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

IntroductionIntroduction

• Stecker, Malkan, & Scully (2006) have made a detailed model of the 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 intergalactic photon density as a function of energy (0.003 eV - 13.6 eV) and redshift (0 < redshift (0 < zz < 6). < 6).

• They then used this to calculate the optical depth of the universe to They then used this to calculate the optical depth of the universe to -rays -rays in the energy range of 4 GeV To 100 TeV for 0 < in the energy range of 4 GeV To 100 TeV for 0 < zz < 5. < 5.

• (E, (E, zz) can be approximated by logarithmic functions which can naturally ) can be approximated by logarithmic functions which can naturally be used to predict power-law steepenings in assumed source spectra of the be used to predict power-law steepenings in assumed source spectra of the form Eform E--SS to observed spectra of the form E to observed spectra of the form E--OO where where OO = = SS + + and and is is

is determined to be a function of is determined to be a function of zz..

• This is particularly useful as it covers a large portion of the operating 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 energy range of air Cerenkov telescope arrays such as H.E.S.S. and MAGIC.MAGIC.

•We deabsorb the spectra of the 7 TeV blazars which have been observed We deabsorb the spectra of the 7 TeV blazars which have been observed in this fashion found in the literature. in this fashion found in the literature.

AbstractWe 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.

Floyd W. SteckerFloyd W. SteckerNASA/GSFCNASA/GSFC

&&Sean T. ScullySean T. Scully

James Madison UniversityJames Madison University

Optical Depth FitsOptical Depth Fits

• Figure 1 shows the optical depth of the universe to Figure 1 shows the optical depth of the universe to -rays from -rays from interactions with photons of the intergalactic background light and CMB for interactions with photons of the intergalactic background light and CMB for -rays having energies up to 100 TeV as calculated in Stecker, Malkan, & -rays having energies up to 100 TeV as calculated in Stecker, Malkan, & Scully (2006). They model the intergalactic background light (IBL) using Scully (2006). They model the intergalactic background light (IBL) using recent Spitzer and Hubble deep survey results. The red curves represents recent Spitzer and Hubble deep survey results. The red curves represents their “baseline” case which is based on more conservative estimates and the their “baseline” case which is based on more conservative estimates and the blue curves represent their “fast evolution” case.blue curves represent their “fast evolution” case.

• Figure 3 shows the fits obtained for the linear functions Figure 3 shows the fits obtained for the linear functions A + BzA + Bz and and C + DzC + Dz again again shown for the fast evolution case. The baseline fits appear similar.shown for the fast evolution case. The baseline fits appear similar.

ConclusionConclusion

• We have derived a useful analytic approximation for determining the effect of We have derived a useful analytic approximation for determining the effect of intergalactic absorption on the spectra of intergalactic absorption on the spectra of -ray sources in the energy range 0.2 -ray sources in the energy range 0.2 TeV < ETeV < E < 2 TeV. < 2 TeV.

• This analytic approximation will be very useful for characterizing source blazar 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 spectra from spectra observed by MAGIC, H.E.S.S. and the upcoming VERITAS telescope array.telescope array.

• Postulating a source spectrum approximated by a power law over this limited Postulating a source spectrum approximated by a power law over this limited energy range of the form:energy range of the form:

ReferencesReferences

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/ 0510449Stecker, F. W. & Scully, S.T. 2006, e-print astro-ph/0608110

Figure 2Figure 2

Figure 1Figure 1

These results are then fit to a form for These results are then fit to a form for (E, z) which is assumed to be (E, z) which is assumed to be logarithmic in Elogarithmic in E for 0.2 TeV < E for 0.2 TeV < E < 2 TeV and has a linear dependence on < 2 TeV and has a linear dependence on zz

over the range 0.04 < z < 0.4. We choose the form:over the range 0.04 < z < 0.4. We choose the form:

(E ,z) =(A+Bz) + (C +Dz)lnE

ΦO =Ke−(A+Bz)E−O

O =S + (z)

where =C +Dz

ΦS (E ) =KE

−S

gives an observed spectrum over the limited energy range of one decade (0.2 - 2 gives an observed spectrum over the limited energy range of one decade (0.2 - 2 TeV):TeV):

• Figure 2 shows the linear fits to the Stecker Figure 2 shows the linear fits to the Stecker et al.et al. optical depths for their optical depths for their fast evolution case in the energy range 0.2 TeV to 2.0 TeV for redshifts of 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 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40. The baseline case looks similar.similar.

Figure 2Figure 2

Table 1Table 1

Blazar Spectral IndicesBlazar Spectral Indices

• Table 1 gives a list of HBLs which have been detected at TeV energies and for Table 1 gives a list of HBLs which have been detected at TeV energies and for which spectral indices (which spectral indices (OO) have been measured. Also given are the observed ) have been measured. Also given are the observed

redshifts of these sources and the source spectral indices (redshifts of these sources and the source spectral indices (SS) derived from the ) derived from the

baseline and fast evolution models using our analytic expressions for baseline and fast evolution models using our analytic expressions for (z) . (z) .

SourceSource zz OO SS (Baseline) (Baseline) SS (Fast Evol) (Fast Evol) ReferenceReference

Mkn 180Mkn 180 0.0450.045 3.33.3 3.03.0 2.92.9 Albert Albert et al. 2006bet al. 2006b

PKS 2005-489PKS 2005-489 0.0710.071 4.04.0 3.53.5 3.43.4 Aharonian Aharonian et al. 2005bet al. 2005b

PKS 2155-304PKS 2155-304 0.1170.117 3.33.3 2.42.4 2.22.2 Aharonian Aharonian et al. 2005aet al. 2005a

H 2356-309H 2356-309 0.1650.165 3.13.1 1.91.9 1.51.5 Aharonian Aharonian et al. 2006aet al. 2006a

1ES 1218+301ES 1218+30 0.1820.182 3.03.0 1.61.6 1.21.2 Albert Albert et al. 2006aet al. 2006a1Es 1101-2321Es 1101-232 0.1860.186 2.92.9 1.51.5 1.01.0 Aharonian Aharonian et al. 2006bet al. 2006b

PG 1553+113PG 1553+113 0.3600.360 4.24.2 1.41.4 0.50.5 Albert Albert et al. 2006bet al. 2006b

• We show in figure 4 the utility of this approximation by assuming an EWe show in figure 4 the utility of this approximation by assuming an E -2-2 source source spectrum for PKS 2155 and applying our absorption formula which yields an spectrum for PKS 2155 and applying our absorption formula which yields an observed spectrum of observed spectrum of O O = 3.3.= 3.3.

Figure 3Figure 3

Figure 3Figure 3