A&A 372, 1071–1077 (2001) Astronomy DOI: 10.1051/0004-6361:20010586 & c ESO 2001 Astrophysics
Physical parameters and emission mechanism in gamma-ray bursts
E. V. Derishev1,V.V.Kocharovsky1,2, and Vl. V. Kocharovsky1
1 Institute of Applied Physics, Russian Academy of Science, 46 Ulyanov st., 603950 Nizhny Novgorod, Russia 2 Dept. of Physics, Texas A&M University, College Station, TX 77843-4242, USA e-mail: [email protected]
Received 13 June 2000 / Accepted 7 March 2001
Abstract. Detailed information on the physical parameters in the sources of cosmological Gamma-Ray Bursts (GRBs) is obtained from few plausible assumptions consistent with observations. We consider monoenergetic injection of electrons and let them cool self-consistently, taking into account Klein-Nishina cut-off in electron- photon scattering. The general requirements posed by the assumptions on the emission mechanism in GRBs are formulated. It is found that the observed radiation in the sub-MeV energy range is generated by the synchrotron emission mechanism, though about ten per cent of the total GRB energy should be converted via the inverse Compton (IC) process into the ultra-hard spectral domain (above 100 GeV). We estimate the magnetic field strength in the emitting region, the Lorentz factor of accelerated electrons, and the typical energy of IC photons. We show that there is a synchrotron-self-Compton constraint which limits the parameter space available for GRBs that are radiatively efficient in the sub-MeV domain. This concept is analogous to the line-of-death relation existing for pulsars and allows us to derive the lower limits on both GRB duration and the timescale of GRB variability. The upper limit on the Lorentz factor of GRB fireballs is also found. We demonstrate that steady-state electron distribution consistent with the Compton losses may produce different spectral indices, e.g., 3/4 as opposed to the figure 1/2 widely discussed in the literature. It is suggested that the changes in the decline rate observed in the lightcurves of several GRB afterglows may be due to either a transition to efficient IC cooling or the time evolution of Klein-Nishina and/or Compton spectral breaks, which are the general features of self-consistent electron distribution.
Key words. radiation mechanisms: non-thermal – ISM: jets and outflows – gamma rays: bursts – gamma rays: theory
1. Introduction of energy carried directly by the emission from the fireball photosphere is small unless Γ ∼> 105 (Derishev et al. 1999). At present, there is a tendency to divide the problem of The fireball model became widespread and almost Gamma-Ray Bursts into two separate problems: the na- undisputed, but in its details there is no agreement among ture of the central engine and the origin of GRB emission. theorists. Even the principal question about the main While the former question is still far from being settled, emission mechanism has not yet received a definite answer, the multi-wavelength observations (e.g., Frail et al. 1997; although synchrotron and inverse Compton emission are Metzger et al. 1997; Reichart 1997; Waxman 1997; see also the favourites (e.g., Paczy´nski & Rhoads 1993; M´esz´aros Piran 1999 for a review), which become available in the et al. 1993; Sari et al. 1998). The existing uncertainty com- past few years, give strong support to the fireball shock plicates the correct interpretation of the growing number model (Rees & M´esz´aros 1992, 1994). In its most general of dissimilar multi-wavelength observations. form, this model considers GRB emission as the result of In this paper we derive constraints on the physical pa- energy dissipation in relativistic shock waves and assumes rameters in the GRB emitting region and present new that all the energy is initially accumulated in the form of arguments in favour of the synchrotron emission mecha- ultrarelativistic outflow (fireball) with a Lorentz factor Γ nism. There are two arguments widely discussed in the greater than 100 (Baring & Harding 1995). The fraction literature in this connection. First, the observed polariza- tion in afterglow emission (Covino et al. 1999; Wijers et al. Send offprint requests to:E.V.Derishev, 1999) is thought to be indicative of synchrotron mech- e-mail: [email protected] anism. Second, it was argued that the electron cooling
Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20010586 1072 E. V. Derishev et al.: Physical parameters and emission mechanism in gamma-ray bursts time is too long to be compatible with high radiative ef- 2. A major part of the fireball kinetic energy is con- ficiency if one assumes self-Compton mechanism as the verted into electromagnetic radiation during the main main source of sub-Mev radiation (Piran 1999). Both ar- GRB pulse. – GRB afterglows decline faster than t−1 and guments are not very restrictive because: a) polarization do not contribute significantly to the total energy budget may be produced by inverse Compton scattering as well (Galama et al. 1998). However, it is possible that the adi- if the radiation background and/or electron distribution abatic regime of the shock deceleration persists for a very is anisotropic, b) the strongest limit on the bulk Lorentz long time, so that the bulk of GRB energy has never been factor imposed by cooling time considerations is for the ex- observed. Another reason to make the second assumption ternal shock model, Γ < 300–400, which is still above the is not to increase the energy requirements, which are al- generally accepted lower limit of ∼100. In this paper we ready rather restrictive unless the fireball forms a narrow show that the additional requirement of high efficiency in jet (e.g., M´esz´aros et al. 1999). sub-MeV gamma-rays relative to other spectral domains 3. GRB emission is generated by relativistic electrons pushes the upper limit on Γ to an unacceptable value of and positrons, which are continuously injected with the ini- ∼25 unless the sub-MeV radiation is generated by syn- tial Lorentz factor γp. Acceleration of an electron takes a chrotron rather than by a self-Compton mechanism. very short time compared to the shock expansion timescale There is also an argument against a synchrotron-self- and electron cooling timescale. – This same assumption Compton model: it is sometimes considered as insuffi- implies that we refer to the synchrotron-self-Compton ciently flexible to account for different low-energy spectral model of GRB emission. Comparison with the other emis- indices provided the electrons form a cooling distribution. sion models favours the synchrotron-self-Compton one, Below we show that this argument is rather weak since which indeed can account for high radiative efficiency. a broad range of spectral indices may be accommodated If one does not postulate the high efficiency of energy within the framework of synchrotron-self-Compton model conversion into electromagnetic radiation, then the num- as long as the cooling distribution is calculated consis- ber of available emission mechanisms increases dramati- tently with total losses. cally (e.g., Shaviv & Dar 1995; Panaitescu et al. 1999) and We introduce the minimum number of a priori assump- it becomes almost impossible to choose only one of them tions and avoid the considerations which would require on the basis of limited observational data. At the same the electron acceleration mechanism to be specified. All time, any model with low efficiency is problematic, as it the assumptions used are explicitly listed in the second can hardly compete with blackbody photospheric emission section, followed by a brief discussion and a comparison in the 10–100 keV range. with other approaches frequently used in the literature. Evolution of the Lorentz factor γe (index e denotes The basic analysis is presented in the third section, and both electrons and positrons) is governed by the accelera- the implications are discussed in the forth section. tion and losses. The Lorentz factor grows until the losses compensate the acceleration term. Thus, electron accel- For numerical estimates we take GRB energy EGRB = 52 eration is terminated at approximately the same Lorentz 10 erg and duration tGRB = 10 s. All other values are measured in the shock comoving frame unless the oppo- factor, γp, which is close to the value that equilibrates site is stated. It should be noted that for two bursts, acceleration and radiative losses. GRB 971214 and GRB 990123, the estimated value of Some authors, however, prefer to consider electron in- ∝ −q energy release approaches 1054 ergs assuming isotropic jection with a power-law spectrum, dne(γe)/dt γe , emission. Since it is very divergent from the average value extending from γmin to infinity (e.g., Sari et al. 1998). (1051–1052 ergs) inferred from the analysis of the log N- The spectrum is integrable (q>2) and hence most of log S curve (Reichart & M´esz´aros 1997), these bursts may the energy is concentrated near γmin. In order not to con- be of different origin. tradict our second assumption, the radiative deceleration timescale for an electron with the Lorentz factor γmin must be smaller than the GRB duration measured in the shock 2. Model assumptions comoving frame. In this case, it can be shown that the contribution of electrons with γe γmin or γe γmin to 1. Most GRB emission is in the form of soft gamma-rays, GRB bolometric luminosity is small. It follows from the i.e., below several MeV. – It would naturally explain why above consideration that the choice of electron injection GRB phenomenon was first detected in this spectral range. spectrum does not matter unless the question about the The observation of optical emission from GRB 990123 exact shape of GRB spectrum is addressed; note that γmin (Akerlof et al. 1999), made simultaneously with the burst in the approach of Sari et al. corresponds to γp in ours and of gamma-rays, confirms our first assumption. However, that the peak in the observed spectrum is at the energy observations do not exclude the possibility that the main determined by the electrons with γe ∼ γp. part of GRB emission may be concentrated in photons 4. The energy dissipated in the shock is efficiently re- with energies greater than 1 TeV, and hence escapes de- distributed all over the shocked gas by large-scale tur- tection because photons in this energy range are strongly bulence and then transferred to radiating particles on a absorbed by infrared background radiation (Primack et al. longer timescale. – We are considering a quasi-stationary 1999). problem, when the energy is stored in heavy particles E. V. Derishev et al.: Physical parameters and emission mechanism in gamma-ray bursts 1073
(protons) and there is a continuous supply of relativis- by incident radiation. Otherwise, the largest fraction of tic electrons which replace those that have decelerated. bolometric luminosity is due to k times comptonized pho- The reason why we used a quasi-stationary formulation tons, where k is the minimum number of consequent up- is that the bottle-neck in the energy transfer path (from scatterings, which rises an average photon energy above protons to large-scale turbulence, then to electrons, then the Klein-Nishina cut-off. The latter statement is valid to radiation) is, most likely, at the first two chains, i.e., when the integral term in Eq. (1) is ignored. This is possi- in a typical GRB, electrons are able to radiate at a much ble even for whr wlr thanks to a very rapid decrease in higher rate than they can gain energy from protons or the transport cross-section σ. It should be noted, however, large-scale turbulence. that this simplification may not be applied in some cases, 5. The fireball is isotropic. – This is a good approxi- as discussed below. mation even for a jet if it has an opening angle θ Γ−1. Let us consider a relativistic shock with the Lorentz If the central engine generates a jet-like outflow, then the factor Γ which radiates an energy Er during a time interval value of EGRB is not the actual GRB energy but rather the τ (in the observer frame). The values of Er and τ are energy calculated assuming isotropic emission. Therefore, either the total GRB energy EGRB and duration tGRB (in the unknown beaming factor does not affect our results. the external shock model), or the energy and duration of individual pulses (in the model of internal shocks), which constitute together what we call a GRB. As measured in 3. Physical parameters in GRB shocks the comoving frame, bolometric luminosity of the source is 2 For the synchrotron-self-Compton model one may repre- Er/Γ τ. Given the expression for the integral luminosity sent the luminosity of a single highly relativistic electron of a single particle (1), one easily arrives at the following in the following form (Ginzburg 1987; Rybicki & Lightman relation: 1979): E 4 r = γ2σ N c(w + w ), (3) Z Γ2τ 3 p T e m lr 4 L(γ )= γ2c σ (w + w )+ σw dω · (1) ∼ e 3 e T m lr hr,ω where Ne is the total number of electrons with γe γp in the GRB shell. The product Ne(wm + wlr)mayberepre- Here wm and wlr are the energy densities of magnetic sented in the form ne(Wm + Wlr), where Wm and Wlr are field and low-energy radiation, respectively, whr,ω is the the total energy of magnetic field and low-energy radiation spectral energy density of high-energy radiation, σT the in the emitting region. Certainly, the sum Wm + Wlr can- Thomson scattering cross-section. The boundary between not exceed a fraction of the bulk kinetic energy which is low-energy and high-energy photons is the Klein-Nishina transferred to the particles at the shock front. According 2 cut-off athω ¯ ' mec /γe. Above the cut-off, the transport to the assumption 2, this fraction, Ei, is of the order of −2 cross-section σ is a function of γeω. It decreases as (γeω) Er/Γ, where the factor Γ appears because Ei is measured 2 for γe¯hω mec and approaches σT in the opposite limit. in the comoving frame. The relative efficiency of Comptonization and syn- Most of the remaining factors in the right-hand side chrotron emission is determined by the Compton y of Eq. (3) can be substituted from Eq. (2), where the parameter (Sari et al. 1996) thickness of the emitting region behind a relativistic shock Z ∞ grows during the time interval τ up to L ∼ Γcτ (in the 2 − ' 2 comoving frame). Finally, Eq. (3) yields y = σTL (γe 1)ne(γe)dγe γpσTneL, (2) 1 > Er/Γ ∼ where n is the number density of electrons with the τic ∼ 1. (4) e Ei Lorentz factors ∼γp and L is the size of the emitting re- gion. For example, when electromagnetic radiation passes Thus, there is only one possibility to satisfy all the adopted through a layer filled with relativistic electrons and the en- assumptions: the observed sub-MeV emission from GRBs 2 should be well above the Klein-Nishina cut-off for elec- ergy of incident photons satisfies the relation ε mec /γe (the classical regime), the power of comptonized radia- trons in the emitting region in order not to generate tion relative to the power of incident radiation is given by too much ultra-hard radiation via the inverse Compton process. Lic/Lin ≡ τic ' 4y/3. Below, we will call τic the optical depth for inverse Comptonization. In general, this relation To specify this requirement quantitatively, it is nec- contains a numerical factor which is different from 4/3 and essary to know the low-energy portion of the GRB spec- ∝ α depends on the geometry of a source. trum. If it is a power-law with the index α (ωIω ω ), 2 then according to assumption 1 we have The condition τic = 1 (together with γp
2 An estimate of γp may be obtained from Eq. (9): ' 4 2 B L wsy γpσTc ne = τicwm. (7) 1 1 3 8π c 3 4 2 ' 1/4 t1 τ γp 200 τic Γ . (14) This relation follows directly from Eq. (1). It is well-known E52 tGRB that each subsequent cascade of Comptonization also leads A significant fraction of the total GRB energy is converted to a τic times increase in the energy density of comptonized via inverse Compton scattering into ultra-hard emission. photons. Finally, one obtains The typical energy of comptonized photons corresponds
Xk 2 2 to the Klein-Nishina cut-off at j B k B ' 1 1 wlr + wm = τic τic , (8) 3 4 2 8π 8π 2 −4 2 t1 τ j=0 εic ∼ Γγpmec ∼ 10 Γ TeV (15) E52 tGRB where the approximate equality is for τ 1. ic in the observer frame. The ratio of energy carried by the After some algebra, i.e., deriving the magnetic field ultra-hard radiation to the energy carried by the sub-MeV strength from Eq. (8) with the help of the relation (3) radiation is and substituting B in Eq. (6), one has the following result 2 α Γmec √ 1 1 ' 3 3 4(k+1) δEic τic 1 1 2(k+1) 3 4 2.5mecεp c τ γpεp γ ' τ Γ k+1 , (9) " #α p 2 ic e¯h 2 E 1/4 1/2 (16) r > × −2 E52 tGRB ∼ 1.3 10 3 . which should be compared with the requirement (5). Thus, t1 τ
√ 1 1 For sufficiently flat spectra (α<1), which are considered 1 1 2(k+1) 3 3 4(k+1) 0 − 3εp − k 2.5mecεp c τ α 4 < k+1 here, the relative energy content of ultra-hard radiation τic ∼ 2 Γ . (10) 2mec e¯h 2 Er is always non-negligible. In the external shock model one > Because we know that α0 ≤ 2andτ ∼> 1 (see Eq. (4)), the has δEic ∼ 1%. Moreover, in the model of internal shocks, ic ∼ conclusion is straightforward: k = 0, except the extreme in which τ 1–10 ms (presumably), the value of δEic case should be close to its limiting value of unity set by the assumption 1, independently on the spectral index α. 3ε2 1/2 3 3 1/4 < p 2.5mecεp c τ Γ ∼ 2 4 4mec e¯h 2 Er 4. Implications of the analysis (11) t3/4 τ 1/2 ∼ 25 1 . The principle outcome of the above analysis is that the ob- 1/4 tGRB E52 served sub-MeV emission in GRBs is generated by the syn- chrotron mechanism. However, the limits given in Eq. (12) That is, the radiation which is observed from GRBs in become mutually exclusive if the sub-MeV spectral range is generated by a synchrotron 1 mechanism. 3 3 2 εp t1 τ −5 Substituting k = 0 into Eq. (10) we find that the value 2 < 10 . (17) mec E52 tGRB of τic must fit in the following window The bursts having parameters in this domain can ra- 3 1 1 1 1 2 3 4 2 0 − εp t τ diate only a minor part of the available energy in the < α 4 < 1 1 ∼ τic ∼ 300 2 , (12) mec E52 tGRB sub-MeV spectral range. Therefore, Eq. (17) defines the E. V. Derishev et al.: Physical parameters and emission mechanism in gamma-ray bursts 1075 synchrotron-self-Compton (SSC) constraint for Gamma- uncertainty in theoretical predictions is large: the maxi- Ray Bursts. mum in the spectrum of inverse Compton radiation may There are two implications of the SSC constraint. It be located at ∼103 TeV. On the other hand, in the external may be treated as a lower limit on GRB duration (the shock model, the location of the maximum is more defi- −4 2 external shock model, τ = tGRB): nite, namely, ∼10 Γ TeV ∼ 1–100 TeV. In this case the ultra-hard emission is inaccessible for direct observation 2 2 × −3 1/3 mec ∼ because photons above several hundred GeV are strongly tGRB > 5 10 E52 s 0.03 s. (18) εp absorbed by the infrared background radiation (Primack et al. 1999), and the observed fluence below 1 TeV is de- On the other hand, Eq. (17) determines the shortest possi- termined by the spectral slope of comptonized radiation ble variability timescale τ in the model of internal shocks: in TeV energy range. To date, there is only one indication 3 1 of sub-TeV emission accompanying GRBs (Atkins et al. m c2 E 2 −5 e 52 ∼ −3 2000). τ>10 3 tGRB 10 s. (19) εp t1 According to our estimates, in both models, the GRB A variability significantly shorter than the limiting du- source may be optically thick for the two-photon absorp- ration 1 ms – if observed in GRB lightcurves – favours tion of the highest energy quanta. Qualitative results of propagation effects or coherent emission mechanisms as a the two-photon absorption are the following (details will primary explanation for short-time pulsations in GRBs. be discussed elsewhere). Each of the absorbed photons In order not to contradict assumption 2, the deceler- produces an electron-positron pair, in which the daugh- ation timescale for an electron with the Lorentz factor ter particles have roughly equal energies. Electrons and positrons have a larger interaction cross-section than pho- γp must be smaller than the GRB duration measured in the shock comoving frame. Since we know the relations tons have. Therefore, if the optical depth for interaction of initial ultra-hard quanta is larger than unity, the same between B, γp and the parameters characterizing a GRB is true for daughter electrons (positrons). The first photon (EGRB, tGRB, τ and Γ), it is possible to use this constraint to set limit on Γ: scattered off by one of these energetic particles takes away about a half of its energy, and in turn may be absorbed. 1 1 3 1 4 8 16 8 σT 2.5εp 2EGRB tGRB 1 Step by step, the radiation becomes softer until the ab- Γ ∼< √ t 4 3 3 GRB sorption threshold is reached. It is this spectral domain 4π 3 e¯hmec τicc tGRB τ (20) where the bulk of energy initially contained in the ultra- 3/16 1 E t 8 ' 1.2 × 103 52 GRB · hard radiation is concentrated. If the absorption thresh- 3/16 5/16 τ old is below 1 TeV, then the reprocessed radiation may τic t1 reach the Earth. A similar picture arises if one considers Exactly the same limit may be derived from the require- the reprocessing of the ultra-hard photons via interaction ment that the total energy of the accelerated electrons with soft GRB radiation scattered in interstellar medium does not exceed the GRB energy. It follows from the above (Derishev et al. 2000). analysis that the accelerated electrons, in the general case, The result τic ∼ 1–30 seems surprising since τic is an are not in equipartition with the magnetic field. integral characteristic of the emitting region, while it de- An important question to be addressed in the theory pends on γp, which is determined by the balance between of synchrotron emission is why the value of εp is nearly acceleration and losses and, therefore, is defined by local invariant. This problem may be reformulated as a ques- conditions. Such a fine tuning in the external shock model tion regarding the electron acceleration mechanism. The may result from the following. We have already noted that simplest reasonable suggestion is that γp is a function of the statement τic = 1 means that the energy densities of magnetic field strength B, which is given by Eq. (13). the magnetic field and synchrotron radiation are equal in To eliminate Γ-dependence (the strongest one in Eq. (6)), the emitting region. Since this region expands with a rela- ∝ −1/3 the acceleration mechanism should provide γp B . tivistic velocity, a large fraction of newly born synchrotron In this case, εp preserves a weak dependence on Er and photons cannot escape it until a GRB shell as a whole 1/6 −1/2 τ, εp ∝ Er τ , where the dependence on τ is likely is decelerated to a Lorentz factor much smaller than the to be hidden by a stronger effect of the cosmological time initial one. During the initial deceleration stage the syn- dilation. chrotron radiation is accumulated to the point at which Several per cent (a few tens per cent is a more likely its energy density becomes nearly equal to the thermal en- figure) of the total GRB energy must be converted in the ergy density of plasma. If strong turbulence in a GRB shell ultra-hard spectral domain via the inverse Compton scat- rapidly builds up a magnetic field of a strength close to the tering. The location of the maximum in the spectrum of equipartition value, then the approximate correspondence comptonized radiation is model-dependent. In the model between the energy density of magnetic field and that of of internal shocks, the maximum (see Eq. (15)) may be at synchrotron radiation is established automatically, thus −6 2 energies as low as 10 Γ TeV ∼ 10–100 GeV, so that the explaining why τic ∼ 1. In the model of internal shocks, number fluence of ultra-hard photons should be of the or- it is usually assumed that the Lorentz factor of succes- der of 103 km−2 even for the weakest bursts. However, the sive shells differs by a factor of few. Nearly all generated 1076 E. V. Derishev et al.: Physical parameters and emission mechanism in gamma-ray bursts radiation remains within the emitting region and the con- The GRB spectrum below εp is a broken power-law dition τic ∼ 1 is satisfied automatically. consisting of two portions with the spectral index 1/2 sep- The situation when τic > 1 and, at the same time, the arated by a steeper part with α =3/4. Therefore, in ad- synchrotron emission is the most efficient cooling mech- dition to the well-known cooling break in the synchrotron anism in the portion of electron distribution with the spectrum there are two others – the lower-energy Klein- highest luminosity yields the largest flexibility in spec- Nishina break, below which the ratio of synchrotron to tral shapes of synchrotron radiation. So far, we considered inverse Compton losses levels off, and the higher-energy the low-energy spectral slope as an independent parame- Compton break, above which synchrotron losses overcome ter, assuming only that α ≤ 2. The complete theory of inverse Compton ones. Locations of all spectral breaks are synchrotron-self-Compton emission, however, should give time-dependent both during the main pulse and at the a definite prediction of α. afterglow stage, and if one is limited to a narrow-band In the simplest approximation only the synchrotron observations, the transition from one spectral slope to an- losses are taken into account, so that partially decelerated other could be interpreted as a change in the decline rate electrons form the following distribution below γp: of a lightcurve. A similar effect may appear for a bolo- metric lightcurve when the balance between synchrotron m c2 dn γ n (γ )= e e = n p · (21) and inverse Compton emissivities is shifted in favor of the e e L e 2 (γe) dt γe latter. ∝ q One more effect may alter the appearance of the low- For a power-law electron distribution, ne(γe) γe ,the q+3 energy part of the GRB spectrum – the synchrotron self- synchrotron spectrum is also a power-law, ωIω ∝ ω 2 . 1/2 absorption. With the help of expressions for γp and τic, Distribution (21) gives the well-known result, ωIω ∝ ω . A different approximation works well when the integral it is not difficult to estimate the self-absorption threshold term in Eq. (1) dominates. In this case, the main contribu- energy (Zheleznyakov 1996). It takes the highest value in tion to the integral is from photons near the Klein-Nishina the model of internal shocks, but even in this model the −1 threshold is hardly above 500 eV in the observer frame. cut-off whose frequency scales as γe . Looking for a power- L∝ 2−α ∝ α law solution, we find that γe if ωIω ω ,andthat ∝ α−2 ne(γe) γe consequently. Thus, α =(α +1)/2andthe 5. Conclusions final result is The analysis in this paper relies to a large extent upon sev- ne ne(γe)= and Iω =const. (22) eral assumptions which have not received yet direct obser- γ e vational confirmation. However, we put forward a number As follows from the above analysis, the GRB sources are at of reasons why these assumptions are consistent with the the border between these two limiting cases. Namely, the known properties of GRBs. Our investigation reveals that, synchrotron losses dominate for electrons with γe ∼ γp, in the range of parameters typical for the detected bursts, but the inverse Compton losses become dominant for less there is no other possibility that accounts for the sub-MeV energetic electrons because the Klein-Nishina cut-off is radiation than synchrotron emission of electrons acceler- shifted to higher photon energies, giving greater wlr.The ated in relativistic shocks. On this basis, we make several fact that all GRBs belong to the transition zone between definite predictions of physical parameters in relativistic two limiting cases makes theoretical analysis more com- shocks of GRB origin. plicated, but also allows for a wider range of solutions. One of the most important conclusions is that physical Let us consider one example to illustrate this. Suppose conditions in GRB emitting regions are qualitatively simi- that electrons with the Lorentz factors between γic and γp lar. Namely, there is not so much freedom in the magnetic lose their energy mainly due to synchrotron radiation. The field strength, which is close to its equipartition value, and electrons in this range form the distribution (21) and pro- in the Lorentz factor of accelerated electrons (Eq. (9)). 1/2 duce the corresponding spectrum ωIω ∝ ω , which ex- The main uncertainty in the energy of comptonized pho- 2 tends from εp down to (γic/γp) εp. If the Klein-Nishina tons arises from differences between external and internal 2 cut-off, εk−n, lies somewhere between (γic/γp) εp and shock models and from poor knowledge of the bulk Lorentz (γic/γp)εp for γe ∼ γp, then the relative importance of the factor. The inverse Compton losses always play a signifi- integral term in Eq. (1) grows until γe <γk−n = εk−n/εp. cant role, so that the ultra-hard emission above 100 GeV Electron distribution between γk−n and γic is determined contains from several to tens per cent of the total GRB by the spectral slope in the region just below εp,where, energy. in this case, the spectral index is α =1/2. Hence, electron We demonstrate that a steady-state electron distribu- −3/2 distribution is given by ne(γe) ∝ γe (see the discussion tion consistent with the Compton losses may produce dif- of Eq. (22)) and the synchrotron spectrum generated by ferent spectral indices, ranging from the widely accepted these electrons has an index α =3/4 between energies 1/2 to 1. In many GRBs, the competition between in- 2 2 (γic/γp) εp and (γk−n/γp) εp. At the lowest energies, the verse Compton and synchrotron losses should produce spectral index is again α =1/2, since the inverse Compton rather complex (power-laws with several breaks) spectra losses saturate when the Klein-Nishina cut-off is shifted in the X-ray and soft γ-ray ranges. The time evolution of above εp. spectral breaks, as well as transition from predominantly E. V. Derishev et al.: Physical parameters and emission mechanism in gamma-ray bursts 1077 synchrotron losses to predominantly inverse Compton Derishev, E. V., Kocharovsky, V. V., & Kocharovsky, Vl. V. losses, may account for the changes in the decline rate 2000, Proceedings of the 5th Huntsville Gamma-Ray Burst observed in the lightcurves of several GRB afterglows. Symposium, 18-22 October 1999, Huntsville, USA, p. 460 The prevalence of a synchrotron emission mechanism Frail, D. A., et al. 1997, Nature, 389, 261 in GRBs imposes the strict limitation on the burst param- Galama, T. 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