Thermal X-ray radiation (PDF) - SRON

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decays back to the 1s orbit by a radiative transition. Usually the ion will then be excited to a higher level by another collision, for example from 2s to 2p, and then it can decay radiatively back to the ground state (1s). However, if the density is very low (n e ≪ n e,crit , Eqn. 3.74–3.75), the probability for a second collision is very small and in that case two-photon emission can occur: the electron decays from the 2s orbit to the 1s orbit while emitting two photons. Energy conservation implies that the total energy of both photons should equal the energy difference between the 2s and 1s level (E 2phot = E 1s −E 2s ). From symmetry considerations it is clear that the spectrum must be symmetrical around E = 0.5E 2phot , and further that it should be zero for E = 0 and E = E 2phot . An empirical approximation for the shape of the spectrum is given by: √ F(E) ∼ sin(πE/E 2phot ). (3.73) An approximation for the critical density below which two photon emission is important can be obtained from a comparison of the radiative and collisional rates from the upper (2s) level, and is given by Mewe, Gronenschild & van den Oord (1986): H − like : n e,crit = 7 × 10 9 m −3 Z 9.5 (3.74) He − like : n e,crit = 2 × 10 11 m −3 (Z − 1) 9.5 . (3.75) For example for carbon two photon emission is important for densities below 10 17 m −3 , which is the case for many astrophysical applications. Also in this case one can determine an average Gaunt factor G 2phot by averaging over all ions. Two photon emission is important in practice for 0.5 kT 5 keV, and then in particular for the contributions of C, N and O between 0.2 and 0.6 keV. See also Fig. 3.25. 3.9 Line radiation Apart from continuum radiation, line radiation plays an important role for thermal plasmas. In some cases the flux, integrated over a broad energy band, can be completely dominated by line radiation (see Fig. 3.25). The production process of line radiation can be broken down in two basic steps: the excitation and the emission process. 3.9.1 Line radiation: excitation Collisional excitation A bound electron in an ion can be brought into a higher, excited energy level through a collision with a free electron. Before we already discussed the case where the excited state is unstable, which sometimes can lead to auto-ionisation. In most cases, however, the excited state is stable and the ion will decay back to the ground level by means of a radiative transition, either directly or through one or more steps through intermediate energy levels. We have seen before that the excitation rate from level i to level j can be written as (Eq. 3.9): S ij = S 0 ¯Ω(Eij /kT)T −1/2 e −E ij/kT , (3.76) For sufficient low density every excitation is followed immediately by a radiative de-excitation to the ground level (or an intermediate level). Apart of a small 49
Figure 3.25: Emission spectra of plasmas with solar abundances. The histogram indicates the total spectrum, including line radiation. The spectrum has been binned in order to show better the relative importance of line radiation. The thick solid line is the total continuum emission, the thin solid line the contribution due to Bremsstrahlung, the dashed line free-bound emission and the dotted line two-photon emission. Note the scaling with Ee E/kT along the y-axis. correction factor C 1 for cascades from higher excited levels to level k, and possibly a correction factor B for decay to intermediate levels or for autoionisation, (3.9) gives the line power from level k to the ground level. The factor B is the so-called branching ratio. Radiative recombination When a free electron is captured by an ion, continuum radiation is produced (freebound emission). The captured electron not always reaches the ground level immediately. We have seen before that in particular for cool plasma’s (kT ≪ I) the higher excited levels are frequently populated. In order to get to the ground state, one or more radiative transitions are required. Apart from cascade corrections from and to higher levels the recombination line radiation is essentially given by (3.49). A comparison of recombination with excitation tells that in particular for low temperatures (compared to the line energy) recombination radiation dominates, and for high temperatures excitation radiation. 50
Page 1 and 2: High Energy Astrophysics Jelle Kaas
Page 3 and 4: 3.1 Introduction Thermal X-ray radi
Page 5 and 6: Figure 3.2: The observed X-ray spec
Page 7 and 8: Figure 3.6: X-ray spectrum of the S
Page 9 and 10: series of alkaline spectra). The no
Page 11 and 12: • The first atomic shell (n = 1)
Page 13 and 14: Z El 1s 2s 2p 3s 3p 3d 4s Ground te
Page 15 and 16: m l1 s 1 m l2 s 2 M L M S +1 + +1
Page 17 and 18: 3.3 Energy levels We have seen the
Page 19 and 20: 3.4 Transitions between different l
Page 21 and 22: Figure 3.10: Transitions between a
Page 23 and 24: 3.5 Abundances of the elements With
Page 25 and 26: 3.6 Basic processes In order to be
Page 27 and 28: leading to Here the constant S 0 is
Page 29: 3.6.3 Radiative transition probabil
Page 32 and 33: Figure 3.12: Fluorescence yield as
Page 34 and 35: The formula of Younger While the Lo
Page 36 and 37: 3.6.6 Excitation-Autoionisation In
Page 38 and 39: 3.6.7 Photoionisation Figure 3.20:
Page 40 and 41: 3.6.9 Radiative recombination Radia
Page 42 and 43: 3.6.10 Dielectronic recombination T
Page 44 and 45: 3.7 The ionisation balance In order
Page 46 and 47: of computing time. Therefore one us
Page 48 and 49: 3.8 Continuum emission processes Af
Page 52 and 53: Inner-shell ionisation The third li
Page 54 and 55: 3.9.3 Line width For most X-ray spe
Page 56 and 57: Table 3.6: The strongest emission l
Page 58 and 59: Table 3.8: Some important iron line
Page 60 and 61: with τ(λ) = τ 0 ϕ(λ) (3.83) wh
Page 62 and 63: Table 3.9: The most important X-ray
Page 64 and 65: where the hydrogen column density N
Page 66 and 67: source itself. Fortunately, with hi
Page 68 and 69: Figure 3.35: Stability for the ioni
Page 70: Table 3.10: Wavelengths in Å of th

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