A Simple Analytic Treatment of the Intergalactic Absorption Effect in Blazar  -ray Spectra

1. A Simple Analytic Treatment of the Intergalactic Absorption Effect in Blazar -ray Spectra Floyd W. Stecker NASA/GSFC & Sean T. Scully James Madison University • Blazar Spectral Indices • Table 1 gives a list of HBLs which have been detected at TeV energies and for which spectral indices (O) have been measured. Also given are the observed redshifts of these sources and the source spectral indices (S) derived from the baseline and fast evolution models using our analytic expressions for  (z) . • Introduction • Stecker, Malkan, & Scully (2006) have made a detailed model of the intergalactic photon density as a function of energy (0.003 eV - 13.6 eV) and redshift (0 < z < 6). • They then used this to calculate the optical depth of the universe to -rays in the energy range of 4 GeV To 100 TeV for 0 < z < 5. • (E, z) can be approximated by logarithmic functions which can naturally be used to predict power-law steepenings in assumed source spectra of the form E-S to observed spectra of the form E-O where O = S +  and  is is determined to be a function of z. • This is particularly useful as it covers a large portion of the operating energy range of air Cerenkov telescope arrays such as H.E.S.S. and MAGIC. • We deabsorb the spectra of the 7 TeV blazars which have been observed in this fashion found in the literature. Abstract We have derived a useful analytic approximation for determining the effect of intergalactic absorption on the spectra of -ray sources in the energy range 0.2 < E < 2 TeV and the redshift range ~0.05 < z < ~0.4. In these ranges, the form of the absorption coefficient (E ) is close to logarithmic. The effect of this energy dependence is to steepen the intrinsic source spectrum such that a source with an approximate power-law spectral index S is converted to one with an observed spectral index O = S +  in the energy range 0.2 - 2 TeV,  (z) is a linear function of z in the redshift range 0.04 - 0.4. We apply this treatment to the spectra of 7 TeV blazars. Table 1 Figure 2 • We show in figure 4 the utility of this approximation by assuming an E-2 source spectrum for PKS 2155 and applying our absorption formula which yields an observed spectrum of O = 3.3. • Optical Depth Fits • Figure 1 shows the optical depth of the universe to  -rays from interactions with photons of the intergalactic background light and CMB for -rays having energies up to 100 TeV as calculated in Stecker, Malkan, & Scully (2006). They model the intergalactic background light (IBL) using recent Spitzer and Hubble deep survey results. The red curves represents their “baseline” case which is based on more conservative estimates and the blue curves represent their “fast evolution” case. Figure 3 • Postulating a source spectrum approximated by a power law over this limited energy range of the form: Figure 1 gives an observed spectrum over the limited energy range of one decade (0.2 - 2 TeV): Figure 2 • Conclusion • We have derived a useful analytic approximation for determining the effect of intergalactic absorption on the spectra of -ray sources in the energy range 0.2 TeV < E < 2 TeV. • This analytic approximation will be very useful for characterizing source blazar spectra from spectra observed by MAGIC, H.E.S.S. and the upcoming VERITAS telescope array. • Figure 3 shows the fits obtained for the linear functions A + Bz and C + Dz again shown for the fast evolution case. The baseline fits appear similar. Figure 3 These results are then fit to a form for (E, z) which is assumed to be logarithmic in E for 0.2 TeV < E < 2 TeV and has a linear dependence on z over the range 0.04 < z < 0.4. We choose the form: References Aharonian, F. et al. 2005a, A & A 430, 865 Aharonian, F. et al. 2005b, A & A 436, L17 Aharonian, F. et al. 2006a, e-print astro-ph/ 0607569 Aharonian, F. et al. 2006b, Nature 440, 1018 Albert, J. et al. 2006a, ApJ 642, L119 Albert, J. et al. 2006b, e-print astro-ph/ 0606161 Stecker, F. W., Malkan, M. A. & Scully, S. T. 2006, ApJ 648, (Sept. 10 Issue), e-print astro-ph/ 0510449 Stecker, F. W. & Scully, S.T. 2006, e-print astro-ph/0608110 • Figure 2 shows the linear fits to the Stecker et al. optical depths for their fast evolution case in the energy range 0.2 TeV to 2.0 TeV for redshifts of 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40. The baseline case looks similar.