Potential of the next generation VHE instruments to probe the EBL (I): the low- and mid-VHE
aa r X i v : . [ a s t r o - ph . C O ] A ug Potential of the next generation VHE instruments toprobe the EBL (I): the low- and mid-VHE
Martin Raue a, ∗ , Daniel Mazin b a Institut f¨ur Experimentalphysik, Universit¨at Hamburg, Hamburg, Germany b Institut de Fisica d’Altes Energies (IFAE), Edifici Cn. Universitat Autonoma de Barcelona,08193 Bellaterra (Barcelona), Spain
Abstract
The di ff use meta-galactic radiation field at ultraviolet to infrared wavelengths -commonly labeled extragalactic background light (EBL) - contains the integratedemission history of the universe. Di ffi cult to access via direct observations, in-direct constraints on its density can be derived through observations of very-highenergy (VHE; E >
100 GeV) γ -rays from distant sources: the VHE photons are at-tenuated via pair-production with the low energy photons from the EBL, leavinga distinct imprint in the VHE spectra measured on earth. Discoveries made withcurrent generation VHE observatories like H.E.S.S. and MAGIC enabled strongconstraints on the density of the EBL, especially in the near-infrared. In this ar-ticle the prospect of future VHE observatories to derive new constraints on theEBL density are discussed. To this end, results from current generation instru-ments will be extrapolated to the future experiment’s sensitivity and investigatedfor their power to enable new methods and improved constraints on the EBL den-sity. Keywords: very-high energy gamma-rays, extragalactic background light, futureinstruments
PACS: ∗ Corresponding author.
Email addresses: [email protected] (Martin Raue), [email protected] (DanielMazin)
Preprint submitted to Astroparticle Physics March 17, 2018 . Introduction
The observation of very-high energy γ -rays (VHE; E >
100 GeV) from distantsources o ff ers the unique possibility to probe the density of the meta-galactic ra-diation field at ultraviolet (UV) to infrared (IR) wavelengths, which is commonlylabeled the extragalactic background light (EBL; typically 0.1-100 µ m). The VHE γ -rays interact with the low energy EBL photons via the pair production process( γ VHE γ EBL → e + e − ) and the flux is attenuated [1, 2]. This attenuation can leavedistinct signatures in the measured VHE spectra. With assumptions about thesource physics and the spectrum emitted at the source location (intrinsic spec-trum), constraints on the density of the EBL can be derived [e.g. 3, 4].The current generation of VHE instruments (H.E.S.S., MAGIC, VERITAS)significantly increased the number of known extragalactic VHE sources from 4in the year 2003 to more than 25 today. These discoveries, combined with theadvanced spectral resolution of these instruments and the wide energy range theycover, led to new strong constraints on the EBL density, in particular at optical tonear-IR (NIR) wavelengths [5, 6, 7]. Since these limits depend on assumptionsabout the source physics, the strong constraints also sparked intense discussionson the validity of the assumptions and possible caveats [e.g. 8, 9, 10, 11, 12, 13].This discussion has not yet converged and there are interesting arguments for bothsides.Current generation systems have recently been upgraded (MAGIC-II) or theupgrades are under construction (H.E.S.S. II). These upgrades are mainly aimedto improve the overall sensitivity by a factor two to three and extend the energyrange toward the lower energy regime of 20 to 100 GeV. This will lead to someimprovements, but a quantitative di ff erence or a breakthrough compared to theperformance of the existing facilities will only be achieved with an order of mag-nitude improvement in sensitivity. The Next Generation Cherenkov TelescopeSystems (NGCTS) are in the advanced planing phase aiming to achieve this orderof magnitude improvement: the Cherenkov Telescope Array (CTA ) [14] and theAdvanced Gamma-ray Imaging System (AGIS ) [15]. Whereas CTA envisionsto improve the sensitivity over a wide energy range from the few tens of GeV tothe multi TeV regime, AGIS mainly concentrates on energies above 100 GeV, anextended field of view and an improvement of the angular resolution.The potential of these upcoming experiments to probe the EBL is the topic of http: // / http: // / ) µ ( λ -1
10 1 10 ) - s r - ( n W m ν I ν Stecker et al. - fast evolutionRaue & Mazin - genericFranceschini et al.
Figure 1: Present day ( z =
0) EBL density of the EBL models / shapes utilized in this study (Steckeret. al: [16]; Raue & Mazin: [17]; Franceschini et al. [18]). Grey markers show measurements andlimits on the EBL density (from [6]). this article. While an order of magnitude improvement in sensitivity for an as-tronomical instrument will always lead to new and unexpected results, this articlewill - as a first step - focus on known results and their extrapolation accordingto the sensitivities of the next generation instruments. Emphasis will be on newtechniques enabled by the performance features (extended sensitivity and energyrange) of the upcoming instruments.For the calculations in the paper a standard Λ CDM cosmology with h = Ω Λ = . Ω M = .
2. Basic assumptions and simulation details
EBL models and attenuation.
The precise level of the EBL density is not wellknown. Solid lower limits from integrated deep galaxies counts at optical andinfrared wavelengths do exist [e.g. 19, 20, 21, 22], but direct measurements arehampered by dominant foregrounds [23]. Over a large wavelength region in theinfrared the best upper limits on the EBL density are derived from VHE observa-tions of distant sources [e.g. 5, 6, 7]. To account for the uncertainty in the EBLdensity two di ff erent approaches are followed here: (i) To illustrate the e ff ect of3 nergy (TeV) -1
10 1 10 A tt e nu a t i on -2 -1
10 1 z = 0.03z = 0.2
SteckerFEGenFran08
Figure 2: Attenuation for VHE γ -rays for the EBL models utilized in this study for sources atredshift z = .
03 (thin lines) and z = . the di ff erent EBL densities two extreme EBL models are used: for the low EBLdensity case the model from [18] (Fran08 in the following) is adopted, for the highmodel the fast evolution case from [16] (SteckerFE in the following) is used. Itshould be noted that the later model is already disfavored by several VHE obser-vations. (ii) Detailed studies of the e ff ect of di ff erent EBL densities are carried outby scaling the EBL density presented in [17] (Gen in the following) and Fran08.The present day EBL densities ( z =
0) for the EBL models utilized in this workare displayed in Fig. 1Fig. 2 displays the resulting attenuation for VHE γ -ray sources at 2 di ff er-ent redshifts ( z = .
03 and 0 .
2) for the models utilized. Several features can beidentified: • At low energies ( <
80 GeV) the spectrum is practically not attenuated.Since this energy range will be sampled by the NGCTSs with high pre-cision, it will be possible to measure the unabsorbed spectrum. • At energies between 80 GeV and 2 TeV the attenuation is increasing dueto the EBL photons in the optical to near-infrared range peak of the EBLdensity. 4
At energies between 2 to 10 TeV a flattening of the attenuation is expected,due to the ∼ λ − behavior of the EBL density in the near to mid-infrared,resulting in a constant attenuation. Such a modulation of the EBL attenu-ation has been considered as a possible key signature for EBL attenuation[e.g. 24, 25]. Unfortunately, the intrinsic weakness of the sources combinedwith the sensitivity of the instruments make it very di ffi cult to probe sucha feature with previous or current generation experiments. For the Steck-erFE model the EBL density in this wavelength range is flatter, resulting ina smoother attenuation from 100 GeV to 10 TeV, suppressing such a feature. • At energies around 10 TeV the turnover in the EBL density towards the far-infrared peak of the EBL results in a strong attenuation, e ff ectively resultingin a cut-o ff in the measured spectra.The strength and the position of these features vary with the distance of the VHEsources, the assumed EBL model, and the overall EBL density. EBL limits from VHE observations.
So far, VHE sources used to derive limits onthe EBL density belong to a single source class, active galactic nuclei (AGNs),and the majority of them to the Blazar sub-class, which are AGNs with strong jetactivity and the jets are closely aligned to the line of sight of the observer. Upto now, mainly two di ff erent methods - and thereby assumptions about the sourceintrinsic spectrum - have been utilized to derive limits on the EBL density: • Spectral concavity.
It is assumed that the overall intrinsic source spectrumat high energies will follow a concave shape, or at least will not show anexponential rise towards the highest energies. These assumptions are wellmotivated by the common leptonic modeling of the sources under investiga-tion (blazars), although di ff erent (maybe more exotic models) can possiblyreproduce such a feature [e.g. 8]. Limits on the EBL density are derived byexcluding EBL densities that would lead to such features in the observedsources. This method naturally probes the EBL at wavelengths from themid to the far-infrared. • Maximum spectral hardness.
To probe the EBL in the optical to near-infrared, it is assumed that the intrinsic source spectrum cannot exceeda certain absolute hardness. While somewhat similar in spirit to the firstmethod the underlying assumptions are stronger, since in the energy rangeof interest (100 GeV to several TeV) the spectral shape of the intrinsic spec-trum is more uncertain. While most of the basic models used to describe the5 nergy (TeV) -2 -1
10 1 10 ) - c m - I n t e g r a l f l u x li m i t ( s -16 -15 -14 -13 -12 -11 -10 % C r a b % C r a b . % C r a b NGCTSHESS IMAGIC IMAGIC IICTA (Bernloehr ’08)Fermi/LAT 1/10 yrs
Figure 3: Integral flux sensitivity (5 σ in 50 h) of the NGCTS used in this study in com-parison to the sensitivity of existing observatories (H.E.S.S.: [26]; MAGIC: [27]; Fermi : ). source spectra indeed imply that the VHE spectrum does not exceed a cer-tain hardness, the absolute value is less certain and possible source intrinsice ff ect (e.g. internal absorption [11]) could complicated the situation.In this paper two di ff erent methods to derive limits on the EBL density will beexplored: (i) utilizing the unabsorbed part of the VHE spectrum and (ii) searchingfor attenuation modulation signatures. While not completely new, it will be shownthat with the NGCTS’s extended energy range paired with its vastly improvedsensitivity it will be possible to utilize these methods e ff ectively for the first time.Method (i) holds the potential to derive limits on the EBL density with a minimalset of assumptions, while method (ii) enables to not only derive upper limits onthe EBL density but to probe the absolute level. E ff ective area, background rate and sensitivity. To simulate the spectra, whichwill be detected by the NGCTS, assumptions about the sensitivity of the instru- e.g. Γ = . − . dN / dE ∼ E − Γ and simple leptonic models. +
85” CTA array presented in [26] is taken and the sensitivity is derived assumingan e ff ective detector area (e ff ective area) and a background rate. For the e ff ectivearea the post cut MAGIC e ff ective area at 20 deg zenith angle ([28]) scaled upby a factor 20 is adopted to reach an e ff ective area exceeding 10 m at energiesabove a few hundred GeV. In addition, the MAGIC e ff ective area is shifted by afactor of 2 to lower energies to reflect the improved sensitivity at low energies. The resulting e ff ective area A NGCTS versus energy E in the energy range 20 GeVto 20 TeV is well described by the function A NGCTS = . · m ( E / (1 + ( E / (1 TeV · . . ) − / . (1)The di ff erential background rate after event selection cuts is approximated by abroken power law function with photon index 3.6 below and 2.7 above the breakenergy of 300 GeV, similar to what is seen in current generation instruments. Theabsolute level of the background flux rate is chosen so that the resulting sensitivitymatches the sensitivity of the CTA ”4 large +
85” array from [26]. The integralsensitivity adopted in this study for the NGCTS in comparison to current genera-tion and future HE / VHE instruments is displayed in Fig. 3. In the overlap regionit follows very well the CTA sensitivity for the ”4 large +
85” array from [26]up to 10 TeV. Compared to current instruments (H.E.S.S., MAGIC, VERITAS)the sensitivity in the core energy range between 100 GeV and 10 TeV is improvedby about one order of magnitude. In addition, the energy range is extended to-ward lower and higher energies. With the chosen parameters for the e ff ective areaand the background rate at low energies significant sensitivity is reached downto energies below 20 GeV, which enables a large overlap region in energy withthe Large Area Telescope (LAT) onboard Fermi satellite. For this energy region,where there is no overlap with the published CTA sensitivity ( <
40 GeV), there isof course a certain degree of freedom in the choice of parameters and thereforethe sensitivity is not very well constrained. In this study only energies between40 GeV and 10 TeV will be used.
Spectrum simulation method.
To calculate the simulated spectrum the number of γ -photon events N S (signal) and background events N BG per energy bin need to be The energy threshold approximately scales linearly with 1 / Area of the mirror area of the singletelescope. For a CTA type NGCTS instruments the largest telescopes are expected to have mirrordiameter in the order of 24 m which gives a factor two larger area compared to 17m for the MAGICmirror. ff ective area folded with the assumed intrinsic sourceflux is integrated over the energy bin; the same is done for the background eventsintegrating over the background rate in the bin. Both numbers are multipliedwith the e ff ective observation time. Di ff erent functions are utilized to describethe intrinsic flux and they will be discussed further in the section where they firstappear. The attenuation of the source flux due to the EBL is calculated followingthe recipe given in [6, 13]: the attenuation is directly folded into the intrinsicspectrum and then the attenuated intrinsic flux function folded with the e ff ectivearea is integrated over the energy bin. The number of signal events is randomlyvaried assuming a Poisson distribution. It is assumed that the background is welldetermined (e.g. via background measurements in a large sky area compared tothe signal region). The error on the number of photons N σ in a bin is derivedutilizing equation 17 from [29] assuming 5 background regions (i.e. an alphafactor of 0.2). The signal in an energy bin is considered significant when allof the following criteria are met: (1) the signal significance exceeds 3 standarddeviations, (2) there are at least 10 excess events in the bin, (3) the number ofexcess events in the bin exceeds 3% of the number of background events. This lastcondition takes into account a systematic error in the determination of the numberof background events. These are rather conservative assumptions, since e.g. incurrent publications on VHE γ -astronomy often energy bins with significancesdown to 1.5 σ or less are included in the analysis.IACT experiments have a limited energy resolution which, for current gener-ation instruments, is in the order of <
15% for energies above 100 GeV [e.g. 30]and <
40% down to 70 GeV [28]. For MAGIC-II an energy resolution of < ∼
50 GeV is achievable [see Fig. 3 of 31]. Due to the, onaverage, higher number of telescopes participating in each event and the increasedmirror size of the large telescopes the energy resolution for an NGCTS is expectedto improve further. Such an energy resolution paired with an energy spectrum un-folding method [e.g. 32] will enable to robustly reconstruct smooth spectral shapes(e.g. power law or log parabola) even down to low energies. The reconstructionof an EBL attenuation structure at mid-energies is possibly more a ff ected by thelimited energy resolution and this will be further discussed at the end of Sect. 4. Simulation example.
Fig. 4 displays simulated spectra for two sources and twoassumed EBL densities for an observation time of 20 h. The intrinsic spectrumis assumed to follow a simple power law ( Φ ( E ) = Φ × ( E / − Γ ), with theparameters adopted so that the EBL attenuated simulated spectrum matches themeasured one. Shown are results for 1ES 1101-232 ( z = . ) - s - ( e r g c m ν F ν -13 -12 -11 -10 -9 Energy (TeV) ) - s - ( e r g c m ν F ν -12 -11 -10 Figure 4: Simulated VHE spectra for two sources and two EBL models (blue:Fran08;red:SteckerFE).
Upper panel:
Lower panel:
PKS 2155-304. Grey markers showthe measured spectra and the measured spectra de-absorbed for EBL attenuation. Red and bluelines are the assumed intrinsic spectra emitted at the source for two di ff erent levels of the EBLdensity, matching the measured de-absorbed spectra. Red and blue markers show the expectedspectrum as measured for a next generation VHE instruments simulated in this work. The dashedline gives the flux of the Crab Nebula. Spectral points below 40 GeV are only shown for illustrativepurpose and are not used in the analysis. Γ VHE ∼
3) distant source, whose discovery at VHE energies enabled to derivestrong limits on the EBL density in the optical to near-infrared [5], and PKS 2155-304, which is a fairly strong VHE source (about 20% Crab in the quiescente state)with a softer spectrum ( Γ VHE ∼ .
3) located at an intermediate redshift of z = . ∼
2% Crab) leads to a simulated spectrum which does not largely increase theenergy range covered compared to the H.E.S.S. measurement of 1ES 1101-232:neither at low energies (due to the hard spectrum) nor at high energies (the strongEBL attenuation suppresses the signal below the NGCTS sensitivity). Even forthe case of the two very di ff erent assumed EBL models, no strong di ff erence inthe simulated spectra is apparent, which could be used to di ff erentiate betweenthe models. This is di ff erent in the case of PKS 2155-304, where, for the di ff erentEBL models, very di ff erent spectra are expected to be measured at lower energies.The behavior at low energies will be discussed further in the next section.
3. Utilizing the unabsorbed part of the spectrum
One of the main features of a NGCTS will be a high sensitivity in the energyrange between 20 and 100 GeV, an energy range which holds the possibility todirectly sample parts of the energy spectrum of a source, which are not a ff ectedby the EBL attenuation. In this section it will be explored how this energy rangecan be utilized to derive limits on the EBL density, and what are possible problemsand caveats. Simulation & analysis chain. The following simulation and analysis chain is uti-lized:1. Calculate EBL attenuation for a specific EBL density and source distance.2. De-attenuate a measured spectrum and fit with power law ( dN / dE = Φ · E − Γ ). The fit results serve as input flux function for the simulated spectrum.3. Simulate spectrum as measured by an NGCTS with calculated input fluxfunction.4. Fit simulated spectrum in a low energy regime (intrinsic spectrum) and highenergy regime (absorbed spectrum). Again, a simple power law function isused in each energy regime. 10 nergy (TeV) -4 -3 -2 -1
10 1 10 ) - s - ( e r g c m ν F ν -13 -12 -11 -10 Figure 5: Example of simulated spectra for di ff erent EBL densities. The base spectrum assumedis the quiescent state spectrum of PKS 2155-304 ( z = . ff erent level of the EBLdensity (black markers) and the corresponding assumed intrinsic spectra (black lines), the sourcespectrum in the GeV energy range as measured by Fermi [33] (purple butterfly), and the energyranges which are used to determine the slope of the simulated spectrum at low (blue) and high(red) energies. Spectral points below 40 GeV are only shown for illustrative purpose and are notused in the analysis. ) µ ( λ -1
10 1 10 ) - s r - ( n W m ν I ν Figure 6: EBL density ( z =
0) for the Fran08 EBL model scaled with a factor 0.7 to 1.7 in steps of0.1. The red dashed curve is the unscaled EBL model.
5. 200 spectra are simulated and mean values are used.An example for this procedure is shown in Fig. 5 for the quiescence spectrum ofPKS 2155-304 ( z = . Fit-range & source intrinsic break. The resulting EBL attenuations for the scaledmodels are shown in Fig. 7 upper left panel. The energy ranges used to fit thepower laws are marked by colored boxes. In the high energy range the attenu-ation follows approximately a power law and since the input spectrum is also apower law, the resulting attenuated spectrum will follow a power law as well. Inthe low energy range no significant absorption is present. As recent
Fermi / LATobservations show, a spectral break is observed between the GeV and the TeVenergy range [34]. For many sources this break can be attributed to a break ex-pected from EBL attenuation. For these sources an NGCTS would be able tosample the intrinsic spectrum down to very low energies. In other cases, e.g.PKS 2155-304, the break between GeV and TeV range is stronger than expectedfrom EBL attenuation, therefore an additional, source intrinsic break is expectedsomewhere between the two energy bands. Currently, the statistics for this energyrange for the sources considered here is not yet su ffi cient to correctly model thebreak. Therefore, for the analysis in this paper the lower edge of the low energy12 nergy (TeV) -2 -1
10 1 10 A tt e nu a t i on -1
101 EBL density scale factor0.6 0.8 1 1.2 1.4 1.6 1.8 F I T Γ H I G H Γ - L O W Γ -2 -1
10 1 10 A tt e nu a t i on -1
101 EBL density scale factor0.6 0.8 1 1.2 1.4 1.6 1.8 F I T Γ H I G H Γ - L O W Γ Figure 7: Results from the power law fit to the simulated spectrum in the low and high energyband using the PKS 2155-304 quiescence spectrum with the Fran08 (upper row) and Gen (lowerrow) EBL model.
Left:
Attenuation of the VHE γ -ray flux resulting from the scaled EBL models.The colored boxes in the background mark the fit range for the power law at low (red) and high(blue) energies. Middle:
Spectral index Γ from the fit of a power law to the low (red) and high(blue) energy range versus the scaling factor of the EBL model. The color shaded bands denotethe error on the spectral index from the fit (RMS of the spectral index distribution). Black crossesmark the intrinsic spectral index that has been utilized. Right:
Spectral break between low andhigh energies (error bands from error propagation). For discussion see main text.
13t range is chosen to start above the
Fermi / LAT energy band (defined as the 5thhighest photon in energy reported in [33], e.g. ∼
40 GeV for PKS 2155-304). Fu-ture observations with
Fermi / LAT, MAGIC-II, and H.E.S.S. II will provide furtherinformation on this issue.
EBL attenuation spectral break.
Fig. 7 upper middle panel shows the spectralindex resulting from the power law fit for the two energy bands for the di ff erentscalings of the EBL model. The markers show the mean spectral index of the fits,with the error given as the RMS of the mean spectral index distribution (shadedbands). As alternative error definition the mean error on the spectral index fromthe fit could be used which gives similar results. The black crosses mark thespectral index utilized for the input source spectrum. It can be seen that the fit inthe low energy band reproduces very well the assumed intrinsic spectral indices. For the highest scaled EBL densities the e ff ect of attenuation becomes relevantin the low energy band and the spectral index from the fit is steeper (larger) thanthe one from the input spectrum. This e ff ect will be discussed in more detailbelow. The right panel of the figures displays the strength of the spectral breakbetween the two power laws Γ LOW − Γ HIGH , with the error bands calculated viaerror propagation. An EBL density scale factor of 0.1 corresponds to one to twostandard deviations di ff erence in the strength of the break. Note that a scalingof 0.1 corresponds to an EBL density of ∼ − sr − at 2 µ m which is of thesame order as the error on the lower limits from integrated source counts at thiswavelength. The detection of a break with certain strength can be converted intoan upper limit of the EBL density (thick dashed line). In principal, a single wellmeasured spectrum is su ffi cient to derive such limits. Since EBL attenuation is aglobal, redshift dependent phenomenon, in general, a combined fit to all availableVHE data should be used to derive limits on the EBL density [see e.g. 6]. This isdiscussed in more details in Sect. 5. EBL attenuation at low energies.
The same analysis has been performed utiliz-ing the Gen EBL model and the results are displayed in Fig. 7 lower row. TheGen EBL density in the ultraviolet to optical is higher than in the Fran08 model(Fig. 1), therefore resulting in a non negligible attenuation in the low energy band The correlation between the EBL density and the spectral index in the low energy band is aresult of the methodology i.e. for each EBL density a corresponding intrinsic spectrum is con-structed. I.e. if the Fran08 EBL model is correct and the intrinsic spectrum follows a power law in theenergy range considered a 1.3 scaling of the model could be excluded with 3 standard deviations. nergy (TeV) -1
10 1 10 A tt e nu a t i on -1
101 Energy (TeV) -1
10 1 10 A tt e nu a t i on -1 Figure 8: Energy dependent upper limits on the attenuation for the Fran08 (left) and the Gen (right)EBL models derived utilizing the PKS 2155-304 quiescence spectrum. Shown are the limits takinginto account the 1 σ error on the flux points (orange filled squares), with the addition of the 1 σ erroron the spectral index of the low energy power law (red filled triangles), and no errors (purple filledcircles). The black line shows the attenuation for the EBL model utilized, grey lines show theattenuation for the EBL model scaled in steps of 0.1. (Fig. 7 lower left panel). Consequently, the power law fit in the low energy bandresults in a too soft spectrum compared to the input source spectrum (Fig. 7 lowermiddle panel). This mis-reconstruction, if taken at face value, would lead to anoverestimated upper limit on the EBL density (Fig. 7 lower right panel). To beable to utilize the low energy part of the spectrum as proxy for the intrinsic spec-trum it is therefore crucial to carefully examine the spectral shape in the energyrange for signs of curvature. A conservative approach would be to correct the fluxpoints in the fit energy range for the attenuation from a maximum EBL beforeperforming the fit. On the other hand, if a high statistic VHE spectrum from adistant source does not show any indication of curvature in this energy regime,tight limits on the EBL density in the ultraviolet to optical EBL can be derived. Energy dependent attenuation limits.
The power law fit to the low energy region,if taken as proxy for the intrinsic spectrum, can also be used to derive energydependent upper limits on the attenuation. Such limits can be extremely useful:the EBL attenuation is an energy dependent process, where certain wavelengthregions of the EBL spectrum are connected to certain VHE energy ranges. Fea-tures in the EBL density, as e.g. expected from the first stars [see e.g. 35], could15herefore also produce features in the attenuation. The resulting energy dependentEBL attenuation limits from such an analysis for the Fran08 and the Gen EBLmodel utilizing the PKS 2155-304 quiesent spectrum are shown in Fig. 8 . As canbe seen from the figure, the dominant source of errors in such an analysis are theuncertainties on the spectral index from the power law fit in the low energy range,since the statistical errors on individual flux points are comparably small. Again,the rejection power is in the order of 1-2 σ per 0.1 scaling of the EBL density atenergies > ff ect of the attenuation ”spill over” in the lowenergy fitting band is visible: due to the EBL attenuation the power law fit is toosoft, resulting in an underestimated EBL attenuation and too strong limits. Flaring states.
Up to here only the quiescent flux state of sources has been con-sidered, since its observation is guaranteed. AGNs do also show extreme flaringbehavior with high fluxes, unfortunately usually only for short periods of time.Here, the VHE spectrum recorded during the extreme flux outburst of PKS 2155-304 in 2006 [36] is investigated. The spectrum is an averaged spectrum of 1.5 hof observations, in which the source showed several strong flares with time-scalesdown to a few minutes. While no strong spectral variations in the VHE spectrumhave been observed during this flare, for the analysis only short observations of6 min length have been considered, demonstrating the power of the NGCTS toderive high quality spectra even on such short time-scales. In addition, the EBLattenuation is a ”stationary” e ff ect in the spectrum, therefore a temporally fineresolved flaring state might enable to distinguish between intrinsic and EBL ef-fects. The resolution of the EBL density achieved for such a 6 min observationof the source in a flaring state is comparable with the one achieved for 20 h ofquiescence observations (Fig. 9 top row). Nearby sources.
Strong flux outbursts in the VHE regime have also been observedin the two nearby sources Mkn 421 and Mkn 501. While the smaller distancesresult in less EBL attenuation and therefore a weaker signature, the overall higherflux levels of these two sources enable to derive spectra with high event statistics.Here, the time-averaged VHE spectrum of Mkn 501 during the 1997 high state isinvestigated, assuming an observation time of 20 h. As can be seen from Fig. 9bottom row, while the overall strength of the break between the two power laws is For this investigation only a single simulated spectrum without applying the statistical dicingof the event numbers is used. BL density scale factor0.6 0.8 1 1.2 1.4 1.6 1.8 F I T Γ -1
10 1 10 A tt e nu a t i on -1 F I T Γ -1
10 1 10 A tt e nu a t i on Figure 9: EBL limit results from power law fits to low and high energy bands of the VHE spectrumusing scaled version of the Fran08 EBL model (see Fig. 7 and 8 for detailed description).
Upperrow:
Results for the VHE spectrum from the flaring state of PKS 2155-304 in 2006 [36] (6 minobservation time),
Lower row:
Results for the averaged high state spectrum of Mkn 501 [37]( z = . . − . . − .
2) comparablelimits can be derived due to the superior statistics. In addition, the problem ofattenuation in the low energy band is less severe. One caveat - at least for the caseof Mkn 421 - is the fact that there are strong indications for an intrinsic (not EBLrelated) break between the GeV and TeV range at relatively high energies (around100 GeV) [34], which would make it di ffi cult to define a proper low energy regionvoid of any curvature. A di ff erent method, discussing the possibilities of how suchhigh quality spectra with a wide energy range produced by a nearby source can beused to test the EBL density, is discussed in the next section.
4. Attenuation modulation at mid-energies
The NGCTS will achieve an unprecedented sensitivity in the intermediate en-ergy range, i.e., between 100 GeV and few TeV. For nearby sources, this energyrange is most sensitive for the EBL density in the optical to infrared regime ( ∼ µ m), which can, thus, be probed very e ffi ciently with an NGCTS measurementof an AGN energy spectrum. Smoothness of AGN spectra.
The measured energy spectra of AGNs in the energyrange between 100 GeV and few TeV follow usually a smooth shape. For mostof the measured sources, a simple power law fit is su ffi cient to describe the avail-able data well, whereas for sources in a flare state (like the flare of PKS 2155-304in 2006) or with a generally high emission state (like Mkn 421), either a curvedpower law or a power law with a cut-o ff are successfully used. The curved powerlaw (also known in the literature as the double-log parabola) is expected to de-scribe the spectra well at energies close to the position of the Inverse-Comptonpeak. The power law with a cut-o ff instead is the expected behavior of a sourcewhich does not provide necessary conditions for acceleration of charged parti-cles to su ffi ciently high energies. All scenarios do have one common feature: themeasured spectra can be described by smooth functions,i.e., no features, wigglesor pile-ups are expected, especially after de-convolving the spectra for the e ff ectof the EBL absorption. This property can, therefore, be used to distinguish be-tween di ff erent overall EBL levels in the optical to infrared regime: whereas the”correct” EBL model and level will produce a smooth intrinsic AGN spectrum, an”incorrect” EBL level would result in a signature (in form of well defined wiggles)in the reconstructed intrinsic spectrum.The strength of the method is that the EBL signatures in the reconstructedAGN spectra will not only be visible (measurable) in the case where the assumed18BL level is higher than the real one, but also in case the assumed EBL level islower than the real one. It is, therefore, the first indirect method to really measurethe EBL density at z = Simulation & analysis chain. The utilized methodology is sketched below:1. Assume an intrinsic spectral shape and the flux level of a known strongextragalactic gamma-ray source.2. Simulate NGCTS spectrum assuming the absorption due to the standardEBL, i.e., with the scaling factor of 1.3. Reconstruct intrinsic spectrum of the source assuming a scaled EBL level.For a scaling, which is di ff erent enough from the standard EBL, the recon-structed AGN spectrum will show distinct wiggles.4. To characterize the presence of the wiggles, a fit by a smooth source func-tion (spectral shape) is performed. The chosen fit shape is the curved powerlaw: d N / d E = N × (cid:16) E − α + β log( E / E ) (cid:17)
5. The resulting χ of the fit is then used to judge if the change in the EBLlevel results in an improbable reconstructed intrinsic spectrum.6. Repeat the simulation 1000 times for the given EBL scaling and computethe mean and the RMS of χ values from the fits to the reconstructed intrin-sic spectrum. Simulation example.
The steps 1–4 of the method are illustrated in Fig. 10 for theVHE spectrum of Mkn 501. The assumed spectral shape and the flux level of theintrinsic spectrum are adapted to the flux measured by HEGRA [37] during theoutburst of the source in 1997: the original data are shown by grey open squaresin the upper panel of the figure. The simulated NGCTS spectrum calculated usingthe ’correct EBL’ (Gen EBL model; scale factor 1) is shown in red, whereas theassumed intrinsic spectrum of Mkn 501 is shown by the solid grey line and the re-constructed intrinsic spectrum is shown by the blue filled circles. The e ff ect of themis-reconstruction of the intrinsic spectrum is shown for the example of an EBLscaled by a factor of 1.3: the reconstructed intrinsic spectrum (green filled trian-gles) clearly shows wiggles in the fit range. The e ff ect of the wiggles is more vis-ible in the lower panel of the figure where the residuals to the best fit function areshown. The wiggles are quantified by a fit in the energy range between 100 GeVand 7 TeV, well before a possible pile-up in the spectrum arises. The choice ofthe fit range is made in order not to bias the result by the level of the EBL above19 - s - E n e r g y d e n s i t y ( e r g s c m -11 -10 -9 Mkn 501, HEGRA, measuredExpected spectrum to be observedReconstruced intrinsic spectrum with ’correct EBL’1.3 × Reconstruced intrinsic spectrum with EBLCrab (MAGIC)
Observation time: 50.0 hours ) ) (E/E log β + α - (E × AGN spectral form: dN/dE = N F / F ) ∆ R es i du a l s ( -0.2-0.100.1 /NDF = 13.6/8, fit probab: 9.4e-02 χ Using correct EBL and HEGRA data, /NDF = 14.0/8, fit probab: 8.1e-02 χ × Using EBL F / F ) ∆ R es i du a l s ( -0.0200.02 /NDF = 13.4/12, fit probab: 3.4e-01 χ Using correct EBL and NGCTS data,
Energy (TeV) F / F ) ∆ R es i du a l s ( -0.0200.02 /NDF = 51.4/12, fit probab: 7.9e-07 χ × Using EBL
Figure 10: Search for signatures at mid-VHE in the Mkn 501 spectrum.
Top panel:
The Mkn 501spectral energy distribution (SED) at very high energies. Shown are: measured spectrum byHEGRA (grey open squares), simulated NGCTS spectrum (red filled squares), assumed intrin-sic spectrum of Mkn 501 (grey solid line), reconstructed intrinsic Mkn 501 spectrum (blue filledcircles) and reconstructed intrinsic spectrum of Mkn 501 assuming an EBL scaling factor of 1.3(green triangles). For comparison, the deabsorbed HEGRA Mkn 501 is shown for the same twoEBL models (filled grey circles and open grey circles, respectively). The Crab Nebula spectrum(grey dashed line) is shown for comparison.
Middle upper panel:
Residuals of the fits to thede-absorbed HEGRA Mrk 501 spectrum for the case of the two di ff erent assumptions about theEBL density. The di ff erence between the two curves (filled and open circles) is very small. TheHEGRA sensitivity is not su ffi cient to decide between the two assumptions. Middle lower panel:
Residuals between the best fit to the SED in case of NGCTS measurement and the spectral pointsfrom the intrinsic spectrum using the correct EBL density.
Bottom panel:
Residuals between thebest fit to the SED for a NGCTS measurement and the spectral points from the intrinsic spec-trum reconstructed using the scaled EBL model. A clear and significant signature (wiggles) in theresiduals is visible, which is quantified by a low probability of the fit. BL scaling factor0.6 0.8 1 1.2 1.4 1.6 1.8 r e d χ
50 hours of observation20 hours of observation
P = 50%P = 1%
P = 0.01%
Figure 11: Quantitative results from the search for EBL signatures in the mid-VHE using theenergy spectrum of Mkn 501. Shown are the reduced χ values from the fits to the reconstructedspectra of Mkn 501 as a function of EBL scaling factor. Blue filled squares and green filled circlesshow the expected result for 20 and 50 hours of NGTCS observations, respectively. The blackhorizontal lines correspond to fit probabilities as labeled. µ m, to which the VHE spectra are very sensitive due to a super exponential de-pendency of the attenuation with the wavelength in that range. Using the correctEBL level to reconstruct the intrinsic spectrum, the intrinsic spectrum is well de-scribed by a smooth function (Fig. 10, middle lower panel). Instead, when usinga ”wrong” scaled EBL density characteristic deviations (wiggles) from a smoothfunction are visible (Fig. 10, lower panel). The wiggles are quantified by a reduced χ value of 51.4 /
12, corresponding to a fit probability of 7 . · − . The small fitprobability for the assumed scaled EBL level implies (under used assumptions)significant presence of the unphysical wiggles and, therefore, an exclusion of thatparticular EBL realization. For comparison, HEGRA measured spectrum is alsode-absorbed using the same two EBL models and the results are shown by greyfilled and open circles in the upper panel. The residuals to the best fits are shownin the middle upper panel. The di ff erence between the two curves (represented bygrey filled and open circles) is not significant and is di ffi cult to see. The similarreduced χ values of 13.6 / / Results of the analysis.
This procedure is repeated 1000 times for every scaledEBL density in order to achieve a solid statistical mean and a 1 σ (68%) cover-age of the reduced χ values. The results are shown in Fig. 11 for two di ff erentNGCTS exposures (20 and 50 hours) plotting the mean reduced χ values in-21luding 68% error bars versus the EBL scaling factor. As a result one can see aparabola-like curve with the minimum at EBL scaling factor of 1.0, which is viaconstruction the correct EBL model. The expected mean reduced χ values areshown by the blue filled squares and the green filled circles for the exposures of20 hr and 50 hr, respectively. The corresponding fit probabilities of P = χ value including its 68% error exceeds the χ value for P = Caveats of the method.
The method presented above is not only sensitive in con-straining the EBL density but it is also a first attempt to resolve the actual EBLlevel. Still, the method has several caveats: (i) There is a possibility that the in-trinsic VHE spectrum is not smooth for some AGNs. For example, several emis-sion regions or several generations of charged emitting particles (e.g., electrons)may produce spectral features which would mimic the signature from a wrongEBL model. Though neither the AGNs observed at low energies with Fermi / LAT,nor the extragalactic VHE γ -ray sources observed so far with IACTs have shownstructured spectra, such wiggles can be interpreted as the result of a wrong EBLmodel only if found to exist in several spectra of di ff erent sources consistently.(ii) The spectral signature shown in Fig. 10 can only be recognized well after along exposure of a source being in a flare state. The data of the Mkn 501 flarefrom 1997 used for the study remains unique so far. This means that it cannotbe expected that a study with such precision can be done on many sources withfuture NGCTS. Still, the indirect EBL measurement based on few strong flareswill be of high importance. (iii) The limited energy resolution of IACTs ( ∼ ff ect the possibility of detecting such a signature. The overall shape ofthe attenuation e ff ect is broad enough in energy to not strongly be a ff ected by thesmoothing of an energy resolution of < ff ects due to events with mis-reconstructed energy may enhance or alter thewiggles. Therefore, an e ffi cient and precise spectral unfolding technique will bekey to overcome these problems for nearby sources. For more distant sources theattenuation signatures get quickly stronger. It will be, therefore, highly interestingto study a strong flaring state from a source at redshift & . . Summary & Conclusions In this paper the potential of a Next Generation Cherenkov Telescope Sys-tem (NGCTS) to study the EBL through observations of VHE spectra from dis-tant sources is explored. In the focus of the study lies the energy range be-tween 40 GeV and 10 TeV, where a factor 10 improvement in sensitivity overcurrent generation experiments is expected. Two di ff erent methods are investi-gated: (i) utilizing the unabsorbed part of the VHE spectrum in the energy range40-100 GeV and (ii) searching for attenuation modulation signatures at energiesbetween 100 GeV to 7 TeV. While some caveats, like e.g. the exact shape of theintrinsic spectra, do exist, overall the two methods show promising results, clearlygo beyond what is possible with current generation instruments.EBL attenuation is a global phenomenon that a ff ects the spectra of all sourcesin the same way. It is therefore quite natural to expand the studies on the EBL bycombining the results from di ff erent methods, sources or source flux states. Thiscan e.g. be done by utilizing log-likelihood methods to combine the constraintsfrom di ff erent sources and methods. In addition only the low and mid-VHEs havebeen investigated. At energies >
10 TeV further signatures from EBL attenuation(”cut-o ff ”) are expected, which have been used extensively in the past to derivelimits on the EBL density in the FIR.In this paper only data from a single instrument - a NGCTS - and minimalassumptions about intrinsic spectrum have been used to derive constraints on theEBL density. AGNs are observed all across the electromagnetic spectrum andthe theory predicts connections between the observations at di ff erent energies. Awealth of multi-wavelength information is therefore accessible, which - in com-bination with a theoretical model - can be used to constrain the spectrum at VHE.A first model-dependent approach to determine the EBL level using a consistentSED modeling of detected blazars was discussed recently by [38]. While a de-tailed discussion of this topic is beyond the scope of this paper, as an example itshould only be mentioned the power of combining the Fermi observations at MeVto GeV energies with observations from an NGCTS: such observations will coverover 9 decades (!) in energy with high precision.The sources under study show strong flux variability in the VHE band. Thehigh sensitivity of a NGCTS will enable to study the energy spectrum on veryshort time-scales in great detail. The time resolution will enable stronger con-straints on the theoretical modeling of the source spectra since the experimentaldata will be available on shorter scales than the relevant changes in the emissionregions. This will further help to disentangle source intrinsic e ff ects and EBL23ttenuation.In this study only the VHE spectra of a few selected known sources have beeninvestigated. The NGCTS will bring new discoveries. With the high sensitivity inthe 20 to 100 GeV range it will be possible to detect fainter sources and sourcesat higher redshift. A (su ffi ciently) large sample of sources will serve a two-foldpurpose: (1) help to improve the understanding of the intrinsic source physics and(2) enable statistical studies of the EBL e ff ects, e.g. by investigating the EBLattenuation features versus redshift. This will also enable to not only probe thepresent day EBL but to study its evolution with redshift. How such a study can beperformed with the help of an NGCTS will be the topic of a second paper. Acknowledgments
MR and DM would like to thank M. Persic and M. Tluczykont for the careful reading ofthe manuscript and useful comments. MR and DM acknowledge fruitful discussion onCTA performance with J. Hinton and D. F. Torres. The authors would like to thank thereferee for helpful comments and suggestions which improved the paper. DM acknowl-edges the support by a Marie Curie Intra European Fellowship within the 7th EuropeanCommunity Framework Programme.
Appendix A. References for VHE spectral data
Source name Redshift ReferenceMkn 501 0.034 [37]PKS 2155-304 0.116 [39], [36]1ES 1101-232 0.188 [5]
Table A.1: VHE spectra used in this publication.
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