Formation of hard very high energy gamma-ray spectra of blazars due to internal photon photon absorption

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1 Mon. Not. R. Astron. So. 387, (2008) doi: /j x Formtion of hrd very high energy gmm-ry spetr of lzrs due to internl photon photon sorption Felix A. Ahronin, 1,2 D. Khngulyn 2 nd L. Costmnte 3 1 Dulin Institute for Advned Studies, 31 Fitzwillim Ple, Dulin 2, Irelnd 2 Mx-Plnk-Institut für Kernphysik, Supferhekweg 1, D69117 Heidelerg, Germny 3 Stnford University, W.W. Hnsen Experimentl Physis Lortory nd Kvli Institute for Prtile Astrophysis nd Cosmology, Stnford, CA , USA Aepted 2008 April 10. Reeived 2008 April 1; in originl form 2008 Jnury 21 1 INTRODUCTION The reent reports on detetions of very high energy (VHE) gmmrys from lzrs with redshifts z 0.1 (see e.g. Hinton 2007, for review) initited renewed detes on the interprettion of TeV gmm-ry spetr of lzrs, in prtiulr in the ontext of the level of the diffuse extrglti kground rdition t optil nd infrred (IR) wvelengths, often lled lso s extrglti kground light (EBL). Initilly, the tight link etween these two topis TeV lzrs nd EBL eme sujet of hot disussions prompted y multi (up to 20) TeV gmm-rys deteted from nery BL L ojet, Mkn 501 (Ahronin et l. 1999), nd y the reports liming detetion of high fluxes of EBL t fr-infrred (FIR) wvelengths (Huser et l. 1998; Shlegel, Finkeiner & Dvis 1998; Lgge et l. 1999; Finkeiner, Devis & Shlegel 2000). However, it ws quikly reognized tht these two lims hrdly E-mil: felix.hronin@dis.ie ABSTRACT The energy spetr of TeV gmm-rys from lzrs, fter eing orreted for interglti sorption in the extrglti kground light (EBL), pper unusully hrd, ft tht poses hllenges to the onventionl models of prtile elertion in TeV lzrs nd/or to the EBL models. In this pper, we show tht the internl sorption of gmm-rys used y intertions with dense nrrow-nd rdition fields in the viinity of ompt gmm-ry prodution regions n led to the formtion of gmm-ry spetr of n lmost ritrry hrdness. This llows signifint relxtion of the urrent tight onstrints on prtile elertion nd rdition models, lthough t the expense of enhned requirements to the ville non-therml energy udget. The ltter, however, is not ritil issue, s long s it n e lrgely ompensted y the Doppler oosting, ssuming lrge (>10) Doppler ftors of the reltivistilly moving gmm-ry prodution regions. The suggested senrio of formtion of hrd gmm-ry spetr predits detetle synhrotron rdition of seondry eletron positron pirs whih might require revision of the urrent stndrd prdigm of spetrl energy distriutions of gmm-ry lzrs. If the primry gmm-rys re of hdroni origin relted to pp or pγ intertions, the internl gmm-ry sorption model predits neutrino fluxes lose to the detetion threshold of the next genertion high-energy neutrino detetors. Key words: BL Lerte ojets: generl diffuse rdition gmm-rys: oservtions gmm-rys: theory. ould e omptile within ny stndrd model of TeV lzrs (see Ahronin 2001, for review). A distint feture of extrglti gmm-ry stronomy is tht VHE gmm-rys emitted y distnt ( 100 Mp) ojets rrive fter signifint sorption used y their intertions with EBL vi the proess γγ e + e (Nikishov 1962; Jelley 1966; Gould & Shrèder 1967). The reonstruted, i.e. the sorption-orreted gmm-ry spetrum from soure t redshift z, J 0 (E) = J os (E) e τ(e,z) depends on the flux nd energy spetrum of EBL through the optil depth τ(e, z). Thus, t energies where τ(e, z) 1, the primry gmm-rys suffer strong spetrl deformtion. The EBL onsists of two emission omponents produed y strs nd prtly sored/re-emitted y dust throughout the entire history of glxy evolution. As result, two distint umps re expeted in the spetrl energy distriution (SED) of EBL t ner-infrred (NIR) nd FIR wvelengths, with mid-infrred (MIR) vlley etween these two umps (see e.g. Huser & Dwek 2001). Generlly, for lmost ll EBL models, τ(e) is strong funtion of energy elow 1 TeV nd ove 10 TeV; etween 1 nd 10 TeV, the energy dependene of τ(e) is muh weker (Ahronin 2001). Consequently, one Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS

2 should expet signifint distortion of the VHE spetr of lzrs t energies elow 1 TeV nd ove 10 TeV, provided tht t these energies τ 1. One n reformulte this sttement in different wy. Nmely, for stndrd ( deent ) intrinsi gmm-ry spetrum, the oserver should detet very soft (steep) spetr t energies elow 1 TeV nd ove 10 TeV from ojets for whih τ 1 t orresponding energies. This ondition is sfely stisfied, given the onstrints on the minimum EBL flux imposed y glxy ounts, for lzrs with redshifts z 0.15 like 1ES nd for nery ojets with z 0.03 like Mkn 501. Even though the deteted gmm-ry spetr from oth ojets in the orresponding energy intervls re indeed quite steep with photon index 3 (Ahronin et l. 1999, 2006), they pper not suffiiently steep to ompenste the funtion f (E) = e τ(e), nd thus to prevent roust onlusion tht the intrinsi VHE gmm-ry spetr of these lzrs re unusully hrd. In the se of Mkn 501, the intrinsi spetrum hs nonstndrd shpe with possile pile-up ove 10 TeV whih hs een interpreted s IR kground TeV gmm-ry risis (Protheroe & Meyer 2000) or need to invoke drmti ssumptions like violtion of the Lorentz invrine (see e.g. Kifune 1999). However, more prgmti view whih presently domintes in oth IR nd gmm-ry stronomil ommunities, trets this risis s somewht exggerted, espeilly given the miguity of extrtion of the truly diffuse extrglti FIR omponent from the muh higher kgrounds of lol origin (see e.g. Huser & Dwek 2001). Nevertheless, the reently reported low limits on the EBL t MIR wvelengths from the Spitzer deep osmologil surveys ppered quite high, for exmple t 70 μm the EBL flux should exeed 7.1 ± 1.0 nw m 2 sr (Dole et l. 2006). This implies tht the prolem is not yet over, nd one my still fe hllenge with the interprettion of the energy spetr of Mkn 501 nd Mkn 421 in the multi-tev energy domin. On the other hnd, the reent detetions of TeV gmm-rys from lzrs with redshifts z 0.15 renewed the potentil prolems nd hllenges for stndrd models of TeV lzrs. This time the issue hs more solid experimentl kground euse the gmm-ry spetr orreted for the interglti sorption pper very hrd ( hrder thn should e ) even for the minimum possile EBL fluxes t optil nd NIR wvelengths. Nmely, the HESS ollortion reported, sed on the detetion of TeV gmm-rys from the BL L ojet 1ES , tht ny signifint devition from the lower limits of EBL determined y the integrted light of glxies resolved y the Hule telesope (Mdu & Pozzetti 2000), would led to very hrd intrinsi gmm-ry spetrum with slope hrterized y photon index Ɣ (Ahronin et l. 2006). The nlysis sed on lrger smple of TeV lzrs leds to the sme onlusion (Mzin & Rue 2007). Reently, the HESS ollortion reported detetion of multi-tev gmm-rys from 1ES , BL L ojet loted t redshift z = (Ahronin et l. 2007). It is remrkle tht the deteted hrd gmm-ry spetrum of this soure with photon index Ɣ os 2.5 extends up to 15 TeV. This, to ertin extent, surprising result n e explined y the shpe of the energy flux of EBL whih etween the NIR nd MIR nds is expeted to e proportionl to λ 1 (Ahronin 2001). Yet, the solute EBL flux, derived from rther onservtive ssumption tht the photon index of the intrinsi spetrum of TeV gmm-rys does not exeed 1.5, ppers gin lose to the EBL lower limit, this time t MIR ( 2 3 nw m 2 sr t 10 μm), derived from the Spitzer glxy ounts (Fzio et l. 2004; Dole et l. 2006). Thus, the gmm-ry oservtions of 1ES nd 1ES n e interpreted s n rgument tht the glxies resolved y the Hule nd Hrd lzr spetr nd internl sorption 1207 Spitzer telesopes provide the ulk of the EBL flux from optil to MIR wvelengths. Given the importne of suh sttement, in prtiulr for understnding of ontriution of the first strs to the EBL (see e.g. Kshlinsky 2005; Mpelli, Slvterr & Ferrr 2006), it is essentil to explore lterntive wys of explntion of very hrd intrinsi gmm-ry spetr or even shrper spetrl fetures (like pile-ups) in TeV lzrs. In this ontext, reently some extreme ssumptions regrding the distriutions of elerted prtiles hve een proposed. In prtiulr, Ktrzynski et l. (2006) rgued tht gmm-ry spetrum s hrd s Ɣ n e formed in synhrotron-self Compton (SSC) model ssuming nrrow-prent eletron distriution, e.g. power lw within E 1 nd E 2, with lowenergy ut-off E 1 not muh smller thn the high-energy ut-off, E 2. In similr lines, Steker, Bring & Summerlin (2007) rgued tht eletron spetr with power-lw index 1.25 s 2ne ommodted within the models of reltivisti shok elertion. It should e noted, however, tht in ompt ojets reltivisti eletrons usully suffer very fst synhrotron losses, therefore the ssumptions out hrd eletron elertion nnot yet gurntee hrd gmm-ry spetr. Indeed, fst synhrotron losses result in n eletron spetrum whih nnot e hrder thn dn/de E 2,independent of the initil (elertion) spetrum (see e.g. Ahronin 2004). If so, the inverse-compton (IC) sttering would result in gmm-ry spetrum steeper thn E 1.5. It should e noted tht if the energy losses of eletrons re dominted y IC sttering in the Klein Nishin limit, the resulting eletron spetrum ppers hrder thn the elertion spetrum. However, the relted gmm-ry spetrum nnot e hrder thn the eletron elertion spetrum euse of the sme Klein Nishin effet (sine it works twie in different diretions) (Khngulyn & Ahronin 2005; Moderski et l. 2005). In priniple, one n void the synhrotron ooling of eletrons, e.g. in old ultrreltivisti wind. However, suh n hypothesis suggested for Mkn 501 (Ahronin, Timokhin & Plysheshnikov 2002), in nlogy with pulsr winds, needs thorough theoretil studies to lrify whether suh old ultrreltivisti winds n e formed nd survived round supermssive lk holes in the ores of tive glti nulei (AGN). In this pper, we suggest new senrio whih llows the formtion of very (in prtie, ritrry) hrd gmm-ry spetr in quite nturl wy. The model is sed on postultion tht gmm-rys efore leving the soure suffer signifint photon photon sorption due to intertions with dense rdition fields inside or in the viinity of ompt gmm-ry prodution region(s). Interestingly, the presene of high-density rdition fields of different origin in the inner prts of lzrs generlly is treted s prolem for the espe of high-energy gmm-rdition from their prodution region, nd, in this regrd, the urrent models of TeV lzrs re designed in wy to void the internl gmm-ry sorption. Below we show tht, in ft, moderte internl photon photon sorption n e lue to the very hrd intrinsi energy spetr of TeV lzrs. 2 INTERNAL ABSORPTION OF GAMMA-RAYS IN BLAZARS When propgting through n isotropi soure of low-frequeny rdition, the gmm-ry sorption t photon photon intertions is hrterized y the optil depth: τ(e) = R ɛ2 0 ɛ 1 σ (E,ε)n ph (ε, r)dε dr, (1) Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

3 1208 F. A. Ahronin, D. Khngulyn nd L. Costmnte where n ph (ε, r) desries the spetrl nd sptil distriutions of trget photons in the soure of size R. With good ury, the totl ross-setion in the monoenergeti isotropi photon field n e represented in the form (see e.g. Ahronin 2004): ( ) σ γγ = 3σ T s + 1 2s 2 2 ln s ln( s + s 1) 2s ( ) s s s The ross-setion depends only on the produt of the primry (E) nd trget photon (ε) energies,s = Eε/m 2 e 4. Close to the threshold, s 1, the pir prodution ross-setion ehves s σ γγ (1/2) σ T (s 1) 3/2. The ross-setion dereses with s lso when s 1: σ γγ (2/3)σ T s 1 ln s. The ross-setion hieves its mximum t s 3.5: σ γγ 0.2 σ T. For n homogeneous soure with nrrow-spetrl distriution of photons (with energy ε), of the order of mgnitude estimtes one n use the pproximtion τ(e) Rσ γγ (E, ε)n( ε). In this se, we should expet mximum sorption effet t gmm-ry energy E m 2 e 4 / ε. Both t lower nd higher energies, the soure eomes more trnsprent, thus we should expet quite strong deformtion of the primry spetrum. In the se τ(e ) 1, the effet ould e drmti, given the exponentil dependene of the sorption on the optil depth. Note tht while for nrrow-spetrl distriution of trget photons, the monoenergeti pproximtion gives quite urte estimte of the effet t E E,tlowenergies, E 1/4E, this pproximtion implies ompletely trnsprent soure (i.e. τ = 0) lthough, non-negligile sorption n lso tke ple elow E. For exmple, euse of intertions with the Wien til, the sorption effet in the lkody rdition field nnot e disregrded even t very low energies, E m 2 e 4 /kt. In Fig. 1 (upper pnel), we present the gmm-ry ttenution ftor, κ = exp( τ) in grey-ody rdition field desried y Plnkin distriution with three different tempertures T = 10 3,10 4 nd 10 5 K lulted for n optil depth fixed t the energy orresponding to the mximum sorption, E m 2 e 4 /kt (Gould & Shrèder 1967): sine the optil depth is funtion of the produt EkT, three urves re identil, ut shifted reltive to eh other y ftor proportionl to the rdition temperture. In Fig. 1, we lso show the ttenution ftors for fixed temperture T = 10 4 K lulted for three different optil depths τ mx = 0.5, 3 nd 6. It is seen tht the gmm-ry ttenution, strting from the energy E 0.1E, grdully inreses up to E E, fter whih the soure eomes more nd more trnsprent [κ exp ( E 1 ln E) 1], nd, onsequently, the primry spetrum strts to reover. As result, in this energy intervl the spetrum ppers hrder thn the primry spetrum. The ottom pnel of Fig. 1 shows the hnge of the slope of gmm-ry spetrum, Ɣ,whih n e interpreted s hnge of the lol photon index, ssuming tht the initil gmm-ry spetrum is desried y power-lw distriution, dn/de E Ɣ 0. The emerging spetrum of gmm-rys in the energy intervl (0.1 1)E is steeper thn the initil spetrum ( Ɣ 0);itreoverstE = E ( Ɣ = 0), nd t energies E E the spetrum eomes signifintly hrder thn the initil spetrum ( Ɣ 0). For exmple, in the se of initil gmm-ry spetrum E 2 nd τ mx = 6, the emerging spetrum of gmm-rys in the energy intervl (1 10)E n e very hrd with Ɣ = Ɣ 0 + Ɣ 0, (2) ΔΓ e τ E, ev : τmx = 6 : τmx = 3 : τmx = : T=10 K 4 2: T=10 K 3 3: T=10 K Figure 1. Upper pnel: ttenution ftor κ = exp( τ) for three different tempertures of trget photons, T = 10 3,10 4 nd 10 5 K (for the optil depth τ mx = 6). For T = 10 4 K, lultions re performed for three different optil depths: τ mx = 6 (, red line), 3 (, green line) nd 0.5 (, lue line). Bottom pnel: vrition of the lol photon index of the gmm-ry spetrum. (See the eletroni version of the pper for olour version of this figure.) lthough the solute flux is suppressed y n lmost three orders of mgnitude t E = E, nd n order of mgnitude t E = 10E. Note tht the requirement of nrrow-spetrl distriution of the trget photons is key ondition for this remrkle effet. It should not neessrily e Plnkin or monoenergeti distriution, ut my hve ny other shpe, for exmple power lw with low-energy ut-off: n(ε) ε α t ε ε 1 nd n(ε) = 0tε ε 1.Inthisse, the low-energy ut-off ε 1 plys similr role s the temperture in the Plnkin distriution. This is demonstrted in Fig. 2 for power-lw distriution of the kground field with α = 2 nd shrp ut-off t ε 1 = 1 nd 10 3 ev. Indeed, for the sme τ mx = 6, the se of ε 1 = 1 ev is quite similr to the se of Plnkin distriution with temperture T = 10 4 K shown in Fig. 1. The min differene ppers in the low-energy prt, E E. The sorption urve in Fig. 2 t low energies is smoother euse the n(ε) ε 2 type distriution provides more high-energy trget photons ompred to the Wien til of the therml distriution, for intertions with low-energy gmm-rys. The hrdening of the initil spetrum used y internl sorption ompenstes, to lrge extent, the steepening of the spetrum due to interglti sorption. This is demonstrted in Figs 3 nd 4. For the EBL flux, we use referene shpe lose to the one lulted y Primk, Bullok & Somerville (2005), ut with two different solute flux normliztions t the wvelength λ = 2.2 μm: u EBL (2.2 μm) = 16 (Fig. 3) nd 32 nw m 2 sr (Fig. 4). The first flux is ftor of 2 lrger thn the lower limit of EBL orresponding to the integrted light ontriuted y resolved glxies (Mdu & Pozzetti 2000), while the seond flux n e treted s n upper limit t 2.2 μm, it is slightly higher thn the fluxes limed from the COBE/DIRBEndTwo-MironAll-SkySurvey(2MASS) mesurements (Cmresy et l. 2001; Wright 2001). Note tht for the primry (unsored) differentil gmm-ry spetrum with Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

4 Hrd lzr spetr nd internl sorption 1209 d ΔΓ e τ : τ = 6 mx : τ = 3 mx : τmx = 0.5 E, ev Figure 2. Upper pnel: ttenution ftor lulted for power-lw distriution of trget photons with low-energy ut-off: n ph ε 2 for ε 1 < ε< nd n ph = 0forε ε 1. Solid urves: ε 1 = 1 ev nd dshed urves: ε 1 = 10 3 ev. The three different optil depth re shown: τ mx = 6 (, red lines), 3 (, green lines) nd 0.5 (, lue lines). Bottom pnel: vritions of the lol photon index of the gmm-ry spetrum. (See the eletroni version of the pper for olour version of this pper.) photon index Ɣ 0 = 2, the ttenution ftor κ = exp( τ) desries the SED of the sored rdition [E 2 dn/de κ(e)]. All urves re otined for soure loted t z = This is the redshift of the BL L ojet 1ES , the gmm-ry oservtions of whih, performed y the HESS ollortion, hve een initilly used to onstrin the EBL flux t optil nd NIR wvelengths (Ahronin et l. 2006). The solid urves in Figs 3 nd 4 (mrked s d ) orrespond to the pure interglti effet (i.e. without the internl sorption). They show strong steepening of the spetrum elow 1 TeV nd ove 10 TeV with notle reovery of the initil shpe round few TeV, whih is explined y the speifi shpe of the EBL energy flux (lose to u EBL λ 1 ) etween 2 nd 10 μm (Ahronin 2001). It is seen tht for the solute flux of EBL with normliztion t 2.2 μm, u EBL (2.2 μm) = 16 nw m 2 sr, the photon index etween 100 GeV nd severl TeV is hnges y Ɣ 2; thus, the intrinsi (soure) spetrum should e very hrd with slope Ɣ = Ɣ os Ɣ 1, where Ɣ os = 2.88 ± 0.17 is the oserved photons index of 1ES (Ahronin et l. 2006). Postulting tht the photon index llowed y onventionl models of gmm-ry prodution in lzrs should not exeed Ɣ 0 = 1.5, n upper limit on the EBL flux, t the level of u EBL (2.2 μm) 10 nw m 2 sr hs een derived y the HESS ollortion (Ahronin et l. 2006). It is seen from Fig. 3 tht this upper limit n e redily inresed y ftor of 1.5, llowing sustntil internl sorption of gmm-rys. Indeed, the joint opertion of internl nd interglti sorptions results in the hnges of the slope of the initil gmm-ry spetrum in the relevnt energy nd y Ɣ 0 to 1.5 for τ mx = 3, nd Ɣ from 0.5 to +0.5 for τ mx = 6. In the ltter se, the overll hnge of the shpe of the initil spetrum from 100 GeV to 5 TeV is quite smll, so hrd TeV gmm-ry spetr n, in priniple, e deteted lso from distnt lzrs. This ssumption n solve, to τ e ΔΓ : τ mx = 6 : τ = 3 mx : τmx = 0.5 d: τ=0 d E, ev Figure 3. Internl nd interglti sorption of gmm-rys. Upper pnel: ttenution ftors. The internl sorption is lulted for Plnkin distriution of trget rdition with temperture T = K. The four dshed urves orrespond to the internl optil depths τ mx = 6 (, red lines), 3 (, green lines), 0.5 (, lue lines) nd 0 (d, lk lines). The orresponding solid urves inlude oth the internl nd interglti sorption. The interglti sorption is lulted for soure t z = (the redshift of the BL L ojet 1ES ), ssuming referene shpe of the EBL spetrum lose to the one lulted y Primk et l. (2005), nd normlized to the EBL flux t 2.2 μm: u EBL (2.2 μm) = 16 nw m 2 sr. Bottom pnel: vrition of the lol photon index. (See the eletroni version of the pper for olour version of this pper.) ertin extent, the prolem relted to the spetr of elerted (prent) prtiles, nd thus (unfortuntely!) relx the onstrints on the EBL tht n e derived from gmm-ry oservtions. Formlly, detetion of not very steep TeV gmm-ry spetr with Ɣ os 4 from distnt (z 0.15) lzrs nnot e exluded even for n EBL flux lose to the limed high EBL fluxes derived from the COBE/DIRBE nd 2MASS mesurements (Cmresy et l. 2001) nd u EBL (2.2 μm) 28 nw m 2 sr. This is demonstrted in Fig. 4. At energies ove 300 GeV, the sorption of gmm-rys in EBL only inreses the photon index y Ɣ 4, while n dditionl internl sorption with τ mx = 10 results in Ɣ 2. Approximtely, the sme result is expeted for low EBL [e.g. t the level of u EBL (2.2μm) = 10 nw m 2 sr], ut for soures loted t z 0.1. In this regrd, the reent lim of detetion of VHE gmm-rys from 3C 279 (z = 0.538) y the MAGIC ollortion (Teshim et l. 2007) n e n indition of signifint gmmry sorption inside the soure. Otherwise, even for the minimum possile EBL flux, the pure interglti sorption would result in n extremely steep VHE gmm-ry spetrum with photon index 5. It is interesting to note tht the ultrviolet (UV) photons of the rod-line emission region of size R m nd luminosity Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

5 1210 F. A. Ahronin, D. Khngulyn nd L. Costmnte e τ ΔΓ : τ = 10 mx : τ = 5 mx : τ = 1 mx d: τ=0 d d E, ev Figure 4. The sme s in Fig. 3, ut the urves re lulted for the internl optil depths 10 (, red lines), 5 (, green lines), 1 (, lue lines) nd 0 (d, lk lines). For EBL, flux is ssumed twie lrger thn in Fig. 3: u EBL (2.2 μm) = 32 nw m 2 sr. (See the eletroni version of the pper for olour version of this figure.) L erg s 1, s derived for 3C 279 (Pin, Flomo & Treves 2005), n serve s perfet trget for internl sorption of highenergy gmm-rys. The internl sorption of gmm-rys signifintly inreses the energy requirements to the soure. For exmple in the se of τ mx = 5, the internl sorption leds to the redution of the oserved flux t 1 TeV y n dditionl ftor of 10. This, omined with the interglti sorption, implies three orders of mgnitude ttenution of the primry rdition (see Fig. 3). For the quiesent stte of 1ES , the orresponding pprent gmm-ry luminosity round 1 TeV is estimted L TeV κ 1 erg s 1. For the ttenution ftor κ(1 TeV) 10 3, it eomes huge, erg s 1, nd perhps one or two orders of mgnitude even lrger in the flring sttes (in nlogy with Mkn 421, Mkn 501 nd PKS ). 1 Nevertheless, even very high gmm-ry fluxes n e ommodted omfortly within the ville energy udget of lzrs, given the strong dependene of the intrinsi luminosity on the. Generlly, it is elieved tht the Doppler ftors of lzrs re s lrge s 10; however, in some ses the Doppler ftors n signifintly exeed this nominl vlue. For exmple, the inrese in the pprent speed oserved in the lzr 3C 279 from 5 to 17 hs een interpreted s evidene of very lrge Doppler ftor δ j 39 of the jet lose to the ore Doppler ftor δ j, L int = L pp δ 4 j 1 The deteted gmm-ry flux round 200 GeV is n order of mgnitude lrger thn t 1 TeV; however, euse of the drmti redution of the sorption effet, the ontriution of low energies to the (sorption orreted) pprent luminosity, is reltively smll. (Jostrnd et l. 2004). The rod-nd spetrl energy distriutions of ertin TeV BL Ls like Mkn 501 lso require quite lrge Doppler ftors, δ j 50 (Krwzynski, Coppi & Ahronin 2002). Finlly, the reently reported vriility of Mkn 501 (Alert et l. 2007) nd PKS (Ahronin et l. 2007) on minute sles provides perhps the most onvining rgument in fvour of Doppler ftors s lrge s δ j or even 100 (see e.g. Ahronin et l. 2007; Begelmn, Fin & Rees 2008). If so, the intrinsi luminosity ould e quite modest, nmely, t the level of L int = (δ j /30) 4 erg s 1 whih, in ft, is not fr from the TeV gmm-ry luminosity of the nery non-lzr type AGN M87 (Ahronin et l. 2006). The ttenution of TeV gmm-rys drmtilly inreses the intrinsi TeV to GeV gmm-ry flux rtio. However, this does not ontrdit the GeV flux upper limits ville from the EGRET oservtions (typilly, t the level of erg m 2 s or higher), espeilly if one tkes into ount tht the energy spetr of gmmrys produed in some prinipl rdition proesses (e.g. through IC sttering or proton synhrotron rdition) t sutev energies re expeted hrder thn E 2. On the other hnd, we ertinly expet signifint GeV gmm-ry emission from TeV lzrs, nd in this respet, the upoming GLAST mesurements with gretly improved (ompred to EGRET) sensitivity, espeilly t multi-gev energies, should provide the first effetive proes of TeV lzrs in the MeV/GeV domin in generl, nd for the internl gmm-ry sorption senrio, in prtiulr. Finlly, in the se of hdroni origin of TeV gmm-rys produed t pp nd/or pγ intertions, the flux of ompnying TeV neutrinos, whih freely penetrte through the internl nd extrglti rdition fields, n e s high s neutrinos m 2 s, i.e. ove the detetion threshold of the next genertion km 3 sle neutrino detetors. The detetion of oth gmm-rys nd neutrinos from TeV lzrs, nd the omprison of fluxes of these two omponents of rdition would provide prinipl informtion out the high-energy proesses in lzrs s well s out the ttenution of gmm-rys due to the (omined) internl nd interglti sorption. An dditionl informtion out the internl photon photon sorption lone (seprted from the extrglti sorption) is ontined in the rdition of seondry (pir-produed) eletrons. 3 RADIATION OF SECONDARY ELECTRONS The propgtion of high-energy gmm-rys through low-energy photon field nnot e redued to the simple effet of sorption. When the gmm-ry photon is sored, its energy is trnsferred to the eletron positron pir. The seondry eletrons interting with the mient mgneti nd rdition fields produe high-energy photons, either vi synhrotron rdition or IC sttering. The synhrotron photons re produed with muh smller energies, thus they do not intert with the kground low-energy photons. In trget field with nrrow-spetrl distriution, IC sttering of the photo-produed eletrons proeeds in the Klein Nishin limit; the upsttered photon reeives the mjor frtion of the eletron energy, thus is le to intert gin with kground photons. The seond genertion pirs gin produe gmm-rys, thus n eletromgneti sde develops. While the energy of gmm-rys interting with EBL dissiptes in the interglti medium, nd in this wy ontriutes to the diffuse extrglti kground rdition, the seondry rdition used y internl sorption my ompny the primry (unsored) frtion of gmm-rys. In this regrd, the development of n eletromgneti sde is not desirle proess, euse it Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

6 Hrd lzr spetr nd internl sorption 1211 E 2 dn γ /de =, intrinsi =, sored =, sding =10TeV, intrinsi =10TeV, sored =10TeV, sding e+09 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 E,eV Figure 5. Gmm-ry spetr used y the internl photon photon sorption (dotted urves) or formed during development of pir sdes (solid urves) in rdition field with temperture T = 10 4 nd optil depth τ mx = 6. It is ssumed tht the energy density of rdition signifintly exeeds the energy density of the mgneti field, u r u B. The spetr of primry gmm-rdition (dshed lines) re ssumed s power lw with exponentil ut-off : dn/de E 2 exp ( E/ ) with = 10 TeV nd =. (See the eletroni version of the pper for olour version of this figure.) msks the distint sorption fetures, nd thus prevents the formtion of very hrd gmm-ry spetr. This is demonstrted in Fig. 5. The sde spetr re lulted ssuming tht the region of prodution of primry gmm-rys is loted in the entre of spheril soure filled with grey-ody rdition with temperture T = 10 4 K nd optil depth τ mx = 6. The spetrum of primry gmm-rys is given in the form: dn/de E 2 e E/ for two vlues of the ut-off energy: = 10 TeV nd =. In Fig. 5, oth the sored nd sde gmm-ry spetr re shown. It is seen tht the development of pir sdes fully wshes out the sorption fetures, nd insted forms stndrd spetrum with mximum ( ump ) round the intertion threshold, (m e 2 ) 2 /kt 100 GeV, followed y steep spetrum ove the ump. The sde spetrum round 1 TeV sturtes t the level of 10 per ent of the primry gmm-ry flux. The spetrum ove 1 TeV hs flt shpe until the effiieny of the sde drops (euse of the progressively deresing optil depth) with grdul trnsition to the sorption regime. There re two wys of signifint redution of the ontriution from the sde omponent to the oserved gmm-rdition. (i) Asorption of gmm-rys outside the prodution region. In this se, the foreground sde rdition nnot sreen the unsored frtion of gmm-rys. Indeed, lthough the energy in the sde rdition exeeds, y ftor of 100, the energy of the unsored frtion of primry rdition (see Fig. 5), for the oserver the primry rdition emitted y reltivistilly moving soure ( lo ) will e muh righter ( δj 4 ) nd shifted to higher energies ( δ j ) ompred to the isotropi sde emission of the surrounding environment. On the other hnd, the prt of the sde developed inside the lo is, of ourse, lso Doppler oosted, therefore the ondition of suppression of the sde omponent n e stisfied when the optil depth within the lo τ 1, i.e. the gmm-ry prodution region is muh smller thn the soure of the optil/uv rdition, l R. Sine the gmm-ry prodution regions in lzrs re elieved to e very ompt, l m, we my onlude tht the soure of the optil rdition should e lrger thn R m. There re mny potentil soures of optil rdition in lzrs (see e.g. Urry & Pdovni 1995). In this pper, we do not intend to speify the origin of the low-energy rdition fields, ut simply note tht n even modest optil soure E dn/de 2 B=100 G B=0.1 G : τ in mx = 6 : τ in mx = 3 : τ in mx = 0.5 T=5x10 4 K log(e/ev) J 0 (E γ ) Figure 6. Synhrotron rdition of seondry eletrons. The primry gmm-ry spetrum is ssumed dn/de E 2 (dotted line). The trget photon field is Plnkin with T = K. The sored gmm-ry spetr nd the orresponding spetr of seondry eletrons re lulted for three optil depths τ in mx = 6 (, red lines), 3 (, green lines) nd 0.5 (, lue lines). The synhrotron rdition is lulted ssuming tht the sorption of gmm-rys tkes ple inside the soure (gmm-ry prodution region) for two vlues of the mgneti field: B = 100 G (solid urves) nd B = 0.1 G (dshed urves). Clultions re performed for the se γ j = 1 (no ulk motion). (See the eletroni version of the pper for olour version of this figure.) loted in the ore of lzr n provide n effetive trget for gmm-ry sorption. The luminosity of this soure is estimted s L O = 12πn ph ktr 2,wheren ph is the verge numer density of rdition. It n e estimted from the ondition σ γγ Rn ph = τ mx. For hrteristi optil depth, τ mx 5 nd temperture T = K, we otin L O (R/10 17 m) erg s 1. (ii) Seondry eletrons ooled through synhrotron rdition. This ondition n e stisfied if the energy density of the mgneti field exeeds the energy density of rdition, B 2 /8π 3 ktn ph γ 2 j or B 0.4(R/10 17 m) 1/2 γ j G. The implitions of suh strong mgneti field for the primry gmm-ry prodution mehnism re disussed in Setion 4. In Fig. 6, the rod-nd SED of the rdition initited y sorption of primry gmm-rys with power-lw spetrum dn/de E 2 is shown, ssuming tht the sorption of gmm-rys tkes ple inside the gmm-ry prodution region. Clultions re performed for three different optil depths τ mx = 0.5, 3 nd 6, fixed temperture of rdition T = K, nd two extreme vlues of the mgneti field, B = 100 nd 0.1 G. In lultions of the eletron spetr, we ssume tht the energy losses of eletrons re dominted y synhrotron ooling. Note tht the spetrum of synhrotron rdition of seondry eletrons hs hrteristi elltype form, i.e. quite similr to the synhrotron spetr formed in the SSC models. However, in the SSC models designed for TeV lzrs the synhrotron pek is result of the mximum energy of elerted eletrons, while the hrd low-frequeny prt of the spetrum is determined y rdition of unooled low-energy eletrons. In the internl gmm-ry sorption senrio, we see similr fetures, ut for different resons. The eletrons in nrrow-nd rdition field re produed with spetrum similr to the spetrum of prent gmm-rys ( E Ɣ 0), ut with ut-offs oth t low nd high energies. These ut-offs re explined y the threshold of the photon photon pir prodution nd y the redution of its ross-setion t highest energies, respetively. Due to the synhrotron ooling, t low energies the eletron spetrum otins stndrd E 2 form, Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

7 1212 F. A. Ahronin, D. Khngulyn nd L. Costmnte E dn/de 2 in : τ mx = 6 in : τ = 3 mx in : τmx = 0.5 T=5x10 4 K γ j=1 γ j=30, δ j=20 log(e/ev) J (E ) 0 γ Figure 7. Impt of the ulk motion on synhrotron rdition of seondry eletrons. The mgnetized lo moves with reltivisti veloity. The synhrotron mximum moves y ftor of δ j /γj 2 nd the distriutions eome somewht wider. The primry gmm-ry spetrum ws ssumed power lw: E 2 γ (is shown y the dotted line). The trget photon field is Plnkin with T = K. The sored spetr re shown y lk solid urves for τ mx = 6(),τ mx = 3()ndτ mx = 0.5 (). We lulte synhrotron rdition from mgnetized region with the verge optil depth (over different diretions) τ in mx = 6 (, red lines), 3 (, green lines) nd 0.5 (, lue lines). The mgneti field is ssumed B = 100 G. Clultions re performed for two different ulk Lorenz ftors: γ j = 1 (no motion, solid urves) nd γ j = 30 (for δ j = 20, dshed urves). (See the eletroni version of the pper for olour version of this figure.) whih grdully trnsforms to E (Ɣ 0+1) type spetrum t intermedite energies nd ut-off t highest energies. The orresponding spetrl fetures re refleted in the synhrotron spetrum power lw with photon index 1.5 t low energies, with smooth trnsition to power lw with photon index Ɣ 0 /2 + 1 t intermedite energies, nd smooth grdul ut-off t highest energies. A signifint differene etween the SSC nd the internl gmm-ry sorption models ppers lso in the rtio of fluxes orresponding to the low- (IR to X-ry) nd high- (gmm) energy peks. While in the SSC senrio, this rtio is determined y the rtio of energy densities of the mgneti nd trget photon fields, in the internl gmm-ry sorption senrio this rtio is silly determined y the effiieny of gmm-ry sorption inside the soure. The mgneti field determines only the position of the synhrotron pek, ut not the flux level. The ltter is determined y the ftor propor- E dn/de 2 j j δ =10, γ =10, B=1 G : T=5x10 4 K : T=5x10 5 K tionl to [1 exp( τ mx )]. For τ mx 1, the dependene on the optil depth lmost disppers. All these fetures n e seen in Fig. 6. The position of the synhrotron pek depends, in quite interesting wy, lso on the Lorenz nd Doppler ftors of the soure. While in the stndrd models of lzrs, the Doppler effet shifts the overll SED towrds higher energies y ftor of δ j,inthe gmm-ry sorption senrio the synhrotron pek is shifted towrds lower energies (see Fig. 7). The reson is quite simple. In the frme of the reltivistilly moving soure illuminted y n externl rdition with hrteristi energy ε, the eletrons re produed with energies E min (m e 2 ) 2 /( εγ j ), thus the position of the synhrotron pek in the frme of the oserver is proportionl to δ j E 2 min δ/γ j 2. Thus, in soure moving towrds the oserver t smll ngle, the position of the synhrotron pek in the frme of the oserver is inversely proportionl to the Doppler ftor δ j,just opposite to the spetrum of gmm-rys whih is shifted towrds higher energies y the sme Doppler ftor. The position of the synhrotron pek depends strongly lso on the verge energy (or temperture) of the trget rdition field. Indeed, with n inrese of the temperture of kground rdition T, the threshold of photon photon intertions, nd onsequently the minimum energy of produed seondry eletrons dereses s E min 1/T, nd hene the synhrotron pek moves towrds lower energies s hν m 1/E 2 min 1/T2. Generlly, the position of the synhrotron pek of pir-produed eletrons depends on the temperture of the trget rdition field, the mgneti field nd the Doppler nd Lorentz ftors of the jet, s hν m BT ( ) 2 δ j /γ 2 j. (3) It is esy to derive simple nlytil expression whih desried the high-energy prt of the synhrotron spetrum, hν hν m, produed y eletrons for whih the soure eomes optilly thin, τ(e) 1. In this se, the prodution spetrum of eletrons Q(E) 1/EdN γ /de (here, we ignore the wek logrithmi term in the photon photon intertion ross-setion). Then, for the powerlw gmm-ry spetrum, dn γ /de E Ɣ 0, the ooled eletron spetrum is lso power lw, dn e /de e E Ɣ0 2, nd orrespondingly the SED of synhrotron rdition, νf ν ν (Ɣ0+1)/2.Forexmple, for Ɣ 0 = 2, the SED of synhrotron rdition is rther steep, νf ν ν 1.5. In ft, euse of the ut-off in the gmm-ry spetrum, the high-energy til of synhrotron rdition is expeted even steeper. This is demonstrted in Fig. 8 where the rod-nd SEDs of rdition initited y gmm-rys in soure t z = re without sorption Downloded from y guest on 12 Septemer 2018 log(e/ev) Figure 8. Impt of the rdition temperture on the spetrl energy distriution of emission initited y primry gmm-rys in jet moving through homogeneous rdition field. The soure is loted t z = The dshed urve is the ssumed primry spetrum of gmm-rys. The solid urves represent the synhrotron rdition of the seondry eletrons s well s the gmm-ry spetr fter the internl nd extrglti sorption. Clultions re performed for two rdition tempertures, T = K (, red lines) nd T = K (, green lines). For oth the ses, δ j = γ j = 10, B = 1G,τ mx = 3. An EBL is ssumed with normliztion of the flux u EBL (2.2 μm) = 16 nw m 2 sr. (See the eletroni version of the pper for olour version of this figure.) C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

8 shown. It is ssumed tht gmm-rys in the frme of the jet moving with Lorentz ftor γ j = 10 hve power-lw distriution with n exponentil ut-off t 1 TeV, dn γ /de E 3/2 exp( E/ 1 TeV). It is lso ssumed tht δ j = γ j (i.e. the viewing ngle is θ 6 ). The lultions re performed for two tempertures of the rdition field through whih the jet propgtes T = nd K, ssuming tht in oth the ses the optil depth inside the moving gmm-ry prodution region (the lo) with homogeneous mgneti field is τ mx = 3. Finlly, for the interglti sorption, templte EBL spetrum is ssumed with normliztion t 2.2 μm tthelevelof16nwm 2 sr. The impt of the temperture on oth the spetrum of rriving gmm-rys nd the synhrotron rdition of seondry eletrons is lerly seen. Note tht while elow 100 GeV the deformtion of the primry gmmry spetrum is used minly y internl sorption, the shrp ut-off t energies ove 10 TeV is due to the severe interglti sorption. In the intermedite-energy rnge etween 100 GeV nd 10 TeV, the internl nd interglti photon photon intertions operte together resulting in quite speifi rod-nd SEDs. The disussion of implitions of these results for speifi strophysil ojets is eyond the sope of this pper. We note only tht our preliminry studies show tht the suggested model, in generl, n stisftorily explin the oserved rod-nd SEDs of TeV lzrs. Hrd lzr spetr nd internl sorption DISCUSSION The energy spetr of VHE gmm-rys from lzrs, fter orretion for interglti sorption, generlly pper very hrd, even for the minimum flux level of EBL determined y the integrted light of resolved glxies t optil (Hule) nd IR (Spitzer)wvelengths. A slight devition from the roust lower limits of EBL leds to unusully hrd intrinsi gmm-ry spetr whih nnot e esily explined within the stndrd prtile elertion nd rdition models. In this pper, we suggest senrio whih n led to the formtion of intrinsi gmm-ry spetr of ritrry hrdness without introduing modifitions in the prtile elertion models. The min ide is tht the gmm-rys efore they leve the soure suffer signifint internl energy-dependent sorption due to the intertions with the mient low-frequeny photons. The existene of dense rdition fields of different origin in lzrs (see e.g. Urry & Pdovni 1995; Celotti, Fin & Rees 1998), omined with the lrge photon photon pir prodution ross-setion, mkes this senrio quite nturl nd effetive, in prtiulr in the ompt ores of lzrs. For the formtion of hrd VHE gmm-ry spetr, the trget rdition field must hve rther nrrow-spetrl distriution or shrp low-energy ut-off, with typil energy of photons of out 1 to 10 ev. Formlly, for very lrge optil depths, this proess n provide n ritrry hrdness of gmm-ry spetr, though t the expense of signifint inrese in the required non-therml energy udget. However, s long s the urrent lzr models require reltivistilly moving gmm-ry prodution regions with lrge Doppler ftors, δ j 30, nd perhps even more (Ahronin et l. 2007; Begelmn et l. 2008), the ville energy udget seems to e not ritil issue. Moreover, even rther moderte internl sorption is suffiient to provide signifint hrdening effet (see Fig. 3). The unvoidle feture of the proposed model is the rdition of seondry eletrons vi synhrotron or IC sttering. If the optil depth inside the gmm-ry prodution region is smll, τ 1, e.g. the gmm-ry soure is muh smller thn the externl soure of optil photons, the seondry eletrons re produed nd rdite minly outside the gmm-ry prodution region. Even in the se of hevy sorption of gmm-rys, the seondry rdition of seondry eletrons n hrdly e deteted. Indeed, sine the intrinsi gmm-ry luminosity is reltively modest, nd the sored energy is re-rdited s n isotropi soure, 2 the lost of the eming ftor drmtilly redues the signl ompred to the primry (Doppler-oosted) rdition. The piture is drmtilly hnged when the gmm-ry soure moves through very dense photon field, suh tht the optil depth inside the soure eomes lrger thn 1. In this se, the min frtion of the sored energy is relesed in the form of seondry eletrons inside the gmm-ry prodution region, nd thus the rdition of the seondry eletrons profits, s the primry gmm-rdition does, from the Doppler oosting. The seondry eletrons re ooled through synhrotron nd/or IC hnnels. The ltter in ft proeeds vi development of pir sdes s long s the typil energies of eletrons or gmm-rys nd the energy of trget photons εe e,γ m 2 e 4. The sde, however, diminishes the energy-dependent sorption fetures, thus the model eomes effetive when the eletrons re ooled predominntly vi synhrotron rdition, i.e. B 2 /8π u r γ j 2 (here, u r is the energy density of trget photons in the l frme). The energy density of the rdition u r = εn ph with n verge energy of trget photons of out ε 1eVmyelinkedtothevlueofτ mx, thus for the effetive suppression of the sde B ( 40π ετmx γ 2 j σ T R ) 1/2 ( τ 1/2 0.5G mx γ j 10 )( ) R 1/2. (4) m Thus, the mgneti field exeeding 1 G should e suffiient to prevent the sde. For suh mgneti fields, the synhrotron rdition of seondry eletrons ppers in the optil to hrd X-ry energy nds. Depending on the optil depth, the synhrotron pek n e higher thn the gmm-ry pek. Interestingly, unlike the lssil synhrotron/ic models, where the rtio of the synhrotron to IC pek is determined y the rtio of u B /u r ; in the internl gmm-ry sorption senrio, the synhrotron pek does not strongly depend on the mgneti field. Whether this senrio n e pplied to the rod-nd SEDs of gmm-ry lzrs, is n interesting issue whih requires speil dedited studies. Finlly, we wnt to disuss riefly the rdition mehnisms of primry gmm rdition. Generlly, the model does not give preferene to the leptoni or hdroni origin of rdition, unless the mgneti field exeeds the estimte given y eqution (4). In this se, the synhrotron-to-ic flux rtio produed y diretly elerted eletrons would e too high, espeilly fter the internl sorption of gmm-rys, ontrry to the deteted SEDs of most of the TeV lzrs. Lrge mgneti fields in the gmm-ry prodution region, typilly B 1G, would fvour gmm-ry prodution y reltivisti protons, with ll dvntges nd disdvntges ommon for hdroni models. The si prolem of hdroni models is linked to the low-intertion rtes whih do not llow the most nturl explntion of the oserved fst gmm-ry vriility of lzrs in terms of rditive ooling. For exmple, in the se of intertions of protons with the mient plsm with numer density n, the hrteristi time of pp intertions with prodution of π 0 -mesons is 2 Unless the eletrons re produed in n environment with very low mgneti field, nd thus re ooled vi IC sttering efore ny notle defletion. Downloded from y guest on 12 Septemer 2018 C 2008 The Authors. Journl ompiltion C 2008 RAS, MNRAS 387,

9 1214 F. A. Ahronin, D. Khngulyn nd L. Costmnte t pp n 1 s. Thus, in order to explin the vriility of gmmrys s short s severl minutes like the TeV flres oserved from PKS nd Mkn 501, the density of plsm should e s lrge s δ 1 j m 3 whih implies very hevy soure nd orrespondingly huge kineti energy E kin = (4/3)πl 3 nm p 2 γ j erg (here, we ssume tht δ γ j ). One my invoke lterntive explntions of the vriility of lzrs, for exmple, due to the diti losses or espe of prtiles from the soure, ut this ssumption leds to drmti redution of rdition effiieny, nd to inrese the energy requirements to the elerted protons. A similr prolem fes the photomeson proesses t intertions of protons with the mient rdition fields. Atully in the internl gmm-ry sorption senrio, this mehnisms seems quite nturl hoie euse the sme kground photons whih sor gmm-rys n ply role of the trget for photomeson intertions. However, euse of the smll rosssetion, the effiieny of this proess gin ppers quite low. The intertion time of protons with energy, E 200 MeV/( εγ j ) ( ε/1ev) 1 (γ j /10) 1 ev (in the frme of the moving soure with Lorentz ftor γ j ) is estimted t pγ 1/(f σ pγ n ph ) (σ γγ /σ pγ )f 1 R/τ 1 mx ( σ pγ m 2 is the verge rosssetion nd f 0.2 is the multipliity of the proess). Thus, we n see tht during the pssge of the soure of optil photons of size R, the protons trnsfer only σ pγ /σ γγ 10 3 frtion of their energy to gmm-rys. If suh low effiieny n e ompensted y very lrge Doppler oosting (e.g. ssuming δ j 100), this hnnel n provide very lrge fluxes of neutrinos, whih unlike gmm-rys do not suffer internl nd extrglti sorption. In the se of ttenution of VHE gmm-ry fluxes y two to three orders of mgnitude, the expeted fluxes of neutrinos from TeV lzrs n e s lrge s the detetion threshold of the km 3 volume high-energy neutrino telesopes, F νμ ( 1TeV) neutrinos m 2 s. It is interesting to note tht, euse of the threshold of photomeson prodution, the intertions of protons of ritrry distriution with nrrow-nd rdition with hrteristi energy ε, result in differentil gmm-ry spetrum whih elow the energy ( ε/1 TeV) 1 ev is extremely hrd, dn/de = onstnt, thus this proess itself n provide very hrd gmm-ry spetr independent of the spetrum of prent protons. Despite ertin ttrtive fetures, this mehnism fes the sme prolem s pp intertions low rdition effiieny. Therefore, it n work only under onditions of extremely lrge Doppler oosting of rdition. The effiieny of VHE gmm-ry prodution n e muh higher in the se of synhrotron rdition of protons, provided tht the elertion of protons proeeds t rte lose to the fundmentl limit, nd the mgneti field in the proton elertor well exeeds 10 G. In prtiulr, in the mgneti field of the order of 100 G, protons n e elerted to energies TeV nd thus n produe VHE synhrotron gmm-rys on time-sles of 10 4 s. 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