1. X-ray Spectroscopy of Coronal Plasmas Ken Phillips Scientific Associate, Natural History Museum, and Honorary Prof., QUB 1

2. Solar Corona: Physical Properties Solar corona has very high temperatures: 10 6 K – 2×10 6 K (1—2 MK) – far higher than photosphere/chromosphere. Densities are low: n (particles m -3 ) ~ 3×10 14 m -3 near chromosphere down to ~ 2 ×10 12 m -3 at 2 solar radii (R s ) from Sun’s centre. Temperature and density are much enhanced over active regions: T ~ 4 MK and n ~ 10 17 m -3. Flare plasmas: formed immediately after a magnetic reconnection event in active regions: T ~ 20 MK and n ~ 10 18 m -3. Last from minutes to many hours. Reduced density and temperature and open magnetic fields at poles, particularly at solar minimum: coronal holes. 2

3. Corona is a fully ionized gas or plasma Because of the high temperature, corona is practically a fully ionized gas (or plasma). Nearly all H and He atoms are fully stripped. So particles are almost entirely protons, α particles (He nuclei), and free electrons. Heavier elements have very small abundances compared with H or He but are most important as radiators of X-ray line emission. (Soft) X-rays are here defined to be in the spectral range 0.1 nm to 10 nm (1 Å to 100 Å). 3

4. Ionization conditions in coronal plasmas Coronal plasmas have relatively low densities and high temperatures. Most elements are therefore in the form of ionized atoms – in most cases multiply ionized. There is an equilibrium in coronal plasmas (assuming that they are steady-state) between ionizations and recombinations – coronal (ionization) equilibrium. 4

5. Coronal Equilibrium Take the case of Fe ions – Fe is one of the most abundant elements after H and He (only C, N, O and Ne are more abundant). For the quiet corona, assuming T=1-2 MK), Fe is in the form Fe +10 to Fe +14 (i.e. 10 to 14 electrons removed from the neutral atom state). What determines which are the most abundant ion stages? 5

6. Fractions of Fe ionization stages in coronal equilibrium Fractions of Fe ions as a function of T (plotted logarithmically) Ion notation: 9 = Fe +9 19 = Fe +19 etc. Note: for corona, Fe +9 to Fe +14 are abundant ionization stages Mazzotta et al. (1998 A&A) corona 6 AR

7. Coronal Equilibrium – ionization/recombination Notation: e - stands for free electron, X an element (e.g. Fe) and X +q an ion of element X with q electrons missing. Ionization (rate coefft. C e ) is by collisions with free electrons: e 1 - + X +q → X +q+1 + e 1 - + e 2 - (e 1 - loses energy, imparting it to ion) Recombination (rate coefft. R r ) occurs by radiative processes: e 1 - + X +q+1 → X +q + h ν (h ν = photon, removes excess energy) and by dielectronic processes (rate coefficient R D ): e 1 - + X +q+1 → (X +q )**(** = doubly excited ion) 7

8. Excitation of X-ray line emission Because of the relatively low densities and high temperatures of coronal plasmas, most ions are in their ground state. One of the most intense lines in the solar X-ray spectrum is due to 16-times ionized Fe (Fe +16 ) at 1.5012 nm. In spectroscopic notation, this is the Fe XVII 1.5012 nm line (Fe XVII = “17 th spectrum of Fe”). This line (like most others) is excited from the ground state of Fe +16 by collisions with free electrons to an outer orbit followed by spontaneous de-excitation back to the ground state. 8

9. Fe +16 (Fe XVII) 1.5012 nm line excitation Ground state of Fe +16 is 1s 2 2s 2 2p 6 1 S 0 A collision of a free electron with the ion takes one of the 2p electrons to a 3d state: 1s 2 2s 2 2p 5 3d 1 P 1 The lifetime of this state is extremely short (roughly 2 x 10 -13 s); normally this state spontaneously de-excites to the ground state, with the emission of the 1.5012 nm line: Fe +16 (1s 2 2s 2 2p 6 1 S 0 ) + e - → Fe +16 (1s 2 2s 2 2p 5 3d 1 P 1 ) + e - → Fe +16 (1s 2 2s 2 2p 6 1 S 0 ) + h ν where h ν = hc / λ corresponds to λ = 1.5012 nm. 9

10. X-ray resonance lines The Fe XVII 1.5012 nm line is an example of an X-ray resonance line – the line is formed by an allowed transition from an excited state of Fe +16 to the ground state. The solar X-ray spectrum is dominated by other resonance lines emitted by other elements. H-like and He-like ions feature prominently – e.g. O VIII Ly-α (1.897 nm), O VII lines (2.160 nm) being examples of lines emitted by H-like O and He-like O ions. 10

11. X-ray Spectrum of decaying solar flare Flare observed by Solar Max FCS instrument, August 25, 1980 11

12. Dielectronic Satellite Lines in the X-ray Spectrum of the Sun In the solar X-ray spectrum, we observe lines that are excited by hot active regions or flares – temperatures range from ~ 4 MK (non-flaring active regions) up to ~ 20 MK (flares). We can use lines formed in the dielectronic recombination process – satellite lines – to get the temperature of such plasmas. Satellite lines are so called because they occur just to the long- wavelength side of associated resonance lines. The ratio satellite/resonance line depends on 1 / electron temperature T e. The satellite line intensity depends strongly on the ion’s atomic number Z (= constant × Z 4 ). 12

13. Satellite line/resonance line int. ratios Based on Gabriel (1972 MNRAS) 13

14. Solar flare spectra of Fe XXV lines and Fe XXIV satellites T e =15.0 MK: Satellites intense compared with Fe XXV resonance line w. T e =17.5 MK: Satellites weaker compared with Fe XXV line w. 14 Lemen et al. (1984 A&A)

15. Electron densities from X-ray line ratios Electron densities N e are more difficult to obtain from X-ray lines but if a pair or group of lines from the same ion exist, the ratio of line intensities can sometimes depend on N e. Consider a 3-level diagram for an ion, with ground level 1, metastable m, and another excited level 3. “Metastable” means that this level has a relatively long lifetime, with small transition probability to the ground state. Suppose the transition 3→1 is allowed (i.e. has a high transition probability). Collisional excitation (rate coefficient C*) from level m to 3 can compete with radiative de-excitation m→1 if the density is high enough. If so, N m A m1 ~ N m N e C * and the line intensity ratio I(m→1) / I(3→1) depends on N e. 15

16. Level diagram for a 3-level ion or atom Line 3→1 is allowed, line m→1 is “forbidden”. 1 m (metastable) Level 3 N 3 A 31 N m N e C* (collisional excitation) N m A m1 (spont. de-excitn.) Ground level (1) 16

17. Density sensitivity of lines of He-like O (O VII lines at 2.2 nm) Plot of density- sensitive ratio R = ratio of a forbidden line to “intercombination” line against N e in cm -3 (multiply by 10 6 to get m -3 ). 17

18. Observations of O VII lines during a solar flare observed by the P78-1 spacecraft (1980) Max. density (~10 18 m -3 ) Low-density spectra 18 Doschek et al. (1981) Decreasing densities

19. X-ray continua Continua are evident in particularly solar flare spectra. They are chiefly due to free-free and free-bound transitions. With crystal spectrometers (the usual instrument to observe solar X-rays), the continuum is sometimes difficult to distinguish from background. With the RESIK spectrometer on the Coronas-F mission, the continuum is seen at wavelengths less than 0.43 nm (4.3 Å) but instrumental background predominates at longer wavelengths. B. Sylwester et al. (2004, IAU) 19

20. Other diagnostics Spectral lines (not necessarily coronal emission lines) can give information about mass motions, e.g. flows of gas or plasma. This is done through the Doppler shifts of spectral lines. In solar flares, X-ray lines indicate huge upflowing plasma flows at the flare onset phase, velocities of several hundred km/s. Spectral line profiles are often broadened beyond the thermal Doppler width, suggesting plasma turbulence. This occurs in the quiet Sun, active regions, and particularly flares. 20

21. Spectral line profiles Spectral lines can be broadened by several mechanisms. If the coronal gas has a Maxwell-Boltzmann distribution of ions, the observed line width (full width at half maximum flux, FWHM obs ) due to thermal Doppler broadening is: where line wavelength = λ, c = vely. of light, v prob = “most probable thermal speed” of the ion, T ion is the ion temperature, m ion = ion mass. 21

22. X-ray lines showing flare short-wavelength shifts Spectra of the Ca XIX resonance line at 0.318 nm (3.18 Å) at four times during a large solar flare: note short- wavelength component to each spectral line.

23. Summary The solar corona is a fully ionized gas with T = 1-2 MK (~4MK in active regions, up to 20MK in flare plasmas). There is strong X-ray emission in the form of lines and continuum. Lines are due to allowed and forbidden transitions in the ions of “trace” elements (e.g. O, Ne, Fe). Which ions are predominant is determined by a “coronal” ionization equilibrium. Lines are excited by electron collisional processes; resonance lines most intense. Dielectronic recombination gives rise to satellite lines the intensities of which give temperature information. There are a few density-sensitive lines – they indicate N e ~ 10 18 m -3 at the maximum of flare plasma development. X-ray spectral line profiles indicate plasma turbulence in flares accompanied by upflows of a few hundred km/s. 23