The implications of the axion like particle from the Fermi-LAT and H.E.S.S. observations of PG 1553+113 and PKS 2155-304
Junguang Guo, Hai-Jun Li, Xiao-Jun Bi, Su-Jie Lin, Peng-Fei Yin
TThe implications of the axion like particle from the Fermi-LAT and H.E.S.S.observations of PG 1553 +
113 and PKS 2155 − Jun-Guang Guo , , Hai-Jun Li , , Xiao-Jun Bi , , Su-Jie Lin , and Peng-Fei Yin Key Laboratory of Particle Astrophysics, Institute of High Energy Physics,Chinese Academy of Sciences, Beijing 100049, China School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
We investigate the axion like particle (ALP)-photon oscillation effect in the high energy γ -rayspectra of PG 1553+113 and PKS 2155 −
304 measured by Fermi-LAT and H.E.S.S.. The choiceof extragalactic background light (EBL) model, which induces the attenuate effect in observed γ -ray spectra, would affect the ALP implication. For the ordinary EBL model that prefers a nullhypothesis, we set constraint on the ALP-photon coupling constant at 95% C.L. as g aγ (cid:46) × − GeV − for the ALP mass ∼
10 neV. We also consider the CIBER observation of the cosmicinfrared radiation, which shows an excess at the wave wavelength of ∼ µ m after the substractionof foregrounds. The high energy gamma-rays from extragalactic sources at high redshifts wouldsuffer from a more significant attenuate effect caused by this excess. In this case, we find thatthe ALP-photon oscillation would improve the fit to the observed spectra of PKS 2155 −
304 andPG 1553+113 and find a favored parameter region at 95% C.L..
I. INTRODUCTION
Axion is a light pseudo-Goldstone boson proposed tosolve the strong CP problem in QCD [1–3]. Many newphysics models beyond the standard model also suggestthe existence of axion-like particles (ALPs) [4, 5]. Theseparticles may play an important role in the evolution ofthe universe and have rich phenomenology in high energyand astrophysics experiments. Considering the effectivecoupling between the ALP and photons, many investi-gations for the ALP-photon conversion effect have beenperformed [6–11]. For instance, the CAST experiment in-vestigated the photon signal induced by the ALPs fromthe Sun and has set a stringent constraint on the ALP-photon coupling as g aγ ≤ . × − GeV − [12].It is promising to explore ALP through the ALP-photon oscillation effect in high energy astrophysical pro-cesses [13]. The initial high energy photons emitted fromthe astrophysical source may be converted into ALP bythe external magnetic field around the source [14–16].Then ALPs propagate in the extragalactic space withoutenergy loss, compared with high energy photons whichcould interact with the extragalactic background light(EBL) background. Finally, these ALPs can be convertedinto detectable high energy photons by the Galactic mag-netic field. Therefore, it is expected that the ALP-photonoscillation would reduce the attenuation effect of highenergy photons from distant sources and affect the finalphoton spectra.Using the data from the observations of high energyphotons, many studies on the ALP-photon conversionhave been performed in the literature [10, 11, 15–39].For instance, the γ -ray spectra from the sources NGC1275 and PKS 2155 −
304 at high redshifts measured byFermi-LAT have been used to set constraints on g aγ inRef. [22] and Ref. [25], respectively. Compared with thedetectable energy range of Fermi-LAT ∼ . γ -ray above O (10 ) GeV, which would opena different window for the ALP research. For instance,The data of PKS 2155 −
304 from H.E.S.S. I observationhas been used to search for ALP in Ref. [18].Compared with H.E.S.S. I, H.E.S.S. II with the fifthtelescope added in 2012 is sensitive to the γ − ray spec-tra at lower energies. The H.E.S.S. II measurements ofthe very high energy (VHE, E (cid:38) −
304 andPG 1553+113 have been reported in Ref. [40]. Thesetwo sources are high frequency peaked BL Lac ob-jects with high statistics in the VHE γ -ray sky. Sincethey are located at high red-shifts (z=0.116 and 0.49for PKS 2155 −
304 and PG 1553+113, respectively), theEBL attenuation effects for their spectra are expected tobe significant. Consequently, the measurements of VHEspectra are suitable to detect the ALP-photon oscillation,which can compensate the EBL attenuation effect.This paper is organized as follows. In Section. II, wedescribe the EBL attenuation effect and introduce thetwo EBL models adopted in this work. In Section. III,we introduce the ALP-photon oscillation effect in the ex-tragalactic source and Milky Way. In Section. IV, wedescribe our fitting method to the observed γ -ray spec-tra. In Section. V, we investigate the implication of ALPin the data for the two EBL models. The conclusions aregiven in Section. VI. II. EBL ATTENUATION EFFECT
Before entering the Galaxy, high energy γ -ray wouldinteract with the EBL and loss energy through the pairproduction γ + γ EBL → e + + e − . This attenuation ef-fect can be described by the factor of e − τ ( E γ ,z ) , where τ ( E γ , z ) is the optical length for the source at redshift a r X i v : . [ a s t r o - ph . H E ] F e b of z τ ( E γ , z ) = (cid:90) z d z (1 + z ) H ( z ) (cid:90) E γ ≥ E th d ω d n d ω ¯ σ ( E γ , ω, z ) , where E th is the threshold energy of the pair production,¯ σ is the integral cross section of the pair production, andd n/ d ω is the proper number density per unit energy ofthe EBL at redshift of z .The main contributions to the EBL at wavelengthsfrom UV to IR are expected to be the starlight anddust re-radiation, accumulated over the history of theuniverse. In order to predict the EBL, the detailed mod-eling of the evolution of galaxy populations is needed.Many EBL models based on empirical or semi-analyticalapproaches have been developed in the literature [41–45]. According to the method dealing with the evolutionof the galaxy populations and the EBL, these models canbe classified into four types [43]. Using the cosmologicalsurvey data from a variety of ground-based experimentsand space telescopes, Franceschini et al. built a backwardevolutionary model to extrapolate the evolution of theEBL [41] (hereafter FRV08 model). The observed galaxyluminosity functions are used to derive the contributionsfrom different galaxy populations based on morphology.In our work, we adopt this EBL model to compute thegamma-ray attenuation effect.It is difficult to directly measure the EBL spectrumdue to the bright foregrounds, such as the zodiacal lightwhich is sunlight scattered by the interplanetary dust.Some efforts have been made to directly derive the EBLat near-IR wavelengths by subtracting the foregroundsfrom the data [46–51]. It is interesting to note thatmany analyses suggest an isotropic excess in the rangeof ∼ − µ m compared with the integrated light fromgalaxies predicted from deep galaxy counts and theoret-ical models. Recently, Ref. [51] reported the derivedEBL in the wavelength range of 0.8 − µ m from theCIBER observation, which is shown in Fig. 1. The ab-solute brightness of the derived EBL is highly dependenton the subtraction of zodiacal light. Assuming the Kel-sall zodiacal light model [52], the residual brightness is42.7 +11 . − . nW · m − sr − at 1 . µ m. Using a model indepen-dent method for the substraction, the derived minimumEBL brightness is 28.7 +5 . − . nW · m − sr − at 1 . µ m, whichstill exceeds the theoretical results.This excess may be explained by a new foregroundcomponent or a new EBL component. For instance,the radiation from the Population III stars at redshifts ∼ −
20 may contribute to this component [53]. Somestudies also investigate the possibility that this compo-nent is produced by the decay of ALP [54–56].It is expected that the high energy γ -ray spectrumof the astrophysical source at high redshifts would suf-fer from a significant attenuation effect after consideringthe excess. Therefore, the VHE gamma-ray observations set constraints on the EBL. There is a conflict betweenthe results from these analyses and the directly derivedEBL at O (1) µ m (see e.g. Ref. [57, 58]). Ref. [38] foundthat this conflict can be reconciled by the oscillation be-tween the photons and ALP and find a ALP parameterregion favored by observations. In this work, we con-sider the EBL model with an excess at O (1) µ m basedon the CIBER result [51] (hereafter Ciber model) and in-vestigate the ALP implication using a different methodto calculate of ALP-photon conversion compared withRef. [38]. We incorporate the CIBER result into theFRV08 spectrum at present and only consider the red-shift evolution for this excess at z ∼ − . ν I ν [ n W / m / s r ] Wavelength [ µ m] CIBERCIBER minFranceschiniAharonian etalIRTS 2015ARAKI 2013Deep Galaxy CountDIRBE-07DIRBE-15Pioneer10/11
FIG. 1: EBL spectra from the CIBER [51], IRTS [49],AKARI [48], COBE/DIRBE [50, 59], and Pioneer 10/11 [60]results. Also shown are the FRV08 EBL model (dashed dot-ted line) provided in Ref. [41].
III. ALP-PHOTON OSCILLATION INPROPAGATION
In this section we describe the ALP-photon oscilla-tion effect in propagation. The ALP-photon conversationarises from the effective coupling between the ALP andphotons through the triangle graph with internal fermionlines. The effective lagrangian is written as L aγ = − g aγ aF µν ˜ F µν = g aγ a E · B , (1)where a is the ALP field, F µν is the electromagnetic fieldtensor, ˜ F µν is the dual tensor, and E and B representthe electric and magnetic field, respectively. The ALP-photon beam can be described by Ψ = ( A , A , a ) T ,where A and A represent the photon transverse po-larization states along two orthogonal directions ˆ x andˆ x , respectively. The ALP-photon beam obeys the Von-Neumann-like equation [15, 16]d ρ d s = [ ρ, M ] , (2)where s represents the traveling distance of the ALP-photon beam along the propagation direction ˆ x ≡ ˆ x × ˆ x , M is the mixing matrix, and ρ is the density matrixof the beam ρ = Ψ ⊗ Ψ † . M is only related with thetransverse magnetic field B ⊥ .Assuming that B ⊥ is aligned along ˆ x , the mixing ma-trix is[14, 35] M = ∆ pl pl ∆ aγ aγ ∆ aa , (3)where ∆ pl = − ω / (2 E ) represents the plasma effectwith the plasma frequency ω pl and photon energy E ,∆ aa = − m a / (2 E ) represents the kinetic term for theALP with mass of m a , and ∆ aγ is the ALP-photon cou-pling term g aγ B ⊥ /
2. The Faraday rotation and QEDvacuum polarization effect are neglected here.If B ⊥ is not aligned along ˆ x , the mixing matrix be-comes M = V ( ψ ) M V † ( ψ ) , (4)with V ( ψ ) = cos ψ sin ψ − sin ψ cos ψ
00 0 1 , (5)where ψ is the angle between B ⊥ and ˆ x . In the gen-eral case, the magnetic field of the astrophysical systemchanges its direction along the propagation direction ˆ x .In order to describe this effect, the propagation path isdivided into n small regions. In each region, the mag-netic field can be approximately treated as a constant.The transfer matrix T ( s ) is given by T ( s ) = n (cid:89) i M ( i ) (6)where M ( i ) represents the mixing matrix in the i-th re-gion.In this work, we consider the high energy γ -ray spec-tra from two extragalactic sources PKS 2155 −
304 andPG 1553+113, which are high-frequency peaked BL Lacobjects. It is known that BL Lac objects are hosted in el-liptical galaxies. However, it is not easy to determine theexact cluster environments around these objects. Thereare evidences that some BL Lac objects are harbouredin small galaxy groups or clusters [61, 62]. Some stud-ies [63, 64] also show that PKS 2155 −
304 is located atthe center of a galaxy cluster. Thus it can be expectedthat the high energy photons emitted from the BL Lacobjects oscillate with ALP in the inter-cluster magneticfield (ICMF). The strength of regular magnetic field inthe galaxy cluster ranges from ∼ µ G to 10 µ G [65].We assume that ICMF is a Gaussian turbulent field asRef. [66], whose mean value is zero and variance is σ B .Since no concrete ICMF model is available, we randomly generate the configuration of ICMF following Ref. [22].100 realizations of ICMF for each source are taken in theanalysis. The fiducial parameters of ICMF are adoptedas Ref. [25], where the typical σ B is taken to be 3 µ G.In this analysis, we do not consider the impact ofthe magnetic field in the extragalactic space. Some re-searches show that the upper limit of its strength is O (1)nG[67], but the exact value remains unclear. Thus onlythe EBL attenuation effect is taken into account for the γ -ray propagation in the extragalactic space.The ALP-photon oscillation would also occur in theMilky Way. The galactic magnetic field consists of twocomponents: the random component in small scale andthe regular component in large scale. The impact of therandom component is neglected here due to the shortcoherent length. For the regular component, we take themodel in Ref. [68].The final transfer matrix consists of the contributionsfrom three regions T ( s ) = T MW T EBL T ICMF , (7)where T MW , T EBL and T ICMF are the transfer functionsin the Galactic magnetic field, EBL, and ICMF, respec-tively. The density matrix can be solved by ρ ( s ) = T ( s ) ρ (0) T † ( s ) , (8)where ρ (0) represents the density matrix for the ini-tial beam, which is assumed to be a pure photon beamwithout polarization ρ (0) = diag(1 , , P γ = ρ + ρ , where ρ ( s ) and ρ ( s ) are the first andsecond diagonal elements in the density matrix ρ ( s ), re-spectively.In Fig. 2, we show the photon survival probability with m a = 1 . × − eV and g aγ = 6 . × − GeV − asa function of the photon energy for one ICMF realiza-tion of PG 1553+113. The EBL model is taken to be theFRV08 model [41]. In order to describe the impact ofthe randomness of ICMF, we also plot the 68% and 95%bands of the photon survival probability using 100 gen-erated realizations of ICMF. The photon survival prob-abilities with only the EBL attenuation effect are alsoshown for comparison. We can see that the oscillationeffect becomes significant above O (10) GeV. For VHE γ -rays above O (300) GeV, the oscillation effect induces alarger survival probability in comparison with the pureEBL absorption effect. IV. ANALYSIS METHOD
In this work, we assume that the initial γ -ray spectrumof PKS 2155 −
304 is described by the broken power Lawwith a transition region[69], F ( E ) = N ( E/E c ) − Γ (1 + ( E/E break ) f ) (Γ − Γ ) /f . (9) PG 1553+113 m a =1.26×10 -8 eV g a γ =6.31×10 -11 GeV -1 P ho t on s u r v i v a l p r obab ili t y E[GeV]
95% contours 68% contours exp(- τ ) one random ICMF FIG. 2: Survival probability of γ -ray emitted fromPG 1553+113 with m a = 1 . × − eV and g aγ = 6 . × − GeV − for the FRV08 model. The solid line representsthe result for one randomly selected realization of ICMF. Thered (yellow) band represents the 68% (95%) bands for 100realizations of ICMF. The dotted dashed line represents thesurvival probability of γ -ray without the ALP-photon oscilla-tion. The spectrum of PG 1553+113 is fitted with a logarith-mic parabola function, F ( E ) = N ( E/E ) − α − β · ln( E/E ) , (10)where N , Γ , E break , f , Γ , α , β , and E are taken tobe free parameters and E c is a normalization parame-ter. Compared with some other spectral forms, thesetwo spectra can provide a better fit to the data underthe null hypothesis. Then we derive the expected γ -rayspectra by using the photon survival probability and fitthe experimental data. The observed spectra given by theH.E.S.S. II (CT5 mono) and Fermi-LAT observations[40]are used in this analysis. In order to include the energyresolution of the experiment, the expected γ -ray flux inan energy bin between E and E is smeared asdΦd E = (cid:82) E E d E (cid:82) ∞ S ( E (cid:48) , E ) F ( E (cid:48) )d E (cid:48) E − E (11)where E and E (cid:48) are the measured and original photonenergies, respectively, and S ( E (cid:48) , E ) is the gaussian func-tion with a standard deviation of σ . Here the energyresolutions of H.E.S.S. II and Fermi-LAT are adopted tobe 25% [40] and 15% , respectively.After integrating the observed energy, the expectedphoton flux isdΦd E = (cid:82) ∞ A ( E (cid:48) , E , E ) F ( E (cid:48) ) dE (cid:48) E − E , (12) https://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/Cicerone/Cicerone_Introduction/LAT_overview.html where A( E (cid:48) , E , E ) is given by A ( E (cid:48) , E , E ) = 12 (cid:20) erf (cid:18) E − E (cid:48) √ σ (cid:19) − erf (cid:18) E − E (cid:48) √ σ (cid:19)(cid:21) , (13)where erf(x) is the error function.Considering the difference between the energy recon-struction of two different kinds of experiments, we also in-troduce an extra parameter to incorporate a possible sys-tematic uncertainty in the analysis. In the fit we rescaleall the energies of the H.E.S.S. II data by a factor f and add a corresponding contribution ( f − /σ f to thelog-likelihood − L . We assume σ f to be 19%, whichequals the systematic uncertainty of the energy scale ofH.E.S.S. II [40].Following Ref. [22], the ALP hypothesis is evaluatedby a likelihood ratio test. The maximal likelihoods un-der the null and ALP hypothesis are denoted by L ( µ | D )and L ( µ | D ), respectively, where µ is the expected pho-ton spectrum with the best fit nuisance parameters, µ ( mu ) is the best fit scenario without ALP (with ALPin the 0.95 quantile), respectively, and D is the observeddata. For each set in ( m a , g aγ ) plane, the adopted ICMFrealization is the one among 100 realizations that cor-responds to the 0.95 quantile of the likelihood distribu-tion(the quantile of the best fit scenario corresponds to1).In order to test the ALP hypothesis, the prob-ability distribution of the test statistic T S ≡− L ( µ | D ) / L ( µ | D )) is required. Note that the re-lation between the spectral irregularities and ALP pa-rameters is non-linear. Moreover only the ALP hypoth-esis depends on the ICMF realizations, while the nullhypothesis is not. Therefore the commonly used Wilks’theorem [70] is not valid in this case. Instead, a Monte-Carlo method is needed to derive the TS distribution.400 sets of mock data for each source are generated inpseudo-experiments that are realized by Gaussian sam-plings [24]. For the sampling, the mean values are takento be the best-fit fluxes under the null hypothesis; thestandard deviations are taken to be the errors of the ex-perimental data. Then we calculate the TS value in thefit for each mock data set and derive the TS distribution.As an example, the TS distribution of PG 1553+113 forthe FRV08 model is shown in Fig. 3. This TS distribu-tion corresponds to a non-central χ distribution, wherethe degree of freedom is 3.59 and non-centrality of thedistribution λ is 0.01. The threshold of TS distributionat 95% C.L. is found to be 8.82 and is used to set theconstraint on the ALP parameter space. V. RESULTSA. FRV08 model
In this section, we investigate the implication of ALPfor the FRV08 EBL model. The best fit spectra under the λ =0.01400 simulations2 σ P r obab ili t y den s i t y CD F TS FIG. 3: TS distribution of PG 1553+113 for the FRV08model. The red line represents the fitted non-central χ distri-bution with d.o.f.=3.59 and λ = 0 .
01. The blue line representsthe cumulative probability function of TS distribution. null and ALP hypothesis for the two selected sources areshown in Fig. 4. It can be seen that the null hypothesiswell fit the data. The values of the best fit reduced χ are shown in the Table. I. TABLE I: The best fit χ and rescale factors for two sourcesin the two EBL models. Under the ALP hypothesis, the bestfit ALP parameters ( m a , g aγ ) in units of (neV , − GeV − )and the effective degrees of freedom of the TS distributionare also listed.Sources PKS 2155 −
304 PG 1553+113EBL models FRV08 Ciber FRV08 CiberBest fit reduced χ w/o ALP 22.27/16 42.45/16 12.95/11 28.46/11Best fit rescalefactor w/o ALP 0.96 0.81 1.12 0.81Best fit χ w ALP 16.31 16.95 10.20 10.51Best fit rescalefactor w ALP 1.00 1.12 1.09 0.89Best fit ALPparameter sets 251.19,1.58 15.85,10 6.31,0.25 15.85,3.16Effective d.o.f ofTS distribution 3.98 3.98 3.52 2.30 Compared with the null hypothesis, the ALP-photonoscillation may reduce the EBL attenuation effect atenergies above ∼ O (10 ) GeV. Therefore, the corre-sponding γ -ray spectra in this energy region may sig-nificantly deviate from the experimental data. The mapsof ∆ χ ≡ χ − χ in the ( m a , g aγ ) plane for thetwo sources are shown in Fig. 5. The boundaries of theexcluded parameter regions can be derived by requiring χ = χ + χ , where χ is the best-fit χ underthe ALP hypothesis. χ depending on the confidence level is taken to be the corresponding threshold of theTS distribution. Note that the probability distributionsof TS with the ALP and null hypothesis are assumedto be same here [22]. For instance, χ at 95%C.L. forPG 1553+113 is taken to be 8.82.We show the 95% C.L. excluded contour forPG 1553+113 in Fig. 5. Considering the constraint fromCAST, we find that the 95% limit from PG 1553+113on the ALP-photon coupling is g aγ (cid:46) × − GeV − in the ALP mass range of ∼ < m a <
16 neV.For PKS 2155 − −
304 are also shown. The limit set by theFermi-LAT collaboration is derived from the fit to itsmeasured spectrum of NGC 1275. Compared with theexperimental data used in this analysis, the NGC 1275data contain more data points with narrow energy binsbelow ∼ ∼ O (1) neV, which correspond to lowcritical energies for the ALP-photon oscillation. ThePKS 2155 −
304 analysis of the H.E.S.S. collaboration fo-cuses on the spectral irregularities induced by the ALP-photon oscillation in the variations of neighboring energybins and provides a stricter limit in comparison with ourresult for PKS 2155 − B. Ciber model
The implication of ALP would change for the CiberEBL model. The best fit spectra of the null and ALPhypotheses for the two sources are shown in the bottompanels of Fig. 4. Compared with the FRV08 model, theexcess at ∼ µ m in the Ciber model induce an additionalattenuation effect above ∼
300 GeV and lead to moresignificant deviations from the data, which can be seenfrom Table. I. The ALP-photon oscillation may compen-sate this additional attenuation effect and improve thefit to the data. This improvement method has beendiscussed for the Fermi-LAT and H.E.S.S. observationsof two sources H2356-309 (z=0.165) and 1ES1101-232(z=0.186) through the χ fit in Ref. [38].We show the improvement regions at 95% C.L. forPKS 2155 −
304 and PG 1553+113 in Fig. 7. The fa-vored ALP parameter region for PG 1553+113 is almosta rectangular region with g aγ (cid:38) . × − GeV − and m a (cid:46)
10 neV. The favored region for PKS 2155 − g aγ (cid:38) × − GeV − and m a (cid:46)
15 neV.Compared with the favored region derived in Ref. [38]( g aγ (cid:38) × − GeV − for 1 neV (cid:46) m a (cid:46)
40 neV),there is no lower boundary on m a in our results. Thisis because that the ALP-photon oscillation effect in theextragalactic space is neglected in this analysis. -13 -12 -11 -10 -1 E d N / d E [ e r g / c m / s e c ] E [GeV]
Best-fit w/o ALPBest-fit w ALPFermi-LATCT5 mono -13 -12 -11 -10 -1 E d N / d E [ e r g / c m / s e c ] E [GeV]
Best-fit w/o ALPBest-fit w ALPFermi-LATCT5 mono -13 -12 -11 -10 -1 E d N / d E [ e r g / c m / s e c ] E [GeV]
Best-fit w/o ALPBest-fit w ALPFermi-LATCT5 mono -13 -12 -11 -10 -1 E d N / d E [ e r g / c m / s e c ] E [GeV]
Best-fit w/o ALPBest-fit w ALPFermi-LATCT5 mono
FIG. 4: Best-fit γ − ray spectra of PKS 2155 −
304 (left panels) and PG 1553+113 (right panels). The green and black linesrepresent the results under the null and ALP hypothesis, respectively. The top and bottom panels represent the results for theFRV08 and Ciber EBL models, respectively. The experimental data include the results from Fermi-LAT and H.E.S.S. II [40]. χ a (eV)1e-121e-111e-101e-09 g a γ ( G e V - ) -6-5-4-3-2-1 0 1 2 3 4CAST 1e-10 1e-09 1e-08 1e-07 1e-06m a (eV)1e-121e-111e-101e-09 g a γ ( G e V - ) -3-2-1 0 1 2 3 4 5CAST FIG. 5: ∆ χ ≡ χ − χ maps of PKS 2155 −
304 (left panel) and PG 1553+113 (right panel). The triangle symbols representthe best fit parameters. -11 -10 -9 -8 -7 g a γ [ G e V - ] m a [eV] H.E.S.S.Fermi-LATPG 1553+113 CAST FIG. 6: The 95% C.L. excluded regions in the ( m a , g aγ ) plane.The green region represents our result for PG 1553+113 with σ B = 3 µ G and the FRV08 model. For comparison, the con-straints from the CAST [12], Fermi-LAT observation of NGC1275[22] and H.E.S.S. observation of PKS 2155 −
304 [18] arealso shown. -11 -10 -10 -9 -8 -7 -6 g a γ [ G e V - ] m a [eV] PKS 2155-304 PG 1553+113 CAST
FIG. 7: Favored ALP parameter region where the fit to thePKS 2155 −
304 and PG 1553+113 observations can be im-proved at 95%C.L..
VI. CONCLUSION
In this work, we investigated the ALP implication inthe Fermi-LAT and H.E.S.S. II gamma-ray observationsof two sources PG 1553+113 and PKS 2155 − m a , g aγ ) plane. For σ B = 3 µ G, the constraint on g aγ at 95% C.L. is g aγ (cid:46) × − GeV − for an ALP massbetween 9 and 16 neV. On the other hand, we foundthat the ALP-photon oscillation would improve the fitto the PKS 2155 −
304 and PG 1553+113 observations forthe Ciber model with an excess at ∼ µ m. The favoredparameter region is given.In future, Cherenkov high energy gamma-ray tele-scopes will provide more accurate results. Thelarge ground-based telescopes, such as CTA[71] andLHAASO[72], will measure the spectra of extragalaticgamma-ray sources at very high energies. Combined withthese results, it is possible to search for the spectral reg-ularities induced by the ALP-photon oscillation and ac-curately investigate the ALP implication in high energyastrophysical processes. Acknowledgments
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