Simultaneous constraints on the spectrum of the extragalactic background light and the intrinsic TeV spectra of Markarian 421, Markarian 501, and H1426+428

Very high energy (similar toTeV) gamma-rays from blazars are attenuated by photons from the extragalactic background light (EBL). Observations of blazars can therefore provide an ideal opportunity for determining the EBL intensity if their intrinsic spectrum is known. Conversely, knowledge of the EBL intensity can be used to determine the intrinsic blazar spectrum. Unfortunately, neither the EBL intensity nor the intrinsic blazar spectrum is known with high enough precision to accurately derive one quantity from the other. In this paper we use the most recent data on the EBL to construct 12 different realizations representing all possible permutations between EBL limits and the detections in the different wavelength regions. These realizations explore a significantly larger range of allowable EBL spectra than any previous studies. We show that these realizations can be used to explore the effects of the EBL on the inferred spectra of blazars. Concentrating on the two relatively nearby (z approximate to 0.03) blazars Mrk 421 and 501, we derive their intrinsic spectra and peak gamma-ray energies for the different EBL realizations. Some EBL spectra give rise to "unphysical" intrinsic blazar spectra, characterized by an exponential rise at high TeV energies. We use the F-test to show that some of these exponential rises are statistically insignificant. Consequently, statements regarding the existence of an "IR background-TeV gamma-ray crisis" are unfounded on the basis of our present knowledge of the EBL. EBL spectra that do give rise to unphysical blazar spectra are regarded as invalid realizations of the EBL. Those that do not thus define new constraints on the EBL spectrum and are used to derive new limits on the intensity and the peak gamma-ray energy of these two blazars. In particular, we derive an upper limit of similar to15 nW m(-2) sr(-1) on the 60 mum EBL intensity and find the peak energies of the Mrk 421 and Mrk 501 sources to be very similar, between 0.5-1.2 and 0.8-2.5 TeV, respectively. We also show that the intrinsic spectrum of Mrk 421 during a period of intense flaring activity has a peak energy that seems to shift to higher energies at higher flux states. For the most distant blazar H1426+428 (z = 0.129), most EBL realizations give rise to spectra that peak between similar to1 and 5 TeV, with some suggesting peaks below 400 GeV and above similar to10 TeV. These results provide important constraints on the different particle acceleration mechanisms and the generation of the gamma-ray emission. Finally, we also show that uncertainties in the absolute calibration of the gamma-ray energies with atmospheric Cerenkov telescopes have an important impact on the intrinsic blazar spectra. These systematic uncertainties will be improved with the next generations of telescopes that will also cover a wider range of gamma-ray energies, providing further insights into the intrinsic spectrum of TeV blazars.