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ASTRONOMY A&A manuscript no. AND (will be inserted by hand later) ASTROPHYSICS Your thesaurus codes are: missing; you have not inserted them February 1, 2008 The Early Afterglow Re’em Sari1 and Tsvi Piran2 1 Theoretical Astrophysics, California Instituteof Technology, Pasadena, CA 91125, USA. 2 Racah Instituteof Physics, The Hebrew University,Jerusalem 91904, Israel , and 9 Department of Physics, Columbia University,New York,NY 10027, USA 9 9 Received December 15, 1996; accepted 1 n a Abstract. We calculatethe expectedspectrumandlight tributionisalwaysgivenbyfourpowerlawsegments,sep- J curves ofthe earlyafterglow.For shortGRBs the peak of aratedbythreecriticalfrequencies:ν theselfabsorption sa 0 theafterglowwillbedelayed,typically,byafewdozensof frequency,ν the cooling frequency andν the character- c m 1 seconds after the burst. The x-ray and γ-ray characteris- istic synchrotronfrequency. ticsofthisdelayedemissionprovideawaytodiscriminate Using the relativistic shock jump conditions and as- 1 v between late internal shocks emission (part of the GRB) suming that the electrons and the magnetic field acquire 5 and the early afterglow signal. Detection of this delayed fractionsǫe andǫB ofthe equipartitionenergy,weobtain: 0 emissionwill provethe internalshock scenarioas produc- 1 ing the GRB, and will pinpoint the initial Lorentz factor ν =1.1×1019Hz ǫe 2 ǫB 1/2( γ )4n1/2. (1) 1 m (cid:16)0.1(cid:17) (cid:16)0.1(cid:17) 300 1 γ0.Intheopticalband,thedominantemissionarisesfrom 0 9 the reverseshock.This shock,carriesanenergy compara- ν =1.1×1017Hz ǫB −3/2 γ −4n−3/2t−2, (2) 9 bleto thatofthe forwardshock.Itradiatesthis energyat c (cid:16)0.1(cid:17) (cid:16)300(cid:17) 1 s / much lowerfrequencies, producing a short opticalflash of ph 15th magnitude or brighter. Fν,max =220µJD2−82(cid:16)0ǫB.1(cid:17)1/2(cid:16)3γ00(cid:17)8n31/2t3s (3) - o str 1. Introduction νsa =220GHz(cid:16)0ǫB.1(cid:17)6/5(cid:16)3γ00(cid:17)28/5n91/5t8s/5 (4) a : In the internal-external scenario, the GRB is produced These scalings generalize the adiabatic scalings obtained v by internal shocks while the afterglow is produced by the by Sari, Piran & Narayan (1998) to an arbitrary hydro- i X interaction of the flow with the ISM. The original fire- dynamic evolution of γ(t). r ballmodelwasinvokedtoexplaintheGamma-RayBursts Fortypicalparameters,νc <νm,sofastcoolingoccurs. a (GRBs) phenomena. It requires extreme relativistic mo- Thespectrumoffastcoolingelectronsisdescribedbyfour tion, with a Lorentz factor γ>∼100. power laws: (i) For ν < νsa self absorption is important Theafterglowobservations,whichfitthetheoryrather and Fν ∝ ν2. (ii) For νsa < ν < νc we have the syn- well,areconsideredasaconfirmationofthefireballmodel. chrotron low energy tail Fν ∝ ν1/3. (iii) For νc <ν <νm However,thecurrentafterglowobservations,whichdetect we have the electron cooling slope Fν ∝ ν−1/2. (iv) For radiation from several hours after the burst onwards, do ν > νm Fν ∝ ν−p/2, where p is the index of the electron not probe the initial extreme relativistic conditions. By power law distribution. the time of the present observations, several hours after In the early afterglow, the Lorentz factor is initially the burst, the Lorentz factor is less than ∼ 10, and it is constant. After this phase, the evolution can be of two independent of the initial Lorentz factor. types (Sari 1997). Thick shells, which correspond to long Afterglow observations, a few seconds after the burst, bursts, begin to decelerate with γ(t) ∼ t−1/4. Only later canprovidethemissinginformationconcerningtheinitial thereisatransitiontodecelerationwithγ(t)∼t−3/8.The phase and prove the internal shock scenario. Such rapid light curves for such bursts can be obtained by substitut- observations are possible, in principle, with future mis- ingthesescalingsinequations1-4.However,fortheselong sions (Kulkarni and Harrison, Private communication). bursts, the complex internal shocks GRB signal would overlap, the smooth external shock afterglow signal. The separationoftheobservationstoGRBandearlyafterglow 2. The Forward Shock would be rather difficult. The synchrotronspectrumfromrelativistic electronsthat For thin shells, that correspond to short bursts, there are continuously accelerated into a power law energy dis- is no intermediate stage of γ(t)∼t−1/4. There is a single 2 Re’em Sari & Tsvi Piran: TheEarly Afterglow tremely small fraction is emitted in the optical band. For t2 example, the prompt optical flash from the GRB would 100 ν=5e+19 be of 21st magnitude if the flux drops according to the t1/2−3p/4 synchrotron low energy tail of F ∼ν1/3. ν A considerably stronger flux is obtained from the re- 10−2 verse shock. The reverse shock contains, at the time it crosses the shell, a comparable amount of energy to the t forward shock. However, its effective temperature is sig- γ nificantly lower (typically by a factor of γ ∼ 300) than tt−−11//44 thatoftheforwardshock.Theresultingpeakfrequencyis 102 ν=5e+17 tt22 therefore lower by γ2 ∼ 105. A more detailed calculation µ J) tt11//22−−33pp//44 shows that the reverse shock frequency is Flux (100 νm =1.2×1014(cid:16)0ǫ.e1(cid:17)2(cid:16)0ǫB.1(cid:17)1/2(3γ000)2n11/2. (6) The cooling frequency is similar to that of the forward t t γ m shock, since both have the same magnetic field and the same Lorentz factor. Using the parameters obtained by ν=4e+14 Granot,PiranandSari(1998),fromtheafterglowofGRB 104 tttt1111////6666 tttt−−−−1111////4444 9ν70=5038,×a1n0d16uHsiznganγd0ν= 3=003w×e1g0e1t4Hfozr ltehaedirnegvetroseasnho8cthk c m tttt1111////2222−−−−3333pppp////4444 magnitudeflash.WithhigherinitialLorentzfactorofγ0 = tttt11111111////3333 104 the flash drops to 13th magnitude. Inverse Compton 102 cooling, if exists, can reduce the flux by ∼2 magnitudes, t t t γ c m while self absoption can influence only very short bursts 100 101 102 103 104 105 withsmallsurfacearea.Therefor,quiteconcervatively,the t (sec) opticalflash shouldbe strongerthan 15thmagnitude and Fig.1. Light curves of the forward (solid) and reverse shouldbesoonseenwithmodernexperiments.Thereverse (dashed) shocks in three energy bands. shock signal is very short living. After the shock crosses the shell, no new electrons are injected and there is no emission above ν . Moreover, ν drops fast with time as transition, at the time t =(3E/32πγ8nm c5)1/3, from a c c γ 0 p the shell’s material cools adiabatically. constant velocity to self-similar deceleration with γ(t) ∼ t−3/8. The possible light curve are illustrated in figure 1. 4. Discussion As the intial afterglow peaks several dozen seconds after the GRB there should be no difficulty to detect it. Theearlyafterglowmulti-wavelengthradiationcouldpro- The detection of delayed emission which fits the light videinterestingandinvaluableinformationontheextreme curvesof figure 1, wouldenable us to determinetγ. Using relativistic conditions that occur atthis stage.The initial tγ we couldproceedto estimate the initialLorentzfactor: emissionfromthe forwardshock,whichcontinueslater as γ0 =240E512/8n11/8(tγ/10s)−3/8. (5) tThheeorbesveerrvseedshaoftcekrgelmowisssioignncaolsulids hinavteheaγst-rroanygs,osrhoxr-tralyivs-. If the second peak of GRB 970228, delayed by 35s, is in- ing, optical component which we expect to be brighter deed the afterglow rise, then γ0 ∼150 for this burst. than15thmagnitude.Someofthecurrentbasicideascon- cerningthefireballmodelsshouldberevisedifsuchsignals will not be seenby new detectors that should become op- 3. The Reverse Shock and the Optical Flash erational in the near future. There are many attempts to detect early opticalemission Acknowledgements. This research was supported by the US- and there is a good chance that this emission will be ob- IsraelBSF95-328andbyagrantfromtheIsraeliSpaceAgency. servedin the near future. A strong 5th magnitude optical R.S. thankstheSherman Fairchild Foundation for support. flash would have been produced if the fluence of a mod- eratelystrong GRBs,10−5erg/s/cm2 wouldhavebeen re- References leased on a time scale of 10s in the optical band. Even a small fraction of this will be easily observed. It is impor- Granot, J., Piran, T. & Sari, R. 1998. astro-ph/9808007. tant, therefore, to explore the expected optical emission Park, H. S.1997, ApJ490, L21. Sari, R.1997, ApJ, 489, L37. from the GRB and the early afterglow. Sari, R.,Piran, T. & Narayan,R. 1998, ApJ, 497, L17. During the GRB andthe initialemissionfromthe for- Sari, R.& Piran, T. 1999, submitted. ward shock the emission peaks in γ-rays, and only an ex-