Blazars as beamlights to probe the Extragalactic Background Light in the Fermi and Cherenkov telescopes era
aa r X i v : . [ a s t r o - ph . C O ] J a n Blazars as beamlights to probe the Extragalactic Background Lightin the Fermi and Cherenkov telescopes era
M. Persic
INAF-Trieste and INFN-Trieste, via G.B. Tiepolo 11, I-34143 Trieste TS, Italy
N. Mankuzhiyil
Udine University and INFN-Trieste, via delle Scienze 208, I-33100 Udine UD, Italy
F. Tavecchio
INAF-Brera, via E. Bianchi 46, I-23807 Merate LC, Italy
The Extragalactic Background Light (EBL) is the integrated light from all the stars that haveever formed, and spans the IR-UV range. The interaction of very-high-energy (VHE:
E >
100 GeV) γ -rays, emitted by sources located at cosmological distances, with the intervening EBL results in e − e + pair production that leads to energy-dependent attenuation of the observed VHE flux. Thisintroduces a fundamental ambiguity in the interpretation of the measured VHE blazar spectra:neither the intrinsic spectra, nor the EBL, are separately known – only their combination is. Inthis paper we propose a method to measure the EBL photon number density. It relies on usingsimultaneous observations of blazars in the optical, X-ray, high-energy (HE: E >
100 MeV) γ -ray(from the Fermi telescope), and VHE γ -ray (from Cherenkov telescopes) bands. For each source,the method involves best-fitting the spectral energy distribution (SED) from optical through HE γ -rays (the latter being largely unaffected by EBL attenuation as long as z ∼ <
1) with a SynchrotronSelf-Compton (SSC) model. We extrapolate such best-fitting models into the VHE regime, andassume they represent the blazars’ intrinsic emission. Contrasting measured versus intrinsic emissionleads to a determination of the γ - γ opacity to VHE photons – hence, upon assuming a specificcosmology, we derive the EBL photon number density. Using, for each given source, different statesof emission will only improve the accuracy of the proposed method. We demonstrate this methodusing recent simultaneous multi-frequency observations of the blazar PKS 2155-304 and discuss howsimilar observations can more accurately probe the EBL. I. INTRODUCTION
The Extragalactic Background Light (EBL), inboth its level and degree of cosmic evolution, reflectsthe time integrated history of light production andre-processing in the Universe, hence the history ofcosmological star-formation. Roughly speaking, itsshape must reflect the two humps that characterizethe spectral energy distributions (SEDs) of galaxies:one arising from starlight and peaking at λ ∼ µ m(optical background), and one arising from warm dustemission and peaking at λ ∼ µ m (infrared back-ground).Direct measurements of the EBL are hampered bythe dominance of foreground emission (interplanetarydust and Galactic emission), hence the level of EBLemission is uncertain by a factor of several.One approach has been modeling the EBL aris-ing from an evolving population of galactic stellarpopulations: however, uncertainties in the assumedgalaxy formation and evolution scenarios, stellar ini-tial mass function, and star formation rate haveled to significant discrepancy among models (e.g.,[13, 14, 21, 23, 25]). These models have been usedto correct observed VHE spectra and deduce (EBLmodel dependent) ’intrinsic’ VHE γ -ray emissions.The opposite approach, of a more phenomenologi- cal kind, deduces upper limits on the level of EBL at-tenuation making basic assumptions on the intrinsicVHE γ -ray shape of AGN spectra: assuming, specif-ically, that the VHE photon index must be Γ ≥ . Fermi /LAT HEspectrum into the VHE domain exceeds the intrin-sic VHE spectrum there ([9]). The only unquestion-able constraints on the EBL are model-independentlower limits based on galaxy counts ([6, 8]). It shouldbe noted, however, that the EBL upper limits in the2–80 µ m obtained by [18] combining results from allknown TeV blazar spectra (based on the assumptionthat the intrinsic Γ ≥ .
5) are only a factor ≈ eConf C091122 sure the EBL that improves on [24] by making amore realistic assumption on the intrinsic TeV spec-trum. Simultaneous optical/X-ray/HE/VHE (i.e.,eV/keV/GeV/TeV) data are crucial to this method,considering the strong and rapid variability displayedby most blazars. After reviewing features of EBLabsorption (sect. 2) and of the SSC emission model(sect. 3), in sect. 4 we describe our technique, in sect. 5we apply it to recent multifrequency observations ofPKS 2155-304 and determine the photon-photon opti-cal depth out to that source’s redshift. In sect. 6 wediscuss our results. II. EBL ABSORPTION
The cross section for the reaction γγ → e ± is ([12]), σ γγ ( E, ǫ ) = 316 σ T (1 − β ) ×× (cid:20) β ( β −
2) + (3 − β ) ln 1 + β − β (cid:21) , (1)where σ T is the Thompson cross section and β ≡ p − ( m e c ) /Eǫ . For demonstration purposes letus assume, following [24], that n ( ǫ ) is the local num-ber density of EBL photons having energy equal to ǫ (no redshift evolution – as befits the relatively lowredshifts accessible to IACTs), z e is the source red-shift, and Ω =1: the corresponding optical depth dueto pair creation attenuation between the source andthe Earth, is (see ([24]) τ γγ ( E, z e ) = cH Z z e √ z d z Z x x ×× Z ∞ mec Ex (1+ z )2 n ( ǫ ) σ γγ (cid:0) xEǫ (1 + z ) (cid:1) d ǫ , (2)where x ≡ (1 − cos θ ), θ being the angle between thephotons, and H is the Hubble constant. We furtherassume, again following [24], that the local EBL spec-trum has a power-law form, n ( ǫ ) ∝ ǫ − . . Then Eq.(1)yields τ ( E, z ) ∝ E . z ηs with η ∼ γ VHE γ EBL → e + e − interaction: τ γγ depends both onthe distance traveled by the VHE photon (hence on z ) and on its (measured) energy E . So the spectrummeasured at Earth is distorted with respect to theemitted spectrum. In detail, the expected VHE γ -rayflux at Earth will be: F ( E )= (d I/ d E ) e − τ γγ ( E ) (dif-ferential) and F ( >E )= R ∞ E (d I/ d E ′ ) e − τ γγ ( E ′ ) dE ′ (in-tegral). III. BLAZAR SSC EMISSION
In order to reduce the degrees of freedom, we use asimple one-zone SSC model (for details see [28, 29]).This has been shown to adequately describe broad-band SEDs of most blazars ([10, 29]) and, for a givenblazars, both its ground and excited states ([27]).The reason for the one-zone model to work is that inmost blazars the temporal variability is clearly dom-inated by one characteristic timescale, which impliesone dominant characteristic size of the emitting region([4]).The emission zone is supposed to be spherical withradius R , in motion with bulk Lorentz factor Γ at anangle θ with respect to the line of sight. Special rela-tivistic effects are described by the relativistic Dopplerfactor, δ = [Γ(1 − β cos θ )] − . The energy spectrumof the emitting relativistic electrons is described by asmoothed broken power-law function of the electronLorentz factor γ , with limits γ and γ and break at γ br . In calculating the SSC emission we use the fullKlein-Nishina cross section.As detailed in [29], this simple model can be fullyconstrained by using simultaneous multifrequency ob-servations. Indeed, the total number of free param-eter of the model is reduced to 9: the 6 parame-ter specifying the electron energy distribution, plusthe Doppler factor δ , the size of the emission region R , and the magnetic field B . On the other hand,from observations ideally one can derive 9 observa-tional quantities: the slopes of the synchrotron bumpafter and above the peak α , (uniquely connected to n , ), the synchrotron and SSC peak frequencies ( ν s , C )and luminosities L s , C , and the minimum variabilitytimescale t var which provides an estimate of the sizeof the sources through R < ct var δ .Therefore, once the relevant observational quanti-ties are known, one can uniquely derive the set of SSCparameters. IV. THE METHOD
The method we are proposing stems from the con-sideration that both the EBL and the intrinsic VHE γ -ray spectra of background sources are fundamentallyunknown. In order to measure the EBL at different z , one should single out a class of sources that is ho-mogeneous, i.e. it can be described by one same emis-sion model at all redshifts. This approach is meant tominimize biases that may possibly arise from system-atically different SED modelings adopted for differentclasses of sources at different distances. So we choosethe class of source that both has the simplest emis-sion model and has the potentiality of being seen fromlarge distances: blazars, i.e. the AGN whose relativis-tic jets point toward the observer so their luminosities eConf C091122
009 Fermi Symposium, Washington, D.C., Nov. 2-5
E >
100 MeV) γ -ray(from the Fermi telescope), and VHE γ -ray (fromCherenkov telescopes) bands. A given SED will bebest-fitted, from optical through HE γ -rays, with aSynchrotron Self-Compton (SSC) model. [Photonswith E ∼ <
100 GeV are largely unaffected by EBL at-tenuation (for reasonable EBL models) as long as z ∼ < e − τ γγ ( E, z ) , the energy-dependent absorption of theVHE emission coming from a source located at red-shift z due to pair production with intervening EBLphotons. Upon assumption of a specific cosmology,the final step is deriving the EBL photon number den-sity.Using, for each blazar, SEDs from different states ofemission will improve the accuracy of the method byincreasing the number of EBL measurements at thatredshift. A. Best-fit procedure: χ minimization In order to fit the observed optical, X-ray and HE γ -ray flux with the SSC model, a χ minimizationis used. We vary the SSC model’s 9 parameters bysmall logarithmic steps. If the variability timescaleof the flux, t var , is known, one can set R ∼ ct var δ ,so the free parameters are reduced to 8. We assumehere γ min =1: for a plasma with n e ≈ O(10) cm − and B ≈ O(0.1) G (as generally appropriate for TeV blazarjets: e.g., [5, 7, 10]), this approximately correspondsto the energy below which Coulomb losses exceed thesynchrotron losses (e.g., [20, 22]) and hence the elec-tron spectrum bends over and no longer is power-law. However, in general γ min should be left to vary –e.g., cases of a ”narrow” Compton component require γ min > χ is followed by larger steps. V. RESULTS: APPLICATION TOPKS 2155-304
We apply the procedure described in Sect. 4 tothe simultaneous SED data set of PKS 2155-304 de-scribed in [2]. The data and resulting best-fit SSCmodel (from optical through HE γ -rays) are shownin Fig.(1). The extrapolation of the model into theVHE γ -ray range clearly lies below the observationalH.E.S.S. data, progressively so with increasing en-ergy. We attribute this effect to EBL attenuation, F obs ( E ; z )= F em ( E ; z ) e − τ γγ ( E ; z ) . The correspondingvalues of τ γγ ( E ; z ) for E =0.23, 0.44, 0.88, 1.70 TeVand z =0.12 are, respectively, τ γγ = 0 .
12, 0.48, 0.80,and 0.87 .We note that the SED analysis of [2] was based ona slightly different SSC model, that involved a three-slope (as opposed to our two-slope) electron spec-trum. This difference may lead to a somewhat differ-ent decreasing wing of the modeled Compton hump,and hence to a systematic difference in the derived τ γγ ( E ; z ). That said, it’s however interesting to notethat the main parameters describing the plasma blob( B , δ , n e ) take on similar values in our best-fit analysisand in [2].In Fig.(2) we compare our determination of τ γγ withsome recent results ([8]) or upper limits ([11, 14, 19]).Whereas our values are generally compatible with pre-viously published constraints, we note that our val-ues closely agree with the corresponding values of [8],which are derived from galaxy number counts andhence represent the light contributed by the stellarpopulations of galaxies prior to the epoch correspond-ing to source redshift z s – i.e., the minimum amount(i.e., the guaranteed level) of EBL. VI. DISCUSSION
The method for measuring the EBL we have pro-posed in this paper is admittedly model-dependent.However, its only requirement is that all the sourcesused as background beamlights should have one sameemission model. In the application proposed here, wehave used a one-zone SSC model where the electronspectrum was a (smoothed) double power law appliedto the SED of the HBL blazar PKS 2155-304. Whilethis choice was encouraged by the current observa-tional evidence fact that seem to HBLs have, withno exception, single-slope
Fermi -LAT spectra ([15]),we could have as well adopted the choice ([2]) of atriple power law electron spectrum in our search forthe best-fit SSC model of PKS 2155-304’s SED. Shouldthe latter electron distribution be shown to provide abetter fit to HBL
Fermi -LAT spectra, then it wouldbecome our choice. In general, what matters to theapplication of this method, is that all source SEDs befit with one same SSC model. eConf C091122
FIG. 1: Data (symbols: from [see 2]) and best-fit SSC model (solid curve) of the SED of PKS 2155-304. The best-fitSSC parameters are: n e = 150 cm − , γ br = 2 . × , γ max = 8 × , α = 1 . α = 3 . R = 3 . × cm, δ = 29 . B = 0 .
056 G. The obtained values of R and δ imply a variability timescale t var ∼ R/ ( cδ ), which is compatible with theobserved value of ≈
12 hr.
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