Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects
AAstronomy & Astrophysics manuscript no. signatures_final c (cid:13)
ESO 2017June 8, 2017
Expected signatures from hadronic emission processesin the TeV spectra of BL Lac objects
A. Zech , M. Cerruti , and D. Mazin (A ffi liations can be found after the references) Received ...; accepted ...
ABSTRACT
Context.
The wealth of recent data from imaging air Cherenkov telescopes (IACTs), ultra-high energy cosmic-ray experiments andneutrino telescopes have fuelled a renewed interest in hadronic emission models for γ -loud blazars. Aims.
We explore physically plausible solutions for a lepto-hadronic interpretation of the stationary emission from high-frequencypeaked BL Lac objects (HBLs). The modelled spectral energy distributions are then searched for specific signatures at very highenergies that could help to distinguish the hadronic origin of the emission from a standard leptonic scenario.
Methods.
By introducing a few basic constraints on parameters of the model, such as assuming the co-acceleration of electronsand protons, we significantly reduced the number of free parameters. We then systematically explored the parameter space of thesize of the emission region and its magnetic field for two bright γ -loud HBLs, PKS 2155-304 and Mrk 421. For all solutions closeto equipartition between the energy densities of protons and of the magnetic field, and with acceptable jet power and light-crossingtimescales, we inspected the spectral hardening in the multi-TeV domain from proton-photon induced cascades and muon-synchrotronemission inside the source. Very-high-energy spectra simulated with the available instrument functions from the future CherenkovTelescope Array (CTA) were evaluated for detectable features as a function of exposure time, source redshift, and flux level. Results.
A range of hadronic scenarios are found to provide satisfactory solutions for the broad band emission of the sources understudy. The TeV spectrum can be dominated either by proton-synchrotron emission or by muon-synchrotron emission. The solutionsfor HBLs cover a parameter space that is distinct from the one found for the most extreme BL Lac objects in an earlier study. Overa large range of model parameters, the spectral hardening due to internal synchrotron-pair cascades, the “cascade bump”, should bedetectable for acceptable exposure times with the future CTA for a few nearby and bright HBLs.
Key words. astroparticle physics; radiative transfer; radiation mechanisms: non-thermal; BL Lacertae objects: individual: PKS2155-304, Mrk 421; gamma rays: galaxies
1. Introduction
The still-open question on the origin of ultra-high-energy cos-mic rays (UHECRs) and astrophysical neutrinos on the onehand, and the wealth of available data from γ -ray emittingblazars on the other (from MeV to TeV energies, see e.g. Ack-ermann et al. 2011; Senturk et al. 2013), has led to renewedinterest in hadronic emission models for those sources. Radia-tive emission in the most common scenarios either comes froma region inside the relativistic jet (e.g. Mannheim 1993; Der-mer & Atoyan 2001; Mücke & Protheroe 2001; Dimitrakoudiset al. 2012; Bosch-Ramon et al. 2012; Böttcher et al. 2013;Mastichiadis et al. 2013; Petropoulou et al. 2015; Diltz et al.2015) or from interactions of escaping hadrons along the pathfrom the source to Earth (e.g. Essey & Kusenko 2010; Esseyet al. 2011; Dermer et al. 2012; Murase et al. 2012; Tavecchio2014). Contrary to the more commonly assumed leptonic sce-narios, in which the two characteristic broad bumps of the non-thermal spectral energy distribution (SED) of blazars are de-scribed with electron-synchrotron and Inverse Compton emis-sion (Konigl 1981; Sikora et al. 1994), hadronic scenarios intro-duce relativistic protons to explain the high-energy bump that isgenerally seen from keV to GeV energies in flat-spectrum ra-dio quasars (FSRQs) and in the MeV to TeV range for BL Lacobjects. In the hadronic framework, this high-energy componentcan be attributed to either proton-synchrotron emission or radia- tion from secondary products of proton-photon or proton-protoninteractions. These kinds of scenarios thus admit the possibilityof a direct link between UHECRs and electromagnetic emissionfrom blazars. They also lead necessarily to the emission of high-energy neutrinos from the decay of proton-induced pions andmuons. This suggests that blazars, or more generally radio-loudactive galactic nuclei (AGNs), of which blazars are a sub-classof objects with their jets assumed to be closely aligned to theline of sight, are potential sources of the PeV neutrinos recentlydetected with IceCube (Aartsen et al. 2013).Even though hadronic emission models in general requirehigher jet powers and face more di ffi culties to account for short-term variability than leptonic models, they still present a viableand very intriguing alternative within the available constraintsfrom current observational data. Future instruments, such as theCherenkov Telescope Array (CTA) (Actis et al. 2011; Acharyaet al. 2013), will be able to probe blazar spectra above a fewtens of GeV and cover the whole very-high-energy range (VHE,energies above 100 GeV) to above 100 TeV, with much bet-ter sensitivity and spectral resolution than current Imaging AirCherenkov telescopes (IACTs). This motivates a search for po-tential signatures in the VHE γ -ray spectrum that would helpdistinguish hadronic scenarios from the simpler leptonic mod-els. Cerruti et al. (2015, hereafter C15) have recently charac-terised the SEDs of a distinct class of so-called ultra-high- Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . H E ] J un & A proofs: manuscript no. signatures_final frequency peaked BL Lac objects (UHBLs) with a stationaryone-zone model that provides a complete treatment of all rel-evant emission processes for relativistic electrons and protons.This model, which will also be used for the current study, allowsus to treat leptonic, hadronic and mixed scenarios with a singlecode. The authors have shown that hadronic and mixed lepto-hadronic scenarios provide an interesting alternative for the in-terpretation of UHBL SEDs, compared to purely leptonic syn-chrotron self-Compton (SSC) models. The latter are found to re-quire extreme parameters for such sources. Two distinct regionswere identified in the parameter space spanned by the source ex-tension and magnetic field strength, leading to interpretations ofthe high-energy bump either as proton-synchrotron dominated(“hadronic” solution; for high magnetic fields of the order ofa few 10 G) or as consisting of a combination of SSC radia-tion and emission from synchrotron-pair cascades triggered byproton-photon interactions and the subsequent decay of the gen-erated pions and other mesons (mixed “lepto-hadronic” solution;for magnetic fields of the order of a few 0.1 G). In each of theseparameter regions, solutions were found with jet powers belowthe Eddington luminosity, distinguishing these objects from themore luminuous blazar classes studied by Zdziarski & Böttcher(2015), which require very high jet powers.Although UHBLs are located at the most extreme end of the“blazar sequence” (Fossati et al. 1998), high-frequency peakedBL Lac objects (HBLs) with a high-energy peak located in the0.1 to 1 TeV range are far more numerous in the current sam-ple of blazars detected with IACTs. They clearly outnumber allother types of blazars detected at these energies . Hadronic solu-tions are routinely proposed as alternatives to the standard SSCscenario for these kinds of sources, but a systematic explorationof (lepto-)hadronic solutions for a given dataset has not yet beenattempted, to the best of our knowledge. A more general studyof the impact of the magnetic field strength and density of thetarget photon field of the proton-synchrotron model is presentedby Mücke et al. (2003). In most of the current literature, very fewa priori physical constraints are imposed and only exemplary so-lutions are presented.After a short description of the physical constraints we im-pose on our model to reduce the number of free parameters(Sect. 2), we explore the characteristics of di ff erent hadronic so-lutions for HBLs with respect to the source extension, magneticfield strength, jet power, and equipartition between the magneticand kinetic energy density in Sect. 3. Then we apply the modelto SEDs of the two HBLs PKS 2155-304 and Mrk 421 from lowflux states in Sect. 4. We describe the di ff erent sets of solutions,and briefly discuss the jet power, deviation from equipartitionand variability timescales they imply. In Sect. 5, we comparethese solutions to a previous study of UHBLs. We then searchthe modelled SEDs for signatures of spectral hardening in theVHE range, which are caused by the emission from synchrotron-pair cascades and from muon-synchrotron radiation, and com-pare these to the expected sensitivity of CTA in Sect. 6. The re-lation of the detectability of such features to the flux level andredshift are explored. Finally, we present a critical discussion ofthese results, their limitations, and implications for UHECR andastro-neutrino searches in Sect. 7.Throughout this work, the absorption on the extragalac-tic background light (EBL) is computed using the model byFranceschini et al. (2008). In Sect. 7, we discuss how this partic-ular choice a ff ects our results. For the transformations between For an up-to-date catalogue of TeV sources, see http://tevcat.uchicago.edu the two nearby blazars under study and the observer on Earth, wehave adopted a standard cosmology with Ω m = . Ω Λ = . , and H =
68 km s − Mpc − .
2. Physical constraints of model parameters
LEHA (see C15) is a code that was developed recently to sim-ulate the stationary emission from BL Lac objects for leptonic,hadronic, and mixed scenarios. In this “blob in jet” code, rela-tivistic populations of electrons and protons are confined withina plasma blob of radius R with a tangled magnetic field ofstrength B and a bulk Lorentz factor Γ . The primary particledistributions follow power laws with self-consistent synchrotroncooling breaks.In addition to synchrotron emission from primary protonsand electrons, and SSC emission, the code also treats proton-photon interactions with meson-production and subsequent de-cay by use of the SOPHIA Monte Carlo package (Mücke et al.2000). Secondary particles from such interactions trigger pair-synchrotron cascades that are followed for several generations.In addition, the muon-synchrotron spectrum is extracted follow-ing slight modifications of the SOPHIA code. In the LEHA code,Bethe-Heitler and photon-photon pair production are calculatedand the synchrotron-pair cascades they trigger are evaluated aswell. Only proton-proton interactions are not considered, be-cause to be e ffi cient this kind of a process would require veryhigh target proton densities inside the jet in our framework.In our application to high-frequency peaked BL Lac objects,the code provides a simple description for a continuous plasmaflow through a stationary or slowly-moving acceleration regioninside the jet, without specification of the acceleration mecha-nism. A flow of accelerated particles is continuously injectedinto a stationary or slowly moving radiation zone and then con-tinues down the jet with bulk Lorentz factor Γ , while expandingadiabatically. This picture is motivated by the fact that very longbaseline interferometry (VLBI) observations of a large sample ofblazars show that although luminous blazar types often exhibitrapidly-moving radio knots, in HBLs they tend to be stationary(e.g. Hervet et al. 2016). The homogeneous, spherical emissionzone of constant radius that we are modelling represents the ra-diation region into which particles are injected. Radiative emis-sion is strongly dominated by emission from this zone, becausethe plasma flow rapidly loses energy through adiabatic expan-sion farther down the jet. For example, when imposing that themagnetic flux be conserved, the magnetic field strength scales as B ∝ R − , implying an energy output through synchrotron emis-sion that is proportional to R − . The decreasing particle density(proportional to R − ) together with the decreasing target photondensity also leads to a rapid reduction in the proton-photon in-teraction rate. In addition, radiative losses will further reduce theemission level, especially at the highest energies where our studyis focused. Therefore only the single acceleration and emissionzone is modelled and emission from the plasma flow fartherdown the jet is neglected.To reduce the number of free parameters and to focus onphysically plausible solutions from the onset, we impose a num-ber of constraints that are based on simplifying assumptionsabout the nature of the emission region and the acceleration pro-cess. These constraints correspond for the most part to those ap-plied by C15: – Leptons and protons are supposed to be co-accelerated andto follow power laws with the same intrinsic index n , beforecooling. This index is assumed to be close to two, consistent Article number, page 2 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects with Fermi-like acceleration mechanisms. However, no spe-cific assumptions are made about the underlying mechanism. – To account for synchrotron cooling of the primary particles,the stationary spectra of primary electrons and protons,which are used as an input to the code, are characterisedby broken power laws with exponential cut-o ff s (see C15,Eq. 1) . The Lorentz factors corresponding to the breakenergies γ ( e ; p ) , break are determined from a comparison ofradiative and adiabatic cooling timescales. The secondspectral slope above these breaks is given by n = n + – The minimum proton Lorentz factor γ p , min is not constrainedand is set to one, whereas for the electron spectrum wegenerally need to adjust the minimum Lorentz factor γ e , min to match constraints from low-energy optical and radiodata. This choice for γ p ; min maximises the proton energydensity u p , which represents a major contribution to the jetpower. It is thus a conservative choice when considering theenergetics of the models. – The maximum proton Lorentz factor γ p ; max , is derived fromthe equilibrium between particle acceleration and energyloss, meaning radiative and adiabatic cooling, through acomparison of their characteristic timescales. The acceler-ation timescale as a function of the Lorentz factor is sim-ply described by τ acc ( γ ) = γ/ψ · mc / ( eB ) with an assumede ffi ciency of ψ = .
1. In the regime where adiabatic cool-ing dominates over radiative cooling, which is the regime ofinterest for HBLs in our framework, the maximum protonLorentz factor is γ p ; max ∝ B · R , (1)as can be seen from Eq. 18 in C15. The same behaviouris found when simply applying the Hillas criterion (Hillas1984) to constrain γ p ; max .The maximum energy of the electron spectrum, definedby the Lorentz factor γ e , max , is left as a free parameterthat we constrain with X-ray data. For the solutions foundhere, the ratio of γ p , max over γ e , max is consistent with thevalues one might expect in di ff usive acceleration for aKraichnan turbulence spectrum, but a specific investigationof the acceleration mechanism is beyond the scope of thepresent work (cf. Biermann & Strittmatter (1987); Mücke &Protheroe (2001) and C15 for more discussion). – The bulk Doppler factor of the emission region is fixed at δ =
30, a typical value for bright VHE-detected BL Lacobjects (Tavecchio et al. 2010). This allows for the observedvariability in those sources when using reasonable sourceparameters, except for the most extreme minute-scale flares(Gaidos et al. 1996; Aharonian et al. 2007; Albert et al.2007), the origin of which are not yet clearly understood.The impact on our study of the value of this parameter isdiscussed briefly in Sect. 7. – We also assume that the viewing angle between the jet axisand the line of sight to the observer is very small, leading to arelation between bulk Doppler factor and bulk Lorentz factorof δ ≈ Γ . (2)This small-angle approximation seems justified when con-sidering that we are investigating particularly bright sourcesin this study.Given these constraints, we are left with: two quantities, B and R , that we treat as free parameters; and five quantities, n , γ e , min , γ e , max , and the normalisation of the electron and protonspectra K ( e ; p ) , that are more or less constrained by the SED fora given choice of the free parameters. To find a complete set ofsolutions for a given source, we first varied n for values closeto two that provided a satisfactory representation of the opticaland X-ray data. Then, for a small set of the selected n values,we scanned B and R while adjusting the particle densities forelectrons and protons with K ( e ; p ) , and the minimum and maxi-mum electron energies to the SED, using the usual “fit-by-eye”method. The flux level of the electron- and proton-synchrotronpeaks in the SED can be kept constant during these scans byvarying the particle densities as K e ; p ∝ R − · B − · f ( γ ( e ; p ) , break , γ ( e ; p ) , max , n ) , (3)where the last term is a function of the maximum particleLorentz factor, the Lorentz factors of the cooling breaks, and thespectral index of the particle distributions, which all influencethe particle content of the source.We also constrained the parameter space of models for agiven SED by requiring that the size of the emission region andthe overall jet power be physically acceptable. A characteristicsize scale for AGNs is given by the Schwarzschild radius R S of the supermassive black hole. Although for blob-in-jet mod-els one generally expects emission regions of a size at least anorder of magnitude larger than the Schwarzschild radius, as aminimum requirement we discarded only those solutions with R < R S . The maximum size of the emission region is usuallylimited by comparing the light-crossing time to the observedvariability timescale of the source, but for the persistent fluxstates we are interested in, the latter information is generally notavailable or not very constraining. This will be discussed morein Sect. 7.The jet power for a two-sided jet was estimated as L j ≈ π R β c Γ ( u B + u e + u p ) + L r , (4)where u B , u e , u p are the co-moving stationary energy densitiesof the magnetic field, electrons and protons, respectively, and L r corresponds to the power in the radiation field (e.g. Dermer et al.2014, and references therein). In hadronic scenarios, u e and L r are generally very small compared to the other components andthus we neglected them. Any additional component due to coldprotons inside the jet were also neglected. As is usually the casein one-zone hadronic scenarios, the jet power was assumed tobe largely dominated by the power from the “blob”. An addi-tional extensive jet could have been added, as is done for certainleptonic models (see e.g. Katarzy´nski et al. 2001; H.E.S.S. Col-laboration et al. 2012; Hervet et al. 2015) if one wants to accountfor electron synchrotron emission in the radio band, but its con-tribution to the total jet power would be much smaller than thatfrom the “blob”. Article number, page 3 of 22 & A proofs: manuscript no. signatures_final
The value of L j is not constrained from first principles, butcan be compared to the Eddington luminosity L edd as an order-of-magnitude reference. Based on measurements of the jet powerof radio-loud AGNs from X-ray cavity data (e.g. Cavagnoloet al. 2010), highly super-Eddington powers are generally notexpected. We conservatively required that acceptable solutionsshould have L j < L edd for a given source.We also derived the ratio η between the kinetic energy den-sity of the relativistic particles, which is largely dominated by u p for all our solutions, and the energy density of the magnetic field u B : η = u p u B . (5)Solutions can then be characterised by their proximity toequipartition between these components ( η = η can be used as an order-of-magnitude reference toselect physically plausible solutions. We required 0 . < η <
3. Hadronic scenarios for high-frequency peakedBL Lac objects
When modelling the SEDs of high-frequency peaked BL Lacobjects within our hadronic scenario, we distinguish two limit-ing cases. These depend on whether the VHE spectrum is dom-inated by proton-synchrotron emission from the primary pro-tons or by muon-synchrotron emission from muons generated inpion decays that follow proton-photon interactions. In general,both components contribute at least to some extent to the VHEspectrum. In all the hadronic scenarios discussed here, the low-energy bump of the SED that covers the optical to X-ray rangeis interpreted as electron-synchrotron radiation . In this scenario, proton-synchrotron emission is responsiblefor the entire high-energy bump. A contribution from muon-synchrotron or cascade emission only appears above several TeVor tens of TeV, where it can lead to small spectral features as willbe discussed below. When the high-energy bump is ascribed toproton-synchrotron emission, the proton-synchrotron peak fre-quency is fixed to the peak frequency of the bump.Solutions with a constant synchrotron peak frequency lie ondiagonal lines in the log B -log R parameter plane that satisfylog R ∝ − / · log B (6)for a given n and δ . This can be seen from Eqs. 20 and 29 inC15. Solutions with higher or lower peak frequencies lie on par-allels towards higher or lower values of R , respectively. This is An alternative definition of “hadronic” models, where the whole SEDis dominated by emission linked to hadrons, is used by Mastichiadiset al. (2013). Such scenarios seem to lead to very high jet powers andare not considered here.
Log(B [G]) 1 0.5 0 0.5 1 1.5 2
Log ( R [ c m ] ) peak, p syn ν syn τ < ad τ ad τ < syn τ Fig. 1.
Location of hadronic solutions in the log R -log B parameterplane. The frequency of the proton synchrotron emission peak remainsconstant along the dashed lines. The solid diagonal line separates theadiabatic cooling dominated domain from the radiative cooling dom-inated domain. The location of the typical solutions for HBLs shownin Figs. 2, 4 and 5 are indicated with markers and numbers. The dot-ted arrow points in the direction of decreasing proton synchrotron peakfrequency. shown schematically in Fig. 1. All the solutions for the HBLswe have studied lie in the adiabatic cooling dominated regime,meaning to the left of the bold line in Fig. 1.When moving along the diagonal line of constant peak fre-quency towards higher B and smaller R while keeping the fluxlevel constant, the equipartition ratio η increases. The magneticenergy density u B increases as B . The proton energy density u p increases roughly as B due to the relation given in Eq. 6 andthe dependence of γ p , max on R and B (cf. Eq. 1). As η increases,proton-photon interactions become more frequent, leading to amore significant contribution from subsequent synchrotron-paircascades and from muon-synchrotron emission. This can be seenin Fig. 2, in which model SEDs are shown for three di ff erentlocations on a diagonal in the log B -log R plane. The proton-synchrotron component remains dominant as long as the peakfrequency is su ffi ciently high and the particle density remainssu ffi ciently low. This is particularly the case for all the hadronicsolutions found for UHBLs, as will be discussed in Sect. 5.Increasing B moves the low energy cut-o ff in the electron-synchrotron spectrum to higher frequencies, as shown in Fig. 2,whereas solutions with large R and small B require large γ e ; min ,so as not to violate constraints from optical and radio data. Verylarge values of γ e ; min are however physically di ffi cult to accountfor, except in very specific scenarios (see for example the dis-cussion by Katarzy´nski et al. 2006).From Eqs. 4 and 6 it can be seen that the jet power decreaseswith 1 / B when moving on the diagonal towards higher B andlower R , as long as the contribution from the magnetic energydensity dominates, meaning η <<
1. Once the proton energydensity dominates, L j remains approximately constant for n ∼ Article number, page 4 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 2.
Variation in the modelled SED when moving along the diagonal in log R -log B space. From left to right, models with log B [ G ] = . . . ff erent models. Solid red and blue lines indicatethe electron and proton synchrotron emission. The dotted and dashed lines show muon-synchrotron emission at the highest energies, and the SSCand muon-synchrotron cascade components at lower energies, as indicated in the legend. The VHE spectrum is absorbed by the EBL, assuming aredshift of 0.116, corresponding to the source PKS 2155-304. The spectral index n is chosen to be 1.9. The two dashed vertical lines are there toguide the eye by marking the approximate peak postitions of the model in the central figure. Log(u_p / u_B) 6 4 2 0 2 4 6
Log ( L [ e r g / s ] ) n1 = 1.9 n1 = 2.1 Fig. 3.
Location of hadronic solutions in log L j -log η parameter space.The markers indicated the same solutions as shown in Fig. 1. Thedashed curve represents the location of the proton-synchrotron solu-tions for a higher spectral index of the particle population. The verticalline marks equipartition between energy density of the magnetic fieldand relativistic protons.
2. The location of the di ff erent solutions in the log L j -log η planeis shown in Fig. 3.In the same figure, a second set of solutions is given for adi ff erent, larger value of n . When increasing n for a given B and R , the proton energy density u p increases because a givenpopulation of protons close to γ p ; max implies a larger populationof protons at lower energy. This also leads to an increase in L j and η . Starting from a given proton-synchroton dominated solution, onecan find an alternative scenario when moving to lower values of B or R (cf. Fig. 1, red and blue lines) or both. This will shiftthe proton-synchrotron peak to a lower frequency, but will alsolead to an increase of η , due to an increase in particle densitythat compensates the smaller emission region or magnetic fieldstrength. In the modelled SED, this results in a stronger presenceof emission from cascades and from the muon-synchrotron com-ponent at high energies. In this scenario, the high-energy bumpis thus represented by a combination of di ff erent proton-inducedcomponents.An example for the transition from a proton-synchrotron to amuon-synchrotron dominated VHE spectrum is shown in Figs. 4and 5. The muon-synchrotron and cascade emission becomesdominant in the TeV range in Fig. 4 in the right panel. Varia-tions in either R or B lead to very similar models, except that bydecreasing only B one lowers the energy cut-o ff in the electron-synchrotron spectrum. Note the small shift in the left slope of thelow-energy bump in Fig. 5 between the three panels.When lowering B or R from a given initial value while keep-ing the flux level constant, the jet power L j decreases as long as u B dominates over u p . As η increases, u p will eventually becomedominant and L j will increase, as can be derived from Eq. 4. Themuon-synchrotron dominated scenario provides an energetic ad-vantage for another reason: due to the combination of severalcomponents in the high-energy bump, the spectral index n isno longer constrained by the often relatively flat high-energyspectrum in the MeV and GeV range, in the ν F ν representa-tion. This scenario can accommodate broad high-energy bumpswith smaller n than the proton-synchrotron scenario, leading toa lower L j due to the smaller proton number density. The combination of spectral components from proton-synchrotron emission and from proton-photon interactions canlead to spectral hardening in the VHE spectrum, as is seen in
Article number, page 5 of 22 & A proofs: manuscript no. signatures_final [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 4.
Variation in the modelled SED when varying R , i.e. moving along the red line in log R -log B space. From left to right, models withlog R [ cm ] = .
7, 15 .
3, and15 . ff erent models.Definition of the di ff erent curves as in Fig. 2. [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 5.
Variation in the modelled SED when varying B , i.e. moving along the blue line in log R -log B space. From left to right, models withlog B [ G ] = .
7, 1 . . ff erent models. Definitionof the di ff erent curves as in Fig. 2. some of the exemplary models in Figs. 2, 4, and 5. The neces-sary condition for this kind of a feature to occur is a su ffi cientlyhigh value of η , such that proton-photon interactions are non-negligible against proton-synchrotron emission. For the proton-synchrotron scenario this is the case for solutions on the diagonaltowards large B and small R , where the muon-synchrotron com-ponent starts becoming visible at the highest energies.This “cascade bump” feature can also be seen in certainmuon-synchrotron solutions. When the muon-synchrotron com-ponent is very prominent, the transition between muon and pro-ton synchrotron emission occurs below the TeV spectrum andcould lead to distinctive features between the Fermi -LAT andTeV energy ranges. In other cases, both the proton and muon-synchrotron emission contribute to the TeV spectrum, which canlead to spectral features from the muon and cascade emissionat the highest observable energies. It should be mentioned thatthis feature is also seen in other hadronic models (e.g. Mückeet al. 2003; Böttcher et al. 2013), but there has been no system-atic study of its dependence on the model parameters and of itsdetectability. Because this feature depends on the relative contri-butions from several components and thus on the exact param-eter set used for a given solution, the only feasible approach toevaluate its prevalence seems to be a case study of a large num-ber of solutions for a few given sources, which is attempted inthe following section.
4. Application to PKS 2155-304 and Mrk 421
We selected two prominent TeV emitting HBLs as exemplarysources for our study, because their broad-band SEDs have been well measured in several multi-wavelength campaigns: Mrk 421in the northern hemisphere and PKS 2155-304 in the southernhemisphere. Because we are interested in the persistent emis-sion from these blazars and do not try to interpret emission fromflares, we focus here on datasets corresponding to low flux states.The nearby blazar Mrk 421 has a redshift of z = . . × M (cid:12) (Woo et al. 2005), and thus a Schwarzschild radius R S , Mrk ∼ . × cm. This corresponds to an Eddington luminosity of L edd , Mrk ∼ . × ergs − .The SED for Mrk 421 taken from Abdo et al. (2011), froma multi-wavelength campaign in 2009 in which the source wasfound in a low flux state, includes: data points from severaltelescopes in the radio and optical band, data from SWIFT (X-rays and UV),
RXTE (X-rays),
Fermi -LAT ( γ -rays), and MAGIC(VHE). The published MAGIC spectrum had been de-absorbedby the authors using the EBL model by Franceschini et al.(2008). To compare the spectral points with our model curve, weabsorbed the published VHE data points using the same model.The high-energy bump of the SED peaks around 100 GeV witha peak energy flux of roughly 8 × − erg cm − s − .The HBL PKS 2155-304 is more distant than Mrk 421, witha redshift of z = . − × M (cid:12) is estimated byAharonianet al. (2007). However, when accounting for the scatter in therelation between bulge luminosity and black-hole mass, its masscould be as low as 2 × M (cid:12) (Rieger & Volpe 2010; McLure& Dunlop 2002). In addition, as pointed out by Aharonian et al.(2007), the host galaxy luminosity might require further confir-mation. We thus considered a range for the Schwarzschild ra- Article number, page 6 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects dius of R S , PKS − ∼ × − × cm, corresponding to L edd , PKS − ∼ × − × erg s − .The SED for PKS 2155-304, taken from Aharonian et al.(2009b), includes data from the ATOM telescope (optical), SWIFT , RXTE , Fermi -LAT, and H.E.S.S. (VHE), all taken dur-ing a multi-wavelength campaign in 2008, in which PKS 2155-304 was found in a relatively low, although not quiescent state.The published VHE data in this case correspond to the absorbedfluxes. The high-energy bump of the SED peaks around a few10 GeV, with a peak energy flux of roughly the same level as forMrk 421.
When we interpreted the high-energy bump as proton syn-chrotron emission, the spectral index of the proton populationwas constrained by the
Fermi -LAT spectrum to n (cid:38) .
0. Thisalso fixed the spectral index of the electron population follow-ing our simple co-acceleration scenario. Given the high magneticfield strengths in this scenario, the entire electron population iscooled by synchrotron radiation and has thus a photon index of n +
1. The parameters γ e ; min and γ e ; max had to be adjusted toobey the constraints from the optical and X-ray emission, whichwe assumed to stem from the same emission region as the high-energy radiation.The high-energy bump could also be modelled as a combi-nation of a proton-synchrotron peak in the Fermi -LAT band anda muon-synchrotron component that dominates the TeV spec-trum. In this case, the spectral index of the proton spectrumwas smaller, meaning that the spectrum was steeper in the high-energy range than in the proton-synchrotron dominated scenario.We found good solutions for 1 . (cid:46) n (cid:46) .
1. Models withsmaller n are no longer compatible with the optical and X-raydata, whereas larger n provide still acceptable representations ofthe SED, but lead to very large jet powers L j > L edd , PKS − .These solutions correspond to a wide range of magnetic fieldstrengths. For B smaller than a few Gauss, the source exten-sion and jet power become very large. On the other hand, B (cid:38)
100 G corresponds to solutions with very small R , closeto R S , PKS − .Two examples of such solutions for PKS 2155-304 areshown in Fig. 6. A visible “cascade bump” appears in the VHEspectrum in both cases. The relevant acceleration and coolingtimescales of the particle populations for these two solutions areshown in Sect. A. In all cases, energy losses are clearly dom-inated by adiabatic losses, and photo-meson losses, which aredominated by photopion production, are the slowest processes.Di ff erences between the two solutions for each source are rela-tively small. The photo-meson time scale is smaller for the solu-tions with smaller R and higher particle densities. The solutionsfor Mrk 421 have smaller source extensions, leading to shortertimescales for adiabatic cooling and thus smaller maximum pro-ton energies.The hadronic solutions for both sources are located insidethe adiabatic-cooling dominated regime in log B -log R space (cf.Fig. 7). For PKS 2155-304, solutions can be found over thewhole physically acceptable range of source extensions. Thecontribution from muon-synchrotron and cascade emission iscompletely negligible for magnetic fields of a few Gauss butincreases up to the same level as proton-synchrotron emissionat the highest allowed magnetic fields, meaning approximately100 G.Large source extensions imply long variability timescalesthat might pose a problem for sources such as PKS 2155-304 and Mrk 421 that are known for their rapid variability, althoughrapid flares and the continuous component likely arise from dif-ferent emission regions (see e.g. H.E.S.S. Collaboration et al.2012). It should also be noted that the minimum Lorentz factorfor the electron distribution can become large for very extendedsources. Although for all the solutions for Mrk 421 that are dis-cussed below γ min does not become larger than about 700, for thePKS 2155-304 models with the largest extensions it can increaseup to 1800.The energy budget of the solutions for PKS 2155-304 can bedominated by the energy density of the protons or of the mag-netic field, as seen in Fig. 8. The jet power becomes large forsolutions with small magnetic fields and thus large emission re-gions. As discussed above, the value of n has a strong influenceon the jet power. For the study presented in Sect. 6, we considerall the solutions shown in Figs. 7 and 8, but the most easily ac-ceptable solutions in terms of jet power and source extension arethose with intermediate values of R and B and a relatively small n . For the SED of Mrk 421, the proton-synchrotron scenario doesnot provide an acceptable solution because the spectral index n is strongly constrained by the optical data, ruling out solutionswith a su ffi ciently flat shape of the high-energy bump to matchthe Fermi -LAT data. Good solutions are restricted to values of1 . (cid:46) n (cid:46) . B smaller than a few 10 G,the muon-synchrotron component is too low compared to theproton-synchrotron component to match the given flux level, andthe proton-synchrotron peak has shifted too far to lower energies,leading to a depression in the TeV spectrum. The hadronic solu-tion proposed by Abdo et al. (2011), using the model by Mücke& Protheroe (2001), which served as an inspiration for thehadronic part of our code, falls into the same region as our so-lutions with log B [ G ] = . R [ cm ] = .
6, even thoughtheir Doppler factor is much smaller with δ = L j < . L edd , Mrk . When comparing solu-tions with the same magnetic field strength and the same pro-ton index n = . ff erence in redshift be-tween them a larger emission region and a higher particle densityare needed for PKS 2155-304, leading to an increased jet powerand a higher maximum proton energy. Although the high-energybump for these parameters is interpreted as muon-synchrotronemission for Mrk 421, proton-synchrotron radiation dominatesin PKS 2155-304.When comparing our solutions for Mrk 421 to the one pro-posed by Abdo et al. (2011), the jet powers are very similar, suchthat log L j [ erg / s ] = . δ in their solution requires compensation through a higher protondensity and leads to a clear dominance of the proton energy withlog( η ) = . Article number, page 7 of 22 & A proofs: manuscript no. signatures_final [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 6.
SEDs for PKS 2155-304 with two hadronic models where proton synchrotron emission (left figure) or muon-synchrotron emission (rightfigure) dominates the TeV spectrum. These solutions correspond to a spectral index of n = . .
9, a magnetic field with log B [ G ] = . .
7, and an emission region of size log R [ cm ] = × and 1 . × , respectively. See Fig. 2 for a description of the di ff erent curves. The datasetis described in the text. Fig. 7.
Source extension vs. magnetic field for HBL models. The dif-ferent symbols correspond to the two di ff erent sources and to di ff erentspectral indices n . The grey band indicates the range of values sug-gested for the Schwarzschild radius of PKS 2155-304, whereas the blueline shows the Schwarzschild radius of Mrk 421. A standard one-zone SSC model cannot account for the observedSEDs if one assumes that the electron input spectrum is a simplepower law that is only modified by a synchrotron cooling break.One-zone SSC solutions require the introduction of an ad hocbroken-power-law shape for the electron distribution, in viola-tion of our physical assumptions.When loosening those assumptions for electron populationsfollowing a broken power law, accurate representations can befound for both SEDs with the exception of the optical data fromthe ATOM telescope in the SED of PKS 2155-304, which seemto require either an additional component (H.E.S.S. Collabora-
Fig. 8.
Jet power vs. equipartition ratio for HBL models. The di ff erentsymbols correspond to the two di ff erent sources and to di ff erent spectralindices n . The grey band indicates the range of values suggested for theEddington luminosity of PKS 2155-304, whereas the blue line showsthe Eddington luminosity of Mrk 421. tion et al. 2012) or a more complicated electron distribution(Aharonian et al. 2009b). When we adjusted the model to theX-ray, γ -ray, and VHE data while constraining the shape of thesynchrotron bump to roughly account for the optical flux, andwhile keeping a fixed Doppler factor of δ =
30, the remainingparameters of the leptonic SSC model were well constrained.The resulting solutions can be seen in Fig. 10. They correspondto a size of the emission region of approximately 7 × cmand approximately 10 cm, a magnetic field strength of 0 .
04 Gand 0 .
08 G and a jet power of 8 × erg s − and 1 × ergs − for PKS 2155-304 and Mrk 421, respectively. Additional so-lutions can be found when modifying δ and compensating withan adjustment of R , B , and the normalisation of the electron pop-ulation. Here we are only interested in the SSC model with the Article number, page 8 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 9.
SEDs for Mrk 421 with two hadronic models where muon-synchrotron emission dominates the TeV spectrum. These solutions correspondto a spectral index n = . .
9, a magnetic field with log B [ G ] = . .
5, respectively, and an emission region of size log R [ cm ] = . × and 5 . × , respectively. See Fig. 2 for a description of the di ff erent curves. The dataset is described in the text. aim of comparing the di ff erent hadronic solutions (Sect. 6) anddo not discuss these models in any detail.Mixed lepto-hadronic scenarios, in which both proton-induced cascades and SSC emission make up the high-energybump in the SED, do not present a possible solution for thetwo HBLs studied here in the framework of our model and withthe constraints we have imposed. Mastichiadis et al. (2013) andDimitrakoudis et al. (2014) show that it is possible to find mod-els for an SED of Mrk 421 for low magnetic fields and relativelysmall emission regions in which the high-energy bump is dom-inated by cascade emission. Their study is based on a datasetfrom observations in 2001 that is less complete than the more re-cent multi-wavelength (MWL) data used in our study, especiallydue to the absence of data from Fermi -LAT. Another importantdi ff erence lies in the additional constraints we impose on ourmodel parameters and on the restriction of our solutions to lowjet powers and equipartition ratios. By imposing small values of γ p ; max , which is considered a free parameter in their model and ischosen to be roughly three orders of magnitude below the valuewe would get from our constraints, and by adjusting the slopesof the electron and proton distributions separately, a distinct setof “leptohadronic-pion” solutions can be found. These solutionsare marked by very steep injection spectra with indices below1.5, a large deviation from equipartition that is typically u p / u B of the order 10 , and very large jet powers of the order 10 ergs − .
5. Comparison to the parameter space of modelsfor ultra-high-frequency peaked BL Lac objects
The application of our lepto-hadronic code to UHBLs is de-scribed in C15, where solutions are given for five UHBLs:1ES 0229 + + + B -log R space and L j - η space are shown in Figs. 11 and 12 for comparison with theHBL solutions . It should be noted that solutions with L j < L edd can be found for each source separately. The same bulk Dopplerfactor of δ =
30 was assumed in that study. Compared to C15, the jet powers shown here are larger by a factor oftwo to account for double-sided jets.
Proton-synchrotron radiation dominates the high-energyspectral bump for a large set of solutions on both sides of thedividing line between di ff erent cooling regimes, as shown inFig.11. Because UHBLs are defined by higher peak frequen-cies of the high-energy bump compared to HBLs, solutions areshifted to the right, parallel to the diagonal band that marks theHBL solutions in Fig. 7. For these models, contributions frommuon-synchrotron and cascade emission are negligible. The en-ergy budget is largely dominated by the energy density of themagnetic field (cf. Fig. 12) and the jet power decreases approxi-mately as 1 / B .It should be noted that whether adiabatic or radiative cool-ing dominates at the highest proton energies depends on the as-sumptions made about the acceleration timescale. This explainswhy Mücke et al. (2003), for example, find solutions for HBLsin which both timescales are comparable at the highest energiesby assuming highly e ffi cient particle acceleration. Independentlyof the actual behaviour of the acceleration timescale, if one as-sumes that the same particle acceleration mechanism is at playin HBLs and UHBLs, it can be seen that UHBLs correspond toa more radiatively-e ffi cient regime in which radiative losses aremore important than for HBLs.The very steep spectral shape required to fit the Fermi -LATdata in UHBLs implies that jet powers are still acceptable evenwith larger values of B and R compared to HBLs. It also leads tosmaller values of η . For this reason, proton-photon interactionsin UHBLs are largely dominated by proton-synchrotron emis-sion and there are no “cascade bumps” even for small sourceextensions. The muon-synchrotron scenario does not allow us torepresent the SEDs of UHBLs because the proton-synchrotronpeak of the model is strongly constrained by the high-energybump and cannot be shifted to lower energies without violatingthe constraints from the Fermi -LAT data.For UHBLs, a set of mixed lepto-hadronic solutions can befound in a more compact region in log B -log R space for val-ues of B between approximately 0 . Article number, page 9 of 22 & A proofs: manuscript no. signatures_final [Hz] ) ν log ( 10 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og ( − − − − − − [Hz] ) ν log ( 10 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. 10.
SEDs for PKS 2155-304 (left figure) and Mrk 421 (right figure) with an SSC model, where only electron synchrotron emission andSSC emission are considered. These solution correspond to a magnetic field with log B [ G ] = − . − .
1, and an emission region of sizelog R [ cm ] = . .
0, respectively. The solid red line corresponds to the electron-synchrotron emission and the dotted green line to the SSCcomponent. The datasets are described in the text.
Fig. 11.
Source extension vs. magnetic field for the UHBL models dis-cussed by C15. The locations for the two di ff erent types of models areshown in black for the proton-synchrotron scenario and in red for themixed lepto-hadronic scenario. The grey band indicates the range ofSchwarzschild radii for the five UHBLs considered. HBLs when we impose our usual constraints, as was discussedin Sect. 4.4. In both scenarios applicable to UHBLs, the protonsynchrotron and mixed lepto-hadronic, contribution from muon-synchrotron emission is small and there is no spectral feature inthe TeV range arising from cascades.
6. Expected “cascade bump” signatures for theCherenkov Telescope Array
The hadronic signatures in the VHE spectrum we are interestedin can be seen at some level over the whole range of solutionsdiscussed in Sect. 4. For these models, we want to test the possi-bility of detecting the “cascade bump” with the future CTA andthus to distinguish the hadronic scenarios from a basic one-zoneSSC model.
Fig. 12.
Jet power vs. equipartition ratio for the UHBL models dis-cussed by C15. The locations for the two di ff erent types of models areshown in black for the proton-synchrotron scenario and in red for themixed lepto-hadronic scenario. The grey band indicates the range ofEddington luminosities for the UHBLs considered. The expected spectra for CTA were simulated using the publiclyavailable instrument response functions for the full southernarray in the case of PKS 2155-304 and for the full northern arrayin the case of Mrk 421. The current layout for the southern arrayled to roughly a two times better di ff erential sensitivity in therange around a few TeV compared to the northern array.For each modelled spectrum, the integrated flux of expected γ -rays and cosmic-ray background events per energy bin wasdetermined and weighted with the e ff ective area from the perfor-mance file. The resulting event rate was then multiplied by theobservation time, yielding the total number of detected eventsper bin. The number of excess events was determined by assum-ing that the γ -rays and cosmic rays follow a Poisson distribu- https://portal.cta-observatory.org/Pages/CTA-Performance.aspx Article number, page 10 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects tion and are subject to the simulated energy resolution of theinstrument. The background rate was assumed to be extractedfrom a region on the sky that is five times larger than the “on-source” region, corresponding to a standard situation for obser-vations in “wobble-mode”. The uncertainty in the number of ex-cess events was calculated using the method by Li & Ma (1983).The excess and its uncertainty were then converted into a spec-tral point with a statistical uncertainty. An example for two sim-ulated CTA spectra is shown in Fig. 13. For the chosen model,one can clearly see the di ff erence in the shape of the simulatedCTA spectra for an SSC and a hadronic scenario. [Hz] ) ν log ( 20 21 22 23 24 25 26 27 28 ] ) s [ e r g c m ν F _ ν l og (
14 13 12 11 10 9 leptonic model [Hz] ) ν log ( 22 23 24 25 26 27 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9 hadronic model
Fig. 13.
Example of testing emission scenarios with CTA: compar-ison of the expected CTA spectra for two specific emission modelsfor PKS 2155-304. A hadronic scenario is shown on the left, in which n = .
1, log B [ G ] = .
1. and log R [ cm ] = .
6, and a standard leptonicSSC model on the right. The exposure time assumed for the simulations,33 hr, is the same as the live time for the H.E.S.S. observations, whichare represented by grey data points above 3 × Hz. H.E.S.S. upperlimits are not shown. Uncertainties in the CTA data points are smallerthan the red squares.
To take into account statistical fluctuations of the γ -ray rateand background rate, and the e ff ect of a limited energy resolu-tion, several realisations of the simulated spectra were generated.For each hadronic model we simulated one hundred spectra andcompared them to one hundred spectra simulated for the SSCmodel for the same source. We verified that a larger numberof realisations is not necessary because it does not significantlychange our results.To compare the simulated hadronic and SSC spectra, firstthe simulated SSC spectra were fitted with a simple logparabolicfunction, where the lower limit of the fitted energy range was ad-justed to optimise the reduced χ of the fit. The form of this func-tion, characterised with three parameters (P1, P2, P3), is givenby:log f (log E ) = P + ( − P − P ∗ (log E − log E ∗ (log E − log E E = -1.The real shape of the overall SSC spectrum bump, which isabsorbed on the EBL, is generally not well represented by a log-parabola. However, if the energy range is restricted to energiesabove about 100 GeV the logparabolic function provides a satis-factory characterisation with typical fit probabilities above 10%.The same fit function is then applied to a second SSC modelfor each source to verify that it does indeed provide a generaldescription of the SSC scenario and not only of a single model. The same fit function applied to hadronic models over thesame energy range usually results in worse reduced- χ values.An example for a logparabolic fit to a realisation of a hadronicmodel and of an SSC model is shown in Fig. 14. log( E [ TeV ] ) 1.5 1 0.5 0 0.5 1 1.5 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 / ndf χ ± ± ± χ ± ± ± χ ± ± ± χ ± ± ± leptonic modelhadronic model log( E [ TeV ] ) 1.5 1 0.5 0 0.5 1 f l u x / f i t Fig. 14.
Example of a logparabolic fit to realisations of simulated spec-tra, upper panel, for an SSC model (black circles, upper fit parameters)and a hadronic model (red squares, lower fit parameters). The spectracorrespond to a 50 hr exposure time on the source PKS 2155-304. Thelower panel shows the ratio of the simulated fluxes over the fit function.
It should be noted that a direct comparison between thesimulated SSC and hadronic spectra, using for example aKolmogorov-Smirnov test, risks being inconclusive. This is be-cause we are only interested in comparing features in the spec-tral shape and not the absolute values of the spectral distributionsbetween two models, which could be significantly di ff erent evenbetween two SSC models that are acceptable solutions for thegiven dataset.All spectra simulated for the SSC and hadronic models for agiven source were fitted with the same function and the values ofthe resulting reduced χ were recorded. The quality of the log-parabolic fit was thus used to discriminate between spectra withSSC and with hadronic shapes. The distributions of the reduced χ were characterised by their mean and standard deviation. Asa simple ad hoc criterion, which can be refined in future stud-ies, we consider that two models start being distinguishable ifthere is no overlap in their reduced χ distributions within onestandard deviation from the mean values, meaning that if (cid:68) χ hadronic (cid:69) − σ hadronic > (cid:68) χ S SC (cid:69) + σ S SC , (8)the results in the following section do not change significantlywhen the mean and width of a Gaussian fit to the reduced χ distribution is used to characterise the di ff erent models, insteadof the mean and standard deviation of the distribution itself. The detectability of the “cascade bump” in the di ff erent hadronicmodels for PKS 2155-304 and Mrk 421 was tested for three Article number, page 11 of 22 & A proofs: manuscript no. signatures_final di ff erent observation times with CTA: 20 hr, 50 hr, and 100 hr.These are typical exposure times used with current IACT ar-rays on a single source when considering that the low-state fluxcan be summed over several observation periods. Both blazarschosen for this study will be observed regularly with CTA, ascalibration sources, but also within the AGN Key Science Pro-gramme (CTA Consortium 2017).The logparabolic function provides a good fit for two inde-pendent SSC models for each of the two sources. In the case ofPKS 2155-304, we compare an SSC model that includes the op-tical points against an alternative model that is not constrainedby the optical emission, supposed in this case to stem from adi ff erent emission region, for example an extended jet. The re-duced χ distributions for one hundred realisations of each ofthe two SSC models are in good agreement for 20 hr and 50 hrexposure times and still have a large overlap for 100 hr. The 1- σ envelope of the resulting reduced χ distributions for fits aboveapproximately 400 GeV is below 1.3 for observations of 20 hror 50 hr and below 2.4 for observations of 100 hr at which pointthe shapes of the simulated SSC spectra do not always match thelogparabolic function very well.In the case of Mrk 421, we compare two SSC models withDoppler factors of δ =
30 and 50, with logparabolic fits aboveapproximately 600 GeV. The 1- σ envelope is below 1.5 for20 hr and 50 hr exposure times and increases to 2.0 for 100 hr. Fig. 15.
Mean values of the reduced χ distributions of logparabolic fitsto one hundred realisations of each model for the SEDs of PKS 2155-304. The abscissa shows the logarithm of the magnetic field strength todistinguish di ff erent hadronic models. The error bars show the standarddeviation of the distributions. The energy range of the fit was chosen toprovide a good reduced χ for two di ff erent SSC models. The grey bandis the union of the 1- σ envelopes of those SSC spectrum fits. When the same logparabolic fits are applied to the hadronicmodels, in most cases the reduced χ of the fit is di ff erent fromthat obtained with the SSC model by more than one standard de-viation for 50 hr of observation time, and in several cases alreadyby 20 hr (cf. Figs. 15 and 17). The di ff erence between SSC andhadronic models becomes clearer as the exposure time increases.When investing 100 hr of observation time, the large majorityof our hadronic models for PKS 2155-304 and for Mrk 421 areclearly distinguishable from the SSC models. Figures 16 and 18show the corresponding fit probabilities (p-values) in terms ofthe mean and standard deviation for the distributions of the loga-rithmic probabilities. For 50 hr of observation time, for example,most hadronic models for PKS 2155-304 have probabilities less Fig. 16.
Mean logarithmic values of the probabilities for the same fitsas Fig. 15 for PKS 2155-304. The abscissa shows the logarithm of themagnetic field strength to distinguish di ff erent hadronic models. Theerror bars show the standard deviation of the distributions. The greyband is the union of the 1- σ envelopes of the SSC spectrum fits. Fig. 17.
Mean values of the reduced χ distributions of logparabolic fitsto one hundred realisations of each model for the SEDs of Mrk 421. Thecaption of Fig. 15 contains more details. than 1 × − , whereas the SSC models have probabilities greaterthan 0.1.For PKS 2155-304, the model with a spectral index of 2.1and a very small magnetic field of 1 G corresponds to a pureproton-synchrotron scenario, in which contributions from muon-synchrotron and cascades are very small and do not lead to sig-nificant features. This model is also the one with the largest jetpower. On the other hand, models with very large magnetic fieldsof B (cid:38)
70 G and dense emission regions also present a chal-lenge, because the contribution from cascades and muon syn-chrotron are strongly absorbed at the highest energies, leading tovery steep and smooth spectra without detectable features. Thesemodels are also disfavoured on physical grounds, because the ra-dius of the emission region is very close to the Schwarzschildradius of the source.Pure proton-synchrotron models for Mrk 421 do not exist, asdiscussed above. Models with very large magnetic fields above (cid:38)
100 G su ff er from the same problems for detection of the “cas-cade bump” as in the case of PKS 2155-304. They are again dis-favoured due to the smallness of the emission region. Article number, page 12 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects
Fig. 18.
Mean logarithmic values of the probabilities for the same fits asFig. 17 for Mrk 421. The abscissa shows the logarithm of the magneticfield strength to distinguish di ff erent hadronic models. The error barsshow the standard deviation of the distributions. The grey band is theunion of the 1- σ envelopes of the SSC spectrum fits. The two sources selected for this case study are particularlybright HBLs, even in their low states. To test how the detectabil-ity of the “cascade bump” depends on the absolute flux level, wescaled the fluxes of an SSC model and of a well distinguishablehadronic model by factors between 0.5 and 0.1 for each of thesources.For a model for PKS 2155-304 with a “cascade bump” de-tectable in 20 hr exposure time, at least 50 hr are needed for a de-tection of the signature when the flux is reduced to 40% of its ini-tial value. For a reduction to 30%, more than 100 hr are needed.When selecting a well-distinguishable model for Mrk 421, inwhich the “cascade bump” is detected in 20 hr, and reducing itsflux to 40% of its initial value, again the signature is only de-tectable in 50 hr of exposure time or more. Around 100 hr areneeded for a flux reduced to 30%. Thus only sources with rela-tively high flux levels during their low states may be consideredfor searches of this spectral signature with CTA.The HBLs PKS 2155-304 and Mrk 421 are nearby sourceswith redshifts of z = .
116 and z = . , respectively. Totest the dependence of the “cascade bump” signature on thesource distance, we artificially redshifted an SSC model and ahadronic model with well-detectable “cascade bumps” to valuesof z = . , . z = . , . , .
7. Discussion
To arrive at the selection of models for the two HBL sources,several physically-motivated simplifying assumptions weremade to reduce the space of the model parameters. They arediscussed in the following paragraphs.Assuming an identical index for the injection spectraof protons and primary electrons significantly reduces theacceptable values of the slope for both spectra and excludespure proton-synchrotron scenarios for the SED of Mrk 421,given the constraints from the optical data. It also restricts theminimum jet power for the solutions for PKS 2155-304, byexcluding solutions with n < .
9. This assumption ignores thecomplexity of the actual acceleration mechanisms that may beat play inside the source and might lead to di ff erent particlespectra for protons and leptons, which are subject to di ff usionon di ff erent length scales. In the same sense, the assumptionof a pure synchrotron cooling break in the electron spectrummight be an over-simplification, as is generally assumed inone-zone SSC models. Nevertheless, the parameter space of oursolutions should not change significantly for particle indicesbefore cooling that are close to the value of around two, whichis expected for Fermi-like acceleration. The stronger constraintcomes from the fact that primary electrons are completelycooled whereas protons are not, resulting in a significantlysteeper stationary spectrum for the electrons. This constraint isa solid consequence of the assumed co-acceleration scenario.The maximum proton energy is determined by an equi-librium between acceleration and loss timescales, and thus inour framework only by the magnetic field B and source radius R . A more sophisticated treatment of particle acceleration,di ff usion, and energy loss may lead to a wider range of max-imum possible proton energies for a given parametrisation ofthe source conditions. More diverse combinations between theproton-synchrotron component and the muon-synchrotron andcascade components might occur. As an order-of-magnitudeestimate, however, the current approach is su ffi cient.We chose to fix the value of the bulk Doppler factor to δ =
30, but the present study may be extended to a range ofvalues. We verified the e ff ect on the resulting models for a given B when varying the Doppler factor to δ =
20 and to δ =
40 whilekeeping the peak positions and peak fluxes of the modelled SEDsconstant. Increasing δ by a factor f δ leads to an increase in theobserved energy flux level “ ν F ν ”that is proportional to f δ . Atthe same time, the frequencies of the electron-synchrotron andproton-synchrotron peak positions increase by a factor f δ . A re-duction in R , which leads to a reduction in γ p ; max given our con-straints, and an adjustment of the maximum electrons Lorentzfactor γ e ; max , are necessary to keep the positions of the peaksfixed at their initial frequencies.Reducing R leads to a linear reduction of γ p ; max and thus toa quadratic reduction in the proton-synchrotron peak frequency.When compensating for the shift in the peak frequency by re-ducing R by a factor f − / δ , the flux level decreases by a factor f − / δ . It is thus still a factor f / δ higher than before the changein δ . This remaining flux increase needs to be o ff set by reducing Article number, page 13 of 22 & A proofs: manuscript no. signatures_final the particle densities by a factor f − / δ . For the proton population,this reduced particle density leads to a smaller contribution fromthe muon-synchrotron and cascade components. Inversely, thesecomponents become more significant when lowering the value of δ while keeping the flux level and peak frequencies seen by theobserver fixed. The low-energy turnover of the modelled SED inthe optical range is kept fixed by decreasing the value of γ min , e when increasing δ , which can lead to more standard values forcertain models.The choice of δ has also an e ff ect on the jet power. Giventhe small-angle approximation (Eq. 2), the jet power is directlyproportional to δ , as can be seen from Eq. 4. When neglectingthe small contributions from the electron population and fromthe radiation fields, the jet power takes the following form in ourapproximation: L j ∝ R δ ( c B + c K p γ p , max ) , (9)with c and c constant. For a given B , when keeping flux leveland peak positions fixed as discussed above, the jet power L j increases linearly with δ if the jet is dominated by the magneticenergy density u B , due to the impact of the factors R and δ .For a jet dominated by the kinetic energy density of the protonpopulation u p and for a proton spectrum with index n ∼
2, thejet power changes as L j ∝ f − δ as a consequence of the additionalchanges in K p and γ p , max .For a typical model for PKS 2155-304, initially in the u p dominated regime, increasing δ from 20 to 40 while adjustingflux level and synchrotron peak positions leads to a decreasein L j by about 15% and a drop in the flux level of the muon-synchrotron and the cascade components of roughly a factorof two in ν F ν . For values of δ in the usual range assumed forblazar emission models, the results presented here should thusnot change fundamentally.To constrain the total jet power for our solutions, we com-pare it to the Eddington luminosity as a natural scale definedby the mass of the central black hole. This is clearly meant asan order-of-magnitude estimate for the maximum acceptable jetpower instead of a strict limit. A di ff erent approach would be toconsider the disk luminosity as a natural scale to compare to thejet power. However, the disk luminosity depends on the radiativee ffi ciency and thus on the physical conditions of the accretiondisk, which is in general not observationally accessible, espe-cially for BL Lac objects, and for which a multitude of modelsexist. In blazars it is generally seen that the jet power is notlimited by the disk luminosity, even for the “standard” leptonicmodels (e.g. Celotti & Ghisellini 2008; Ghisellini et al. 2010). Inthe case of Mrk 421, one can estimate the disk luminosity fromthe detectable emission of the broad line region. Sbarrato et al.(2012) provide a value of 0 . × erg s − for the luminosityof the broad line region for this source, translating to roughly10 erg s − for the disk luminosity (see e.g. Ghisellini 2013),meaning about 5 × − L edd , Mrk . For a typical jet power of0.03 L edd , Mrk (cf. Fig. 8), the ratio of jet power over diskluminosity would be less than 100. Although these values stillrequire a relatively ine ffi cient accretion process, the hadronicinterpretation for HBLs does not su ff er from the extremeenergetic requirements derived by Zdziarski & Böttcher (2015)for a set of hadronic models, which they applied to FSRQs andlow- and intermediate-frequency-peaked BL Lac objects.The study presented here was carried out using the model ofthe EBL by Franceschini et al. (2008), which is frequently used for the interpretation of VHE data and has been shown to beconsistent with a range of observed sources (Biteau & Williams2015). Although the dependency of our results on the chosenmodel is not very strong, given that the sources under study arenot very distant, we note that it was shown that the “cascadebump” signature becomes less well defined when assuming ahigher opacity of the EBL (Zech et al. 2013). On the other hand,models with a more transparent EBL favour a detection of thesignature.Any change in the CTA performance curves also has animpact on our results. When studying for example the de-tectability of the Mrk 421 models with the southern performancefiles, one clearly sees a significant improvement due to thebetter coverage at the highest energies that comes from alarger number of medium-sized telescopes and the additionalsmall-size telescopes not foreseen for the northern site. Modelswith undetectable “cascade bumps” for 100 hr exposures withthe northern performance curves show clear detectability whenusing the southern performance curves instead. The public per-formance curves used here represent preliminary expectationsof the instrumental response functions for preliminary arraylayouts. Once the actual performance of the final CTA arraysis established the results might thus di ff er from our currentpredictions.The long exposure times of up to 100 hr for the study thatwe are proposing require multiple separate pointings during thevisibility periods of the sources. These pointings will be takenover several months or even years and will very likely containdata from di ff erent flux states. When extracting a spectrum fromthese data, one will have to be very careful with the treatmentof flux and spectral variability. As discussed by Abdo et al.(2011) in the case of a long-term campaign on Mrk 501, it willbe important to exclude periods of flaring activity to build thespectrum from data in a low, persistent flux level. Based on pastobservations of HBLs with the current generation of Cherenkovtelescopes, it seems that significant spectral variability in theVHE band occurs only during flaring episodes. Although someflux variability was detected in the long-term low-state VHElightcurve of Mrk 421 (Aleksi´c et al. 2015), significant spectralvariability was seen neither in the Fermi-LAT data from 0.1to 400 GeV, nor in the MAGIC data over the 4.5 months ofobservations (Abdo et al. 2011). Long-term VHE data fromPKS 2155-304 from H.E.S.S. also indicate only very smallspectral variations during non-flaring periods (H.E.S.S. Collab-oration et al. 2010), which has been confirmed with more recentdata (Chevalier et al. 2015). The risk of introducing spectral fea-tures due to a combination of data from di ff erent periods shouldthus be small if the datasets are carefully selected and combined.A final but important point concerns the method applied inthis study to characterise spectral features in the simulated SEDs.The fit, by χ minimisation, of a simple function to the simulatedspectrum points represents a robust and rapid first approach, butmore sophisticated techniques will certainly be applied to anal-yse CTA spectra. For the spectral analysis of current IACT data,maximum likelihood methods applied to forward folding of dif-ferent spectral shapes have become a standard technique. Thedirect analysis of VHE data using realistic model shapes as un-derlying hypothesis, instead of power laws and logparabola, pos-sibly through the use of libraries of modelled SEDs over a rangeof acceptable parameters, would be a next step and could be builton current techniques used for the analysis of X-ray data. Ideally, Article number, page 14 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects one would apply such methods to a full and simultaneous MWLdataset. It can thus be realistically expected that the search forspectral features in actual CTA data will be more e ff ective thanthe simple approach proposed here for a first evaluation of thedetectability of the “cascade bump”. Even in the relatively low states the present study is focusingon, some flux variability was found during the MWL campaignsof Mrk 421 and PKS 2155-304. For the latter source, Aharonianet al. (2009a) report a small overall variability, characterised byfractional rms, at the 30% level in the MWL light curves of thecampaign that covered twelve nights. The optical, X-ray, andVHE light curves show flux-doubling on timescales of days. ForMrk 421, Abdo et al. (2011) report only low flux variability dur-ing the 2009 campaign that covered 4.5 months. A more in-depthstudy by Aleksi´c et al. (2015) finds significant variability at allwavelengths, which is highest in X-rays, with variations that aretypically smaller than a factor of two. The authors find variabil-ity in the X-ray and VHE bands on day timescales, and in theoptical and UV band on weekly or longer timescales.When requiring that the size of the emission region be su ffi -ciently small for the assumed Doppler factor δ =
30, to allow forvariability of the order of one day one can use the usual light-crossing time argument to arrive at a limiting radius: R ≤ c t var δ/ (1 + z ) . (10)This translates into a constraint on the source extension of R (cid:46) × cm for both sources. Although this kind ofan additional constraint would be of no consequence for ourselection of models for Mrk 421, which already present smallemission regions, a few models for PKS 2155-304 would beexcluded. This concerns the models with the most important jetpowers.Apart from variability timescales, correlated behaviour be-tween di ff erent wavelength bands is another observable char-acteristic that might help distinguish leptonic from hadronicscenarios. Aharonian et al. (2009a) find a correlation betweenthe optical and VHE bands for PKS 2155-304 on timescales ofdays, but no correlation between optical and Fermi -LAT data.Although our stationary model does not permit us to studyvariability, the scenarios that ascribe the
Fermi -LAT flux toproton-synchrotron emission and the VHE flux mostly to muon-synchrotron emission might explain a di ff erence in the variabil-ity patterns between these two domains, if confirmed. Muon-synchrotron emission is a consequence of proton-photon inter-actions and thus subject to correlated variations with the targetphoton field, meaning the electron-synchrotron emission respon-sible for the optical and X-ray spectrum in our interpretation, al-though time-lags between the high- and low-energy componentswould need to be evaluated for a given set of source parameters.According to Aleksi´c et al. (2015), Mrk 421 shows a positivecorrelation between the VHE and X-ray fluxes with zero timelag during the 2009 MWL campaign. The authors claim thatas a consequence, the direct high-energy correlation supportsleptonic models over hadronic ones. In general, correlated be-haviour between the di ff erent energy bands in the lepto-hadronicmodel can be accounted for in a co-acceleration or co-injectionscenario and via the proton-photon interactions. However, thedetailed behaviour can be complex and needs to be studied withtime-dependent models (e.g. Mastichiadis et al. 2013; Diltz et al.2015). The authors also report an anticorrelation between the opti-cal and UV band on the one hand, and the X-ray band on theother, whereas they report that there does not seem to be a cor-relation with the radio band. If the emission in the optical andUV band and the X-ray emission come from di ff erent emissionregions and the anticorrelation is a coincidence, we would haveless constraints on our model on the n parameter, but might re-quire higher γ e ; min values because the optical and UV data wouldstill present upper limits. An obvious limitation of the present study is the fact that thehadronic models were only compared to the most standardone-zone SSC models. More complex scenarios might wellproduce comparable spectral hardening in the VHE spectra, butthe higher degree of complexity that is generally accompaniedby a larger number of free parameters would need to be welljustified against the basic hadronic scenario proposed here. Apotentially similar spectral feature might arise in the scenariosdiscussed in the following paragraphs.Emission from second-order SSC, meaning a second upscat-tering of a fraction of high-energy photons on the relativisticelectrons in a standard SSC model, could in principle lead toan additional spectral component at high energies. In the case ofHBLs however, this component is in general completely negligi-ble compared to first-order SSC. Inverse-Compton upscatteringof the bulk of the first-order SSC photons on the electron pop-ulation around the break energy would take place deeply withinthe Klein-Nishina regime.A di ff erent e ff ect that can lead to spectral hardening in theradiative emission from electrons is described by Moderski et al.(2005). In sources with strong external photon fields, where elec-tron cooling is dominated by the Inverse Compton process, ahardening or pile-up in the steady-state electron spectrum canform for energies where cooling becomes ine ff ecient due toKlein-Nishina e ff ects. This would result in an upturn or ”bump”in the synchrotron spectrum. However, the e ff ect is expected tobe negligible for the high-energy Inverse Compton spectrum,where the hardening of the steady-state electrons is in compe-tition with a softening of the emission due to the same Klein-Nishina e ff ects. We would thus not expect an appreciable fea-ture from this e ff ect, particularly for HBLs, for which externalphoton fields can usually be neglected and synchrotron coolingdominates over Inverse Compton cooling for the electron popu-lation.Multi-zone SSC models could in principle generate spectralhardening at TeV energies. One could image emission from afirst zone dominating the SED over almost the entire observableenergy range, whereas SSC emission from a second, more com-pact zone would only only appear at VHE energies. Althoughthe Klein-Nishina e ff ect would limit the high-energy reach of asecond SSC component, this kind of a scenario could still bepossible and might be di ffi cult to distinguish from the hadronic“cascade bump”. Information on spectrally resolved variabilitymight be needed to rule against or in favour of each scenario.An additional spectral component in leptonic models mightalso arise from external Compton emission caused by the up-scattering of photons from external fields, such as broad line re-gion, disk emission, dust torus, stellar radiation field...etc. ForHBLs, this kind of a component is not expected to contributesignificantly to the SED due to the weakness or absence of thenon-detectable external photon fields. If such a component was Article number, page 15 of 22 & A proofs: manuscript no. signatures_final present, potential VHE features would also be limited by theKlein-Nishina e ff ect.Spectral hardening in the VHE band might arise for scenar-ios in which γ -rays in a certain energy range are absorbed onexternal photon fields in the source, for example from the broadline region (Senturk et al. 2013; Poutanen & Stern 2010), accre-tion disk, or torus (Donea & Protheroe 2003), and where the fluxrecovers at higher energies. However, these kinds of absorptionfeatures would be expected to occur instead in the Fermi -LATband with a flux recovery in the low VHE band. Besides, as dis-cussed above, although external photon fields are very likely toplay an important role for flat-spectrum radio quasars, they areusually considered negligible for HBLs (see also the discussionby H.E.S.S. Collaboration et al. 2013).Spectral hardening in the VHE range is also predicted by sce-narios in which ultra-energetic photons or protons escape fromthe source and trigger particle cascades by interactions with theEBL and cosmic microwave background (CMB) (e.g. Aharonianet al. 2002; Essey et al. 2011; Murase et al. 2012; Aharonianet al. 2013; Taylor et al. 2011). However, this kind of a compo-nent would be expected for sources with relatively high redshifts.It would also not exhibit the same spectral shape and temporalbehaviour.
The HBL PKS 2155-304 is frequently observed with theH.E.S.S. IACT array. According to Chevalier et al. (2015), about260 hr of data were taken between 2004 and 2012, excluding thevery luminous flares seen in 2006. Even so, the long-term lightcurve shows flux variations by a factor of a few. When assum-ing, very roughly, a ten times better sensitivity for CTA withrespect to H.E.S.S., the currently available VHE dataset on thissource would correspond to maybe 40 hr of an equivalent CTAexposure. This would include di ff erent flux states and does notaccount for the increasing gap between the current IACT sen-sitivities and the expected CTA performance at energies abovea few TeV, where the additional performance of the small-sizetelescopes in the southern array becomes important (Bernlöhret al. 2013). It would in any case be interesting to study the com-plete set of available data to probe the most prominent “cascadebump” features. A similarly rich dataset might also be availableon Mrk 421 from observations with the MAGIC and VERITASIACTs. For this blazar, 840 hr of TeV data had been collectedwith the Whipple IACT (Acciari et al. 2014), albeit with a lowersensitivity than current arrays.The two sources we have studied here are foreseen to beobserved frequently with CTA. Given their brightness in theVHE range, they will be used as calibration sources and theyare also prominently included in the proposed AGN Key ScienceProject (CTA Consortium 2017). Their long-term light curve willbe studied with regular observations over an important fractionof the lifetime of CTA. Deep exposures over shorter time rangesare also foreseen, to help derive high-quality spectra in a singlestate. Even if observation times of up to 100 hr will be di ffi cultto achieve over a short time range, observations from a few sea-sons could be summed, as long as the sources show su ffi cientlysimilar flux states.In general, nearby bright HBLs are expected to be thebest candidates to search for the “cascade bump” signature.According to the TeVCAT catalogue (see footnote on page 2)there are currently twenty-two known VHE emitting HBLs with z < .
15 that could be considered for such a search, but only the sources with high fluxes during low states are promising targets.Apart from PKS 2155-304 and Mrk 421, about twelve knownHBLs seem promising targets when excluding UHBLs andsources with very faint fluxes, meaning below 2% of the Crabflux above 200 GeV, in low or average states: Mrk 501, PKS2005-489, RGB J0152 + + + + + + + + γ p , max will need to be investigated further. The maximum energy of the proton population is constrainedby a comparison of the assumed acceleration timescale and theshortest cooling timescale, as explained in Sect. 2. For Mrk 421,we find maximum proton Lorentz factors up to γ p , max ∼ × for the models presented here that correspond to an energy ofabout 10 eV. Proton-synchrotron solutions for PKS 2155-304with large extensions of the emission region around 10 cm have γ p , max values up to about 10 , meaning proton energies up toabout 10 eV. When accounting for Doppler boosting of the par-ticle energies, certain solutions permit us thus to reach maximumproton energies close to what is required to account for the mostenergetic UHECRs, based on our simplistic description of the ac-celeration and loss timescales. In addition, a rapidly decreasingfraction of protons with Lorentz factors above γ p , max is expectedfrom the exponential tail of the particle distribution. The mostenergetic UHECRs might however be nuclei (e.g. Abbasi et al.2015), which we do not consider in our code, instead of protons.The use of the Monte Carlo code SOPHIA allows us to di-rectly extract the neutrino spectra for a given model, which onlyneeds to be transformed to the observer frame on Earth. As de-tailed in Cerruti et al. (2015), we carefully account for the ra-diative cooling of muons before extracting the neutrino spectraresulting from muon decay. The expected neutrino flux is di-rectly related to the importance of proton-photon interactionsinside the source, when ignoring potential neutrino productionthrough neutron decay and UHECR interactions outside of thesource. Scanning the parameter space for a given source insteadof proposing only a single solution makes it possible to estimatea range of possible neutrino spectra for the source within ourlepto-hadronic framework.Figures 19 and 20 show two solutions each for the two HBLsunder study, for models with di ff erent magnetic field strengths. Article number, page 16 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects
Although the relatively small parameter space of hadronic so-lutions for Mrk 421 is reflected in a small di ff erence betweenthe expected neutrino spectra for this source, the spread is muchmore significant in the case of PKS 2155-304. For the latter, so-lutions close to the pure proton-synchrotron scenario lead to alow flux with a high energy peak, whereas solutions with a sig-nificant contribution from muon-synchrotron and cascade emis-sion result in higher neutrino fluxes with lower peak energies. log ( E [eV] )14 15 16 17 18 19 20 21 22 ] ) s [ e r g c m ν F ν l og (
15 14 13 12 11 10 9 8
PKS 2155 304 model 1PKS 2155 304 model 2
Fig. 19.
Expected neutrino spectra on Earth (all flavours combined)for two hadronic models for PKS 2155-304. ‘Model 1’ has a smalllog B [ G ] = .
3, whereas ‘Model 2’ has a much larger log B [ G ] = . log ( E [eV] )14 15 16 17 18 19 20 21 22 ] ) s [ e r g c m ν F ν l og (
15 14 13 12 11 10 9 8 7
Mrk 421 model 1Mrk 421 model 2
Fig. 20.
Expected neutrino spectra on Earth (all flavours combined) fortwo hadronic models for Mrk 421. ‘Model 1’ has a log B [ G ] = . B [ G ] = . Contrary to the lepto-hadronic models discussedby Petropoulou et al. (2015), which have a small γ p , max ,large jet power, and are dominated by proton-photon interac-tions, the models selected following our criteria lead to neutrinospectra that peak at higher energies. For the sources studiedhere, the expected neutrino emission seems out of reach for theIceCube telescope (cf. Aartsen et al. 2014) when consideringlow γ -ray flux states. Flaring activity, if related to hadronicprocesses, can significantly increase the neutrino production,as discussed by Petropoulou et al. (2016). Next-generationinstruments with a higher energy reach, like ARA (ARA Collab-oration et al. 2015) or GRAND (Martineau-Huynh et al. 2016),might have a better chance of reaching the required high-energy sensitivity for a detection in this scenario. A more in-depthstudy of this topic will be treated in a dedicated publication.
8. Conclusions
We explore the parameter space of the one-zone hadronic blazaremission model for two bright VHE HBLs, PKS 2155-304 andMrk 421, during low emission states. Satisfactory realisationsof the model, where the high-energy emission is interpretedas a combination of proton-synchrotron, muon-synchrotron andproton-photon induced cascade emission, can be found for arange of parameters. The muon-synchrotron and cascade emis-sion become more prominent as the density of the emission re-gion is increased while its size is reduced. The TeV spectrumcan be dominated by proton-synchrotron or muon-synchrotronemission, depending on the chosen solution.The mixed lepto-hadronic models found for UHBLs (C15)for magnetic fields of strengths intermediate between those fortypical proton-synchrotron and SSC models do no provide sat-isfactory solutions for the HBLs under study, given our choiceof simplifying assumptions about the particle populations andon the acceptable jet power. Muon-synchrotron emission, on theother hand, cannot dominate the TeV spectrum for UHBLs. ThusHBLs and UHBLs seem to populate distinct parameter spaces ofthe lepto-hadronic one-zone model.All the hadronic models found for the two sources understudy show a hardening in the multi-TeV spectrum at some level,due to the emission from synchrotron-pair cascades that are in-duced by proton-photon interactions. This adds to the dominantproton- or muon-synchrotron emission at these energies. Using asimple logparabolic fit to distinguish between the expected spec-tral shapes from pure SSC and from hadronic emission, we showthat this characteristic “cascade bump” should be detectable formost models with CTA within 50 hr, or in a few cases within100 hr, of observation time. This is especially the case for thosemodels that present preferred solutions due to low jet powersand plausible extensions of the emission region. The faint spec-tral feature is only expected to be detectable in nearby HBLs, ofredshifts smaller than approximately 0 .
15 and with flux levels atleast a few tenths of those of the sources under study. We identifyof the order of ten known TeV blazars that might be consideredfor future searches for such a signature. Although the “cascadebump” permits the distinction between a standard one-zone SSCmodel and a simple one-zone hadronic model, confusion withsignatures from more complex SSC scenarios has not been stud-ied here and cannot be excluded a priori.
Acknowledgements.
The authors wish to acknowledge discussions with C. Bois-son, H. Sol, S. Inoue, D. Pelat, G. Henri, A. Reimer, J.-P. Ernenwein, and L.Stawarz that greatly helped improve this work.This paper has gone through internal review by the CTA Consortium.
References
Aartsen, M. et al. 2013, Science, 342, 1242856 1Aartsen, M. G., Ackermann, M., Adams, J., et al. 2014, ApJ, 796, 109 17Abbasi, R., Bellido, J., Belz, J., et al. 2015, ArXiv e-prints [ arXiv:1503.07540 ]16Abdo, A. A., Ackermann, M., Ajello, M., et al. 2011, ApJ, 736, 131 6, 7, 14, 15Acciari, V. A., Arlen, T., Aune, T., et al. 2014, Astroparticle Physics, 54, 1 16Acharya, B. S., Actis, M., Aghajani, T., et al. 2013, Astroparticle Physics, 43, 31Ackermann, M., Ajello, M., Allafort, A., et al. 2011, ApJ, 743, 171 1Actis, M., Agnetta, G., Aharonian, F., et al. 2011, Experimental Astronomy, 32,193 1Aharonian, F., Akhperjanian, A. G., Anton, G., et al. 2009a, A&A, 508, 561 15
Article number, page 17 of 22 & A proofs: manuscript no. signatures_final
Aharonian, F., Akhperjanian, A. G., Anton, G., et al. 2009b, ApJ, 696, L150 7, 8Aharonian, F., Essey, W., Kusenko, A., & Prosekin, A. 2013, Phys. Rev. D, 87,063002 16Aharonian, F. et al. 2007, ApJ Lett, 664, 72 3, 6Aharonian, F. A., Timokhin, A. N., & Plyasheshnikov, A. V. 2002, A&A, 384,834 16Albert, J., Aliu, E., Anderhub, H., et al. 2007, ApJ, 669, 862 3Aleksi´c, J., Ansoldi, S., Antonelli, L. A., et al. 2015, A&A, 576, A126 14, 15ARA Collaboration, Allison, P., Bard, R., et al. 2015, ArXiv e-prints[ arXiv:1507.08991 ] 17Bernlöhr, K., Barnacka, A., Becherini, Y., et al. 2013, Astroparticle Physics, 43,171 16Bettoni, D., Falomo, R., Fasano, G., & Govoni, F. 2003, A&A, 399, 869 6Biermann, P. L. & Strittmatter, P. A. 1987, ApJ, 322, 643 3Biteau, J. & Williams, D. A. 2015, ApJ, 812, 60 14Bosch-Ramon, V., Perucho, M., & Barkov, M. V. 2012, A&A, 539, A69 1Böttcher, M., Reimer, A., Sweeney, K., & Prakash, A. 2013, ApJ, 768, 54 1, 4,6Cavagnolo, K. W., McNamara, B. R., Nulsen, P. E. J., et al. 2010, ApJ, 720, 10664Celotti, A. & Ghisellini, G. 2008, MNRAS, 385, 283 14Cerruti, M., Boisson, C., & Zech, A. 2013, A&A, 558, A47 4Cerruti, M., Zech, A., Boisson, C., & Inoue, S. 2015, MNRAS, 448, 910 1, 2, 3,4, 9, 10, 16, 17Chevalier, J., Kastendieck, M. A., Rieger, F., et al. 2015, ArXiv e-prints[ arXiv:1509.03104 ] 14, 16CTA Consortium. 2017, in prep. 12, 16Dermer, C. D. & Atoyan, A. 2001, ArXiv [ astro-ph/0107200 ] 1Dermer, C. D., Cerruti, M., Lott, B., Boisson, C., & Zech, A. 2014, ApJ, 782, 823Dermer, C. D., Murase, K., & Takami, H. 2012, ApJ, 755, 147 1Diltz, C., Böttcher, M., & Fossati, G. 2015, ApJ, 802, 133 1, 15Dimitrakoudis, S., Mastichiadis, A., Protheroe, R. J., & Reimer, A. 2012, A&A,546, A120 1Dimitrakoudis, S., Petropoulou, M., & Mastichiadis, A. 2014, AstroparticlePhysics, 54, 61 9Donea, A.-C. & Protheroe, R. J. 2003, Astroparticle Physics, 18, 377 16Essey, W., Kalashev, O., Kusenko, A., & Beacom, J. F. 2011, ApJ, 731, 51 1, 16Essey, W. & Kusenko, A. 2010, Astroparticle Physics, 33, 81 1Fossati, G., Maraschi, L., Celotti, A., Comastri, A., & Ghisellini, G. 1998, MN-RAS, 299, 433 2Franceschini, A., Rodighiero, G., & Vaccari, M. 2008, A&A, 487, 837 2, 6, 14Gaidos, J. A., Akerlof, C. W., Biller, S., et al. 1996, Nature, 383, 319 3Ghisellini, G. 2013, in European Physical Journal Web of Conferences, Vol. 61,European Physical Journal Web of Conferences, 05001 14Ghisellini, G., Tavecchio, F., Foschini, L., et al. 2010, MNRAS, 402, 497 14Hervet, O., Boisson, C., & Sol, H. 2015, A&A, 578, A69 3Hervet, O., Boisson, C., & Sol, H. 2016, A&A, 592, A22 2H.E.S.S. Collaboration, Abramowski, A., Acero, F., et al. 2012, A&A, 539, A1493, 7, 8H.E.S.S. Collaboration, Abramowski, A., Acero, F., et al. 2010, A&A, 520, A8314H.E.S.S. Collaboration, Abramowski, A., Acero, F., et al. 2013, A&A, 552, A11816Hillas, A. M. 1984, ARA&A, 22, 425 3Katarzy´nski, K., Ghisellini, G., Tavecchio, F., Gracia, J., & Maraschi, L. 2006,MNRAS, 368, L52 4Katarzy´nski, K., Sol, H., & Kus, A. 2001, A&A, 367, 809 3Konigl, A. 1981, ApJ, 243, 700 1Kotilainen, J. K., Falomo, R., & Scarpa, R. 1998, A&A, 336, 479 6Li, T.-P. & Ma, Y.-Q. 1983, ApJ, 272, 317 11Mannheim, K. 1993, A&A, 269, 67 1Martineau-Huynh, O., Kotera, K., Bustamente, M., et al. 2016, in EuropeanPhysical Journal Web of Conferences, Vol. 116, European Physical JournalWeb of Conferences, 03005 17Mastichiadis, A., Petropoulou, M., & Dimitrakoudis, S. 2013, MNRAS, 434,2684 1, 4, 9, 15McLure, R. J. & Dunlop, J. S. 2002, MNRAS, 331, 795 6Moderski, R., Sikora, M., Coppi, P. S., & Aharonian, F. 2005, MNRAS, 363, 95415Mücke, A., Engel, R., Rachen, J. P., Protheroe, R. J., & Stanev, T. 2000, Com-puter Physics Communications, 124, 290 2Mücke, A. & Protheroe, R. J. 2001, Astroparticle Physics, 15, 121 1, 3, 7Mücke, A., Protheroe, R. J., Engel, R., Rachen, J. P., & Stanev, T. 2003, As-troparticle Physics, 18, 593 2, 6, 9Murase, K., Dermer, C. D., Takami, H., & Migliori, G. 2012, ApJ, 749, 63 1, 16Petropoulou, M., Coenders, S., & Dimitrakoudis, S. 2016, Astroparticle Physics,80, 115 17Petropoulou, M., Dimitrakoudis, S., Padovani, P., Mastichiadis, A., & Resconi,E. 2015, MNRAS, 448, 2412 1, 17 Poutanen, J. & Stern, B. 2010, ApJ, 717, L118 16Rieger, F. M. & Volpe, F. 2010, A&A, 520, A23 6Sbarrato, T., Ghisellini, G., Maraschi, L., & Colpi, M. 2012, MNRAS, 421, 176414Senturk, G. D., Errando, M., Boettcher, M., & Mukherjee, R. 2013, ApJ, 764,119 1, 16Sikora, M., Begelman, M. C., & Rees, M. J. 1994, ApJ, 421, 153 1Tavecchio, F. 2014, MNRAS, 438, 3255 1Tavecchio, F., Ghisellini, G., Ghirlanda, G., Foschini, L., & Maraschi, L. 2010,MNRAS, 401, 1570 3Taylor, A. M., Vovk, I., & Neronov, A. 2011, A&A, 529, A144 16Woo, J.-H., Urry, C. M., van der Marel, R. P., Lira, P., & Maza, J. 2005, ApJ,631, 762 6Zdziarski, A. A. & Böttcher, M. 2015, MNRAS, 450, L21 2, 14Zech, A., Cerruti, M., & CTA Consortium, f. t. 2013, ArXiv e-prints[ arXiv:1307.3038 ] 14 LUTH, Observatoire de Paris, CNRS, Université Paris Diderot, PSLResearch University, 5 Place Jules Janssen, 92190 Meudon, Francee-mail: [email protected] LPNHE, Université Pierre et Marie Curie Paris 6, Université DenisDiderot Paris 7, CNRS / IN2P3, 4 Place Jussieu, F-75252, Paris Cedex5, Francee-mail: [email protected] Institute for Cosmic Ray Research, University of Tokyo, JapanArticle number, page 18 of 22. Zech et al.: Expected signatures from hadronic emission processes in the TeV spectra of BL Lac objects
Appendix A: Examples of relevant timescales formodels for PKS 2155-304
The following figures show the relevant acceleration and cool-ing timescales for the di ff erent particle populations considered inthe code as a function of the Lorentz factor of the particles. Thevertical dashed line labelled “p gyroradius” indicates the protonLorentz factor γ p , max that corresponds to a gyro-radius of the sizeof the radius of the emission region. The results shown here cor-respond to the exemplary models for PKS 2155-304 shown inFig. 6. ) γ log(5 6 7 8 9 10 11 12 l og ( t/ s ) acceleration p adiabatic loss synchrotron lossphoto meson loss p gyroradius acceleration esynchrotron e synchrotron mu decay musynchrotron pi decay pi Fig. A.1.
Relevant timescales for PKS 2155-304 for the model shown inFig. 6 in the left panel. ) γ log(5 6 7 8 9 10 11 12 l og ( t/ s ) acceleration p adiabatic loss synchrotron lossphoto meson loss p gyroradius acceleration esynchrotron e synchrotron mu decay musynchrotron pi decay pi Fig. A.2.
Relevant timescales for PKS 2155-304 for the model shown inFig. 6 in the right panel.
Appendix B: Examples of relevant timescales formodels for Mrk 421
The following figures show the relevant acceleration and coolingtimescales for the di ff erent particle populations considered inthe code as a function of the Lorentz factor of the particles.The vertical dashed line labelled “p gyroradius” indicates theproton Lorentz factor γ p , max that corresponds to a gyro-radius ofthe size of the radius of the emission region. The results shownhere correspond to the exemplary models for Mrk 421 shown inFig. 9. ) γ log(5 6 7 8 9 10 11 12 l og ( t/ s ) Fig. B.1.
Relevant timescales for Mrk 421 for the model shown in Fig. 9in the left panel. For a description of the di ff erent lines, see Sect. Aabove. ) γ log(5 6 7 8 9 10 11 12 l og ( t/ s ) Fig. B.2.
Relevant timescales for Mrk 421 for the model shown in Fig. 9in the right panel. For a description of the di ff erent lines, see Sect. Aabove. Article number, page 19 of 22 & A proofs: manuscript no. signatures_final
Appendix C: Examples of models for PKS 2155-304
The following figures show all the hadronic models forPKS 2155-304 for an intermediate index of the proton spectrum n = . n = . n = . ff erent curves. [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.1.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.2.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.3.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.4.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.5.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.6.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.7.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.8.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. C.9.
SED for PKS 2155-304 with a hadronic model with a magneticfield of log B [ G ] = . R [ cm ] = . & A proofs: manuscript no. signatures_final
Appendix D: Selected models for Mrk 421
The following figures show all the hadronic models for Mrk 421for an intermediate index of the proton spectrum n = . n = . n = . ff erent curves. [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. D.1.
SED for Mrk 421 with a hadronic model with a magnetic fieldof log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. D.2.
SED for Mrk 421 with a hadronic model with a magnetic fieldof log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. D.3.
SED for Mrk 421 with a hadronic model with a magnetic fieldof log B [ G ] = . R [ cm ] = . [Hz] ) ν log ( 12 14 16 18 20 22 24 26 28 ] ) s [ e r g c m ν F ν l og (
14 13 12 11 10 9
Fig. D.4.
SED for Mrk 421 with a hadronic model with a magnetic fieldof log B [ G ] = . R [ cm ] = ..