document: the detection of x - ray , optical and radio afterglows from some well - localized gamma - ray bursts ( grbs ) definitely shows that at least most long grbs are of cosmological origin ( e.g. , costa et al . 
   1997 ; frail et al . 1997 ; galama et al . 1998 ; akerlof et al . 1999 ; zhu et al . 1999 ) . 
   the so called fireball model is thus strongly favoured . 
   however , we are still far from resolving the puzzle of grbs ( piran 1999 ; van paradijs , kouveliotou & wijers 2000 ) . 
   a major problem is that we do not know whether grbs are due to highly collimated jets or isotropic fireballs , so that the energetics involved can not be determined definitely ( e.g. , pugliese , falcke & biermann 1999 ; kumar & piran 2000 ; dar & rjula 2000 ; wang & loeb 2001 ; rossi , lazzati & rees 2002 ) . 
   this issue has been extensively discussed in the literature . 
   generally speaking , three methods may help to determine the degree of beaming in grbs . 
   first , based on analytic solutions , it has been proposed that optical afterglows from a jetted grb should be characterized by a break in the light curve during the relativistic phase , i.e. , at the time when the lorentz factor of the blastwave is @xmath0 , where @xmath1 is the half opening angle ( rhoads 1997 ; kulkarni et al . 
   1999 ; mszros & rees 1999 ) . 
   some grbs such as 990123 , 990510 are regarded as good examples ( castro - tirado et al . 1999 ; wijers et al . 
   1999 ; harrison et al . 1999 
   ; halpern et al . 2000 ; pian et al . 2001 ; castro ceron et al . 2001 ; sagar et al . 2001 ) . 
   however , detailed numerical studies show that the break is usually quite smooth ( panaitescu & mszros 1998 ; moderski , sikora & bulik 2000 ) , and huang et al . 
   went further to suggest that the light curve break should in fact occur at the trans - relativistic phase ( huang et al . 
   2000a , b , c , d ) . additionally , many other factors can also result in light curve breaks , for example , the cooling of electrons ( sari , piran & narayan 1998 ) , a dense interstellar medium ( dai & lu 1999 ) , or a wind environment ( dai & lu 1998a ; chevalier & li 2000 ; panaitescu & kumar 2000 ) . 
   all these facts combine together to make the first method not so conclusive . 
   second , gruzinov ( 1999 ) argued that optical afterglows from a jet can be strongly polarized , in principle up to tens of percents . 
   some positive observations have already been reported ( wijers et al . 1999 ; rol et al . 
   2000 ) . but 
   polarization can be observed only under some particular conditions , i.e. , the co - moving magnetic fields parallel and perpendicular to the jet should have different strengths and we should observe at the right time from the right viewing angle ( gruzinov 1999 ; hjorth et al . 
   1999 ; mitra 2000 ) . 
   the third method was first proposed by rhoads ( 1997 ) , who pointed out that due to relativistic beaming effects , @xmath2-ray radiation from the vast majority of jetted grbs can not be observed , but the corresponding late time afterglow emission is less beamed and can safely reach us . 
   these afterglows are called orphan afterglows , which means they are not associated with any detectable grbs . the ratio of the orphan afterglow rate to the grb rate might allow measurement of the grb collimation angle . 
   great expectations have been put on this method ( rhoads 1997 ; mszros , rees & wijers 1999 ; lamb 2000 ; paczyski 2000 ; djorgovski et al . 2001 ) . 
   in fact , the absence of large numbers of orphan afterglows in many surveys has been regarded as evidence that the collimation can not be extreme ( rhoads 1997 ; perna & loeb 1998 ; greiner et al . 
   1999 ; grindlay 1999 ; rees 1999 ) . 
   recently dalal , griest & pruet ( 2002 ) argued that measurement of the grb beaming angle using optical orphan searches is extremely difficult . 
   the main reason is that when the afterglow emission from a jet begins to go into a much larger solid angle than the initial burst does , the optical flux density usually becomes very low . generally speaking 
   , this problem can be overcome by improving the detection limit . 
   in fact , an interesting result was recently reported by vanden berk et al . 
   ( 2002 ) , who discovered a possible optical orphan at @xmath3 . 
   they suggested that grbs should be collimated .    in this article , we will point out another difficulty associated with the third method : there should be many `` failed gamma - ray bursts ( fgrbs ) '' , i.e. , baryon - contaminated fireballs with initial lorentz factor @xmath4 . 
   fgrbs can not be observed in gamma - rays , but their long - lasting afterglows are detectable , thus they will also manifest themselves as orphan afterglows . 
   our paper is organized as follows . in section 2 
   we explain the concept of fgrbs . 
   section 3 describes the difficulty in distinguishing an fgrb orphan and a jetted grb orphan . 
   some possible solutions that may help to overcome the difficulty are suggested . 
   section 4 is a brief discussion . 
   occurring in the deep universe , grbs are the most relativistic phenomena ever known . the standard fireball model ( mszros & rees 1992 ; dermer , bttcher & chiang 1999 ) requires that to successfully produce a grb , the initial lorentz factor of the blastwave should typically be @xmath5  1000 during the main burst phase ( piran 1999 ; lithwick & sari 2000 ) . generally speaking 
   the requirement of ultra - relativistic motion is to avoid the so called `` compactness problem '' . 
   a modest variation in the lorentz factor will result in a difference of the opacity of the high - energy @xmath2-ray photons by a factor of @xmath6 ( totani 1999 ) . 
   additionally , assuming synchrotron radiation , the observed peak frequency is strongly dependent on @xmath2 , @xmath7 ( mszros , rees & wijers 1998 ) . 
   thus a lorentz factor of @xmath8 makes the blastwave very inefficient in emitting @xmath2-ray photons . 
   so , to successfully produce a grb , we need @xmath5  1000 . however , theoretically it is not easy to construct a model to generate such ultra - relativistic motions . 
   currently there are mainly two kinds of progenitor models , the collapse of massive stars ( with mass @xmath9 ) , or the collision of two compact stars ( such as two neutron stars or a neutron star and a black hole ) . 
   since a baryon - rich environment is involved in all these models , some researchers are afraid that the baryon - contamination problem may exist . but this problem maybe is not as serious as we previously expected . 
   let us first take the collapsar model ( macfadyen & woosley 1999 ) as an example . 
   we can imagine that the baryon mass and energy released in different collapsar events should vary greatly , then @xmath10 of the resultant fireballs may also vary in a relatively wide range . in most cases , @xmath10 should be very low ( i.e. , @xmath4 ) , but there still could be a few cases ( e.g. , one percent or even one in a thousand ) in which the fireball is relatively clean so that the blastwave can be successfully accelerated to @xmath5  1000 and produces a grb . 
   since the collapsar rate is high enough in a typical galaxy , there should be no problem that such collapsars can meet the requirement of grb rate ( i.e. , @xmath11  @xmath12 event per typical galaxy per year , under isotropic assumption ) . 
   cases are similar in the collisions of two compact stars .    in short 
   , we can not omit an important fact : if grbs are really due to isotropic fireballs , then there should be much more failed grbs ( i.e. , fireballs with lorentz factor much less than one hundred , but still much greater than unity ) 
   . these fgrb fireballs can contain similar initial energy as normal grb fireballs , i.e. , @xmath13  @xmath14 ergs , but they are polluted by baryons with mass @xmath15  @xmath16 . 
   radiation from these fgrbs should mainly be in x - ray bands in the initial bursting phase , not in @xmath2-ray bands . 
   in fact , bepposax team has reported the discovery of several anomalous events named as fast x - ray transients , x - ray rich grbs , or even x - ray - grbs . 
   they resemble usual grbs except that they are extremely x - ray rich ( frontera et al . 
   2000 ; kippen et al . 
   2001 ; gandolfi & piro 2001 ) . 
   observational data on this kind of events are being accumulated rapidly . 
   recent good examples include grbs 011030 , 011130 and 011211 ( gandolfi et al . 
   2001a , b ; ricker et al . 2001 ) . 
   we propose that these events are probably just fgrbs . 
   huang et al . ( 1998 ) and dai , huang & lu ( 1999 ) have pointed out that for afterglow behaviour , the parameter @xmath17 is decisive , while @xmath18 is only of minor importance , especially at late stages . 
   so , fgrbs should also be associated with prominent afterglows . in figure  1 
   we compare the theoretical optical afterglows from fgrbs with those from isotropic grbs and jetted grbs . 
   we can see that the light curve of an fgrb afterglow differs from that of a successful isotropic burst only slightly , i.e. , only notable at early stages . in our calculations , we have used the methods developed by huang et al.(1999a , b , 2000b , d ) , i.e. , for the dynamical evolution of isotropic fireballs we use @xmath19 where @xmath20 is the swept - up mass and @xmath21 is the radiation efficience . 
   ( 1 ) has been proved to be proper in both ultra - relativistic phase and non - relativistic phase ( huang , dai & lu 1999a , b ) . 
   for jetted ejecta , the following equation is added ( huang et al . 
   2000b , d ) , @xmath22 where @xmath23 is the blastwave radius , and the co - moving sound speed @xmath24 is given realistically by @xmath25 with @xmath26 the adiabatic index . 
   in fact , in beamed grb models , there should also be many fgrbs , i.e. , beamed ejecta with @xmath27 . 
   we call them beamed fgrbs . 
   afterglow from beamed fgrbs has also been illustrated in figure  1 . in this article 
   emphasises will be put on isotropic fgrbs , so by using `` fgrbs '' we will only mean isotropic fgrbs unless stated explicitly . 
   both fgrbs and jetted but off - axis grbs can produce isolated fading objects , i.e. , orphan afterglows . 
   theoretically , when orphan afterglows are really discovered observationally , it is still risky to conclude that grbs are beamed . 
   we should study these orphans carefully to determine whether they come from fgrbs or jetted grbs . 
   however , we will show below that it is not an easy task . 
   usually the light curve of grb afterglows is plotted as @xmath28 vs. @xmath29 , where @xmath30 is the flux density at observing frequency @xmath31 and @xmath32 is observer s time measured from the burst trigger . in such plots , 
   the behaviour of afterglows from isotropic grbs and jetted ones are possibly quite different . 
   the former is generally characterized by a simple flat straight line with slope @xmath33  @xmath34 and the latter can be characterized by a break in the light curve or by a steep straight line with a slope sharper than @xmath35 ( figure  1 , also see huang et al . 2000a , b , c , d ) . 
   but for orphan afterglow observations , the derivation of such a @xmath28  @xmath29 light curve is not direct : we do not know the trigger time so that the exact value of @xmath32 for each observed data point can not be determined .    as the first step , the best that we can do is to produce a light curve with a linear time axis , which , however , is of little help for unveiling the nature of the orphan . 
   figure 2 illustrates the matter . in this figure 
   we plot @xmath28 vs. @xmath32 for the two kinds of orphans theoretically . 
   the uncerntainty in trigger time means the observed light curve can be shifted along x axis , while the unknown distance results in a shift along y axis . 
   we see that after some simple manipulations , the segment ab on the dashed curve ( i.e. , from @xmath36 d to @xmath37 d ) can be shifted to a place ( a@xmath38b@xmath38 ) that differs from the solid line only slightly . 
   it hints that a linear light curve as long as @xmath39 days is still not enough . 
   note that the solid and the dashed curves in figure 2 are only two examples . 
   the variation of some intrinsic parameters , such as @xmath17 , @xmath40 , @xmath10 , @xmath41 , @xmath42 , @xmath43 , @xmath44 and @xmath45 as defined in the caption of figure 1 , can change the shape of the two curves notably , thus brings in much more difficulties .    in figure 3 
   , we compare the theoretical @xmath28  @xmath29 light curves of optical afterglows from fgrbs and jetted but off - axis grbs directly . to investigate the influence of the uncertainty in trigger time 
   , we also shift the light curve of fgrbs by @xmath46 d , @xmath47 d and @xmath48 d intentionally . from the dashed curves 
   , we can see that the shape of the fgrb afterglow light curve is seriously affected by the uncertainty of the trigger time . 
   but fortunately , these dashed curves still differ from the theoretical light curve of the jetted grb orphan markedly , i.e. , they are much flatter at very late stages . 
   this means it is still possible for us to discriminate them . in figure  4 , 
   similar results to figure  3 are given , but this time the light curve of the jetted grb orphan is shifted . 
   again we see that the two kinds of orphans can be discriminated by their late time behaviour . 
   figures 3 and 4 explain what we should do when an orphan afterglow is discovered . 
   first , we have to assume a trigger time for it arbitrarily , so that the logarithmic light curve can be plotted . 
   we then need to change the trigger time to many other values to see how the light curve is affected . in all our plots 
   , we should pay special attention to the late time behaviour , which will be less affected by the uncertainty in the trigger time . if the slope tends to be @xmath49  @xmath34 , then the orphan afterglow may come from an fgrb event . 
   but if the slope tends to be steeper than @xmath35 , then it is very likely from a jetted but off - axis grb . 
   in fact , from figure 1 , we know that for all kinds of grbs , either successful or failed , the optical afterglow approximately follows a simple power - law decay at late stages ( i.e. , @xmath50 ) so that the light curve is a straight line . 
   in such a relation , if we shift the time by @xmath51 , @xmath52 then the line would become curved . 
   the slope at each point on the curve is @xmath53 for positive @xmath51 values the lines bend up - ward , while for negative values the lines bend down - ward . 
   it hints that in plotting the orphan afterglow light curve , we could select the trigger time properly to get a straight line at late stages , then we can determine not only the late time slope , but also the true trigger time . 
   in other words , we can use @xmath54 as the condition to determine the trigger time and to get the straight line at late stages . 
   however , we must bear in mind that it is in fact not an easy task . 
   first , to take the process we need to follow the orphan as long as possible , and the simple discovery of an orphan is obviously insufficient . note that currently optical afterglows from most well - localized grbs can be observed for only less than 100 days . 
   it is quite unlikely that we can follow an orphan for a period longer than that . 
   second , since the orphan is usually very faint , errors in the measured magnitudes will seriously prevent us from deriving the straight line . due to all these difficulties , a satisfactory light curve is usually hard to get for most orphans . 
   we see that measurement of the grb beaming angle using orphan searches is not as simple as we originally expected . 
   in fact , it is impractical to some extent . 
   recently it was suggested by rhoads ( 2001 ) that grb afterglows can be effectly identified by snapshot observations made with three or more optical filters . 
   the method has been successfully applied to grb 001011 by gorosabel et al . 
   it is believed that this method is also helpful for orphan afterglow searches . 
   however , please note that a jetted grb orphan and an fgrb one still can not be discriminated directly . 
   we have shown that the derivation of a satisfactory light curve for an orphan afterglow is difficult . 
   the major problem is that we do not know the trigger time . 
   anyway , there are still some possible solutions that may help to determine the onset of an orphan afterglow . 
   firstly , of course we should improve our detection limit so that the orphan afterglow could be followed as long as possible . 
   the longer we observe , the more likely that we can get the true late - time light curve slope . 
   secondly , we know that fgrbs usually manifest themselves as fast x - ray transients or x - ray - grbs . if an orphan can be identified to associate with such a transient , then it is most likely an fgrb one . in this case 
   , the trigger time can be well determined . 
   thirdly , maybe in some rare cases we are so lucky that the rising phase of the orphan could be observed . for a jetted grb 
   orphan the maximum optical flux is usually reached within one or two days and for an fgrb orphan it is even within hours . 
   then the uncertainty in trigger time is greatly reduced . 
   additionally , a jetted grb orphan differs markedly from an fgrb one during the rising phase . 
   the former can be brightened by more than one magnitude in several hours ( see figures  1  4 ) , while the brightening of the latter can hardly be observed . 
   so , if an orphan afterglow with a short period of brightening is observed , then it is most likely a jetted grb orphan . 
   of course , we should first be certain that it is not a supernova . 
   fourthly , valuable clues may come from radio observations . in radio bands 
   , the light curve should be highly variable at early stages due to interstellar medium scintillation , and it will become much smoother at late times . 
   so the variability in radio light curves provides useful information on the trigger time . and 
   fifthly , in the future maybe gravitational wave radiation or neutrino radiation associated with grbs could be detected due to progresses in technology , then the trigger time of an orphan could be determined directly and accurately . 
   in fact , with the successful detection of gravitational waves or neutrino emission , our understanding on grb progenitors will surely be promoted greatly ( paolis et al . 
   2001 ) . 
   sixthly , the redshift of the orphan afterglow can help us greatly in determining the isotropic energy involved , which itself is helpful for inferring the trigger time . 
   seventhly , the microlensing effect may be of some help . 
   since the size of the radiation zone of a jetted grb orphan is much smaller than that of an fgrb one , they should behave differently when microlensed . 
   finally , although a successful detection of some orphan afterglows does not directly mean that grbs be collimated , the negative detection of any orphans can always place both a stringent lower limit on the beaming angle for grbs and a reasonable upper limit for the rate of fgrbs . 
   to successfully produce a grb , the blastwave should be ultra - relativistic , with lorentz factor typically larger than 100  1000 . however , in almost all popular progenitor models , the environment is unavoidably baryon - rich . 
   we believe that only in very rare cases can an ultra - relativistic blastwave successfully break out to give birth to a grb , and there should be much more failed grbs , i.e. , fireballs with lorentz factor much less than 100 but still much larger than unity . 
   in fact , this possibility has also been mentioned by a number of authors , such as mszros & waxman ( 2001 ) . 
   owing to the existence of fgrbs , there should be many orphan afterglows even if grbs are due to isotropic fireballs . 
   then the simple discovery of orphan afterglows does not necessarily mean that grbs be highly collimated . to make use of information from orphan afterglow surveys correctly 
   , we should first know how to discriminate a jetted grb orphan and an fgrb one . 
   this can be done only by checking the detailed afterglow light curve . 
   however , we have shown that the derivation of a satisfactory light curve for an orphan afterglow is difficult . 
   the major problem is that we do not know the trigger time .    in section 3.2 , 
   some possible solutions to the problem are suggested . 
   unfortunately many of these solutions are still quite impractical in the foreseeable future , which means measure of grb beaming angle using orphan afterglow searches is extremely difficult currently . 
   however , special attention should be paid to the second solution . 
   usually , fgrbs manifested themselves as fast x - ray transients during the main burst phase , while jetted but off - axis grbs went unattended completely . if the fast x - ray transients ( or x - ray - grbs ) observed by bepposax are really due to fgrbs , then afterglows should be detectable . 
   we propose that this kind of events should be followed rapidly and extensively in all bands , just like what we are doing for grbs . 
   if observed , afterglows from these anomalous events can be used to check our concept of fgrbs , and even to test the fireball model under quite different conditions ( i.e. , when @xmath4 ) . 
   also , these fgrbs can provide valuable information for our understanding of grbs , especially on the progenitor models . 
   note that beamed fgrbs can also give birth to fast x - ray transients if they are directed toward us , but afterglows from such a beamed fgrb and an isotropic fgrb can be discriminated easily from the light curves ( see figure  1 ) . 
   it is very interesting to note that optical afterglows from two x - ray - grbs , 011130 and 011211 , have been observed ( garnavich , jha & kirshner 2001 ; grav et al . 
   their redshifts were measured to be @xmath55 0.5 and 2.14 respectively ( jha et al . 2001 ; fruchter et al . 
   2001 ) , eliminates the possibility that they were ordinary classic grbs residing at extremely high redshifts ( @xmath56 ) . 
   we propose that they should be fgrbs ( either isotropic or beamed ) or just jetted grb `` orphan '' . 
   however , the observational data currently available are still quite poor so that we could not determine their nature definitely . as for other x - ray - grbs without a measured redshift , 
   the possibility that they were at redshifts of @xmath57 can not be excluded . 
   finally , the concept of fgrbs is based on the fact that most popular progenitor models for grbs are baryon - rich . 
   but cases are quite different for another kind of progenitor models where strange stars are involved . 
   strange stars , composed mainly of u , d , and s quarks , are compact objects which are quite similar to neutron stars observationally ( alcock , farhi & olinto 1986 ) . a typical strange star ( with mass @xmath58 ) 
   can have a normal matter crust of less than @xmath59 ( alcock , farhi & olinto 1986 ) , or even as small as @xmath60 ( huang & lu 1997a , b ) . 
   then baryon contamination can be directly avoided if grbs are due to the phase transition of neutron stars to strange stars ( cheng & dai 1996 ; dai & lu 1998b ) or collisions of binary strange stars . in these models 
   , there should be very few fgrbs . 
   we thank an anonymous referee for valuable comments and suggestions . 
   yfh thanks l. j. gou and x. y. wang for helpful discussion . 
   this research was supported by the special funds for major state basic research projects , the national natural science foundation of china ( grants 10003001 , 19825109 , and 19973003 ) , and the national 973 project ( nkbrsf g19990754 ) .    note added after acceptance * ( this paragraph might not appear in the published version ) * : the optical orphan at z=0.385 reported by vanden berk et al . 
   ( 2002 ) has recently been proved to be an unusual radio - loud agn ( gal - yam et al . 
   2002 , astro - ph/0202354 ) , and x - ray grb 011211 was found to be in fact an ordinary classic grb ( frontera et al . 
   , gcn 1215 ) . 
   additionally , the optical identification of x - ray grb 011130 might also be incorrect ( frail et al . , gcn 1207 ) . 
   we sincerely thank nicola masetti for private communication . 
   alcock c. , farhi e. , olinto a. , 1986 , apj , 310 , 261 akerlof c. et al . 
   , 1999 , nat , 398 , 400 castro ceron j. m. et al . 
   , 2001 , a&a , submitted ( astro - ph/0110049 ) castro - tirado a. et al . , 1999 , 
   sci , 283 , 2069 cheng k. s. , dai z. g. , 1996 , phys . 
   lett . , 77 , 1210 chevalier r. a. , li z. y. , 2000 , apj , 536 , 195 costa e. et al . , 1997 , nat , 387 , 783 dai z. g. , huang y. f. , lu t. , 1999 , apj , 520 , 634 dai z. g. , lu t. , 1998a , mnras , 298 , 87 dai z. g. , lu t. , 1998b , phys . 
   , 81 , 4301 dai z. g. , lu t. , 1999 , apj , 519 , l155 dalal n. , griest k. , pruet j. , 2002 , apj , 564 , 209 dar a. , rjula a. d. , 2001 , astro - ph/0012227 dermer c. d. , bttcher m. , chiang j. , 1999 , apj , 515 , l49 djorgovski s. g. et al . , 2001 , proc . ix marcel grossmann meeting , eds . 
   v. gurzadyan , r. jantzen , and r. ruffini , singapore : world scientific ( astro - ph/0106574 ) frail d. a. , kulkarni s. r. , nicastro s. r. , feroci m. , taylor g. b. , 1997 , nat , 389 , 261 frontera f. et al . , 
   2000 , apj , 540 , 697 fruchter a. et al . , 2001 , 
   gcn 1200 galama t. j. et al . , 1998 , 
   apj , 500 , l101 gandolfi g. et al . , 2001a , gcn 1118 gandolfi g. et al . , 2001b , gcn 1188 gandolfi g. , piro l. , 2001 , http://www.ias.rm.cnr.it/ias-home/sax/xraygrb.html garnavich p. m. , jha s. , kirshner r. p. , 2001 
   , gcn 1181 gorosabel j. et al . , 2001 , 
   a&a , in press ( astro - ph/0110007 ) grav t. et al . , 2001 , gcn 1191 greiner j. , voges w. , boller t. , hartmann d. , 1999 , a&as , 138 , 441 grindlay j. e. , 1999 , apj , 510 , 710 gruzinov a. , 1999 , apj , 525 , l29 harrison f. a. et al . , 1999 , 
   apj , 523 , l121 halpern , j. p. et al . , 2000 , apj , 543 , 697 hjorth j. et al . , 1999 , 
   sci , 283 , 2073 huang y. f. , dai z. g. , wei d. m. , lu t. , 1998 , mnras , 298 , 459 huang y. f. , dai z. g. , lu t. , 1999a , mnras , 309 , 513 huang y. f. , dai z. g. , lu t. , 1999b , chin . 
   lett . , 16 , 775 huang y. f. , dai z. g. , lu t. , 2000a , a&a , 355 , l43 huang y. f. , dai z. g. , lu t. , 2000b , mnras , 316 , 943 huang y. f. , dai z. g. , lu t. , 2000c , chin . 
   phys . lett . , 17 , 778 huang y. f. , gou l. j. , dai z. g. , lu t. , 2000d , apj , 543 , 90 huang y. f. , lu t. , 1997a , a&a , 325 , 189 huang y. f. , lu t. , 1997b , chin 
   , 14 , 314 jha s. , kirshner r. p. , matheson t. , garnavich p. m. , monnelly g. p. , vanderspek r. k. , 2001 , gcn 1183 kippen r. m. , woods p. m. , heise j. , int zand j. , preece r. d. , briggs m. s. , 2001 , astro - ph/0102277 kulkarni s. r. et al . , 1999 , 
   nat , 398 , 389 kumar p. , piran t. , 2000 , apj , 535 , 152 lamb d. q. , 2000 , phys . 
   report , 333 , 505 lithwick y. , sari r. , 2001 , apj , 555 , 540 macfadyen a. i. , woosley s. e. , 1999 , apj , 524 , 262 mszros p. , rees m. j. , 1992 , mnras , 257 , 29p mszros p. , rees m. j. , 1999 , mnras , 306 , l39 mszros p. , rees m. j. , wijers r. a. m. j. , 1998 , apj , 499 , 301 mszros p. , rees m. j. , wijers r. a. m. j. , 1999 , new astron , 4 , 303 mszros p. , waxman e. , 2001 , phys rev lett , 87 , 171102 mitra a. , 2000 , a&a , 359 , 413 moderski r. , sikora m. , bulik t. , 2000 , apj , 529 , 151 paczyski b. , 2000 , pasp , 112 , 1281 panaitescu a. , kumar p. , 2000 , apj , 543 , 66 panaitescu a. , mszros p. , 1998 , 
   apj , 493 , l31 paolis f. d. , ingrosso g. , orlando d. , perrone l. , 2001 , astro - ph/0107589 perna r. , loeb a. , 1998 , apj , 509 , l85 piran t. , 1999 , phys . 
   report , 314 , 575 pian e. et al . 
   , 2001 , a&a , 372 , 456 pugliese g. , falcke h. , biermann p. l. , 1999 , a&a , 344 , l37 rees m. j. , 1999 , a&as , 138 , 491 rhoads j. , 1997 , apj , 487 , l1 rhoads j. , 2001 , apj , 557,943 ricker g. et al . , 2001 , 
   gcn 1165 rol e. et al . , 
   2000 , apj , 544 , 707 rossi e. , lazzati d. , rees m. j. , 2002 , mnras , in press ( astro - ph/0112083 ) sagar r. , pandey s. b. , mohan v. , bhattacharya d. , castro - tirado a. j. , 2001 , bull . 
   india , 29 , 1 sari r. , piran t. , narayan r. , 1998 , apj , 497 , l17 totani t. , 1999 , mnras , 307 , l41 vanden berk d. e. et al . , 2002 , 
   apj submitted ( astro - ph/0111054 ) van paradijs j. , kouveliotou c. , wijers r. a. m. j. , 2000 , ara&a , 38 , 379 wang x. , loeb a. , 2001 , apj , 552 , 49 wijers r. a. m. j. et al . , 1999 , 
   apj , 523 , l33 zhu j. et al . , 1999 ,
summary: it is believed that orphan afterglow searches can help to measure the beaming angle in gamma - ray bursts ( grbs ) . 
   great expectations have been put on this method . 
   we point out that the method is in fact not as simple as we originally expected . due to the baryon - rich environment that is common to almost all popular progenitor models 
   , there should be many failed gamma - ray bursts , i.e. , fireballs with lorentz factor much less than 100  1000 , but still much larger than unity . 
   in fact , the number of failed gamma - ray bursts may even be much larger than that of successful bursts . 
   owing to the existence of these failed gamma - ray bursts , there should be many orphan afterglows even if grbs are due to isotropic fireballs , then the simple discovery of orphan afterglows never means that grbs be collimated . unfortunately , to distinguish a failed - grb orphan and a jetted but off - axis grb orphan is not an easy task . 
   the major problem is that the trigger time is unknown . some possible solutions to the problem 
   are suggested . 
   = -0.5 in    stars : neutron  ism : jets and outflows  gamma - rays : bursts