onto the NS/BH. If the accretion does not lead the NS to its critical mass, an XRF occurs, while when the BH is present or formed by accretion, a BdHN occurs. When the binaries are not disrupted, XRFs lead to NS-NS and BdHNe lead to NS-BH. The short bursts, originating in NS-NS, are subclassified as (IV) short gamma-ray flashes (S-GRFs) and (V) short GRBs (S-GRBs), the latter when a BH is formed. There are (VI) ultra-short GRBs (U-GRBs) and (VII) gamma-ray flashes (GRFs), respectively formed in NS-BH and NS-WD. We use the occurrence rate and GW emission of these subclasses to assess their detectability by Advanced LIGO-Virgo, eLISA, and resonant bars. We discuss the consequences of our results in view of the announcement of the LIGO-Virgo Collaboration of the source GW 170817 as being originated by a NS-NS.