  The energy spectrum of the Blazar type galaxy Markarian 501 (Mrk 501) as
measured by the High-Energy-Gamma-Ray Astronomy (HEGRA) air Cerenkov telescopes
extends beyond 16 TeV and constitutes the most energetic photons observed from
an extragalactic object. A fraction of the emitted spectrum is possibly
absorbed in interactions with low energy photons of the diffuse extragalactic
infrared radiation, which in turn offers the unique possibility to measure the
diffuse infrared radiation density by TeV spectroscopy. The upper limit on the
density of the extragalactic infrared radiation derived from the TeV
observations imposes constraints on models of galaxy formation and stellar
evolution. One of the recently published ideas to overcome severe absorption of
TeV photons is based upon the assumption that sources like Mrk 501 could
produce Bose-Einstein condensates of coherent photons. The condensates would
have a higher survival probability during the transport in the diffuse
radiation field and could mimic TeV air shower events. The powerful
stereoscopic technique of the HEGRA air Cerenkov telescopes allows to test this
hypothesis by reconstructing the penetration depths of TeV air shower events:
Air showers initiated by Bose-Einstein condensates are expected to reach the
maximum of the shower development in the atmosphere earlier than single photon
events. By comparing the energy-dependent penetration depths of TeV photons
from Mrk 501 with those from the TeV standard-candle Crab Nebula and simulated
air shower events, we can reject the hypothesis that TeV photons from Mrk 501
are pure Bose-Einstein condensates.
