One-zone SSC model for the core emission of Centaurus A revisited
Maria Petropoulou, Eva Lefa, Stavros Dimitrakoudis, Apostolos Mastichiadis
aa r X i v : . [ a s t r o - ph . H E ] N ov Astronomy & Astrophysics manuscript no. ver˙211013 c (cid:13)
ESO 2018June 4, 2018
One-zone SSC model for the core emission of Centaurus Arevisited
Petropoulou, M., Lefa, E., Dimitrakoudis, S. and Mastichiadis, A.
Department of Physics, University of Athens, Panepistimiopolis, GR 15783 Zografos, GreeceReceived.../Accepted...
ABSTRACT
Aims.
We investigate the role of the second synchrotron self-Compton (SSC) photon generation to the multiwavelengthemission from the compact regions of sources that are characterized as misaligned blazars. For this, we focus on thenearest high-energy emitting radio galaxy Centaurus A and we revisit the one-zone SSC model for its core emission.
Methods.
We have calculated analytically the peak luminosities of the first and second SSC components by, first, derivingthe steady-state electron distribution in the presence of synchrotron and SSC cooling and, then, by using appropriateexpressions for the positions of the spectral peaks. We have also tested our analytical results against those derived froma numerical code where the full emissivities and cross-sections were used.
Results.
We show that the one-zone SSC model cannot account for the core emission of Centaurus A above a few GeV,where the peak of the second SSC component appears. We, thus, propose an alternative explanation for the origin ofthe high energy ( & . ∼ erg/s, provided that the injectionspectra are modelled by a power-law with a high value of the lower energy cutoff. Finally, we find that the contributionof the core emitting region of Cen A to the observed neutrino and ultra-high energy cosmic-ray fluxes is negligible. Key words. radiation mechanisms: non-thermal – gamma-rays: general – Radio galaxies: Centaurus A
1. Introduction
Centaurus A (Cen A) is the nearest radio galaxy to earthwith a luminosity distance D L ≃ . and, therefore,one of the best labarotories for studying the physics of radiolobes, relativistic outflows, shock formation, thermal andnon-thermal emission mechanisms. Due to its proximity,emission from the extended lobes and jet as well as fromits nucleus has been detected across the electromagneticspectrum (see e.g. Israel (1998) for a review). In radio wave-lengths it has an FRI morphology (Fanaroff & Riley 1974),while in higher energies (X-rays) is regarded as a misalignedBL Lac object (Morganti et al. 1992; Chiaberge et al. 2001)in agreement with the unification scheme of Active GalacticNuclei (AGN) (Padovani & Urry 1990, 1991). Although theangle between the jet axis and our line of sight is large, itis still not well constrained mainly due to the assumptionsused in its derivation (see e.g. Hardcastle et al. 2003); itranges between 15 ◦ (Hardcastle et al. 2003) up to 50 ◦ − ◦ (Tingay et al. 1998).Gamma-ray emission ( ∼ . −
10 GeV) from Cen Ahas been detected by EGRET (Hartman et al. 1999) butthe identification of the γ -ray source with the core wasrather uncertain due to large positional uncertainties. Therecent detection of very high energy (VHE) emission ( ∼ TeV) from the core of Cen A by H.E.S.S. (Aharonian et al.2009) along with the
Fermi satellite observations above 100MeV from the core (Abdo et al. 2010a) and X-ray data Although there is still considerable debate on its distance,see e.g. Ferrarese et al. 2007; Majaess 2010; Harris et al. 2010we will adopt this value as a representative one. from various telescopes make now possible the constructionof a well sampled Spectral Energy Distribution (SED) forits nuclear emission which requires physical explanation.Whether the HE/VHE core emission originates from verycompact or extended regions is still unclear because of lack-ing information regarding the variability in the GeV/TeVenergy ranges and of the current resolution of γ -ray instru-ments. This complicates further the attempts of fitting themultiwavelength (MW) core emission.The one-zone synchrotron self-Compton (SSC) modelis one of the most popular emission models due toits simplicity and to the small number of free param-eters. In the past it has been successfully applied tothe SEDs of various blazars – see e.g. Ghisellini et al.(1998); Celotti & Ghisellini (2008) for steady-state mod-els and Mastichiadis & Kirk (1997); B¨ottcher & Chiang(2002) for time-dependent ones. Note, however, thatrapid flaring events and recent contamporeneous MWobservations of blazars pose problems to homogeneousSSC models (Begelman et al. 2008; B¨ottcher et al. 2009;Costamante et al. 2009). If FRIs are indeed misaligned BLLac objects, then one expects that the one-zone SSC modelapplies also successfully to their MW emission (see e.g.Abdo et al. (2009b) for M87 and Abdo et al. (2009a) forNGC 1275). We note, however, that alternative emission We note that high-energy (HE) emission was also detectedfrom the radio lobes of Cen A (Abdo et al. 2010b), while a recentanalysis by Yang et al. (2012) shows that this emission extendsbeyond the radio lobes. However, we will not deal with the lobeemission in the present work. 1. Petropoulou et al.: SSC model for Cen A revisited models have also been proposed (e.g. Giannios et al. (2010)for M87). In the case of Centaurus A it is still the leadinginterpreting scenario for the core emission, at least belowthe TeV energy range (Chiaberge et al. 2001; Abdo et al.2010a; Roustazadeh & B¨ottcher 2011).However, there is a subtle point that must be taken intoaccount when applying one-zone models to FRIs: due to thelarge viewing angle the Doppler factor δ cannot take largevalues (in most cases δ <
5) in contrast to blazars wheretypical values are δ ∼ −
30, while even higher values(40 < δ <
80) appear in the literature (Konopelko et al.2003; Aleksi´c et al. 2012). Thus, unless the observed γ -rayluminosity of FRIs is by a few orders of magnitude lowerthan the one of blazars, the injection power of relativis-tic radiating electrons must be high enough to account forit . The above imply that in cases where the radius of theemitting source is not very large, higher order SSC photongenerations may, in general, contribute to the total SEDand are not negligible as in the case of blazars.In the present work we focus on Cen A as a typical ex-ample of a misaligned blazar. We show that the simple ho-mogeneous SSC model cannot fully account for its MW coreemission due to the emergence of the second SSC photongeneration. We, therefore, present an alternative scenariowhere the SED up to the GeV energy range is attributedto SSC emission of primary electrons, while the GeV-TeVemission itself is attributed to photohadronic processes.The present work is structured as follows: in Section 2we calculate analytically using certain approximations thepeak luminosities of the synchrotron and SSC (first and sec-ond) components for parameters that are relevant to Cen A;in the same section we test our results against those ob-tained from a numerical code that employs the full expres-sions for the cross sections and emissivities of all processes.In Section 3 we show the effects that the second SSC com-ponent has on the overall one-zone SSC fit of the MW coreemission of Cen A. In Section 4 we introduce a relativisticproton distribution in addition to the primary electron one,and present the resulting leptohadronic fits to the emittedMW spectrum; we also discuss the resulting neutrino andultra-high energy cosmic ray emission. Finally, we concludein Section 5 with a discussion of our results.
2. Analytical arguments
The calculation of the steady-state electron distribution inthe case of a constant in time power-law injection under theinfluence of synchrotron and SSC (in the Thomson regime)cooling can be found in Lefa & Mastichiadis (2013) – here-after LM13. However, in the present section and for reasonsof completeness, we derive the analogous solution for mo-noenergetic electron injection. On the one hand, this choicesignificantly simplifies our analytical calculations. On theother hand, it is justified since the power-law photon spec-trum in the range 10 − Hz is very steep and it can betherefore approximated by the synchrotron cutoff emissionof a monoenergetic electron distribution. We remind that for emission from a spherical region thatmoves with a Doppler factor δ , the relation between the lumi-nosity as measured in the rest-frame L ′ and the observed one L obs is L obs = δ L ′ . We assume that electrons are being injected at γ and sub-sequently cool down due to synchrotron and SSC losses.Here we assume that all scatterings between electrons andsynchrotron photons occur in the Thomson regime, whichis true for parameter values related to the spectral fittingof Cen A (see Sections 2.2 and 3). The electron distribu-tion cools down to a characteristic Lorentz factor γ c wherethe escape timescale ( t e , esc ) equals the energy loss timescaleand it is given by γ c = 3 m e c σ T t e , esc ( u B + u s ) , (1)where t e , esc = R/c , R is the size of the emitting region, u B is the magnetic energy density and u s = m e c Z ǫ max ǫ min d ǫ ǫn s ( ǫ ) , (2)is the energy density of synchrotron photons. The integra-tion limits in eq. (2) are ǫ max = bγ and ǫ min = bγ , where b = B/B cr and B cr = 4 . × G. In what follows, all en-ergies that appear in the relations will be normalized withrespect to m e c , unless stated otherwise. Here we assumethat γ c is much smaller than γ , which further implies thatthe particle escape is less significant than the energy lossesin shaping the electron distribution at the particular en-ergy range. Thus, the electron distribution n e at the steadystate is described by the kinetic equation below Q ( γ ) = 43 m e c σ T c ∂∂γ (cid:2) γ n e ( γ ) ( u B + u s ) (cid:3) (3)where and Q ( γ ) = Q δ ( γ − γ ) is the injection rate perunit volume of electrons having Lorentz factors in the range( γ, γ + dγ ). Under the δ -function approximation for the syn-chrotron emissivity, the differential number density of syn-chrotron photons is given by – see e.g. Mastichiadis & Kirk(1995), n s ( ǫ ) = A ǫ − / n e (cid:18)r ǫb (cid:19) , (4)where A = 23 Rσ T u b b − / . (5)and u b is the dimensionless magnetic energy density, i.e. u b = u B /m e c . Plugging eqs. (2) and (4) into eq. (3) wefind Q δ ( γ − γ ) = 43 σ T c ∂∂γ (cid:2) γ n e ( γ ) G e (cid:3) , (6)where G e depends on the electron distribution as G e = (cid:18) u b + 43 σ T Ru b Z γ γ c d x x n e ( x ) (cid:19) . (7)An ansatz for the solution n e of the above integro-differential equation is n e ( γ ) = k e γ − p with k e and p be-ing the parameters to be determined. By substituting theabove solution into eq. (6) we find that p = 2 and that k e satisfies the following quadratic equation (cid:18) σ T Ru b γ (cid:19) k e + u b k e − Q σ T c = 0 , (8)
2. Petropoulou et al.: SSC model for Cen A revisited with k e being the positive root k e = 38 σ T Rγ − r Q Rγ cu b ! . (9)It is more convenient to express k e in terms of the electroninjection compactness ℓ inje , which is defined as ℓ inje = σ T L inje πRm e c , (10)where L inje is the total injection luminosity of electrons.Using the relation between Q and ℓ inje for monoenergeticinjection, i.e. Q = 3 ℓ inje cσ T R γ (11)we find k e = 38 σ T Rγ − s ℓ inje ℓ B , (12)where the ‘magnetic compactness’ ℓ B = σ T Ru b was intro-duced. There are two limiting cases that can be studieddepending on the ratio 12 ℓ inje /ℓ B . – Synchrotron dominated cooling or ℓ inje << ℓ B /
12 wherewe find k e ≈ ℓ inje σ R u b γ + O (cid:0) ( ℓ inje /ℓ B ) (cid:1) (13) – Compton dominated cooling or ℓ inje ≫ ℓ B /
12 where wefind k e ≈ (cid:18) ℓ inje R σ u b γ (cid:19) / . (14) The relation between the electron injection rate andthe normalization of the distribution at the steady-state(eqs. (9) or (12)) is crucial for the correct calculation ofthe peak luminosities. The calculation is complete whenthe proper expressions of the emissivities and of the ener-gies where the peaks appear are taken into account. Ourresults, for each emission component, are presented below.
Synchrotron component
In the optically thin to synchrotron self-asborption regime,which is the case considered here, the differential syn-chrotron luminosity per unit volume is given by J syn ( ǫ ) =( c/R ) u s ( ǫ ); we note that the units of J syn are erg cm − s − per dimensionless energy ǫ . Under the δ -function approxi-mation for the synchrotron emissivity, the peak luminosity(per unit volume) of the corresponding component ( L synpeak )emerges at ǫ synpeak = bγ and it is given by L synpeak ≡ ǫJ syn ( ǫ ) | ǫ = ǫ synpeak = 23 σ T m e c u b γ k e (15)or using eq. (12) L synpeak = u b m e c R − s ℓ inje ℓ B . (16) We note that if we were to use the full expression for thesynchrotron emissivity (e.g. Rybicki & Lightman 1979), thepeak in a νF ν plot would appear at a slightly different en-ergy than bγ . First SSC component
For parameter values related to the spectral fitting ofCen A, e.g. for γ = 10 and b ∼ − we find γ ǫ synpeak = bγ <<
1, i.e. scatterings between the maximum energyelectrons with the whole synchrotron photon distributionoccur in the Thomson regime. Under the above assump-tion the peak luminosity (per unit volume) of the first SSCcomponent ( L ssc , ) emerges at ǫ ssc , = bγ e − − α for p < bγ γ e − − α for p > α = ( p − / p is the power-law index of the electron distribution at thesteady state – see e.g. Gould (1979). In our case the energyof the peak is given by the first branch of the above equationsince p = 2. The peak luminosity is then given by L ssc , ≡ ǫ J ssc , ( ǫ ) | ǫ = ǫ ssc , = c πR m e c ǫ n (1)ssc ( ǫ ) , (18)where n (1)ssc is the differential number density of SSC photons(1st generation) that is given by n (1)ssc ( ǫ ) = 4 πRc σ T c Z ǫ max ǫ min d ǫ n s ( ǫ ) ǫ I e ( ǫ , ǫ ) , (19)where I e ( ǫ , ǫ ) = Z min[ γ , / √ ǫ /ǫ ]max[ γ c , / √ ǫ /ǫ ] d γ n e ( γ ) γ F C ( q, Γ e ) . (20)Here F C ( q, Γ e ) is the Compton kernel F C = 2 q ln q + (1 + 2 q )(1 − q ) + 12 (Γ e q ) e q (1 − q ) (21)andΓ e = 4 ǫγ and q = ǫ /γ Γ e (1 − ǫ /γ ) . (22)In the Thomson limit, which therefore applies in our case,Γ e << ǫ /γ <<
1; the Compton kernel takes thenthe simplified form F C ≈ ǫ γ ǫ ln (cid:18) ǫ γ ǫ (cid:19) + ǫ γ ǫ + 1 − (cid:18) ǫ γ ǫ (cid:19) ! . (23)Following Blumenthal & Gould (1970) – henceforth BG70– we assume that the energies of the scattered photons lieaway from the high- and low-energy cutoffs. Since the inte-grand of I e is a steep function of γ , the upper cutoff doesnot contribute to the integration, and I e is written as I e = 12 k e (cid:16) ǫ ǫ (cid:17) − / Z d yy / (cid:0) y ln y + y + 1 − y (cid:1) == 4 k e (cid:16) ǫ ǫ (cid:17) − / C (24)
3. Petropoulou et al.: SSC model for Cen A revisited where y = ǫ γ ǫ and C = 0 . ≃
1. The above expressionis then inserted in eq. (19) and we find n (1)ssc ( ǫ ) = 8 πR σ k e u b b − / C ln Σ ǫ − / , (25)for 4 bγ < ǫ < bγ . In the above, ln Σ is the Comptonlogarithm which also depends on ǫ . In reality, ln Σ changesfunctional form at ǫ ⋆ = bγ γ but for the case studied here( p = 2) the departure of n (1)ssc from a pure power-law withindex − /
2, at least away from the cutoffs, is not significant– see also eqs.(27)-(28) in Gould (1979). Inserting the aboveexpression into eq. (18) we find L ssc , = 3 √ e u b m e c R − s ℓ inje ℓ B (26)where we have neglected the factor C ln Σ . Whether ourchoice is justified or not it will be tested later on, by com-paring eq. (26) against the results obtained with the nu-merical code. Second SSC component
As already mentioned in the introduction, in the case ofblazars, higher order scatterings, i.e. between electrons andSSC photons of the first generation, are negligible (e.g. seeBloom & Marscher 1996). On the other hand, SSC mod-elling of SEDs from radio galaxies requires, in general, highelectron compactnesses ( ℓ inje ) due to the deamplified radia-tion; of course, this is a rather qualitative argument sincethe determination of ℓ inje depends also on the absolute valueof the observed flux, the ratio of the peak luminosities ofthe low- and high-energy humps and the size of the emit-ting region. Here we proceed to calculate analytically thepeak luminosity of the second SSC component, which willbe then compared to the synchrotron and first SSC peakluminosities.An analogous calculation to that of eq. (19) for the sec-ond generation of SSC photons is, in principle, more com-plicated because of the Klein-Nishina effects, which for theparameters considered here, become unavoidable. In fact,the scatterings of electrons with SSC photons from the firstgeneration occur only partially in the Thomson and Klein-Nishina regimes. Thus, one must use the full expression ofthe Compton kernel (e.g. eq. (2.48) in BG70), which hin-ders any further analytical calculations. In order to proceed,however, we used a simplified version of the single electronCompton emissivity j ssc , ( ǫ ) = j δ (cid:18) ǫ − γ ǫ (cid:19) H (cid:18) − γǫ (cid:19) , (27)where the step-function introduces an abrupt cutoff inorder to approximate the Klein-Nishina supression and j = 4 / σ T cγ u ssc , . Here u ssc , = m e c R d ǫ ǫ n (1)ssc and n (1)ssc is approximated by a single power-law, i.e. it is givenby eq. (25) without the logarithmic term. The differentialluminosity of the second SSC component (per unit volume)is then simply J ssc , = 43 σ T c Z γ max γ c d γ Z ǫ ssc , ǫ ssc , d ǫ I ( ǫ , ǫ , γ ) , (28) where I = γ n e ( γ ) u ssc , ( ǫ ) δ (cid:18) ǫ − γ ǫ (cid:19) H (cid:18) − γǫ (cid:19) . (29)After making the integration over γ we find J ssc , = σ T c √ u , k e ǫ − / I ( ǫ ) , (30)where I = Z ǫ ssc , ǫ ssc , d ǫ ǫ H (cid:0) ǫ − / γ ǫ (cid:1) H ( E min − ǫ ) . (31)Here E min = min[3 / ǫ , / γ ǫ ], ǫ ssc , = 4 / bγ , ǫ ssc , =4 / bγ and u , = 8 πm e c R σ u b b − / k e . (32)The integral of eq. (31) results in the logarithmic termln Σ , where Σ is the ratio of the effective upper and lowerlimits of the first SSC photon distribution, which do not,in principle, coincide with the actual cutoffs. For the pur-poses of the present study, however, we will neglect thecontribution of the logarithmic term. In most cases, thescatterings that result in the second SSC photon genera-tion are only partially in the Klein-Nishina regime and thequantity ǫ J ssc , peaks at ǫ ssc , = γ e − − α , where α isthe spectral index of the first SSC component and equalsto 1 / L ssc , is given by L ssc , ≡ ǫ J ssc , ( ǫ ) | ǫ = ǫ ssc , (33)= 8 π √ e m e c R σ u b b − / γ / k e or after replacing k e L ssc , = 9 √ m e c e u b b / Rγ / − s ℓ inje ℓ B . (34)Finally, using eqs. (26) and (34) we define the ratio ζ as ζ ≡ L ssc , L ssc , = 34 b / γ / − s ℓ inje ℓ B . (35)In general, if ζ > th –SSC generation is larger than that of the pre-vious one. This succession ceases, however, due to Klein-Nishina effects, as in our case. If the electron cooling issynchrotron dominated ( ℓ inje << . × − ℓ B ), we find ζ > ℓ inje > . γ / , R − / ℓ / , where we used the no-tation Q x ≡ Q/ x in cgs units. In this regime, both con-straints on ℓ inje cannot be satisfied simultaneously for typicalvalues of γ and R , thus, making the Compton catastrophenot relevant. On the other hand, in the Compton coolingregime ( ℓ inje > . × − ℓ B ), ζ becomes larger than unityif ℓ inje > γ , R − / ℓ / .
4. Petropoulou et al.: SSC model for Cen A revisited
Table 1.
Peak luminosities (in logarithm) of the syn-chrotron, first and second SSC components along with theratio ζ of the two SSC peak luminosities. In each row thenumerical (N) and analytical (A) values are shown as thefirst and second values respectively. ℓ inje log L synpeak log L ssc , log L ssc , ζ − -4.16 (N) -6.63 -9.64 9 . × − -3.85 (A) -6.10 -9.2010 − -3.16 -4.65 -6.66 8 . × − -2.85 -4.13 -6.2010 − -2.22 -2.77 -3.84 6 . × − -1.97 -2.40 -3.60 In this paragraph we will compare the analytical expres-sions given by eqs. (16),(26) and (34) with those obtainedfrom the numerical code described in Mastichiadis & Kirk(1995, 1997), where we have used the full expression forthe synchrotron and Compton emissivities (c.f. eqs. (6.33)and (2.48) in Rybicki & Lightman (1979) and BG70 respec-tively).For the comparison we used B = 4 G, R = 10 cm, γ = 10 and three indicative values of the electron injec-tion compactness, i.e. ℓ inje = 10 − , − and 10 − . Our re-sults are summarized in Table 1, where the first and secondvalue in each row correspond to the numerical and analyt-ical ones respectively; the ratio ζ given by eq. (35) is alsoshown. The magnetic compactness for the parameters usedhere is ℓ B = 0 . ℓ inje /ℓ B = 2 . × − and 2 . × − for ℓ inje = 10 − and 10 − respectively.Although, for the highest ℓ inje considered here, electrons coolpreferentially through the ICS of synchrotron photons, westill find ζ < ∼ −
3. Inparticular, our approximation for the position of the syn-chrotron peak (see Section 2.2) is the main cause for thedifferences appearing in the first column of Table 1. In gen-eral however, our approximations used for the derivation ofeqs. (16),(26) and (34) are reasonable, even in the third caseof ℓ inje = 10 − , where u ssc , ≈ u B + u s ); we remind thatour analysis neglects the energy density of SSC photons inthe electron cooling.
3. One-zone SSC fit to the core emission of Cen A
The emission from the core of Cen A has the double-peakedshape observed in many blazars with the low-and high-energy humps peaking at the infrared and sub-MeV energyranges respectively (Jourdain et al. 1993; Chiaberge et al.2001). The one-zone SSC model, where relativistic elec-trons are responsible for the radiation observed in low andhigh energies has been successfully applied over the yearsto various blazars and recently to FRI galaxies such as M87(Abdo et al. 2009b). Although it is also the dominant in-terpreting scenario for the core emission of Cen A it can-not explain the observed SED up to the TeV energy range(Abdo et al. 2010a; Roustazadeh & B¨ottcher 2011), sincethe emitting region is compact enough for signifant ab-sorption of TeV gamma-rays on the infrared photons pro- duced inside the source (Abdo et al. 2010a; Sahakyan et al.2013). Note also that before the detection of Cen A at VHEgamma-rays, its whole SED was successfully reproduced bysingle zone SSC models (Chiaberge et al. 2001).In this paragraph we attempt a similar application tothe MW emission of Cen A, having in mind though, that thesecond SSC photon generation emerges in the SED for (i)high enough electron injection compactnesses, (ii) small sizeof the emitting region and (iii) relatively low Lorentz factorof electrons – see also eqs. (16), (26) and (34). We note alsothat the combination of the low electron Lorentz factor withweak magnetic fields, as often used in SSC models, impliesthat the second generation Compton scatterings occur onlypartially in the Thomson regime. For this reason, the secondSSC component is expected to be much steeper than thefirst one.Under the assumption of monoenergetic electron in-jection the parameters that must be determined in thecontext of an one-zone SSC model are five: B , R , δ , γ and ℓ inje ; for power-law and broken power-law injection theunkwnown parameters increase to seven and nine respec-tively – see e.g. Mastichiadis & Kirk (1997); Aleksi´c et al.(2012). Because of no detections of variability in theHE/VHE regimes, the available observational constraintsare only four: (i) the ratio of the observed peak frequencies ν ssc , /ν synpeak ; (ii) the peak synchrotron frequency ν synpeak =3 . × Hz; (iii) the ratio of the observed peak fluxes( νF syn ν ) peak / (cid:0) νF ssc , ν (cid:1) peak ; (iv) the synchrotron peak flux( νF syn ν ) peak ≈ × − erg cm − s − . From constraints(i) and (ii) we can determine the injection Lorentz factor ofelectrons γ and find a relation between the magnetic fieldstrength B and the Doppler factor δ respectively: γ = vuut ν ssc , ν ssc , = 1 . × (36)and B = B cr hν synpeak δγ m e c = 8 δ − G , (37)where we neglected the factor 1 + z due to the small valueof the redshift ( z = 0 . ℓ inje ℓ B = 112 − e √ (cid:0) νF ssc , ν (cid:1) peak ( νF syn ν ) peak ! ≃ R and δR ≃ δ − cm . (39)Finally, using eqs. (38) and (39) we find ℓ inje ≃ − δ − . (40)Since the viewing angle of the jet is in the range 15 ◦ − ◦ the Doppler factor cannot exceed the value 3.7, whereas Here we imply mononergetic injection at γ . In the case ofsteep power-law injection between γ min and γ max , the minimumLorentz factor of electrons plays the role of γ . 5. Petropoulou et al.: SSC model for Cen A revisited Table 2.
Parameter values for the one-zone SSC modelfit to the SED of Cen A shown in Fig. 1. For comparisonreasons, the respective values of the SSC fit by Abdo et al.(2010a) are also shown.
Parameter ModelSSC SSC (Abdo et al. 2010a)R (cm) 4 × × B (G) 6 6.2 δ γ e , min . × γ br – 800 γ e , max p e , – 1.8 p e , ℓ inje . × − × − ℓ B . × − . × − values as low as 0.52 have been used in the literature(Roustazadeh & B¨ottcher 2011). From this point on we willadopt the representative value δ = 1, which for an angle30 ◦ implies a bulk Lorentz factor Γ = 7. The derived values( γ = 1 . × , B = 8 G, R = 10 cm, ℓ inje = 10 − and δ = 1) were then used as a stepping stone for a more de-tailed fit to the SED, where we assumed the injection of asteep power-law electron distribution for better reproduc-ing the photon spectrum above 10 Hz. The parametervalues, which are only slightly different from the analyti-cal estimates, are listed in Table 2. In the same table arealso listed for comparison reasons the values of the SSC fitby Abdo et al. (2010a). We note that the parameter thatdiffers the most between their fit and ours is the maxi-mum Lorentz factor of the electrons. Assuming that thefastest acceleration timescale of electrons is set by their gy-ration timescale, the maximum Lorentz factor is saturatedat γ sat ≃ × due to synchrotron losses in a magneticfield of 6 G. It is safe, therefore, to assume that γ e , max = 10 (see also Roustazadeh & B¨ottcher (2011) for a comment onthis point). Our model SED is shown with solid line in Fig. 1and a few features of it are worth commenting:1. The steady state electron distribution is completelycooled, i.e. t syn ( γ min ) << R/c . The emission belowthe peak of the first bump in the SED is attributedto the synchrotron radiation of cooled electrons below γ min and, therefore, it has spectral index α = 1 /
2. Theinverse Compton scatterings of these low-energy syn-chrotron photons ( x < bγ ) with the whole electrondistribution occur in the Thomson regime. The result-ing spectrum has also an index α = 1 / ∼ Hz up to ∼ Hz, it fails in the
Fermi en-ergy range (grey and black circles in Fig. 1) due to theemergent second SSC photon generation, whose peakappears as a small bump at ∼ Hz. In addition,since most of the scatterings occur in the Klein-Nishinaregime, the photon spectrum above that bump steepensabruptly.3. The ratio of the second to the first SSC peak luminosi-ties is ∼ .
05 as it can be seen from Fig. 1. For the pa-rameter values that we derived at the beginning of thissection, the analytical expressions given by eqs. (26) and -13-12-11-10-9-8 10 15 20 25 30 l og ν F ν ( e r g c m - s - ) log ν (Hz) SSC Fig. 1.
SED of the core emission from Cen A with an one-zone SSC fit. This includes non-simultaneous observationsfrom low-to-high frequencies: filled triangles (TANAMIVLBI), grey filled squares (
Suzaku ), open triangles (
Swift -XRT/
Swift -BAT), grey circles (1-year Fermi-LAT byAbdo et al. 2010a), black circles (4-year Fermi-LAT bySahakyan et al. 2013), black filled squares (H.E.S.S. byAharonian et al. 2009) and black open squares are archivaldata from Marconi et al. (2000). The solid line is our one-zone SSC model fit with same slightly different parametersthan those used in Abdo et al. (2010a). For the parametersused see Table 2.(34) predict a ratio ∼ .
08, which is in good agreementwith the numerical one.4. An attempt to fit the SED using the maximum possibleDoppler factor ( δ = 3 .
7) would result in smaller val-ues of R , B and ℓ inje than those listed in Table 2. Thiswould suppress electron cooling, i.e. near/mid-infraredand X-ray observations could not be modelled unlessone would assume the injection of a broken power-lawelectron distribution.
4. Addition of a relativistic proton component
In the previous section we showed that the one-zone SSCmodel fails to reproduce the core emission of Cen A for en-ergies above a few GeV. A recent analysis of
Fermi datafrom four years of observations resulted in the detectionof HE emission up to ∼
50 GeV (Sahakyan et al. 2013).It is now believed that this part of the spectrum alongwith the TeV data is produced by a second componentthat originates either from a compact (sub-pc) or froman extended ( ∼ kpc) region. Multiple SSC emitting com-ponents (Lenain et al. 2008), non-thermal processes at theblack hole magnetosphere (Rieger & Aharonian 2009), pho-topion and photopair production on background (UV orIR) (Kachelrieß et al. 2010) or SSC photons (Sahu et al.2012), γ -ray induced cascades in dust torus surroundingthe high-energy emitting source (Roustazadeh & B¨ottcher2011), non-thermal emission from relativistic protons andelectrons that are being injected and accelerated at thebase of the jet and cool as they propagate along it(Reynoso et al. 2011), are proposed scenarios that fallinto the first category, whereas scenarios such as inverse
6. Petropoulou et al.: SSC model for Cen A revisited
Compton scattering of background photons in the kpc-scalejet (Hardcastle & Croston 2011) belong to the second one.Here we propose an alternative explanation for the TeVand the HE emission in the
Fermi energy range, whichmay as well be labeled as a ‘compact origin’ scenario.We assume that inside the compact emission region (e.g. R = 4 × cm) relativistic protons, that have been co-accelerated to high-energies along with the electrons, arebeing injected in the source. In a co-acceleration scenariothe ratio of the maximum Lorentz factors achieved by elec-trons and protons is ∼ m e /m p , as predicted for exam-ple by first order fermi and stochastic acceleration models(see e.g. Rieger et al. 2007). For this reason and given that γ e , max = 10 we assume that γ p , max = 1 . × , which fur-thermore does not violate the Hillas criterion since the cor-responding gyroradius is r g = 4 . × cm. To reduce thenumber of free parameters in our model we further assumethat the accelerated distributions of protons and electronshave the same power-law index ( p p = p e ), although the re-sulting photon spectrum is insensitive to the exact value p p . In order to follow the evolution of a system whereboth relativistic electrons and protons are being in-jected with a constant rate in the emitting region weused the time-dependent numerical code as presented inDimitrakoudis et al. (2012) – hereafter DMPR12. The vari-ous energy loss mechanisms for the different particle speciesthat are included in our code are – Electrons: synchrotron radiation; inverse Compton scat-tering – Protons: synchrotron radiation; photo-pair (Bethe-Heitler pair production) and photo-pion interactions – Neutrons: photo-pion interactions; decay into protons – Photons: photon-photon absorption; synchrotron self-absorption – Neutrinos: no interactions.Photohadronic interactions are modelled using the re-sults of Monte Carlo simulations. In particular, forBethe-Heitler pair production the Monte Carlo resultsby Protheroe & Johnson (1996) were used – see alsoMastichiadis et al. (2005). Photo-pion interactions were in-corporated in the time-dependent code by using the resultsof the Monte Carlo event generator SOPHIA (M¨ucke et al.2000).
As a starting template for the parameters describing theprimary leptonic component, we first used the one pre-sented in Table 2. Then, we added five more parametersthat describe the relativistic proton component in orderto fit the HE/VHE emission; we refer to this as Model 1.The main difference between Models 1 and 2 is the value ofDoppler factor, which is assumed to be higher in the secondmodel. Subsequently, this affects, as already stated in point(4) of the previous section, the values of other parameterssuch as the electron injection luminosity. The parameterswe used for our model SEDs shown in Fig. 2 are listed inTable 3. In general, the addition of a relativistic protoncomponent successfully explains the HE emission detectedby the
Fermi satellite by both of our models. However, theTeV emission detected by H.E.S.S. can be satisfactorily ex-plained only by Model 2. A zoom in the γ -ray energy range -14-13-12-11-10-9-8 10 15 20 25 30 l og ν F ν ( e r g c m - s - ) log ν (Hz) SSCModel 1Model 2 Fig. 2.
Leptohadronic fit of the MW core emission of Cen Ausing the parameter sets shown in Table 3. Models 1 and2 are shown with dotted and dashed-dotted lines, respec-tively. For comparison reasons, the one-zone SSC fit shownin Fig. 1 is overplotted with solid line. All other symbolsare the same as in Fig. 1. -15-14-13-12-11-10-9 20 22 24 26 28 30 l og ν F ν ( e r g c m - s - ) log ν (Hz) SSCModel 1Model 2 Fig. 3.
Zoom in the γ -ray energy range of the MW corespectrum of Cen A. The model spectra are overplotted withdifferent line types marked on the plot.of the SED along with the model spectra is shown in Fig. 3.In what follows, we will first discuss the common featuresof Models 1 and 2 and, then, we will comment on theirdifferences.In both models, gamma-ray emission is attributed to thesynchrotron radiation from secondary electrons producedvia Bethe-Heitler pair production and photopion interac-tions as well as to the π decay. The hardening of the spec-trum at E ∼ .
7. Petropoulou et al.: SSC model for Cen A revisited -16-15-14-13-12-11-10-9-8 10 15 20 25 30 l og ν F ν ( e r g c m - s - ) log ν (Hz) Model 1No Bethe-HeitlerNo p γ Fig. 4.
Contribution of the photohadronic processes tothe high energy part of the spectrum. Our model spec-tra when all processes are included are shown with solidlines, whereas when photopair and photopion processes areseperately neglected are shown with dashed and dottedlines, respectively. The dash-dotted curve corresponds tothe proton synchrotron emission. For the parameters usedsee Model 1 in Table 3.
Table 3.
Parameter values used for our model SED shownin Fig. 2.
Parameter Model 1 Model 2R (cm) 4 × . × B (G) 6 3.5 t cr . × s 7 . × s δ θ ◦ ◦ t e , esc /t cr γ e , min . × . × γ e , max p e ℓ inje . × − . × − t p , esc /t cr γ p , min × × γ p , maxa . × . × p p ℓ injp × − . × − u r (erg/cm ) b u e (erg/cm ) 1.9 2.3 u p (erg/cm ) 6.8 15.4 u B (erg/cm ) 1.4 0.5 L inje (erg/s) c . × . × L injp (erg/s) 1 . × . × L r (erg/s) 2 . × . × Here γ p , max ≃ ( m p /m e ) γ e , max . b The energy densities refer to the steadystate of the system as measured in thecomoving frame. c The values refer to observed luminosities. for photopair and photopion interactions with the rela-tivistic protons, although external photon fields, such asthe radiation from the accretion disk and/or the scat-tered emission from the Broad Line Region, could alsobe important (Atoyan & Dermer 2003a). The number den-sity of synchrotron photons scales as n syn ( ǫ ) ∝ ǫ − / for ǫ syncool < ǫ < ǫ synpeak , where ǫ syncool ≃ . × − and ǫ synpeak =2 . × − . Thus, protons with Lorentz factors down to γ p & /ǫ synpeak ≈ × can interact with this photon fieldthrough Bethe-Heitler pair production. Synchrotron pho-tons cannot, however, serve as targets for photopion in-teractions, since this would require γ p ǫ synpeak & m π /m e orequivalently γ p & γ p , max . Thus, pion production is solelyattributed to interactions of protons with the SSC photonfield (see also Sahu et al. 2012). For example, protons withLorentz factors γ p & . × and 1 . × can interactwith the upper ( ǫ ssc , ≈ .
2) and lower ( ǫ ssc , ≈ × − )cutoff of the SSC photon distribution, respectively. For afixed proton energy, the efficiency of both photopair andphotopion interactions depends on the number density ofthe target field. For the particular set of parameters, one ex-pects that interactions between the high-energy part of theproton distribution and the low-energy part of the photonfields are more efficient in the production of γ -rays. This isillustrated in Fig. 4, where the emitted spectra of Model 1are shown when (i) all processes are included (solid line),(ii) Bethe-Heitler pair-production (dashed line) and (iii)photopion production (dotted line) are omitted. It becomesevident that the main contribution to the high-energy partof the spectrum comes from the Bethe-Heitler pair produc-tion process. Moreover, the proton synchrotron emission isby many orders of magnitude lower than the emission fromthe other components of hadronic origin – see dash-dottedline in the same figure.For the values of γ p , min and p p used in the fit, therequired injection compactness for obtaining an observ-able high-energy emission signature is ℓ injp = 4 × − and7 . × − for Models 1 and 2, respectively. This corre-sponds to observed injection luminosities L inj , op ≃ . × erg/s and 2 . × erg/s for the two models, respectively .For a black hole mass M BH = 5 × M ⊙ (Marconi et al.2006; Neumayer 2010) the Eddington luminosity is L Edd =6 . × ( M BH /M ⊙ ) erg/s and, therefore, the proton in-jection luminosity in both models is only a fraction of it,i.e. L inj , op = ξL Edd with ξ ≈ − . We note also that therequired luminosity of the relativistic proton componentis comparable to that of the leptonic one and, therefore,low compared to the values 10 − erg/s that are in-ferred from typical hadronic modelling of blazars (see e.g.B¨ottcher et al. 2013). For the chosen parameters the emit-ting region is particle dominated with u p + u e ≈ κ i u B , where κ = 6 and κ = 36 for Models 1 and 2, respectively. Wenote also that the radiative efficiency η γ , which we defineas η γ = L r / ( L inje + L injp ), is high for both models; specifi-cally, the values listed in Table 3 indicate η γ, = 0 .
98 and η γ, = 0 . For the calculation we used the definition of the proton in-jection compactness ℓ injp = L op , inj σ T / (4 πRδ m p c ), where thefactor δ takes into account Doppler boosting effects for radia-tion emitted from a spherical volume.8. Petropoulou et al.: SSC model for Cen A revisited any theoretical model of particle injection and acceleration.However, any effort to extend such a steep power-law distri-bution ( p p = 4 . − .
5) down to γ p = 1 is excluded from theenergetics. As an indicative example, we used the param-eter values of Model 1 listed in Table 3 except for a lowervalue of the minimum Lorentz factor. In order to obtaina good fit to the SED for γ p , min = 2 × , the requiredproton injection luminosity increases by almost three or-ders of magnitude, i.e. L injp = 6 × erg/s. Since thereis no physical reason for such high values of the minimumproton energy, one can interpret it as the break energy of abroken power-law distribution. In such case, the power-lawbelow the break must be rather flat, e.g. p p = 1 . − .
0, inorder to avoid too high proton luminosities. A detailed fitusing broken power-law energy spectra lies, however, out-side the scope of this work. In any case, since there is noknown plausible physical scenario that predicts either highvalues of γ p , min or broken power-law energy spectra with∆ p p ≥ .
5, the sub-Eddington proton luminosities listed inTable 3 can be considered as a lower limit of those retrievedusing a more realistic proton distribution.The key difference between Models 1 and 2 is the as-sumed value of the Doppler factor. In Model 1, where wedid not allow any Doppler boosting of the emitted radiation( δ = 1), we cannot explain the VHE emission. However,by assuming a slightly higher value for the Doppler fac-tor the intrinsic absorbed spectrum is boosted by a factor ∼ δ in frequency and of ∼ δ in flux, respectively. Theboosting effect when combined with the fact that all otherparameter values are of the same order of magnitude asthose of Model 1, results in a model spectrum that sat-isfactorily goes through the H.E.S.S. data points. In thelight of the recent analysis of the four-year Fermi-LAT data(Sahakyan et al. 2013) that implies a common origin of theHE and VHE emission, we believe that Model 2 describesbetter the emitting region of the core. Note that the con-nection between the GeV and TeV emission could not besuggested by the previously available one-year Fermi-LATobservations (Abdo et al. 2010a) – see grey circles in Fig. 3. The detailed neutrino spectra (of all flavors) obtained usingthe numerical code of DMPR12 for both models listed inTable 1 are shown in Fig. 5. The neutrino spectra fromboth models peak at ∼ GeV, while above that en-ergy they can be approximated as power-laws with slopes p ν ∼ . ∼ .
6, respectively. This is in agreement withthe approximate relation p ν ≈ ( p p − . / . × GeV(Model 1) and 10 GeV (Model 2) is due to the cutoff ofthe proton injection distribution. Although photohadronicprocesses are significant in modelling the photon spectraabove a few GeV, the peak fluxes of neutrinos emittedthrough the charged pion and muon decay are far belowthe upper limit of the IceCube 40-string (IC-40) config-uration (Abbasi et al. 2011) – see grey line in the samefigure. The neutrino production efficiency that is definedas η ν = L ν / ( L inje + L injp ), is approximately 2 × − and2 × − for Models 1 and 2, respectively. Thus, we findthat η ν << η γ , where the radiative efficiency was found tobe ∼ .
8. This differentiates the leptohadronic models pre-sented here from others applied to blazar emission, where -18-16-14-12-10-8 2 3 4 5 6 7 8 9 10 l og ν F ν ( e r g / s e c / c m ) log E (GeV)IC-40Model 1Model 2 Fig. 5.
Neutrino spectra of all flavors as obtained in Models1 (solid line) and 2 (dashed line) using the numerical codeof DMPR12. The thick solid line shows the IC-40 upperlimit.neutrino efficiencies as high as 0 . η ν ≃ η γ (e.g. Reimer 2011) andsuch low values are to be expected in cases of strong mag-netic fields, weak target photon fields and/or low protoninjection compactness; the latter applies to our case.Cen A has been under consideration as a potentialsource of ultra high energy cosmic rays (UHECR) fromas early as 1978 (Cavallo 1978), and its proximity toour galaxy compared to all other AGN has even in-spired models where it is the sole originator of UHECR(Biermann & de Souza 2012). Recently, the Pierre AugerObservatory (PAO) has shown an excess in UHECRwithin 18 ◦ of Cen A (Pierre Auger Collaboration et al.2007) and, although that region contains a high densityof nearby galaxies, further analysis has shown that someof those UHECR may have originated from Cen A itself(Farrar et al. 2013; Kim 2013). For our two models wehave obtained distributions for both the escaping protonsand neutrons. While the former are susceptible to adia-batic energy losses, and thus any calculation of their fluxwould constitute an optimistic upper limit, the latter canescape unimpeded and decay into protons well away fromthe core (Kirk & Mastichiadis 1989; Begelman et al. 1990;Giovanoni & Kazanas 1990; Atoyan & Dermer 2003b). InFig. 6 we have plotted the flux of protons resulting fromthe decay of neutrons that escape from the emitting region.Since we have not treated cosmic-ray (CR) diffusion in theintergalactic magnetic field, which generally decreases theCR flux that arrives at earth, our model spectra should beconsidered only as an upper limit. For both models, thepeak fluxes are far lower than the observational limit ofPAO. Although that makes Cen As core an unlikely sourceof UHECR, those could potentially originate from its lobesinstead (e.g. Gopal-Krishna et al. 2010).
9. Petropoulou et al.: SSC model for Cen A revisited -8-6-4-2 0 2 16 17 18 19 20 21 l og E N ( E ) ( e V / s ec / c m / s r) log E (eV)Model 1Model 2 Fig. 6.
High energy proton spectra resulting fromthe neutron decay as obtained in Models 1 (solidline) and 2 (dashed line) without taking into accountthe effects of diffusion in the intergalactic magneticfield. The UHECR spectrum as observed by Auger(The Pierre Auger Collaboration et al. 2011), HiRes-I(High Resolution Fly’S Eye Collaboration et al. 2009) andTelescope Array (Abu-Zayyad et al. 2013) is overplottedwith black open triangles, grey filled circles and black filledsquares, respectively.
5. Summary/Discussion
One-zone SSC models for AGN emission have been widelyused to fit, with varying degrees of success, the SED ofblazars. The discovery of high energy emission from an-other class of AGN, i.e. that of radio galaxies, poses newchallenges to these models: if radio galaxies are misalignedblazars, then the observed emission should come from a re-gion moving with a relatively large angle with respect toour line-of-sight. This implies a rather small value for theDoppler factor that, for a given flux level of the source,can be compensated only by a large value of the so-calledelectron compactness parameter.It is well known that sources with high electron, andconsequently high photon compactnesses, are subject tostrong Compton scattering. This usually leads to higherorder generations of SSC, while, in extreme conditions itmight lead to the ‘Compton catastrophe’. As clearly theseconditions are not apparent in the MW spectra of radiogalaxies, one could, by reversing the above arguments, findlimits on the parameters used to model the SED of thesesources.As an example, in the present paper we have attemptedto fit the SED of the nearby radio galaxy Cen A, that hasbeen observed both at GeV and TeV energies. Most re-searchers agree that the emitting source is characterizedby a low value of the Doppler factor ( δ ≃ − ℓ inje ≥ ℓ B /
12, where ℓ inje and ℓ B are theelectron and magnetic compactnesses respectively. The cal-culation of the luminosity of the second SSC component ismore complicated as scatterings occur in both the Thomsonand Klein-Nishina regimes. However, adopting the oft usedcut-off approximation for the latter, we were able to finda closed expression for the luminosity which, in addition,agrees well with numerical calculations – the same can besaid for the other two components (i.e. synchrotron andfirst SSC) as evidenced by Table 1.Using the relations described above as a stepping stone,we have obtained in Section 3 a fit to the SED of Cen A.Limiting the Doppler factors by neccessity to small values,we find that the one-zone SSC model can successfully fitthe SED up to 10 Hz. At that frequency the peak of thesecond SSC component appears, which is then followed by asteep power-law segment due to Klein-Nishina effects. Thiscauses, typical one-zone SSC modelling to fail at fitting thehigh energy observations of Cen A.In order to fit the emission at frequencies above 10 Hz,we have introduced, in Section 4.1, a hadronic componentwhich, we assume, is co-accelerated to high energies alongwith the leptonic one. Assuming that the two populationsshare the same characteristics, i.e. their injection power-laws have the same slope and their maximum cutoffs arerelated to each other through a simple relation stemmingfrom the Fermi acceleration processes, we found that ac-ceptable fits to the SED of Cen A can be obtained for pro-ton injection luminosities of the same order of magnitudeas the electron one (see Table 3). Interestingly enough, fitsusing δ = 2 can attribute the TeV observations to hadronicemission, while fits with δ = 1 fail to do so due to strongphoton-photon attenuation.In Section 4.1 we have also showed that γ p , min ≫ γ p , min may be interpreted as thebreak energy of a broken-power law at injection. On theother hand, one could, in principle, reconcile the hypothet-ical low values of γ p , min and the high values of L injp byconsidering also as targets for photohadronic interactionsexternal photon fields, such as diffuse and/or line emissionfrom the Broad Line Region (BLR). In the case of Cen A,however, the lack of strong broad emission lines implies thatthese photon fields are negligible (Alexander et al. 1999;Chiaberge et al. 2001). Another possible photon target fieldcould be the mid-IR radiation that is believed to be asso-ciated with cool dust in the nuclear region of Cen A (e.g.Karovska et al. 2003). For the observed fluxes, which rangefrom 1 to 100 Jy (Israel 1998; Karovska et al. 2003), thenumber density of mid-IR photons as measured in the restframe of the high-energy emitting region is by many ordersof magnitude lower than that of the internally producedsynchrotron photons. Thus, incorporating the IR photonfield in the calculations presented here would not lower therequirement of high proton luminosities.The consideration of relativistic protons in the emittingregion is inevitably related to the neutrino emission, sinceproton interactions with the photon fields present in the
10. Petropoulou et al.: SSC model for Cen A revisited source result in charged meson production. In Section 4.2we have presented the neutrino spectra calculated for bothour models. For the employed parameters the efficiency ofpion production is very low and this can also be seen atthe low peak neutrino fluxes which are by many orders ofmagnitude below the IceCube upper limit.Furthermore, high energy neutrons resulting from pho-topion interactions are an effective means of facilitating pro-ton escape from the system, as they are unaffected by itsmagnetic field and their decay time is long enough to al-low them to escape freely before reverting to protons (e.g.Kirk & Mastichiadis 1989; Begelman et al. 1990). A furtheradvantage is that they are unaffected by adiabatic energylosses that the protons may sustain in the system as it ex-pands (Rachen & M´esz´aros 1998). Those effects make themexcellent candidates of UHE protons. For our model param-eters, i.e. steep injection proton spectra and small values ofthe Doppler factor, the obtained proton distributions peakin the range 10 − eV, where the effects of CR diffu-sion in the intergalactic magnetic field cannot be neglected.Since in the present work we have not treated CR diffusion,our results should be considered as an upper limit. Still,these are well below the observed CR flux at such energies.In the light of recent results suggesting Cen A to be the ori-gin of some UHECR events observed by PAO (Farrar et al.2013; Kim 2013) and our model results, the core of Cen Acannot be the production site of UHECR.Our analysis has shown that Cen A can be explainedby means of a leptohadronic model as was the case ofMrk 421 (Mastichiadis et al. 2013). However, contrary tothat source, a one zone SSC model fails to reproduce theSED of Cen A mainly due to complications arising fromthe appearance of the second SSC component. Althoughthis feature has been overlooked by many researchers itmay play a crucial role in fitting the SEDs of radio galax-ies, as these require high electron luminosities, making theconditions very favourable for its appearance. Acknowledgements
We would like to thank the referee Dr. Markus B¨ottcherfor his suggestions and for pointing out several misprintsin the manuscript. This research has been co-financed bythe European Union (European Social Fund ESF) andGreek national funds through the Operational Program”Education and Lifelong Learning” of the NationalStrategic Reference Framework (NSRF) - Research FundingProgram: Heracleitus II. Investing in knowledge societythrough the European Social Fund. EL acknowledges finan-cial support from the thales project 383549 that is jointlyfunded by the European Union and the Greek Governmentin the framework of the programme “Education and lifelonglearning”.
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