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 (CI B) using different CIB models. We show that a non-negligible absorption of gamma-rays due to the CIB could take place already in the low-energy (sub-T eV) domain of the spectrum of Mkn 501. This implies that the data of the lo w-energy threshold CAT telescope contain very important information about t he CIB at short wavelengths, 0.4 mu m less than or equal to lambda less tha n or equal to 3. mu m. The analysis of almost simultaneous spectroscopic me asurements 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 wi th typical "starlight spectrum" around 1 mu m should be between 5 and 35 nW m(-2) sr(-1) (99% CL), with most likely value around 20 nW m-2 sr(-1). Als o we argue that the CAT gamma-ray data alone allow rather robust upper limi ts on the GIB. lambda F-lambda less than or equal to 60 nW m(-2) sr(-1) at 1 mu m, taking into ac count that for any reasonable scenario of gamma-ray production the differential intrinsic spectrum of gamma-rays hardly could b e flatter than dN/dE proportional to E-1. This estimate agrees, within stat istical and systematic uncertainties, with recent reports about tentative d etections of the CIB at 2.2 and 3.5 mu m by the Diffuse Infrared Background Experiment (DIRBE), as well as with the measurements of the background rad iation at optical wavelengths from absolute photometry. The high flux of CI B at I few mu m wavelengths implies a significant distortion of the shape o f the initial (source) spectrum of gamma-rays from Mkn 501 at sub-TeV energ ies. The "reconstructed" intrinsic gamma-ray spectrum shows a distinct peak in the Spectral Energy Distribution (SED) around 2 TeV with a flux by a fa ctor of 3 higher than the measured flux. The energy spectrum of gamma radia tion from both sides of the peak has power-law behavior with photon index a lpha similar or equal to 1.5 below 3 TeV, and alpha similar or equal to 2.5 above 2 TeV. This agrees with predictions of SSC model. We also discuss th e impact of the intergalactic absorption effect in derivation of the SSC pa rameters for the jet in Mkn 501.