How EUV emission lines are formed in solar coronal plasmas

1. How EUV emission lines are formed in solar coronal plasmas Ken Phillips Visiting Prof. MSSL May 3, 2011

2. EUV spectrometers looking at the corona Hinode EIS ( 170-210 Å, 250-290 Å) SOHO CDS (NIS 308 - 633Å, GIS 151 - 785Å ) SOHO SUMER ( 390 – 805 Å, 780 - 1610Å) Also have “monochromatic” images from instruments like TRACE and SDO/AIA – images are formed over narrow wavelength intervals that include one or more strong emission line(s).

3. Coronal EUV spectrum EUV spectrum (100 Å – 1000 Å) characterized by emission lines and faint continuum. Emission lines are emitted by ions of elements such as Si, Fe. The ions are excited, i.e. raised to a higher-energy state, then relax back to the ground state or to a lower-energy state, releasing energy as photons at a specific wavelength. How ions are excited and the flux of the emission lines are the subjects of these lectures.

4. Conditions in the corona In the quiet Sun, T = 1.106K – 2.106K (1-2 MK), N (particle no. density) decreases from 108-109 cm-3 going outwards Active regions: T = 3-5 MK, N = 1010 – 1011 cm-3. Flares: T up to 30 MK, N = 1011 – 1012 cm-3 (near impulsive stage). At these temperatures, the coronal gas is a fully ionized plasma, i.e. its principal components are protons (H nuclei), alpha particles (He nuclei), and free electrons.

5. Basic composition of the corona Chemical composition reflects the rest of the Sun’s composition, i.e. 90% H, 10% He. All the H and He atoms are stripped of their electrons, so the particles are: Protons (H nuclei) 43% Alpha particles (He nuclei) 5% Electrons 52% (so NH/Ne = ratio of number densities of H and e’s = 0.82).

6. Particle dynamics f(v) v

7. Particle speeds So for T = 2MK, vth = 7800 km/s [electrons] vth = 180 km/s [protons] vth = 90 km/s [He nuclei] So electrons are always the most mobile of particles.

8. Excitation of ions Let’s consider how a specific ion is excited – take the case of Fe+11, an Fe atom with 11 electrons removed. Normally, most Fe+11 ions are in their “ground state” (g) in the corona. But if a particle should “hit” it and raise it to an excited state, it is liable to de-excite spontaneously to emit a photon. Suppose a particle with energy of at least 64 eV “hits” an Fe+11 ion; Fe+11 may be excited to an energy level (we call it m). On de-excitation, the photon emitted has a wavelength of 193 Å – a very intense “Fe XII” emission line visible in the Hinode EIS range.

9. Note on ion and spectrum notation Fe+11 etc. is the notation for ions (in this case, it means an Fe atom with charge +11 units, or 11 electrons missing from normal retinue of 26). Fe XII is the spectrum number, i.e. the spectrum produced by various transitions of electrons in the Fe+11 ion. So Fe XII is not just an alternative notation for Fe+11. However, hardly anyone recognizes this ... (even CHIANTI, C. W. Allen, a co-author of “Ultraviolet & X-ray Spectroscopy of the Solar Atmosphere”.... )

10. Which particles will excite Fe+11 ions? Could they be photons? – corona is bathed in a sea of photons emitted by the photosphere. But average energy is ~2 eV – not nearly enough to do excitation. But the particles making up the coronal plasma, average energy [=(3/2) kT] corresponding to 2MK is 260 eV -- more than enough to excite the 193 Å line. Since electrons are by far the most mobile of coronal particles, they will be the most likely to encounter an Fe+11 ion. Thus, electron collisional excitation is the dominant excitation process in the corona for EUV lines (though occasionally proton excitation is significant).

11. Electron collisional excitation An electron encountering a target ion like an Fe+11 ion will impart some of its energy depending on its total energy and the distance of closest approach to the target ion. As the potential due to the e’s charge is e/r, long-range collisions may be as important as close-range ones. But there is a limit, the Debye length, which for the quiet-Sun corona is a few mm.

12. Collisional excitation (contd) The probability for excitation is given by wave functions ψ. In principle, the collision cross section involves a term like ∫ψ(e/r)ψ*dτwhere e/r is the potential due to the electron’s charge. There are various ways of calculating this: Coulomb-Born, distorted wave, R-matrix (in increasing order of sophistication). CHIANTI gives source material for cross sections, giving a guide as to the accuracy of the atomic calculations.

13. Spectral line excitation: 2-level approximation v (cm) Ion σ (cm2) Consider a tube containing free electrons with speed distribution f(v) striking an ion, cross section σ. Tube length = v (cm), i.e. the length an electron would go in 1 second if it was directed towards the target ion. f(v) is normally a Maxwell-Boltzmann distribution for speeds (unless there are significant non-thermal effects, as in flare impulsive stages).

14. Collisional excitation: 2-level ion The collisional rate coefficient Cgm = ʃ f(v) σ v dv measures the rate of excitations of Fe+11 ions to level m from the ground state g. Units are cm3 s-1. f(v) = Maxwell-Boltzmann distribution. Assume that the ion (in this case, Fe+11) has only 2 energy levels. If the ions spontaneously decay to their ground state g, then Ng Ne Cgm = Nm Amg= no. of excitations cm-3 s-1. where Amg = radiative transition probability, in s-1. For the Fe XII 193 Å line, Amg = 1011 s-1. So as soon as the Fe+11 ion is excited to level m, it spontaneously de-excites.

15. Level diagram for 2-level ionTake the case of Fe XII 193 Å line Energy Upper level m Collisional excitation Rate = Ng Ne Cgm cm-3 s-1 Radiative de-excitation Rate = N1 A10 cm-3 s-1 Ground level g Energy difference of m above g = ΔEgm = “excitation energy”. ΔEgm = 64 eV for the Fe XII 193 Å line.

16. Simple case: two-level ion Before we had Ng Ne Cgm = Nm Amg This is the no. of excitations cm-3 s-1. It’s also the no. of photons emitted cm-3 s-1. Now Cgm is approximately given by where ΔEgm = excitation energy. So the collisional rate coefficient decreases exponentially with ΔE but it increases with T.

17. Photon emission from the Fe XII 193 Å line 1 cm3 of coronal material will emit Ng Ne Cgm = Nm Amg photons per second. So at the distance of the Earth (or more exactly Hinode/SOHO/SDO) = R, the flux of photons F’gm (cm-2 s-1) is -- the flux of Fe XII 193 Å photons at distance R from 1 cm3 of coronal material.

18. Flux of Fe XII 193 Å line photons Make this substitution: i.e. Ng is assumed to be the no. density of Fe+11 ions (hardly any Fe+11 ions are in an excited state). Remember that NH/Ne = 0.8. Let emitting volume = ΔV (cm3). Then photon flux is

19. G(T) for 2-level ion Let’s set G(T) to be Therefore, Suppose the volume ΔV is isothermal, with T = T0. Then

20. Emission measure (Volume) emission measure = Ne2V= a property of the emitting volume. Sometimes (as in CHIANTI) the emission is assumed to come from a uniform layer of the solar atmosphere, and column emission measures Ne2h are used instead of volume emission measures. Here, h = the thickness of the atmospheric layer (the radius of the atmospheric layer is ~ the solar radius R0). The line flux is replaced by specific intensity (units photons cm-2 s-1sr-1).

21. More general case: multi-level ions

22. More general case (contd.) Number density of ions in excited level j = Njcan be expressed in terms of other known solar parameters: where: Nj/Nionis the relative populationof the excited level; Nion/NFeis the ionization fraction(from ionization equilibrium calculation, and is a function of T); NFe/NH is the abundance of Ferelative to H; NH/Ne is 0.8 (electrons supplied by H and He atoms).

23. More general case (contd.) So the total flux is given by: photons cm-2 s-1 Note R = distance of spectrometer from Sun. For Hinode, this is not quite 1 A.U. (Sun-Earth distance varies by +/- 2% throughout the year). For SOHO, R = distance of Sun – 1.5.106 km. These are small differences, so shouldn’t matter too much unless you are doing a detailed comparison of Hinode and SOHO or doing a time series over the course of a year.

24. Definition of G(T) function Recall flux of an EUV line is Let’s define So (as before): If the emitting volume is isothermal (T=T0), then

25. Fe ionization stages in coronal equilibrium Fractions of Fe ions as a function of T (plotted logarithmically) = Nion/NFe Ion notation: 11 = Fe+11 19 = Fe+19 etc. Based on Mazzotta et al. (1998). Later works (Bryans et al. 2009) differ somewhat, not too seriously.

26. Ion fractions and G(T) Let F(T) = NFe+11 / NFe. F(T) has an “upside-down parabola” shape when it and T are plotted logarithmically. This determines the shape of G(T), since for a 2-level ion approx., G(T) = F(T) exp(-ΔE/kT)/T1/2. For ultraviolet lines, ΔE is relatively small and so the exponential term is ~1. Therefore, G(T) has almost the same shape as F(T). Note: for X-ray lines, ΔE is large (typically 2 or 3 × kT for kTexpressed in keV), so G(T) does not have the same shape as F(T).

27. Element abundances To determine element abundances is far from easy. Most abundances quoted in papers are from analyses of photospheric data: see e.g. Asplund et al. (2009, Ann. Rev. Astr. Astroph. 47, 481). The method involves measuring strengths of absorption (Fraunhofer) lines and relating them to “curves of growth”. Arguments continue about the role of 3-D motions caused by granules & their effect on measured abundances. For iron, Asplund et al. give NFe/NH = 3.2.10-5.

28. Coronal element abundances Coronal abundances are derived from emission line flux ratios, so a different method from photospheric abundance determinations. They have been found to be different, but it wasn’t clear at first whether this was due to measurement errors. Feldman et al. (2000, Phys. Scripta 61, 222) give evidence for a dependence on first ionization potential (FIP): elements with low FIP (< 10 eV) like Fe are enhanced by x4 in the corona; elements with high FIP have coronal abundances = photospheric abundances. Evidence from X-ray spectrometers on Mercury MESSENGER and RHESSI suggests the coronal abundance of Fe is 2.6 x photospheric. This may apply to other low-FIP elements.

29. Why it’s always better to see coronal features in EUV/X-rays than white light EUV or X-ray emission is (for a given T) proportional to emission measure, or to Ne2. White-light emission is Thomson-scattered photospheric radiation, i.e. light from photosphere scattered off free electrons in corona. Surface brightness of corona = Ne x cross section for Thomson scattering, i.e. depends on Ne.

30. Do these images illustrate this point? SDO/AIA 193A M. Druckmueller’s 2009 eclipse picture. Hinode XRT

31. Using CHIANTI for spectral information CHIANTI is a very useful atomic physics package (data base and software) that will enable you to plot spectra in the Hinode EIS (or any EUV/X-ray) range. It is IDL-based. It also has many routines for plotting functions like G(T), ion fractions. There are tables of abundances, atomic physics parameters (like wavelengths, A-values). It’s free! Main web site: http://www.chiantidatabase.org

32. CHIANTI web site home page

33. Direct access files in CHIANTI Click on this link to get the data base files that CHIANTI uses to do spectral calculations. You can also read files in ssw. On my Windows desktop, I have CHIANTI data base files on C:\ssw\packages\chianti\dbase\ For example: in the folder “ioneq”, there are all the various ionization equilibrium calculations,e.g. Mazzotta et al. 1998 = mazzotta_etal.ioneq). In the folder “abundance”, there are various solar element abundance sets, e.g. Feldman et al. (2002) = sun_coronal.abund All the files are ASCII-readable.

34. CHIANTI: calculating a spectrum Use the command IDL> ch_ss - the spectral synthesis program, to calculate the EUV spectrum of the solar corona between 160 and 200 Å. Assume an electron density Ne = 1010 cm-3 (active region-type density). Use the ionization fractions of Bryans et al. (2009), bryans_etal_9.ioneq Use a single T and EM or maybe a DEM (differential emission measure) for an active region. Assume no photo-excitation but include proton excitation (this might be important for certain lines).

35. CHIANTI: synthesizing the spectrum Second stage of ch_ss: synthesizing the spectrum that you calculated in the first part. Here, assume the same range. Use a spectrometer that has a resolution (FWHM) of 0.05 Å. This should be less than the thermal Doppler width of (e.g.) Fe IX lines in this region (~0.02 Å). Bin width (number of points defining each line’s profile) = 0.01 Å. Save the spectrum or create a ps file.

36. G(T) functions Relative fluxes for 8 Fe X lines listed below. The fluxes are relative to the strongest line at 174.5310 Å IDL> gofnt,’fe_10’,170,180, temp,g,desc then you can save temp,g,desc in an IDL sav file.

37. Plotting ionization fractions Use command IDL> plot_ioneq,'fe’ to get this plot. You can save the quantities and re-plot them on the more familiar log scale.

38. Lines at ~193 Å: Fe XII, Ca XVII, and Fe XXIV T=2MK T=10MK At flare temperatures, Fe XXIV and Ca XVII lines predominate. Fe XII predominates at quiet coronal Ts.

39. Other CHIANTI files Under the dbase folder, you can find all the atomic data for each element used in CHIANTI. For example, go to s (for S = sulphur) to find folder containing data for each ion: s_16 = S XVI (should be S+15!). Wavelengths, transitions etc. are in s_16.wgfa, Upsilon (excitation coefficients) in s_16.splups etc.

40. References to work cited. On the relation of collisional excitation rate coeffts. to oscillator strengths, see van Regemorter, ApJ, 136, 906 (1962). On photospheric abundances, see Asplund, ARAA, 43, 481 (2005) and Asplund et al., ARAA, 47, 481 (2009). See also Bahcall et al., ApJ, 631, 1281 (2005). On coronal abundances, see Feldman & Laming, Phys Scripta, 61, 222 (2000). For solar FIP effect models, see Henoux, ASR, 15 (no. 7), 23 (1995); Laming, ApJ, 614, 1063 (2004); see Nordon & Behar, A&A, 482, 639 (2008) for inverse FIP effect in stellar flares (also works by J. Drake et al.). On the relation of Einstein A, B values to oscillator strengths (gf values) and “line strength” (S), see Allen’s Astrophysical Quantities (3rd edition), p. 59.