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 recently advanced a new classification of GRBs in seven different subclasses all with binary progenitors and 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). So we have opened an ample new scenario for the role of GWs both as sources and as a determining factor in the coalescence process of the progenitors. Consequently, 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 sub-classified 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 which envisages as progenitor a tight binary composed of a CO$_{\rm core}$ and a NS or BH companion. There is extensive literature on the processes of GRB emission via this IGC scenario and this approach has obtained a clear confirmation, with unprecedented high precision, by the explanation of the X-ray flares in BdHNe. Similarly, the short bursts, originating in NS-NS mergers, are sub-classified 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 estimated occurrence rate of the above sub-classes and their GW emission to assess their detectability by Advanced LIGO, Advanced Virgo, eLISA, and resonant bars.