Astroparticle Physics

5.6 Binaries 71one obtains, using E = v × B with v ⊥ B, electrical fieldstrengths of|E| ≈vB= 10 15 V/m . (5.22)This implies that singly charged particles can gain 1 PeV =1000 TeV per meter. However, it is not at all obvious howpulsars manage in detail to transform the rotational energyinto the acceleration of particles. Pulsars possess a rotationalenergy ofE rot = 1 2 Θ pulsar ωpulsar 2 = 1 22 5 mR2 pulsar ω2 pulsar (5.23)≈ 7 × 10 42 J ≈ 4.4 × 10 61 eV(T pulsar = 30 ms, M pulsar = 2 × 10 30 kg, R pulsar = 20 km,ω = 2π/T ). If the pulsars succeed to convert a fraction ofonly 1% of this enormous energy into the acceleration ofcosmic-ray particles, one obtains an injection rate ofdE≈ 1.4 × 10 42 eV/s , (5.24)dtif a pulsar lifetime of 10 10 years is assumed.If one considers that our galaxy contains 10 11 stars andif the supernova explosion rate (pulsar creation rate) is assumedto be 1 per century, a total number of 10 8 pulsars haveprovided energy for the acceleration of cosmic-ray particlessince the creation of our galaxy (age of the galaxy ≈ 10 10years). This leads to a total energy of 2.2 × 10 67 eV for anaverage pulsar injection time of 5 × 10 9 years. For a totalvolume of our galaxy (radius 15 kpc, average effective thicknessof the galactic disk 1 kpc) of 2 × 10 67 cm 3 this correspondsto an energy density of cosmic rays of 1.1 eV/cm 3 .One has, of course, to consider that cosmic-ray particlesstay only for a limited time in our galaxy and are furthermoresubject to energy-loss processes. Still, the above presentedcrude estimate describes the actual energy density ofcosmic rays of ≈ 1eV/cm 3 rather well.energy production rateenergy density of cosmic rays5.6 Binaries“The advantage of living near a binaryis to get a tan in half the time.”AnonymousBinaries consisting of a pulsar or neutron star and a normalstar can also be considered as a site of cosmic-ray-particleacceleration. In such a binary system matter is permanently