Formation of hard VHE gamma-ray spectra of blazars due to internal photon-photon absorption

0.47 MB·English

by  F. Aharonian

Mon.Not.R.Astron.Soc.000,1–10() Printed2February2008 (MNLATEXstylefilev2.2)
Formation of hard VHE gamma-ray spectra of blazars due
to internal photon-photon absorption
Felix A. Aharonian⋆1,2, D.Khangulyan2 & L. Costamante3
8 1Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin2, Ireland
0 2Max Planck Institut fu¨r Kernphysik, Saupfercheckweg 1, D69117 Heidelberg, Germany
0 3Stanford University,W.W. Hansen Experimental Physics Laboratory &
2 Kavli Institute for Particle Astrophysics and Cosmology, Stanford, CA 94305-4085, USA

n
a
J Accepted. Received; inoriginalform

1
2
ABSTRACT

] The energy spectra of TeV gamma-rays from blazars, after being corrected for inter-
h
galatic absorption in the Extragalactic Background Light (EBL), appear unusually
p
- hard, a fact that poses challenges to the conventional models of particle acceleration
o inTeVblazarsand/ortotheEBLmodels.Inthispaperweshowthattheinternalab-
r sorptionofgamma-rayscausedbyinteractionswithdensenarrow-bandradiationfields
t
s inthe vicinityofcompactgamma-rayproductionregionscanleadto the formationof
a
gamma-rayspectra ofanalmostarbitraryhardness.This allowssignificantrelaxation
[
ofthecurrenttightconstraintsonparticleaccelerationandradiationmodels,although

1 at the expense of enhanced requirements to the available nonthermal energy budget.
v Thelatter,however,isnotacriticalissue,aslongasitcanbe largelycompensatedby
8 theDopplerboosting,assumingverylarge(>30)Dopplerfactorsoftherelativistically
9
moving gamma-ray production regions. The suggested scenario of formation of hard
1
gamma-ray spectra predicts detectable synchrotron radiation of secondary electron-
3
positron pairs which might require a revision of the current “standard paradigm” of
.
1 spectralenergydistributions ofgamma-rayblazars.If the primarygamma-raysareof
0 hadronicoriginrelatedto pp or pγ interactions,the “internalgamma-rayabsorption”
8
model predicts neutrino fluxes close to the detection threshold of the next generation
0
high energy neutrino detectors.
:
v
keywords: BL Lacertae objects: general, gamma-rays: tronomy is that VHE gamma-rays emitted by dis-
i
X theory,gamma-rays: observations, diffuseradiation tant (> 100 Mpc) objects arrive after significant ab-
r sorption caused by their interactions with EBL via
a the process γγ e+e− (Nikishov 1962; Jelley 1966;
→
Gould and Schr`eder1967). The reconstructed, i.e. the
1 INTRODUCTION
absorption-corrected gamma-ray spectrum from asourceat
Therecentreportsondetectionsofveryhighenergy(VHE) aredshiftz,J0(E)=Jobs(E)eτ(E,z)dependsonthefluxand
gamma-rays from blazars with redshifts z > 0.1 (for a re- energy spectrumof EBL throughtheoptical depthτ(E,z).
view see e.g. Hinton (2007)) initiated renewed debates on Thus, at energies where τ(E,z) > 1, the primary gamma-
the interpretation of TeV gamma-ray spectra of blazars, rayssuffer strong spectral deformation.
in particular in the context of the level of the diffuse ex- TheEBLconsistsoftwoemissioncomponentsproduced
tragalactic background radiation at optical and infrared by stars and partly absorbed/re-emitted by dust through-
wavelengths, often called also as Extragalactic Background out the entire history of galaxy evolution. As a result, two
Light (EBL). Initially, the tight link between these two distinctbumpsareexpectedinthespectralenergydistribu-
topics - TeV blazars and EBL - became a subject of hot tion (SED) of EBL at near infrared (NIR) and far infrared
discussions prompted by multi (up to 20) TeV gamma- (FIR) wavelengths, with a mid-infrared (MIR) “valley” be-
rays detected from a nearby BL Lac object, Mkn 501 tween these two bumps(see e.g. Hauser and Dwek (2001)).
(Aharonian et al. 1999), and by the reports claiming de- Generally,foralmostallEBLmodels,τ(E)isastrongfunc-
tection of high fluxes of EBL at far infrared wavelengths tion of energy below 1 TeV and above 10 TeV; between 1
(Hauser et al. 1998;Schlegel et al. 1998;Lagage et al. 1999; and 10 TeV theenergy-dependenceof τ(E)is much weaker
Finkbeineret al. 2000). However, it was quickly recognised (Aharonian 2001). Consequently, one should expect signif-
thatthesetwoclaimshardlycouldbecompatiblewithinany icant distortion of the VHE spectra of blazars at energies
standardmodelofTeVblazars(see,forareview,Aharonian below 1 TeV and above 10 TeV, provided that at these
(2001)). energies τ > 1. One can re-formulate this statement in a
A distinct feature of extragalactic gamma-ray as- different way. Namely, for a standard (“decent”) intrinsic
2 Aharonian, Khangulyan & Costamante
gamma-ray spectrum, the observer should detect very soft at MIR ( 2 3 nW/m2sr at 10 µm), derived from the
≈ −
(steep) spectra at energies below 1 TeV and above 10 TeV Spitzer galaxy counts (Fazio et al. 2004; Dole et al. 2006).
fromobjectsforwhichτ >1atcorrespondingenergies.This Thus,thegamma-rayobservationsof1ES1101-232and1ES
conditionissafelysatisfied,giventheconstraintsonthemin- 0229+200canbeinterpretedasanargumentthatthegalax-
imum EBL flux imposed by galaxy counts, for blazars with ies resolved by the Hubble and Spitzer telescopes provide
redshifts z > 0.15 like 1ES 1101-232 and for nearby ob- thebulkoftheEBLfluxfrom opticaltomidinfraredwave-
jects with z 0.03 like Mkn 501. Even though the detected lengths. Given the importance of such a statement, in par-
∼
gamma-ray spectra from both objects in the correspond- ticularforunderstandingofcontributionofthefirststarsto
ing energy intervals are indeed quite steep with a photon theEBL (seee.g. Kashlinsky (2005); Mapelli et al. (2006)),
index 3 (Aharonian et al. 1999; Aharonian et al. 2006a), it is essential to explore alternative ways of explanation of
∼
they appear not sufficiently steep to compensate the func- veryhardintrinsicgamma-rayspectraorevensharperspec-
tion f(E)=eτ(E), and thus to prevent a robust conclusion tral features (like pile-ups) in TeV blazars. In this context,
that theintrinsic VHE gamma-ray spectra of these blazars recently some extreme assumptions regarding the distribu-
are unusually hard. tions of accelerated particles have been proposed. In par-
In the case of Mkn 501, the intrinsic spectrum has ticular, Katarzynski et al (2006) argued that a gamma-ray
a “non-standard” shape with a possible pile-up above 10 spectrumashardasΓ0 0.7canbeformedinaSSCmodel
∼
TeVwhichhasbeeninterpretedasa“IRbackground-TeV assuming a narrow parent electron distribution, e.g. power-
gamma-raycrisis”(Protheroe and Meyer 2000)oraneedto lawwithinE1andE2,withalow-energycutoffE1notmuch
invokedramatic assumptions likea violation of theLorentz smaller than the high energy cutoff, E2. In similar lines,
invariance (see e.g. Kifune (1999)). However, a more prag- Steckeretal(2007)arguedthatelectronspectrawithpower
matic view which presently dominates in both infrared and law index 6 1 can be accommodated within the models of
gamma-ray astronomical communities, treats this “crisis” relativisticshockacceleration.Itshouldbenoted,however,
as somewhat exaggerated, especially given the ambiguity that in compact objects relativistic electrons usually suf-
of extraction of the truly diffuse extragalactic FIR compo- fer very fast synchrotron losses, therefore the assumptions
nent from the much higher backgrounds of local origin (see abouthardelectronacceleration cannotyetguaranteehard
e.g.HauserandDwek(2001)).Nevertheless,therecentlyre- gamma-ray spectra. Indeed, the radiatively cooled electron
ported low limits on the EBL at mid infrared wavelengths spectrum cannot be harder than dN/dE E−2, indepen-
∝
from the Spitzer deep cosmological surveys appeared quite dent of the initial (acceleration) spectrum (see e.g. Aha-
high, for example at 70 µm the EBL flux should exceed ronian 2004). If so, the inverse Compton scattering would
> 7.1 1.0 nW/m2s (Dole et al. 2006). This implies that resultinagamma-rayspectrumsteeperthanE−1.5.Infact,
±
the problem is not yet over, and one may still face a chal- the Klein-Nishina effect makes the spectrum even steeper.
lenge with the interpretation of the energy spectra of Mkn In principle, one can avoid the synchrotron cooling of elec-
501 and Mkn 421 in themulti-TeV energy domain. trons, e.g. in a cold ultrarelativistic wind. However such a
On the other hand, the recent detections of TeV hypothesissuggestedforMkn501(Aharonian et al. 2002),in
gamma-rays from blazars with redshifts z > 0.15 renewed analogywithpulsarwinds,needsthoroughtheoreticalstud-
thepotentialproblemsandchallengesforstandardmodelsof ies to clarify whether such cold ultrarelativistic winds can
TeVblazars.Thistimetheissuehasamoresolidexperimen- beformed andsurvivedaround supermassiveblack holesin
tal background, because the gamma-ray spectra corrected thecores of AGN.
for the intergalactic absorption appear very hard (“harder Inthispaperwesuggestanewscenariowhichallowsfor-
thanshouldbe”)evenfortheminimumpossibleEBLfluxes mationofvery(inpractice,arbitrary)hardgamma-rayspec-
at optical and NIR wavelengths. Namely, the HESS collab- tra in a quite natural way. The model is based on a postu-
oration reported, based on the detection of TeV gamma- lation that gamma-raysbefore leavingthesource suffersig-
rays from the BL Lac object 1ES 1101-232, that any sig- nificant photon-photon absorption due to interactions with
nificant deviation from the lower limits of EBL determined dense radiation fields inside or in the vicinity of compact
by the integrated light of galaxies resolved by the Hubble gamma-rayproductionregion(s).Interestingly,thepresence
telescope (Madau and Pozzetti 2000), would lead to very of high density radiation fields of different origin in the in-
hard intrinsic gamma-ray spectrum with a slope character- nerpartsofblazarsgenerallyistreatedasaproblemforthe
ized by a photon index Γ 6 1.5 (Aharonian et al. 2006a). escape of high energy gamma-radiation from their produc-
0
The analysis based on a larger sample of TeV blazars leads tion region, and, in this regard, the current models of TeV
to the same conclusion (Mazin and Raue 2007). Recently, blazars are designed in a way to avoid theinternal gamma-
the HESS collaboration reported detection of multi-TeV ray absorption. Below we show that, in fact, a moderate
gamma-raysfrom1ES0229+200,aBLLacobjectlocatedat internalphoton-photonabsorptioncanbeacluetothevery
a redshift z=0.1396 (Aharonian et al. 2007a). It is remark- hard intrinsic energy spectra of TeV blazars.
able that the detected hard gamma-ray spectrum of this
sourcewithaphotonindexΓ 2.5extendsupto15TeV.
obs
∼
This, to a certain extent surprising result can be explained
by the shape of the energy flux of EBL which between the 2 INTERNAL ABSORPTION OF
NIR and MIR bands is expected to be proportional to λ−1 GAMMA-RAYS IN BLAZARS
(Aharonian 2001).Yet,theabsoluteEBLflux,derivedfrom
a rather conservative assumption that the photon index of When propagating through an isotropic source of low-
the intrinsic spectrum of TeV gamma-rays does not exceed frequency radiation, the gamma-ray absorption at photon-
1.5, appears again close to the EBL lower limit, this time photon interactions is characterized by theoptical depth
Hard gamma-ray spectra of blazars due to internal absorption 3
R ǫ2
τ(E)= σ(E,ε)n (ε,r)dεdr , (1)
ph
Z0 Zǫ1
c
where n (ε,r) describes the spectral and spatial distribu-
ph
tions of target photons in the source of size R. With a
good accuracy, the total cross-section in the monoenergetic
isotropic photon field can be represented in the form (see b
e.g. Aharonian 2004): −τe
3σ 1 1 1
σγγ = 2sT2 s+ 2lns− 6 + 2s ln(√s+√s−1)− a: τ m a x = 6
h(cid:16) (cid:17) b: τ = 3
4 1 1 a max
s+ 1 . (2) c: τ = 0.5
9 − 9s − s 1 2 3 max
r #
(cid:16) (cid:17) 5
1: T=10 K
The cross section depends only on the product of the pri- 4
mary (E) and target photon (ε) energies, s = Eε/m2c4. 2: T=10 K
e 3 3
Close to the threshold, s 1, the pair production 3: T=10 K
cross-section behaves as σ → (1/2)σ (s 1)3/2. The
γγ T
≈ −
cross-section decreases with s also when s 1: σ Γ
(2/3)σ s−1lns. The cross-section achieves its≫maximuγmγ a≈t ∆ 0
T
s 3.5: σ 0.2σ .
≈ Foraγhγom≈ogeneToussourcewithanarrowspectraldistri- −2 1 2 3
butionofphotons,fororderofmagnitudeestimatesonecan
use the approximation τ(E) Rσγγ(E,ε¯)n(ε¯). In this case E, eV
≃
weshouldexpectmaximumabsorptioneffectatgamma-ray
energy E⋆ m2c4/ε¯. Both at lower and higher energies, Figure 1. Upper pannel: Attenuation factor κ = exp(−τ) for
the source b≈ecomees more transparent, thus we should ex- threedifferenttemperaturesoftargetphotons,T =103K,104K,
pect a quite strong deformation of the primary spectrum. and105 K (for the optical depth τmax =6). For T =104 Kcal-
In the case τ(E⋆) > 1, the effect could be dramatic, given culationsareperformedforthreedifferentopticaldepths:τmax=
0.5 (blue), 3 (green), 6 (red). Bottom pannel: Variation of the
the exponential dependence of the absorption on the opti-
localphotonindexofthegamma-rayspectrum.
caldepth.Notethatwhileforanarrowspectraldistribution
of target photons the monoenergetic approximation gives a
quite accurate estimate of the effect at E E⋆, at low en- rays in the energy interval (0.1 1)E⋆ is steeper than the
ergies,E 61/4E⋆,thisapproximationimp≫liesacompletely initial spectrum(∆Γ>0);it rec−oversat E =E⋆ (∆Γ=0),
transparentsource(i.e.τ =0)although,anon-negligibleab- and at energies E >E⋆ thespectrum becomes significantly
sorptioncantakeplacealsobelowE⋆.Forexample,because harderthan theinitial spectrum (∆Γ60). Forexample, in
of interactions with the Wien tail, the absorption effect in the case of initial gamma-ray spectrum E−2 and τ = 6,
max
theblack-bodyradiationfieldcannotbedisregardedevenat the emerging spectrum of gamma-rays in the energy inter-
very low energies, E m2c4/kT. val (1 10)E⋆ can be very hard with Γ = Γ +∆Γ 0,
≪ e − 0 ∼
In Fig.1 (upper panel) we present the gamma-ray at- although theabsolutefluxissuppressedbyan almost three
tenuation factor, κ = exp( τ) in a grey-body radiation ordersof magnitudeat E =E⋆,and an orderof magnitude
−
field described by Planckian distribution with three dif- at E =10E⋆.
ferent temperatures T = 103 K, 104 K, and 105 K cal- Note that the requirement of a narrow spectral distri-
culated for an optical depth fixed at the energy corre- bution of the target photons is a key condition for this re-
sponding to the maximum absorption, E⋆ m2c4/kT markableeffect. It should not necessarily be a Planckian or
≈ e
(Gould and Schr`eder1967): Since the optical depth is a monoenergetic distribution, but may have any other shape,
function of the product E kT, three curves are identical, forexamplepower-lawwithalow-energycutoff:n(ε) ε−α
· ∝
butshiftedrelativetoeachotherbyafactorproportionalto at ε > ε , and n(ε) = 0 at ε 6 ε . In this case, the low-
1 1
theradiation temperature.InFig.1 weshow also theatten- energy cutoff ε plays a similar role as the temperature in
1
uationfactorsforafixedtemperatureT =104 Kcalculated the Planckian distribution. This is demonstrated in Fig. 2
for three different optical depths τ = 0.5, 3, and 6. It for a power-law distribution of the background field with
max
is seen that the gamma-ray attenuation, starting from the α=2 and sharp cutoff at ε =1 eV and 10−3 eV. Indeed,
1
energy E 0.1E⋆, gradually increases up to E E⋆, af- for the same τ = 6, the case of ε = 1 eV is quite sim-
max 1
∼ ∼
ter which the source becomes more and more transparent ilar to the case of Planckian distribution with temperature
(κ exp[ E−1lnE] 1), and, consequently, the primary T = 104 K shown in Fig.1. The main difference appears
spe∝ctrum−startstorec→over.Asaresult,in thisenergyinter- in the low-energy part, E E⋆. The absorption curve in
valthespectrumappearsharderthantheprimaryspectrum. Fig.2 at low energies is sm≪oother, because the n(ε) ε−2
∝
Thebottom panelof Fig.1 shows thechangeof theslope of typedistribution providesmore high-energytarget photons
gamma-ray spectrum, ∆Γ, which can be interpreted as a compared to the Wien tail of the thermal distribution, for
change of the local photon index, assuming that the initial interactions with low-energy gamma-rays.
gamma-ray spectrum is described by a power-law distribu- The hardening of the initial spectrum caused by inter-
tion, dN/dE E−Γ0. The emerging spectrum of gamma- nal absorption compensates, to a large extent,the steepen-
∝
4 Aharonian, Khangulyan & Costamante
u (2.2 µm) = 16 nW/m2sr, the photon index between
EBL
100 GeV and several TeV is changes by ∆Γ 2, thus, the
∼
intrinsic(source)spectrumshouldbeveryhardwithaslope
c c
Γ=Γ ∆Γ 1,whereΓ =2.88 0.17 istheobserved
obs obs
− ∼ ±
photonsindexof1ES101-232(Aharonian et al. 2006a).Pos-
tulatingthatthephotonindexallowedbyconventionalmod-
b b els of gamma-ray production in blazars should not exceed
−τe Γ0 = 1.5, an upper limit on the EBL flux, at the level
of u (2.2 µm) 10 nW/m2sr has been derived by the
EBL
≈
HESScollaboration(Aharonian et al. 2006a).Itisseenfrom
Fig.3 that this upper limit can be readily increased by a
a: τ = 6
max factor of 1.5, alowing a substantial internal absorption of
b: τ = 3 a a gamma-rays. Indeed, the “joint operation” of internal and
max
c: τ = 0.5 intergalactic absorptions results in the changes of the slope
max
a a of the initial gamma-ray spectrum in the relevant energy
band by ∆Γ 0 to 1.5 for τ = 3, and ∆Γ from -0.5 to
max
3 ∼
b b +0.5 for τmax = 6. In the latter case, the overall change of
theshapeof theinitial spectrum from 100 GeV to5TeV is
Γ c c quite small, so hard TeV gamma-ray spectra can in princi-
∆ 0
ple be detected also from distant blazars. This assumption
can solve, to a certain extent, the problem related to the
−2
spectraofaccelerated (parent)particles,andthus(unfortu-
nately!) relax the constraints on the EBL that can be de-
rived from gamma-ray observations. Formally, a detection
E, eV
of not-very-steep TeV gamma-ray spectra with Γ 6 4
obs
Figure 2. Upper pannel: Attenuation factor calculated for a from distant (z > 0.15) blazars cannot be excluded even
power-lawdistributionoftargetphotonswithalow-energycutoff: for an EBL flux close to the claimed high EBL fluxes de-
nph∝ε−2 forε1<ε<∞andnph=0forε6ε1.Solidcurves: rived from the COBE/DIRBE and 2MASS measurements
ε1 =1eV; dashed curves: ε1 =10−3 eV. Threedifferent optical (Cambresy et al. 2001), uEBL(2.2µm) 28 nW/m2sr. This
depth are shown: τmax = 0.5 (blue), 3 (green), 6 (red). Bottom is demonstrated in Fig.4. At energies≈above 300 GeV the
pannel: Variations of the local photon index of the gamma-ray
absorption of gamma-rays in EBL only increases the pho-
spectrum.
ton index by ∆Γ > 4, while an additional internal absorp-
tion with τ = 10 results in ∆Γ 6 2. Approximately the
max
ing of the spectrum due to intergalactic absorption. This is same result is expected for low EBL (e.g. at the level of
demonstratedinFigs.3and4.FortheEBLfluxweusa“ref- uEBL(2.2µm) = 10 nW/m2sr), but for sources located at
erence” shape close to the one calculated by Primack et al. z 0.1. In this regard, the recent claim of detection of
≫
(2005), but with two different absolute flux normalizations VHE gamma-rays from 3C 279 (z =0.538) by the MAGIC
atthewavelengthλ=2.2µm:u (2.2µm)=16nW/m2sr collaboration (Teshima et al. 2007) can be an indication of
EBL
(Fig.3) and 32 nW/m2sr (Fig.4). The first flux is a fac- significant gamma-ray absorption inside the source. Other-
tor of two larger than the low-limit of EBL correspond- wise, evenfor theminimum possible EBL flux,thepurein-
ing to the integrated light contributed by resolved galax- tergalactic absorption would result in an extremely steep
ies (Madau and Pozzetti 2000), while the second flux can VHE gamma-ray spectrum with a photon index > 5. It
be treated as an upper limit at 2.2µm (it is slightly higher is intersting to note that the UV photons of the broad-
thanthefluxesclaimedfromtheCOBE/DIRBEand2MASS line emission region of a size R 1017 cm and luminosity
∼
measurements (Wright et al. 2001; Cambresy et al. 2001). L 2 1044 erg/s (Pian et al. 2005) can serve as a perfect
∼ ×
Notethatfortheprimary(unabsorbed)differentialgamma- targetforinternalabsorptionofhighenergygamma-raysin
ray spectrum with a photon index Γ = 2, the attenuation 3C 279.
0
factor κ = exp( τ) describes the SED of the absorbed ra-
−
diation (E2dN/dE κ(E)). All curves are obtained for
∝
a source located at z = 0.186. This is the redshift of the
BL Lacobject 1ES 101-232, thegamma-ray observations of Theinternalabsorptionofgamma-rayssignificantlyin-
which by the HESS collaboration have been initially used creases the energy requirements to the source. For example
to constrain the EBL flux at optical and NIR wavelengths in the case of τ = 5, the internal absorption leads to
max
(Aharonian et al. 2006a). the reduction of the observed flux at 1 TeV by an addi-
ThesolidcurvesinFigs.3and4(markedas“d”)corre- tional factor of 10. This, combined with the intergalactic
spondtothepureintergalacticeffect(i.e.withouttheinter- absorption, implies 3 orders of magnitude attenuation of
nal absorption). They show strong steepening of the spec- the primary radiation (see Fig.3). For the quiescent state
trumbelow1TeVandabove10TeVwithanoticeablerecov- of 1ES 101-232, the corresponding apparent gamma-ray lu-
eryoftheinitialshapearoundafewTeV,whichisexplained minosity around 1 TeV is estimated L 1044κ−1 erg/s.
TeV
bythespecificshapeoftheEBLenergyflux(closetou For the attenuation factor κ(1 TeV) 1≃0−3, it becomes
EBL
λ−1)between2and10µm(Aharonian 2001).Itisseentha∝t huge, 1047 erg/s, and perhaps one or∼two orders of mag-
fortheabsolutefluxofEBLwithanormalization at2.2µm, nitude even larger in the flaring states (in analogy with
Hard gamma-ray spectra of blazars due to internal absorption 5
d
d
c
c
b
b
−τ −τe
e
a: τ = 10
a max a
b: τ = 5
max
a: τ m a=x 6 c: τ m a=x 1
b: τ m a =x 3 d: τ =0
c: τ = 0.5
max
d: τ =0 a
a
b
b
Γ Γ
∆ ∆
c
c
d
d
E, eV
E, eV
Figure 4. The same as in Fig.3, but the curves are calculated
Figure 3. Internal and intergalactic absorption of gamma-rays. fortheinternal optical depths 10 (a), 5(b), 1(c) and0(d). For
Upperpannel:Attenuationfactors.Theinternalabsorptioniscal- EBLfluxisassumedtwicelargerthaninFig.3:uEBL(2.2µm)=
culatedforaPlanckiandistributionoftargetradiationwithtem- 32nW/m2sr.
perature T =5×104 K.Threedashed curves correspond tothe
internal optical depths τmax = 6 (a) 3 (b), 0.5 (c), 0 (d). The
corresponding solid curves include both the internal and inter-
galacticabsorption.Theintergalacticabsorptioniscalculatedfor
asourceatz=0.186(theredshiftoftheBLLacobject1ES101- available from the EGRET observations (typically, at the
232), assuming a reference shape of the EBL spectrum close to level of 10−10 erg/cm2s or higher), especially if one takes
the one calculated by Primack et al. (2005), and normalized to into account that the energy spectra of gamma-rays pro-
the EBL flux at 2.2 µm: uEBL(2.2 µm)=16 nW/m2sr. Bottom ducedinsomeprincipalradiationprocesses(e.g.throughin-
pannel: Variationofthelocalphotonindex. verse Compton scattering or proton synchrotron radiation)
at sub-TeV energies are expected harder than E−2. On the
otherhand,wecertainlyexpectGeVgamma-raysfromTeV
Mkn421,Mkn501andPKS2155-304)1.Nevertheless,since
blazars,andinthisrespect,theupcomingGLASTmeasure-
there is little doubt that gamma-rays are produced in rel-
ments with significantly improved (compared to EGRET)
ativistically moving jets with a Doppler factor δ > 30 or
sensitivity,especially atmulti-GeVenergies,shouldprovide
even > 100, as it follows from the recently reported vari-
the first effective probes of TeV blazars in the MeV/GeV
ability of Mkn 501 (Albert et al. 2007) and PKS 2155-304
domainingeneral,andforthe“internalgamma-rayabsorp-
(Aharonian et al. 2007b)onminutescales(seee.g.Fabianet
tion” scenario, in particular.
al.(2007)),theintrinsicluminosityL =L δ−4,couldbe
int app Finally, in the case of hadronic origin of TeV gamma-
quitemodest,namely,atthelevelof1039 1041 erg/swhich,
− rays produced at pp and/or pγ interactions, the flux of ac-
infact,isnotfarfromtheTeVgamma-rayluminosityofthe
companying TeV neutrinos, which freely penetrate through
nearbynon-blazartypeAGNM87(Aharonian et al. 2006b).
theinternalandextragalacticradiationfields,canbeashigh
The attenuation of TeV gamma-rays dramatically in- as 10−10 neutrinos/cm2s, i.e. above the detection threshold
creasestheintrinsicTeVtoGeVgamma-rayfluxratio.This
ofthenextgenerationkm3scaleneutrinodetectors.Thede-
does not, however, contradict the GeV flux upper limits
tectionofbothgamma-raysandneutrinosfromTeVblazars,
andthecomparisonoffluxesofthesetwocomponentsofra-
diation would provide principal information about thehigh
1 The detected gamma-ray flux around 200 GeV is an order of
energyprocessesinblazars,aswellasabouttheattenuation
magnitude larger than at 1 TeV, however, because of dramatic
reductionoftheabsorptioneffect,thecontributionoflowenergies of gamma-rays due to the (combined) internal and inter-
to the (absorption-corrected) apparent luminosity, is relatively galacticabsorption.Anadditionalinformationaboutthein-
small. ternal photon-photon absorption alone (separated from the
6 Aharonian, Khangulyan & Costamante
the development of pair cascades fully washes out the ab-
1
sorption features, and instead forms a standard spectrum
with a maximum (“bump”) around the interaction thresh-
old, (m c2)2/kT 100GeV,followedbyasteepspectrum
e
∼ ∼
0.1 abovethe“bump”.Thecascadespectrumaround1TeVsat-
N /dEγ EE0==∞∞,, ianbtsroinrbsiecd urates at the level of 10 percent of the primary gamma-ray
2Ed E00=∞, cascading flux. The spectrum above 1 TeV has a flat shape until the
E=10TeV, intrinsic
0.01 E00=10TeV, absorbed efficiencyof thecascadedrops(becauseoftheprogressively
E0=10TeV, cascading decreasing optical depth) with a gradual transition to the
“absorption” regime.
Therearetwowaysofsignificantreductionofthecontri-
0.001
1e+09 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 butionfromthecascadecomponenttotheobservedgamma-
E,eV
radiation.
Figure 5. Gamma-ray spectra caused by the internal photon-
photon absorption (dotted curves) or formed during a develop- (i) Absorption of gamma-rays outside the production re-
mentofpaircascades(solidcurves)inaradiationfieldwithtem- gion.Inthiscasethe“foreground”cascaderadiationcannot
perature T = 104 and optical depth τmax = 6. It is assumed screen the unabsorbed fraction of gamma-rays. Indeed, al-
thatthe energydensityofradiationsignificantlyexceeds theen- thoughtheenergyinthecascaderadiationexceeds,byafac-
ergy density of the magnetic field, ur ≫uB. The spectra of pri- torof100,theenergyoftheunabsorbedfractionofprimary
mary gamma-radiation (dashed lines) are assumed as “power-
radiation(seeFig.5),fortheobservertheprimaryradiation
law with exponential cutoff”: dN/dE ∝ E−2exp(−E/E0) with emitted by a relativistically moving source (’blob“) will be
E0=10TeVandE0=∞. much brighter ( δ4) and shifted to higher energies ( δ )
∝ j ∝ j
comparedtotheisotropiccascadeemissionofthesurround-
ingenvironment.Ontheotherhand,thepartofthecascade
extragalacticabsorption)iscontainedintheradiationofsec-
developedinsidetheblobis,ofcourse,alsoDopplerboosted,
ondary (pair-produced) electrons.
therefore the condition of suppression of the cascade com-
ponent can be satisfied when the optical depth within the
′
blob τ 1, i.e. the gamma-ray production region is much
3 RADIATION OF SECONDARY ELECTRONS smaller≪thanthesourceoftheoptical/UVradiation,l R.
≪
Since th gamma-ray production regions in blazars are be-
Thepropagation ofhighenergygamma-raysthroughalow-
lieved to be very compact, l 1014 1016 cm, we may
energy photon field cannot be reduced to the simple effect ∼ −
conclude that the source of the optical radiation should be
ofabsorption.Whenthegamma-rayphotonisabsorbed,its
larger than R 1015 1017 cm. There are many poten-
energy is transfered to the electron-positron pair. The sec- ∼ −
tialsourcesofopticalradiationinblazars(seee.g.Urryand
ondaryelectronsinteractingwiththeambientmagneticand
Padovani 1995). In this paper we do not intend to spec-
radiationfieldsproducehighenergyphotons,eitherviasyn-
ify the origin of the low-energy radiation fields, but simply
chrotron radiation orinverseCompton scattering. Thesyn-
notice that an even modest optical source located in the
chotron photons are produced with much smaller energies,
core of a blazar can provide an effective target for gamma-
thus they do not interact with the background low-energy
ray absorption. The luminosity of this source is estimated
photons.Inatarget fieldwith narrowspectral distribution,
as L = 12πn kTR2c, where n is the average number
inverseComptonscatteringofthephoto-producedelectrons O ph ph
density of radiation. It can be estimated from the condi-
proceedsintheKlein-Nishinalimit;theupscatteredphoton
tion σ Rn = τ . For a characteristic optical depth
receives the major fraction of the electron energy, thus is γγ ph max
τ 5 and temperature T = 5 104 K, we obtain,
abletointeractagainwithbackgroundphotons.Thesecond max ∼ ×
L 2 1043(R/1017 cm) erg/s.
O
generation pairs again produce gamma-rays, thus an elec- ≃ ×
tromagnetic cascade developes. (ii) Secondary electrons cooled through synchrotron radia-
While the energy of gamma-rays interacting with EBL tion. This condition can be satisfied if the energy density
dissipatesintheintergalactic medium,andinthiswaycon- of the magnetic field exceeds the energy density of radia-
tributes to the diffuse extragalactic background radiation, tion, B2/8π > 3kTn or B > 0.4(R/1017 cm)−1/2 G. In
ph
the secondary radiation caused by internal absorption may Fig. 6 the broad-band SED of the radiation initiated by
accompany the primary (unabsorbed) fraction of gamma- absorption of primary gamma-rays with a power-law spec-
rays. In this regard, the development of an electromagnetic trumdN/dE E−2isshown,assumingthattheabsorption
∝
cascadeisnotadesirable process,becauseitmasksthedis- ofgamma-raystakesplaceinsidethegamma-rayproduction
tinct absorption features, and thus prevents the formation region.Calculationsareperformedforthreedifferentoptical
of very hard gamma-ray spectra. This is demonstrated in depthsτ =0.5, 3,and 6,afixedtemperatureofradiation
max
Fig.5.Thecascadespectraarecalculatedassumingthatthe T =5 104 K,andtwoextremevaluesofthemagneticfield,
·
regionofproductionofprimarygamma-raysislocatedinthe B = 100 G and B = 0.1 G. In calculations of the electron
center of a spherical source filled with grey-body radiation spectra we assume that the energy losses of electrons are
with temperature T = 104 K and optical depth τ = 6. dominated by synchrotron cooling. Note that the spectrum
max
The spectrum of primary gamma-rays is given in the form: of synchrotron radiation of secondary electrons has a char-
dN/dE E−2e−E/E0 for two values of the cutoff energy: acteristicbell-typeform,i.e.quitesimilartothesynchrotron
∝
E = 10 TeV and E = . In Fig. 5 both the absorbed spectraformedinthesynchrotron-selfCompton(SSC)mod-
0 0
∞
and cascade gamma-ray spectra are shown. It is seen that els. However, in the SSC models designed for TeV blazars
Hard gamma-ray spectra of blazars due to internal absorption 7
J (E ) T=5x10 4 K
BB==100.10 GG T=5x10 4 K 0 γ γγ j ==130, δ =20 J 0 (E γ )
c j j
a a c
b b
E
d
N/ E
2E d a: τ i n = 6 c N/d c
b: τ m in a =x 3 b 2E d a: τ i n = 6
max max b
a
c: τ i n = 0.5 b: τ in = 3
max max
c: τ i n = 0.5 a
max
log(E/eV)
log(E/eV)
Figure6.Synchrotronradiationofsecondaryelectrons.Thepri- Figure 7. Impact of the bulk motion on synchrotron radiation
mary gamma-ray spectrum is assumed dN/dE ∝ E−2 (dotted
of secondary electrons. The magnetized blob moves with a rela-
line). The target photon field is Planckian with T = 5·104 K.
tivistic velocity.The synchrotron maximum moves by a factor of
Ttτrihaneofa=bses6coor(bnade),da3ryg(abem)le,mcatanr-odrna0sy.5asr(pece)cc.atTrlcahuelaasntydendcthfhorerotctrhoorrnreeersapodpointaidtciiaonlngdiessppcteahcls-- δmja/rγyj2gaanmdmtah-eradyisstpriebcutrtuiomnswbaescoamsseumsoemdepwohwaetr-wlaiwde:r∝. TEhγ−e2p(riis-
max shown by the dotted line). The target photon field is Planckian
culatedassumingthattheabsorptionofgamma-raystakes place
with T = 5·104 K. The absorbed spectra are shown by black
inside the source (gamma-ray production region) for two values
of the magnetic field: B = 100 G (solid curves) and B = 0.1 G solidcurvesforτmax=6(a), τmax=3(b)andτmax=0.5(c).We
calculate synchrotron radiation from a magnetized region with
(dashedcurves).
the average optical depth (over different directions) τin = 6(a,
max
red lines), 3(b, green lines) and 0.5(c, blue lines). The magnetic
field is assumed B =100 G. Calculations are performed for two
the synchrotron peak is a result of the maximum energy of
accelerated electrons, while the hard low-frequency part of differentbulkLorenzfactors:γj =1(nomotion)andγj =30(for
δj =20).
the spectrum is determined by radiation of uncooled low-
energy electrons. In the ”internal gamma-ray absorption“
scenario we see similar features, but for different reasons. Doppler effect shifts the overall SED towards higher ener-
Theelectronsinanarrow-bandradiationfieldareproduced gies by a factor of δ , in the ”gamma-ray absorption“ sce-
j
with a spectrum similar to the spectrum of parent gamma- nario the synchrotron peak is shifted towards lower ener-
rays ( E−Γ0), but with cutoffs both at low- and high en- gies (see Fig.7) The reason is quite simple. In the frame of
∝
ergies. These cutoffs are explained by the threshold of the therelativisticallymovingsourceilluminatedbyanexternal
photon-photon pair production and by the reduction of its radiation with a characteristic energy ε , the electrons are
0
cross-section at highest energies, respectively. Due to the producedwithenergiesE >(m c2)2/(ε γ ),thusthepo-
min e 0 j
synchrotron cooling, at low energies the electron spectrum sition of the synchrotron peck in the frame of the observer
obtainsastandard E−2form,whichgraduallytransforms is proportional to δ E2 δ/γ2. Thus in a source moving
toa E−(Γ0+1)typ∝espectrumatintermediateenergiesand towards the observejr matina∝smallj angle, the position of the
∝
acutoffathighestenergies.Thecorrespondingspectralfea- synchrotron peak in the frame of the observer is inversely
tures are reflected in the synchrotron spectrum - a power- proportional to the Doppler factor δ , just opposite to the
j
law with aphoton index1.5 at low energies, with a smooth spectrumofgamma-rayswhichisshiftedtowardshigheren-
transitiontoapower-lawwithaphotonindexΓ0/2+1atin- ergies bythe same Doppler factor.
termediateenergies, andasmooth gradualcutoffathighest The position of thesynchrotron peak dependsstrongly
energies. A significant difference between the SSC and the also on the average energy (or temperature) of the target
”internalgamma-rayabsorption“modelsappearsalsointhe radiation field.Indeed,with an increase of thetemperature
ratio of fluxes corresponding to the low (IR to X-ray) and of background radiation T, the threshold of photon-photon
high(gamma)energypeaks.WhileintheSSCscenariothis interactions, and consequently the minimum energy of pro-
ratio is determined by the ratio of energy densities of the duced secondary electrons decreases as E 1/T, and
min
∝
magnetic and target photon fields, in the”internal gamma- hence the synchrotron peak moves towards lower energies
ray absorption“ scenario this ratio is basically determined as hν 1/E2 1/T2. Generally, the position of the
m ∝ min ∝
bytheefficiencyofgamma-rayabsorptioninsidethesource. synchrotronpeakofpairproducedelectronsdependsonthe
The magnetic field determines only theposition of thesyn- temperatureofthetargetradiationfield,themagneticfield,
chrotron peak, but not the flux level. The latter is deter- and theDoppler and Lorentz factors of thejet, as
τmmianxed by1,tthheefdaecptoerndpernocpeorotniotnhael toopt(i1ca−l deexppt[h−aτlmmaxo]s)t.dFiosr- hνm ∝BT−2(δj/γj2) . (3)
≫
appears. Allthese features can beseen in Fig. 6. Itis easy toderiveasimple analytical expression which de-
Thepositionofthesynchrotronpeakdepends,inaquite scribed the high energy part of the synchrotron spectrum,
interesting way, also on the Lorenz and Doppler factors of hν hν , produced by electrons for which the source be-
m
≫
the source. While in the standard models of blazars the comes optically thin, τ(E) 6 1. In this case the produc-
8 Aharonian, Khangulyan & Costamante
tion spectrum of electrons Q(E) 1/EdN /dE (here we cores of blazars. For the formation of hard VHE gamma-
γ
∝
ignore the weak logarithmic term in the photon-photon in- ray spectra, the target radiation field must have a rather
teractioncross-section).Then,forthepower-lawgamma-ray narrow spectral distribution or a sharp low-energy cutoff,
spectrum, dN /dE E−Γ0, the cooled electron spectrum with a typical energy of photons of about 1 to 10 eV. For-
γ
is also power-law, d∝N /dE E−Γ0−2, and correspond- mally,forverylargeopticaldepths,thisprocesscanprovide
e e
ingly the SED of synchrotron∝radiation, νF ν−(Γ0+1)/2. an arbitrary hardness of gamma-ray spectra, though at the
ν
∝
For example, for Γ = 2, the SED of synchrotron radia- expense of a significant increase of the required nonther-
0
tion is rather steep, νF ν−1.5. In fact, because of the mal energy budget. However, as long as the current blazar
ν
∝
cutoff in the gamma-ray spectrum, the high energy tail models require relativistically-moving gamma-ray produc-
of synchrotron radiation is expected even steeper. This is tionregionswithlargeDopplerfactors,δ >30,andperhaps
j
demonstrated in Fig. 8 where the broad-band SEDs of ra- evenmore(Aharonian et al. 2007b;Fabian et al. 2007),the
diation initiated by gamma-rays in a source at z = 0.186 available energy budget seems tobe not a critical issue.
are shown. It is assumed that gamma-rays in the frame The unavoidable feature of the proposed model is the
of the jet moving with a Lorentz factor γ = 10 have a radiation of secondary electrons via synchrotron or inverse
j
power-lawdistributionwithanexponentialcutoffat1TeV, Comptonscattering.Iftheopticaldepthinsidethegamma-
dN /dE E−3/2exp( E/1TeV). It is assumed also that ray production region is small, τ 1, e.g. the gamma-ray
γ
∝ − ◦ ≪
δ = γ (i.e. the viewing angle is θ 6 ). The calcula- source is much smaller than the external source of optical
j j
≈
tions are performed for two temperatures of the radiation photons, the secondary electrons are produced and radiate
field through which thejet propagates - T =5 104 K and mainly outside the gamma-ray production region. Even in
×
T = 5 105 K, assuming that in both cases the optical the case of heavy absorption of gamma-rays, the secondary
×
depthinside themovinggamma-ray production region (the radiation of secondary electrons can hardly be detected.
blob)withahomogeneousmagneticfieldisτ =3.Finally Indeed, since the intrinsic gamma-ray luminosity is rela-
max
fortheintergalacticabsorptiona”template“EBLspectrum tively modest, and the absorbed energy is re-radiated as
is assumed with a normalization at 2.2 µm at the level of anisotropic source2,thelost ofthebeamingfactordramat-
16 nW/m2ster. Theimpact of thetemperatureon both the ically reduces thesignal compared to theprimary (Doppler
spectrumofarrivinggamma-raysandthesynchrotronradi- boosted) radiation.
ation of secondary electrons is clearly seen.Notethat while The picure is dramatically changed when the gamma-
below 100 GeV the deformation of the primary gamma-ray ray source moves through a very dense photon field, such
spectrumiscausedmainlybyinternalabsorption,thesharp thattheopticaldepthinsidethesourcebecomeslargerthan
cutoff at energies above 10 TeV is due to the severe inter- 1.Inthiscasethemainfractionoftheabsorbedenergyisre-
galactic absorption. In the intermediate energy range be- leasedintheformofsecondaryelectronsinsidethegamma-
tween 100 GeV and 10 TeV the internal and intergalactic ray production region, and thus the radiation of the sec-
photon-photon interactions ”operate“ together resulting in ondary electrons profits, as the primary gamma-radiation
quite specific broad-band SEDs. The discussion of impli- does, from the Doppler boosting. The secondary electrons
cations of these results for specific astrophysical objects is are cooled through synchrotron and/or inverse Compton
beyond the scope of this paper. We note only that our pre- channels. The latter in fact proceeds via development of
liminary studies show that the suggested model in general pair cascades as long as the typical energies of electrons or
can satisfactorily explain theobserved broad-band SEDs of gamma-raysandtheenergyoftargetphotonsεE m2c4.
e,γ ≫ e
TeV blazars. Thecascade,however,diminishestheenergy-dependentab-
sorption features, thus the model becomes effective when
the electrons are cooled predominantly via synchrotron ra-
diation,i.e.B2/8π >u .Theenergydensityoftheradiation
4 DISCUSSION r
u =ε¯n withanaverageenergyoftargetphotonsofabout
r ph
The energy spectra of VHE gamma-rays from blazars, af- ε¯ 1eV is estimated from thecondition τmax>1, thusfor
∼
ter correction for intergalactic absorption, generally appear theeffective suppression of thecascade
very hard, even for the minimum flux level of EBL deter- B>(40πε¯/σ l)1/2 0.5(l/1015cm)−1/2τ1/2 G (4)
minedbytheintegrated light ofresolved galaxies atoptical T ≈ max
(Hubble)andinfrared(Spitzer)wavelengths.Aslightdevia- For an optical depth τ 1 and the size of the
max
∼
tion from therobust lower limits of EBL leads tounusually gamma-raysourcel 1016 cm,themagneticfieldexceeding
∼
hard intrinsic gamma-ray spectra which cannot be easily 0.1Gshouldbesufficienttopreventthecascade.Forsmaller
explained within the standard particle acceleration and ra- gamma-ray production regions, e.g. l 1014 cm, the mag-
∼
diation models. In this paper we suggest a scenario which netic field should be larger than 1 G. For such magnetic
can lead to the formation of instrinsic gamma-ray spectra fields the synchrotron radiation of secondary electrons ap-
of arbitrary hardness without introducing modifications in pearsintheopticaltohardX-rayenergybands.Depending
the particle acceleration models. The main idea is that the on the optical depth, the synchrotron peak can be higher
gamma-rays before they leave the source suffer significant than the gamma-ray peak. Interestingly, unlike the classi-
internal energy-dependent absorption due to interactions cal ”synchrotron/Inverse-Compton“ models, where the ra-
with the ambient low-frequency photons. The existence of
dense radiation fields of different origin in blazars (see e.g.
UrryandPadovani(1995))combinedwiththelargephoton- 2 Unless the electrons are produced in an environment with a
photon pair production cross-section, makes this scenario verylowmagneticfield,andthusarecooledviainverseCompton
quite natural and effective, in particular in the compact scatteringbeforeanynoticeabledeflection.
Hard gamma-ray spectra of blazars due to internal absorption 9
without absorption
δ =10, γ =10, B=1 G
j j
E
d a
N/ a b
d
2
E
4 b
a: T=5x10 K
5
b: T=5x10 K
log(E/eV)
Figure8.Impactoftheradiationtemperatureonthespectralenergydistributionofemissioninitiatedbyprimarygamma-raysinajet
movingthroughahomogeneousradiationfield.Thesourceislocatedatz=0.186.Thedashedcurveistheassumedprimaryspectrunof
gamma-rays.Thesolidcurvesrepreesentthesynchrotronraduiationofthesecondaryelectronsaswellasthegamma-rayspectraafterthe
internalandextragalacticabsorption.Calculationsareperformedfortworadiationtemperatures,T =5×104 K(a)andT =5×105 K
(b).Forbothcasesδj =γj =10,B=1G,τmax=3.AnEBLisassumedwithanormalizationofthefluxuEBL(2.2µm)=16nW/m2str.
tio of the synchrotron to IC peak is determined by the ra- play a role of the target for photomeson interactions.
tiou /u ,in the”internalgamma-ray absorption“ scenario However, because of the small cross-section, the efficiency
B r
thesynchrotronpeakdoesnotstronglydependonthemag- of this process again appears quite low. The interaction
netic field. Whether this scenario can be applied to the the time of protons with energy, E > 200 MeV/(ε¯γ)
j
broad-band SEDs of gamma-ray blazars, is an interesting 2 1016(ε¯/1 eV)−1(γ/10)−1 eV (in the frame of th≃e
j
×
issue which requires special dedicated studies. moving source with a Lorentz factor γ ) is estimated
j
anismFsinoafllyp,riwmeawryangtamtomdais-rcaudssiabtiroinefl.yGtehneerraaldlyia,ttihone mmoecdhe-l 1tp0γ−2≈8 c1m/(2fσispγthnephacv)er∼ag(eσγcγro/sσsp-sγe)cft−io1nR/acnτdm−a1fx (<0.σ2pγis>th≈e
∼
doesnotgiveapreferencetotheleptonicorhadronicorigin multiplicityoftheprocess).Thus,wecanseethatduringthe
of radiation, unless the magnetic field exceeds the estimate passage of the source of optical photons of size R, the pro-
given by Eq.(4). In this case the synchrotron-to-IC flux ra- tonstransferonlyσpγ/σγγ 10−3fractionoftheirenergyto
∼
tio produced by directly accelerated electrons would be too gamma-rays.Ifsuchalowefficiencycanbecompensatedby
high,especiallyaftertheinternalabsorptionofgamma-rays, very large Doppler boosting (e.g. assuming δj 100), this
∼
contrary to the detected SEDsof most of the TeV blazars. channel can provide very large fluxes of neutrinos, which
Large magnetic fields in thegamma-ray production re- unlike gamma-rays do not suffer internal and extragalactic
gion,typicallyB>1G,wouldfavorgamma-rayproduction absorption. In the case of attenuation of VHE gamma-ray
by relativistic protons, with all advantages and disadvan- fluxes by 2 to 3 orders of magnitude, the expected fluxes
tages common for hadronic models. The basic problem of of neutrinos from TeV blazars can be as large as the de-
hadronicmodelsislinkedtothelowinteractionrateswhich tection threshold of the km3 volume high energy neutrino
do not allow the most natural explanation of the observed telescopes, Fνµ(>1 TeV)≈10−11 neutrinos/cm2s.
fast gamma-ray variability of blazars in terms of radiative It is interesting to note that, because of the threshold
cooling. For example, in the case of interactions of protons ofphotomesonproduction,theinteractionsofprotonsofar-
withtheambientplasmawithnumberdensityn,thecharac- bitrary distribution with a narrow band radiation with a
teristictimeofppinteractionswithproductionofπ0-mesons characteristic energy ε¯, result in a differential gamma-ray
is t 1015n−1 s. Thus, in order to explain the variabil- spectrum which below theenergy 1016(ε¯/1 TeV)−1 eV is
pp ≈ ≈
ity of gamma-rays as short as several minutes like the TeV extremelyhard,dN/dE =const,thusthisprocessitselfcan
flaresobservedfrom PKS21555-301 andMkn501, theden- provide very hard gamma-ray spectra independent of the
sityofplasmashouldbeaslargeas5 1012δ−1 cm−3 which spectrum of parent protons.
× j
implies a very heavy source and correspondingly huge ki- Despite certain attractive features, this mechanism
netic energy Ekin = (4/3)πl3nmpc2γj 1055 erg (here we faces the same problem as pp interactions - a low radia-
≈
assumethatδ≈γj).Onemayinvokealternativeexplanations tion efficiency. Therefore it can work only under conditions
of the variability of blazars, e.g. due to the adiabatic losses of extremely large Doppler boosting of radiation. The effi-
or escape of particles from the source, but this assumption ciency of VHE gamma-ray production can be much higher
leadstodramaticreductionofradiationefficiency,andtoan in the case of synchrotron radiation of protons, provided
increasetheenergyrequirementstotheacceleratedprotons. that the acceleration of protons proceeds at a rate close to
A similar problem face the photomeson processes at thefundamentallimit, andthemagnetic fieldin theproton
interactions of protons with the ambient radiation fields. accelerator well exceeds 10 G. In particular, in the mag-
Actually in the ”internal gamma-ray absorption“ scenario netic field of order 100 G, protons can be accelerated to
this mechanisms seems a quite natural choice because the energies 1020 TeV and thus can produce VHE synchrotron
same background photons which absorb gamma-rays can gamma-rays on timescales of 104 s. Although due to the
10 Aharonian, Khangulyan & Costamante
self-regulatedsynchrotroncutoff(Aharonian 2000)thespec- Urry,C.M. and Padovani, P., 1995, PASP,107, 803
trum of gamma-rays is limited by sub-TeV energies, an ob- Wright, E.L., 2001, ApJ, 555, 538.
server detects Doppler boosted gamma-radiation extending
to multi-TeV energies. The characteristic feature of this
mechanism is the very large electromagnetic energy con-
tainedintheblob,1/6l3B2 2 1048 erg,hardX-rayemis-
≈ ×
sion of the secondary (pair-produced) electrons, and negli-
gible fluxesof neutrinos.
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