A Simple Analytic Treatment of the Intergalactic Absorption Effect in Blazar -ray Spectra
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A Simple Analytic Treatment of the A Simple Analytic Treatment of the Intergalactic Absorption Effect in Intergalactic Absorption Effect in Blazar Blazar -ray Spectra -ray Spectra Introduction Introduction • Stecker, Malkan, & Scully (2006) have made a detailed Stecker, Malkan, & Scully (2006) have made a detailed model of the intergalactic photon density as a function model of the intergalactic photon density as a function of energy (0.003 eV - 13.6 eV) and redshift (0 < of energy (0.003 eV - 13.6 eV) and redshift (0 < z z < 6). < 6). • They then used this to calculate the optical depth of They then used this to calculate the optical depth of the universe to the universe to -rays in the energy range of 4 GeV To -rays in the energy range of 4 GeV To 100 TeV for 0 < 100 TeV for 0 < z z < 5. < 5. • (E, (E, z z ) can be approximated by logarithmic functions ) can be approximated by logarithmic functions which can naturally be used to predict power-law which can naturally be used to predict power-law steepenings in assumed source spectra of the form E steepenings in assumed source spectra of the form E - S to to observed spectra of the form E observed spectra of the form E - O where where O = = S + + and and is is determined to be a function of is is determined to be a function of z z . . • This is particularly useful as it covers a large This is particularly useful as it covers a large portion of the operating energy range of air Cerenkov portion of the operating energy range of air Cerenkov telescope arrays such as H.E.S.S. and MAGIC. telescope arrays such as H.E.S.S. and MAGIC. • We deabsorb the spectra of the 7 TeV blazars which have We deabsorb the spectra of the 7 TeV blazars which have been observed in this fashion found in the literature. 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. Floyd W. Stecker Floyd W. Stecker NASA/GSFC NASA/GSFC & & Sean T. Scully Sean T. Scully James Madison University James Madison University Optical Depth Fits Optical Depth Fits • Figure 1 shows the optical depth of the universe to Figure 1 shows the optical depth of the universe to -rays from interactions with photons of the -rays from interactions with photons of the intergalactic background light and CMB for intergalactic background light and CMB for -rays having -rays having energies up to 100 TeV as calculated in Stecker, Malkan, energies up to 100 TeV as calculated in Stecker, Malkan, & Scully (2006). They model the intergalactic & Scully (2006). They model the intergalactic background light (IBL) using recent Spitzer and Hubble background light (IBL) using recent Spitzer and Hubble deep survey results. The red curves represents their deep survey results. The red curves represents their “baseline” case which is based on more conservative “baseline” case which is based on more conservative estimates and the blue curves represent their “fast estimates and the blue curves represent their “fast evolution” case. evolution” case. • Figure 3 shows the fits obtained for the linear functions Figure 3 shows the fits obtained for the linear functions A A + Bz + Bz and and C + Dz C + Dz again shown for the fast evolution case. The again shown for the fast evolution case. The baseline fits appear similar. baseline fits appear similar. Conclusion Conclusion • We have derived a useful analytic approximation for We have derived a useful analytic approximation for determining the effect of intergalactic absorption on the determining the effect of intergalactic absorption on the spectra of spectra of -ray sources in the energy range 0.2 TeV < E -ray sources in the energy range 0.2 TeV < E < < 2 TeV. 2 TeV. • This analytic approximation will be very useful for This analytic approximation will be very useful for characterizing source blazar spectra from spectra observed by characterizing source blazar spectra from spectra observed by MAGIC, H.E.S.S. and the upcoming VERITAS telescope array. MAGIC, H.E.S.S. and the upcoming VERITAS telescope array. • Postulating a source spectrum approximated by a power law Postulating a source spectrum approximated by a power law over this limited energy range of the form: over this limited energy range of the form: References 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 Figure 2 Figure 1 Figure 1 These results are then fit to a form for These results are then fit to a form for (E, z) which is (E, z) which is assumed to be logarithmic in E assumed to be logarithmic in E for 0.2 TeV < E for 0.2 TeV < E < 2 TeV < 2 TeV and has a linear dependence on and has a linear dependence on z z over the range 0.04 < z < over the range 0.04 < z < 0.4. We choose the form: 0.4. We choose the form: ( E , z ) =( A + Bz )+( C + z )ln E Φ O =Ke −( A + Bz ) E − O O = S + ( z ) where = C + z Φ S ( E )=KE − S gives an observed spectrum over the limited energy range of gives an observed spectrum over the limited energy range of one decade (0.2 - 2 TeV): one decade (0.2 - 2 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 fast evolution case in the optical depths for their fast evolution case in the energy range 0.2 TeV to 2.0 TeV for redshifts of 0.05, 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 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40. The baseline case looks similar. baseline case looks similar. Figure 2 Figure 2 Table 1 Table 1 Blazar Spectral Indices Blazar Spectral Indices • Table 1 gives a list of HBLs which have been detected at Table 1 gives a list of HBLs which have been detected at TeV energies and for which spectral indices ( TeV energies and for which spectral indices ( O ) have been ) have been measured. Also given are the observed redshifts of these measured. Also given are the observed redshifts of these sources and the source spectral indices ( sources and the source spectral indices ( S ) derived from ) derived from the baseline and fast evolution models using our analytic the baseline and fast evolution models using our analytic expressions for expressions for (z) . (z) . Source Source z z O S (Baseline) (Baseline) S (Fast Evol) (Fast Evol) Reference Reference Mkn 180 Mkn 180 0.045 0.045 3.3 3.3 3.0 3.0 2.9 2.9 Albert Albert et al. 2006b et al. 2006b PKS 2005-489 PKS 2005-489 0.071 0.071 4.0 4.0 3.5 3.5 3.4 3.4 Aharonian Aharonian et al. 2005b et al. 2005b PKS 2155-304 PKS 2155-304 0.117 0.117 3.3 3.3 2.4 2.4 2.2 2.2 Aharonian Aharonian et al. 2005a et al. 2005a H 2356-309 H 2356-309 0.165 0.165 3.1 3.1 1.9 1.9 1.5 1.5 Aharonian Aharonian et al. 2006a et al. 2006a 1ES 1218+30 1ES 1218+30 0.182 0.182 3.0 3.0 1.6 1.6 1.2 1.2 Albert Albert et al. 2006a et al. 2006a 1Es 1101-232 1Es 1101-232 0.186 0.186 2.9 2.9 1.5 1.5 1.0 1.0 Aharonian Aharonian et al. 2006b et al. 2006b PG 1553+113 PG 1553+113 0.360 0.360 4.2 4.2 1.4 1.4 0.5 0.5 Albert Albert et al. 2006b et al. 2006b • We show in figure 4 the utility of this approximation by We show in figure 4 the utility of this approximation by assuming an E assuming an E -2 -2 source spectrum for PKS 2155 and applying our source spectrum for PKS 2155 and applying our absorption formula which yields an observed spectrum of absorption formula which yields an observed spectrum of O O = = 3.3. 3.3. Figure 3 Figure 3 Figure 3 Figure 3
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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 - PowerPoint PPT Presentation
Transcript of A Simple Analytic Treatment of the Intergalactic Absorption Effect in Blazar -ray Spectra
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
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