Photons to axion-like particles conversion in Active Galactic Nuclei
PPhotons to axion-like particles conversion in Active GalacticNuclei
Fabrizio Tavecchio
INAF – Osservatorio Astronomico di Brera,Via E. Bianchi 46, I–23807 Merate, Italy ∗ Marco Roncadelli
INFN, Sezione di Pavia, Via A. Bassi 6, I – 27100 Pavia, Italy † Giorgio Galanti
Dipartimento di Fisica, Universit`a dell’Insubria,Via Valleggio 11, I – 22100 Como, Italy ‡ The idea that photons can convert to axion-like particles (ALPs) γ → a in oraround an AGN and reconvert back to photons a → γ in the Milky Way magneticfield has been put forward in 2008 and has recently attracted growing interest. Yet,so far nobody has estimated the conversion probability γ → a as carefully as allowedby present-day knowledge. Our aim is to fill this gap. We first remark that AGNwhich can be detected above 100 GeV are blazars , namely AGN with jets, with oneof them pointing towards us. Moreover, blazars fall into two well defined classes: BLLac objects (BL Lacs) and Flat Spectrum Radio Quasars (FSRQs), with drasticallydifferent properties. In this Letter we report a preliminary evaluation of the γ → a conversion probability inside these two classes of blazars. Our findings are surprising.Indeed, while in the case of BL Lacs the conversion probability turns out to be totallyunpredictable due to the strong dependence on the values of the somewhat uncertainposition of the emission region along the jet and strength of the magnetic fieldtherein, for FSRQs we are able to make a clear-cut prediction. Our results are ofparamount importance in view of the planned very-high-energy photon detectors likethe CTA, HAWK, GAMMA-400 and HISCORE. Keywords: axion, photon propagation
Introduction – Many extensions of the Standard Model of particle physics – and chieflyamong them superstring theories – generically predict the existence of axion-like particles(ALPs) (for a review, see [1, 2]), which are spin-zero, neutral and extremely light bosons –to be denoted by a – closely resembling the axion (for a review, see [3]) apart from two factsthat makes them as much as model-independent as possible. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] a r X i v : . [ a s t r o - ph . H E ] A p r • Possible couplings to fermions and gluons are discarded and only their two-photoncoupling aγγ is taken into account. • The ALP mass m is totally unrelated to their aγγ coupling constant 1 /M . The mostrobust lower bound on M is set by the CAST experiment CERN which yields M > . · GeV for m < .
02 eV [4]. Somewhat weaker bounds are
M > . · GeV for m <
M > . · GeVfor m < . · − eV from the lack of ALP detection supposedly emitted by supernova1987A [6].As a consequence, ALPs are described by the Lagrangian L = 12 ∂ µ a ∂ µ a − m a + 1 M E · B a , (1)where E and B denote the electric and magnetic components of the field strength F µν .Observe that because E is perpendicular to the γ momentum, the structure of the last termin Eq. (1) implies that only the component B T transverse to the γ momentum couplesto a . Throughout this Letter, E is the electric field of a propagating photon while B isan external magnetic field. Accordingly, the mass matrix of the aγ system is off-diagonal,thereby implying that the propagation eigenstates differ from the interaction eigenstates.Therefore γ ↔ a oscillations take place much in the same way that occurs for massiveneutrinos of different flavor, apart from the need of B in order to compensate for the spinmismatch [7, 8]. However, in the situations to be addressed below also the one-loop QEDvacuum polarization in the presence of B has to be taken into account and is described bythe effective Lagrangian [9–11] L HEW = 2 α m e (cid:104)(cid:0) E − B (cid:1) + 7 (cid:0) E · B (cid:1) (cid:105) , (2)where α is the fine-structure constant and m e is the electron mass. So, throughout thisLetter the considered ALP Lagrangian is L ALP = L + L HEW .In order to avoid any misunderstanding, the symbol E denotes henceforth the energy rather than the electric field.Let us now turn our attention to very-high-energy (VHE) astrophysics, namely to ob-served photons with energies in the range 100 GeV < E <
100 TeV and to their extragalacticsources, the majority of which are Active Galactic Nuclei (AGN). Generally speaking, AGNare powered by a supermassive black hole (SMBH) with M SMBH ∼ − M (cid:12) lying atthe centre of a bright galaxy and accreting matter from the surrounding, which – beforedisappearing into the SMBH – heats up emitting an enormous amount of radiation. Nearly10 % of AGN supports two opposite relativistic jets (with a bulk Lorentz factor γ (cid:39) − Blazars are AGN with one jet pointing – merelyby chance – almost exactly towards the Earth. Blazars fall into two broad classes: BL Lacobjects (BL Lacs) – which represent the great majority of extragalactic sources detectedin the VHE band – and flat spectrum radio quasars (FSRQs) [12]. As a rule, the blazarspectral energy distribution (SED) shows two broad humps, the first one peaking at lowfrequency – from IR to soft-X rays, depending on the specific source – while the second onein the γ -ray band. In BL Lacs the latter component extends to VHE, often reaching multi-TeV energies. In the widely assumed leptonic models, the VHE γ -ray emission is the resultof the inverse Compton (IC) scattering of soft photons by relativistic electrons in the jet.Moreover, it is widely accepted that the dominant soft photon population derives – throughthe synchrotron mechanism – by the same electrons that scatter them into the VHE band.This is the scheme which lies at the basis of the so-called synchrotron self Compton (SSC)model [13, 14].Yet, the VHE band is plagued by the existence of the extragalactic background light (EBL)which is the light emitted by galaxies during the whole cosmic history and extends from thefar-infrared to the near-ultraviolet (for a review, see [15]). What happens is that when aVHE γ emitted by a distant blazar scatters off an EBL γ it has a good chance to disappearinto an e + e − pair [16, 17]. Indeed, according to conventional physics this effect becomesdramatic even for E above a few TeV (see the Fig. 1 of [18]), a fact that drastically reducesthe γ -ray horizon at increasing E .A breakthrough came in 2007 when it was first realized [19] (see also [20]) that γ → a → γ oscillations taking place in intergalactic space can greatly decrease the EBL dimmingfor sufficiently far-away blazars and high enough E provided that a large-scale magneticfield in the 0 . − true photon and sometimes as an ALP. When it propagates asa photon it undergoes EBL absorption, but when it propagates as an ALP it does not .Therefore, the effective photon mean free path in extragalactic space λ γ, eff ( E ) is larger than λ γ ( E ) as predicted by conventional physics. Correspondingly, the photon survivalprobability becomes P γ → γ ( E ) = exp (cid:0) − D s /λ γ, eff ( E ) (cid:1) , where D s is the blazar distance. So,because of the exponential dependence on the mean free path even a small increase of λ γ, eff ( E ) with respect to λ γ ( E ) produces a large enhancement of P γ → γ ( E ), thereby givingrise to a drastic reduction of the EBL dimming.Before proceeding further, a remark is in order. From time to time a tension between thepredicted EBL level causing photon absorption and observations in the VHE range has beenclaimed [22, 23], but a subsequent better determination of the EBL properties has shownthat no problem exists. Actually, after a long period of uncertainty on the EBL preciseproperties, nowadays a convergence seems to be reached [15], well represented e.g. by themodels of Franceschini, Rodighiero and Vaccari (FRV) [24] and of Dom´ınguez et al. [25].Nevertheless, it has been claimed that VHE observations require an EBL level even lowerthan that predicted by the minimal EBL model normalized to the galaxy counts only [26].This is the so-called pair-production anomaly , which is based on the Kolmogorov test andso does not rely upon the estimated errors. It has thoroughly been quantified by a globalstatistical analysis of a large sample of observed blazars, showing that measurements inthe regime of large optical depth deviate by 4.2 σ from measurements in the optically thinregime [27]. Systematic effects have been shown to be insufficient to account for such thepair-production anomaly, which looks therefore real. Actually, the discovery of new blazarsat large redshift like the observation of PKS 1424+240 have strengthened the case for thepair-production anomaly [28]. Quite recently, the existence of the pair-production anomalyhas been questioned by using a new EBL model and a χ test, in which errors play insteadan important role [29]. Because the Kolmogorov test looks more robust in that it avoidstaking errors into account, we tend to believe that the pair-production anomaly is indeed atthe level of 4.2 σ . It looks tantalizing that for a suitable choice of the free parameters it hasbeen shown that the mechanism discussed above provides a solution to the pair-productionanomaly [27, 30]. An even more amazing fact is that for the same choice of the free parameteralso the observed redshift-dependence of the blazar spectra is naturally explained [31].Coming back to our main line of development, as a follow-up of the previous proposalsthat γ → a conversions occur in AGN [32, 33], a complementary scenario was put forwardin 2008 [34]. Schematically, VHE photons are simply assumed to substantially or evenmaximally convert to ALPs inside a blazar, so that the emitted flux can consist in up to 1 / / γ → a conversion probability P γ → a ( E ) insidethe two classes of blazars as carefully as possible consistently with the presently availableknowledge. So, the aim of this Letter is basically to speed up the presentation of our results.A more thorough analysis along with all relevant calculations will be the subject of a futuremuch more detailed paper. BL Lacs – They are the simplest blazars, and so we better start from them. Denoting by y the coordinate along the jet axis, in order to achieve our goal two quantities are needed wherethe photon/ALP beam propagates: the transverse magnetic field B T ( y ) and the electrondensity n e ( y ) profiles. Because the electrons are accelerated in shocks generated in the flow,the VHE photons are produced in a well-localized region R VHE pretty far from the centralengine. So, four crucial parameters are: the distance d VHE of R VHE from the centre, thesize of R VHE , and the values of B T, VHE and n e, VHE inside it. The SSC diagnostics applied tothe SED of BL Lacs [41] provides the main physical quantities concerning R VHE . They are B T, VHE = 0 . − n e, VHE (cid:39) · cm − , leading to a plasma frequency of 8 . · − eV.The quantity d VHE is difficult to determine directly, because the current instrumental spatialresolution is still too poor. A common indirect way consists in inferring d VHE from the size R VHE of R VHE , assumed to be a measure of the jet cross-section, derived in turn from spectralmodels and the observed variability timescale. Typical values lie in the range 10 − cm.Whenever the jet aperture angle θ jet is measurable – which is certainly the case for BL Lacs ata relatively large distance – it is generally found θ jet (cid:39) . d VHE = R VHE /θ jet (cid:39) − cm.Beyond R VHE photons travel outwards unimpeded until they leave the jet with a typicallength of 1 kpc and propagate into the host galaxy. Given the fact that d VHE is a fairly largequantity, the component of B relevant for us is the toroidal part which is transverse to thejet axis and goes like y − [42]. The same conclusion follows from the conservation of themagnetic luminosity if the jet conserves its speed [43]. Moreover, recent work has succeededto observationally characterize the B structure over distances in the range 0 . −
100 pc inseveral jets of BL Lacs through polarimetric studies, showing unambiguously that in BLLacs B is indeed substantially ordered and predominantly traverse to the jet [44]. We stressthat in particular these results are inconsistent with a domain-like structure of B in the jetas assumed e.g. in [35, 36]. Turning next to the electron density, under the usual assumptionthat the jet has a conical shape we expect that it goes like y − . Whence B T ( y ) = B T, VHE d VHE y , n e ( y ) = n VHE d y , (3)for y > d VHE . Observe that Eqs. (3) holds true in a frame co-moving with the jet, so thatthe transformation to a fixed frame is effected by E → γE . We remark that this relation isstrictly true if the jet is observed at an angle θ v = 1 /γ with respect to the jet axis. Moregenerally, the transformation reads E → E δ , where δ is the relativistic Doppler factor (fordetails, see [12]). Here we have γ = 15. FIG. 1: Plot of P γ → a ( E ) for a BL Lac taking M = 5 · GeV. The different curves correspondto B = 0 . . . d VHE = 10 cm (bottom), 3 · cm (middle), 10 cm (upper). FIG. 2: Plot of P γ → a ( E ) for a BL Lac taking M = 5 · GeV. The different curves correspondto B = 0 . . . d VHE = 10 cm (bottom), 3 · cm (middle), 10 cm (upper). FSRQs – These are the most powerful blazars and are in a sense a more complicated versionof BL Lacs. The additional components are: (1) the broad line region (BLR) consisting in aspherical shell of many clouds photo-ionized by the radiation from the matter accreting ontothe SMBH, located at about d BLR (cid:39) cm from the centre and rapidly rotating aboutit; (2) a dusty torus reprocessing part of the above radiation in the infrared band; (3) theradio lobes consisting in a hot non-thermal plasma inflated where the jets collide with theextragalactic gas. Because both the BLR and the dusty torus lie beyond R VHE and are quiterich of ultraviolet and infrared photons, respectively, they give rise to a huge absorption of γ rays with E γ > −
20 GeV through the same γγ → e + e − process considered above. Onthe other hand, the lobes – being magnetized – represents a further conversion region. Thejets in FSRQs are longer and less prone to instabilities than those of the weaker BL Lacs.Presently, concerning the VHE γ -ray emission region R VHE we take d VHE larger by a factorof 3 as compared to the BL Lac case, based on the larger variability time scales [45]. Themodeling of the SED with state-of-the-art emission models provides B T, VHE = 1 −
10 G and n VHE (cid:39) cm − [45]. The geometry and the intensity of B in the jet beyond R VHE are farless clear than in the case of BL Lacs. In fact, there are indications that B has a globallyordered structure, but its inclination angle ϕ with respect to the jet axis does not have aunique value for all sources, actually covering the whole interval 0 − ◦ . For definiteness,we assume the same profiles of B T ( y ) and n e ( y ) as in Eq. (3), taking ϕ = 45 ◦ and γ = 10.Radio polarimetric observations yield a good amount of information about the structureand the intensity of B in the radio lobes. Specifically, one gets a turbulent B which canbe modelled as a domain-like structure with homogenous strength B = 10 µ G, coherencelength 10 kpc and random orientation in each domain.
FIG. 3: Plot of P γ → a ( E ) for a FSRQ taking M = 5 · GeV. The different curves correspond to B = 1 G (solid blue), 2 G (dashed cyan), 5 G (long dashed, green) and 10 G (dot red). The threepanels correspond to three values of the distance of the emitting region, namely d VHE = 3 · cm(bottom), 10 cm (middle), 3 · cm (upper). FIG. 4: Plot of P γ → a ( E ) for a FSRQ taking M = 5 · GeV. The different curves correspond to B = 1 G (solid blue), 2 G (dashed cyan), 5 G (long dashed, green) and 10 G (dot red). The threepanels correspond to three values of the distance of the emitting region, namely d VHE = 3 · cm(bottom), 10 cm (middle), 3 · cm (upper). Results – Because of lack of space, we cannot report the explicit calculation of the γ → a conversion probability P γ → a ( E ) which is anyway a straightforward application of the tech-nique discussed in great detail in [20]. We assume as benchmark values m ≤ − eV as wellas M = 5 · GeV and M = 5 · GeV. Basically, our results can be summarized asfollows.Owing to the leading role played by the QED term, in the case of BL Lacs P γ → a ( E )shows a rather complex behaviour and a strong dependence on B T, VHE and d VHE , as shownin Figs. 1 and 2. As a consequence, P γ → a ( E ) turns out to be intrinsically unpredictable . Inaddition, as M decreases only for the largest considered values of the magnetic field takesthe conversion probability sizable values and no oscillatory behaviour shows up.On the contrary, for FSRQs due to the efficient γ ↔ a oscillations in the radio lobes –which actually leads to the equipartition among the three degrees of freedom – the peculiarfeatures exhibited by BL Lacs get smoothed out and below 20 GeV we get P γ → a ( E ) = 1 / M . Above 20 GeV instead the above-mentioned absorption leadsto a drastic reduction of the emitted ALP flux. Altogether, in the case of FSRQs we make aclear-cut prediction which is exhibited in Figs. 3 and 4, which is again almost independentof the value of M .Our results are of great importance for the planned very-high-energy detectors like theCTA, HAWK, GAMMA-400 and HISCORE, and for those based on the techniques discussedin [46–48]. Moreover, we stress that all analyses of the scenario of γ → a conversion in ablazar and a → γ reconversion in the MW should be properly revised according to thepresent conclusions. Acknowledgments – We thank Alessandro De Angelis, Luigina Feretti and Marcello Girolettifor useful discussions. F. T. acknowledges contribution from a grant PRIN-INAF-2011. Thework of M. R. is supported by INFN TAsP and CTA grants. [1] J. Jaeckel, A. Ringwald, Ann. Rev. Nucl. Part. Sci. 60 (2010) 405-437.[2] A. Ringwald, Phys. Dark Univ. 1 (2012) 116-135.[3] J. E. Kim, G. Carosi, Rev. Mod. Phys. 82 (2010) 557-601.[4] S. Andriamonje et al. [CAST collaboration], JCAP 04 (2007) 010.[5] A. Ayala et al. , Phys. Rev. Lett (2014) 191302.[6] A. Payez et al. , JCAP (2015) 006.[7] P. Sikivie, Phys. Rev. Lett. 51 (1983) 1415-1417; (E) ibid. 52(1984) 695.[8] G. G. Raffelt, L. Stodolsky, Phys.Rev. D 37 (1988) 1237-1249.[9] W. Heisenberg, H. Euler, Z. Phys. 98 (1936) 714-732.[10] V. S. Weisskopf, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 14 (1936) 6.[11] J. Schwinger, Phys. Rev. 82 (1951) 664-679.[12] C. M. Urry, P. Padovani, Pub. of the Astron. Soc. of the Pacific 107 (1995) 803-845.[13] S. D. Bloom, A. P. Marscher, Astrophys. J. 461(1996) 657-663.[14] F. Tavecchio, L. Maraschi, G. Ghisellini, Astrophys. J. 509 (1998) 608-619.[15] E. Dwek, F. Krennrich, Astroparticle Phys. 43 (2013) 112-133.[16] R. J. Gould, G. P. Schr´eder, Phys. Rev. 155 (1967) 1408-1411.[17] G. G. Fazio, F. W. Stecker, Nature 226 (1970) 135-136. [18] A. De Angelis, G. Galanti, M. Roncadelli, Mon. Not. R. Astron. Soc. 432 (2013) 3245-3248.[19] A. De Angelis, M. Roncadelli, O. Mansutti, Phys. Rev. D 76 (2007) 123011.[20] A. De Angelis, G. Galanti, M. Roncadelli, Phys. Rev. D 84 (2011) 105030; (E) ibid. 84 (2013)105030.[21] R. Durrer, A. Neronov, Ann. Rev. Astron. Astrophys. 21 (2013) 62.[22] R. J. Protheroe and H. Meyer, Phys. Lett. B (2000) 1-6.[23] F. T. Aharonian et al. [H.E.S.S. Collaboration], Nature (2006) 1018-1021.[24] A. Franceschini, G. Rodighiero, E. Vaccari, Astron. Astrophys. (2008) 837-852.[25] A. Dom´ınguez et al. , Mon. Not. R. Astron. Soc. (2011) 2556-2578.[26] T. M. Kneiske, H. Dole, Astron. Astrophys. 515 (2010) A19.[27] D. Horns and M. Meyer, JCAP02