3.7. CIB Limits from TeV -Ray Observations

Indirect evidence for the brightness of the CIB comes from observations of TeV -rays from blazars. A beam of high-energy photons can be strongly attenuated by e+e- pair production through collisions with low-energy photons ( Nikishov 1962, Jelley 1966, Gould & Schréder 1966). The + b e+ + e- interaction cross section of a -ray photon of energy E with isotropically distributed background photons b of energy b is sharply peaked at ~ 1.5 × 10-25 cm2 (Nikishov 1962). This peak occurs at energies for which the product Eb 4 (me c2)2 1 MeV2, or b(µm) 1.24 E (TeV) (Guy et al. 2000). Hence, infrared photons are particularly effective at attenuating -rays of energies ~ 1-100 TeV.

If the production of second-generation -ray photons appearing from the direction of the source can be neglected, then the observed -ray flux at energy E from the source, Jobs(E), is simply related to the intrinsic source flux, J0(E), by

 (1)

where is the optical depth for - interaction. For a given E, the optical depth is proportional to the number density of background photons. Therefore, very high energy -ray sources can, in principle, be used to probe the intensity of the CIB if they happen to be relatively nearby (Stecker et al. 1992). Determination of the CIB from -ray observations requires: (a) knowledge of the intrinsic spectrum of the -ray source, (b) knowledge of the spectral shape of the CIB, and (c) the assumption that the attenuation takes place in the intergalactic medium by the CIB instead of in the source itself or its immediate vicinity (Böttcher & Dermer 1995, Protheroe & Biermann 1997, Bednarek & Protheroe 1999).

The probing of the CIB with very high energy -ray photons has recently become practical with the development of imaging atmospheric Cerenkov telescopes, such as the Whipple Observatory, the High Energy Gamma-ray Array (HEGRA), and the Cerenkov Array at Themis (CAT). The first extragalactic -ray source detected at TeV energies was the blazar Markarian (Mrk) 421, located at redshift z 0.031 (Punch et al. 1992). Two more sources, Mrk 501 and 1ES2344 + 514, at respective redshifts z 0.034 and z 0.044, have been detected since, but the latter source was only detected once, with marginal significance. Catanese & Weekes (1999) have reviewed the -ray observatories and observations (see also McConnell & Ryan 2000). Since all of the detected extragalactic TeV -ray sources are located at very low redshift, one can safely neglect evolutionary effects in the CIB, which may be important in calculating the opacity to more distant sources (Section 4.4).

In the first applications of this technique, Stecker & De Jager (1993), De Jager et al. (1994), Dwek & Slavin (1994) combined GeV observations of Mrk 421 obtained by the Energetic Gamma-ray Experiment Telescope on board the Compton Gamma-ray Observatory (Lin et al. 1992) with TeV observations obtained by the Whipple Observatory (Punch et al. 1992), to infer the intrinsic energy distribution of the source and to search for evidence of a high-energy cutoff in its spectrum due to attenuation. Background limits derived from their analyses are shown in Figure 4. The problems of ascertaining reliable evidence for intergalactic attenuation were illustrated by Biller et al. (1995), who showed two equally acceptable fits to the spectrum of Mrk 421, the first requiring no attenuation, the second requiring significant CIB attenuation. Taking into account the uncertainties in the extrapolation of the source spectrum from GeV to TeV energies and in the spectral shape of the CIB, Biller et al. (1995) derived a conservative upper limit of ~ 250 h nW m-2 sr-1 for the CIB at 10 µm.

 Figure 4. Cosmic infrared background limits implied by TeV -ray observations. (Dashed lines) Limits derived from Mrk 421 data: DJSS, De Jager et al. (1994); DwSl, Dwek & Slavin (1994); B98, Biller et al. (1998). (Solid lines) Limits derived from Mrk 501 data: StF, Stanev & Franceschini (1998); Funk, Funk et al. (1998); Guy, Guy et al. (2000). (Solid square) Limit is from Mrk 501 (Mannheim 1998). All limits were scaled to a Hubble constant of H0 = 100 km s-1 Mpc-1 ( I H0). (Shaded region) The extragalactic background light limits defined by the data in Figure 5.

Stanev & Franceschini (1998) were the first to apply the attenuation analysis to Mrk 501, using high-quality TeV -ray data obtained by the HEGRA experiment between March and October 1997, when the source was unusually bright. The observed spectrum was fit by varying the spectral index of the -ray source spectrum and the normalization of the CIB spectrum, which was taken to be the model spectrum of Franceschini et al. (1991). The best fit to the observations was consistent with no absorption. A less model-dependent result was obtained by adopting the flattest allowable -ray source spectrum and a flat I spectrum within the CIB wavelength bin that contributes most to the attenuation at a given -ray energy. This approach yielded CIB upper limits, the most restrictive being 7 h nW m-2 sr-1 in the 4 to 25 µm wavelength range.

A similar approach was adopted by Funk et al. (1998), who fitted the Mrk 501 spectrum by an unattenuated power law up to 10 TeV, which suggests that (10 TeV) < 1. By assuming a spectral shape for the CIB based on the models of MacMinn & Primack (1996), they derived an upper limit of 4 h nW m-2 sr-1 at ~ 40 µm, consistent with previous estimates. Biller et al. (1998) derived new CIB upper limits using minimal assumptions on the source or the CIB spectra. Approximating the CIB by a series of flat I spectra in discrete wavelength intervals, they calculated the -ray opacity at various -ray energies. Constraining the overall index of the differential photon spectrum of the source to be between 2.3 and 2.8, they derived an upper limit of 16 h nW m-2 sr-1 in the 4 to 15 µm interval. Mannheim (1998) derived an upper limit on the maximum allowed attenuation assuming a power law TeV -ray spectrum for Mrk 501, which implied a CIB limit of (3-5) h nW m-2 sr-1 at 25 µm.

Recent simultaneous multiwavelength observations of Mrk 501 and Mrk 421 have provided new constraints on the intrinsic source spectrum. The observed double-humped nature of the spectra of Mrk 421 and 501, with peaks at X-ray (~ 10 keV) and -ray (~ 1 TeV) energies, and the rapid, correlated variations of their X-ray and TeV spectra (Catanese & Weekes 1999), are most readily explained in the framework of the homogeneous synchrotron self-Compton (SSC) model. The SSC model and other competing models are described by Dermer et al. (1997), Sikora (1997), McConnell & Ryan (2000). In the SSC model, the same electrons that produce the synchrotron radiation also upscatter the synchrotron photons in the jet to TeV energies by the inverse Compton process. The model produces a double-peaked spectral energy distribution with a synchrotron (S) peak in the X-ray regime and an inverse Compton (IC) peak in the ~ 0.1-1 TeV energy regime.

Guy et al. (2000) pointed out that the position and intensity of the IC peak in Mrk 501 is affected by the -ray interactions with the optical and near-infrared photons of the EBL. Adopting the spectral shape of the EBL predicted by Primack et al. (1999) (model LCDM; see Section 5.2.3), they calculated the TeV opacity and reconstructed the source spectrum for various scaling factors for the EBL intensity. Making the general assumption that the flux of the source, F, should not rise between 4 and 17 TeV, and that its spectral slope at 600 GeV should be similar to that of the X-ray spectrum at 1 keV, they found that the scaling factor must be less than about 2.5, setting CIB upper limits (1) of 58 h, ~ 6 h, and ~ 35 h nW m-2 sr-1 at 1, 20, and 80 µm, respectively.

Other studies have used the spectral observations, such as the locations of the S and IC peaks, their variability, and the hardening of the synchrotron spectrum, to constrain the parameter space of the SSC model. For example, Konopelko et al. (1999) argue that the intrinsic source spectrum of Mrk 501 must be flat in F in order to comply with the observational constraints and therefore see the observed hardening of the spectrum with energy as evidence for intergalactic absorption. Adopting the Malkan & Stecker (1998) model for the EBL with the addition of a stellar emission component (the details of which have not been published), they derived an essentially flat spectrum from 300 GeV to 20 TeV. However, these results are at variance with those derived by Guy et al. (2000), presumably because of differences in the stellar emission models that produce the ~ 1 TeV IC peak in the source spectrum. Sambruna et al. (2000) succeeded in modeling the observed spectrum of Mrk 501 with the SSC model. Such a fit would imply no evidence for any intergalactic attenuation. However, the model overpredicts the 10 TeV flux by a factor of 2.5, a discrepancy regarded by them as only marginal evidence for intergalactic attenuation.

New upper limits on the CIB were derived by Dwek (2001: Appendix) and Renault et al. (2001), who explored the range of "allowable" CIB spectra with only the minimal assumption that the intrinsic -ray spectrum of Mrk 501 be nonincreasing at energies above ~ 4 TeV. Dwek reported preliminary upper limits of 7 h and 14 h nW m-2 sr-1 in the 6 to 30 µm interval and at 60 µm, respectively. Renault et al. found an upper limit of 7 h nW m-2 sr-1 in the 5 to 15 µm interval.

Figure 4 summarizes representative upper limits on the CIB determined from TeV -ray observations. Dashed and solid lines are limits determined from observations of Mrk 421 and 501, respectively. Limits based on Mrk 501 are seen to be generally more restrictive. The lowest limits are in the 5 to 30 µm range since the observed ~ 1 to 15 TeV -rays interact most strongly with infrared photons in this wavelength range. The shaded region in Figure 4 is provided to allow comparison with other EBL measurements (see Section 3.10).

The determinations of CIB intensities from -ray attenuation studies are somewhat model dependent and are further uncertain because of the possibility that some attenuation may occur within the -ray source. However, even with the current limited data and uncertainties, the -ray observations are providing valuable constraints on the CIB in the difficult 5 to 60 µm range.