Astroparticle Physics

126 6 Primary Cosmic Rayscess because both emission and absorption processes areinvolved. Therefore, an optically dense bremsstrahlungsource which absorbs its own radiation would also producea blackbody spectrum. The emission P of a black-body is given by Planck’s lawenergy spectraν 3P ∼e hν/kT − 1 . (6.81)For high energies (hν ≫ kT ) P can be described by anexponentialP ∼ e −hν/kT , (6.82)while at low energies (hν ≪ kT ), because ofe hν/kT = 1 + hν +··· , (6.83)kTthe spectrum decreases to low frequencies likeP ∼ ν 2 . (6.84)The total radiation S of a hot body is described by theStefan–Boltzmann law,S = σT 4 , (6.85)Fig. 6.50Standard X-ray spectra originatingfrom various production processeswhere σ is the Stefan–Boltzmann constant.Typical energy spectra for various production mechanismsare sketched in Fig. 6.50.6.4.3 Detection of X Rayspassive collimatorsThe observation of X-ray sources is more demanding comparedto optical astronomy. X rays cannot be imaged withlenses since the index of refraction in the keV range is veryclose to unity. If X rays are incident on a mirror they willbe absorbed rather than reflected. Therefore, the direction ofincidence of X rays has to be measured by different techniques.The most simple method for directional observationis based on the use of slit or wire collimators which aremounted in front of an X-ray detector. In this case the observationaldirection is given by the alignment of the spaceprobe. Such a geometrical system achieves resolutions onthe order of 0.5 ◦ . By combining various types of collimatorsangular resolutions of one arc minute can be obtained.