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THE ASTROPHYSICAL JOURNAL, 496 : 1031õ1043, 1998 April 1
( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

OBSERVATION AND MODELING OF HIGH-n IRON L-SHELL LINES FROM INTERMEDIATE ION STAGES B. J. WARGELIN,1,2 P. BEIERSDORFER,3 D. A. LIEDAHL,3 S. M. KAHN,1,4 AND S. VON GOELER5
Received 1997 June 23 ; accepted 1997 October 31

ABSTRACT The spectra of highly ionized iron species between 7 and 9 ñ have been studied using data obtained at the Princeton Large Torus tokamak under plasma conditions similar to those present in solar and stellar ÿares. The wavelengths of many iron lines are measured with very high accuracy (j/*j up to 4 ] 104), along with several other lines in species such as He-like Al XII and Mg XI. Theoretical spectra that predict both the wavelength and the intensity of Fe emission lines are compared with the observed spectra and are used to make accurate line identiïcations. Virtually all the observed iron lines are found to arise from n \ 4, 5, and 6 ] 2 transitions in Fe XXIõXXIV, and many lines are identiïed for the ïrst time. Several transitions are shown to have diagnostic applications, and a detailed analysis of the density sensitivity of Fe XXII lines is presented. Subject headings : atomic data õ line : identiïcation õ Sun : X-rays, gamma rays õ X-rays : general
1

. INTRODUCTION

Emission lines arising from n \ 4 ] 2 and n \ 5 ] 2 transitions in highly ionized iron species such as Fe XXIõ XXIV have been observed for many years in the X-ray spectra of solar ÿares (Doschek, Meekins, & Cowans 1972 ; Seely & Feldman 1986 ; McKenzie et al. 1985 ; Fawcett et al. 1987) and are expected to be seen in most classes of X-ray sources by next generation X-ray spectroscopy satellite missions such as the Advanced X-Ray Astrophysics Facility (AXAF) and the X-Ray Multi-Mirror Mission (XMM). Many of these lines are quite prominent, and several can be used to infer the physical parameters of the emitting gas, including electron density, temperature, charge-state distribution, and deviations from coronal ionization equilibrium. Instrumental considerations also encourage the study of 4 ] 2 and 5 ] 2 transitions. Most of these lines fall between 7 and 9 ñ, a range particularly well suited for study using stable and high-resolution diraction crystals such as ammonium dihydrogen phosphate (ADP), with lattice spacing 2d \ 10.648 ñ. In addition, the photon energy is above the low-energy cuto below which most detectorsî quantum efficiency rapidly declines because of photoaborption in windows or surface layers. In particular, AXAFîs eective area, when using either grating/detector combination, peaks in just this energy range. Likewise, for astrophysical sources, photoabsorption by circumstellar and interstellar material is less problematic than it is at longer wavelengths. Finally, most 4 ] 2 and 5 ] 2 lines are well separated, requiring a resolving power of only a few

1 Department of Physics and Space Sciences Laboratory, University of California, Berkeley, CA 94720. 2 Present address : Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138. 3 Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550. 4 Present address : Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027. 5 Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543.

hundred for eective application of diagnostic line-intensity ratios. Clear illustrations of the importance of accurate atomic rate data (for Fe L-shell emission in particular) in analyzing astrophysical X-ray spectra were recently provided by the Advanced Satellite for Cosmology and Astrophysics (ASCA). Several observations showed that existing plasma-emission models, or rather, the emission rates they incorporated, could not provide adequate ïts to the spectral data for any set of physically reasonable plasma parameters (Drake et al. 1994 ; Fabian et al. 1994 ; White et al. 1994). Indeed, subsequent atomic modeling results showed that the intensity of the 3 ] 2 line complex relative to that of the 4 ] 2 blend had been underestimated by a factor of approximately 2 (Liedahl, Osterheld, & Goldstein 1995). These errors were discovered during an analysis of astrophysical spectra with a resolving power of only 20 (near 10 ñ); the highresolution spectral data expected from future missions will provide even greater challenges for spectral modeling codes. Using theoretical atomic models (Doschek et al. 1972 ; Bromage et al. 1978 ; Fawcett et al. 1987) and comparisons with laser plasma spectra (Boiko, Faenov, & Pikuz 1978 ; Fawcett & Ridgeley 1979), many of the transitions seen in solar spectra between 7 and 9 ñ have been identiïed. Several important features remain unidentiïed, however, and very little quantitative work has been done on the diagnostic uses of iron lines in this wavelength band (see Mason & Storey 1980). With adequate knowledge of relevant atomic parameters, however, plasma diagnostics based on 4 ] 2 and 5 ] 2 lines sometimes can be more useful than those relying on the more familiar 3 ] 2 transitions. In this paper we present spectra of highly ionized iron between 7.1 and 9.0 ñ obtained at the Princeton Large Torus (PLT) tokamak, which has temperatures and densities similar to those in solar and stellar plasmas. We compare these high-resolution spectra with results from a detailed atomic model of Fe ions, which allows us to make several new line identiïcations and to develop density diagnostics for astrophysical use. The wavelengths of many lines are measured with unprecedented precision, and a few previously published identiïcations are corrected. We also identify and accurately measure the wavelengths of several 1031


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lines from other common elements that occur in this wavelength region. In ° 2 we discuss plasma conditions in the PLT tokamak, the spectrometer used, and our analysis and calibration procedure. In ° 3 we describe the HULLAC computational suite and the assumptions made in our calculations. In ° 4 we present our observations and line identiïcations, and in ° 5 we discuss line-intensity ratios that can be used as diagnostics.
2

gen plasma during each shot to study emission spectra, either for wavelength calibration or for diagnosis of plasma parameters. Temperature and density can also be measured independently using Thomson scattering and Michelson interferometry, respectively. 2.2. Spectrometer We used a high-resolution vacuum spectrometer with a Bragg crystal and Johann geometry, as described by Beiersdorfer et al. (1989), to record the X-ray spectra presented here. A curved ADP crystal (57.3 cm radius of curvature) focused X-rays from the plasma onto a positionsensitive detector according to the Bragg equation, j \ 2d sin h, where d is the crystal plane spacing (2d \ 10.648 ñ for ADP) and h is the Bragg angle of diraction. In this geometry, diracted X-rays having dierent wavelengths originate from dierent regions of the plasma. The ïrst element of our detector was a ÿat "" chevron îî conïguration microchannel plate, which was coated with approximately 3000 ñ of CsI to increase X-rayõtoõelectron conversion efficiency. Secondary electrons were proximityfocused onto a ïber-optic surface coated with about 8 kmof P-20 phosphor. Light signals then traveled down two ïberoptic tapers to two 1024 channel Reticon photodiode arrays. During each plasma discharge, the array was read out every 4 ms over a period of 192 ms for a total of 48 spectra. Ideally, the detector face would be curved to match the Rowland circle, but since our detector was relatively small, focusing errors did not signiïcantly degrade resolution ; the crystal could also be slightly pivoted on its axis, and diffracted lines could still be adequately focused on the microchannel plate face. To extend the wavelength coverage of the spectrometer further (the bandpass for a single crystal position was typically 1 ñ), the entire spectrometer was tilted, which required careful repositioning of the detector along the Rowland circle deïned by the crystal position and orientation. Our data were obtained using three detector positions, covering three partially overlapping wavelength regions that we refer to as short-, medium-, and long-wavelength ranges. Each of these data sets was further subdivided into two halves by the two-piece ïber-optic taper. The result was six sets of data, each of which required its own wavelength calibration. Because of the nonlinear dispersion characteristics of the spectrometer and slight spatial distortions in the microchannel plate and optical tapers, it was necessary to map out dispersion curves actively in order to obtain the desired wavelength measurement accuracy. 2.3. Calibration To calibrate the wavelengths of observed lines, we injected very small amounts of sodium or magnesium into the plasma by using the laser "" blow-o îî method (Marmar, Cecchi, & Cohen 1975). Approximately 15 ms after injection and 35 ms after the start of data acquisition, the injected ions began emitting prominent K series (1s2 1S õ1s np 1P ) 0 1 and Lyman series lines.6 Figure 1 shows some typical spectra obtained before and during calibration line emission. Sodium and magnesium were chosen as calibrators because a large number of their K and Lyman emission
6 We use the "" K îî label only for He-like emission lines, in order to distinguish them from the H-like Lyman lines.

. DATA COLLECTION

2.1. T he Princeton L arge T orus T okamak Tokamaks, designed for fusion research, have provided abundant information about the physics of highly charged ions (von Goeler et al. 1981 ; Hinnov 1982 ; Peacock, Stamp, & Silver 1984 ; Beiersdorfer et al. 1989). Virtually all existing tokamaks have stainless steel containment vessels, so there is always some background emission arising from highly ionized iron, as well as from smaller amounts of chromium, nickel, and other metals that are sputtered from the chamber walls or limiter plate. Indeed, early tokamaks were unable to attain their expected plasma temperatures because so much energy was lost via radiation from ambient iron ions. Subsequent tokamaks have been designed to minimize sputtering from interior surfaces and often use coatings of low-Z elements such as Be, B, and C so that emission from sputtered ions will be at lower power and photon energies. Tokamaks have plasma conditions similar to those found in stellar coronae, particularly ÿares, which have typical densities of 1011õ1013 cm~3 and temperatures up to a few times 107 K. As a result, spectra from a given element are similar, and results from laboratory observations can often be applied directly to astrophysical sources. Previous laboratory identiïcations of 4 ] 2 and 5 ] 2 transitions in Fe ions have made extensive and eective use of laser plasmas (Boiko et al. 1978 ; Fawcett & Ridgeley 1979), which typically have densities of order 1020 cm~3. At such high densities, however, opacity and satellite broadening eects are often signiïcant, and metastable levels may be collisionally excited to higher levels, which results in radiative transitions that rarely occur in astrophysical X-ray sources. Another dierence is that tokamak plasmas are much larger than laser plasmas, which allows the eective use of curved crystal spectrometers that can be used to map out detailed dispersion curves and provide extremely accurate wavelength measurements. Precise line positions make it easier to identify transitions when comparing observations with theoretical predictions, and they permit more reliable lineintensity measurements when lines are partially blended. The experiments described here were performed on the PLT (Hosea, Goldston, & Colestock 1985), a medium-size tokamak with major and minor radii of 134 and 40 cm, respectively. Typical central electron temperatures when using ohmic heating are 0.8õ3.0 keV [corresponding to (1õ 3.5) ] 107 K], with temperatures falling toward the chamber walls following a roughly Gaussian proïle. Lineof-sightõaveraged electron densities are in the range of (0.2õ 10.0) ] 1013 cm~3, with a typical value of a few times 1013. Densities are highest in the center of the plasma and have a somewhat ÿattened parabolic spatial proïle. A typical plasma discharge, or "" shot,îî lasts about 1 s, and trace amounts of other elements can be injected into the hydro-


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FIG. 1.õExample spectra taken (a) during and (b) before calibration line emission. Each spectrum was collected over a period of 28 ms. The calibration lines are from the Lyman series of hydrogenic Na XI. (The intensity of Lyf is enhanced by charge-exchange recombination of bare Na XII with trace amounts of neutral hydrogen.) Background emission from Fe ions is present in both spectra, along with a few emission lines from residual Al and Se.

lines fall within the 7õ9 ñ range under study, and theoretical calculations of their wavelengths are very accurate. A list of the reference lines used is found in Table 1, along with the estimated uncertainty of each lineîs wavelength. We used the results of Garcia & Mack (1965) for the H-like lines. Their calculations include the weighted contributions of all n ] 1 components (not just the 2P and 2P terms) 3@2 and are accurate to better than 0.0001 ñ. For 1@2 Lya, Mg which has an asymmetric line proïle (Lya and Lya at 8.4192 and 8.4246 ñ are not resolved in 1our data),2 we allowed an uncertainty of 0.0003 ñ to account for any errors introduced by our assumption of a 2 : 1 intensity ratio of the two Lya components. For the He-like lines we used the predictions of U. I. Safronova (1986, private communication), which we believe are more accurate than the wavelengths listed in Kelly (1987, pp. 186, 215). The uncertainty we assumed for each line is generally the dierTABLE 1 WAVELENGTH CALIBRATION LINES Ion Mg10` ...... Mg10` ...... Mg10` ...... Na10` ...... Na10` ...... Na10` ...... Na10` ...... Mg10` ...... Na10` ...... Mg11` ...... Na10` ...... Na9` ....... Na9` ....... Na9` ....... Transition Kv Kd Kc Lyg Lyf Lyv Lyd Kb Lyc Lya Lyb Kv Kd Kc Wavelength (ñ) 7.2247 7.3103 7.4731 7.63936 7.67662 7.73477 7.83318 7.8503 8.02107 8.42100 8.45950 8.6863 8.7885 8.9830 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0002 0.0001 0.0003 0.0001 0.0004 0.0003 0.0002 References 1 1 1 2 2 2 2 3 2 2 2 1 1 1

ence between Safronovaîs and Kellyîs values and makes ample allowance for the fact that the He-like calculations are for only the 1s np 1P ] 1S transitions. Weak tran1 0 sitions from other excited levels (such as 1snp 3P ) will 1 slightly shift the centroid of the blended line, but this eect is negligible for all the He-like calibration lines appearing in our spectra except for Mg Kb. In that case, the eective wavelength of the Mg Kb blend was itself calibrated using nearby Na Lyman lines, which provided a net wavelength accuracy of ^0.0002 ñ. The intrinsic resolving power of the spectrometer when perfectly focused was estimated to be 3500 (Beiersdorfer et al. 1989). The FWHM of the Doppler-broadened lines was measured to be as small as 0.003 ñ (about six detector channels), corresponding to j/*j B 2500. Since the center of a strong line can be measured to a small fraction of its FWHM, the wavelength dierences between lines can be determined with high precision. In most cases, however, it is impossible to exploit this potential precision fully in wavelength measurements because the exact dispersion curve is not well determined. As mentioned previously, however, the crystal in our spectrometer could rotate over a small range without signiïcantly degrading the spectral resolution. Such rotations move the diracted spectrum across the face of the detector, but the angular separations of line pairs (determined by the Bragg diraction condition) remain the same even though their physical separation on the detector changes. We utilized this fact to map out a very precise dispersion curve for each of the six data sets (two detector halves for each of three detector positions) by observing how the channel spacing between pairs of calibration lines changed as those lines moved across the detector. Deïning i as dh/dN, where h is the Bragg angle and N is the detector channel number, the angular separation *h between any two lines is then i(N)dN , (1) N1 where h and N are, respectively, the Bragg angle and 1 detector 1 channel number corresponding to the ïrst line, and h and N correspond to the second line. 2 Taking pairs of calibration lines with known detector 2 positions (channel numbers) and wavelengths (Bragg angles), we can then determine i(N) by using linear leastsquares methods to ïnd the best polynomial ït. Once i is known as a function of N, the wavelength of any line can be calculated based upon the wavelength and position of a single calibration line using the equation j where *h \ unknown \ 2 d sin (h ] *h) , cal (2) *h \ h [ h \ 2 1

P

N

2

REFERENCES.õ(1) U. T. Safronova, private communication, (2) Garcia & Mack 1965 ; (3) this work, measured using nearby Na10` Lyman series lines.

i(N)dN . (3) Ncal We determined i(N) for each data set using calibration data that were statistically weighted according to the uncertainty in each lineîs ïtted channel position (using Voigt proïles) and wavelength (see Table 1). Second-order polynomials gave acceptable ïts to ïve of the calibration data sets, while the ïrst half of the medium-wavelength data required a third-order ït. That data set was exceptionally well constrained by its numerous and strong Na Lyman

P

N

unknown


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WARGELIN ET AL.

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series lines and permitted the wavelengths of several Fe lines to be measured to 0.0002 or 0.0003 ñ. Near the ends of our spectral coverage, wavelength calibration was somewhat less precise for several reasons : (1) spectral resolution was worse because the crystal was at nonoptimal angles ; (2) calibration-line wavelengths were not as accurately known ; (3) both calibration and Fe lines were generally weaker. It was also observed that the positions of the longest wavelength lines drifted slightly during the course of a shot, but this phenomenon was very repeatable, and we minimized its impact by comparing calibration and Fe-emission data taken from identical time groups. As a result, a calibration accuracy of 0.001 ñ or better was maintained over the entire range studied.
3

. CALCULATED SPECTRA

The model spectra were calculated using the HULLAC atomic physics package. For the problem at hand, HULLAC was used to calculate the atomic structure of the ions Fe XXIõXXIV, the radiative decay rates, and the rate coefficients for electron impact excitation. These atomic data were then used to calculate the distribution of level populations within each charge state according to the equations of statistical equilibrium, from which the line spectrum follows. Model spectra from Cr XXIõXXII were also calculated since those ions have some emission lines in the wavelength range under study. The atomic structure and radiative rates are calculated ab initio using a relativistic, multiconïguration, parametricpotential method in intermediate coupling (Klapisch et al. 1977). HULLAC was developed for optimum performance with highly charged high-Z ions, for which intermediate coupling using j-j basis states is most appropriate. In this paper, LS-coupling notation is used when such a term can be unambiguously assigned (as for all Li-like and Be-like states, and B-like states with a 2s2 core). For B-like transitions involving a 2s electron, and for all C-like transitions, j-jõcoupling notation has been used, along with LS terms suggested by other authors for previously identiïed lines. The models used in the calculations are given in Table 2. Radiative transitions include the multipoles E1, E2, M1, and M2. The collisional cross sections are calculated according to the quasi-relativistic distorted wave approximation (Bar-Shalom, Klapisch, & Oreg 1988). Collisionalrate coefficients c (units of cm3 s~1) are found by averaging vp(v) over a Maxwellian velocity distribution. The rate coefïcients for collisional excitation from all states within conïgurations (2s2p)k to all excited states (2s2p)k~1nl in the models are calculated, as well as the 2l ] 2l@ intrashell excitations.

Coupling of excited states to levels in adjacent charge states through inner shell ionization, dielectronic recombination (DR), and radiative recombination is ignored for several reasons. K-shell ionization of Fe ions in their ground states produces no emission in the spectral band studied here. DR, on the other hand, contributes D10% of the total line ÿux, varying with temperature and ion species (Liedahl et al. 1995). For plasma temperatures of interest here, DR involving excitation of an L-shell electron is most important. Each such recombination begins with a radiationless capture of the form (2s2p)k ] e ] (2s2p)k~1nln@l@ (n, n@ º 3), which may stabilize with the emission of an X-ray satellite line. The excited but bound state left by stabilization, (2s2p)knl, cascades to the ground state, with the eventual emission of another X-ray. Of the two X-rays produced as a consequence of DR, only the satellite is distinct from the line produced directly through electron impact excitation and can, in principle, be identiïed. The satellite spectrum is, however, composed of a large number of weak lines, and except for the possibility of detecting the long-wavelength shoulders (unresolved satellites) of resonance lines of the recombining ion, DRdriven lines in these ions are generally too weak to select out from spectra measured in tokamak experiments. Ignoring recombination therefore cannot lead to line misidentiïcation because of satellite contamination. Likewise, intensity enhancement of nonsatellite lines produced through DR-initiated cascades is too small an eect to isolate. Radiative recombination is even less important than DR in driving 4 ] 2 and 5 ] 2 line emission in these ions (under conditions near coronal equilibrium) because the generally small rates are dominated by capture into the n \ 2 and n \ 3 levels, bypassing the higher n levels. Charge transfer from neutral hydrogen, in contrast, preferentially populates high-n levels, roughly n \ 9 õ11 for the Fe charge states of interest here. Since radiative decays tend to proceed to the lowest energy level allowed by selection rules, most of those high-n levels either decay directly to a ground level (e.g., 10s ] 2p), or fall as far as they can to intermediate-n levels with l \ l \ n [ 1 (e.g., 10h ] 5g), which then decay via ' *n \ *l \ 1 steps along the so-called Yrast chain (e.g., 5g ] 4f ] 3d ] 2p). Such transitions are not expected to contribute appreciably to our spectra, and charge exchange is therefore not considered in our modeling calculations. As shown in Table 2, two C-like Fe models were used in the calculations. As indicated, the 676 level model does not include the n \ 3 or n \ 4 shells. These were omitted in the calculations of 5 ] 2 and 6 ] 2 Fe XXI spectra simply to keep the size of the models manageable. This introduces

TABLE 2 CHARACTERISTICS OF ATOMIC MODELS USED IN CALCULATING MODEL SPECTRA Name Fe XXI ....... Fe Fe Fe Cr Cr XXII ...... XXIII ...... XXIV ...... XXI ....... XXII ...... Isosequence C C B Be Li Be Li Number of Levels 1004 676 735 302 42 166 42 n l ' 4 3 4 4 4 4 4 Number of Radiative Rates 132959 63370 74338 12034 330 12019 331 Number of Collisional Ratesa 18662 12099 10341 2900 118 2911 118

' 5 6b 6 7 7 7 7

a Each rate computed on a 6 point temperature grid. b Model does not include levels with principal quantum numbers n \ 3or4.


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small errors in the branching ratios of radiative transitions from n \ 5 and n \ 6 excited states, but the resulting errors in relative line intensities are also small and have no bearing on the results presented here.
4.

OBSERVED SPECTRA AND LINE IDENTIFICATIONS

Some 60 shots, each with 48 time-binned spectra, were scanned for prominent features, and approximately 50 lines of high statistical signiïcance and reproducibility were discerned, not counting the Na and Mg calibration lines. A composite spectrum is shown in Figure 2 with each feature labeled (see ïgure legend for labeling convention). Well over 30 Fe lines were identiïed, along with 10 lines from other elements, including Li-like Cr XXII. The composite spectrum combines spectra collected using eight dierent detector-position or crystal-angle settings, which were chosen based on (1) high signal-to-noise ratio, (2) high resolution, and (3) exclusion of lines from elements other than Fe and Cr. In a few cases, it was impossible to avoid inclusion of some weak calibration lines below 7.5 ñ, as well as a few lines from Al and Se. Those lines were excised from the composite spectrum (and labeled in parentheses) to facilitate comparison with the model spectrum, which includes emission from only Fe and Cr ions. The component spectra were joined at 7.505, 7.814, 7.881, 7.958, 8.006, 8.106, 8.352, 8.413, 8.453, 8.498, 8.566, 8.851, and 8.943 ñ, and their relative amplitudes and continuum levels were adjusted so that overlapping lines had approximately equal strength. As mentioned in ° 2.2, within individual spectra focused X-rays of dierent wavelengths arise from dierent regions of the tokamak plasma, i.e., regions that have dierent temperatures, densities, and plasma column depths. Thus it can be seen that lines near the two ends of the composite spectrum become increasingly weak, since the spectrometer was collecting X-rays emitted near the edges of the tokamak plasma. Indeed, below about 7.4 ñ, only a low-temperature, short-column portion of the plasma can be observed, and no lines from highly ionized Fe are seen. The theoretical spectra used to identify transitions in the observed data are also shown in Figure 2, with line widths set to 0.0063 ñ FWHM (corresponding to j/*j \ 1270 at 8 ñ). Two such spectra are shown ; both are composed of the same lines with the same intensities, but one employs line wavelengths that have been slightly adjusted (as described later in this section) to agree more closely with the observed spectrum, while the other uses the directly computed, uncorrected wavelengths. This illustrates how slight dierences in line wavelengths can alter the appearance of spectra. As discussed in ° 3, the theoretical model includes emission from Fe XXIõXXIV and Cr XXII. Because the observed spectrum has been assembled from several shots, each occurring under somewhat dierent circumstances and each line originating from a dierent part of the plasma, the relative emission measure of each ion included in the theoretical model was adjusted "" by eye îî to match the observed data as well as possible. For simplicity, we set a temperature of 1000 eV for all ionsõthe relative line strengths within a given charge state depend only weakly on temperatureõ and adjusted the relative ion abundances as follows : Fe XXIV, 1.00 ; Fe XXIII, 0.78 ; Fe XXII, 0.61 ; Fe XXI, 0.063 ; Cr XXII, 0.78. Emission from Cr XXI, although calculated,

was not included in the model spectrum because it was not observed in the data. As will be discussed in ° 5, the spectra of B- and C-like Fe depend on electron density ; the spectrum shown assumes a density of 1013.5 cm~3. As can be seen, the resulting theoretical and observed spectra match very well, with generally excellent agreement in wavelengths and relative intensities. In Table 3 we list our Fe-line identiïcations, along with a comprehensive compilation of previous theoretical and observational work on Fe spectra between 7 and 9 ñ with wavelength accuracies of 1 or 2 mñ. The wavelengths reported by McKenzie et al. (1985) are also included (following a slight correction) even though the accuracy they quote is only 3 mñ. Although their solar observations are of high quality and resolution, the measured wavelengths of well-studied transitions in hydrogenic and helium-like ions for lines between approximately 7.2 and 8 ñ are systematically 3 or 4 mñ longer than the known values, which indicates a calibration error. We therefore reduced their measured wavelengths by 0.003 ñ for lines shortward of 8 ñ, which brings their results into excellent agreement with other measurements. Since our emphasis is on astrophysical applications, Table 3 does not include lines that have been observed only in laser plasma spectra, since many of those lines arise from doubly excited states, which can only be excited in extremely high density environments (Bromage et al. 1978). Using the same inclusion criteria as those used for Table 3, Table 4 lists unidentiïed lines that are believed to come from Fe based on a priori knowledge of plasma constituents. Table 5 lists lines from elements other than Fe that were observed in our spectra, several of which are prominent in solar ÿare spectra and have important diagnostic applications. Nearly all of our wavelength measurements are accurate to 1 mñ. Two exceptions are included in Tables 3 and 4, with uncertainties of 0.003 ñ or more : line E1 (at D7.478 ñ) because of blending with residual Mg Kc emission, and line U4 (at D9.009 ñ) because it was at the very edge of our spectral coverage and resolution was poor. In those cases where a measurement is accurate to better than 1 mñ, the uncertainty in the last digit (tenths of 1 mñ) is indicated in parentheses. We are able to measure the wavelengths of 27 lines to better than 1 mñ. Five of those lines have been previously measured to an accuracy of 0.0007 ñ by Seely & Feldman (1985), and our agreement with their results is excellent. No accuracy estimates are provided for the theoretically calculated wavelengths listed in Table 3, but agreement between our calculations and observed values is excellent for the Fe XXIV lines. Agreement among the Fe XXIII lines is equally good, except for the six lines arising from transitions to the 2s2p 1P level (lines E11, E10, E5, E4, E2, and part of the E1 blend), 1 each of which had observed wavelengths that were approximately 0.010 ñ shorter than those predicted by theory. We are unable to explain this discrepancy, but note that if the calculated energy of the 2s2p 1P level is 1 decreased from 95.1 to 93.2 eV (above the 2s21S ground state), the wavelengths of all six lines are brought 0 within to 0.001 ñ of their respective observed values. It is interesting that the calculations of Fawcett et al. (1987) apparently have a similar error in the energy of the 2s2p 1P level, but 1 no other Fe XXIII levels. For transitions in B-like Fe XXII, our calculated wave-


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FIG. 2.õObserved and model spectra. The observed spectrum is a composite ; the dierent sections have been adjusted in amplitude to maintain reasonably consistent line intensities, but no other adjustments have been made to account for the instrumental response, or for the variety of plasma temperatures and densities represented in the data. Portions of the spectrum below D7.4 ñ and above D8.8 ñ are of lower quality because of unavoidable instrumental eects. Small gaps in the data (with labels in parentheses) are where non-Fe emission lines have been excluded for clarity. The labeling convention for Fe and Cr lines is as follows : L for Li-like Fe XXIV, E for Be-like Fe XXIII, B for B-like Fe XXII, and C for C-like Fe XXI ; Cr for Cr XXII ; U for unidentiïed. Model spectra are shown both with and without wavelength adjustments. For the adjusted spectrum, 0.7 eV was added to each C-like line, 1.2 eV to each B-like line, and 1.9 eV to the six Be-like transitions having lower level 2s2p 1P (lines E11, E10, E5, E4, E2, and part of E1). As explained in the text, these few 1 systematic corrections bring virtually all model lines into excellent agreement with observed wavelengths. Calibration lines from Na and Mg are shown across the top.

lengths are systematically about 6 or 7 mñ longer than the measured values ; if 1.2 eV is added to the theoretical energies of all Fe XXII lines listed in Table 3, then the maximum dierence between calculated and measured wavelengths is only 0.001 ñ (excluding the three tentatively identiïed B-like lines that will be discussed in ° 4.3). The theoretical wavelengths for the C-like lines are all approximately 0.004 ñ longer than those experimentally measured (equivalent to a dierence of 0.6 eV), except for line C4, which has a calculated wavelength 0.007 ñ shorter than that observed. On theoretical grounds we expect HULLAC predictions to be more reliable than previous predictions, since the HULLAC models include more energy levels (n \ 6 or 7) ' and predict emergent line intensities rather than just oscillator strengths. Intensity predictions based solely on oscillator strengths can be misleading when levels are populated by mechanisms other than direct dipole electron impact excitation, or when they decay via forbidden transitions or multiple branches. A good example is provided by the Fe XXIV 4 ] 2 lines. Although the radiative rates (and thus

oscillator strengths) for 2sõ 4d (*L \ 2) transitions are negligibly small, the 4d levels are populated from the 2s level by nondipole collisional excitation and then decay via fully allowed transitions to produce 4d ] 2p lines (L9 and L7) that are just as strong as the 4p ] 2s lines (L5 and L6). Our expectations are met by the excellent agreement between measurements and theory with regard to wavelengths (after the few systematic adjustments described above) and relative line intensities within each ion species. This gives us conïdence in our line identiïcations even when they may disagree with previous work. In the following subsections we discuss the results in more detail, beginning with emission from dierent ion stages of Fe, followed by unidentiïed Fe lines, and concluding with emission from elements other than Fe. 4.1. L ithium-like Fe XXIV Fe XXIV has 10 signiïcant emission lines between 7.1 and 9 ñ, of which we are able to observe the eight that lie above 7.4 ñ. Agreement between observation and theory is ex-


TABLE 3 IRON SPECTRAL LINES Line Identiïcationa L1 ............. L2 ............. L3 ............. L4f ............ E1g ............ j obs (ñ)b 7.169c 7.370c 7.437d 7.438c 7.457d D7.478d 7.472c 7.498d 7.6812 7.680c 7.682i 7.733d 7.733c 7.752d 7.865d 7.9009 7.902j 7.901c 7.936d 7.9857 7.986j 7.986i 7.984k 7.983c 7.9960 7.996j 7.996i 7.992k 7.993c 8.0904 8.091j 8.1536 8.153i 8.1684 8.167c 8.2036 8.2326 8.232j 8.233i 8.231k 8.231c 8.274d 8.273c 8.271k 8.2850 8.2854 8.285c 8.289k 8.3038 8.3040 8.305j 8.305i 8.303k 8.303c 8.3161 8.3160 8.317j 8.318i 8.316k 8.316c j calc (ñ) 7.1649d,e 7.1692d,e 7.368d 7.3670e 7.437d 7.4363e 7.461d 7.4601e 7.473d (7.489)d 7.475h 7.506d 7.687d (7.683)d (7.680)h 7.736d 7.734h 7.757d 7.870d 7.911d 7.886h 7.947d 7.986d 7.9862e 7.985j 7.986l 7.979m 7.996d 7.9964e 7.995j 7.996l 7.989m 8.097d 8.074j 8.157d 8.174d 8.206d 8.234d 8.232j 8.2322e 8.232l 8.225m 8.283d

Fe Ion XXIV XXIV XXIV XXIV XXIII (XXIII) XXIII XXII (XXIII) (XXIII) XXIII XXII XXII XXIII XXIII XXIV

Transition 2s 2S õ5p 2P (weighted average \ 7.1664 ñ) 1@2 3@2, 1@2 2p 2P õ5d 2D 1@2 3@2 2p 2P õ5d 2D 3@2 5@2 Tentative identiïcation : 2p 2P 3@2 õ5s 2S 1@2

2s21S õ2s5p 1P 0 1 (28% from 2s2p 1P õ2s6d 1D ) 1 2 2s2p 1P õ2s6s 1S 1 0 2s22p 2P õ2s26d 2D 1@2 previously identiïed line 2s2p 3P õ2s5d 3D in Fe XXIIIh) 3@2 (dominates 1 2 2s2p 3P õ2s5d 3D 2 3 2s22p 2P õ2s26d 2D 3@2 5@2,3@2 2s22p 2P õ2s2p 5p (J \ 1/2, 3/2) 1@2 1@2 1@2, 3@2 2s2p 1P õ2s5d 1D 1 2 2s2p 1P õ2s5s 1S 1 0 2s 2S õ 4p 2P 1@2 3@2

E2f ............ B1g ............

(4)d

E3 ............. B2f ............ B3f ............ E4f ............

(5)d

E5f ............ L5 .............

(2)d

L6 .............

(4)d

XXIV

2s 2S õ 4p 2P 1@2 1@2

B4 ............. C1f ............ B5f ............ C2f ............ L7 .............

(3)d (5)d (4)d (9)d (4)d

XXII XXI XXII XXI XXIV

2s22p 2P õ2s25d 2D 1@2 3@2 2s22p 1@2 2p 1@2 (J \ 0) õ2s22p 1@2 6d (J \ 1) 3@2

2s22p 2P õ2s25d 2D 3@2 5@2, 3@2 2s22p 2p (J \ 1) õ2s22p 6d (J \ 2) 1@2 3@2 1@2 5@2 2p 2P õ 4d 2D 1@2 3@2

B6f ............

XXII XXIV

Tentative identiïcation : 2s2p 2p (J \ 5/2) õ2s2p 5d (J \ 7/2) ; previous identiïcation h : 3@2 1@2 Fe XXIII 2s2p 3P õ2p4p 3D 3@2 3@2 2 3 2p 2P õ 4s 2S 1@2 1@2

L8 .............

(4)d (7)n

E6 .............

(3)d (7)n

8.287d 8.2862e 8.279m 8.284l 8.304d 8.305j 8.306h 8.306m

XXIII

2s21S õ2s4p 1P 0 1

L9 .............

(3)d (7)n

8.319d 8.3171e 8.317j 8.317l 8.311m

XXIV

2p 2P õ 4d 2D ; also Fe XXIII 2s2s 1S õ2s4p 3P , at j \ 8.317 ;dj the shoulder on 5@2, 5 ] 0 1 the3@2 long side is 3@2 2 transitions in Fe XXII and Fe XXI calc


TABLE 3õContinued Line Identiïcationa L10 ........... j obs (ñ)b 8.3761 8.3757 8.376i 8.371c 8.4053 8.4055 8.406c 8.529d 8.528k 8.529c 8.546d 8.550j 8.547k 8.550c 8.5740 8.573j 8.574i 8.575c 8.6172 8.616j 8.619i 8.614k 8.614c 8.640d 8.644j 8.643c 8.663d 8.660j 8.664c 8.714d 8.715j 8.714c 8.720d 8.722j 8.723c 8.736d 8.734j 8.736c 8.753d 8.752k 8.752c 8.8149 8.815j 8.811i 8.812k 8.814c 8.906d 8.906j 8.906k 8.908c 8.9748 8.976j 8.975i 8.977c (7)d (7)n j calc (ñ) 8.376d 8.3758e 8.373l 8.368m 8.421d

Fe Ion XXIV

Transition 2p 2P õ 4s 2S ; also about 15% from Fe XXII 2s2p 2p (J \ 3/2) õ2s2p 5s(J \ 1/2) 3@2 1@2 1@2 3@2 1@2 at j \ 8.387 ;d the shoulder on the short side is a 6 ] 2 Cr XXII line calc Tentative identiïcation : 2s2p 2p (J \ 1/2) õ2s2p 5d (J \ 3/2) ; observed intensity 1@2 3@2 1@2 5@2 is about twice that predicted 2s2p 3P õ2s4d 3D 0 1 2s2p 3P õ2s4d 3D 1 2, 1 [and 2s22p 2p (J \ 1) õ2s2 2p 5d (J \ 2, 1, 0)] 1@2 3@2 3@2 3@2 2s22p 2p (J \ 0) 3P õ2s22p 5d (J \ 1) 3D 1@2 2p 1 [and 2s21@2 2p (J 0 2) õ2s1@2p 3@2d (J \ 3)] \ 22 5 1@2 3@2 3@2 3@2 2s2p 3P õ2s4d 3D 2 3

B7f ............

(6)d (7)n

XXII XXIII XXIII (XXI) XXI (XXI) XXIII

E7 .............

8.529d 8.527h 8.551d (8.547d) 8.552j 8.548h 8.578d (8.581)d 8.573j 8.617d 8.618j 8.615h

E8g ............

C3g ............

(8)d

E9 .............

(6)d

C4 .............

8.633d

XXI XXI XXII XXII XXII XXII XXIII

2s22p

1@2

2p

3@2

(J \ 1) õ2s22p

1@2

5d (J \ 2) 5@2 5d (J \ 3), 2s22p 2p (J \ 2) õ2s22p 5d (J \ 3) 5@2 3@2 3@2 3@2 5@2

C5f ............

8.668d

2s22p

1@2

2p

3@2

(J \ 2) õ2s22p

1@2

B8 .............

8.720d 8.713j 8.728d 8.723j 8.744d

2s22p

1@2

2P

õ2s2p 4p (J \ 3/2) 1@2 1@2 3@2 õ2s2p 4p (J \ 1/2) 1@2 1@2 3@2 õ2s2p 4p (J \ 3/2) 1@2 1@2 1@2

B9 .............

2s22p

1@2

2P

B10f ...........

2s22p

1@2

2P

B11f ...........

8.769d

E10 ...........

(4)d

8.826d 8.826j 8.794h

Tentative identiïcation : 2s 22p 2P õ2s2p 4p (J \ 1/2) ; observed intensity is about 1@2 1@2 1@2 1@2 twice that predicted ; previous identiïcation : h Fe XXIII 2p21D õ2p4d 1F but very weak 2 3 at normal densities, and j \ 8.737d calc 2s2p 1P õ2s4d 1D 1 2

E11 ...........

8.918d 8.919j

XXIII

2s2p 1P õ2s4s 1S 1 0

B12 ...........

(6)d

8.982d 8.976j 8.952h

XXII

2s22p 2P õ2s24d 2D 1@2 3@2

a b c d e f g h i j k l m n

Labeling convention : L for Li-like Fe XXIV, E for Be-like Fe XXIII, B for B-like Fe XXII, C for C-like Fe XXI, U for unidentiïed. Numbers in parentheses give the uncertainty of the measured wavelength in tenths of 1 mñ. When no error is listed, the uncertainty is 1 or 2 mñ. Laser plasma observations by Boiko et al. 1978. This work. Theoretical calculations by Vainshtein & Safronova 1985. New identiïcation. Clariïcation of previously published identiïcation. Theoretical calculations by Bromage et al. 1978. Solar observations (with wavelength corrections) by McKenzie et al. 1985. Solar observations and theoretical calculations by Fawcett et al. 1987. Laser plasma observations by Fawcett & Ridgeley 1979. Theoretical calculations by Edlen 1979. Theoretical calculations by Doschek et al. 1972. Solar observations by Seely & Feldman 1986.


MODELING OF HIGH-n IRON L-SHELL LINES cellent, except for the wavelength and intensity of L4 (2p 2P õ5s 2S ). The measured wavelength of L4 is at 3@2 1@2 least 0.003 ñ lower than predicted, and its observed intensity is roughly 3 times higher than predicted. It is possible that the "" true îî 2p 2P õ5s 2S transition is obscured by 3@2 1@2 the wing of Mg Kc, and that line L4 is in fact some other, unknown transition, but we are unable to suggest any likely candidates. We therefore label our identiïcation of L4 as tentative. 4.2. Beryllium-like Fe XXIII Of the 11 Fe XXIII transitions listed, four are new. They are the 6 ] 2 and 5 ] 2 analogs of the previously identiïed 4 ] 2 transitions 2s2p 1P õ2s4d 1D (E10 at 8.815 ñ) and 1 2 2s2p 1P õ2s4s 1S (E11 at 8.906), and correspond to, respec1 0 tively, line E1 at D7.478 ñ (in which the 2s2p 1P õ2s6d 1D 1 2 transition has about one-third of the intensity of the previously identiïed 2s21S õ2s5p 1P transition) ; E2 at 7.498 ñ ; E4 at 7.901 ñ (which0had been1 incorrectly assigned to a line at 7.883 ñ by Bromage et al. 1978 in their study of the Boiko et al. 1978 laser plasma spectra) ; and E5 at 7.936 ñ. The wavelength of the E1 blend is not well measured in our data, but when the 1.9 eV correction (see ° 4) is applied to the 2s2p 1P õ2s6d 1D component, we predict a centroid 1 of 7.474 ñ for the blend.2 was found that the E8 line is also It a blend, consisting of a Be-like line and a cluster of 5 ] 2 transitions in C-like Fe. 4.3. Boron-like Fe XXII There are several new or reidentiïcations of Fe XXII lines, including a few density-sensitive lines whose use as diagnostics will be discussed in ° 5. Lines B1 and B2 are 6 ] 2 transitions, which are quite strong in some of our spectra. The B1 transition 2s22p 2P õ2s 26d 2D was found to 1@2 3@2 dominate a previously identiïed but much weaker transition in Fe XXIII. Nearly as strong as B1 are lines B2 and B3

1039

(a newly identiïed 5 ] 2 transition), but their wavelengths could not be measured as precisely because they were partially obscured by the so-called w and z lines of He-like Al XII (see Table 5). The identiïcation of B5 (along with the C-like line, C1) solves a puzzle in a series of solar ÿare spectra reported 25 years ago by Doschek et al. (1972). They observed six strong lines or blends between 7.95 and 8.40 ñ and were able to correctly identify four as transitions in Fe XXIV and XXIII, leaving two unknown features around 8.10 and 8.16 ñ. They correctly suggested that the ïrst line (which we label B4) might be the 2s22p 2P õ2s25d 2D transition in Fe XXII 1@2 3@2 but were puzzled by the second "" doublet îî feature, which did not weaken over time (as the ÿare cooled and the ions recombined) like any of the other lines. That second feature is the blend of C1 and B5 (8.154 and 8.168 ñ, respectively). As the ÿare cooled and B-like emission decreased, the net intensity of the C1/B5 blend was maintained by emission from the increasing population of C-like ions. The B5 line itself consists of two transitions, one of which is sensitive to density. The only other new Fe XXII identiïcation that we consider ïrm is the B10 line at 8.736 ñ, but we have also made three other tentative line identiïcations : B6 at 8.274 ñ, B7 at 8.4053 ñ, and B11 at 8.753 ñ. All of these features have been observed in laser plasma spectra, and B7 has also been seen quite distinctly in a solar spectrum by Seely & Feldman (1986). Our model calculations showed that earlier identiïcations of B6 and B11 by Bromage et al. (1978) were incorrect ; the intensities of their proposed lines are negligible at astrophysical (coronal) densities, and the expected wavelength of their proposed B11 transition is o by at least 0.015 ñ. Our own identiïcations of these three lines, however, also must be treated with caution because of disagreements between observation and calculation that are

TABLE 4 UNIDENTIFIED IRON LINES Line Identiïcationa None ......... None ......... None ......... None ......... U1 ............ U2 ............ j obs (ñ)b 7.919c 7.949e 8.141e 8.2557 (7)f 8.560d 8.919d 8.918c 8.920e 8.921g 8.937d D9.009d 9.006c 9.006g Always present, but usually weak in our data ; intensity may scale with that of U3

Comments Weak, probably Fe XXI 2s22p 2p (J \ 1) õ2s2p 2p 6p (J \ 2, 1) at j \ 7.924 ;d 1@2 3@2 1@2 3@2 3@2 calc we observe a weak feature at 7.919 ñ We observe a weak feature at D7.950 ñ We observe a weak feature at 8.138 ñ

U3 ............ U4 ............

Probably from the same ion as U2 Previous identiïcation : h Fe XXII 2s2p24P 5@2 õ2s2p4d (3P)4D 7@2 , but very weak at normal densities

a Labeling convention : L for Li-like Fe XXIV, E for Be-like Fe XXIII, B for B-like Fe XXII, C for C-like Fe XXI, U for unidentiïed. b Numbers in parentheses give the uncertainty of the measured wavelength in tenths of 1 mñ. When no error is listed, the uncertainty is 1or2 mñ. c Solar observations and theoretical calculations by Fawcett et al. 1987. d This work. e Solar observations (with wavelength corrections) by McKenzie et al. 1985. f Solar observations by Seely & Feldman 1986. g Laser plasma observations by Boiko et al. 1978. h Theoretical calculations by Bromage et al. 1978.


1040

WARGELIN ET AL.
TABLE 5 NON-IRON EMISSION LINES Line Identiïcation Se1 ........... Al w .......... Al xy ......... Mg Kb ...... Al z .......... Se2 ........... Se3 ........... Se4 ........... Cr1 ........... Cr2 ........... Cr3 ........... j obs (ñ) 7.6907 7.7573 7.8067 7.8503 7.8722 7.8779 7.9667 7.9744 8.519 8.777 8.8444 (3) (2) (5) (2)d (3) (3) (7) (6) (6) j ref (ñ) 7.685a 7.7573b 7.8065b,c 7.8507e 7.8721b 7.874a 8.516f,g 8.7749g 8.8442g

Vol. 496

Ion Se24` Al11` Al11` Mg10` Al11` Se24` Se23` Se23` Cr21` Cr21` Cr21`

Transition 2s22p61S õ2s22p53d 1P 1 1s21S õ102p 1P s 0 1 1s21S õ1s2p 3P 1s21S0õ1s3p 1P2, 1 0 1 1s21S õ1s2s 3S 0 1 2s22p61S õ2s22p53d 3D 0 1 2s 2S õ5p 2P 1@2 3@2, 2p 2P õ5d 2D 1@2 1@2 3@2 2p 2P õ5d 2D 3@2 5@2

a Measured wavelength from Boiko et al. 1978. b Theoretical wavelength from Drake 1988. c Weighted average of 15% 7.8038 ñ and 85% 7.8070 ñ ; weights derived from relative upper level populations of 5 : 3, and branching ratios of 0.107 and 1.0. d Measured line includes small but signiïcant contributions from 1s3l levels other than 1s3p 1P , which slightly shift the centroid of the line. 1 e Theoretical wavelength from U. I. Safronova 1986, private communication. f Weighted average of 67% 8.5140 ñ and 33% 8.5183 ñ. g Theoretical wavelength from Vainshtein & Safronova 1985.

signiïcantly larger than for any of the other lines we have identiïed. Speciïcally, for these lines, j õj ranges calc obs between 0.003 and 0.009 ñ (after applying the systematic 1.2 eV B-likeõline energy correction), and I /I varies calc obs between 1 and 1 . There 2 one 3 is other B-like worth mentioning, even though we cannot resolve it on our spectrum. Lying within the B-like emission cluster between 8.70 and 8.76 ñ is a densitysensitive transition, 2s22p 2P õ2s2p 4p (J \ 5/2), 3@2 3@2 3@2 3@2 which we predict lies at 8.730 ñ (following the 1.2 eV correction). Although relatively weak in our spectrum, the relative intensity of this transition is predicted to increase by a factor of more than 5 between 1013 and 1014 cm~3 so that it becomes stronger than the B10 line, but because of blending with nearby lines, it is somewhat difficult to use it as a density diagnostic. Fortunately, there is a pair of B-like lines around 9.0 ñ that are very strong, well separated from other lines, and whose intensity ratio is a function of density (see ° 5). 4.4. Carbon-like Fe XXI All ïve of the C-like features that we identify in Table 3 have been observed in solar spectra, including the relatively weak C2 line, which can be discerned in the spectra of Doschek et al. 1972. Only one of those lines, however, has been previously (partially) identiïed : the C3 line at 8.574 ñ. At low densities, C3 is the brightest of all the C-like 5 ] 2 features. This line is actually a blend of four transitions, although at densities below 1014 cm~3 the densityinsensitive transition originally identiïed by Fawcett et al. (1987) is strongest. The other three transitions are 2s22p 2p (J \ 2) õ2s22p 5d (J \ 3), 2s22p 2p 1@2 3@2 3@2 3@2 (J \ 2) õ2s22p 5d (J \ 2), and 2s22p 2P (1@2 2) õ J \ 3@2 3@2 \5@2 with relative strengths 3@2 approx1@2 2s22p 5d (J 1), of 3@2 3@2 imately 7 : 3 : 1. Between 1011 and 1013 cm~3 their intensity increases almost 6 times faster than density, and their combined strength equals that of the density-insensitive transition at around 3 ] 1013 cm~3. Like C3, the C4 and C5 lines (C5 is a blend with two dominant transitions) are also

density sensitive, and surpass C3 in intensity above approximately 1014 cm~3. These and other potential diagnostic lines are discussed further in ° 5.1. 4.5. Unidentiïed L ines We are unable to identify a number of lines we observed. Those lines, and any other unclassiïed lines previously seen in solar spectra between 7.0 and 9.1 ñ, are listed in Table 4. The line at 7.871 ñ seen by Fawcett et al. (1987) in a solar ÿare spectrum is undoubtedly from Al XII 1s21S õ1s2s 3S , 0 1 and is not listed. Although there are some features in the model spectrum near U2, U3, and U4, they are much too small compared to the predicted intensities of E10 and B12 to explain the relative intensities of the observed lines. (Recall that lines near the edge of the spectrum are suppressed by instrumental eects.) In our eorts to identify the lines in question, satellite lines of iron and emission from C-, N-, and O-like nickel were investigated using HULLAC, but no plausible candidates were found. Although deïciencies in the atomic models, exotic plasma processes in the tokamak or solar corona, emission from trace elements, and similar explanations cannot be entirely excluded, we suggest that most of the unclassiïed lines likely come from lower ionization stages of iron such as N-like Fe XX and O-like Fe XIX. Because of the complexity in modeling those ions, particularly with the high-n atomic levels that would be required (n º 5), and because of uncertainties in the relative intensities of the unidentiïed lines near the edge of the spectrum, we have not pursued those investigations further. 4.6. Non-Fe Emission L ines In addition to emission from Fe ions (and the calibration lines from Na and Mg), we also observed lines from three other elements that were present in the tokamak as impurities : Al, Se, and Cr. The aluminum is from the housing of a probe used to make plasma-edge measurements. The selenium was left over from injection during a preceding experiment and appeared only in the early stages of our experiment. Chromium, like iron, is a component of the


No. 2, 1998

MODELING OF HIGH-n IRON L-SHELL LINES

1041

stainless-steel containment vessel and is always present, although at only about 10% the level of iron. Nickel is also present for the same reason, but as described above, was not observed. The remaining few percent of the stainless steel chamber consists mostly of manganese, which has negligible emission at such a low concentration. Ten emission lines from the above three elements are listed in Table 5, along with Mg Kb, a calibration line that was itself calibrated using Na Lyman lines as discussed in ° 2.3. The Al lines are He-like Ka transitions, speciïcally the resonance line (1s21S õ1s2p 1P ), intercombination line 0 1 blend (1s21S õ1s2p 3P with 85% from 3P ), and for0 2, 1 1 bidden line (1s21S õ1s2s 3S ). We believe that our wave0 1 length measurements of these lines known respectively as w, x, y, and z in the notation of Gabriel (1972) are the most accurate to date, and note that they are essentially in perfect agreement with the predictions of Drake (1988). Se1 and Se2, the two most prominent selenium lines we observe, are from transitions in Ne-like Se XXV. These lines are quite strong in one of our shots, allowing us to determine their wavelengths with an uncertainty of only 0.0003 ñ. The wavelengths we measure are about 0.004 ñ longer than those measured by Boiko et al. (1978). Based on previous work (Beiersdorfer et al. 1989), we also identiïed Se3 and Se4 as transitions in Na-like Se XXIV. As discussed before, our theoretical model includes Li-like Cr XXII and Be-like Cr XXI. Emission from chromium is generally weak, but we are able to conïdently identify three lines as 5 ] 2 transitions in Cr XXII. There are some indications of 6 ] 2 and 7 ] 2 emissions at 8.365, 8.099, 8.065, and 8.041 ñ, but these features are weak and are not listed in the table. No emission from Cr XXI is observed.
5.

two lines at 9.067 and 9.070 ñ. (Wavelengths were derived by adding the usual 1.2 eV B-likeõion correction to our HULLAC-calculated energies. The measured and calculated wavelengths of the 8.975 ñ B12 line are in excellent agreement, and although we cannot measure the wavelengths of the other two lines because they lie just longward of our spectrometer limit, we expect their theoretical wavelengths to be accurate to within 0.001 ñ.) A schematic of the mechanism responsible for the behavior of those 4 ] 2 lines is shown in Figure 4. A key feature is that the ïrst excited state 2s22p can decay only by a slow 3@2 M1 transition to the ground state. Below 1012 cm~3, collisional excitation rates are sufficiently low so that the decay is still fast enough to prevent any signiïcant population buildup in the metastable level, while at high densities the ratio of 2p and 2p populations approaches its LTE 3@2 1@2 value of 2. Between those two limits the 2p population, 3@2 relative to the ground state population, increases from D0.01 at 1012 cm~3 to D1.5 at 1016 cm~3. The second essential feature is that collisional excitation from the 2p 1@2 level preferentially populates the 4d level (at 7.5 times the 3@2 of 1 keV), while the rate for the 4d level, at a temperature 5@2 2p level tends to populate the 4d level (by a ratio of 5.3 3@2 The net result is that the population of the 4d level 5@2 to 1). 5@2 increases with density faster than that of 4d , leading to an 3@2 ñ 4d ] increase in the relative intensity of the 9.0675@2 2p line. Virtually the same mechanism and analogous 3@2 levels apply for n \ 3, 5, and higher. energy

DENSITY DIAGNOSTICS

The density sensitivities of Fe XXI and Fe XXII spectra have been discussed by Doschek et al. (1973) for the 3 ] 2 transitions, Mason & Storey (1980), who include calculations of the 4 ] 2 lines, and Fawcett et al. (1987), who treat the 4 ] 2 spectrum from an experimental point of view. In general, the density sensitivity of Fe L-shell spectra derives from the buildup of population in low-lying metastable states at densities exceeding D1012 cm~3. Each of those low-energy excited levels can then serve as a platform for excitation to higher energy levels via electron collisions, often producing a set of lines that is distinct from that observed at low densities, and whose intensity varies more rapidly with electron density than lines produced by excitation from the ground state. At low densities (\D1011 cm~3), C-like Fe XXI lines are excited from the 2s22p2 (J \ 0) ground state, but at high 1@2 densities the upper levels of the C4 and C5 transitions are populated primarily by collisions from the 2p 2p 1@2 3@2 (J \ 1) and 2p 2p (J \ 2) levels, respectively ; the upper 1@2 density-sensitive transitions included in 3@2 levels of the three the C3 blend are populated by collisions from both of these metastable levels. While the C3, C4, and C5 lines may be useful as diagnostics, a more detailed explanation is beyond the scope of this paper, and we will concentrate instead on B-like line diagnostics. An illustration of the density sensitivity of B-like Fe XXII spectra is shown in Figure 3, which presents model results for 4 ] 2, 5 ] 2, and 6 ] 2 transitions. The two most prominent features are the line at 8.975 ñ and a blend of

FIG. 3.õTheoretical spectra of B-like Fe XXII at electron temperature of 1000 eV, for densities of (a) 1012 cm~3 and (b) 1014 cm~3. Emissivity units are arbitrary but the same for both panels. Spectra are plotted with a FWHM resolution of 0.003 ñ.


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FIG. 4.õSchematic diagram of processes responsible for the density sensitivity of B-like Fe XXII 4 ] 2 lines. Relative magnitudes of collisionalrate coefficients are represented by the thickness of the solid lines. Dotted lines indicate relevant radiative decay channels, with wavelengths (in angstroms) and radiative branching ratios (in parentheses). At low densities the dominant process is excitation of the 4d level from ground. At 3@2 high densities the 4d level is excited from the metastable 2p level, 5@2 which is fed by cascades mostly through the 2s2p 2p (J \ 1/2,3@2 5/2) 3/2, levels, and which decays by a slow M1 transition 3@2 ground. to 3@2

FIG. 5.õFe XXII 4 ] 2 line intensity ratios vs. log n . The solid curve is e the ratio of the intensities of the primary 9.067]9.070 ñ and 8.976 ñ lines, while the dashed curve is the ratio when weak nearby lines (within 0.015 ñ of the primary lines) are included. The analogous curves for the 5 ] 2 lines (at 8.168 and 8.090 ñ) are shifted upward by approximately 0.035 and 0.050, respectively.

Model predictions of the 4 ] 2 line ratio versus density are shown in Figure 5, with the ratio rising from about 0.5 at n \ 1013 cm~3 to 1.5 at 1015 cm~3. In addition to the ploteof the ratio of the 8.975 ñ and 9.067]9.070 ñ lines, a second curve illustrates the eect of ïnite spectral resolution, in which all nearby B-like lines are summed with the main peaks. In the example shown, a resolution bin of *j/j \ 1/300 has been used, centered on the primary lines. The dierence between the two curves is small since the other B-like lines are relatively weak, but in a real spectrum the contribution of lines from other ion species must also be considered. Corresponding curves for the 5 ] 2 lines (at 8.090 and 8.168 ñ) are very similar, as one would expect, and are oset vertically from the 4 ] 2 curves by 0.035 (for the pure lines) and 0.050 (with *j/j \ 1/300). Unfortunately, the 9.067 ñ line is just longward of our spectrometer limit, so we cannot apply the 4 ] 2 diagnostic to our data. We are, however, able to use other sets of diagnostic linesõthe 5 ] 2 analogs at 8.090 (B4) and 8.168 ñ (B5) ; the cluster of B-like lines between 8.70 and 8.77 ñ (B8õB11) ; and the C-like C3, C4, and C5 lines between 8.6 and 8.7 ñõto deduce an electron density of 3 ] 1013 cm~3 in the Fe XXI and XXII line-forming regions of our tokamak plasma. We can also apply the B-like 4 ] 2 diagnostic to the 1985 July solar ÿare spectrum reported by Fawcett et al. (1987). They measured a line ratio of I(9.073)/I(8.976) \ 0.54, indicating a density of D3 ] 1013 cm~3, slightly higher than their suggested value of D1013 cm~3, which was derived using uncertain collision strengths and branching ratios. Features are also seen at 8.090 and 8.168 ñ in that ÿare spectrum, but they are probably too weak to apply the 5 ] 2 line diagnostic eectively.
6

. SUMMARY

We have presented results from a study of the spectrum

of highly ionized Fe between approximately 7 and 9 ñ, and conïrmed most previous line identiïcations while also cataloging over a dozen new lines, including transitions in Be-like Fe XXIII, B-like Fe XXII, and C-like Fe XXI. A method of calibrating the wavelengths of emission lines from extended sources with very high accuracy was described, and the results were compared with a comprehensive list of previous theoretical work and solar and laboratory observations. Secondary products of that calibration are what we believe to be the most accurate wavelength measurements to date of the Al Ka complex and Mg Kb. Theoretical spectra were calculated with the HULLAC atomic modeling package and compared with observed spectra. HULLAC employs detailed level accounting to compute emission rates, rather than relying on scaled oscillator strengths, and also uses more complete atomic models (through n \ 6 or 7) than in previous works, so its predictions of relative line intensities should be more reliable. Agreement with observations was generally quite good with regard to both wavelengths and intensities, although a few systematic wavelength errors were seen and some lines remained unidentiïed. The use of Fe L-shell line ratios as density diagnostics was examined, and a plot of B-like Fe XXII line ratios versus density provided, which we used to infer a value for electron density in a previously reported solar ÿare. The wavelength and intensity information presented here will provide a similar utility for the analysis of X-ray spectra from astrophysical sources once high-resolution spectra become available. In addition to the Fe lines studied here, a number of emission lines from hydrogenic and heliumlike Na, Mg, and Al also lie in the 7õ9 ñ wavelength regime. Several of those lines, particularly the He-like Al XII 2 ] 1 lines (w, x, y, and z) and He-like Mg Kb and Mg Kc, are useful as diagnostics but may be blended with Fe L-shell emission lines. For example, even a resolving power of 500 would be insufficient to separate the Al w-resonance line from B2, Mg Kb


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from B3, or Mg Kc from E1 and L4. (Note that the B2 and B3 lines were not even "" known îî until this work.) Since Fe L-shell emission is often a prominent component of astrophysical spectra, it is vital that any plasma codes being used to analyze spectral data incorporate a sufficiently complete list of reliable line emission rates, not only to account for all the ÿux in the iron lines themselves, but also to give accurate diagnostic information derived from He-like lines in this region.

The authors wish to thank Janet Felt and Tom Gibney for support provided in accessing the PLT data ïles. This work was supported by the NASA X-Ray Astronomy Research and Analysis Program under grant NAGW-4185. Work performed at the Lawrence Livermore National Laboratory and the Princeton Plasma Physics Laboratory was performed under the auspices of the US Department of Energy under contracts W-7405-ENG-48 and DE-AC0276-CHO-3073, respectively.

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