Astroparticle Physics

6.2 Neutrino Astronomy 107The setup of a prototype detector in the antarctic ice isshown in Fig. 6.29. In a first installation of photomultiplierstrings at depths of 810 up to 1000 meters it turned out thatthe ice still contained too many bubbles. Only for depthsbelow 1500 m the pressure is sufficiently large (≥ 150 bar)that the bubbles disappear yielding an excellent transparencywith absorption lengths of about 300 m. The working principleof the detector could be demonstrated by measuringatmospheric muons and muon neutrinos. For a ‘real’ neutrinotelescope, however, the present AMANDA detectoris still too small. To be able to record the fluxes of extragalacticneutrinos, a volume of 1 km 3 is needed. The originalAMANDA detector is continuously upgraded so thatfinally such a big volume will be instrumented (IceCube).Figure 6.30 shows a muon event in AMANDA. The followingexample will confirm that volumes of this size are reallyrequired.It is considered realistic that a point source in our galaxyproduces a neutrino spectrum according tointeraction ratein a ν detectordN= 2 × 10 −11 100dE ν Eν 2 [TeV2 ] cm−2 s −1 TeV −1 . (6.52) 60 mice surface0mThis leads to an integral flux of neutrinos ofΦ ν (E ν > 100 TeV) = 2 × 10 −11 cm −2 s −1 (6.53)(see also Fig. 6.23 for extragalactic sources).The interaction cross section of high-energy neutrinoswas measured at accelerators to beσ(ν µ N) = 6.7 × 10 −39 E ν [GeV] cm 2 /nucleon . (6.54)190 m380 m810 m1000 m1520 mFor 100 TeV neutrinos one would arrive at a cross sectionof 6.7 × 10 −34 cm 2 /nucleon. For a target thickness of onekilometer an interaction probability W per neutrino ofW = N A σdϱ= 4 × 10 −5 (6.55)is obtained (d = 1km= 10 5 cm, ϱ(ice) ≈ 1g/cm 3 ).The total interaction rate R is obtained from the integralneutrino flux Φ ν , the interaction probability W, the effectivecollection area A eff = 1km 2 , and a measurement time t.This leads to an event rate of 70 m 120 mfree of bubbles1950 mFig. 6.29Setup of the AMANDA detectorat the Sourth Pole (AMANDA –Antarctic Muon And NeutrinoDetector Array)R = Φ ν WA eff (6.56)