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gamma - ray burst ( grb ) spectra often extend to very high energies with no indication of attenuation by photon - photon interactions . this implies substantial relativistic bulk motion of the radiating material with lorentz factors in the range of @xmath13 to @xmath14 . at cosmological distances , grbs require an energy reservoir on the order of @xmath15 erg . the likely sources of such a reservoir would be the rest mass of a compact object released during a merger ( e.g. , either neutron star neutron star or neutron star  black hole ) . however , most detailed calculations of mergers occur on time scales of less than 1 s , much less than the observed durations of grbs ( often @xmath13 s and sometimes @xmath14 s ) . two classes of models have arisen that explain various ( but not all ) aspects of the observations . in the `` external '' shock models ( @xcite ) , the release of energy during the merger is very quick , and a relativistic shell forms that expands outward for a long period of time ( @xmath16 to @xmath17 s ) . at some point , interactions with the external medium ( hence the name ) cause the energy of the bulk motion to be converted to gamma - rays . although the shell might produce gamma - rays for a long period of time , the shell keeps up with the photons such that they arrive at a detector over a relatively short period of time . if the shell has a velocity , @xmath18 , with a corresponding bulk lorentz factor , @xmath19 , then photons emitted over a period @xmath20 arrive at a detector over a much shorter period , @xmath21 . although this model is consistent with the short energy release expected for a merger and the observed long time scale of grbs , we have argued that it can not explain the long complex time histories except under extreme conditions ( @xcite ) . in particular , we argue from kinematic considerations that the long gaps often seen in grbs are inconsistent with local spherical symmetry , that the rapid time variability implies that only a small fraction of the shell becomes active , and that the observed average envelope of emission is inconsistent with that expected from a relativistic shell . these arguments are contained in @xcite , and @xcite . in addition , @xcite , @xcite , and @xcite argue from hydrodynamic considerations that the external shock model can not provide the energy or timescales observed in grbs . the alternative theory is that a central site releases energy in the form of a wind or multiple shells over a period of time commensurate with the observed duration of the grb ( @xcite ) . the gamma - rays are produced by the internal interactions within the wind ; hence these scenarios are often referred to as internal shock models . these models have two weaknesses : first , there is a concern that internal shocks are rather inefficient ( although , see @xcite ) , and second , the long , complex time history of a grb must be postulated at the central site . on the other hand , the free parameters associated with the multiple shells can probably explain any observed time history ( @xcite ) . the need to explain long time histories was further complicated by the discovery of the x - ray afterglows lasting hours ( @xcite ) , the optical afterglows lasting weeks to months ( @xcite ) , and the radio afterglows lasting many months ( @xcite ) . these extended time scales appear too long to have been produced by a lingering central site made by a merger . in addition , the observed power law decay is expected from many external shock models ( @xcite ) . @xcite suggested that the initial gamma - ray phase is due to internal shocks from a relativistic wind ( or multiple shells ) that merge into a single relativistic shell which then produces the afterglows in a manner similar to the external shock models . this model avoids the difficulty of explaining the rapid variability of the gamma - ray phase with a single shell while retaining the long time scale capability of the single shell for the afterglows . the purpose of this paper is to demonstrate that the external shock model can not utilize the full surface of shells . fundamentally , it arises because of the relatively rapid time variability of the gamma - ray phase . @xcite use this as an argument that external shock models would require too much energy . however , this should not be considered a strong argument that the grb phase is not external shocks since there are several scenarios that can utilize only a portion of the shell s surface . we also analyze the time variability recently observed by asca in the x - ray afterglow of gb970828 ( @xcite ) and show that its time variability implies low surface utilization in the x - ray afterglow phase as well . to understand the problem caused by rapid variability , one must emphasize the difference between arrival time at the detector ( which we denote with @xmath8 ) and coordinate time ( equivalent to laboratory time , the detector rest frame time , _ and _ the rest frame of the central explosion , denoted by @xmath20 ) . coordinate time is measured by clocks placed at all locations within the frame and can measure when the photons were produced . in contrast , a detector ( such as batse ) measures when the photons arrive at a single location . these two times are related as @xmath22 where @xmath23 is the angle between the direction of motion of the emitting material and the direction to the detector . the large bulk lorentz factor means that the shell is almost certainly moving directly at the observer s detector ( i.e. , we must be looking at the shell head - on rather than looking at the sides of a jet , so @xmath23 is small . when @xmath23 is 0 , @xmath24 . in contrast , the lorentz transformation between the time in the rest frame of the detector ( @xmath20 ) and time in a frame moving with the shell ( @xmath25 ) , is @xmath26 . consider the early behavior of the shell . assume that clocks are placed along the path of the shell in the detector s rest frame . these clocks report coordinate time , that is , the time the shell passes the location of the clocks . consider an extreme case such as @xmath27 . clocks placed with a spacing of @xmath28 cm will see the shell pass their locations at times separated by @xmath29 s. because the shell is viewed by the detector head - on , its movement causes the shell to keep up with the photons it produces such that photons that were separated by @xmath29 in the detector s rest frame , arrive at the detector separated by a much shorter interval @xmath30 . if the shell expands in the detector rest frame for @xmath17 seconds , the photons all arrive at the detector within 5 s. note that this contraction of the photon arrival time is not the result of a lorentz transformation . rather , it reflects that a detector at a single location measures when photons arrive , not necessarily the relative time they were emitted .    in the early phase of the shell s expansion , @xmath3 is effectively constant ( @xmath31 ) such that @xmath32 . eventually , the shell begins to deaccelerate as it sweeps up the interstellar medium ( ism ) . without detailed knowledge of the physical process that generates the gamma rays , it is not clear if the expansion is adiabatic or dominated by radiation losses . however , both solutions lead to a power law decay ( @xcite ) , and we will show that our conclusions only depend on the power law nature of the decay and not the exact index of the power law . for the sake of an example , we will assume that the expansion is adiabatic . the energy required to sweep up an ism mass of @xmath33 is @xmath34 ( @xcite ) . let @xmath35 be the initial energy deposited into the shell such that @xmath36 , where @xmath37 is the original mass of the shell . if @xmath38 is the density of the ism , one can solve for the radius of the shell as a function of the coordinate time by solving @xmath39 here ,  is the angular size of the ejecta to account for the situation where the expansion is mechanically confined to a jet . the arrival time of the photons as a function of the coordinate time that the photons were emitted can be found from @xmath40 and @xmath41 . figure 1 shows @xmath20 as a function of @xmath8 for a typical situation ( @xmath42 erg , @xmath43 atom @xmath44 ) . it is unclear what fraction of the shell s energy is converted to gamma - rays . observations imply that the energy in gamma - rays _ if the explosion is isotropic _ is on the order of @xmath15 erg . if   is much less than @xmath45 , much less energy is required ( implying many more unseen events ) . the observations only limit the energy per @xmath45 steradian to be @xmath46 erg . we scale our solutions to @xmath42 erg which assumes that @xmath47 1% of the energy is converted to gamma - rays . there are three phases of the @xmath48 relationship : the initial constant-@xmath3 phase , a phase where @xmath49 , and a final phase when the shell becomes nonrelativistic where @xmath20 is @xmath8 plus a constant . here , @xmath50 is @xmath35 in units of @xmath51 erg and @xmath52 is the ism density in units of 1 atom @xmath44 . the second and third phase is only weakly dependent on the initial conditions . neither depends on the initial @xmath53 , and they depend on the other parameters to the 1/4 power . thus , except for the duration of the first phase , different bursts ought to have similar @xmath48 relationships . if one assumes the extreme nonadiabatic case that the momentum of the shell is conserved rather than the energy , then the 1/4 power becomes 1/7 . many other indexes as possible ( see @xcite ) . although the exact nature of the conversion of bulk motion to gamma - rays is unclear , we argue that the gamma - ray phase must be contained in the first phase where @xmath54 . we note that many grbs show a similar time of arrival structure ( e.g. , observed subpeak widths ) at the end of the burst and at the beginning of the burst . in the first phase , the observed arrival time structure ( @xmath7 ) is related to the emission time as @xmath55 such that a constant subpeak width can occur if the emission time is constant in coordinate time . in the second phase , @xmath56 such that constant subpeak width can only occur if the emission time ( @xmath57 ) scales as @xmath58 . this is consistent with our scaling of @xmath42 erg , which allows the first phase to last 200 s ( see figure 1 ) . the afterglows probably occur in the @xmath59 phase where @xmath3 is more modest . as one can see from figure 1 , our view of grbs becomes quite distorted because we only measure arrival time at the earth rather than the time of emission in the earth s rest frame ( remember , no lorentz transformations are involved ) . it is often said that grbs are quite quick , say 30 s. actually , in the external shock models , they occur longer by @xmath60 or , perhaps , up to @xmath61 s if @xmath3 is @xmath14 . the afterglow period seems to cover a very large dynamic range from @xmath14 s to @xmath17 s. actually , because @xmath59 , the dynamic range is only a factor of 10 . in the external shock model , there is a single shell , and the rapid variability we observe can only be accounted for by a nonuniform production of gamma - rays by the shell . consider batse bursts 1883 and 2993 shown in figure 2 . they have very similar overall envelopes of emission and similar intensities . burst 2993 , however , has stronger deviations from the envelope in the form of multiple peaks . presumably this structure arises because various patches ( or emitting `` entities '' ) on the shell randomly become active . in the case of burst 1883 , so many entities become simultaneously active that the overall envelope appears quite smooth , whereas in the case of burst 2993 , fewer entities become active so random fluctuations in the number of simultaneously active entities cause the peak structure to be spiky . in this view , each observed peak in not necessarily caused by a single entity , but the peak structure is caused by random variations in the number of active entities ( see @xcite ) .    in @xcite and @xcite , we showed that the expected envelope of the grb phase has a `` fred '' like shape ( fast rise , exponential decay although the decays are often just slower , not necessarily exponential ) . the expected envelope is a power law , @xmath62 , where @xmath63 is the spectral number index ( typically @xmath64 ) . ( note that this power law refers to the grb phase in constrast to the well observed power law decay found in the afterglows . ) in @xcite , we showed that the volume that contributes to a set period of time , @xmath7 , is constant . the @xmath65 envelope comes from the beaming . thus , if the entities form randomly , one can expect that the rate of entities causing peaks is effectively constant during the decay phase . indeed , the presence of long gaps in grbs is one of our key arguments that the grb phase is not due to a simple single shell . gaps require large causally disconnected regions to coordinate their lack of emission ( see @xcite and @xcite ) . we define the `` surface filling factor '' as the fraction of the shell s surface that becomes active . let @xmath66 be the area of an entity and @xmath67 be the number of entities that ( randomly ) become active during the interval @xmath68 . if @xmath69 is the area of the shell that can contribute during @xmath68 , then the surface filling factor is @xmath70 where @xmath71 is the fraction of the visible area of the shell ( @xmath72 ) that contributes during the interval @xmath68 . the number of entities can be determined from the observed fluctuations in the time history . the overall envelope is due to the beaming , so the residue variations about the overall envelope are due to a combination of the poisson variations in the number of entities and the poisson variations associated with the count statistics . assume for the moment that the contribution due to the count statistics are small such that the variations come from the poisson variations in the number of contributing entities . we first remove the envelope by fitting a polynomial function to it . the observations are divided by the polynomial function , so the result is a flat envelope with variations due to the number of entities that , on average , are active simultaneously . the rate of occurrence of the entities , @xmath73 , can be found directly from the variations because the observed mean level is @xmath74 where @xmath75 is some constant and the variance is @xmath76 . we define @xmath77 to be the observed mean level of the flattened envelope and @xmath78 to be the root mean square of the flattened envelope . in the case of no contribution from the counting statistics , @xmath73 would be @xmath79 . here , we have implicitly assumed that all entities are identical . this is supported by the fact that peaks within grbs usually are similar to each other . the actual root mean square of the flattened envelope is a combination of the variance due to the entities and the variance due to the counting statistics , @xmath80 . we assume they add in quadrature , that is , @xmath81 . we estimate @xmath82 to be root mean square of many monte carlo realizations of the flattened envelope . the rate of occurrence of entities is @xmath83 this rate is the number of events per the time scale of the entities . thus , the total number of entities that occur within a period @xmath68 is @xmath84 where @xmath85 is the time scale for a single entity . we have consider several scenarios that relate the size of an entity causing a peak to an observed peak duration , @xmath85 ( see table 1 in @xcite ) . here , we consider the two most likely scenarios for the formation of a peak : regions that grow and regions formed by the interaction with the ism . consider a gamma - ray producing region that grows at the speed of sound , @xmath86 , for a period @xmath87 in the rest frame of the shell where presumably the region is symmetric . this growth might be associated with a developing shock . let @xmath88 be the radius of the region in the rest frame along the direction of the motion and @xmath89 be the radius in the perpendicular direction such that @xmath90 the sizes in the rest frame of the detector are related to the sizes in the rest frame of the shell as : @xmath91 and @xmath92 . combining the effects of the movement of the shell during the growth with the maximum size that the entity can grow in time @xmath57 , we find that the duration in arrival time is ( see table 1 of @xcite ) : @xmath93^{1/2}~. \eqno(\neweq)\ ] ] the size of the emitting entity is @xmath94}~~. \eqno(\neweq)\ ] ]    the alternative cause of a peak resulting from the shell is that the shell interacts with an ambient object such as an ism cloud . presumably , the object is symmetric such that @xmath95 . ( we use lower case @xmath96 for an object that grows in a shell and upper case @xmath97 for an ambient object . ) we assume the case of a `` collapsible '' object ( such as an ism cloud , cf . the contribution to the peak duration from time the shell takes to move through the cloud ( i.e. , @xmath98 $ ] ) is negligible compared to the time the shell takes to engage the perpendicular size of the object . this engagement time is caused by the curvature of the shell . at an angle @xmath23 from the line of sight , the time to engage the object is @xmath99 . note that table 2 of @xcite was incorrect for @xmath100 ; see @xcite . at a typical angle of @xmath101 , @xmath102 and @xmath103 thus , both the case of shocks that grow from a seed and the case of shells running into ambient objects are similar . if @xmath104 , then @xmath66 from equation ( ) is 16/13 times larger than from equation ( ) . these two scenarios only differ by a constant the order of unity . the final ingredient for the calculation of the surface filling factor is the area of the shell visible to the observer : @xmath105 where @xmath106 is either the angular width of the shell [ i.e. , @xmath107 ) ] or it is @xmath108 , whichever is smaller . before the shell starts to deaccelerate , presumably @xmath106 is larger than @xmath109 . using @xmath110 , the above was derived for the adiabatic case . more generally , equation ( b ) becomes @xmath119 where @xmath120 is 1 for the adiabatic case and 0 for the radiative ; @xmath121 is a parameter that varies from 0 to 1 depending on whether most of the energy or most of the mass is concentrated at low @xmath3 s ; and @xmath122 is a parameter that varies from 0 to 1 depending on whether the emitting electrons are radiatively efficient or adiabatic ( see @xcite ) . more involved power laws are possible when one includes variations in the ambient material ( see @xcite ) . the surface filling factor from equation ( ) depends on @xmath123 . for a power law relationship between @xmath20 and @xmath8 , @xmath124 . assuming that each entity is similar in the rest frame , different deaccelerations ( i.e. , various values of @xmath120 , @xmath122 , @xmath121 ) only modify the equation for @xmath5 by a numerical factor on the order of @xmath125 . we conclude that surface filling factors found in the next section are roughly what one would find for any deacceleration scenario as long as @xmath126 . the consistency of the peak duration throughout the gamma - ray phase implies that @xmath3 is rather constant . in this case , the surface filling factor is a function of @xmath71 ( from eq . [ ] ) , and the direct observables ( @xmath127 , and @xmath8 ) . the constant @xmath116 is either 16 or 13 depending on whether the source of the entity is due to ambient objects or shocks that grow , respectively . if ambient objects were involved , we would expect to see peaks with a wide range of durations , perhaps a power law distribution . in fact , most grb peaks are about the same size ( @xcite ) , so we will use @xmath128 for the gamma - ray phase . to estimate @xmath71 , one needs to estimate the fraction of the visible shell ( i.e. , @xmath72 , the area within a beaming angle of @xmath2 ) that contributes to the signal during time @xmath8 . unfortunately , we do not know how , in general , to map the amount of active area of a shell to the observed time history . only in the particular case of a fred - like burst can we reliably estimate @xmath71 . for a fred - like burst , the curvature of the shell delays the photons from the region of the shell at angle @xmath2 by @xmath129 where @xmath129 is the time that the shell expands before producing gamma - rays . from @xcite and @xcite , one can find @xmath129 from the shape of the profile . given that the profile shape is @xmath130 , @xmath129 is @xmath131 where @xmath132 is the duration of the burst that contains 50% of the event counts ( see batse catalog , @xcite ) . here , @xmath63 is the spectral number index , typically @xmath64 . thus , if one uses @xmath133 , then the profile is from the region of the shell out to an angle of @xmath2 , and @xmath134 .    for long complex bursts , we can not easily detect a fred - like shape . in lieu of an exact estimate , we will use the rule found for fred - like bursts : @xmath135 . in table 1 , we list 6 fred - like bursts and 46 long complex bursts that were bright and had sufficient time structure for estimating parameters . the first column gives the batse trigger number . the second column gives @xmath73 as found from equation ( ) . the third column gives an estimate of @xmath85 , the temporal width of a single entity . in most cases , this was estimated from the width of the autocorrelation function . for four of the fred - like bursts , the profiles were rather smooth ( presumably due to a larger number of entities being simultaneously active ) so we used a typical value for @xmath85 ( i.e. , 0.5 s ) . the 4-th column is @xmath132 and the next two columns are , respectively , the surface filling factor and its propagated error based on equation ( ) .    in figure 3 we show the distribution of surface filling factors as a function of burst duration @xmath132 . the solid squares are the fred - like bursts , and the open squares are the long complex bursts . although some of the smooth fred - like bursts can have surface filling factors near unity , most bursts have values on the order of @xmath136 .      in figure 4 , we show the time history of burst gb970828 observed by the asca satellite , from 28.9 to 48.9 hours after the gamma - ray phase ( cf . @xcite ) . at about 36.1 hours , there was a flare that lasted about 2 hours . @xcite also reported variations from a simple power law decay in the x - ray afterglow of gr970508 . these two examples of deviations from a power law decay are quite different . in the case of the @xcite observation , the flare is relatively narrow ( i.e. , @xmath137 is small ) . in the case of the @xcite observation , the deviation could be a step function increase in the intensity ( i.e. , @xmath138 , although there is a data gap from 22 to 65 hr after the grb that obscures the nature of the deviation ) . we will emphasize the @xcite observation because the narrow nature of the flare gives much stricter limits on the relativistic shell ( see   5 ) . except for earth occultations , asca continuously observed the afterglow from 28.9 to 48.9 hr after the grb . the observations have been prorated into samples of equal duration in figure 4 . consider how case c in equation ( ) applies to gb970828 . we must estimate the fraction of the shell that contributes to the 20 hours of observations , @xmath71 . we can estimate a lower limit on @xmath71 , and therefore , an upper limit on @xmath5 . in case c we assume that the whole shell was active , but only a fraction ( @xmath71 ) of it contributed during the asca observation . the narrowest annulus that contributes during any particular observation is one with a width equal to the size of a single entity . at a typical angle of @xmath2 , @xmath71 can be as small as @xmath139 at smaller angles , @xmath71 would be smaller , but that is counteracted by the fact that the peak in the asca observation is clearly much smaller than the whole observation , such that the annulus responsible for the observation must be larger than we used in equation ( ) . we only have observations covering a small range of time , so we can not use equations ( ) and ( ) to estimate @xmath67 . however , there are probably only a few active entities because we see only one peak in figure 4 . hence , we will use @xmath140 as the maximum number of entities involved in the asca flare . thus , using case c , @xmath5 is , at most , @xmath141 , a value very similar to what is obtained in the gamma - ray phase . in figure 3 , the asca flare for case c is represented by the solid triangle .    in the situation of case b , we do not know   or @xmath71 . however , the smallest @xmath71 when the shell s angular size is limited to   is @xmath142 such that @xmath143^{-1/4 }   { \gamma \delta t_p \over t^{1/4 } } = { 1.6 \times 10^{-5}n_n \over \sqrt{{\rm d}\omega } }   \bigg[\initialcon\bigg]^{-1/8 }   { \delta t_p \over t^{5/8}}~~. \eqno(\neweq)\ ] ] using , @xmath144 and @xmath145 , the maximum @xmath5 under case b is @xmath146 .    in summary , @xmath137 in the asca flare is @xmath147 which implies a filling factor of @xmath9 . the x - ray afterglow suffers from the same time history problems that the gamma - ray phase has : peaks do not have the value of @xmath137 expected from a shell whose surface quasi - uniformly emits photons . the rapid variations in grb time histories imply emitting entities the size of @xmath148 . assuming a _ single _ expanding shell , these entities must form on a much larger surface , @xmath149 . we have defined @xmath5 ( given by eq . [ ] ) to be the fraction of the surface of the shell which becomes active , that is , generates emitting entities . a crude estimate of @xmath5 is @xmath150 . because both the classic gamma ray burst phase and the recently discovered x - ray afterglow phase can have flares with @xmath151 , both time periods can suffer from an inefficient utilization of a single relativistic shell .    in the case of the gamma - ray phase , there is a simple explanation : the gamma - ray source is not a single relativistic shell , but rather , reflects activity at some central site that produces @xmath0 erg s@xmath1 for up to several hundred seconds . other observations , particularly gaps seen in the gamma - ray time histories ( @xcite ) , also argue for a central engine . the x - ray afterglow , however , is widely interpreted as being a single relativistic shell ( @xcite ) . therefore , we will concentrate our discussion on how to accommodate flares during the x - ray afterglow . these arguments could also be applied to the gamma - ray phase . of the two examples of deviations from a power law in the x - ray afterglow , the @xcite event ( gb970828 ) is much more restrictive than the @xcite event ( gb970508 ) . gb970828 has a narrow flare whereas gb970508 appears to be roughly a step function . a step function is similar to a fred - like deviation which is approximately what one would _ expect _ if most of the observable surface of a relativistic shell interacts with a large ism cloud ( i.e. , @xmath137 should be @xmath152 , @xcite ) . thus , gb970828 might be an afterglow with a low surface filling factor whereas gb970508 has a high surface filling factor . a common misconception is that one can just use an ism cloud that covers most of the shell s surface and , therefore , make a flare that substantially changes the emission . this does not work because the curvature of the expanding shell prevents the shell from engaging the cloud instantaneously . rather , the portion of the shell at @xmath153 requires a time @xmath154 longer to reach the cloud . even if the cloud happens to have a concave shape such that the shell reaches the cloud simultaneously over a wide range of angles , the resulting photons at @xmath101 must travel further to the detector resulting in emission that is delayed by @xmath155 . indeed , the delay of the photons due to the curvature is identical to the scenario of a shell that expands without producing photons for a long time and then emits only over a small range of times ( the @xmath156 case in @xcite ) . the result is a fred - like flare ( like gb970508 ) whose duration , @xmath7 , is about @xmath8 , rather than a small fraction of @xmath8 as indicated by the asca observations for gb970828 . the shell will have well - defined curvature because all points on it are moving at nearly the same speed , that is , the speed of light . in any case , there is no reason to believe that variations in the ambient material would cause the shell to develop into a plane wave oriented towards the observer such that the photons produced by an interaction with an ism cloud or a shock would arrive as a short flare . _ only the instantaneous interaction between two plain parallel surfaces oriented perpendicularly to our line of sight can produce a short peak from large surfaces . _    we see six possible explanations for flares with small @xmath137 that produce large changes in the observed intensity . these explanations are explained below and represented in figure 5 . a key issue is the size of the corresponding energy reservoir required in each case . to intercompare these energy requirements , we use that a typical peak corresponds to an isotropic luminosity , @xmath157 , equal to @xmath158 erg s@xmath1 . the total energy reservior is required to have @xmath159 where @xmath160 is the average duration of the event ( say , 30 s ) and @xmath161 is the fraction of the total energy that is converted into gamma - rays ( say @xmath162 ) . if the emission is isotropic , then the total energy is about @xmath163 erg . since we can not observe the energy released at angles much greater than @xmath164 , any model can reduce the required energy reservior to @xmath165 . although the energy requirement can be made small , a single shell that emits nearly uniformly over  ( see fig . 5a ) is not consistent with the observed time structure since a uniform shell always results in a fred - like shape . the following scenarios can produce bursts with peaks with small @xmath137 :    1 . the simplest way to have short powerful flares is to invoke a central engine . in a central engine , there are multiple releases of energy at the central site over a time scale commensurate with the observed duration of the grb . each release makes a peak in the time history . indeed , small @xmath137 and gaps are the key kinematic reasons why the grb phase is likely to be a central engine ( @xcite ) . it is possible for a large fraction of the surface of the shell to be active , and the flare region might still be small , because @xmath161 or the energy content of the shell varies strongly as a function of position on the shell . that is , the photons @xmath166 s@xmath1 at the flare site must be larger than the rest of the shell by a factor of @xmath167 ( see fig . 5b ) . for example , some photon production rates scale as @xmath168 , so a single region with a @xmath3 that is 10 times larger than other regions could produce emission that doubles the overall count rate . this would give the appearance that @xmath5 is @xmath169 . if the energy content of the shell is constant as a function of angle and @xmath161 varies , then the required total energy is about @xmath170 . if @xmath161 is constant , and the energy content of the shell varies , then the total required energy is @xmath165 . the third explanation is that the local spherical symmetry of the shell is broken into many emitting regions on a scale much smaller than @xmath2 where only a fraction @xmath5 of the surface converts its energy into photons . the regions are small enough ( @xmath171 ) to make peaks with small @xmath137 ( see fig . 5c ) . here it is assumed that all regions of the shell has equal energy content but much of it is wasted because most regions do not produce gamma - rays . thus , this scenario requires an energy reservoir of @xmath170 , that is , @xmath172 _ more _ energy than a simple shell . if  is large , this scenario could require @xmath173 to be as large as @xmath174 erg . @xcite invoke this explanation and the resulting need for more energy to argue against a single relativistic shell . that arguement should not be considered particularly strong since we have several scenarios that do not waste the energy and/or  could be small . the fourth explanation is that the local spherical symmetry is broken because the outflow of material is in narrow fingers that occupy only a fraction @xmath5 of the shell s surface ( see fig . this is basically the same geometry as the previous case except those regions that do not emit gamma - rays do not have energy content . since no energy is wasted in non - emitting regions , this scenario requires an energy reservoir of only @xmath165 , that is , about what one would expect from a simple shell . the fifth explanation is that  is very small , so small that the emission lasts only @xmath85 even if the entire  region is gamma - ray active . this requires  to be @xmath175 . the requried total energy is correspondingly small : @xmath176 erg . this explanation has one narrow ejecta that needs to go through a gamma - ray emitting phase for each peak in the grb time history . in the above explanation ( number 4 ) , there are many narrow ejecta , so each one only has to become gamma - ray active only a few times to make a grb time history with hundreds of peaks . the last explanation attributes the duration of the grb to the spreading out in time of the emission because of different conditions as a function of @xmath23 ( see fig . this is what we called a `` thick shell with substructure '' in @xcite . it would have been better to call it a `` thick emitting region with substructure '' since the actual emitting shell must always be thin ( cf . effectively , @xmath5 is unity but it appears to be small because the assumptions involved in equation ( ) are not valid . let @xmath177 be the time that the @xmath178-th section of a shell at @xmath179 expands before becoming active . let @xmath180 be the speed of the material at @xmath179 . the relative time that the emission from two different regions ( @xmath178 and @xmath181 ) arrive at our detector is @xmath182 explanations 3 and 4 , above , assume that all @xmath177 s and @xmath180 s are equal such that we can estimate the size of the shell from it s fred - like appearance and peaks arrive at different times because they come from different @xmath179 s . of course , most bursts are not fred - like . in this explanation , all @xmath179 regions become active ( so @xmath5 = 1 ) , but the peaks that would have added up to make the fred - like envelope are scattered in time because of the different @xmath177 s and @xmath180 s . to disrupt the fred - like shape , @xmath183 s must vary by a factor of at least 2 from what they would be if everything was constant with @xmath23 . consider the effect of different times of emission ( i.e. , different @xmath177 s but similar @xmath180 s ) . the @xmath177 s would have to vary by about a factor of 2 to change @xmath183 s by a factor of 2 . consider constant @xmath177 s but different @xmath180 s . to spread out out the emitting regions so their distance from us varies by about @xmath8 requires that @xmath184 or that the radius of the shell is @xmath185 the @xmath186 and @xmath187 would have to vary by about @xmath188 . such differences could arise from different baryon loading as a function of @xmath23 . there are two observations that argue against this explanation . first , even the bursts with fred - like envelopes show low filling factors ( see the solid squares in fig . second , if the @xmath186 s differ by @xmath188 , then peak near the end of the burst should have widths that are at least a factor of 2 wider . bursts normally do not appear to have such a trend . this explanation requires an energy reservoir like a uniform shell : @xmath165 .    in conclusion , both the gamma - ray phase and the x - ray afterglow show similar rapid variability , both have values of @xmath189 that are similar . such variability implies that either grbs are central engines , or that the local spherical symmetry is broken on a scale much smaller than @xmath2 . in the last case , the structure can either be due to variations in @xmath3 as a function of @xmath23 ( perhaps due to small scale variations in the baryon loading , explanation 6 above ) , or due to only a fraction @xmath5 of the shell becoming active ( explanations 3 , 4 , 5 above ) . the required total energy is @xmath190 , @xmath191 and @xmath192 for explanations 3 , 4 , and 5 , respectively . using typical values , the total energy can vary from @xmath174 to @xmath193 erg . we note that explanation 5 ( a jet much narrower than @xmath2 ) is the only explanation that can also easily explain gaps in the time history . we thank cheng ho and chuck dermer for useful comments . jay norris provided the time histories analyzed for figure 3 . this work was done under the auspices of the us department of energy and was funded in part by the nasa gro guest investigator program . rccccc 143 & 1.5 & 1.10 & 6.7 & 2.43 & 0.812 219 & 3.0 & 0.51 & 6.3 & 2.37 & 1.184 249 & 1.8 & 1.43 & 6.7 & 3.75 & 1.312 257 & 42.7 & 0.50 & 28.5 & 7.21 & 2.181 394 & 2.8 & 0.76 & 37.0 & 0.55 & 0.157 467 & 6.7 & 0.50 & 8.8 & 3.65 & 0.956 469 & 5.2 & 0.26 & 4.0 & 3.20 & 0.450 563 & 79.8 & 0.50 & 8.6 & 44.41 & 7.823 647 & 4.7 & 0.90 & 16.8 & 2.43 & 1.636 660 & 2.7 & 0.26 & 5.5 & 1.22 & 0.633 676 & 2.8 & 0.76 & 18.4 & 1.11 & 0.668 678 & 4.1 & 0.32 & 20.5 & 0.62 & 0.185 829 & 3.4 & 0.38 & 6.0 & 2.10 & 1.740 841 & 2.1 & 0.45 & 5.8 & 1.54 & 0.708 1122 & 2.9 & 0.51 & 6.1 & 2.38 & 0.979 1141 & 10.0 & 1.54 & 6.9 & 21.47 & 8.346 1288 & 0.6 & 0.89 & 100.2 & 0.05 & 0.016 1440 & 0.4 & 0.51 & 2.8 & 0.69 & 0.230 1541 & 1.0 & 0.48 & 10.6 & 0.44 & 0.255 1606 & 2.9 & 0.51 & 53.4 & 0.27 & 0.088 1625 & 3.7 & 0.47 & 10.0 & 1.67 & 0.557 1652 & 2.6 & 0.83 & 23.9 & 0.86 & 0.468 1663 & 3.9 & 1.02 & 10.6 & 3.61 & 1.370 1676 & 1.3 & 0.32 & 30.8 & 0.13 & 0.032 1815 & 2.5 & 0.32 & 10.8 & 0.72 & 0.249 1883 & 120.2 & 0.50 & 3.6 & 100 & 13.420 2067 & 2.4 & 0.64 & 6.9 & 2.14 & 0.918 2080 & 4.0 & 0.32 & 22.7 & 0.55 & 0.328 2083 & 2.4 & 0.38 & 7.6 & 1.18 & 0.319 2090 & 0.3 & 0.26 & 8.6 & 0.10 & 0.039 2110 & 3.6 & 0.70 & 7.5 & 3.22 & 0.475 2138 & 0.9 & 0.77 & 12.0 & 0.57 & 0.214 2156 & 1.1 & 0.78 & 92.0 & 0.09 & 0.031 2213 & 0.3 & 0.90 & 51.6 & 0.05 & 0.013 2228 & 1.5 & 0.38 & 30.3 & 0.19 & 0.038 2329 & 2.5 & 0.70 & 7.4 & 2.32 & 0.786 2436 & 0.9 & 0.90 & 24.6 & 0.32 & 0.197 2450 & 2.6 & 0.26 & 11.9 & 0.54 & 0.377 2533 & 1.8 & 0.45 & 26.0 & 0.30 & 0.127 2586 & 1.3 & 0.26 & 7.9 & 0.40 & 0.143 2700 & 1.5 & 0.32 & 32.6 & 0.14 & 0.035 2798 & 3.8 & 1.02 & 9.0 & 4.19 & 0.599 2812 & 0.5 & 0.38 & 14.1 & 0.14 & 0.036 2831 & 1.5 & 0.51 & 66.0 & 0.11 & 0.037 2855 & 1.8 & 0.83 & 13.2 & 1.11 & 0.344 2889 & 1.3 & 0.38 & 20.6 & 0.24 & 0.047 2929 & 2.4 & 0.19 & 14.1 & 0.31 & 0.178 2984 & 1.5 & 0.26 & 11.8 & 0.31 & 0.117 2993 & 8.4 & 0.26 & 17.7 & 1.17 & 0.574 3035 & 4.0 & 0.58 & 35.8 & 0.62 & 0.109 3057 & 3.7 & 0.77 & 13.4 & 2.05 & 1.569 3128 & 2.2 & 0.26 & 14.1 & 0.39 & 0.106 970828 & & 7200 & @xmath194 & 0.10 &    = --2 costa , et al . , 1997 , nature , 387 , 783 dar , a. , 1998 , submitted to apjl , astro - ph/9709231 fenimore , e.  e. , madras , c.  d. , & nayakshin , s. , 1996 , apj 473 , 998 , astro - ph/9607163 fenimore , e.  e. , ramirez - ruiz , e. , & sumner , m.  c. , 1998 , gamma - ray bursts : 4th huntsville symposium , eds . meegan , preece , & koshut , ( aip proc . 428 ) pg 657 , astro - ph/9712303 fenimore , e. e. , & sumner , m. c. , 1997 , all - sky x - ray observations in the next decade , eds . matsuoka , m. , & kawai , n. , pg 167 , astro - ph/9705052 frail , d. , kulkarni , s.  r. , nicastro , l. , feroci , m. , & taylor , g.  b. , 1997 , nature , 389 , 261 kobayshi , s. , piran , t. , & sari , r. , 1997 , apj , 490 , 92 meegan , c.  a. , et al . 1996 , apjs , 106 , 65 , p. , & rees , m. j. , 1993 , apj , 405 , 278 , p. , & rees , m. j. , 1997 , apj , 476 , 232 , p. , rees , m.  j. , & wijers , r.  a.  m.  j. , 1998 , apj submitted , astro - ph/9709273 metzger , m.  r. , et al . 1997 , nature , 387 , 878 norris , j.  p. , et al . , 1996 , apj 459 , 393 panaitescu , a. , & , p. , 1998 , apj submitted piran , t. , & sari , r. , 1997 , apj 485 , 270 piro , l. , et al . , 1997 , a&a submitted rees , m. j. , & , p. , 1994 , apj , 430 , l93 rees , m. j. , & , p. , 1998 , apjl , submitted , astro - ph/9712252 reichart , d. , 1997 , apj , 485 , l57 sari , r. , & piran , t. , 1997a , apj in press sari , r. , & piran , t. , 1997b , mnras in press sari , r. , piran , t. , & narayan , r. , 1998 , preprint astro - ph/9712005 sumner , m.  c. , & fenimore , e.  e. , 1998 , gamma - ray bursts : 4th huntsville symposium , eds . meegan , preece , & koshut , ( aip proc . 765 , astro - ph/9712302 tavani , m. , 1997 , apj , 483 , l87 waxman , e. , kulkarni , s. r. , & frail , d.  a. , 1998 , apj , submitted , astro - ph/9709199 wijers , r.  a.  m.  j. , rees , m.  j. , & , p. , 1997 , mnras , 288 , l51 yoshida , a. , et al . , 1998 , gamma - ray bursts : 4th huntsville symposium , eds . meegan , preece , & koshut , ( aip proc . 428 ) pg 441
the variability observed in many complex gamma - ray bursts ( grbs ) is inconsistent with causally connected variations in a single , symmetric , relativistic shell interacting with the ambient material ( `` external shocks '' ) . 
 rather , either the central site must produce @xmath0 erg s@xmath1 for hundreds of seconds ( `` internal shocks '' ) or the local spherical symmetry of the shell must be broken on an angular scale much smaller than @xmath2 where @xmath3 is the bulk lorentz factor for the shell . the observed variability in the external shock models arises from the number of causally connected regions that ( randomly ) become active . 
 we define the `` surface filling factor '' to be the ratio of the area of causally connected regions that become active to the observable area of the shell . from the observed variability in 52 batse bursts 
 , we estimate the surface filling factor to be typically @xmath4 although some values are near unity . 
 we find that the surface filling factor , @xmath5 , is @xmath6 in both the constant @xmath3 phase ( which probably produces the grb ) and the deaccelerating phase ( which probably produces the x - ray afterglows ) . here 
 , @xmath7 is a typical time scale of variability and @xmath8 is the time since the initial signal . 
 we analyze the 2 hr flare seen by asca 36 hr after the grb and conclude that the surface filling factor must be small ( @xmath9 ) in the x - ray afterglow phase as well . 
 compared to the energy required for an isotropic shell , @xmath10 , explanations for low surface filling factor can either require more energy ( @xmath11 erg ) or less energy ( @xmath12 erg ) . 
 thus , the low filling factor can not be used as a strong argument that grbs must be internal shocks . 
 = 1 # 1#2#1