Prompt emission of high-energy photons from gamma ray bursts

Transcription

1 Mon. Not. R. Astron. Soc. 380, 78 9 (007) doi: /j x Promt mission of high-nrgy hotons from gamma ray bursts Nayantara Guta and Bing Zhang Dartmnt of Physics and Astronomy, Univrsity of Nvada Las Vgas, Las Vgas, NV 89154, USA Acctd 007 May 5; Rcivd 007 May 3; in original form 007 Aril 10 ABSTRACT Within th intrnal shock scnario, w considr diffrnt mchanisms of high-nrgy (>1 MV) hoton roduction insid a gamma ray burst (GRB) firball and driv th xctd high-nrgy hoton sctra from individual GRBs during th romt has. Th hoton sctra of ltonic and hadronic origins ar comard within diffrnt sts of aramtr rgims. Our rsults suggst that th high-nrgy mission is dominatd by th ltonic comonnt if th fraction of shock nrgy carrid by lctrons is not vry small (.g. ɛ > 10 3 ). For vry small valus of ɛ, th hadronic mission comonnt could b comarabl to or vn xcd th ltonic comonnt in th GV TV rgim. Howvr, in this cas a much largr nrgy budgt of th firball is rquird to account for th sam lvl of th obsrvd sub-mv sctrum. Th firballs ar thrfor xtrmly infficint in radiation. For a canonical firball bulk Lorntz factor (.g. Ɣ = 400), missions abov 10 GV ar attnuatd by two-hoton air roduction rocsss. For a firball with an vn highr Lorntz factor, th cut-off nrgy is highr, and missions of 10 TV PV du to π 0 -dcay can also sca from th intrnal shocks. Th flux lvl is, howvr, too low to b dtctd by currnt TV dtctors, and ths hotons also suffr attnuation by xtrnal soft hotons. Th GLAST Larg Ara Tlsco can dtct romt mission of bright long GRBs abov 100 MV. For short GRBs, th romt mission can b only barly dtctd for narby bright ons with rlativly long durations (.g. 1 s). With th obsrvd high-nrgy sctrum alon, it aars that thr is no clan ictur to tst th ltonic vrsus hadronic origin of th gamma rays. Such an issu may b, howvr, addrssd by collcting both romt and aftrglow data. A modrat-to-high radiativ fficincy would suggst a ltonic origin of high-nrgy hotons, whil a GRB with an xtrmly low radiativ fficincy but an xtndd high-nrgy mission comonnt would b consistnt with (but not a roof for) th hadronic origin. Ky words: gamma-rays: bursts. 1 INTRODUCTION Th study of gamma ray bursts (GRBs) has bn on of th most intrsting aras in astrohysics in th ast fw yars. Ongoing obsrvational and thortical invstigations ar disclosing th hysical origin, charactristics of ths objcts as wll as bringing nw uzzls to us. GRT dtctd high-nrgy hotons from fiv GRBs coincidnt with triggrs from th BATS instrumnt (Jons t al. 1996). GRB was dtctd by GRT indndnt of BATS triggr, which has xtndd mission and with th highst nrgy hoton of 18 GV (Hurly t al. 1994). Gonzalz t al. (003) discovrd a distinct high-nrgy comonnt u to 00 MV in GRB that has a diffrnt tmoral volution with rsct to th low-nrgy comonnt. Although vn highr nrgy gamma rays/nutrinos hav not bn firmly dtctd from GRBs yt, Atkins t al. (000) hav rovidd tntativ vidnc of TV mission from GRB A. For a long tim, GRBs hav bn idntifid as otntial sourcs of ultrahigh-nrgy cosmic rays (Waxman 1995; Vitri 1997). Within th standard firball ictur (.g. Mészáros 006), thr ar about a dozn mchanisms that can roduc GV TV gamma rays from GRBs (.g. Zhang t al. 007). Mor thortical and obsrvational fforts ar ndd to fully undrstand high-nrgy mission from GRBs. From th thortical asct, it is ssntial to invstigat th rlativ imortanc of various mission comonnts to idntify th dominant mchanisms undr crtain conditions. Th high-nrgy hoton sctra xctd from GRBs during th romt and th aftrglow hass hav bn drivd by various grous. In th scnario of xtrnal shock modl th high-nrgy hoton sctra during th arly aftrglow has du to synchrotron and synchrotron slf-comton (SSC) mission by shock-acclratd rlativistic lctrons and rotons hav bn studid (Mészáros, Rs & Paathanassiou -mail: nayan@hysics.unlv.du (NG); bzhang@hysics.unlv.du (BZ) C 007 Th Authors. Journal comilation C 007 RAS

2 Promt high-nrgy hotons from GRBs ; Mészáros & Rs 1994; Panaitscu & Mészáros 1998; Totani 1998; Wi & Lu 1998; Chiang & Drmr 1999; Drmr, Bottchr & Chiang 000a; Drmr, Chiang & Mitman 000b; Panaitscu & Kumar 000; Sari & sin 001; Zhang & Mészáros 001; Fan t al. 007; Gou & Mészáros 007). In th cas of a strong rvrs shock mission comonnt, th SSC mission in th rvrs shock rgion or th crossing invrs-comton (IC) rocsss btwn th forward and rvrs shock rgions ar also imortant (Wang, Dai & Lu 001a,b; P r & Waxman 005). Th discovry of X-ray flars in arly aftrglows in th Swift ra (Burrows t al. 005) also ons th ossibility that scattring of th flaring hotons from th xtrnal shocks can giv strong GV mission (Fan & Piran 006; Wang, Li & Mészáros 006). Th ffct of cosmic infrard background on high-nrgy dlayd gamma rays from GRBs has bn also widly discussd in th litratur (Dai & Lu 00; Stckr 003; Razzaqu, Mészáros & Zhang 004; Wang t al. 004; Casanova, Dingus & Zhang 007; Muras, Asano & Nagataki 007). Th most imortant high-nrgy mission comonnt is blivd to b mittd from th romt has. Swift arly X-ray aftrglow data suggst that th GRB romt mission is of intrnal origin, unlik th xtrnal-origin aftrglow mission (Zhang t al. 006, cf. Drmr 007). Th most widly discussd intrnal modl of romt mission is th intrnal shock modl (Rs & Mészáros 1994). Within th intrnal shock modl th sctrum of high-nrgy hotons xctd during th romt has has bn studid (Pilla & Lob 1998; Bhattacharj & Guta 003; Fragil t al. 004; P r & Waxman 004; Razzaqu t al. 004; P r, Mészáros & Rs 006). Th various rocsss of high-nrgy hoton roduction in th intrnal shocks ar lctron synchrotron mission, SSC of lctrons, synchrotron mission of rotons, hoton roduction through π 0 dcay roducd in roton hoton ( γ ) intractions and radiations by scondary ositrons roducd from π + dcays. In this ar, w considr all ths rocsss slf-consistntly with a smi-analytical aroach and study th rlativ imortanc of ach comonnt within th intrnal shock scnario. Th drivd hoton sctra ar corrctd for intrnal otical dth for air roduction, which is nrgy-dndnt and also dnds on various othr aramtrs of GRBs, for xaml, thir variability tims, luminositis, th low-nrgy hoton sctra insid GRBs, and hoton sctral brak nrgis. If th lctrons cool down by synchrotron and SSC mission to trans-rlativistic nrgis, thn thy accumulat nar a valu of Lorntz factor of around unity. Th accumulatd lctrons affct th high-nrgy hoton sctrum by dirct-comton scattring and othr rocsss, which mak th sctrum significantly diffrnt from th brokn owr laws considrd in this work, s (P r, Mészáros & Rs 005; P r t al. 006) for dtaild discussions. In any cas, for th valus of aramtrs considrd in th rsnt ar this ffct is not significant. GLAST s (Ghrls & Michlson 1999) burst monitor (GBM) will dtct hotons in th nrgy rang of 10 kv 5 MV and Larg Ara Tlsco (LAT) will dtct hotons in th nrgy rang of 0 MV 1000 GV. With a larg fild of viw (> sr for LAT), GLAST will dtct high-nrgy hotons from many GRBs and on a nw ra of studying GRBs in th high-nrgy rgim. This is sulmntd by AGIL (Longo, Cocco & Tavani 00), which is dsignd to obsrv hotons in th nrgy rang of kv and 30 MV 50 GV and also has a larg fild of viw. Thr ar svral othr ground-basd dtctors, for xaml, Whil/VRITAS (Horan t al. 007), Milagro (Atkins t al. 004), which hav bn sarching or will sarch for TV hotons from GRBs. Dtctions or non-dtctions of high-nrgy gamma rays from GRBs with sac-basd and ground-basd dtctors in th nar futur would mak major sts in rvaling th hysical nvironmnt, bulk motion, mchanisms of articl acclration and high-nrgy hoton roduction, hoton dnsitis, tc., of GRBs. LCTRON SYNCHROTRON RADIATION W dfin th following thr rfrnc frams. (i) Th comoving fram or th wind rst fram is th rst fram of th outflowing jcta xanding with a Lorntz factor Ɣ with rsct to th obsrvr and th cntral ngin; (ii) th sourc rst fram is attachd to th GRB cntral ngin at a rdshift z; and (iii) th obsrvr s fram is th rfrnc fram of th obsrvr on arth, which is rlatd to th sourc rst fram by th rdshift corrction factor. W dnot th quantitis masurd in th comoving fram with rims. Th shock-acclratd rlativistic lctrons los nrgy by synchrotron radiation and SSC in th shock rgion. Assuming a owr-law distribution of frsh lctrons acclratd from th intrnal shocks and considring a continuous injction of lctrons during th roagation of th shocks, th rlativistic rimary lctron numbr distribution in th comoving fram can b xrssd as a brokn owr law in nrgy: (Sari, Piran & Narayan 1998): { dn ( ),m < <,c d 1,c < (1) in th cas of slow cooling, whr,m is th minimum injction nrgy of lctrons and,c is th nrgy of an lctron that loss its nrgy significantly during th dynamic tim-scal, known as th cooling nrgy of th lctrons. If th lctrons ar cooling fast so that vn th lctrons with th minimum injction nrgy hav coold during th dynamical tim-scal, by considring continuous injction of lctrons from th shock th comoving lctron numbr distribution can b xrssd as { dn ( ),c < <,m d 1,m <. () If th lctrons cool down to subrlativistic nrgis, thn thy accumulat nar lctron Lorntz factor γ 1. This ffct may distort th high-nrgy hoton sctrum by dirct-comton scattring (P r t al. 005, 006), and w focus on th aramtr rgim whr this ffct is not significant. Th nrgis in th sourc rst fram and th comoving fram ar rlatd as Ɣ, whr Ɣ is th avrag bulk Lorntz factor of th GRB firball in th romt has. Th xrssion for th minimum injction nrgy of lctrons in th comoving fram is,m = m c γ m ɛ g() m ɛ, whr g() = for and g() 1/6 for = (Razzaqu & Zhang 007), m 1 and m ar th masss of roton and lctron, rsctivly, and γ m c is th avrag intrnal nrgy of rotons in th comoving fram. W hav assumd to b γ C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

3 80 N. Guta and B. Zhang of th ordr of unity (in rincil γ could b smallr than unity). Th total intrnal nrgy is distributd among lctrons, rotons and th intrnal magntic filds within th intrnal shocks. Th fractions of th total nrgy carrid by lctrons, rotons and intrnal magntic filds ar rrsntd by ɛ, ɛ and ɛ B, rsctivly, whr ɛ + ɛ + ɛ B = 1. W hav assumd that all th lctrons and rotons ar acclratd in intrnal shocks. In rality, th shock-acclratd articls may b only a fraction of th total oulation and additional fractional aramtrs (ξ, ξ ) may b introducd (.g. Bykov & Mészáros 1996). In such a cas, th following tratmnts ar still gnrally valid by r-dfining ɛ = ɛ /ξ and ɛ = ɛ /ξ, whil th rlation ɛ + ɛ + ɛ B = 1 still holds. Th rlativistic lctrons los thir nrgy by synchrotron radiation and IC scattring (Panaitscu & Mészáros 1998; Sari & sin 001; Zhang & Mészáros 001). Th comoving cooling brak nrgy in th rlativistic lctron sctrum can b drivd by comaring th cooling and th dynamical tim-scals. Th comoving cooling tim-scal t cool of lctrons is a convolution of th cooling tim-scals for synchrotron radiation t syn and for IC scattring t IC : 1 = (3) t cool t syn t IC W dnot U as th intrnal nrgy dnsity of th intrnal shock, and U and U B as th nrgy dnsitis of lctrons and magntic filds, rsctivly. Th nrgy dnsity of th synchrotron radiation is U,syn = ηu 1+Y = ηɛu 1+Y (Sari & sin 001), whr th radiation fficincy of lctrons is η = [(,c /,m ), 1] for slow and fast cooling, rsctivly, and Y = L,IC = U,syn = η ɛ /ɛ B (4) L,syn U B dnots th rlativ imortanc btwn th IC and th synchrotron mission comonnts. 1 L,IC and L,syn ar th luminositis of radiations mittd in SSC and synchrotron mission of rlativistic lctrons, rsctivly. Th invrs of th cooling tim-scal of lctrons can b xrssd by th owr dividd by nrgy ( = m γ c ), 1 = 4 t cool 3 σ,tβ γ c m c (U B + U,syn ) = 4 3 σ,tβ γ cuɛ B m c (1 + Y ), (5) whr σ,t is Thomson cross-sction of lctrons, β 1 is th dimnsionlss sd of th rlativistic lctrons. Th comoving dynamical tim-scal is t dyn Ɣt v, whr Ɣ is th avrag Lorntz factor of th GRB, and t v is th variability tim in th sourc rst fram of th GRB, which dnots th variability tim-scal of th cntral ngin. Throughout th ar, w assum that lctron synchrotron radiation from th intrnal shocks is th mchanism that owr th romt gamma-ray mission in th sub-mv band. Howvr, for standard aramtrs within this scnario th cooling tim-scal of lctrons is much shortr than th dynamical tim-scal of GRBs. As a rsult th flux dnsity dn [ γ,s( γ,s) γ,s γ,s ] blow th cooling brak nrgy is roortional to 1/ γ,s and cannot xlain th hardr sctral indics obsrvd in many GRBs (Ghisllini, Clotti & Lazzati 000). If th magntic fild cratd by intrnal shocks dcays on a lngth-scal much shortr thn th comoving width of th lasma, thn th rsulting synchrotron radiation can xlain som of th broadband GRB sctra obsrvd by Swift (P r & Zhang 006). In this cas th ffctiv dynamical tim-scal is shortr by a factor of f c than its actual valu. Hnc, th ratio of th cooling and th dynamical tim-scal can b xrssd as t dyn t cool = f c (6) at th cooling nrgy =,c. Th xrssion of th lctron cooling nrgy in th comoving fram can b writtn as,c = γ,c m c = m c 3m c f c 4Ɣt v σ,t cuɛ B (1 + Y ) = 530 kv t v, Ɣ 5 f c, L iso,51 ɛ B, 1 (1 + Y ). (7) Hr and throughout th txt th convntion Q x = Q/10 x is adotd in cgs units. In th abov xrssion L iso is th luminosity corrsonding to th nrgy iso carrid by all articls and th magntic filds in th shocks. It is a fraction of th wind (outflow) luminosity L iso ηl w, whr η is th fficincy of convrting th kintic nrgy of th wind to th shock intrnal nrgy. Th luminosity L iso and intrnal nrgy U ar rlatd as U = L iso /(4πƔ r is c), whr r is = Ɣ ct v is th intrnal shock radius. Th synchrotron sctrum is a multisgmnt brokn owr law (Sari t al. 1998) saratd by svral braks, including th mission frquncy from lctrons with th minimum injction nrgy, th cooling brak frquncy, and th synchrotron slf-absortion frquncy (Rybicki & Lightman 1979). In th intrnal shocks, th magntic fild in th comoving fram can b xrssd as (Zhang & Mészáros 00): B G(ξ 1 ɛ B, 1 ) 1/ L 1/ iso,51 r 1 is,13 Ɣ 1 = G (ξ 1ɛ B, 1 L iso,51 ) 1/ Ɣ 3t, (8) v, whr ξ is th comrssion ratio, which is about 7 for strong shocks. Th synchrotron slf-absortion nrgy ( ssa ) in intrnal shocks can b xrssd as (Li & Song 004; Fan t al. 005; cf. P r & Waxman 004): ( ssa 0.4 kvl /7 γ,s,51 Ɣ3/7 r 4/7 is,13 B 1/7 5 = 0.69 kvl 5/14 iso,51 t 5/7 v, Ɣ 8/7 (ξ 1 ɛ B, 1 ) 1/14 ɛ η 1 + Y ) /7, (9) 1 Strictly saking, such a tratmnt is valid for th IC rocss in th Thomson rgim. Howvr, this is also a rasonabl aroximation if th ak of th sctral nrgy distribution of th IC comonnt is in th Thomson rgim, which is gnrally th cas for th calculations rformd in this ar. C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

4 Promt high-nrgy hotons from GRBs 81 whr L γ,s = L iso ɛ η /(1 + Y ) is th isotroic gamma-ray luminosity du to synchrotron radiation. Th cooling brak nrgy,c and th minimum injction nrgy,m of th lctrons dfin two brak nrgis in th synchrotron hoton sctrum. Th cooling brak nrgy in th hoton sctrum in th sourc rst fram is γ,c = Ɣ 3h [ ] (,c B c 4π m c m c 1.9 tv, Ɣ VƔ f ) ( ) c, B 5 L iso,51 ɛ B (1 + Y ) =.8Vt ξ 1/ 1 Ɣ 4 f c, v,. (10) (L iso,51 ɛ B, 1 ) 3/ 1 + Y Not that γ,c vry snsitivly dnds on Ɣ and som othr aramtrs so that it could bcom a larg valu whn aramtrs chang. For xaml, for B = 10 4 G, Ɣ = 400, f c = 500, L iso = rg s 1, t v = 0.01 s and ɛ B = 0.1 w gt γ,c 1.9 MV. Th brak nrgy in th hoton sctrum du to th minimum lctron injction nrgy is γ,m = Ɣ 3h ( ) ( ),m B ( ) c 4π m c m c 0.58 MVƔ ɛ B 5 ɛ = 8.5 MV ɛ (ξ 1 ɛ 1/( 1. B, 1L iso,51) Ɣ ɛ t v, ) (11) Assuming ssa < γ,m,s < γ,c,s th hoton nrgy sctrum from synchrotron radiation of slow-cooling rlativistic lctrons is as follows: dn γ,s ( γ,s ) γ,s d γ,s 4/3 γ,s γ,m,s 4/3+( 3)/ γ,s ( 3)/ γ,m,s 4/3+( 3)/ γ,c,s 1/ γ,s ( )/ ssa < γ,s γ,m,s γ,m,s < γ,s γ,c,s γ,c,s γ,s. (1) In th cas of slow-cooling lctrons for vry small valus of ɛ (.g. 10 3, which is rlvant whn th hadronic mission comonnt bcoms imortant), th brak in th hoton sctrum du to th minimum injction nrgy of lctrons gos blow th synchrotron slf-absortion nrgy. Th ordr in th sctral brak nrgis bcoms γ,m,s < ssa < γ,c,s, and th sctrum is also modifid. Th sctral indics of th lctron synchrotron sctrum for diffrnt ordring of th sctral brak nrgis ar drivd by Granot & Sari (00). For γ,m,s < γ,s < dn γ,s( γ,s) d γ,s ssa, th sctral indx of γ,s is 7/, and for γ,s < γ,m,s th sctral indx is 3. Th indics of th sctrum btwn ssa, γ,c,s and abov γ,c,s rmain as ( 3)/ and ( )/, rsctivly. Whn ssa is gratr than both γ,m,s and γ,c,s thir rlativ ordring bcoms unimortant. In that cas th sctral indics of γ,s dn γ,s( γ,s) d γ,s ar 7/ btwn γ,m,s and ssa, and ( )/ abov ssa. Blow γ,m,s th indx is 3. For fast-cooling lctrons th synchrotron hoton nrgy sctrum for ssa < γ,c,s < γ,m,s is γ,s 4/3 ssa < γ,s γ,c,s dn γ,s ( γ,s ) γ,s γ,c,s d γ,s 5/6 γ,s 1/ γ,c,s < γ,s γ,m,s. (13) 5/6 γ,m,s γ,s γ,c,s γ,m,s ( 1)/ ( )/ γ,s Whn th ordring of brak nrgis in th hoton sctrum bcoms γ,c,s < ssa < γ,m,s, th hoton nrgy sctrum is γ,s 13/8 ssa < γ,s γ,c,s dn γ,s ( γ,s ) γ,s γ,c,s d γ,s 9/8 γ,s 1/ γ,c,s < γ,s γ,m,s. (14) 9/8 γ,m,s γ,s γ,c,s γ,m,s ( 1)/ ( )/ γ,s Th total nrgy mittd in synchrotron radiation by rlativistic lctrons is iso η ɛ /(1 + Y ). Th normalization constant for th synchrotron hoton nrgy sctrum can b calculatd from γ,max dn γ,s( γ,s) η ɛ γ,s d γ,s = iso γ,min d γ,s (1 + Y ). (15) Th maximum lctron nrgy,max can b calculatd by quating th acclration tim and th shortr of th dynamical and cooling tim-scals of th rlativistic lctrons. Th xrssion of th acclration tim-scal is t acc = πζ r L( )/c = πζ /B c. Hr r L ( ) is th Larmor radius of an lctron of nrgy in a magntic fild B, ζ can b xrssd as ζ β sh y, whr β sh is th vlocity of th shock in th comoving fram of th unshockd mdium and y is th ratio of diffusion cofficint to th Bohm cofficint Rachn & Mészáros (1998). In ultrarlativistic shocks β sh 1 and numrical simulations for both aralll and obliqu shocks givs ζ 1. With t acc = min[t cool, t dyn ], (16) on can driv th maximum comoving lctron nrgy [ ( B 5 Ɣ 6,max = min 8.5 t ) v, 1/ ], Ɣ t v, B 5 GV. (17) L iso,51 ɛ B (1 + Y ) For lctrons, th cooling trm (first trm in th brackt) always dfins th maximum lctron nrgy. Th maximum synchrotron hoton nrgy in th sourc rst fram can b thn drivd as γ,max = Ɣ 3h ( ) ( ) ( ),max B c Ɣ 7 = 0.48 GV B 5 tv, Ɣ = 10 GV. (18) 4π m c m c L iso,51 ɛ B, 1 (1 + Y ) 1 + Y This is usd in quation (15) to dfin th normalization of th sctrum. Th rsult has a vry st dndnc on Ɣ. W also not that B is not an indndnt aramtr, but can b calculatd from othr aramtrs according to quation (8). For xaml, for Ɣ = 400, L iso = C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

5 8 N. Guta and B. Zhang rg s 1, t v = 0.01 s and ɛ B, ɛ 0.1, th magntic fild is of th ordr of 10 4 G and th maximum hoton nrgy bcoms a fw hundrd GV. 3 LCTRON INVRS-COMPTON SCATTRING Th rlativistic lctrons can b IC scattrd by low-nrgy synchrotron hotons insid th GRB firball and transfr thir nrgy to high-nrgy hotons. Blow, w driv th IC hoton sctrum using th lctron and synchrotron hoton sctra: dn ( ) 1 dn ( ) dnγ,s ( γ,s ) d d γ,s. (19) d d d γ,s Th lctron Lorntz factor (γ ), IC and synchrotron hoton nrgis (, γ,s ) ar rlatd as γ γ,s, this can b usd to simlify th abov quation. Th final xrssion for th IC hoton sctrum considring slow cooling of lctrons is dn ( ) d 4/3 4/3+( 3)/ γ,m,i ( 3)/ 4/3+( 3)/ γ,m,i 1/ γ,c,i ( )/ 4/3+( 3)/ γ,m,i 1/ γ,c,i ( )/ γ,k ( ) ssa,i < γ,m,i γ,m,i < γ,c,i γ,c,i < γ,k γ,k <. (0) Hr ssa,i = γ,m ssa, γ,m,i = γ,m γ,m,s, and γ,c,i = γ,c γ,c,s, whr γ,m =,m /m c = g()(m /m )(ɛ /ɛ ) and γ,c =,c /m c ar Lorntz factors corrsonding to th minimum injction nrgy of lctrons and th cooling brak nrgy of lctrons. In th cas of fast cooling γ,m,i > γ,c,i and th IC hoton sctrum has to b modifid accordingly: dn ( ) d 4/3 5/6 γ,c,i 1/ 5/6 γ,c,i ( 1)/ γ,m,i 5/6 γ,c,i ( 1)/ γ,m,i ( )/ ssa,i < γ,c,i γ,c,i < γ,m,i γ,m,i < γ,k ( )/ γ,k ( ), γ,k <. (1) In quation (1), th xrssions for ssa,i, γ,c,i and γ,m,i ar ssa,i = γ,c ssa, γ,c,i = γ,c γ,c,s and γ,m,i = γ,m γ,m,s. Whn γ,s Ɣ m c4 th cross-sction for IC scattring dcrass as th scattring ntrs th Klin Nishina (KN) rgim. A brak in th hoton sctrum at = γ,k aars whn th KN ffct bcoms imortant. W dfin a aramtr κ = γ,ak, whr Ɣ m γ,ak =max [ γ,c,s ; γ,m,s ]. Th KN rgim starts whn κ = 1 (.g. Fragil t al. 004), and c4 γ,k = Ɣ m c4 Ɣ =.5 GV. () γ,ak γ,ak,mv In th KN rgim, th missivity of lctrons dcrass by κ, and th hoton nrgy sctral indx simly follows th lctron nrgy sctral indx, that is, ( ). Th IC hoton sctrum in quation (0) can b normalizd as γ,max,i dn ( ) η ɛ Y d = iso, γ,m,i d 1 + Y whr γ,max,i = Ɣ,max is du to th KN ffct. (3) 4 PROTON SYNCHROTRON RADIATION Rlativistic rotons los nrgy by synchrotron radiation and hoto-ion (π 0, π + ) roduction insid GRBs. Thy intract with th low-nrgy hotons in th GRB nvironmnt and ions ar roducd. Thr is a thrshold nrgy for this intraction ( γ ) to han, γ 0.3 GV Ɣ, whr and γ ar roton, hoton nrgy in th sourc rst fram, rsctivly. Th π 0 s dcay to a air of high-nrgy hotons, whil th π + s dcay to nutrinos and ltons. Th thrshold condition thrfor suggsts that th hoton-ion rlatd high-nrgy sctrum is tyically mor nrgtic than th lctron IC sctrum. W assum that th roton sctrum in th intrnal shocks can b xrssd as a owr law in roton nrgy. W considr a roton sctral indx similar to lctrons for our rsnt discussion. Sinc rotons ar oor mittrs, w only considr th scnario of slow-cooling in th comoving roton sctrum: { dn ( ),m < <,c d 1,c <, (4) whr,m is th minimum injction nrgy of th rotons and,c is brak nrgy in th sctrum du to roton cooling. Th minimum injction nrgy,m = γ m c g(), whr g() = for and g() 1/6 for =. Th cooling brak nrgy can b drivd by 1 comaring th comoving and th cooling tim-scals. Th invrs of th cooling tim-scal t cool of a roton is 1 = (5) t cool t syn t π Th hoto-ion cooling tim-scal t π has bn drivd arlir in th contxt of stimation of nutrino fluxs from GRBs (Waxman & Bahcall 1997; Guta & Zhang 007). If f π is th fraction of roton nrgy going to ion roduction in th rsonanc of γ intractions, on C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

6 Promt high-nrgy hotons from GRBs 83 has 1/t π f π/t dyn whr th comoving tim-scal is t dyn = Ɣ t v. Th ak valu of γ intraction cross-sction at th rsonanc is σ γ = cm. This is much highr than th Thomson cross-sction for rotons σ,t = ( m m ) σ,t, whr σ,t = cm. W thrfor nglct th IC rocss of rotons. Substituting for t syn and t π in quation (5), w gt 1 = 4 t cool 3 σ,tβ cuɛ B m c m c + f π, (6) Ɣt v whr, β is dimnsionlss sd of rlativistic rotons. W us th gnral xrssion for f π from Guta & Zhang (007) ( 1.34 α 1 ) α 1 α +1 b < b f π ( ) = f 0 ( 1.34 α 1 1 ) α1, (7) 1 α 1 +1 b > b whr 0.9L iso,51 1 η ɛ f 0 = 810Ɣ 4t. (8) v, γ,ak,mv 1/(α ) 1/(α 1 ) 1 + Y In our rsnt discussion, α = ( + )/ and α 1 = ( + 1)/. γ,ak,mv is th ak nrgy in th lctron synchrotron hoton sctrum xrssd in MV, and L iso,51 is th GRB luminosity in unit of rg s 1, which is th tyical valu for GRB luminositis. b = 0.3Ɣ / γ,ak,gv GV is th thrshold roton nrgy for intraction with hotons of nrgy γ,ak,gv. For tyically obsrvd valus of GRB aramtrs on has b 1 PV. Th brak nrgy in th roton sctrum du to roton cooling can b calculatd by comaring th comoving and cooling tim-scals of rotons as discussd in th cas of lctrons in Sction. W assum β 1 thn for < b th xrssion of cooling brak nrgy in th comoving fram is,c = f ( c 4 Ɣt v 3 σ,tβ cuɛ B m + f ) α 1 1 ( = 108 GV f c, 0.16 L ) iso,51ɛ B f α 1 1 +, (9) c4 b Ɣt v α + 1 Ɣ t v, Ɣ 6 tv, b (PV)Ɣ t v, α + 1 whr f c = t dyn t cool dn γ,s ( γ,s ) γ,s d γ,s. Th synchrotron hoton sctrum from rlativistic rotons is { ( 3)/ γ,s γ,m,s < γ,s γ,c,s γ,c,s 1/ (30) γ,s ( )/ γ,c,s < γ,s Th minimum injction nrgy in th hoton sctrum from roton synchrotron radiation is rlatd to that from lctron synchrotron radiation as (Zhang & Mészáros 001): ( ) γ,m,s ( ) 3,m m =. (31) γ,m,s,m m Th cooling brak nrgy in th hoton sctrum from roton synchrotron radiation is th charactristic synchrotron hoton nrgy for roton nrgy,c. To normaliz th roton synchrotron sctrum, it is imortant to find out th rlativ imortanc btwn roton synchrotron radiation and γ intractions. Similar to th tratmnt of lctrons, on can dfin Y = L,γ = σ γ U,syn = σ γ Y, (3) L,syn σ,t U B σ,t whr L,γ and L,syn ar th luminositis of radiations mittd in γ intractions and synchrotron mission of rotons, rsctivly. Not that rotons intract with th synchrotron mission of th lctrons, so that Y ntrs th roblm. quation (3) suggsts that Y is usually much gratr than unity sinc σ γ σ,t. As a rsult, most of th roton nrgy is lost through γ intraction rathr than roton synchrotron radiation. Th roton synchrotron hoton sctrum can b normalizd as γ,max,s γ,m,s γ,s dn γ,s( γ,s) d γ,s d γ,s = iso ɛ η 1 + Y, whr η = (,c /,m ) α. Th maximum roton synchrotron hoton nrgy is drivd by γ,max,s = Ɣ 3h (,max 4π m c ) B c m c, whr,max is again dfind by comaring th comoving acclration tim with th shortr of th comoving dynamical and cooling tims scals (,max [50 = min B 6 Ɣ6 t ) v, 1/ ], Ɣ t v, B 6 TV. (34) L iso,51 ɛ B (1 + Y ) or (( ) 1/ ),max [191 = min ξ 1 Ɣ 3 1/ t v,, 08 ] 10 4 (ξ 1 ɛ B, 1 L iso,51 ) 1/ TV. (35) ɛ B, 1 L iso, Y Ɣ (33) In this dfinition, on avrag rotons loos 0 r cnt nrgy in th tim-scal of t π. Although it is not strictly th -folding tim-scal usually usd to dfin cooling, for ordr-of-magnitud stimats this is good nough. C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

7 84 N. Guta and B. Zhang 5 π 0 DCAY Th rlativistic rotons intract with th low-nrgy hotons and hoto-ions (π 0, π + ) ar roducd as a rsult. Th robabilitis of π 0 and π + roduction ar 1/3 and /3, rsctivly. Pions subsquntly dcay, that is, π 0 γγ and π + µ + ν µ ν µ ν µ ν +. As th cross-sction for th γγ intractions is much highr than th ak valu of γ intraction cross-sction, abov th thrshold nrgy of air roduction γγ intractions ar xctd to dominat ovr γ intractions. If th hoton nrgy is m c 1 MV in th comoving fram, thn in th sourc rst fram it is of th ordr of a fw hundrd MV as th Lorntz factors ar tyically of th ordr of fw hundrd for canonical GRBs. For xaml, for Ɣ = 400 th hotons of nrgy 400 MV can roduc hoto-ions by intraction with rotons of minimum nrgy 10 TV. Th π 0 tyically carris 0 r cnt of th roton s nrgy and th hotons roducd in π 0 dcay shar its nrgy qually. Hnc, th minimum nrgy of th hotons roducd from π 0 dcay is xctd to b 10 r cnt 1 TV. Th hoton sctrum roducd from π 0 dcay has bn drivd blow using th roton sctrum dfind in quation (4) and assuming th fraction f π /3 of rotons nrgy gos to π 0 s: { dn γ,π 0( γ,π 0) γ,π 1 f π ( γ,π 0) γ,π 0 γ,π 0 γ,π 0,c, (36) 0 d γ,π γ,π 0 γ,π 0 > γ,π 0,c whr, γ,π 0,c = 0.1,c. For th xrssion for f π, s quation (7), which contains a brak nrgy. Th brak nrgy in th hoton sctrum containd within f π is γ,π 0,b = 0.03Ɣ /ɛ br,gv GV assuming 10 r cnt of th roton s nrgy gos to th hoton roducd via π 0 dcay. ɛ br is th brak nrgy in th low-nrgy hoton sctrum (in th scnario of slowly cooling lctrons it is th cooling brak nrgy in th hoton sctrum and for fast cooling lctrons it is th hoton nrgy corrsonding to th minimum injction nrgy of lctrons). Th hoton flux can b normalizd in th following way: γ,π 0,max dn γ,π 0( γ,π 0) γ,π 0 d γ,π 0 = iso ɛ η Y, (37) d γ,π 0 γ,π Y,min whr γ,π 0,min=30Ɣ GV and γ,π 0,max = 0.1,max. Although high-nrgy hotons ( TV) ar absorbd by lowr nrgy hotons and + airs ar roducd, at xtrm nrgis th air roduction cross-sction dcrass with incrasing nrgy (Razzaqu t al. 004). Hnc, ultrahigh-nrgy hotons can sca from th intrnal shocks for suitabl aramtrs dnding on th valus of thir various aramtrs and th low-nrgy hoton sctra. 6 SYNCHROTRON RADIATION OF POSITRONS PRODUCD IN π + DCAY Th shock-acclratd rotons may intract with th low-nrgy hotons to roduc π + s along with π 0 s as discussd in th rvious sction. Th π + s subsquntly dcay to muons and nutrinos. Th nrgtic muons dcay to ositrons and nutrinos (γ π + µ + ν µ + ν µ ν µ ν ). Th chargd ions, muons and th ositrons ar xctd to los nrgy through synchrotron radiation and IC insid th shock rgion. As th Thomson cross-sction for ositrons is much largr than ions or muons, thy ar xctd to mit much mor radiation comard to th havir chargd articls. On th othr hand, sinc ths ositrons ar vry nrgtic, most IC rocsss han in th KN rgim. W thrfor nglct th contribution of th ositron IC rocsss. Th ositron synchrotron sctrum roducd in γ intractions can b drivd in th following way. Th fraction of th rotons nrgy tranfrrd to ions is dnotd by f π (quation [7]). If w assum that th final stat ltons shar th ion s nrgy qually thn on fourth of th ion s nrgy gos to th ositron. Th nrgy of th ositron sctrum dn( + ) at th nrgy d + + can b xrssd using th roton sctrum dfind in quation (4): { dn( +) + f π ( +) + + +,c, (38) d > +,c whr, +,c is th cooling brak nrgy in th ositron scrum and ( 1.34 α 1 ) + α 1 α +1 f π ( +) = f + + < + b b 0, (39) 1.34 α 1 1 α 1 +1 ( + + b ) α1 1 + > + b whr f 0 has bn dfind in quation (8), + b = 0.05 b, b = 0.3 GVƔ /ɛ br,gv, and ɛ br,gv is th brak nrgy in th hoton sctrum as dfind arlir. Th ositron sctrum in quation (38) can b normalizd using th total nrgy carrid by th ositrons, +,max dn( +)( +) + d + = 1 ɛ η Y iso. (40) d Y,min Th maximum and minimum ositron nrgis ar +,max = 0.05,max and +,min = 15Ɣ GV (which is 6 TV for Ɣ = 400). Th synchrotron hoton sctrum from th ositrons can b subsquntly drivd using th sam tratmnt for rimary lctrons as discussd in Sction. Th IC mission is in th KN rgim and thrfor not imortant. Also, hotons having nrgis abov a fw hundrd GV ar annihilatd by lowr nrgy hotons as discussd in th following sction. Th rlativistic muons roducd in π + dcay los nrgy by synchrotron radiation. W comar th dcay and synchrotron nrgy loss tim-scals of th high-nrgy muons. Th maximum nrgis of ositrons can b calculatd in this way. If th muons dcay bfor losing nrgy significantly high-nrgy ositrons ar roducd carrying C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

8 Promt high-nrgy hotons from GRBs 85 aroximatly 5 r cnt of th initial roton s nrgy. On th othr hand, if th muons los nrgy bfor thy dcay lowr nrgy ositrons ar roducd. Ths ositrons radiat nrgy and roduc lowr nrgy hotons. Th muons initially carry aroximatly 10 r cnt of th rlativistic rotons nrgy hnc, w xct th low-nrgy hoton flux roducd by cooling of ositrons is lowr than that roducd by rlativistic lctrons if ɛ and ɛ ar comarabl. 7 INTRNAL PAIR-PRODUCTION OPTICAL DPTHS OF HIGH-NRGY PHOTONS Insid GRBs high-nrgy hotons intract with low-nrgy hotons to roduc lctron-ositron airs (.g. Baring & Harding 1997; Lithwick & Sari 001). Th otical dth dnds on th valus of various aramtrs of th GRB firball. W follow th aroach discussd in Bhattacharj & Guta (003) to driv intrnal otical dths of GRBs in dtail. For two hotons (a high-nrgy hoton γ h and a low-nrgy hoton γ l ), th air roduction cross-sction dnds on th nrgis of th hotons and th angl btwn thir dirctions of roagation. Th cross-sction is (Brsttskii, Lifshitz & Pitavskii 198): σ γh γ l ( γ h, γ l,θ) = 3 [ 16 σ T(1 β ) (3 β 4 )ln 1 + ] β β ( β ), (41) 1 + β whr σ T is th Thomson cross-sction, and β = [1 ( γ l,th / γ l )] 1/ is th cntr of mass dimnsionlss sd of th air roducd. Th thrshold nrgy of air roduction with a high-nrgy hoton of nrgy γ h is γ l,th = (m c ) γ h (1 cosθ). (4) For th hotons with nrgy highr than th thrshold nrgy, th air roduction cross-sction dcrass with incrasing hoton nrgy (Jauch & Rohrlich 1955; Razzaqu t al. 004). In this work, w calculat intrnal otical dths in diffrnt nrgy rgims using th cross-sctions with diffrnt nrgy dndncis. Th man fr ath for γ h γ l intractions l γh γ l can b calculatd using th low-nrgy hoton sctrum: ( ) l 1 γ h γ l θ ( dn γ h,θ) = d γl γl ( γ l σ d γ γh γ l γ h, γ l,θ ), (43) l and l 1 γ h γ l ( γ h ) = 1 γ l,th +1 1 d(cos θ)(1 cos θ)l 1 γ h γ l θ ( γ h,θ), (44) whr dnγ l ( γ ) l is th scific numbr dnsity of low-nrgy hotons insid th GRB. Th low-nrgy hoton sctrum is obsrvationally d γ l known, as rvald by gamma-ray dtctors such as BATS and Swift. Thortically, it corrsonds to th lctron synchrotron comonnt as discussd in Sction, which is a brokn owr-law sctrum saratd by th synchrotron slf-absortion brak, th minimum injction brak and th cooling brak. Th low-nrgy hoton flux is rlatd to th obsrvd luminosity through γl,max dn γ l ( γ l ) γl d γ d γl = U γ = L so l,ssa γ l 4πcr is Ɣ, (45) whr L so is th isotroic gamma-ray luminosity. W hav takn it to b qual to th luminosity of th synchrotron hotons mittd by lctrons: L so = L,syn = ɛη L iso 1+Y. In quation (44) w hav thr variabls: angl θ and hoton nrgis γ l and γ h. To simlify th intgration in quation (44), w transform th intgral with a nw variabl following Gould & Schrdr (1967): s = γ l γ h (1 cos θ) = γ l = s (m c ) γ 0 (46) l,th with s 0 = γ l γ h (m c, and = 1 (1 cos θ). As ) β = (1 1/s) 1/, th air roduction cross-sction can b xrssd as a function of th nw variabl s. It is thn ossibl to writ quation (44) as l 1 γ h γ l ( γ h ) = 3 8 σ T whr Q[s 0 ( γ l )] = ( ) m c 4 [ γ h s0 ( γ l ) 1 m c4 γ h sσ (s)ds, dn γ l ( γ l ) γ l d d γ γ l l ] Q [ s 0 ( γ l )], (47) and σ (s) = 16 σ γh γ l 3 σ T. For modrat valus of s w us σ (s) 1 and for s 1 it can b aroximatd as σ (s) ln(s)/s. Th xrssions for Q[s 0 ( γ l )] ar (s 0 1)/ and s 0(ln s 0 1), rsctivly, in th two cass. Substituting for Q[s 0 ( γ l )] in quation (47) w driv th final xrssion for lγ 1 h γ l ( γ h ). Th intrnal otical dth τ int ( γ h ) is th ratio of comoving tim-scal and th man tim btwn two air roduction intractions: τ int ( γ h ) = r is Ɣc cl 1 γ h γ l ( γ h ). (49) C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9 (48)

9 86 N. Guta and B. Zhang Th final hoton nrgy sctrum to b obsrvd on arth from narby GRBs (nglcting furthr attnuations with th infrard background and cosmic microwav background) can b obtaind by corrcting th original flux for th intrnal otical dth and th rdshift z of th sourc: γ,ob dn γ,ob ( γ,ob ) d γ,ob = 0 1 4πdz (1 + z) dn γ ( γ ) γ x[ τ int ( γ )], (50) d γ whr d z = c z dz (51) H 0 + m (1 + z ) 3 is th comoving distanc of th sourc, H 0 = 71 km s 1 Mc 1 is th Hubbl constant, and = 0.73 and m = 0.7 ar adotd in our calculations. 8 PHOTON SPCTRUM FROM SCONDARY LCTRONS AND POSITRONS Th scondary airs carry a significant fraction of nrgy in th rimary sctrum, and this nrgy is r-radiatd and convrtd to hotons. A mor ralistic tratmnt should considr a hoton-air cascad rocss, which rquirs numrical calculations (P r & Waxman 004; P r t al. 006). Hr instad w stimat th mission from th scondary airs. W first calculat th hoton nrgy sctra gnratd by diffrnt hysical rocsss as discussd arlir. Th hoton sctra ar thn corrctd for intrnal otical dths and subsquntly th total nrgis carrid by ths hotons ar calculatd by intgrating th corrctd hoton nrgy sctra ovr hoton nrgis. If w subtract th total nrgis carrid by ths high-nrgy hotons from thir intial nrgis bfor including th ffcts of intrnal otical dths, w gt th nrgis of th scondary and + roducd in γγ intractions. Ths airs ar xctd to hav sctral indics similar to th high-nrgy hotons. With th knowldg of thir sctral indics and th total nrgis carrid by thm th synchrotron hoton sctra radiatd by ths scondary ltons ar calculatd. For th aramtrs adotd in this ar, it turns out that th mission contribution from th scondaris is blow th mission lvl of th rimaris, and hnc, dos not significantly modify th obsrvd th sctrum. W thrfor do not includ this comonnt in Figs 1 5, but caution that such a fdback rocss could b otntially imortant for th aramtr rgims with high oacity. W rfr to P r & Waxman (004) and P r t al. (006) for mor dtaild tratmnts of such cass. 9 SYNTHSIZD SPCTRA AND DTCTABILITY Using th rocdur dlinatd abov, w hav calculatd th broad-band mission sctrum from intrnal shocks for a wid rang of aramtr rgims. In articular w focus on th various high-nrgy mission comonnts discussd abov and thir rlativ significanc. Our rsults ar rsntd in Figs 1 5. In ach st of calculations w hav rsntd th intrnal otical dth aftr th final hoton nrgy sctrum. For articls acclratd by ultrarlativistic shocks th sctral indx is xctd to b about.6 Lmoin & Plltir (003). Aftrglow modlling suggsts a largr scattr of valus for rlativistic shocks, but =.3 is clos th man valu of th data (Panaitscu & Kumar 000). In all our calculations, th sctral indics of rlativistic lctrons and rotons ar both assumd as =.3. Figs 1 4 ar th calculations for a tyical long GRB with duration T 90 = 0 s at rdshift z = 1 (10 s in th sourc rst fram). Sinc w do not know th hysical condition of th intrnal shocks from th first rincils, w vary th aramtr rgim in a wid rang. In ach st of calculations, w dsign th aramtrs to mak th lctron synchrotron mission aking at th sub-mv rang ( 0.36, 0.13, 0.6 and 0.5 MV for Figs 1,, 3 and 4, rsctivly), as suggstd by th data. Th global nrgtics of th GRB is also adjustd so that th gamma-ray luminosity in th sub-mv rang is about rg s 1 as suggstd by th obsrvations. Th variability tim-scal for ths calculations is takn as t v = 0.01 s. Th bulk Lorntz factor is adotd as Ɣ = 400 in Figs 1 3, as suggstd by th rcnt arly otical aftrglow obsrvations (Molinari t al. 007). In ordr to chck how Ɣ affcts th sctra, w also calculat th cas of Ɣ = 1000 for th aramtr st of Fig. 1, which is rsntd in Fig. 4. In all th figurs, th diffrnt comonnts of th hoton nrgy sctrum from a GRB for both lctrons () and rotons () ar dislayd with diffrnt lin styls/colours. Th obsrvd nrgy fluxs γ,ob dn γ,ob ( γ,ob ) γ,ob in unit of rg cm s 1 ar lottd against th obsrvd hoton nrgy γ,ob (V). Th grn long dashd curvs rrsnt th synchrotron mission from th rlativistic lctrons. Th short dashd curvs (blu) rrsnt th IC sctrum from nrgtic lctrons; th dash dottd curvs (light blu) rrsnts th synchrotron mission of th rlativistic rotons; th tril short dashd curvs (orang) rrsnt for th synchrotron mission of th rlativistic ositrons roducd in π + dcays; th ultrahigh-nrgy mission comonnt from π 0 dcays is shown by th doubl short dashd curvs (black) in th xtrmly high-nrgy rgim. Th thin black solid lins rrsnt th synthsizd sctra of various comonnts without including th ffct of air roduction attnuation. Dnding on aramtrs, th air oacity bcoms imortant in th GV TV rang. Th thick black solid lins rrsnt th final hoton sctrum aftr including th intrnal otical dths. In ordr to chck whthr th rdictd high-nrgy comonnts ar dtctabl by GLAST, w also lot an indicativ GLAST snsitivity thrshold in th 100 MV 100 GV nrgy rang. Th GLAST snsitivity stimat is basd on th critrion of dtcting at last a fw hotons in th band basd on th avrag ffctiv ara and hoton incoming znith angl of LAT. Background is ngligibl for GRB dtctions. This givs a rough flunc thrshold of 10 7 rg cm (B. Dingus, 007, rivat communication). Th flux thrsholds adotd in all th figurs ar thrfor drivd from th obsrvd durations. For T 90 = 0 s, this givs a flux thrshold of 10 8 rg cm s 1. Th snsitivity of VRITAS to hoton abov nrgy 00 GV has also bn shown in our figurs with ink dottd lin. It is 10 8 rg cm s 1 (D. Horan, 007, rivat communication). C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

10 Promt high-nrgy hotons from GRBs 87 Figur 1. A ltonic-comonnt-dominatd slow cooling sctrum. (a): th diffrnt comonnts of th hoton nrgy sctrum from th intrnal shocks for th following aramtrs in th slow-cooling rgim: iso = rg, L iso = 10 5 rg s 1, t v = 0.01 s and f c = 500. Th thick solid black curv rrsnts th final sctrum aftr including th ffct of intrnal otical dths. Th thin solid black curv rrsnts th synthsizd sctrum bfor including th ffct of intrnal otical dths. Th long dashd (grn) curv is th lctron synchrotron comonnt; th short dashd (blu) curv is th lctron IC comonnt; th doubl short dashd (black) curv on th right sid is for π 0 dcay comonnt; th tril short dashd (orang) lin rrsnts th synchrotron radiation roducd by ositrons gnratd in π + dcays; th dash dottd (light blu) lin rrsnts th roton synchrotron comonnt. Th tiny rd horizontal lin btwn 10 8 and V rrsnts GLAST s thrshold. Th ink dottd horizontal lin abov V rrsnts th snsitivity of VRITAS xrimnt. (b) Intrnal otical dths lottd against nrgy for th aramtrs adotd in (a). Fig. 1 is a standard slow-cooling ltonic-dominant cas. Th shock quiartition aramtrs ar ɛ = 0.4 and ɛ B = 0.. Th isotroic shock luminosity is L iso = 10 5 rg s 1. Th slow cooling factor f c = 500 is adotd, which suggsts that th ost-shock magntic fild dcays on a lngth-scal shortr than th comoving scal (P r & Zhang 006). Th thick black lin shown on th right sid around V is th π 0 comonnt aftr including th ffct of absortion du to air roduction, indicating th rduction of air oacity at high nrgis (Fig. 1b, s also Razzaqu t al. 004). In this figur, th brak nrgis in th hoton nrgy sctrum aar of th ordr of ssa < γ,m < γ,c in th lctron synchrotron and IC sctral comonnts. Th sctral indx of th hoton nrgy sctrum is 4/3 btwn ssa and γ,m, ( 3)/ btwn γ,m and γ,c, and ( )/ abov γ,c. Sinc ɛ is larg, th ltonic comonnts ar many ordrs of magnitud strongr than th hadronic comonnts. Th valu of Y is much largr than 1, so that th roton synchrotron comonnt is blow th comonnts du to π 0 dcay and ositron synchrotron radiation. W vary th valus of th quiartition aramtrs (ɛ, ɛ B, ɛ ) and study th variations in th hoton nrgy fluxs gnratd by various rocsss. Th mission lvl of th lctron IC sctral comonnt dcrass with dcrasing ɛ (fixing ɛ B ) sinc Y is dcrasing. Morovr, as w dcras ɛ th minimum injction nrgy of lctrons γ,m also dcrass. In th slow cooling rgims, it is γ,c that dfins th ak nrgy in th lctron synchrotron sctrum, which could b adjustd to th sub-mv rang by adoting a suitabl f c valu. Th chang in γ,m thrfor mainly affcts th calculatd intrnal otical dth. By lowring ɛ, w chck th aramtr rgim whr th hadronic comonnt bcoms comarabl. Sinc ltrons ar much mor fficint mittrs than rotons, th aramtr rgim for th hadronic comonnt to b comarabl to th ltonic comonnt in th high-nrgy rgim is ɛ /ɛ m /m < A similar conclusion has bn drawn for th xtrnal shocks (Zhang & Mészáros 001). In Fig., with ɛ = 10 3, ɛ B = 0.05 and ɛ = In ordr to adjust γ,c to th sub-mv rang, f c = is ndd. In ordr to match th obsrvd 3 Proton nrgy loss and thir contribution to high-nrgy hoton mission in th arly aftrglow has has bn studid arlir by P r & Waxman (005). Our rsults for th romt mission has ar gnrally consistnt with thm. In ordr for th roton synchrotron comonnt to b significant, vn smallr ɛ (than 10 3 ) is dmandd. Considring that hoton-ion mission is mor fficint than roton synchrotron mission, th condition ɛ /ɛ m /m < 10 3 can allow th hadronic comonnts to b comarabl to (but not dominant ovr) th ltonic comonnts. C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

11 88 N. Guta and B. Zhang Figur. A slow-cooling sctrum with significant hadronic contribution. (a): Th sctra of various comonnts. Paramtrs: ɛ = 10 3, ɛ B = 0.05, ɛ = 0.849, t v = 0.01 s, f c = 50000, iso = rg and L iso = rg s 1. Th sam lin styls hav bn usd as in Fig. 1. (b): Th corrsonding intrnal otical dths. MV mission flux by lctron synchrotron, a larg nrgy budgt is ndd du to a small ɛ : iso = rg and L iso = rg s 1. Such a larg nrgy budgt has bn suggstd bfor (Totani 1998), but aftrglow obsrvations and modlling in th r-swift ra hav gnrally disfavord such a ossibility (Panaitscu & Kumar 00). In th Swift ra, howvr, a larg aftrglow kintic nrgy for som GRBs is not ruld out. For xaml, th bright aftrglow of GRB dmands a hug kintic nrgy if th aftrglow is roducd by isotroic xtrnal shocks (Mundll t al. 007; Schady t al. 007). Modlling som X-ray aftrglows blow th cooling frquncy rquirs a low ɛ B and/or a larg aftrglow kintic nrgy at last for som GRBs (Zhang t al. 007). W thrfor still considr such a ossibility. In Fig., th brak nrgy in th hoton nrgy sctrum du to th minimum injction nrgy of lctrons is blow th synchrotron slf-absortion nrgy. Th brak nrgis aar of th ordr of γ,m < ssa < γ,c in th synchrotron and IC lctron sctra. Th sctral indx of th hoton nrgy flux is 7/ btwn γ,m and ssa, ( 3)/ btwn ssa and γ,c, and ( )/ abov γ,c. W can s that in th TV nrgy rgim byond th maximum lctron synchrotron nrgy, th ositron synchrotron mission from π + dcay bcoms dominant. Morovr, whn ɛ is small, Y is small, hnc Y bcoms small. In this cas th roton synchrotron comonnt bcoms comarabl to th sctral comonnts du to synchrotron radiation of th scondary ositrons and π 0 dcays. Th intrnal otical dth is lottd in Fig. (b), which aks at a highr nrgy than that in Fig. 1(b). If th ost-shock magntic fild dos not dcay within a short distanc (f c = 1), intrnal shocks ar in th standard fast-cooling rgim. W calculat such a cas in Fig. 3. Th shock aramtrs ar ɛ = 0.6, ɛ B = 0., L iso = 10 5 rg s 1, iso = rg. In this cas, th brak nrgis aar as of th ordr of C < ssa < m. Th hoton nrgy sctral indics ar 13/8, 1/ and ( )/, rsctivly, in th thr nrgy rgims. Th air oacity dnds on th bulk Lorntz factor. Whn Ɣ is larg nough, th ultrahigh-nrgy hotons would hav lowr intrnal otical dth and may sca from th intrnal shocks (Razzaqu t al. 004). To tst this, in Fig. 4, w r-calculat with th aramtr st for Fig. 1, but incras Ɣ to Th slow-cooling aramtr f c is adjustd to 50 to maintain th sub-mv nrgy ak. Th rsults indd suggst that th attnuation of th high-nrgy hotons is wakr. Th obsrvational brakthough in 005 suggsts that at last som short GRBs ar low-flunc, narby vnts that hav a distinct rognitor than long GRBs (Barthlmy t al. 005; Brgr t al. 005; Fox t al. 005; Ghrls t al. 005; Villasnor t al. 005; Bloom t al. 006). To chck th rosct of dtcting short GRB romt mission with high-nrgy dtctors such as GLAST, w rform a calculation C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

12 Promt high-nrgy hotons from GRBs 89 Figur 3. A ltonic-comonnt-dominatd fast-cooling sctrum. (a): Th sctra of various comonnts. Paramtrs: ɛ = 0.6, ɛ B = 0., ɛ = 0., t v = 0.01 s, f c = 1, iso = rg and L iso = 10 5 rg s 1. Th sam lin styls hav bn usd as in Fig. 1. (b): Th corrsonding intrnal otical dths. for th aramtrs of a short GRB in Fig. 5. Du to thir short durations, short GRB dtctions ar favorabl for high luminosity and rlativly long durations. W thrfor tak an otimistic st of aramtrs with L iso = rg s 1, T 90 = 1s,andz = 0.1. Othr aramtrs includ: Ɣ = 800, t v = 1 ms, ɛ = 0.4, ɛ B = 0., ɛ = 0.4, f c = 50. Th hoton flux from synchrotron radiation of lctrons aks at 0.1 MV. Fig. 5(a) suggsts that th high-nrgy comonnt of such a burst is barly dtctabl by GLAST. Th intrnal otical dth of this st of aramtrs dos not grow to vry larg valus (maximum 10), so that th attnuation signatur is not significant in Fig. 5(a). Th di around svral V corrsonds to th otical dth ak, abov which th attnuatd flux starts to ris. Th abrut dro at svral V corrsonds to th disaaranc of th lctron IC comonnt at high nrgis. 10 CONCLUSIONS AND DISCUSSION W hav calculatd th broad-band sctrum of GRBs from intrnal shocks for a wid rang of aramtr rgims. W did not tak into account th xtrnal attnuation of TV hotons by th infrard radiation background and that of th PV hotons by th cosmic microwav background. Ths xtrnal rocsss would furthr attnuat our calculatd sctrum in high-nrgy rgims, and rrocss th nrgy to dlayd diffus mission (Dai & Lu 00; Stckr 003; Razzaqu t al. 004; Wang t al. 004; Casanova t al. 007; Muras t al. 007). Such rocsss ar not rlvant for most of th calculations rsntd, howvr, sinc th intrnal attnuation alrady cuts th obsrvd sctrum blow TV. Thy ar, howvr, imortant for high Lorntz factor cass in which mor high-nrgy hotons ar lakd out of th intrnal shock rgion. Th xtrnal attnuation is also rominant for high-nrgy mission from th xtrnal rvrs/forward shocks and th xtrnal IC rocsss rlatd to X-ray flars. Ths rocsss hav bn xtnsivly discussd in othr ars (rfrncd in Introduction) and thy ar not discussd in this ar. For narby GRBs (.g. z < 0.3), TV mission is transarnt. It is ossibl that ground-basd Chrnkov dtctors such as VRITAS, Milagro would dtct TV gamma rays from narby nrgtic GRBs. In rvious tratmnts of hadronic comonnts from intrnal shocks (Bhattacharj & Guta 003; Fragil t al. 004), th shockacclratd rotons ar assumd to carry m /m tims mor nrgy than lctrons. This ffctivly fixd ɛ m /m, which is not justifid from th first rincil. In this ar, w hav takn all th quiartition aramtrs ɛ, ɛ and ɛ B as fr aramtrs, and xlor th rlativ imortanc of various comonnts in diffrnt aramtr rgims. Th dominant hadronic comonnt mission bcoms intrsting only whn ɛ is xtrmly small. Givn th sam obsrvd lvl of sub-mv sctrum, th total nrgy budgt of th GRB nds to b vry larg. C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9

13 90 N. Guta and B. Zhang Figur 4. Th cas of a highr Lorntz factor. (a): Th sctra of various comonnts. Paramtrs: Ɣ = 1000 and f c = 50. All th othr aramtrs ar th sam as in Fig. 1. (b): Th corrsonding intrnal otical dths. Inscting th calculatd sctra for diffrnt aramtr sts (Figs 1 4), on finds that thr is no clan ictur to tst th ltonic vrsus hadronic origin of th gamma rays. Such an issu may b, howvr, addrssd by collcting both romt and aftrglow data. A modrat-tohigh radiativ fficincy would suggst a ltonic origin of high-nrgy hotons, whil a GRB with an xtrmly low radiativ fficincy but an xtndd high-nrgy mission comonnt would b consistnt with (but not a roof for) th hadronic origin. Th romt mission roducd by ltons including th ffct of air roduction has bn discussd by P r & Waxman (004), P r t al. (006). Thy calculatd th mrgnt hoton sctra for GRBs locatd at z = 1. Th lowr cut-off nrgy in th hoton flux roducd by ltons is dtrmind by th synchrotron slf-absortion nrgy, th minimum injction nrgy or th cooling nrgy dnding on th valus of th various GRB aramtrs. Our ltonic-comonnt-dominatd cass ar consistnt with thir rsults, although w do not xlor cass with vry high comactnss. If th lctrons cool down to trans-rlativistic nrgis, thn thir high-nrgy sctrum significantly dviats from brokn owr law (P r t al. 005, 006). For our choic of valus of th GRB aramtrs this ffct is not imortant. Razzaqu t al. (004) stimatd th intrnal otical dth for air roduction and showd that at PV nrgis th otical dth dcrass with incrasing hoton nrgis. W hav rdrivd th otical dths for valus of GRB aramtrs. Th rsults ar gnrally consistnt with that of Razzaqu t al. (004) xct that th growth of otical dth with incrasing nrgy is mor gradual bfor th otical dth ak. This is a rsult of including th whol low-nrgy hoton sctrum (rathr than th thrshold nrgy hotons) for calculating th air roduction otical dth. Th otical dths dnd on th cross-sction of γγ intractions, th low-nrgy hoton sctra, th various brak nrgis in thos sctra, luminositis, variability tims and th GRB Lorntz factors. A chang in valus of any of ths aramtrs may affct th valus of th otical dths at various nrgis. For high bulk Lorntz factors, th π 0 comonnt may aar in th final sctra du to th rducd otical dths around PV nrgy. Howvr, ths ultrahigh-nrgy hotons will b immdiatly absorbd in th GRB nighbourhood by cosmic microwav hotons (Stckr 003). Th rradiatd nrgy by th + airs would non th lss contribut to th diffus high-nrgy gamma-ray background (Casanova t al. 007). Ucoming gamma-ray dtctors hav a good chanc of dtcting romt mission from GRBs and rval thir hysical natur during th romt has. Dtction of th hadronic comonnts is difficult but it would b ossibl to infr th dominanc of ths comonnts by a coordinatd broadband obsrvational camaign if thy ar indd imortant. Mor gnrally, dtction or non-dtction of high-nrgy hotons in th romt has would constrain th valus of various GRB aramtrs. In articular, th air attnuation fatur would hl to constrain th bulk Lorntz factor of th firball. Comard with GRT, GLAST has a 10 tims largr collcting ara and a largr fild of C 007 Th Authors. Journal comilation C 007 RAS, MNRAS 380, 78 9