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standard energy release is a general phenomenon in astrophysical sources with ( nearly ) fixed masses .
the most bright example is provided by core collapse supernova explosions . when a neutron star results from such a collapse , its binding energy @xmath1 is released in the form of neutrino .
measurements of neutron star masses all indicate a strikingly very narow range near 1.4 @xmath2 ( thorsett and chakrabarty 1999 ) , although the underlying fundamental reason for this is still unknown .
another example is type ia supernovae involving explosions of a white dwarf with the chandrasekhar mass .
apparently , a similar standard energy must be released during binary neutron star coalescences , mostly in the form of gravitational waves ( roughly , 90% ) and neutrino ( roughly , 10% ) , as follows from numerical calculations ( ruffert and janka 1998 ) .
can gamma - ray bursts ( grb ) join the class ?
although their origin has not been yet firmly established , the most probable models include binary neutron star coalescences ( as first suggested by blinnikov et al .
1984 ) and collapses of very massive stars ( e.g. woosley 1993 , paczyski 1998 ) . note that assuming grb as standard candles and using the position of grb 970228 ( the first grb with low - energy afterglow ) on the @xmath3@xmath4 diagram , its redshift was predicted to be @xmath5 immediately after its discovery ( lipunov , postnov , prokhorov 1997 ; lipunov 1998 ) , which is in the excellent agreement with measurements of the redshift of the host galaxy of this grb ( @xmath6 ) made two years later ( djorgovski et al .
. this may be not a pure coincidence .
intense optical studies of grbs have resulted in a rapidly increasing number of redshift measurements .
now redshifts of 8 grbs are known ( see table 1 ) .
this enables us to calculate distances and effective ( i.e. assuming spherical symmetry ) energy release in gamma - rays @xmath7 .
this energy , as seen from table 1 , varies in a broad range from @xmath8  erg to @xmath9  erg .
this fact can be treated as a wide proper luminosity function of grbs .
the actual energy release @xmath10 may be significantly lower than @xmath7 due to a possible beaming of gamma - ray emission . if beaming angle @xmath11 , then the actual energy release @xmath12 .    in the general case
, the distribution of @xmath7 may be affected by both the proper energy release distribution @xmath13 and the beaming factor distribution @xmath14 . here
we show that the existing observations of grbs conform with the hypothesis of a standard energy release @xmath10 in the underlying grb explosions , and the apparent dispersion in the detected energy can be explained by the beaming factor @xmath15 .
the observed detected energy can be explained by both distribution of beaming angles and by some universal shape of the emission diagram in grbs .
in table 1 we list eight grbs with measured redshifts .
we excluded grb 980425 , which possibly relates to sn 1998 bw in a close ( 40 mpc ) galaxy .
we included into the table 1 grb 980329 with high redshift @xmath165 , which was indirectly deduced ( palazzi et al .
1998 ; fruchter 1999 ) and can be excluded from our consideration .
this however has an insignificant effect on the final conclusions .    [
cols="^,^,^,<,^",options="header " , ]      + a ) data from briggs et al .
1999 + b ) djorgovski et al .
1999 + c ) vreeswijk et al .
1999 +    of these eight grbs , three ( grb970228 , grb970508 , grb980613 ) display about the same effective energy release of @xmath17@xmath18 ergs .
they form the weakest group of grbs .
another three grbs ( grb971214 , grb980703 , grb990510 ) form the intermediate group with the effective energy release @xmath19@xmath20  ergs , i.e. 2050 times as bright as the first group . the last two grbs ( grb  980319 and grb  990123 ) are the brightest among all grbs with the effective energy release @xmath21 and @xmath22  ergs , respectively ( 500 and 300 times brighter than the first group )
. we should note that the dispersion in energy release for grbs from the first group is much smaller than for bursts from the second and the third groups .
the mean reshift in these groups shows tendency to grow with energy : @xmath23 , @xmath24 , @xmath25 .
this correlation is natural in the hypothesis of beaming : the narrowest beams corresponding to the largest observed energies should be detected less frequently from a given radius and thus will be observed from larger distances to give a comparable number of detections with weaker energies .
grb  990123 shows some evidence for a significant beaming @xmath26 ( kulkarni et al .
1999 ) which is deduced from the break in the optical afterglow light curve .
such a break is expected to occur when the lorentz - factor of the expanding relativistic shell @xmath27 matches the inverse beaming angle @xmath28 ( rhoads 1999 ) .
the true energy release for this grb thus becomes @xmath29  erg , close to the weakest group of grb effective energy .
this may imply that grbs from the weakest group occur almost spherically - symmetrically and @xmath30 for this bursts and the energy release @xmath31  ergs is a fundamental value for _ all _ grbs .
a smooth broad - band change is observed in the slope of the afterglow of the recent grb  990510 ( harrison et al .
1999 ) , which can also be explained by beaming , so the actual energy release in this case is again smaller .
in contrast , no indication of beaming is seen for longest observed optical afterglows of grb  970508 and grb  970228 , and for them the observed energy release @xmath7 is approximately the same , about @xmath32 erg .
let us postulate the standard energy release in all grbs to be @xmath0 ergs .
the three groups of grbs by their @xmath33 ratio are schematically shown in fig .
this distribution is fairly flat and can be treated in two different ways .
it can both reflect the dispersion of in beaming factors of individual bursts and be explained by a universal shape of the gamma - ray emission diagram of grbs with the standard energy release .
consider first beaming angle distribution . in this hypothesis
the standard energy @xmath34 ergs is assumed to be deposited into cones with different opening angles @xmath35 .
for the sake of simplicity we shall assume euclidean space .
then the observed energy in each group is @xmath36 and by assumption @xmath37 let @xmath38 be the spatial concentration of grb sources , @xmath39 be the fraction of sources with corresponding @xmath40 so that @xmath41 the limiting distance from which a grb form i - th group can be observed is @xmath42 so that the number of i - th events potentially observed is @xmath43 solving eqs .
( 1 - 4 ) we obtain @xmath44 , @xmath45 , @xmath46 and the corresponding opening angles @xmath47 , @xmath48 ( we used @xmath49 which is valid for @xmath50 ) .
this distribution is illustrated by fig .
2 .    =    .
in this hypothesis we assume that for some reason in _ all _ grb the standard energy @xmath10 is always deposited into a universal emission diagram , with the observed number of events from different grb groups coming from different viewing angles with respect to the symmetry axis of the diagram ( fig .
3 ) . then eq . ( 1 ) modifies into @xmath51 where @xmath52 characterizes the fraction of the total energy which is collimated into the cone @xmath53 , eq .
( 2 ) reads @xmath54 normalization ( 3 ) transits into @xmath55 ( here we neglect overlapping between the cones since @xmath56 ; this would yield a minor correction ) , and eq .
( 4 ) becomes @xmath57    solving system ( 6 - 8 ) we arrive at @xmath58 , @xmath59 , @xmath60 collimated into the cones with opening angles @xmath61 ( isotropic emission ) , @xmath62 , and @xmath48 , respectively .
note that in this variant the total energy release turns out to be by @xmath1622% larger and is @xmath63 ergs .
this diagram is illustrated by fig .
we have shown that the observed distribution of grb energies can be explained by the hypothesis of the standard energy release @xmath0 ergs .
two situations are possible , either the beaming angle differs from burst to burst , or there is a universal emssion diagram in each burst , the observed difference coming from different viewing angles . at this stage , we do nt discuss any physical model for such a diagram .
possibly , grbs observed as different parts of thus shaped energy release can have different physical features ( for example , some spectral or temporal peculiarities ) .
the opposite point of view is that the energy release in grbs can vary by orders of magnitude and beaming is not significant ( e.g. totani 1999 ) .
although so far we can not distinguish between different possibilities ( i.e. whether the observed @xmath7 distribution is due to different beaming , or due to different true energy release , or both ) , the increased statistics of grb redshift measurements , which is expected in the near future , can be used to discriminate between these points of view .
the increase in statistics , however , can not discriminate between the two possible variants discussed in this paper , because both beaming angle distribution and the universal diagram can discribe an arbitrary number of groups of grbs with an arbitrary number of events inside each group .
the hypothesis of a standard energy release can be discarded if ( a ) a grb with mush smaller @xmath7 than @xmath10 is observed ; ( b ) an inconsistency is found of the predicted cone angle @xmath35 to the value mesaured by some means ; ( c ) the mean redshift of grb in groups does not increase with observed energy @xmath7 . apart form a doubtful case of grb  980425 possibly associated with sn 1998bw , no grbs with smaller than @xmath64 erg energy have been observed .
the determination of beaming angles from the existing observational data is also not very accurate now ( see sari , piran and halpern 1999 for more detail ) .
the mean redshift of grbs do increase , on average , with observed energy ( see fig .
we show that the distribution of observed energies of grb with known redshifts can be explained by the hypothesis of the standard energy release @xmath0 ergs . 
 two situations are possible , either the beaming angle differs from burst to burst , or there is a universal emssion diagram in each burst , the observed difference being due to different viewing angles .