1305.2162v1 [detection of the cosmic gamma ray horizon from multiwavelength observations of blazars]

8/13/2019 1305.2162v1 [Detection of the Cosmic Gamma Ray Horizon From Multiwavelength Observations of Blazars]

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Draft; May 10, 2013Preprint typeset using LATEX style emulateapj v. 08/13/06

DETECTION OF THE COSMIC -RAY HORIZON FROM MULTIWAVELENGTH OBSERVATIONS OFBLAZARS

A. Domnguez1, J. D. Finke2, F. Prada3,4,5, J. R. Primack6, F. S. Kitaura7, B. Siana1, D. Paneque8,9

Draft; May 10, 2013

ABSTRACT

The first statistically significant detection of the cosmic -ray horizon (CGRH) that is independentof any extragalactic background light (EBL) model is presented. The CGRH is a fundamental quantityin cosmology. It gives an estimate of the opacity of the Universe to very high energy (VHE) -rayphotons due to photon-photon pair production with the EBL. The only estimations of the CGRHto date are predictions from EBL models and lower limits from -ray observations of cosmologicalblazars and-ray bursts. Here, we present homogeneous synchrotron/synchrotron self-Compton (SSC)models of the spectral energy distributions of 15 blazars based on (almost) simultaneous observationsfrom radio up to the highest energy -rays taken with the Fermisatellite. These synchrotron/SSCmodels predict the unattenuated VHE fluxes, which are compared with the observations by imagingatmospheric Cherenkov telescopes. This comparison provides an estimate of the optical depth of theEBL, which allows a derivation of the CGRH through a maximum likelihood analysis that is EBL-model independent. We find that the observed CGRH is compatible with the current knowledge ofthe EBL.Subject headings: cosmology: observations - diffuse radiation galaxies: formation galaxies: evolu-

tion gamma-rays: observations

1. INTRODUCTION

Very high energy (VHE; 30 GeV30 TeV) photons donot travel unimpeded through cosmological distances inthe Universe. A flux attenuation is expected due tophoton-photon pair production with the lower energyphotons of the extragalactic background light (EBL) inthe ultraviolet, optical, and infrared (IR; e.g., Nikishov1962; Gould & Schreder 1967; Stecker, de Jager & Sala-mon 1992; Salamon & Stecker 1998). The EBL is theradiation emitted by star formation processes (star lightand star light absorbed/re-emitted by dust) plus a smallcontribution from active galactic nuclei (AGNs) inte-grated over redshift over all the cosmic star-formationhistory (e.g., Hauser & Dwek 2001; Dwek & Krennrich2012). Due to the properties of the interaction, a VHEphoton of a given energy interacts mainly with an EBLphoton within a well defined and narrow wavelengthrange. Therefore, a signature of the EBL spectral distri-bution is expected in the observed VHE spectra of extra-galactic sources (Ackermann et al. 2012b; Abramowski etal. 2013; Yuan et al. 2013).

An interesting feature in the observed VHE spectra of

1 Department of Physics & Astronomy, University of California,Ri e side CA 92521 USA albe tod@ c ed

extragalactic sources as a consequence of EBL absorptionis given by the cosmic-ray horizon (CGRH), which hasnot been clearly observed yet. The CGRH is by defini-tion the energy, E0, at which the optical depth of thephoton-photon pair production becomes unity as a func-tion of redshift. Therefore, it gives an estimate of howfar VHE photons can travel through the Universe. Due

to the exponential behavior of the flux attenuation, analternative definition is the energy at which the intrinsicspectrum is attenuated by the EBL by a factor of 1/e(see e.g., Aharonian 2004). (The intrinsic source spec-trum is the one that we would observe if there were noeffect from the EBL, also known as the EBL-correctedspectrum.)

An extreme category of AGNs, known as blazars, hasbeen shown to be the best target for extragalactic VHEdetections. They are characterized by having their en-

ergetic -ray jets pointing towards us. In fact, mostof the extragalactic sources already detected by imag-ing atmospheric Cherenkov telescopes (IACTs) such asH.E.S.S., MAGIC, and VERITAS (Hinton 2004; Lorenz2004; Weekes et al. 2002, respectively) are blazars10.The observations of broadband spectral energy distribu-tions (SEDs) of blazars show that they are characterizedby a double peaked shape and that their emission cov
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2 DOMINGUEZ ET AL.

The direct observation of the CGRH in the VHE spec-tra of blazars remains elusive. This is due to two mainobservational difficulties. First, the lack of knowledgeof the intrinsic spectra at VHE. Extensive multiwave-length campaigns from radio up to -rays are needed inorder to predict the unattenuated VHE emission from thesynchrotron/SSC model with enough precision. Thesecampaigns should preferably be simultaneous due to theshort-time flux variability of blazars (e.g., Aleksic et al.2011a,b). In this situation, the typical procedure in theliterature to estimate the intrinsic VHE spectrum is ei-ther to assume a limit for the hardness of the slopeE

with = 1.5 (Aharonian et al. 2006) or to extrapolatethe Fermi-Large Area Telescope (LAT) spectrum up tohigher energies (Georganopoulos, Finke & Reyes 2010;Orr, Krennrich & Dwek 2011).

Second, it has been possible only in recent years to de-tect a considerable number of blazars in the GeV energyrange to allow us a statistical analysis. A large sample isnecessary to reject intrinsic behaviors in the sources thatmimic the effect of the CGRH. This improvement hasbeen made thanks to the large data sets provided by theFermisatellite (Ackermann et al. 2011) and the IACTs.

The only estimations of the CGRH so far are EBL-model-dependent lower limits from VHE observations ofblazars (Albert et al. 2008), lower limits fromFermi-LATobservations of blazars (Abdo et al. 2010b), and the pre-dictions from EBL models (e.g., Franceschini, Rodighiero& Vaccari 2008; Kneiske & Dole 2010; Finke, Razzaque& Dermer 2010; Domnguez et al. 2011a, hereafter D11;Gilmore et al. 2012; Stecker, Malkan & Scully 2012). (Atable with a classification and description of the ingre-dients of these EBL models can be found in the pro-ceeding by Domnguez 2012.) Indeed, an independentobservation of the CGRH will also provide a completelyindependent and new test to the modeling of the EBLand consequently constraints on galaxy evolution. Fur-thermore, the CGRH measurement also can be useful toestimate the cosmological parameters with a novel andindependent methodology (Blanch & Martinez 2005a,b,c;Domnguez & Prada, submitted). The detection of theCGRH is a primary scientific goal of the Fermi -rayTelescope (Hartmann 2007).

This paper is organized as follows. Section 2 describesthe blazar catalog used in our analysis. The methodologyis explained in Section 3. Section 4 shows the results ob-tained from our analysis and in Section 5 the results arediscussed. Finally, a brief summary of the main resultsis presented in Section 6.

Throughout this paper a standard CDM cosmologyis assumed, with m = 0.3, = 0.7, and H0 =

1 1 (

Ackermann et al. 2011) and the new Fermi-LAT hard-spectrum catalog (1FHL, Ackermann et al., in prepara-tion), which include two and three years ofFermi-LATdata, respectively. The second FermiAGN catalog con-tains fluxes in the following six energy bins: 30100 MeV,100300 MeV, 300 MeV1 GeV, 13 GeV, 310 GeV and10100 GeV. TheFermihard-spectrum catalog containsfluxes for the sources with the highest-energy emissionin three bins that reach higher energy than the onesused in the second-year catalog (1030 GeV, 30100 GeVand 100500 GeV). Our final catalog includes data fromIACTs as well. We use simultaneous VHE data fromIACTs when available; otherwise the IACT observationclosest in time to the lower-energy data is used follow-ing the suggestions by Zhang et al. (2012). Table 1 liststhe 15 sources in the set of blazars that we study here.The catalog presented in Zhang et al. (2012) contains24 blazars, however we could not use all of them due tonon-detections either by Fermior the IACTs, which areessential for applying our methodology (see Section 3).

Our catalog covers a wide redshift range fromz = 0.031to z 0.5 and all 15 blazars are classified as BL-Lacsources (which are typically characterized by rapid andlarge-amplitude flux variability and significant opticalpolarization). We note that in the cases of PG 1553+113and 3C 66A the redshifts are uncertain, but still thesesources are included in the analysis. A redshift in therange 0.395 < z 0.58 is estimated for PG 1553+113by Danforth et al. (2010, the upper limit is 1). Theblazar 3C 66A typically is cited as having a redshift ofz = 0.444, which is used here as well (cf. Bramel et al.2005; Finke et al. 2008).

3. METHODOLOGY

Our methodology consists of finding the best-fittinghomogeneous synchrotron/SSC models from multiwave-length data as simultaneous as possible from radio to thehighest-energy-rays detected by theFermi-LAT for theblazars in our catalog. These models predict the unatten-uated VHE fluxes, which are compared with detectionsby IACTs. The ratios between the unattenuated and de-tected VHE fluxes give an estimate of the EBL opticaldepth. By means of a maximum likelihood techniquethat is independent of any EBL model and that is basedonly on a few physically motivated assumptions, we thenderive the CGRH for each blazar.

3.1. Broadband spectral-energy-distribution fitting andoptical-depth data estimation

For every blazar in our sample, we built a quasi-simultaneous SED based on the data collected by Zhang


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Detection of the cosmic -ray horizon 3

model includes photoabsorption by photons internal tothe blob. Since BL Lac objects and their presumed mis-aligned counterparts, FR I radio galaxies usually lackoptically thick dust tori (Donato, Sambruna & Gliozzi2004; Plotkin et al. 2012) we do not include photoab-sorption from this radiation source, although it could inprinciple be important. We note that for 1ES 1959+650,there is evidence for an optically thick dust component(Falomo et al. 2000). However, we did not obtain positiveresults with this source, as discussed in Section 5 below.The fitting technique is double nested, with the innerloop fitting the synchrotron component with a particu-lar electron distribution. In this paper, we use a brokenpower-law for the electron distribution with an exponen-tial cutoff at high energies, that is, atmax. In some cases(Mrk 421, 1ES 2344+514, PKS 2005489, H 2356309,1ES 218+304, and 1ES 1101232) we found that a sin-gle power-law with exponential cutoff was sufficient toprovide good fits. Our fits have as free parameters theelectron indices p1, p2; the minimum, maximum, andbreak electron Lorentz factors, min,max, andbrk, re-spectively; and the overall normalization. Often minand max were kept constant during the fit. The outerloop fit the SSC model the high energy data, and hasthree free parameters: the Doppler factor, D; the mag-netic field strength, B; and the minimum variabilitytimescale,tv,min. We assume that the bulk Lorentz fac-tor bulk = D. In the fits, tv,min was kept constant,with only D and B as free parameters. We discuss inmore detail our choices of tv,min below. In the fits, wespecifically leave off the IACT data; we only fit the IRthrough the LAT -rays. We use any radio points asupper limits, since this emission is likely from anotherregion of the jet. We leave out the IACT data becausefor this fit, we are fitting data which are unaffected byEBL attenuation. In some of the more distant sources,the highest energy LAT point (at energy 224 GeV)can suffer significant attenuation. Therefore, we removethis data point for sources at z > 0.05. This choiceis supported by a variety of observational evidences (seePrimack et al. 2011; Domnguez 2012). Once we have theresulting model curve from our fit that includes the ex-trapolation to VHE energies (the overall model is shownwith a black line in the insets of Figure 1), we use thisas the unattenuated/intrinsic spectrum for the source.We compare it with the flux observed from the IACTdetection to calculate the absorption optical depth,

(E, z) = lndF

dE

int

/dF

dE

obs

(1)

for photons observed in an energy bin centered at energy

turn constrained by the observed variability timescalethrough light travel time arguments so that tv,min tv(e.g., Finke, Dermer & Bottcher 2008). For consis-tency, we used the same tv,min for all of our blazars,tv,min = 104 s and tv,min = 105 s. As we see in Sec-tion 4, the choice of variability time makes very littledifference to the model curve, although it has a large ef-fect on the model fit parameters, which are not the focusof this paper. Thus we are confident that the choice oftv,min has little effect on our resulting measurement of(E, z). However, although the two SSC models are sim-ilar they predict different VHE fluxes, which allows us toinclude the uncertainty in the variability timescale in ouranalysis.

It should be noted that several sources have been ob-served to have extremely rapid ( 102 s) variabilitytimescales (e.g., Aharonian et al. 2007). These rapidflares are quite rare, and since we have chosen SEDsfrom blazars in a quiescent state, we think these shorttimescales (and the small emitting regions they imply)are unlikely. Furthermore, we have fit several of our ob-

jects with tv,min= 102 s and found the resulting Doppler

factors to be extremely high, a few hundred, and intwo cases (1ES 1101232 and 3C 66A) as high as 1000.We believe these high Doppler factors to be unreasonablyhigh.

3.2. Maximum likelihood polynomial fitting

We assume that log10() (as obtained from equa-tion 1) may be described by a third-order polynomialin log10(E),

log10() =a0+a1log10(E) +a2log210(E) +a3log

310(E)

(2)where E is in units of TeV. Lower order polynomials

are not sufficient to describe the optical depth. Higherorder polynomials introduce too many degrees of freedomand increase the computational time without increasingthe precision of our analysis. This shape of the opacity(which is the integral of the EBL spectral intensity andthe pair-production cross section; see e.g., Domnguez etal. 2011a) is expected in the VHE range for two main rea-sons. First, the EBL SED must have a smooth shape asa consequence of the galaxy SEDs that produce the EBLand second because of the continuity of the cross-sectionof the pair-production interactions (e.g., Dwek & Kren-nrich 2005). A maximum likelihood method that scansthe parameter space is adopted to compute the likeli-hood of the estimated data given the different polyno-mials log10() (blue crosses in Figure 1) for each blazar.The four parameters of the third order polynomial are


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4 DOMINGUEZ ET AL.

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

log10

Mkn421 (fast) (z= 0.031)E0 = (10.42 7.72)TeV

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

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1010

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E2dN/dE[ergcm2

s1]

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

og10

Mkn421 (slow) (z= 0.031)E0= (11.91 8.79)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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E2dN/dE[ergcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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log10

Mkn501 (fast) (z= 0.034)E0 = (11.85 16.84)TeV

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log10

(/Hz)

1013

1012

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1010

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E2dN/dE[ergcm2

s1]

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

og10

Mkn501 (slow) (z= 0.034)E0= (2.28 1.02)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log10

( /Hz)

1013

1012

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1010

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E2dN/dE[ergcm2

s1]

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

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3

log10

1ES2344+514(fast) (z= 0.044)E0= None

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

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E2dN/dE[ergcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

og10

1ES2344+514(slow) (z= 0.044)E0 = (6.65 21.49)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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2

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1

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lo

g10

1ES1959+650(fast) (z= 0.048)E0= None

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

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0

1

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o

g10

1ES1959+650(slow) (z= 0.048)E0= None

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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E2dN/dE[ergcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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log10

PKS2005-489(fast) (z= 0.071)E0= (1.99 0.26)TeV

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

1012

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E2dN/dE[ergcm2

s

1]

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

og10

PKS2005-489(slow) (z= 0.071)E0= (2.09 0.25)TeV

1 0 1 2 1 4 1 6 18 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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E2dN/dE[ergcm2

s

1]

1

0

1

2

3

log10

WComae(fast) (z= 0.102)E0= None

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

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1

0

1

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og10

WComae(slow) (z= 0.102)E0= (2.35 0.00)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

log10

PKS2155-304(fast) (z= 0.116)E0= (0.77 0.17)TeV

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

1012

1011

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E2dN/dE[e

rgcm2

s1]

1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

og10

PKS2155-304(slow) (z= 0.116)E0= (0.88 0.05)TeV

1 0 1 2 1 4 1 6 18 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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E2dN/dE[e

rgcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

log10

H1426+428(fast) (z= 0.129)E0= (6.23 7.64)TeV

10 12 1 4 1 6 1 8 2 0 2 2 24 2 6 2 8log

10(/Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

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1

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1

2

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og10

H1426+428(slow) (z= 0.129)E0= (13.24 16.81)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10( /Hz)

1013

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E2dN/dE[ergcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

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1

2

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log10

1ES0806+524(fast) (z= 0.138)E0= (0.35 0.04)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10(/Hz)

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

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1

2

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og10

1ES0806+524(slow) (z= 0.138)E0= (0.85 0.01)TeV

10 1 2 1 4 1 6 1 8 2 0 22 2 4 2 6 2 8log

10(/Hz)

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

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log10

1ES1011+496(fast) (z= 0.212)E0= None

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10(/Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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og10

1ES1011+496(slow) (z= 0.212)E0= None

10 1 2 1 4 1 6 1 8 2 0 22 2 4 2 6 2 8log

10(/Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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log10

PG1553+113(fast) (z= 0.395)E0 = (0.22 0.01)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10(/Hz)

1013

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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og10

PG1553+113(slow) (z= 0.395)E0= (0.26 0.02)TeV

10 1 2 1 4 1 6 1 8 2 0 22 2 4 2 6 2 8log

10(/Hz)

1013

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E2dN/dE[ergcm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

3

log10

PG1553+113(fast) (z= 0.580)E0 = (0.26 0.01)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log

10(/Hz)

1013

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E2dN/dE[erg

cm2

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1.5 1.0 0.5 0.0 0.5 1.0 1.5log10 (Energy/TeV)

3

2

1

0

1

2

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og10

PG1553+113(slow) (z= 0.580)E0= (0.20 0.01)TeV

10 1 2 1 4 1 6 1 8 2 0 22 2 4 2 6 2 8log

10(/Hz)

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3C66A(fast) (z= 0.444)E0 = (0.29 0.02)TeV

1 0 1 2 1 4 1 6 1 8 20 2 2 2 4 2 6 2 8log10 (/Hz)

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og10

3C66A(slow) (z= 0.444)E0= (0.31 0.02)TeV

10 1 2 1 4 1 6 1 8 2 0 22 2 4 2 6 2 8log10 (/Hz)

1013

1012

1011

1010

109

E2dN/dE[ergcm2

s1]

Figure 1. continued

certainties estimated from the maximum likelihood anal-ysis using the likelihood distributions of the polynomialparameters. In our analysis, we also consider the sys-tematic uncertainties in the LAT measurements. Their

effect is estimated by artificially hardening and softeningthe overall SEDs of PKS 2005489 (a blazar with lowstatistical uncertainties). First, the fluxes of the threelowest-energy LAT data for PKS 2005489 are decreasedby 10% (which is the typical Fermi-LAT systematic un-certainty of the effective area, Ackermann et al. 2012a)and the three highest-energy LAT bins are increased influx by 10%. The overall SED fit is done with these newpoints, and the energy where = 1 is estimated, usingthe procedure described in section 3. This procedure is

repeated by increasing by 10% the three lowest-energyLAT data of PKS 2005489 whereas decreasing by 10%the three highest-energy LAT data. This allows us to es-timate an average systematic uncertainty of 20% in theenergy where = 1 for PKS 2005489. We thus as-sume the systematic uncertainty from the uncertainty inthe LAT is 20% for all sources. The observed CGRH isshown in Figure 2 with blue circles, the statistical uncer-tainties are shown with darker blue lines, and the statis-tical plus systematic uncertainties (added in quadrature)

with lighter blue. A completely independent estimationof the CGRH from the EBL model described in D11 isalso shown with its uncertainties, which are thoroughlydiscussed in D11. The uncertainties in the EBL modelingare larger in the far-IR region for the reasons discussedin D11. This leads to the larger uncertainties in the es-timation of the CGRH from the EBL modeling at thelower redshifts. The reason is that this is the EBL re-

the data). The uncertainties in these estimates are sig-nificantly larger since, in general, they are given by theextrapolation of the most likely polynomial outside theenergy range of the Cherenkov detections.

5. DISCUSSION

In this work, we present an estimation of the CGRHbased on a multiwavelength compilation of blazars thatincludes the most recent Fermi-LAT data. We stressthat our estimation of the CGRH is derived with onlya few physically-motivated constraints. These resultsrepresent a major improvement with respect to previousworks. These previous works provide only lower limits forthe CGRH such as the EBL-model dependent limits esti-mated by Albert et al. (2008) (that are based on a mod-ified parameterization of the EBL models presented byKneiske, Mannheim & Hartmann 2002). Other CGRHlimits are presented by Abdo et al. (2010b) using onlyFermi-LAT observations.

The Fermi-LAT hard-source catalog (Ackermann etal., in preparation) is included in our analysis. The in-clusion of this data set in our multiwavelength blazarcatalog is essential for the right estimation of the CGRHsince these measurements help to resolve the shape of theinverse Compton peak.

The optical depth is calculated using equation 1,which describes the ratio between the intrinsic flux fromthe synchrotron/SSC models and the observed flux byIACTs. Then, these data are fitted to polynomials ofthird order imposing some constraints. We also requirean increasing and monotonic behavior of the polynomi-als. Polynomials of order lower than three would not


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10 DOMINGUEZ ET AL.

0.01 0.1 1

Redshift

0.1

1

10

Cosmic-rayhorizon,

E0

[TeV]

This work

Domnguez+ 11

1ES0

806+52

4

Mkn50

1

1ES1

101-23

2

Mkn42

1

1ES1

218+30

4

PKS2

005-48

9

3C66A

PG155

3+113

PKS2

155-30

4

Fig. 2.Estimation of the CGRH from every blazar in our sample plotted with blue circles. The statistical uncertainties are shown withdarker blue lines and the statistical plus 20% of systematic uncertainties are shown with lighter blue lines. The CGRH calculated fromthe EBL model described in Domnguez et al. (2011a) is plotted with a red-thick line. The shaded regions show the uncertainties from theEBL modeling, which were derived from observed data.

on the blazar spectra since it allows us a wider range ofspectral indices (i.e., this results in a rather conservativehypothesis for our analysis). For this same reason, weprefer to use as conservative upper limits the results byMazin & Raue (2007) rather than the newer results by

Meyer et al. (2012) that are based on a more constrain-ing spectral condition. The EBL evolution is expected toaffect the optical depth calculated at higher redshifts. Toaccount for this effect we evolve conservatively the EBLupper limits at all wavelengths as (1 + z)5 (in the co-moving frame) when calculating the optical depths fromthese EBL limits from Mazin & Raue (2007). We notethat this is a robust limit given the fact that the maxi-mum evolution (which is dependent on the wavelength) is(1 + z)2.5 in a realistic model such as D11 for 0 z 0.6

(the redshift range of our blazar catalog).The third constraint that we apply for our fits is to re-quire only monotonically increasing functions for log10()as a function of log10(E). This condition is also expectedfor any realistic EBL spectral intensity, which comes fromgalaxy emission, given the increasing behavior of thepair-production interaction with energy. Interestingly,we see in Figure 1 that in most cases the IACT obser

dom, see Table 1. The uncertainties of the two lowestredshift blazars (Mkn 501 and Mkn 421) are systemati-cally higher because the optical depth for these cases be-comes unity at energies larger than the energies observedby the Cherenkov telescopes. Therefore, in these cases

= 1 is given by an extrapolation of the polynomialsrather than an interpolation between observed energies(see Fig. 1) leading to greater uncertainty. For the case of1ES 2344+514 with fast flux variability timescale, a valueofE0 in agreement with the estimation by the D11 EBLmodel is derived. However, for this case the uncertaintiesare larger thanE0 and therefore no useful constraint canbe derived. For the case of 1ES 2344+514 with slow fluxvariability timescale, the SSC predicted flux is lower thanthe flux given IACT data. For H 1426+428, both flux

variability timescales give uncertainties in the measure-ment ofE0larger thanE0and therefore no constraint canbe derived. In both cases the synchrotron/SSC modeldoes not seem to correctly fit the multiwavelength data.Our maximum likelihood procedure cannot be applied toany flux state on four blazars (1ES 1959+650, W Comae,H 2356309 and 1ES 1011+496). There are different ex-planations for this fact Some blazars have shown flux


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Detection of the cosmic-ray horizon 11

0.01 0.1 1

Redshift

0.01

0.1

1

10

Cosmic-rayhorizon,

E0

[TeV]

= 1

= 0.5

= 2 = 3

Fig. 3.Energy values at which the optical depth is 0.5 (blue squares), 1 (red circles), 2 (green triangles) and 3 (magenta diamonds)from both the blazars presented in the current analysis and the EBL model described in Domnguez et al. (2011a). The shaded regionsshow the uncertainties from the EBL modeling (the same colors are used for each modeled optical depths as for the data), which werederived from observed data. The different data for a given blazar are slightly shifted in thex-axis for clarity.

Explorer12 (RXTE) with the time range of the IACT ob-servation for those four blazars where our maximum like-lihood procedure could not be applied (see the Appendixfor more details). Clearly 1ES 1011+496 was indeed de-tected by the IACTs in flaring states. The situation for

1ES 1959+650 is not clear. And the light curve of theH 2356309 observation was rather irregular. We couldnot find X-ray data for W Comae in the ASM databasebut this source was clearly detected in TeV in a strongflare (Acciari et al. 2008).

The synchrotron/SSC model is the standard modelfor fitting high-peaked TeV BL Lac objects, and doesseem to provide a good fit to their broadband SEDs(e.g., Zhang et al. 2012). However, there are some al-ternatives. High-peaked BL Lac objects are not thought

to have a significant contribution to the -ray flux fromscattering external photon sources, but there are someexceptions, such as the eponymous BL Lac (Abdo etal. 2011c). It has also been suggested that for somesources, a lepto-hadronic model provides a better fit,such as 1ES 0414+009 (Aliu et al. 2012). Non-variableTeV emission unrelated to the rest of the broadbandSED could originate from Compton scattering of the cos

possible that the electron-positron pairs created by theVHE-ray interactions with EBL photons can Compton-scatter the CMB, producing -rays observable by theLAT (Neronov & Vovk 2010; Tavecchio et al. 2010; Tay-lor, Vovk & Neronov 2011; Dermer et al. 2011; Vovk et

al. 2012). This would complicate the modeling process,since it would add other, poorly-constrained parameters(Tavecchio et al. 2011). Nonetheless, the simple syn-chrotron/SSC is a very attractive model, due to its suc-cess at fitting a large number of objects, and its relativelysmall number of free parameters. The existence of axion-like particles could also allow the-rays to avoid the pho-toabsorption process, changing the expected VHE spec-trum (Sanchez-Conde et al. 2009; Domnguez, Sanchez-Conde & Prada 2011). A detailed broadband modeling

including all these non-standard considerations is out ofthe scope of this work.In summary, we built a catalog of 15 blazars from

Zhang et al. (2012) by requiring a good multiwavelengthspectral coverage and TeV detections. After fitting asynchrotron/SSC model to each source, there were fourblazars where the TeV detection was at higher fluxesthan the flux extrapolation from the models As de


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12 DOMINGUEZ ET AL.

allow a reliableE0 estimation.The agreement between the CGRH observation pre-

sented in this work and the expected values from D11indicates that these possibilities described above might

not be relevant for many blazars. Furthermore, Figure 3gives more information on the optical-depth shape de-rived from our methodology. This figure shows that theenergies at which the optical depths are 0.5, 1 (the stan-dard definition of CGRH), 2 and 3 are still compati-ble with the D11 model. The uncertainties are gener-ally higher at different from 1 due to the fact thatthe Cherenkov detections do not span the energy rangeneeded in order to derive a better estimation of thoseenergies. As seen in Figure 1, the polynomials cut

the horizontal lines of constant optical depths gener-ally in wider energy ranges for values different from1 (i.e., log10() = 0). The agreement between the ob-served CGRH and the expected CGRH from D11 isalso consistent with 3C 66A being located at a redshiftslightly lower than z 0.44413 and PG 1553+113 at0.395 z 0.58. An independent confirmation ofthese redshifts will give support to both the current EBLknowledge and our methodology to derive the CGRH. Byassuming an EBL model, it is possible to estimate red-

shifts using EBL attenuation in a realistic way consider-ing the overall SED of the blazars (see the proceeding byMankuzhiyil et al. 2011). However, we note that someprevious estimation of the redshift is necessary in orderto fit the synchrotron/SSC models (Abdo et al. 2010a,2011a).

Orr, Krennrich & Dwek (2011) claimed that recentEBL models such as D11 are incompatible with IACTsobservations at more than 3. They based their conclu-sions in an analysis of 12 blazars using two different

methods that they call Method 1 and Method 2. Theirmore constraining results are derived from Method 2 (seesection 3.2 in Orr, Krennrich & Dwek 2011). This ap-proach is based on the expected difference between spec-tral indexes when the VHE spectrum is fitted by a bro-ken power law. This spectral difference is attributed toEBL attenuation, setting limits on the intensity of thelocal EBL. We consider their results inconclusive. TheirMethod 2 relies on the assumption that the VHE spec-tra may be well fitted by broken power laws. We per-

formed F-tests on all the fits of their blazar sample totest whether broken power laws (fitted by two differentspectral indexes) could be actually considered better fitsto the observed VHE spectra than simple power laws (fit-ted by a single spectral index)14 The F-tests performedfor every one of their spectra show that for only 2 out of12 cases (RGB J0152+017 and 1ES 1101-232) the spectra

the synchrotron/SSC fits of Figure 1, this is not a realis-tic assumption due to the shape of the inverse Comptonpeak. Furthermore, we show in the present work thata more sophisticated SSC-based analysis is compatible

with the current EBL knowledge.Some authors have treated the Fermi-LAT spectrum,

extrapolated into the VHE regime, as an upper limit onthe intrinsic spectrum, and used this to compute up-per limits on (E, z) (Georganopoulos, Finke & Reyes2010; Meyer et al. 2012). This provides only upper lim-its on (E, z) rather than measurements, as we derivehere. However, their techniques involve fewer assump-tions about the blazar emission model and variability ofthe SED (see the discussion above). Thus, the two tech-

niques are complementary.Recently, Ackermann et al. (2012b) and Abramowski

et al. (2013) claimed the detection of an imprint of theEBL in the blazar spectra. Ackermann et al. (2012b)base their analysis on Fermi-LAT data from z 0.2 to1.6, whereas Abramowski et al. (2013) use H.E.S.S. datafrom blazars located atz 0.1. These works do not giveany results in terms of the CGRH but we are able toestimate it from their results. We find that the resultspresented in our analysis are compatible with the results

from these two independent works, which supports ourconclusions.

From our results, we can conclude that the EBL datafrom direct detection by Cambresy et al. (2001), Mat-sumoto et al. (2005), and Bernstein (2007) are likelycontaminated by zodiacal light. This possibility has indi-rectly been proposed previously by several authors suchas Aharonian et al. (2006), Mazin & Raue (2007), andAlbert et al. (2008) using EBL upper limits but we con-firm these results using a more robust approach.

6. SUMMARY

The CGRH horizon is detected in this work for thefirst time from a multiwavelength sample of blazars thatincludes the more recent Fermi-LAT data. Only a fewgeneral and physically motivated constraints on the EBLwere necessary. As we see from our analysis the obser-vational estimation of the CGRH is compatible withinuncertainties with the derivation by the observationalEBL model described by Domnguez et al. (2011a), which

is in agreement with the observational EBL model byFranceschini, Rodighiero & Vaccari (2008) and the theo-retical methodology followed by Somerville et al. (2012)and Gilmore et al. (2012). All these EBL models are real-istic representations of the current knowledge of the EBL(Domnguez et al. 2011b; Primack et al. 2011; Domnguez2012). We have shown the ability of our methodology


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Detection of the cosmic-ray horizon 13

proved statistics that Fermi will provide. The futureCherenkov Telescope Array is expected to provide VHEspectra with a better energy resolution, observed up tohigher energies, and increase considerably the number

of sources, which indeed will improve the CGRH deter-mination. These prospects together with the increasingnumber of simultaneous multiwavelength observationalcampaigns (e.g., Abdo et al. 2011a,b,d) are promisingfor a better estimation of the optical depths due to EBLattenuation using our methodology and for the estima-tion of the CGRH to z >0.5.

ACKNOWLEDGMENTS

The authors thank Marco Ajello, M. A. Sanchez-

Conde, Seth Digel and David Williams for fruitful discus-sions. We thank Soebur Razzaque for useful commentson the draft and the anonymous referee for improving themanuscript. We acknowledge the support of the Span-ish MICINNs Consolider-Ingenio 2010 Programme un-der grant MultiDark CSD2009-00064. JRP acknowledgesthe support from a FermiGuest Investigator grant andalso from the NASA ATP grants NNX07AGG4G, NSF-AST-1010033 and NSF-AST-0607712.

The FermiLAT Collaboration acknowledges generousongoing support from a number of agencies and insti-tutes that have supported both the development and theoperation of the LAT as well as scientific data analysis.

These include the National Aeronautics and Space Ad-ministration and the Department of Energy in the UnitedStates, the Commissariat a lEnergie Atomique and theCentre National de la Recherche Scientifique / InstitutNational de Physique Nucleaire et de Physique des Par-ticules in France, the Agenzia Spaziale Italiana and theIstituto Nazionale di Fisica Nucleare in Italy, the Min-istry of Education, Culture, Sports, Science and Technol-ogy (MEXT), High Energy Accelerator Research Organi-zation (KEK) and Japan Aerospace Exploration Agency

(JAXA) in Japan, and the K. A. Wallenberg Foundation,the Swedish Research Council and the Swedish NationalSpace Board in Sweden.

Additional support for science analysis during the op-erations phase is gratefully acknowledged from the Is-tituto Nazionale di Astrofisica in Italy and the CentreNational dEtudes Spatiales in France.

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157

APPENDIXIn general, our multiwavelength data are taken from Zhang et al. (2012). Therefore, we refer to the reader to that

paper for details. Here, we briefly discuss the SED variability for individual sources. Unless otherwise stated, the LATdata are from the 2FGL (Ackermann et al. 2011), which are integrated between 2008 August and 2010 August, andthe 1FHL (Ackermann et al., in preparation), which are integrated between 2008 August and 2011 August.

Mrk 421: The data for the SED of this source are entirely simultaneous, and little variability was detected,although a few small LAT flares are evident (Abdo et al. 2011d). There does not seem to be correlated variabilitybetween the X-rays and LAT -rays.

Mrk 501: The SED is from 2006, taken from Anderhub et al. (2009), and is not simultaneous with the LAT data.Variability was of the order of a factor of two in VHE -rays, X-rays, and optical. Variability did not appear tobe correlated, although the observations are quite sparse.

1ES 2344+514: Most of the multi-wavelength data are taken from 2005-2006 (Albert et al. 2007a) and are notvariable, nor are they simultaneous with the LAT data. The LAT data showed minimal variability as well.

1ES 1959+650: The data are from a multiwavelength campaign in 2006 where the optical and X-ray bands werein high state and showing significant variability. However, the VHE data were at the lowest fluxes ever detectedfor this source.

PKS 2005

489: No significant variability on timescale less than a year was found by Aharonian et al. (2005).The X-ray data are from a high state of X-ray emission taken in 1998, whereas the VHE data are from 2009

when the source was in a similar X-ray state as in 1998 (Kaufmann et al. 2009).

W Comae: The TeV data were taken during a strong VHE flare in 2008 (Acciari et al. 2008).

PKS 2155304: All the data, including the LAT data are simultaneous, and variability was on the order ofa factor of two in the X-rays and VHE -rays. The X-ray, VHE -ray, and optical variability appears to beapproximately correlated.

H 1426+428: No simultaneous broadband data are found for this source.

1ES 0806+524: No significant variability was found on a timescale of months (Acciari et al. 2009a).

H 2356309: The TeV and X-ray data were taken simultaneously in 2005 (Abramowski et al. 2010), whereas thedata for the optical and other X-ray bands were taken in 2004. In the VHE, significant variations of flux weredetected in a timescale of months.

1ES 1218+304: The optical as well as the X-ray data were taken quasi-simultaneously in 2005. The VHE datawere taken between the end of 2008 and middle of 2009 The TeV emission for this source showed day-scale


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ZETAL.

TABLE 2The measured and predicted cosmic -ray horizon.

Source Redshift E0 E0 (fast/slow)(a) [TeV] E0 (E0)stat (E0)

(b)sys [TeV] ED11 E

(c)D11 [TeV] IACT reference

Mkn 421 0.031 10.42 7.72/11.91 8.79 11.14+9.568.44 2.23 9.72

+1.853.17 Abdo et al. (2011d)

Mkn 501 0.034 11.85 16.84/2.28 1.02 5.20+23.493.94 1.04 8.75

+1.683.31 Acciari et al. (2011)

1ES 2344+514 0.044 None/6.65 21.49 None 6.01+1.203.23 Albert et al. (2007a)

1ES 1959+650 0.048 None/None None 5.12+1.022.99 Tagliaferri et al. (2008)

PKS 2005489 0.071 1.99 0.26/2.09 0.25 2.04+0.300.31 0.41 1.83

+0.341.06 Kaufmann et al. (2009)

W Comae 0.102 None/None None 0.90+0.090.18 Acciari et al. (2008)

PKS 2155304 0.116 0.77 0.17/0.88 0.05 0.82+0.110.22 0.16 0.77

+0.070.13 Aharonian et al. (2009)

H 1426+428 0.129 6.23 7.64/13.24 16.81 None 0.68+0.060.11 Aharonian et al. (2002)

1ES 0806+524 0.138 0.35 0.04/0.85 0.01 0.55+0.310.24 0.11 0.64

+0.050.10 Acciari et al. (2009a)

H 2356-309 0.165 None/None None 0.54+0.040.07 Abramowski et al. (2010)

1ES 1218+304 0.182 0.58 0.02/0.46 0.02 0.52+0.080.08 0.10 0.49

+0.040.06 Acciari et al. (2010)

1ES 1101232 0.186 0.41 0.02/0.39 0.01 0.40+0.030.02 0.08 0.48

+0.040.06 Aharonian et al. (2006)

1ES 1011+496 0.212 None/None None 0.43+0.030.05 Albert et al. (2007b)

3C 66A 0.444 0.29 0.02/0.31 0.02 0.30+0.030.03 0.06 0.23

+0.020.02 Acciari et al. (2009b); Aleksic et al. (2011a)

PG 1553+113 0.500+0.0800.105 0.24 0.01/0.23 0.02 0.23

+0.050.03 0.05 0.21

+0.020.02 Aleksic et al. (2010)

Note. The 15 blazars in our catalog are listed with their estimated redshifts. The energyE0 is shown for the two different variability timescales (tv,min = 104 s for the

fast model and tv,min = 105 s for the slow model) and its combined value as described in the text in the columns (a) and (b), respectively. The combinedE0 is given withits statistical and systematic uncertainties (see text for details). TheE0 estimated from the EBL model discussed in Domnguez et al. (2011a) (ED11 ED11) is given aswell in column (c). None means that our methodology output no solution for the E0.

1305.2162v1 [detection of the cosmic gamma ray horizon from multiwavelength observations of blazars]

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