You are an expert at summarizing long articles. Proceed to summarize the following text: 
on february 1974 , at the same aaas meeting in san francisco where the discovery of grbs by the vela satellites was publicly announced @xcite , the possible relation of grbs with the `` moment of gravitational collapse '' leading to a bh formation was advanced ( see * ? ? ? @xcite considered , for definiteness , the vacuum polarization process occurring in an overcritical kerr - newman bh ( knbh ) . evidence was given for : a ) the formation of a vast amount of @xmath7-baryon plasma ; b ) the energetics of grbs of the order of @xmath8  erg , where @xmath9 is the bh mass , implying their cosmological origin ; c ) the ultra - high energy cosmic rays with energy up to @xmath10  ev originating from such an extreme electrodynamical process . soon after , the role of an @xmath7 plasma for the origin of grbs was also considered by @xcite . it took almost thirty years to clarify some of the analogies and differences between these two processes of @xmath7-pair creation leading , respectively , to the alternative concepts of  fireball " and  fireshell " @xcite .    already in @xmath11 , well before the establishment of the grb cosmological nature and energetics , @xcite gave support to the cosmological interpretation of grbs and indicated in merging ns binaries their possible origin . they also pointed out the relevance of such ns ns mergers for the occurrence of r - process , as well as for the emission of gravitational radiation , indicating the uncertainty in the determination of their rate of occurrence .    following the launch of the compton satellite and the observations by the batse detector @xcite , a phenomenological classification based on the prompt @xmath12 duration was advanced : grbs were classified into long grbs for @xmath13  s , and short grbs for @xmath14  s @xcite .    shortly after @xcite indicated the possible cosmological origin of short grbs originating in binary ns mergers . they also introduced the clear indication of the role of @xmath15 annihilation leading to the formation of an @xmath7 plasma . this paper was followed by a large number of theoretical works including the gravitational wave emission in newtonian , post - newtonian , and general relativistic treatments ( see , e.g. , * ? ? ? * ) , as well as the @xmath15 annihilation leading to an @xmath7 plasma ( see , e.g. , @xcite and @xcite and references therein ) .    soon after the paper by @xcite , @xcite also supported the cosmological origin of grbs and introduced the concept of bh - accretion - disks , produced by the collapse of a very massive star . such a system was indicated by its author as a _ collapsar _ and was assumed to be the origin of ultrarelativistic jets expected to occur by the same author in long grbs . for a recent review see . after the determination of the cosmological nature of grbs @xcite and the confirmation of their outstanding energy ( @xmath16 erg ) , we returned to our grb scenario @xcite . in a period of four years , from 1997 to 2001 , we developed a fully relativistic grb theoretical model examining , as well , the dynamics of the @xmath7 plasma originating the grb emission ( the fireshell model , see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and section  [ sec : fireshell ] ) . the fireshell model applies to both short and long grbs .    the origin of short grbs from ns ns ( or ns - bh ) binaries as `` in - states '' has been confirmed by strong observational and theoretical evidences . in this article we address specifically some of the latest results within the fireshell model @xcite on the possible presence or absence of a bh formation in ns ns mergers , the consequent classification of short bursts into s - grfs , when no bh is formed ( see section  [ sec : descr_s - grfs ] ) , and s - grbs , when a bh is formed ( see section  [ sec : descr_sgrbs ] ) , and the computation of their occurrence rate ( see section  [ sec : rates ] ) . the application of the fireshell model to the case of long grbs followed a longer path for reaching a proper understanding of the overall phenomenon . the first application of our model to a long grb was implemented on grb 991216 @xcite . in these papers a clear difference between the thermal component observed at the transparency of the @xmath7 plasma , the proper grb ( p - grb ) emission @xcite , and the non - thermal remaining part , later called prompt emission @xcite , was evidenced . this fully relativistic approach was not readily accepted by the grb community , also in view of its objective technical complexity and novelties in the theoretical physics scenario . some authors attempted to describe the grb phenomenon by simplified newtonian approaches , e.g . , those based on the concept of _ magnetars _ . as the detailed observations of the x - ray afterglow by the _ swift_-xrt were obtained , as well as the high energy emission by the fermi - lat @xcite , our model has correspondingly evolved pointing out the precise common power - law behavior of the rest - frame @xmath17@xmath18 kev x - ray luminosity light curves @xcite , as well as the nesting properties @xcite . as pointed out in the present article , the concept of long grbs has evolved into xrfs and bdhne , depending on the possible presence or absence of a bh in their formation process ( see also * ? ? ? it is appropriate to recall that the quest for having progenitors for the collapsar hypothesized by @xcite led to an interesting direction of research dealing with a binary system composed of two very massive stars of @xmath19  m@xmath20 each . the large masses involved in these systems were introduced in order to form a bh at the end of their evolution . similarly , the large amount of angular momentum of the system would guarantee the formation of an accretion disks needed in the collapsar model @xcite . up to six different scenarios were there envisaged leading to a _ collapsar _ , as well as a few leading , alternatively , to a variety of binary compact systems . the need for choosing low - metallicity massive stars followed from the expectation of the formation large bhs in their evolution @xcite . the elimination of h from metal - rich massive stars would follow naturally , but the formation of a bh was not expected in their final stage of evolution @xcite . the spatial and temporal coincidence of a long grb explosion with an optical sn , first observed in the association between grb 980425 and sn 1998bw , created a profound conceptual turmoil in the grb community . woosley and collaborators postulated the birth of a sn out of a collapsar .    in our approach , grbs were supposed to originate from the bh formation , while sne were expected to lead only to nss ( see , e.g. , * ? ? ? * and references therin ) . we consequently introduced a new paradigm to explain the coincidence of these two qualitative and quantitative different astrophysical events in space and time : the birth of a sn and the occurrence of a grb . the induced gravitational collapse ( igc ) paradigm was then introduced . this approach differs from alternative descriptions of the grb - sn coincidences occurring , e.g. , in the _ magnetars _ and the _ collapsar _ models , where the two events are coming from a single progenitor star , and takes full advantage of the recent observations of sne ibc in interacting binary systems .    in a first formulation we considered a finely tuned process : the grb triggering the explosion of a binary companion star very close to the onset of the sn @xcite this scenario soon led to the alternative igc paradigm in which a co@xmath0 undergoes a sn explosion in presence of a ns companion in a tight binary system . this is also by itself an unlikely event which in order to occur needs a fine tuning of the initial conditions of the binary system . this scenario was shown to be consistent with population synthesis analysis @xcite . the sn explosion induces a hypercritical accretion of its ejecta onto the companion ns , leading to the formation of a more massive ns ( mns ) , when the ns critical mass @xmath21 is not reached , or to the formation of a bh with the associated grb emission in the opposite case ( see , e.g. , * ? ? ? * ; * ? ? ? the igc scenario was first tested and verified in grb 090618 . it soon became clear that the occurrence of a grb is far from being a single event , but it is part of an authentic laboratory composed of a variety of astrophysical relativistic phenomena preceeding and following the prompt grb emission . we adopted as progenitor of our co@xmath0ns binary system the massive binaries independently considered in @xcite and @xcite . in our case , the late evolution of such massive binary systems do not lead to a collapsar , nor to an hypernova , but to a much richer and vast number of possibilities , made possible by our igc paradigm . consistently with the considerations by @xcite , indicating that xrfs , x - ray rich bursts , and all long grbs are part of a same population which we show to originate in the hypercritical accretion process of the sn ejecta onto a binary companion ns .    in agreement with the considerations by @xcite for a sub - classification of long bursts into low - luminous and high - luminous grbs , we have divided the long bursts into two different scenarios depending on the distance between the co@xmath0 and the ns binary companion @xcite . correspondingly two different sub - classes of long bursts , both originating in the hypercritical accretion process of the igc scenario , have been shown to exist @xcite : the xrfs , which clearly include low - luminous grbs , such as grb 060218 @xcite , when no bh is formed ( see section  [ sec_3_prot_rat ] ) , and the bdhne , such as grb 130427a @xcite , when a bh is formed ( see section  [ sec : descr_bdhne ] ) . their occurrence rates have been computed ( see section  [ sec : rates ] ) . instead of proposing just a new classification , we also give the description of its underlying physical origin : the hypercritical accretion process of the sn ejecta onto a binary companion ns , with the full associated theoretical treatments at the basis of the igc paradigm .    to the above four sub - classes of long and short bursts , we have recently added a new hybrid sub - class of ultrashort grbs ( u - grbs ) which , as recently pointed out in @xcite , can originate during the further evolution of the bdhne out - states . indeed , nearly 100@xmath22 of the ns - bh binaries which are the outcome of bdhne remain bound . their orbital velocities are high and even large kicks are unlikely to unbind these systems . they represent a new family of ns - bh binaries unaccounted for in current standard population synthesis analyses ( see , e.g. , * ? ? ? * and section  [ sec : rate5 ] ) . the above considerations based on the igc paradigm and the ns - ns paradigm as progenitors encompass and classify into sub - classes most of the known astrophysical systems related to grbs . we finally recall the existence of a class of long grbs occurring in a low density circumburst medium ( cbm ) with density @xmath23 @xmath24 , with hybrid short / long burst properties in their @xmath25-ray light curves : 1 ) an initial spike - like harder emission and 2 ) a prolonged softer emission observed up to a hundred seconds . these bursts do not have an associated sn , even though in the case of a low value of the cosmological redshift its detection would not be precluded . the prototype of such systems is grb 060614 @xcite . the progenitor for this class of long bursts has been identified in a binary system composed of a ns and a white dwarf ( wd ) @xcite . their merger leads to a mns with additional orbiting material , but not to an authentic grb . we refer to these systems , historically addressed as disguised short grb , as gamma - ray flashes ( grfs ) , see , e.g. , grb 060614 , @xcite and grb 071227 , @xcite ) .    in the following we adopt the term _ burst _ only for those systems leading to the bh formation , namely to s - grbs , u - grbs and bdhne . we refer to the term _ flash _ , instead , only for those systems not leading to the bh formation , namely to s - grfs , grfs and xrfs ( see fig .  [ fig : summary ] ) . the main topic addressed in the present article is to estimate the rates of occurrence of the xrfs , bdhne , s - grfs , s - grbs , u - grbs , and grfs and to give a generel description of these grb sub - classes . in section  [ sec : fireshell ] we present a short summary on the fireshell model . in section  [ sec:1052erg ] we discuss the @xmath26  erg lower limit in binary systems leading to bh formation . after describing the observational properties of the above sub - classes , their interpretation within the igc paradigm , the ns - ns merger scenario and the fireshell scenario , we present some prototypes ( see sections  [ sec_3_prot_rat ] , [ sec : descr_bdhne ] , [ sec : descr_s - grfs ] , [ sec : descr_sgrbs ] , [ sec : rate5 ] , and [ sec : ds ] , respectively ) . we then proceed in section  [ sec : rates ] to estimate their observed occurrence rates and to compare and contrast our results with those outlined in the literature ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we then draw some general conclusions in section  [ sec : conclusions ] . a standard flat @xmath27cdm cosmological model with @xmath28 , @xmath29 , and @xmath30 km s@xmath31 mpc@xmath31 is adopted throughout the paper . a summary of acronyms used throughout the paper is shown in table  [ acronyms ] . .alphabetic ordered list of the acronyms used in this work . [ cols="<,^",options="header " , ]     the prototype of grfs is grb 060614 and has been analyzed by @xcite . from the analysis of its p - grb emission a baryon load @xmath32 and a lorentz factor at the transparency condition @xmath33 have been found . from the fit of the light curve of the prompt emission it has been infereed that this burst occurred in a cbm with density @xmath34@xmath35  @xmath24 , which is typical of galactic halos where ns  ns and ns wd mergers occur . analogous results were obtained for the grf 071227 : @xmath36 and @xmath37@xmath38  @xmath24 @xcite . further analyses on other grf examples will be presented elsewhere . the observed grb occurrence rate is defined by the convolution of both ( likely redshift - dependent ) luminosity function , which describes the fraction of bursts with isotropic equivalent luminosities in the interval @xmath39 and @xmath40 , and cosmic grb occurrence rate , which gives the number of sources at different redshifts . the definition of both of these functions is still an open issue and depends on _ a priori _ assumptions and some investigations have been carried out in the literature ( see , e.g. , , for long bursts , @xcite , for short bursts , and @xcite , for both long and short bursts ) . to complicate the matter , also the instrumental sensitivity threshold , the field of view @xmath41 , and the operational time @xmath42 of the various detectors @xmath43 observing grbs introduce additional uncertainties to the problem .    in the following we ignore the possible redshift - evolution of the luminosity function . thus , if @xmath44 events are detected by various detectors in a finite logarithmic luminosity bin from @xmath39 to @xmath45 , the total local event rate density of bursts between observed minimum and maximum luminosities , @xmath46 and @xmath47 respectively , is defined as ( see * ? ? ? * ) @xmath48 where @xmath49 and the comoving volume is given by @xmath50^{1/2}}\ , \ ] ] where @xmath51 is the luminosity distance . the dimensionless function @xmath52 describes the grb cosmic redshift - dependent event rate density . in the following we assume no redshift dependency , therefore we set @xmath53 . the maximum redshift @xmath54 in eq . ( [ eq : rate2 ] ) defines the maximum volume inside which an event with luminosity @xmath55 can be detected . this redshift can be computed from the @xmath56  s - bolometric peak luminosity @xmath55 , @xmath57-corrected from the observed detector energy band into the burst cosmological rest - frame energy band @xmath56@xmath58  kev @xcite , and the corresponding @xmath56  s - threshold peak flux @xmath59 , which is the limiting peak flux to allow the burst detection ( see * ? ? ? * for details ) . therefore , @xmath60 can be defined via @xmath61 where we duly account for the @xmath57-correction .    within the assumptions that the grb luminosity function does not evolve with redshift and that @xmath53 , we investigate the evolution with the redshift of the grb rates by separating the bursts into several redshift bins . as suggested in @xcite , this can be done in each redshift interval @xmath62 by changing the integration limits of eq . ( [ eq : rate2 ] ) into @xmath63 and min@xmath64 $ ] , where @xmath65 is the maximum redshift for the j@xmath66 redshift bin . finally , from eq . ( [ eq : rate ] ) we derive an event rate @xmath67 in each redshift bin around @xmath68 .    in the following we adopt the following fields of view and operational times for various detectors : _ beppo_-sax , @xmath69  sr , @xmath70  y ; batse , @xmath71  sr , @xmath72  y , hete-2 , @xmath73  sr , @xmath74  y ; _ swift_-bat , @xmath75  sr , @xmath76  y ; _ fermi_-gbm , @xmath77  sr , @xmath78  y. we assume no beaming correction in computing the rates of the grb sub - classes . the local rate of s - grfs , obtained from the sample of sources listed in table  [ tab : s - grfs ] , is @xmath79  gpc@xmath80  y@xmath31 and it is in agreement with the estimates obtained from the whole short burst population detected by the _ swift_-bat detector ( and , therefore , including also s - grbs and grfs ) and reported in the literature ( @xmath56@xmath18  gpc@xmath80  y@xmath31 , see , e.g. , * ? ? ? * and references therein ) . in particular our local rates with @xmath53 agrees with recent more precise estimates : a ) @xmath81  gpc@xmath80  y@xmath31 for @xmath82  erg / s and for @xmath52 described by a power law merger delay model @xcite ; b ) @xmath83 , @xmath84 , and @xmath85  gpc@xmath80  y@xmath31 for @xmath86  erg / s and @xmath52 described as gaussian , log - normal and power law merger delay models , respectively @xcite . the evolution of the s - grf rate in various redshift bins is shown in fig .  [ fig : ratesfam ]  ( c ) . this rate decreases as a power law from the local value in the interval @xmath87 to a value of @xmath88gpc@xmath80 y@xmath31 in the interval @xmath89 . also in the case of s - grfs the increasing sampled comoving universe volume and the threshold of the detectors play a fundamental role in the observed decrease of their rate at larger distances . previously we have identified and described four s - grbs in @xcite , e.g. , grb 081024b , grb 090227b , grb 090510 , and grb 140619b . here we present two additional new members of this class : grb 060801 ( at @xmath90 and with @xmath91 , in this work ) and grb 140402a ( at @xmath92 and with @xmath93 , ruffini et al . in preparation ) . from these six s - grbs detected by the _ fermi _ and the _ swift _ satellites , we obtain via eqs . ( [ eq : rate])([eq : rate2 ] ) a local rate @xmath94  gpc@xmath80  y@xmath31 . with only six sources , we could not build the evolution with the redshift of such systems .      in @xcite , we have estimated an updated observed rate for the xrfs at @xmath95 based on the method outlined in @xcite and @xcite . in this work , we consider the complete list of xrfs shown in table  [ tab : xrfs ] and the method outlined in @xcite . from eq . ( [ eq : rate])([eq : rate2 ] ) the local rate of xrfs is @xmath96gpc@xmath80 y@xmath31 , where the attached errors are determined from the @xmath97 confidence level of the poisson statistic @xcite . within the extent of our different classification criteria and different choices for @xmath52 , our estimate is in agreement with those reported for low - luminous long grbs in @xcite and @xcite , and in particular with the value of @xmath98gpc@xmath80 y@xmath31 , obtained by @xcite with the same method .    in the igc scenario the xrf out - states are ns ns binary systems . for a reasonable sets of binary initial conditions , populations synthesis simulations performed by @xcite provide a ns ns formation rate @xmath99@xmath100  gpc@xmath80 y@xmath31 . ns formation rate accounts for other possible channels in the population synthesis models , in addition to the one we considered from the xrfs . it is interesting , nevertheless , that our predicted rate is consistent with that obtained by @xcite obtained .    for the same above reason , our rate of xfrs can be also compared with the ns ns merger rate proposed by @xcite . in this historical paper , the ns ns merger rate is derived from the strong assumption that each merger ejects always the same amount of material r - process classified and the heavy r - process material . @xcite obtain a rough estimate of @xmath101@xmath102  gpc@xmath80 y@xmath31 , which is marginally consistent to the upper value of the local xrf rate .    the evolution of the xrf rate in various redshift bins is shown in fig .  [ fig : ratesfam ]  ( a ) . it decreases from a value of @xmath103gpc@xmath80 y@xmath31 in the interval @xmath104 to a value of @xmath105gpc@xmath80 y@xmath31 in the interval @xmath106 . this effect is mainly due to the intrinsic low luminosities of the bulk of the xrf population ( @xmath107@xmath108  erg / s , see , e.g. , @xcite ) and to the threshold of the detectors : at increasing sampled universe comoving volumes , these low luminous xrfs become undetectable , therefore at higher redshifts the total xrf rate decreases . we proceed now in estimating the rate of bdhne from the total sample of @xmath109 sources ( see table  [ tab : bdhne ] ) . from eq . ( [ eq : rate])([eq : rate2 ] ) the local rate of bdhne is @xmath110  gpc@xmath80  y@xmath31 . our estimate is in agreement with two recent estimates obtained from long bursts with @xmath111  erg / s and by assuming @xmath112 : a ) the value of @xmath113  gpc@xmath80  y@xmath31 obtained by @xcite , even though limited to the _ swift _ long bursts and including long some bursts with @xmath114  erg , obtained from a grb inferred cosmic rate independent on the star formation rate ; b ) the value of @xmath115  gpc@xmath80  y@xmath31 obtained by @xcite with the same method and including the star formation rate dependence .    in the igc scenario the bdhne out - states are ns bh binary systems . following again the work by @xcite , populations synthesis simulations ( which accounts also for alternative scenarios to that of the igc model ) provide a ns  bh formation rate of @xmath116@xmath117  gpc@xmath80 y@xmath31 . also in this case , even though a straightforward comparison is not possible , the bdhne rate is consistent with the ns bh formation rate obtained by @xcite . the evolution of the bdhn rate in various redshift bins is shown in fig .  [ fig : ratesfam ]  ( b ) . it slightly decreases from the local value in the interval @xmath87 to a value of @xmath118gpc@xmath80 y@xmath31 in the interval @xmath119 . as stated for the case of xrfs , this effect occurs because for increasing sampled universe comoving volumes , only the most luminous bdhne are detectable , even though in a less marked way than the case of the xrfs . as pointed out in section  [ sec : rate5 ] , nearly 100@xmath22 of the bdhne leads to bound ns - bh binaries , which are the progenitor systems of u - grbs @xcite . if we include the possibility of other channels of formation for these ns - bh binaries , we can safely assume the bdhn local rate as a lower limit for these u - grbs , e.g. , @xmath110 gpc@xmath80  y@xmath31 . from this consideration , it appears that the u - grbs have the second higher rate among the short bursts after the s - grfs . we proceed now in estimating the rate of grfs from the total sample of @xmath18 sources ( see table  [ tab : dsgrbs ] ) . from eq . ( [ eq : rate])([eq : rate2 ] ) we obtain a local rate @xmath120  gpc@xmath80  y@xmath31 , and represent the first estimate for these kind for bursts originating from ns  wd mergers .    due to the limited number of sources in our sample , we limited the study of the grf rate evolution in two redshift bins , as shown in fig . [ fig : ratesfam ]  ( d ) . the rate starts from a value consistent with the above local rate , in the redshift interval @xmath121 , to a value of @xmath122gpc@xmath80 y@xmath31 , in the interval @xmath123 . also for grfs , the cutoff in the rate at higher redshift occurs because for increasing sampled universe comoving volumes only the most luminous sources are detectable . however this effect , as in the case of s - grfs , is more pronounced due to their intrinsically weaker luminosities , when compared to those of s - grbs . ( a ) ( b ) ( c ) ( d ) the remarkable progress reached in understanding the grb phenomenon has been made possible by the outstanding spectral and temporal information acquired from x - rays , @xmath25-rays and high energy observatories , as well as from optical and radio data obtained by telescopes all over the planet . at the same time this result has been fostered by a novel deeper theoretical understanding in the physics and astrophysics of wd ( see , e.g. , * ? ? ? * ) , ns ( see , e.g. , * ? ? ? * ; * ? ? ? * ) and bh ( see , e.g. , * ? ? ? consequently the understanding of the grb phenomenon has evolved from an elementary paradigm based on a single jetted emission process as postulated in the fireball model ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and reference therein ) to an authentic astrophysical laboratory involving many - body interactions between different astrophysical systems encountering previously unexplored regimes and observational evidence .    in the introduction we review the increasing number of grb observations which have led likewise to the theoretical progress in the understanding of the grb phenomena . while the role of ns  ns ( or ns - bh ) binaries as `` in - states '' of short grbs has been widely accepted and confirmed by strong observational and theoretical evidence , the identification of the progenitor systems for long grbs followed a more difficult path . initially , theoretical models based on a single progenitor were proposed : a _ collapsar _ @xcite , or a _ magnetar _ ( see , e .g . then , the role of binary progenitor systems composed of two very massive stars for long grbs was recognized by @xcite , where several different scenarios were there envisaged leading to a _ collapsar _ @xcite , as well as a few leading , alternatively , to a variety of binary compact systems . these considerations were addressed by our group in a set of papers assuming that the birth of a sn and the occurrence of a grb were qualitatively and quantitatively different astrophysical events in space and time . this led to the necessity of introducing the igc paradigm . in the igc paradigm the long grb - sn coincidence originates from co@xmath0ns binary progenitors system . this approach differs from alternative descriptions , e.g. , the _ magnetars _ and the _ collapsar _ models , where the two events are coming from a single progenitor star .    in section  [ sec : fireshell ] we review the fireshell model for grbs ( see , e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and its general description which can be applied to any source of an optically thick baryon - loaded @xmath7 plasma , i.e. , in the quantum - elctrodynamical process expected in the formation of a bh ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as in the case of a pair plasma created via @xmath124 mechanism in a ns ns merger @xcite , or in the hyper - accretion disks around bhs @xcite .    in section  [ sec:1052erg ] , we discuss the role of the @xmath26  erg energy critical value introduced to discriminate between binary systems leading to the formation of a mns ( xrfs , s - grfs and grfs ) , with energy lower than the above critical value , and those leading to the formation of a bh ( bdhne , s - grbs and u - grbs ) , with energy larger than the above critical value . the value of @xmath26  erg is derived by considering the hypercritical accretion process onto a ns leading to an energy release in form of neutrinos and photons , given by the gain of gravitational potential energy of the matter accreted in the ns . this includes the change of binding energy of the ns while accreting both matter and angular momentum @xcite . a typical ns mass of @xmath125  m@xmath20 has been assumed , as observed in galactic ns binaries . a ns critical mass in the range of @xmath126  m@xmath20 up to @xmath127 depending on the equations of state and angular momentum ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * for details ) has been assumed .        in section  [ sec_3_prot_rat ] , we describe the properties of xrfs ( see fig . [ fig : ffff ] ) . in these systems the distance between the co@xmath0 and the ns companion is @xmath128  cm . the hypercritical accretion process is not sufficient to push the ns beyond its @xmath129 and an mns is formed ( see , e.g. , * ? ? ? * ; * ? ? ? * ) . in table [ tab : xrfs ] we list the xrfs considered in this work , as well as the spectral , temporal and luminosity analysis of selected prototype , e.g. , grb 060218 . the complete theoretical simulation of this prototype is presented in @xcite .    in section  [ sec : descr_bdhne ] we consider the bdhne , for which the binary separation between the co@xmath0 and the ns binary companion is @xmath130  cm and the hypercritical accretion process trigger the gravitational collapse of the ns into a bh ( see , e.g. , * ? ? * ; * ? ? ? we show here an updated list of bdhne ( see table  [ tab : bdhne ] ) , as well as a diagram summarizing some of the key properties and prototypes ( see fig . [ fig : ffff ] ) , analyzed within the igc paradigm and the fireshell model ( see , e.g. , grb 090618 and grb 130427a ) .    in section  [ sec : descr_s - grfs ] , we outline the properties of s - grfs listed in table  [ tab : s - grfs ] and shown in fig . [ fig : ffff ] . these systems coincide with the short bursts considered in . they originate in ns - ns mergers leading to the formation of a mns and possibly a binary companion , in order to fulfill the conservation of energy and momentum @xcite .    in section  [ sec : descr_sgrbs ] we present s - grbs originating in ns - ns mergers leading to the formation of a bh ( see fig .  [ fig : ffff ] ) . we give , in table  [ tab : sgrbs ] , their updated list . we then describe their prototypes , analyzed within the fireshell model ( see , e.g. , grb 090227b and grb 140619b ) , and outline the key role of the p - grb identification for their description , as well as the analysis of the gev emission .    in section  [ sec : rate5 ] , motivated by the results obtained by @xcite , where it was shown that nearly 100@xmath22 of the ns - bh binaries , namely the out - states of the bdhne , remain bound , we add the description of this not yet observed , but theoretically predicted sub - class of u - grbs , unaccounted for in current standard population synthesis analyses .    in section  [ sec : ds ] , we review the properties of the grfs listed in table  [ tab : dsgrbs ] and shown in fig . [ fig : ffff ] . we recall and describe the results obtained from the sources analyzed within the fireshell model ( see , e.g. , grb 060614 , @xcite and grb 071227 , @xcite ) . the most important result of the present article is the estimate the rates of occurrence of the xrfs , bdhne , s - grfs , s - grbs , u - grbs , and grfs sub - classes . in section  [ sec : rates ] , we introduce the procedure outlined in @xcite for estimating the local rates and their evolution with the redshift of the above sub - classes of long and short bursts , assuming no beaming ( note : the recent observation of the absence of gev emission associated to a bdhn may limit this assumption ) . by ignoring possible redshift - evolution of the grb sub - classes luminosity functions and assuming that the grb cosmic event rate density is redshift - independent ( e.g. , @xmath53 ) , the above method duly takes into account observational constraints , i.e. , the detector solid angle coverage of the sky @xmath131 and sensitivities which in turn define a maximum volume of observation depending on the intrinsic luminosity of the sources ( see section  [ sec : rates ] and @xcite for details ) . we obtain :    * an s - grf local rate of @xmath79  gpc@xmath80  y@xmath31 ( see section  [ sec : sgrfs3 ] ) ; * an s - grb local rate of @xmath132  gpc@xmath80  y@xmath31 ( see section  [ sec : sgrbs3 ] ) ; * an xrf local rate of @xmath96gpc@xmath80 y@xmath31 ( see section  [ sec : xrfs3 ] ) ; * a bdhn local rate of @xmath110  gpc@xmath80  y@xmath31 ( see section  [ sec : bdhne3 ] ; for the above reason this rate coincides with that of the u - grbs , see section  [ sec : ugrbsrate ] ) ; * a grf local rate of @xmath120  gpc@xmath80  y@xmath31 ( see section  [ sec : dsgrb3 ] ) . the local rates of s - grfs , xrfs , and bdhne , are in agreement , within the extent of the different classification criteria , with those reported in the literature . the local rates of s - grbs and grfs are , instead , new ones following from the classification proposed in this work . the evolution with the redshift of the rates of xrfs , bdhne , s - grfs , and grfs is shown in fig . [ fig : ratesfam ] . it is certainly of interest to compare and contrast these results obtained from the direct observations of the sources in our new classification with the results computed from population synthesis models . any possible disagreement will give the opportunity to identify possible missing links in the evolutionary phases within population synthesis analysis . we are now in a position to apply the above rates of s - grfs , s - grbs and u - grbs to assess the detectability and the expected number of gravitational wave detections by ligo from ns - ns and ns - bh binaries ( ruffini et al . , in preparation ) . we are also ready to apply the above bdhn rate to give an estimate of the contribution of grbs to cosmic rays ( ruffini et al . , in preparation ) .    before concluding , in support of the classification proposed in this article , we recall that the luminosity light curves of the gev emission is uniquely observed in both bdhne and s - grbs . in both cases it follow a precise power - law behavior with time @xmath133 ( see @xcite , @xcite and fig . [ gevtotal ] ) . an outstanding conclusion of this paper is that in both bdhne and s - grbs , where the presence of the bh is predicted , the turn - on of this gev emission occurs after the p - grb emission and at the beginning of the prompt emission phase ( see figs . [ rad_ind_tot ]  ( d ) and [ shortxo ]  ( d ) ) . this commonality , in such different systems , as well as their energy requirements ( see tab .  [ tab : lat ] and fig . [ gevtotal ] ) are naturally explained if we assume , as indicated in @xcite , that this gev emission originates by accretion processes in the newly - born bh . we have pointed out in @xcite how the total energy of the gev emission can be expressed in term of the gravitational binding energy of matter accretion into kerr bhs ( see ruffini & wheeler 1969 , in problem 2 of @xmath134 104 in @xcite ) . this energetics requirement could not be fulfilled in the case of accretion onto a ns , in view of the much smaller value of the gravitational binding energy when compared to the case of a rotating bh ( see e.g. * ? ? ? * ) . on the general issue of the origin of the jetted gev emission , and not just of its energetics , we refer to the last paragraph of the conclusions of the paper by @xcite . we have added a table . [ tab : lat ] with the values of the gev emission for both the case of s - grbs and bdhne . these energy releases up to @xmath16 erg can be explained by the occurrence of accretion onto a rotating bh with mass in the range of @xmath135@xmath18  m@xmath20 . it is also clear from fig . [ gevtotal ] that s - grbs and bdhne have gev emission sharing a common luminosity pattern and originating , in both cases , from a newly - born kerr bh @xcite . this picture includes also the first scenario of an igc considered in @xcite where an exploding @xmath136 is in a close binary system with an already formed bh companion . in view of the hypercritical accretion process of the sn ejecta onto an already formed bh , these systems have @xmath137 erg and @xmath138 mev . their out - states are a binary composed of a more massive bh and a @xmath139ns . such systems , which we refer to as bh - sne , are expected to be the late evolutionary stages of x - ray binaries such as cyg x-1 or cyg x-3 ( see , e.g. , * ? ? ? * ) . lcccc source & z & @xmath140 & @xmath141 & @xmath142 + & & ( mev ) & ( @xmath26 erg ) & ( @xmath26 erg ) +   + 081024b & @xmath143 & @xmath144 & @xmath145 & @xmath146 + 090510 & @xmath147 & @xmath148 & @xmath149 & @xmath150 + 140402a & @xmath151 & @xmath152 & @xmath153 & @xmath154 + 140619b & @xmath155 & @xmath156 & @xmath157 & @xmath158 +   + 080916c & @xmath159 & @xmath160 & @xmath161 & @xmath162 + 090902b & @xmath163 & @xmath164 & @xmath165 & @xmath166 + 110731a & @xmath167 & @xmath168 & @xmath169 & @xmath170 + 130427a & @xmath171 & @xmath172 & @xmath173 & @xmath174 +    in conclusion we have computed the occurence rate of short and long bursts following a new classification and obtaining figures in good agreement with the ones derived from population synthesis models . essential to the classification have been the following new considerations :    * the binary nature of the progenitors and their separation ; * the essential role of the hypercritical accretion process onto a ns member of a close binary system . the possible reaching of @xmath21 by the accretion process and the formation of a bh ; * the activity of the newly - born bhs originating the energetic prominent gev emission , which can be explained in terms of the gravitational energy release by accreting matter onto a kerr bh . this classification is now open to a verification by the addition of new grbs sources and offer new possibilities of theoretical and observational activities including :    * the reaching of new observational constraints on the value of the ns critical mass @xmath21 and the minimum mass of a bh , which play a fundamental role in defining the separatrix among the different classes of our classification . * having elucidated the role of the activities of the newly - born bh in explaining the energetics of the gev emission , in order to identify its microphysical process , the study of fundamental issues of general relativistic quantum electrodynamical processes appears to be open to further lines of inquiry ( see , e.g. , * ? ? ? * and references therein ) ; * it is conceivable that the sizable enlargement of the database of grbs and of their spectral and luminosity time varability may open the possibilty of further enlarging the above classification . we thank the editor and the referee for their comments which helped to improve the presentation and the contextualization of our results this work made use of data supplied by the uk swift science data center at the university of leicester . j.a.r . acknowledges the support by the international cooperation program capes - icranet financed by capes - brazilian federal agency for support and evaluation of graduate education within the ministry of education of brazil . m.k . and y. a. are supported by the erasmus mundus joint doctorate program grant n. 20131471 and 2014 - 0707 , respectively , from eacea of the european commission . m.m . acknowledges the partial support of the project n 3101/gf4 ipc-11 , and the target program f.0679 of the ministry of education and science of the republic of kazakhstan . in fig .  [ fig : fluence ] we compare and contrast the sources in tab .  [ tab : lat ] , all exhibiting a gev emission , with 2 s - grfs and 1 xrf which , as theoretically expected within the fireshell model , do not exhibit any gev emission . all these sources were in the optimal position ( @xmath175 from the lat boresight ) for the detection of the gev emission . in the left panel we plot the values of @xmath141 and of the isotropic energy in the _ fermi_-lat energy band or the corresponding upper limits if not observed . these upper limits were obtained by using the unbinned likelihood analysis which was performed assuming an integration time of @xmath176  s after the flash trigger , a radius of the source region of @xmath177 and a zenith angle cut of @xmath178 . this plot observationally supports the theoretical expectation , made in @xcite and quoted in section  [ sec : descr_s - grfs1b ] above , that s - grfs have , if any , gev fluxes necessarily @xmath179@xmath180 times weaker than those of s - grbs , although their @xmath141 is only a factor @xmath181 smaller . motivated by a request of the referee , we also plotted in the right panel , the values of the fluence observed by _ fermi_-gbm and by _ fermi_-lat or the corresponding upper limits if not observed ( computed as above ) .    from both plots it is clear that the upper limits to the gev emission of s - grfs and xrfs are much lower than what one may expect from the extrapolation to lower energies of the one observed in bdhne and s - grbs . this is a further clear observational support to the absence , theoretically implied by the fireshell model , of any gev emission associated to s - grfs and xrfs ( see sections  [ sec : xrfs1b ] and [ sec : descr_s - grfs1b ] above ) . , h. , & ruffini , r. , eds . 1975 , astrophysics and space science library , vol . 48 , neutron stars , black holes and binary x - ray sources ; proceedings of the annual meeting , san francisco , calif . , february 28 , 1974    , j. 2003 , in american institute of physics conference series , vol . 662 , gamma - ray burst and afterglow astronomy 2001 : a workshop celebrating the first year of the hete mission , ed . g.  r. ricker & r.  k. vanderspek , 229236                                                                                                                      , r. , bernardini , m.  g. , bianco , c.  l. , et  al . 2005 , in american institute of physics conference series , vol . 782 , xith brazilian school of cosmology and gravitation , ed . m.  novello & s.  e.  perez bergliaffa , 42                                                                        , i.  b. , klebesadel , r.  w. , & evans , w.  d. 1975 , in annals of the new york academy of sciences , vol . 262 , seventh texas symposium on relativistic astrophysics , ed . p.  g. bergman , e.  j. fenyves , & l.  motz , 145158
there is mounting evidence for the binary nature of the progenitors of gamma - ray bursts ( grbs ) . for a long grb , 
 the induced gravitational collapse ( igc ) paradigm proposes as progenitor , or  in - state " , a tight binary system composed of a carbon - oxygen core ( co@xmath0 ) undergoing a supernova ( sn ) explosion which triggers hypercritical accretion onto a neutron star ( ns ) companion . for a short grb 
 , a ns - ns merger is traditionally adopted as the progenitor . 
 we divide long and short grbs into two sub - classes , depending on whether or not a black hole ( bh ) is formed in the merger or in the hypercritical accretion process exceeding the ns critical mass . for long bursts , when no bh is formed we have the sub - class of x - ray flashes ( xrfs ) , with isotropic energy @xmath1 erg and rest - frame spectral peak energy @xmath2  kev . when a bh is formed we have the sub - class of binary - driven hypernovae ( bdhne ) , with @xmath3 erg and @xmath4  kev . in analogy , 
 short bursts are similarly divided into two sub - classes . when no bh is formed , short gamma - ray flashes ( s - grfs ) occur , with @xmath1 erg and @xmath5  mev . when a bh is formed , the authentic short grbs ( s - grbs ) occur , with @xmath3 erg and @xmath6  mev . 
 we give examples and observational signatures of these four sub - classes and their rate of occurrence . from their respective rates it is possible that `` in - states '' of s - grfs and s - grbs originate from the `` out - states '' of xrfs . 
 we indicate two additional progenitor systems : white dwarf - ns and bh - ns . 
 these systems have hybrid features between long and short bursts . in the case of s - grbs and bdhne evidence 
 is given of the coincidence of the onset of the high energy gev emission with the birth of a kerr bh .