Astroparticle Physics

138 6 Primary Cosmic Raysb) Estimate for (ν µ ↔ ν τ ) oscillations with maximummixing (sin 2θ = 1), E ν = 1 GeV and under theassumption of m νµ ≪ m ντ (that is, m ντ ≈ √ δm 2 )the mass of the τ neutrino, which results if the ratioof upward-to-downward-going atmospheric muonneutrinos is assumed to be 0.54.c) Does the assumption m νµ ≪ m ντ make sense here?Problems for Sect. 6.31. Estimate the detection efficiency for 1 MeV photons in aNaI(Tl) scintillation counter of 3 cm thickness.(Hint: Use the information on the mass attenuation coefficientfrom Fig. 6.37.)2. Estimate the size of the cosmological object that hasgiven rise to the γ -ray light curve shown in Fig. 6.48.3. What is the energy threshold for muons to produce Cherenkovlight in air (n = 1.000 273) and water (n =1.33)?4. The Crab Pulsar emits high-energy γ rays with a powerof P = 3 × 10 27 W at 100 GeV. How many photonsof this energy will be recorded by the planned GLASTexperiment (Gamma-ray Large Area Space Telescope)per year if isotropic emission is assumed? What is theminimum flux from the Crab that GLAST will be able todetect (in J/(cm 2 s))? (Collecting area of GLAST: A =8000 cm 2 , distance of the Crab: R = 3400 light-years.)5. The solar constant describing the solar power arriving atEarth is P S ≈ 1400 W/ m 2 .a) What is the total power radiated by the Sun?b) Which mass fraction of the Sun is emitted in 10 6years?c) What is the daily mass transport from the Sun deliveredto Earth?Problems for Sect. 6.41. The radiation power emitted by a blackbody in its dependenceon the frequency is given by (6.81). Convertthis radiation formula into a function depending on thewavelength.2. The total energy emitted per second by a star is called itsluminosity. The luminosity depends both on the radius of