Astroparticle Physics

6.3 Gamma Astronomy 115v = c n = 299 710 637 m/s (6.75)photoncorresponds to a kinetic electron energy ofE kin = E total − m 0 c 2 = γm 0 c 2 − m 0 c 2()= (γ − 1)m 0 c 2 1= √1 − v 2 /c − 1 m 0 c 22()1= √ − 1 m 0 c 2 (6.76)1 − 1/n 2()n= √n 2 − 1 − 1 m 0 c 2 ≈ 21.36 MeV .The production of Cherenkov radiation in an optical shockwave (Fig. 6.41) is the optical analogue to sound shockwaves which are created when aeroplanes exceed the velocityof sound.altitude [km]2520151050-5 0 +5lateral width [km]Fig. 6.40Monte Carlo simulation of anelectromagnetic shower in theatmosphere initiated by a photon ofenergy 10 14 eV. All secondarieswith energies E ≥ 3 MeV areshown {14}Fig. 6.41Emission of Cherenkov radiation inan optical shock wave by particlestraversing a medium of refractiveindex n with a velocity exceedingthe velocity of light in that medium(v >c/n)In this way energetic primary γ quanta can be recordedat ground level via the produced Cherenkov light eventhough the electromagnetic shower does not reach sea level.The Cherenkov light is emitted under a characteristic angleof( ) 1θ C = arccos . (6.77)nβFor electrons in the multi-GeV range the opening angle ofthe Cherenkov cone is only 1.4 ◦ . 55 Actually the Cherenkov angle is somewhat smaller (≈ 1 ◦ ),since the shower particles are produced at large altitudes wherethe density of air and thereby also the index of refraction issmaller.Cherenkov angle