Sp.-V/AQuan/1999/10/07:19:58 Page 207 Chapter 10 γ -Ray and Neutrino Astronomy R.E. Lingenfelter and R.E. Rothschild 10.1 Continuum Emission Processes ............. 207 10.2 Line Emission Processes ................. 208 10.3 Scattering and Absorption Processes .......... 213 10.4 Astrophysical γ -Ray Observations ........... 216 10.5 Neutrinos in Astrophysics ................ 235 10.6 Current Neutrino Observatories ............. 237 10.1 CONTINUUM EMISSION PROCESSES Important processes for continuum emission at γ -ray energies are bremsstrahlung, magneto- bremsstrahlung, and Compton scattering of blackbody radiation by energetic electrons and positrons [1–6]. 10.1.1 Bremsstrahlung The bremsstrahlung luminosity spectrum of an optically thin thermal plasma of temperature T in a volume V is [3] 1/2 π 6 π 2 32 e 2 mc 2 L(ν)brem = Z neniVg(ν, T ) exp(−hν/kT), 3m2c4 3kT where the index of refraction is assumed to be unity, m is the electron mass, Z is the mean atomic 1/2 charge, ne and ni are the electron and ion densities, and the Gaunt factor g(ν, T ) ≈ (3kT/πhν) for hν>kT and T > 3.6 × 105 Z 2 K, or −38 2 −1/2 −1 −1 L(ν)brem ≈ 6.8 × 10 Z neniVg(ν, T )T exp(−hν/kT) erg s Hz . 207 Sp.-V/AQuan/1999/10/07:19:58 Page 208 208 / 10 γ -RAY AND NEUTRINO ASTRONOMY 10.1.2 Magnetobremsstrahlung The synchrotron luminosity spectrum of an isotropic, optically thin nonthermal distribution of −S relativistic electrons with a power-law spectrum, N(γ ) = N0γ , interacting with a homogeneous magnetic field of strength, H,is[5] . 3 (S−1)/2 0 8e 3e (S+1)/2 (1−S)/2 L(ν)synch ≈ VN0 H ν 3mc2 4πmc or −23 (S+1)/2 6 (S−1)/2 −1 −1 L(ν)synch ≈ 3.60 × 10 VN0 H (4.2 × 10 /ν) erg s Hz . 10.1.3 Compton-Scattered Blackbody Radiation The Compton-scattering (cs) luminosity spectrum of an optically thin, isotropic nonthermal distribution −S of relativistic electrons with a power-law spectrum, N(γ ) = N0γ , interacting with blackbody photons having a temperature T is [5] 4 (3−S)/2 4e h (S−3)/2 (1−S)/2 L(ν)cs ≈ VN0wbbT ν 3m2c3 3.6k or −26 (S−3)/2 10 (S−1)/2 −1 −1 L(ν)cs ≈ 4.22 × 10 VN0wbbT (7.5 × 10 /ν) erg s Hz , where wbb is the energy density of the blackbody radiation. 10.2 LINE EMISSION PROCESSES Important processes for line emission at γ -ray energies are electron–positron annihilation, nuclear deexcitation, decay of radio nuclei, and radiative capture (see Tables 10.1–10.3). 10.2.1 Electron–Positron Annihilation Radiation Positron annihilation can occur either via a direct interaction with a free electron or via positronium formed by charge exchange with a bound electron or by radiative combination with a free electron (e.g., [7–12]). See Figure 10.1. Direct annihilation (da) leads to line emission, e+e− → 2γ , at a mean energy, 7 +kTe/2, Te 10 K, ν = 2 + / , 7 < < 10 , h da mec 3kTe 4 10 Te 10 K 10 +kTe, Te > 10 K, 2 where mec = 510.9991 keV and Te is the temperature of the annihilating electrons and positrons. The direct-annihilation line spectrum can be approximated by a Gaussian with a linewidth [12] 4 0.50 9 da ≈ 0.87(Te/10 K) keV, for Te 10 K, and at higher temperatures the width [10] da ≈ kTe, 9 for Te 10 K. 2 The cross section for direct annihilation of a positron of energy γ mec with an electron at rest [1] is σ γ 2 + γ + γ + 3 T 4 1 2 3 σ(γ)da = ln(γ + γ − 1) − , 8(γ + 1) γ 2 − 1 γ 2 − 1 4 2 4 where the Thomson cross section, σT = 8πe /(3m c ) = 0.6652 barn (b). Sp.-V/AQuan/1999/10/07:19:58 Page 209 10.2 LINE EMISSION PROCESSES / 209 Figure 10.1. Positron-annihilation rates in a thermal medium per unit density as a function of temperature, for annihilation directly with free electrons (Rda/ne) or with bound electrons (Rda/nH), and via positronium formation by radiative combination with free electrons (Rrc/ne) or by charge exchange with neutral hydrogen (Rce/nH), from [8]. Annihilation via positronium formation leads to line emission only from the singlet parapositron- ium, para-Ps → 2γ , which forms 25% of the time. The mean energy of the positronium line, 2 2 hνps = mec − (R/4n ), where the Rydberg R = 0.0136 keV, and n is 1 for the ground state. The parapositronium annihilation line spectrum can be approximated by a Gaussian with a 4 0.44 linewidth rc ≈ 0.80(T/10 K) keV for radiative combination (rc), valid at least from 8 000 to 6 10 K, and a Gaussian linewidth ce ≈ 6.4 keV for charge exchange (ce), since the parapositronium mean life of ∼ 10−10 s is much less than the energy loss time [12]. The total number of 511 keV line photons emitted per positron annihilation, + γ511/e = 2 − 1.5 fps, where fps is the fraction of positrons that annihilate via positronium. Annihilation via positronium formation leads to three-photon continuum emission from the triplet orthopositronium, ortho-Ps → 3γ , which forms 75% of the time. The spectrum [7] of this emission is 2 η(1 − η) 2(1 − η) 2(1 − η)2 2 − η ( ν) γ = + ( − η) − ( − η) + , P h 3 2 2 2 2 ln 1 3 ln 1 (π − 9)mec (2 − η) η (2 − η) η where η = hν/mc2 is the photon energy, and the spectrum is normalized to unity. Sp.-V/AQuan/1999/10/07:19:58 Page 210 210 / 10 γ -RAY AND NEUTRINO ASTRONOMY , Table 10.1. Nuclear deexcitation γ -ray lines.a b Energy Emission Excitation Mean life (MeV) mechanism processes (s) ∗ . ∗ − 0.429 1 7Be 0 429 → g.s. 4He(α, n)7Be 1.9 × 10 13 ∗ . ∗ − 0.477 6 7Li 0 478 → g.s. 4He(α, p)7Li 1.1 × 10 13 ∗ 4He(α, n)7Be()7Li (10%) 6.6 × 106 ∗ . ∗ − 0.718 3 10B 0 718 → g.s. 12C(p, x)10B 1.0 × 10 9 ∗ − 16O(p, x)10B 1.0 × 10 9 + ∗ 12C(p, x)10C(e )10B 27.78 + ∗ 16O(p, x)10C(e )10B 27.78 ∗ . ∗ − 0.846 8 56Fe 0 847 → g.s. 56Fe(p, p )56Fe 9.1 × 10 12 + ∗ 56Fe(p, n)56Co(e ; )56Fe 9.6 × 106 ∗ . ∗ . ∗ − 1.238 3 56Fe 2 085 → 56Fe 0 847 56Fe(p, p )56Fe 1.0 × 10 12 + ∗ 56Fe(p, n)56Co(e ; )56Fe (67%) 9.6 × 106 ∗ . ∗ − 1.274 5 22Ne 1 275 → g.s. 22Ne(p, p )22Ne 5.2 × 10 12 ∗ − 22Ne(α, α’)22Ne 5.2 × 10 12 + ∗ 22Ne(p, n)22Na(e ; )22Ne 1.2 × 108 + ∗ 24Mg(p, x)22Na(e ; )22Ne 1.2 × 108 + ∗ 25Mg(p, x)22Na(e ; )22Ne 1.2 × 108 + ∗ 28Si(p, x)22Na(e ; )22Ne 1.2 × 108 ∗ . ∗ − 1.368 5 24Mg 1 369 → g.s. 24Mg(p, p )24Mg 1.9 × 10 12 ∗ − 24Mg(α, α )24Mg 1.9 × 10 12 ∗ − 28Si(p, x)24Mg 1.9 × 10 12 ∗ . ∗ − 1.408 3 55Fe 1 408 → g.s. 56Fe(p, pn)55Fe 5.5 × 10 11 + ∗ 56Fe(p, 2n)55Co(e ; )55Fe (18%) 9.1 × 104 ∗ . ∗ − 1.408 4 54Fe 1 408 → g.s. 56Fe(p, x)54Fe 1.2 × 10 12 ∗ . ∗ − 1.434 1 52Cr 1 434 → g.s. 56Fe(p, x)52Cr 9.8 × 10 13 ∗ + ∗ 56Fe(p, x)52Mn (e ; )52Cr 1.8 × 103 + ∗ 56Fe(p, x)52Mn(e ; )52Cr 7.0 × 105 ∗ . ∗ − 1.633 6 20Ne 1 634 → g.s. 20Ne(p, p )20Ne 1.0 × 10 12 ∗ − 20Ne(α, α )20Ne 1.0 × 10 12 + ∗ − 20Ne(p, n)20Na(e )20Ne (80%) 6.4 × 10 1 ∗ − 24Mg(p, x)20Ne 1.0 × 10 12 ∗ − 28Si(p, x)20Ne 1.0 × 10 12 ∗ . ∗ . ∗ − 1.635 2 14N 3 948 → 14N 2 313 14N(p, p )14N 6.9 × 10 15 ∗ − 14N(α, α )14N 6.9 × 10 15 ∗ − 16O(p, x)14N 6.9 × 10 15 ∗ . ∗ − 1.779 0 28Si 1 779 → g.s. 28Si(p, p )28Si 6.8 × 10 13 ∗ − 28Si(α, α )28Si 6.8 × 10 13 ∗ − 32S(p, x)28Si 6.8 × 10 13 ∗ . ∗ − 1.808 6 26Mg 1 809 → g.s. 26Mg(p, p )26Mg 6.9 × 10 13 ∗ − 26Mg(α, α )26Mg 6.9 × 10 13 + ∗ 26Mg(p, n)26Al(e ; )26Mg 3.2 × 1013 + ∗ 27Al(p, pn)26Al(e ; )26Mg 3.2 × 1013 + ∗ 28Si(p, x)26Al(e ; )26Mg 3.2 × 1013 ∗ . ∗ − 2.230 2 32S 2 230 → g.s. 32S(p, p )32S 2.4 × 10 13 ∗ − 32S(α, α )32S 2.4 × 10 13 ∗ . ∗ − 2.312 6 14N 2 313 → g.s. 14N(p, p )14N 9.8 × 10 14 ∗ − 14N(α, α )14N 9.8 × 10 14 + ∗ 14N(p, n)14O(e )14N 101.9 ∗ − 16O(p, x)14N 8.7 × 10 14 + ∗ 16O(p, x)14O(e )14N 101.9 Sp.-V/AQuan/1999/10/07:19:58 Page 211 10.2 LINE EMISSION PROCESSES / 211 Table 10.1. (Continued.) Energy Emission Excitation Mean life (MeV) mechanism processes (s) ∗ . ∗ . ∗ − 2.613 8 20Ne 4 248 → 20Ne 1 634 20Ne(p, p )20Ne 9.2 × 10 14 ∗ − 20Ne(α, α )20Ne 9.2 × 10 14 ∗ − 24Mg(p, x)20Ne 9.2 × 10 14 ∗ − 28Si(p, x)20Ne 9.2 × 10 14 ∗ .