Allen's Astrophysical Quantities
1 (keV) = 1.6021 × 10 −9 erg = 1.6021 × 10 −16 J: the kilo-electron-volt. E (keV) = 12.398 [λ (Å)] −1 : the energy of a photon. E (keV) = 0.862T (10 7 K): the characteristic energy, kT , of a thermal source. ν (Hz) = 2.998 × 10 18 [λ(Å)] −1 = 2.418 × 10 17 E (keV). T (K) = 1.160 × 10 7 [kT (keV)]. 1 µJy = 10 −29 erg cm −2 s −1 Hz −1 = 10 −32 W m −2 Hz −1 : the micro-Jansky. Spectra are usually presented as the dependence of spectral irradiance (spectral flux density) I , on wavelength λ (Å),
... avelength λ (Å), frequency ν (Hz), or photon energy E (keV or erg). To convert from one to the other: CHARACTERISTIC X-RAY TRANSITIONS Energies of absorption edges and emission lines are given in Table 9 .1. All energies are in keV. EMISSION MECHANISMS AND SPECTRA Continuum Models X-ray spectra have historically been compared to three simple models that imply emission from: (a) high-energy electrons moving in a magnetic field; (b) thermal electrons in an optically thin plasma with temperature, T > 3 × 10 7 K; and (c) thermal radiation from an optically thick object. These spectra are: (a) Power law, I (E) = AE −α , α = spectral index. (b) Thermal bremsstrahlung, I (E, T ) = AG(E, T )Z 2 n e n i (kT ) −1/2 e −E/kT . Densities of electrons and positive ions are n e and n i , respectively, and G is the Gaunt factor, a slowly varying function with increasing value as E decreases [1, 2]. When E kT , G ≈ 0.55 ln(2.25kT /E), and when E ∼ kT , G ≈ (E/kT ) −0.4 is an adequate approximation . When electrons are relativistic, the Gaunt factor can be approximated as G = [0.9 + 0.75(kT /mc 2 )](E/kT ) −1/4 + 1.9(kT /mc 2 )(E/kT ) −1/6 + 3.4(kT /mc 2 ) 2 (E/kT ), an approximation better than 20% in the range (kT /mc 2 ) ≤ 1, (E/kT ) ≤ 6 . (c) Blackbody radiation, Early observations were usually well fit using these simple models. Spectra of actual sources are, of course, more complex. There are emission lines, absorption edges, and, usually, scattering and absorption in material surrounding, or close to, the sources. Observations with high spectral resolution and good counting statistics, or those covering a broad spectral range, require more complex models for good fits .