aa r X i v : . [ a s t r o - ph . H E ] N ov Jets at all ScalesProceedings IAU Symposium No. 275, 2010G.E. Romero, R.A. Sunyaev & T. Belloni, eds. c (cid:13) Hadronic jet models today
Marek Sikora Nicolaus Copernicus Astronomical Center,Bartycka 18, 00-716 Warsaw, Polandemail: [email protected]
Abstract.
The matter content of relativistic jets in AGNs is dominated by a mixture of protons,electrons, and positrons. During dissipative events these particles tap a significant portion of theinternal and/or kinetic energy of the jet and convert it into electromagnetic radiation. Whileleptons – even those with only mildly relativistic energies - can radiate efficiently, protons need tobe accelerated up to energies exceeding 10 − eV to dissipate radiatively a significant amountof energy via either trigerring pair cascades or direct synchrotron emission. Here I review variousconstraints imposed on the role of hadronic non-adaiabatic cooling processes in shaping the highenergy spectra of blazars. It will be argued that protons, despite being efficiently acceleratedand presumably playing a crucial role in jet dynamics and dissipation of the jet kinetic energyto the internal energy of electrons and positrons, are more likely to remain radiatively passivein AGN jets. Keywords. galaxies: active, (galaxies:) BL Lacertae objects: general, galaxies: jets, (galaxies:)quasars: general, gamma rays: theory
1. Introduction
Production of relativistic jets in AGN is very likely mediated by rotation of large scalemagnetic fields in magnetosphere of black hole and/or accretion disk (Blandford 1976;Lovelace 1976; Phinney 1983; Camenzind 1986; McKinney & Blandford 2009). This leadsto a formation of Poynting flux dominated outflows. Those in turn can at some pointbe converted to the matter dominated jets (Komissarov et al. 2007; Tchekhovskoy et al.2009; Lyubarsky 2010; Komissarov 2010), with a terminal Lorentz factor Γ ∼ P j / ˙ M c where P j is the rate of energy extraction from rotating BH and/or accretion disk and ˙ M is the mass flux. Depending on whether a jet is launched in the BH magnetosphere or bythe accretion disk, the mass flux is expected to be dominated by electron/positron pairsor by protons.Presence of protons in AGN jets is indicated by the low-energy cutoffs in the radiospectra of hot spots in radio-lobes (Blundell et al. 2006; Stawarz et al. 2007; Godfrey etal. 2009) and by circular polarization and Faraday Rotation in radio cores (Vitrishchaket al. 2008; Park & Blackman 2010). If so, such protons might manifest their presencealso via radiative contribution to high energy spectra in blazars, by synchrotron emissionof pair cascades triggered by photo-meson process and by direct synchrotron emission ofprotons and mesons (Mannheim & Biermann 1992; Mannheim 1993; Rachen & M´esz´aros1998; Aharonian 2000). Whether such a contribution can be significant is the main is-sue of this presentation. We start with a short review of the leading hadronic models( § § § § §
2. Hadronic models - basic features
Luminous blazars - ’photo-meson’ models
Luminous blazars are hosted by quasars which, when observed away from the axis of thejet, form population of FRII type double radio sources. They are powered by accretiononto BHs with masses typically of the order of 10 solar masses and their accretionluminosities are in the range 10 − erg s − . However, when such jets are orientedclose to the line of sight, these quasars are seen as being dominated by nonthermalradiation of jets, with the apparent luminosities 10 − erg s − and spectra dominatedby the broad high energy component peaking in the 1-100 MeV band. This radiationshows high amplitude variability on time scales from years down to days and even hours,implying the strong dissipative events taking place not far from the base of a jet. There theenergy densities of the magnetic and radiation fields are very large, providing conditionsfor acceleration of protons up to energies of 10 − GeV, and for cooling them via inelasticcollisions with soft photons (Sikora et al. 1987). For typical background radiation fieldsmost of proton energy is converted to mesons and this initiates processes which accordingto proposers of hadronic models are responsible for γ -ray production in luminous blazars(Mannheim & Biermann 1992).These processes are dominated by the following channels. In approximately 90% col-lisions, the produced mesons are pions. In 2/3 of them they are the neural pions ( π )and in 1/3 of them – the positive pions π + . Neutral pions almost immediately decay intophotons which in turn trigger pair-cascades driven by photon-photon pair production andtheir synchrotron radiation. Escaping radiation is the product of 3rd and 4th generationof pairs (radiation of the first two are totally converted to e + e − -pairs). The resultingelectromagnetic spectrum is predicted to form the high energy component peaked in the γ -ray band, with a high energy break at hν br ∼ −
30 GeV, where τ γγ → e + e − ≃
1, andlow energy tail in the X-ray band with a slope α X > . pγ → n + π + and nγ → p + π − . Thecharged pions decay producing muons ( π ± → µ ± + ¯ ν µ /ν µ ), and the muons decay pro-ducing positrons/electrons ( µ ± → e ± + ¯ ν e /ν e + ν µ / ¯ ν µ ). The resulting electrons/positronsjoin the pair cascade triggered by the decays of the neutral pions and together withthe synchrotron emission of muons (Rachen & M´esz´aros 1998) contribute an additional ∼ Low luminosity TeV BL Lac objects - proton-synchrotron models
The low luminosity BL Lac objects are hosted by radio-galaxies of type FR I. Just asFR II radio sources, they are associated with giant elliptical galaxies, with central BHmasses of the order of 10 M ⊙ , but with the jet powers at least 3 orders of magnitudelower than in the radio-loud quasars and extremely low accretion luminosities. Dopplerboosted nonthermal radiation from their jets reaches TeV energies, and the luminositypeak of the high energy spectral component is located at GeV energies. Resulting fromthe low radiative environment, energy losses of ultra-relativistic protons in theses objectsare presumably dominated by direct synchrotron emission of protons. This mechanismwas suggested by Aharonian (2000) to be the primary source of γ -rays in low luminosityBL Lac objects. Main spectral features of such models, as is in the case of synchrotron ra-diation of electrons, are directly related to the magnetic field intensities and the injectionfunction of relativistic particles (here of protons). They produce photons with averageenergies ν p,syn = (2 e/ (3 πm p c )) γ p B ′ D and energy spectra with the slopes α = ( q p − / α = q p / B ′ is theintensity of magnetic field in the jet co-moving frame, D is the Doppler factor, q p is the adronic jet models Q p ∝ γ − q p p , and α is the index of theradiation energy flux, F ν ∝ ν − α . Application of those formulae indicates that protonsaccelerated up to Lorentz factors γ p ∼ and cooled in magnetic fields B ′ ∼
100 Gaussmay produce spectra reaching TeV energies and with the luminosity peak located near ν p,syn,max . An investigation whether these parameters are feasible – given the constraintsimposed on γ p,max by jets with the limited power and magnetisation – is given in §
3. Radiative efficiencies
Time scalesAcceleration .Time scale of the proton acceleration as measured in the co-moving frame of the flowis t ′ acc = f R L /c = m p ce f γ p B ′ , (3.1)where R L is the Larmor radius, B ′ is the magnetic field intensity, and f is the parameterwhich in the case of shock acceleration depends on the spectrum of magnetic turbulenceand on the velocity of the upstream-flow (Rieger et al. 2007) and for mildly relativisticshocks is expected to be at least of the order of 10. Adiabatic losses
Assuming that cross-sectional radius of the source is of the order of the cross-sectionalradius of the jet, R , relativistic plasma moving down the jet with a Lorentz factor Γundergoes energy losses due to adiabatic expansion. For conical jets with the half-openingangle θ j ≡ R/r < / Γ, where r is the distance of the source in a jet, the time scale ofthe adiabatic losses is (Moderski et al. 2003) t ′ ad = 32 R ( θ j Γ) c . (3.2) Photo-meson process
Time scale of the energy losses via the photo-meson process can be estimated usingthe approximate formula (Begelman et al. 1990) t ′ pγ ∼ h σ pγ K pγ i cn ′ ph ( ν ′ > ν ′ th ) , (3.3)where h σ pγ K pγ i ∼ . × − cm is the product of the photo-meson cross-sectionand inelasticity parameter averaged over the resonant energy range, n ′ ph ( ν ′ > ν ′ th ) = R ν ′ th n ′ ν d n ′ ν , hν ′ th ≃ m π c /γ p is the threshold photon energy and m π is the rest mass ofthe pion. The target radiation field is provided by the internal and external sources. Theinternal seed soft radiation is dominated by synchrotron emission of primary (directlyaccelerated) electrons, the external one – by re-scattered/reprocessed disk radiation. Ap-proximating the broad synchrotron spectral component by a power-law function with theenergy-flux index α = 1 and denoting its luminosity by L s , we have n ′ ph ( int ) ( ν ′ > ν ′ th ) ∼ L s πm π c R D γ p . (3.4)Spectra of external radiation fields are in turn narrow and therefore can be approxi-mated by mono-energetic functions. Hence, n ′ ph ( ext ) ∼ ξL d Γ4 πcr hν ext = ξL d ( θ j Γ) πcR Γ hν ext for γ p > m π c /hν ext , (3.5) Marek Sikoraand n ′ ph,ext = 0 for γ p < m π c / (Γ hν ext ), where L d is the luminosity of the accretiondisk and ξ is the fraction of this luminosity rescattered/reprocesssed on a spatial scalecorresponding with a distance r of the source in a jet. Synchrotron emission
Time scale of the proton cooling via the synchrotron process is t ′ p,syn = 34 (cid:18) m p m e (cid:19) m e cσ T u ′ B γ p , (3.6)where u ′ B = B ′ / (8 π ) is the magnetic energy density.3.2. ’Mono-energetic’ efficiencies In order to illustrate efficiencies of the proton acceleration and cooling processes weintroduce their dimensionless rates, as scaled by the adiabatic losses rates, τ i ≡ t ′− i /t ′ ad .They are: τ acc ≃ . × − B ′ Rf ( θ j Γ) γ p ≃ . σ/ . / L / j, ( f /
10) (Γ /
10) ( θ j Γ) 1 γ p, , (3.7) τ ( int ) pγ ∼ . × − L s γ p ( θ j Γ) D R ≃ L s, ( θ j Γ) (Γ / R γ p, , (3.8) τ ( ext ) pγ ∼ . × − ξL d ( θ j Γ) hν ext Γ R ≃ . ξL d ) ( θ j Γ)( hν ext / / R , (3.9)and τ p,syn = 1 . × − RB ′ γ p θ j Γ ≃ . σ/ . L j, ( θ j Γ) (Γ / R γ p, , (3.10)where L B ≃ cu ′ B πR Γ = σL j / (1 + σ ) is the magnetic energy flux, L j = L M + L B isthe total jet power, σ ≡ L B /L M , and L M is the energy flux of the rest mass. Assuming σ < L B ∼ σL j .The ’scaled’ quantities, L j, , γ p, , R , L s, , and ( ξL d ) are defined in the usualway, i.e. X n ≡ X/ n . 3.3. Maximal proton energies
Maximal proton energies – if limited only by adiabatic losses – can be found from τ acc = 1 to be γ p ( τ acc = 1) ≃ × ( σ/ . / L / j, ( f /
10) (Γ /
10) ( θ j Γ) , (3.11)Stronger limits are imposed if dominant energy losses are non-adiabatic, i.e. for τ cool = τ pγ + τ p,syn >
1. For energy losses dominated by photo-meson process with the targetradiation field provided by internal sources or by proton-synchrotron radiation γ p,max = γ p ( τ acc = 1) Min[1; p R/R c ] . (3.12)where in the 1st case (photo-meson process) R ( pγ ) c ≃ . × L s, ( σ/ . / L / j, ( θ j Γ) (Γ / ( f /
10) [cm] . (3.13)and in the 2nd case (proton-synchrotron radiation) R ( syn ) c ≃ . × ( σ/ . / L / j, ( f /
10) ( θ j Γ) (Γ / [cm] . (3.14) adronic jet models τ ( ext ) pγ is predicted to be lower than unity for any proton energyand therefore γ p,max is not expected to be affected.3.4. Total efficiencies
Radiative efficiency of a given cooling process can be estimated using formula η i ≃ R γ p,max η i ( γ p ) Q γ p γ p dγ p R γ p,max Q γ p γ p dγ p , (3.15)where η i ( γ p ) ≃ Min[ τ i ; 1] and Q γ p is the proton injection function.We calculate such efficiencies below assuming power-law injection of protons Q γ p ∝ γ − q p p with q p = 2. This specific value of the index is chosen because efficiencies obtainedfor q p = 2 provide upper limits of efficiencies available for q p > η i ≃ γ p,max /γ p )ln γ p,max for R < R c , (3.16)and η i < / ln γ p,max for R > R c , where in case of ’internal’ photo-meson process, R c isgiven by Eq.(13) and γ ( pγ ) p = γ p ( τ ( int ) pγ = 1) ≃ . × ( θ j Γ)) (Γ / R L s, , (3.17)while in case of proton-synchrotron emission, R c is given by Eq.(14) and γ ( syn ) p = γ p ( τ p,syn ) ≃ . × ( θ j Γ) (Γ / R ( σ/ . L j, . (3.18)For energy losses dominated by photo-meson process with externally produced seedphotons, at any distance larger than r = Γ R ( τ ( ext ) p,γ = 1)( θ j Γ) ≃ . × ( hν ext / / ( ξL d ) ( θ j Γ) [cm] (3.19) τ ( ext ) p,γ η ( ext ) pγ ≃ τ ( ext ) pγ ln ( γ p,max /γ p,th )ln γ p,max , (3.20)where γ p,th = m π c / (Γ hν ext ) ≃ . × / ((Γ / hν ext /
4. Observational constraints
Luminous blazars
In order to account for the γ -ray luminosities of powerful blazars, radiative efficiencyhas to be η i > . L γ, (Γ / ( η diss / . L j, , (4.1) Marek Sikorawhere η diss is the fraction of the jet energy flux dissipated in the ’blazar zone’. As it canbe verified using approximate formulae presented in § q p = 2. For our fiducialparameters it is about 10 % for the photo-meson process with intenally produced seedphotons and much less for others. For slope q p ∼ . η ∼ − .Hadronic models may have also problems to explain very hard X-ray spectra of lu-minous blazars. Those blazars often have slopes α x < . e ± –products of the cascades powered by hadrons – one needs to assume inefficient coolingof ultra-relativistic electrons/positrons up to energies γ e > . × ( hν/ / B ′ (Γ / . (4.2)Inefficient cooling of such energetic electrons/positrons implies very weak magnetic fieldsand, therefore, puts strong constraints on the efficiency of the proton acceleration andon efficiency of photo-meson energy losses via limitation of the maximal proton energy.Furthermore, as Sikora et al. (2009) demonstrated, in order to avoid overproduction ofX-rays in these magnetically weak sources by SSC radiation of primary electrons, it isnecessary to assume the source sizes of the order of parsecs, and for such sources theefficiency of the photo-meson process is further reduced.4.2. Low luminosity BL Lac objects
In these objects, because of low radiation energy densities – both in jets themselvesand in the surroundings of the jet – the non-adiabatic energy losses of protons are pre-sumably dominated by the proton-synchrotron mechanism. However, noting that suchobjects are hosted by weak radio-galaxies, with the jet powers L j erg s − , ef-ficiency of synchrotron-proton models is also expected to be strongly reduced becauseweaker magnetic fields. In order to keep them at reasonable level more compact sourcesmust be assumed. However, even in the case of most relativistic protons, the requiredsize of the source to provide sufficiently strong magnetic fields for efficient cooling isunreasonably small (see Eq. (3.14), R c ∼ . × ( σ/ . / L / j, ( f /
10) ( θ j Γ) (Γ / [cm] . (4.3)This is 3 orders less than the gravitational radius of the BH with mass M BH ∼ M ⊙ .Considering the minimal cross-sectional radius of a jet to be R ∼ cm, which for θ j ∼ / Γ corresponds with a distance 100 gravitational radii of the 10 M ⊙ BH – requiredto be at least of this order to accelerate the jet up to Γ ∼
10 (Komissarov et al. 2007) –we can find using Eqs. (3.10) and (3.11) that τ p,syn ( γ p,max ) ≃ . × − ( σ/ . L j, ) / ( f /
1) ( θ j Γ) (Γ / R . (4.4)This indicates that even for such extreme parameters as f ∼ σ ∼ γ -ray luminosities L γ ∼ erg s − , unless one assumes very hard( q p <
1) proton injection spectra and adopts significantly larger total jet power.The main purpose of proton-synchrotron models was to explain the relatively stableshape of the TeV spectra in variable low luminosity BL Lac objects (Aharonian 2000).Obviously, the critical issue of such models is whether protons can reach sufficientlylarge energies to produce synchrotron spectra extending up to TeV energies. Combining adronic jet models hν p,syn,max ≃ × − ( σ/ . / L / j, ( f / (Γ / ( θ j Γ) R [TeV] . (4.5)One can see that spectra may extend to TeV energies only if assuming f ∼ σ ∼
1, andjet powers L j > erg s − .
5. Protons in leptonic models
Disproving interpretation of high energy spectra of blazars produced via hadronicmodels does not disprove the presence of protons in AGN jets. They simply are expectedto be radiatively inefficient but are likely to dominate the jet energy flux and stronglyaffect the dynamics of dissipation processes via shocks in the regions of low magnetizationparameter ( σ < . < q e <
2. If it is true, then the number of electrons joining protons in thestochastic acceleration process can be lower than the number of protons by significantfactor. Hence, the high efficiency of blazar radiation may indicate that q e <
1, or thatthere is a significant pair content.In the ERC (External-Radiation-Compton) models (Sikora et al. 1994) of γ -ray pro-duction in luminous blazars such a low-energy tail should be observed in the 30keV–1MeV spectral energy range. Unfortunately, these bands are observationally poorly cov-ered, particularly above 20 keV. A number of blazars have been detected up to ∼ < q e <
2. This, together with the location of the break in the energy range1 − n e /n p ∼
10) pair content,implied also by studies of the bulk-Compton and Compton-rocket effects (Sikora & Made-jski 2000; Ghisellini & Tavecchio 2010). At energies <
20 keV most blazars have softerX-ray spectra, but they can result from the contribution of the SSC process and/or fromthe superposition of X-rays produced at different locations in a jet, such as the orphanX-ray outburst detected in 3C279 (Abdo et al. 2010).
6. Conclusions
For realistic jet powers ( L j L Edd in luminous blazars and L j − L Edd in lowluminosity BL Lac objects), limited magnetization ( σ . q p > failto : Marek Sikora • reproduce γ -ray luminosities of blazars; • explain formation of very hard X-ray spectra in luminous blazars; • provide the spectral extension up to TeV energies in low luminosity blazars.Nevertheless, as indicated by several independent observations, protons are present inAGN jets and presumably play key role in dissipation processes in shocks. In particular,they transfer a fraction of the dissipated energy to electrons/positrons helping them toreach threshold energies for further acceleration by stochastic mechanisms and producethe observed γ -ray spectra via the ERC and SSC scenarios. However, significant paircontent may be required to achieve reasonable effiecincy of that energy transfer. Acknowledgements
I thank G. Madejski, K. Nalewajko and L. Stawarz for helpful comments. The workwas supported by Polish grant MNiSW NN203 301635.
References
Abdo, A.A., et al. 2010,
Nature , 463, 919Aharonian, F.A. 2000,
New Astron. , 5, 377Amato, E., & Arons, J. 2006,
ApJ , 653, 325Amano, T., & Hoshino, M. 2009,
ApJ , 690, 244Beckmann, V., Ricci, C., & Soldi, S. 2010, arXiv:
ApJ , 362, 38Blandford, R.D. 1976,
MNRAS , 176, 465Blundell, K.M., Fabian, A.C., Crawford, C.S., et al. 2006,
ApJ , 644, L13Camenzind, M. 1986, A&A, 156, 137Ghisellini, G., Della Ceca, R., Volonteri, M., et al. 2010,
MNRAS , 405, 387Ghisellini, G., & Tavecchio, F. 2010, arXiv:
ApJ , 695, 707Komissarov, S.S. 2010, arXiv:
MNRAS , 380, 51Lovelace, R.V.E. 1976,
Nature , 262, 649Lyubrasky, Y.E. 2010, MNRAS, 402, 353Mannheim 1993 1993, A&A, 269, 67Mannheim, K., & Biermann. P.L. 1992,
A&A , 253, L21McKinney, J.C., & Blandford, R.D. 2009,
MNRAS , 394, L126McNaron-Brown, K., Johnson, W.N., Jung, G.V., et al. 1995,
Apj , 451, 575Moderski, R., Sikora, M., & B la˙zejowski, M. 2003,
A&A , 406, 855Park, K., & Blackman, E.G. 2010,
MNRAS , 403, 1993Phinney, E.E. 1983, PhD Thesis, Cambridge UniversityRachen, J.P., & M´esz´aros, P. 1998,
Phys.Rev.D , 58, 123005Rieger, F.M., Bosch-Ramon, V., & Duffy, P. 2007,
ApSS , 309, 119Sikora, M., Begelman, M.C., & Rees, M.J. 1994,
ApJ , 421, 153Sikora, M., Kirk, J., Begelman, M., & Schneider, P. 1987,
ApJ , 320, L81Sikora, M., & Madejski 2000,
ApJ , 534, 109Sikora, M., Stawarz, L., Moderski, M., Nalewajko, K., & Madejski, G.M. 2009,
ApJ , 704, 38Sironi, L. & Spitkovsky, A. 2010, arXiv:
ApJ , 662, 213Tchekhovskoy, A., McKinney, J.C., & Narayan, R. 2009, ApJ, 699, 1789Vitrishchak, V.M., Gabuzda, D.C., Algaba, et al. 2008,
MNRAS , 391, 124Zhang, S., Collmar, W., & Sch¨onfelder, V. 2005
A&A , 444, 767 adronic jet models Discussion
BEDNAREK: Can curvature energy losses of protons be important in AGNs?SIKORA: They cannot be. This is because following particle acceleration processes inshocks or reconnection regions, relativistic protons are injected with a broad distribu-tion of pitch angles. Such protons (as well as all other charged particles) spiral aroundmagnetic field lines rather than slide on them.YUAN: There are two kinds of B field in a jet. One is a large scale helical field, anotherbeing turbulent in a shock front. When we calculate radiation spectrum, we use turbulentone, but when we calculate polarization, we seem to use the large scale ordered field.SIKORA: Properly calculated polarization must take into account both, the tangled/turbulentmagnetic fields compressed and/or generated in a shock, as well, as the large scale mag-netic fields transmitted through the shock.DERMER: Acceleration to high energies is faster for ions than protons. How do yourconclusions change if you consider Fe rather than p?SIKORA: For approximately solar abundances of AGN plasmas the number of heavynuclei is ≫ Z times smaller than of protons. Therefore, despite the fact that heavynuclei are accelerated Z times faster, they contribute to radiative processes much lessthan protons and our main conclusion that hadronic models cannot reproduce γ -rayluminosities of blazars remains valid.PIRAN: Auger indicates that UHECRs are nuclei. It is much easier to calculate nuclei.Nuclei will diffuse in the intergalactic field and can propagate only up to ∼
10 Mpc.This suggestes that Cen A is the main source of UHECRs if those are nuclei and if theintergalactic magnetic field is > −9