Constraints on the cosmic infra - red background based on BeppoSAX and CAT spectra of Markarian 501

The TeV and X-ray data obtained by the imaging Cherenkov telescope CAT and X-ray satellite BeppoSAX during the remarkable flare of Mkn 501 in April 16, 1997 are used to constrain the flux of the Cosmic Infrared Background (CIB) using different CIB models. We show that a non-negligible absorption of γ-rays due to the CIB could take place already in the low-energy (sub-TeV) domain of the spectrum of Mkn 501. This implies that the data of the low-energy threshold CAT telescope contain very important information about the CIB at short wavelengths, 0.4 µm≤ λ ≤ 3. µm. The analysis of almost simultaneous spectroscopic measurements of Mkn 501 in a high state by CAT and BeppoSAX in the framework of the standard homogeneous Synchrotron-Self-Compton (SSC) framework model leads to the conclusion that the density of the near-infrared background with typical " starlight spectrum " around 1 µm should be between 5 and 35 nW m −2 sr −1 (99% CL), with most likely value around 20 nW m −2 sr −1. Also we argue that the CAT γ-ray data alone allow rather robust upper limits on the CIB, λF λ ≤ 60 nW m −2 sr −1 at 1 µm, taking into account that for any reasonable scenario of γ-ray production the differential intrinsic spectrum of γ-rays hardly could be flatter than dN/dE ∝ E −1. This estimate agrees, within statistical and systematic uncertainties, with recent reports about tentative detections of the CIB at 2.2 and 3.5 µm by the Diffuse Infrared Background Experiment (DIRBE), as well as with the measurements of the background radiation at optical wavelengths from absolute photometry. The high flux of CIB at ≤ few µm wavelengths implies a significant distortion of the shape of the initial (source) spectrum of γ-rays from Mkn 501 at sub-TeV energies. The " reconstructed " intrinsic γ-ray spectrum shows a distinct peak in the Spectral Energy Distribution (SED) around 2 TeV with a flux by a factor of 3 higher than the measured flux. The energy spectrum of gamma radiation from both sides of the peak has power-law behavior with photon index α 1.5 below 2 TeV, and α 2.5 above 2 TeV. This agrees with predictions of SSC model. We also discuss the impact of the intergalactic absorption effect in derivation of the SSC parameters for the jet in Mkn 501.