The nature of the intrinsic spectra from the VHE emission of H 2356-309 and 1ES 1101-232

The VHE emission from the HBLs H 2356-309 and 1ES 1101-232 were observed by HESS telescopes during 2004--2007. Particularly the observation in 2004 from H 2356-309 and during 2004--2005 from 1ES 1101-232 were analyzed to derive strong upper limits on the EBL which was found to be consistent with the lower limits from the integrated light of resolved galaxies. Here we have used the photohadronic model corroborated by two template EBL models to fit the observed VHE gamma-ray data from these two HBLs and to predict their intrinsic spectra. We obtain very good fit to the VHE spectra of these two HBLs. However, the predicted intrinsic spectra are different for each EBL model. For the HBL H 2356-309, we obtain a flat intrinsic spectrum and for 1ES 1101-232 the spectrum is mildly harder than 2 but much softer than 1.5.


I. INTRODUCTION
The high energy γ-rays coming from the distant blazar jets to the Earth are attenuated by pair production with the soft photons [1,2]. There are mainly two important sources of these soft photons, namely, synchrotron photons intrinsic to the jet and the external ambient photons from the extragalactic background light (EBL). As we understand, the blazar spectra are highly variable and have wider range of variability. Although we have learned a lot about them, the present understanding of their radiation process is still incomplete to reliably predict the intrinsic TeV spectrum, and thus to disentangle absorption from intrinsic features. It is hoped that modeling of the blazar spectral energy distribution (SED) by taking into account properly the emission mechanism can take care of the intrinsic extraneous effect due to its environment. The total absorption of the TeV γ-rays depends on the local density of the low energy photons at the origin, the distance traveled (redshift z) and also the energy of the high energy γ-rays E γ . For higher energy γ-rays the absorption process leads to the steepening of the observed spectrum thus reducing the observed flux.
So the observed blazar spectrum contains valuable information about the history of EBL in the line-of-sight and the intrinsic properties of the source.
The EBL effect on the blazar spectrum can be calculated by subtracting the foreground sources from the diffuse emission. However, the foreground zodiacal light and galactic light introduce large uncertainties in such measurements and make it difficult to isolate the EBL contribution from the observed multi-TeV flux from distant blazars. Strict lower limits are derived from the source counts and rather loose upper limits come from direct measurements.
Nevertheless, an indirect approach is to utilize the very high energy (VHE) γ-ray spectra from blazars by assuming a power-law behavior for the intrinsic spectrum. So, long term studies of many high frequency peaked BL Lacerate objects (HBLs) of different redshifts during periods of activity such as flaring will provide invaluable insights into the emission mechanisms responsible for the production of VHE γ-rays as well as the absorption process due to EBL. In recent years, the continuing success of highly sensitive Imaging Atmospheric Cherenkov Telescopes (IACTs) such as VERITAS [3], HESS [4] and MAGIC [5] have led to the discovery of many new extragalactic TeV sources which in turn resulted in constraining the flux density of the EBL over two decades of wavelengths from ∼ 0.30 µm to 17 µm [5][6][7][8][9][10].
Blazars detected at VHE are predominantly HBLs and flaring in VHE seems to be a com-mon phenomenon in these objects, although it is not yet understood properly. In general this VHE emission is explained by leptonic models [11][12][13][14] through SSC scattering process.
Due to the absorption of the primary VHE photons by EBL, the corresponding intrinsic spectrum becomes harder than the observed one. Normally in the SSC model the intrinsic photon spectrum has a spectral index α int > 1.5 (discussed in Sec.III) in the energy range where electron cooling via synchrotron and/or IC energy loss is efficient and the hard spectrum with α int = 1.5 is considered as a lower bound. It is difficult to produce harder spectra (α int < 1.5) in the one-zone SSC scenario. The orphan flaring in multi-TeV γ-rays and blazars with hard gamma ray spectra are troublesome to deal with the standard SSC scenario. Multi-TeV emission from two HBLs, 1ES 1101-232 (z=0.186) and H 2356-309 (z=0.165) were observed by the HESS Cherenkov telescopes [15] and at that time these were the most distant sources. Due to the lack of reliable EBL data, different EBL SEDs were assumed to construct the intrinsic spectra from the observed VHE spectra. The assumed EBL SEDs were in general agreement with the EBL spectrum expected from galaxy emission.
Although, the constructed intrinsic spectra were compatible with a power-law, the intrinsic spectrum of the HBL 1ES 1101-232 was rather hard and such hard spectra had never been observed before in the spectra of closest, less absorbed TeV blazars e.g. Mrk 421 and Mrk 501 [16][17][18][19][20] and are difficult to explain with the standard leptonic or hadronic scenarios [21] for blazar emission. Also the resulting EBL upper limits were found to be consistent with the lower limits from the integrated light of resolved galaxies and seems to exclude a large contribution to the EBL from other sources. From the analysis in ref. [15], it was inferred that the Universe is more transparent to gamma rays than previously anticipated. Later on, harder spectra have also been observed from many HBLs [22][23][24]. Thereafter, many scenarios are suggested to achieve very hard VHE spectra which are discussed in ref. [25] and references therein. Also alternative photohadronic scenarios are proposed to explain the VHE emission [26,27]. The structured jet (spine-layer) model is also proposed to explain the high energy emission from blazars [28,29].
In this work our goal is to use the photohadronic model of Sahu et al. [30] and different template EBL models [31,32] to re-examine the VHE spectra of HBLs 1ES 1101-232 and H 2356-309 and to calculate their intrinsic spectra. Here, we assume that the Fermi accelerated protons in the blazar jet have a power-law behavior and the observed VHE spectra of the HBLs are related to the proton spectrum.
The paper is organized as follows: In Sec. 2 we discuss different EBL models which are used for our calculation. The photohadronic model of Sahu et al. [30] is discussed concisely in Sec. 3. We discuss the results obtained for the VHE observations of HBLs H 2356-309 and 1ES 1101-232 in Sec.4 and finally we briefly summarize our results in Sec. 5.

II. EBL MODELS
Considering the uncertainty associated with the direct detection of the EBL contribution, a wide range of models have been developed to model the EBL SED based on our knowledge of galaxy and star formation rate and at the same time incorporating the observational inputs [31][32][33][34][35][36][37]. Mainly three types of EBL models exist: backward and forward evolution models and semi-analytical galaxy formation models with a combination of information about galaxy evolution and observed properties of galaxy spectra. In the backward evolution scenarios [34], one starts from the observed properties of galaxies in the local universe and evolve them from cosmological initial conditions or extrapolating backward in time using parametric models of the evolution of galaxies. This extrapolation induces uncertainties in the properties of the EBL which increases at high redshifts. However, the forward evolution models [31,33] predict the temporal evolution of galaxies forward in time starting from the cosmological initial conditions. Although, these models are successful in reproducing the general characteristics of the observed EBL, cannot account for the detailed evolution of important quantities such as the metallicity and dust content, which can significantly affect the shape of the EBL. Finally, semi-analytical models have been developed which follow the formation of large scale structures driven by cold dark matter in the universe by using the cosmological parameters from observations. This method also accounts for the merging of the dark matter halos and the emergence of galaxies which form as baryonic matter falls into the potential wells of these halos. Such models are successful in reproducing observed properties of galaxies from local universe up to z ∼ 6.
The VHE γ-rays from distant sources interact with the EBL to produce electron-positron pairs thus depleting the VHE flux by a factor of e −τγγ . Here τ γγ is the optical depth of the process γγ → e + e − which depends on the energy of the γ-ray (E γ ) and the redshift (z). For the present study we choose two different EBL models by Franceschini et al. [31] and Inoue et al. [32] (hereafter EBL-F and EBL-I respectively). The attenuation factor e −τγγ of these  that below ∼ 500 GeV, these two models behave almost the same and above this energy there is a slight difference in their behavior.
In Fig.2, we have compared the attenuation factor of EBL-F and EBL-I for z=0.186. The behavior of both these models are similar to the one at redshift z=0.165 which can be seen by comparing Fig.1 and 2. Here in Fig.2 we have also plotted the attenuation factor of ref.
[15] for z=0.186 with two different normalizations. To determine an upper limit of the EBL model, Aharonian et al [16] assumed a previously known shape for the SED of the EBL .
This curve, is then renormalized to fit the measurements made by the HESS collaboration at Doppler factor D as the blob (for blazars Γ D). A detail description of the photohadronic model and its geometrical structure is discussed in ref. [30]. The injected spectrum of the Fermi accelerated charged particles having a power-law spectrum dN/dE ∝ E −α with the power index α ≥ 2 is considered here.
In the compact inner jet region, the Fermi accelerated high energy protons interact with the background photons with a comoving density n γ,f to produce the ∆-resonance and its subsequent decay to neutral and charged pions will give VHE γ-rays and neutrinos respectively. In the flaring region we assume n γ,f is much higher than the rest of the blob n γ (non-flaring) i.e. n γ,f ( γ ) n γ ( γ ). As the inner jet is buried within the blob, we can't calculate n γ,f directly. So we use the scaling behavior of the photon densities in the inner and the outer jet regions as follows: which assumes that the ratio of photon densities at two different background energies γ 1 and γ 2 in the flaring and the non-flaring states remains almost the same. The photon density in the outer region can be calculated from the observed flux from SED. By using Eq. (1), the n γ,f can be expressed in terms of n γ . It is shown in Refs. [27,39] that super Eddington luminosity in protons is required to explain the high energy peaks. In a normal jet, the photon density is low, which makes the photohadronic process inefficient [40]. However, in the present scenario it is assumed that during the flaring the photon density in the inner jet region can go up so that the ∆-resonance production is moderately efficient, which eliminates the extreme energy requirement [19].
In the observer frame, the π 0 -decay TeV photon energy E γ and the target photon energy γ satisfy the condition The above condition is derived from the process pγ → ∆. Also, the observed TeV γ-ray energy and the proton energy E p are related through E p 10 E γ . It is observed that for most of the HBLs, the D is such that, γ always lies in the lower tail region of the SSC band.
So it is the low energy SSC region which is responsible for the production of multi-TeV γ-rays in the photohadronic model. The efficiency of the pγ process depends on the physical conditions of the interaction region, such as the size, the distance from the base of the jet, expansion time scale (or dynamical time scale of the blob t d = R f ) and the photon density in the region which is related to the optical depth τ pγ of this process.
Correcting for the EBL contribution, the observed VHE flux F γ can be expressed in terms of the intrinsic flux F γ,int by the relation where the intrinsic flux can be given as [20] The SSC energy γ and the observed energy E γ satisfy the kinematical condition given in Eq.
(2) and Φ SSC is the SSC flux corresponding to the energy γ which is known from the leptonic model fit to the multi-wavelength data. Here the only free parameter is the spectral index α. For a given multi-TeV flaring energy and its corresponding flux, we can always look for the best fit to the spectrum which will give the value of A γ . Also it is to be noted that, blazars are highly variable objects and characterized by very wide range of different spectra. Our model depends on the value of Φ SSC which can be different for separate epochs of observations and accordingly the value of A γ can vary. However, in principle α should be kept constant for a given acceleration mechanism. In the leptonic model, the SSC photon flux in the low energy tail region is a power-law given as Φ SSC ∝ β γ , where β > 0. By using the relation in Eq. (2) we can express γ in terms of the observed VHE γ-ray energy E γ which will give Φ SSC ∝ E −β γ and again by replacing Φ SSC in Eq.(4) we get and the intrinsic differential power spectrum for VHE photon is a power-law given as However, due to the nonlinearity of τ γγ the observed VHE flux will not behave as a single power-law. Hardness of the intrinsic spectrum depends on the value of α for a given leptonic model which fixes the value of β.

IV. RESULTS
The    The intrinsic fluxes are also shown.

A. H 2356-309
The high frequency peaked BL Lac object H 2356-309 is hosted by an elliptical galaxy located at a redshift of z = 0.165 [43] and was first detected in X-rays by the satellite experiment UHURU [44] and subsequently by the Large Area Sky Survey experiment onboard the HEAO-I satellite [45]. Also in optical band it was observed [46]. In 2004, H 2356-309 was observed simultaneously in X-rays by RXTE, in optical by ROTSE-III, in radio by Nancay decimetric telescope (NRT) and in VHE for about 40 hours (June to December 2004) by HESS telescopes. It was observed that during this period, the X-ray spectrum measured above 2 eV was softer and the flux was ∼ 3 times lower than the one measured by BeppoSAX in 1998 in the same energy band but in a comparatively quiescent state.
Since   [15] which was analyzed to constraint the EBL contribution.
Here we would like to mention that the photohadronic model is applicable not only to VHE flaring but also to VHE (multi-TeV) emission from the blazars under discussion. In the photohadronic scenario this range of E γ corresponds to Fermi accelerated protons in the energy   is observed that by taking F γ,int = 2.6 × 10 −12 erg cm −2 s −1 for EBL-F (red curve) we can fit the observed data very well which is shown in Fig. 3. In the same plot we have also shown the photohadronic fit (black curve). The photohadronic fit and the multiplication by a constant factor are indistinguishable. A good fit to the data is obtained in photohadronic model for α = 2.5 and A γ = 7.1. The constant F γ,int implies that β 0.5 and exact fit to the Φ SSC in the energy range 8.3 M eV ≤ γ ≤ 41.5 M eV gives β = 0.49 which is shown in Fig. 5 (red line). Also this gives the spectral index α int 2 for the intrinsic spectrum [48].
In Fig. 4 we have also rescaled the attenuation factor of EBL-I (red curve) by F γ,int = 2.7 × 10 −12 erg cm −2 s −1 to fit the observed VHE data and for comparison the photohadronic model fit (blue curve) is also shown. The best fit for the photohadronic model is achieved here for α = 2.8 and A γ = 6.0. We observe that the rescaling and the model fit are very different from each other and the photohadronic model fit is better than the rescale one.
We also observe that the EBL-I (blue curve) correction to the photohadronic fit does not give a constant F γ,int , but a power-law with F γ,int ∝ E −0.3 γ and the intrinsic spectral index is α int 2.3.
To compare the predictions of different EBL models and the result of ref. [15] with P0.4 scaling (red curve), we have plotted these results in Fig. 6. We observe that all these models fit well to the observed data. For E γ < 300 GeV the EBL-F (black curve) predict slightly lower flux than the rest. Also for E γ > 2.7 TeV these predictions slightly differ from each other. Although the EBL-F (black dotted curve) and ref. [15]  The Bethe-Heitler (BH) pair production process pγ → pe + e − can also compete with the photohadronic process, but strongly depends on the angle between the photon and the emitted leptons. In the BH process, the electron-position pair can emit synchrotron photons.
It is shown that this process can produce a third peak in-between the synchrotron peak and the IC peak [49]. For this to happen, the protons and electrons energies have to be very high [50]. It the present scenario, the maximum energy of a proton and also an electron in the jet is ∼ 10 TeV. For a magnetic field of 0.16 G, an electron of energy 10 TeV will emit a synchrotron photon with maximum energy γ ∼ 0.8 MeV, which is an order of magnitude smaller than the lowest SSC photon energy γ = 8.3 MeV taking part in the photohadronic process to produce ∆-resonance. Leptons produced from pion and muon decay, pair creation and BH process will have energies less than 10 TeV and again the synchrotron photons from these leptons will have energies less than 0.8 MeV. The BH process may be important for very high energy protons and electrons, but here it does not play an important role and will not enhance the SSC photon flux in the energy range 8.3 M eV ≤ γ ≤ 41.5 M eV unless the magnetic field is high.   We also fit the corrected data with the EBL-I (blue curve) correction to the photohadronic model and compare with other fits in Fig. 8. A good fit is obtained for α = 2.8 and A γ = 6.6. Again, this new A γ corresponds to a 10% increase in the flux compared to the original fit. A power-law fit (red dotted curve) with I = I 0 E −Γ γ,T eV , where Γ = 2.97 and I 0 = 4.69 × 10 −13 erg cm −2 s −1 [41], is shown for comparison. Although the EBL-F and EBL-I fits to the observe data are similar, for E γ < 200 GeV and E γ > 2 TeV we can see a difference in their behavior. Also both these fits are different from the power-law fit.
We have also fitted the 2005 and 2006 data using the EBL-F (black curve), EBL-I (blue curve) and a power-law (red dotted curve) for comparison in Figs. 9 and 10 respectively. There is no way to directly measure the photon density in the inner compact region in the observed VHE ranges. Nonetheless, by assuming the scaling behavior of the photon densities for different energies in the inner and the outer jets as shown in Eq.(1), we relate the unknown densities of the inner region with the known one in the outer region. In the outer jet this range of γ lies in the low energy tail region of the SSC band and the sensitivity of the currently operating γ-ray detectors are not good enough to detect these photons.
The hidden jet has a size R f < R b = 7.5 × 10 15 cm and here we take R f ∼ 10 15 cm. Also by assuming the central black hole has a mass of M BH ∼ 10 9 M and using the constraint on the highest energy proton flux and the maximum luminosity of the inner jet to be smaller than the Eddington luminosity, the pγ optical depth satisfies 0.005 τ pγ 0.097. For our estimate we take τ pγ = 0.01 which gives the photon density in the inner jet region n γ,f 2 × 10 10 cm −3 .
The radio maps of this HBL show an one-sided, not well-collimated jet structure at a few kpc distance from the core [53].    used to constructed the synchrotron and SSC SED using one zone leptonic model [42,55] and the parameters for the best fit are given in Table- which is shown in Fig. 11.
In Fig. 12, we rescale the attenuation factor of EBL-F by F γ,int = 3.6×10 −12 erg cm −2 s −1 to fit the observed VHE data (red curve). It shows that the rescaling can't fit the VHE data above 1.5 TeV. However, a good fit to the VHE flare data is obtained for α = 2.2 and A γ = 39.0 in the photohadronic model with EBL-F (black curve ) correction and this corresponds to an intrinsic spectrum with α int = 1.81.
Again by multiplying F γ,int = 3.7 × 10 −12 erg cm −2 s −1 to the attenuation factor of EBL-I we can fit well the observed data below 1 TeV. However, above 1 TeV the fitted curve differs from the observed data as shown in Fig. 13 (red curve). In the same figure we have also shown the photohadronic model with the EBL-I correction fit (blue curve) to the observed data for α = 2.3 and A γ = 28.0. The photohadronic fit almost coincides with the rescaling of the attenuation factor and having α int = 1.91 which is softer than the one by EBL-F.
In Fig. 14, we have compared all these models and the fit of ref. [15]. So the photohadronic scenario gives milder intrinsic spectral index compared to the one by ref. [15] in their original fit.
In 1ES 1101-232, the BH process will produce leptons with energies below < 30 TeV and synchrotron emission from these electrons and positrons in 0.1 G magnetic field in the inner jet region will produce synchrotron photons below 3 MeV energy range. Thus, these photons will not contribute for the enhancement of the photon flux in the low energy tail region of the SSC band.
We have also calculated the photon density in the inner jet region. For this we have taken the central black hole mass M BH ∼ 10 9 M and the inner jet region has a size R f ∼ 10 15 cm. Using the constraint on the highest energy proton flux and the maximum luminosity of the inner jet to be smaller than the Eddington luminosity we get 0.001 τ pγ 0.29. We take τ pγ ∼ 0.01 which gives n γ,f 2 × 10 10 cm −3 in the inner jet region. al. [15] to derive strong upper limits on the EBL which was found to be consistent with the lower limits from the integrated light of resolved galaxies. While the intrinsic spectrum of H 2356-309 found to be flat, for 1ES 1101-232 it was hard α int ≤ 1.5. Here we have used the photohadronic model accompanied by two template EBL models EBL-F and EBL-I to fit the observed VHE data from these two HBLs and to predict their intrinsic spectra.
Although the blazar jet environment plays an important role in attenuating the VHE γ-rays, the absorption of it within the jet is neglected by assuming that the intrinsic flux takes care of this extraneous effect.
An important ingredient for the photohadronic scenario is the SSC flux Φ SSC . From the simultaneous multi-wavelength observations of these HBLs, one-zone leptonic models are constructed to fit the observed data well and the resulting parameters and Φ SSC are used here for the analysis of our results. In the photohadronic model the intrinsic flux The α int of the EBL-I is softer then the EBL-F which is again softer than the fit by ref. [15]. In future, for a better understanding of the EBL effect and the role played by the SSC