910 DOSCHEK ET AL. Vol. 518

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1 THE ASTROPHYSICAL JOURNAL, 518:909È917, 1999 June 20 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. A COMPARISON OF MEASUREMENTS OF SOLAR EXTREME-ULTRAVIOLET SPECTRAL LINE INTENSITIES EMITTED BY C, N, O, AND S IONS WITH THEORETICAL CALCULATIONS E. E. DOSCHEK,1 J. M. LAMING,2,3 G. A. DOSCHEK,3 U. FELDMAN,3 AND K. WILHELM4 Received 1998 October 12; accepted 1999 January 21 ABSTRACT Atomic data for ionized atoms are important for many astrophysical applications. The launch of the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) extreme-ultraviolet (EUV) spectrometer aboard the Solar and Heliospheric Observatory (SOHO) allows us to test the accuracy of certain computed relative excitation rate coefficients and transition probabilities for a number of important astrophysical ions. We use spectral line intensity ratios derived from SUMER spectra to compare these quantities with the best available theoretical calculations for transitions within the ions C II, N III, N IV, O III, OIV, OV, SIII, SIV, and S V. The results of this work are important for many current and upcoming NASA astrophysics missions. In addition to the published atomic data, we calculate some new atomic data using the Hebrew University Lawrence Livermore Atomic Code (HULLAC). Our comparison of measured intensity ratios with theoretical predictions reveals signiðcant discrepancies between the predicted and measured intensity ratios for several ions, particularly for S III, S IV, and S V. S III and S IV produce strong line emission in the Io torus. We discuss the methods we used to ensure that our ratios are accurate, the possible e ects of Lyman continuum absorption on our data, and the ramiðcations of ignoring dielectronic capture resonances in certain transitions as a possible explanation for some of the discrepancies. Subject headings: Sun: abundances È Sun: UV radiation 1. INTRODUCTION Accurate atomic data for ionized atoms are needed for analyzing spectroscopic data from a number of launched and soon-to-be-launched astrophysics space missions that contain high spectral resolution ultraviolet, extremeultraviolet (EUV), and X-ray spectrometers. For example, launched missions include the International Ultraviolet Explorer (IUE), the Advanced Satellite for Cosmology and Astrophysics (ASCA), the Extreme Ultraviolet Explorer (EUV E), the Hopkins Ultraviolet Telescope (HUT), the Hubble Space Telescope (HST ), and the Solar and Heliospheric Observatory (SOHO). Upcoming missions include the Advanced X-Ray Astrophysical Facility (AXAF), the Far Ultraviolet Spectroscopic Explorer (FUSE), and the X-Ray Multimirror Mission (XMM). The accuracy of atomic data is crucial for the interpretation of the spectra from these missions in terms of the physical conditions in the astrophysical sources. Many atomic data resources for astrophysicists, e.g., the CHIANTI atomic data and analysis base (Dere et al. 1997), are new and still incomplete. They rely on ongoing work and an ever-changing body of fundamental atomic data. Most of the atomic data are difficult to test directly through laboratory experiments, although valuable experiments have been carried out (e.g., Datla et al. 1987; Fang, Kwong, & Parkinson 1993). It is therefore highly desirable to attempt to verify atomic data calculations using any means available. 1 NRL Student Volunteer, Yale University, P.O. Box , New Haven, CT Sachs Freeman Associates, Inc., Largo, MD E. O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, DC Max-Planck-Institut fu r Aeronomie, D37191, Katlenburg-Lindau, Germany. 909 Optically thin spectral line intensities from ionized atoms depend on many factors, such as the excitation model, the temperature and/or density, the element abundance, the plasma emission measure (N2 V, where N is the electron e e density and V is the plasma volume in which the spectral line is emitted), and the ionization balance. Although many of these factors depend on the emitting source characteristics, it is possible to Ðnd certain line ratios that are nearly independent of the physical conditions in which the lines are emitted or the particular element abundance in the source, and instead depend primarily on fundamental atomic physics parameters. Measurements of such line ratios provide tests of the atomic physics parameters used in the excitation model. The Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on SOHO provides an unprecedented opportunity to test certain atomic data. SUMERÏs high-resolution extreme-ultraviolet solar spectra cover a larger wavelength range than was available with previous high-resolution instrumentation, allowing a number of tests that have not been previously possible. Within the SUMER wavelength range there exist many line ratios that are, or nearly are, independent of physical conditions in the solar atmosphere. SUMER spectra refer to portions of the solar atmosphere known as the chromosphere, transition region, and corona. This covers a temperature range from about 104 Kuptoa few million degrees. Ions in the transition region and coronal portions of the atmosphere are produced by electron impact ionization and radiative and dielectronic recombination. Excitation of atomic levels in an ion is produced primarily by electron impact excitation (for some transitions resonance excitation and proton excitation are also important). De-excitation is produced by spontaneous radiative decay and/or collisions with electrons and/or protons. Blackbody radiative excitation is almost always

2 910 DOSCHEK ET AL. Vol. 518 insigniðcant. Thus, the atomic parameters important for spectral line ratios in the solar transition region and corona are electron impact excitation rate coefficients and radiative transition probabilities. We have identiðed a number of line ratios in SUMER spectra that allow tests of relative electron impact excitation rates and/or ratios of transition probabilities for C II, NIII, N IV, OIII, OIV, OV, SIII, SIV, and S V. The tests are really tests of a collisional/radiative excitation model for each ion that employs detailed balance in determining atomic level populations. In some cases, however, particular excitation rate coefficients dominate the population of the relevant upper levels. The ions we consider produce spectral lines that are signiðcant in many astrophysical applications. In addition to obvious solar and stellar applications, we note that the ions S III and S IV are important constituents of the Io torus, and their spectra have been used to interpret conditions in the torus (e.g., Hall et al. 1994; Thomas, Innes, & Lieu 1996). In 2 we describe the SUMER instrument, spectra, and data reduction and analysis procedures. In 3 we describe the ion excitation model and discuss our sources of atomic data. Results are given in 4, and a discussion of the results and conclusions are given in THE SUMER SPECTROMETER AND SPECTRA 2.1. T he SUMER Spectrometer The SUMER instrument is a normal-incidence spectrometer with two detectors (A and B) that operate over the Ðrst-order wavelength ranges 780È1610 A and 660È1500 A, respectively. A region of the Sun is imaged onto one of four possible entrance slits of the spectrometer by an articulated telescope mirror. Each slit is oriented in the north-south direction when SOHO is in its nominal attitude, which it was for the spectra we consider in this paper. The slits used to obtain the spectra we discuss have dimensions 1@@ ] 300@@ and 1@@ ] 120@@. The spectra are stigmatic along the slit length with a spatial resolution of 1@@ (about 700 km at the SunÏs distance). In this paper we use data obtained with detector B. The efficiency of detector B is highest from about 800 to 1250 A, though no lines discussed in this paper are either so short or so long that the detector is extremely inefficient near their wavelengths. Each detector has 1024 spectral pixels and 360 spatial pixels. The 1024 pixel spectral range corresponds to a 44 A wavelength window. The two 120@@ long slits can be moved to image a selected solar region on either the top, middle, or bottom of the total 360@@ spatial range of the detectors. The central 22 A section of each detector is coated with KBr in order to increase its efficiency. Shifting the wavelength range by 13 A between exposures ensures that each line is seen on both the bare and the coated portions of the detectors. The efficiencies of the bare and coated portions of the detector have a di erent functional dependence on wavelength. This fact can sometimes be used to distinguish between Ðrst- and second-order lines by comparing the intensity of a line as seen on the bare and on the coated portions of the detector. More detailed descriptions of the SUMER instrument can be found in Lemaire et al. (1997) and Wilhelm et al. (1995, 1997) T he Spectra and Data Reduction The spectra used in this paper are known as reference spectra.ïï Reference spectra are spectra of the entire SUMER wavelength range, or a large portion of it, obtained periodically for di erent types of solar regions, e.g., quiet-sun regions, coronal holes, and weak active regions. A reference spectrum observation sequence consists of obtaining a series of 44 A wide spectra, proceeding from short to long wavelengths in 13 A increments with a constant exposure time that depends on the brightness of the observed region. The reference spectra we discuss were recorded on 1996 October 1 and 11 and 1997 February 5, and are all spectra of quiet-sun regions. So-called quiet-sun regions are regions away from solar active regions where magnetic Ðelds are strong (hundreds to several thousand gauss in the photosphere) and where transient events such as solar Ñares occur. Although the morphology and intensity distribution of solar features observed in quiet regions by highresolution imaging spectrometers vary continuously, values of quantities such as electron temperature and density that are averaged over space seem to vary little in time. Constancy of the solar emission on average over space and time is necessary for our work because spectral lines obtained at much di erent wavelengths were recorded at times that could di er by minutes to a few hours and often were not recorded at the precise same spatial locations on the Sun. Prior to the dates of our observations, SUMER had the capability of compensating for the rotation of the Sun during an observation sequence. That is, if it were desired to observe di erent emission lines of a solar region, SUMER would automatically track the region during the time necessary to change wavelengths. This capability was not available for our observations, and the SUMER slit was pointed at a Ðxed position as the reference spectra were obtained. The SunÏs rotation brought di erent but still neighboring quiet-sun regions into the Ðeld of view of the slit. In terms of angular measurement from SOHO, the SunÏs rotation brings new regions within the Ðeld of view of the SUMER slit at a rate of about 10@@ hr~1. Details of our observations are given in Table 1. We selected spectra for reduction that contained spectral lines of the ions speciðed in 1. We chose each spectrum such that the lines of interest were on the KBr portion of the detector, with two exceptions: (1) The wavelength of the 661 A line of S IV was too short for the line to be placed on the KBr; however, at such a short wavelength there is little di erence in the efficiency of the bare and KBr-coated portions of the detector. (2) The very intense 629 A O V line was measured in second order on the bare portion of the detector because of a blend with a Ðrst-order S II line. The selected spectra were reduced using the standard SUMER data reduction techniques, i.e., the data were Ñat-Ðelded ÏÏ and destretched.ïï Analysis of the spectra proceeded as follows. Using Interactive Data Language, we Ðrst displayed a spectrum as a two-dimensional image for visual inspection. Displaying the spectrum allowed us to see immediately whether it incorporated any small dynamical events (e.g., explosive events) that might interfere with our results by producing signiðcant line intensity changes over time and/or space. No strong dynamical events were observed in any of the spectra. We then summed the count rate for each line along the slit. By summing along the slit we improved our counting statistics and averaged over small-scale spatial variations of intensities. We continued by summing the

3 No. 2, 1999 MEASURED AND CALCULATED SOLAR EUV INTENSITIES 911 TABLE 1 QUIET-SUN REFERENCE SPECTRA Exposure Time per Approximate Start Date of Size of Slit Pointing of Spectrum Time/End Time Observation (arcsec) Slita (s) (UT) 1996 Oct ] 120 3, :37:11/20:43: Oct ] 120 3, :16:09/07:21: Feb ] 300 0, [ :51:59/08:06:28 a Pointing coordinates of the middle of the spectrometer slit in arcseconds relative to Sun center deðned as 0, 0. The Ðrst value is east-west (positive is west); the second value is north-south (positive is north). number of counts within each spatially summed spectral line over wavelength and removed from this sum the underlying continuum intensity. We converted these total counts in spectral lines to physical intensities (ergs cm~2 s~1) using the SUMER radiometry program. Finally, we used these intensities to form line intensity ratios, since the absolute intensities depend on solar conditions and are not fundamental atomic quantities. A sample spectrum, summed over the slit length, is shown in Figure 1. Typically, a single 44 A spectral region contains a number of strong lines from ions that are formed over a rather large range of solar temperatures. The increasing continuum toward longer wavelengths in the Ðgure is due to the H I free-bound continuum with its edge at 912 A. We chose the ions mentioned in 1 for investigation because of the visibility of their spectra by the SUMER instrument and in the solar spectrum in general. The lines we consider are all ground conðguration transitions intense enough to be easily identiðed in the SUMER spectra. We also picked mostly unblended lines in the hopes of achieving a higher precision in our measurements. We found the intensities of some blended lines, however, if the degree of blending was not too severe to permit an accurate intensity to be obtained. Feldman et al. (1997) discuss the spectral lines in the SUMER wavelength range and their possible blends. 3. THE ATOMIC DATA As mentioned in 1, excitation of ions in the hotter regions of the solar atmosphere is produced primarily by electron impact excitation, and the degree of ionization as a function of temperature is determined by balancing electron impact ionization with radiative and dielectronic recombination. We assume the ionization balance of Arnaud & FIG. 1.ÈSample SUMER spectrum in the 750È790 A region. The data have been integrated over the slit length to improve counting statistics. The increasing continuum toward long wavelengths is due to the H I free-bound continuum. The quantum efficiency of the KBr and the bare detector surface are similar over the 750È790 A region, and therefore transitions between these two portions of the detector are not visually apparent.

4 TABLE 2 OBSERVED AND THEORETICAL INTENSITY RATIOS INTENSITY RATIOb AVERAGE PREDICTED WAVELENGTHa INTENSITY INTENSITY TRANSITION (A ) 1996 October October February 5 RATIOb RATIOb C II (2.5 ] 104 K)c 2s22p 2P È2s2p2 2P @2 3@2 2s22p 2P È2s2p2 2P , @2,3@2 1@2,3@2 2s22p 2P È2s2p2 2P @2 1@2 2s22p 2P È2s2p2 2S @2 1@2 2s22p 2P È2s2p2 2S * @2 1@2 N III (7.9 ] 104 K) 2s22p 2P È2s2p2 2P @2 3@2 2s22p 2P È2s2p2 2P @2 1@2 2s22p 2P È2s2p2 2P @2 3@2 2s22p 2P È2s2p2 2P @2 1@2 2s22p 2P È2s2p2 2S @2 1@2 2s22p 2P È2s2p2 2S @2 1@2 2s22p 2P È2s2p2 2D * @2 3@2 2s22p 2P È2s2p2 2D , @2 3@2,5@2 N IV (1.6 ] 105 K) 2s2 1S È2s2p 1P s2 1S 0 È2s2p 3P * O III (1.0 ] 105 K) 2s22p2 3P È2s2p3 3P s22p2 3P 0 È2s2p3 3P , s22p2 3P 1 È2s2p3 3P 0, * s22p2 3P 2 È2s2p3 3D s22p2 3P 1 È2s2p3 3D , ,3 O IV (1.6 ] 105 K) 2s22p 3P È2s2p2 2D s22p 2P 1@2 È2s2p2 2D 3@ , s22p 3P 3@2 È2s2p2 4P 3@2,2@ * @2 5@2 O V (2.5 ] 105 K) 2s2 1S È2s2p 1P s2p 3P 0 È2p2 3P s2p 3P 1 È2p2 3P s2p 3P 0 È2p2 3P , s2p 3P 1,2 È2p2 3P 1, s2 1S È2s2p 2 3P * S III (5.0 ] 104 K) 3s23p2 3P È3s23p3d 3D s23p2 3P 0 È3s23p3d 3D s23p2 3P 1 È3s23p3d 3D s23p2 3P È3s23p3d 3D d s23p2 3P È3s23p3d 3D d s23p2 3P È3s3p3 3S d s23p2 3P È3s3p3 3S s23p2 3P È3s3p3 3P s23p2 3P È3s3p3 3P , ,2 1,2 3s23p2 3P È3s3p3 3D d s23p2 3P È3s3p3 3D s23p2 3P È3s3p3 3D * S IV (1.0 ] 105 K) È3s23d 2D 5@ s23p 2P 1@2 È3s3p2 2P 3@ s23p 2P 1@2 È3s3p2 2P 1@ È3s3p2 2P 3@ È3s3p2 2P 1@ s23p 2P 1@2 È3s3p2 2S 1@ È3s3p2 2S 1@ s23p 2P 1@2 È3s3p2 2D 3@ È3s3p2 2D 5@ *

5 MEASURED AND CALCULATED SOLAR EUV INTENSITIES 913 TABLE 2ÈContinued INTENSITY RATIOb AVERAGE PREDICTED WAVELENGTHa INTENSITY INTENSITY TRANSITION (A ) 1996 October October February 5 RATIO RATIOb È3s3p2 2D 3@ È3s3p2 4P 5@ S V (1.6 ] 105 K) 3s2 1S 0 È3s3p 1P s2 1S 0 È3s3p 3P e* a The lines marked with asterisks are the lines to which the intensities of the other lines are compared. b Ergs are used for intensity units, not photons. c The temperature of maximum ion concentration assuming ionization equilibrium (Arnaud & RothenÑug 1985). d Blend. e Blend with second-order O III ( A in Ðrst order). RothenÑug (1985). The populations of excited levels in an ion are determined by detailed balance, i.e., A B n ; A ] N ; Ce ] N ; Cd j ji e ji e ji i:j i;j i:j \N ; n Ce ] N ; n Cd ] ; n A, (1) e i ij e i ij i ij i:j i;j i;j where n is the number population of level j, A is the j ji spontaneous transition probability from level j to level i, N e is the electron density, and C is the collisional excitation (superscript e) or de-excitation (superscript d) rate coefficient between levels i and j. The collisional excitation rate coefficient can be expressed, assuming a Maxwellian velocity distribution, as 8.63 ] 10~6 P A = Ce \ )ij B (E) exp [ E de, (2) ij u kt 3@2 kt i e *Eij e where E is the incident kinetic energy of the colliding particle, u is the statistical weight of the level i, k is BoltzmannÏs i constant, T is the electron temperature, ) is the collision e ij strength for excitation from level i to level j, and *E is the ij threshold energy for the i ] j transition. The collision strength is related to the impact excitation cross section, and the collisional de-excitation rates in equation (1) are related to the excitation rates by a well-known relationship (e.g., see Doschek 1985). Although electron direct impact excitation is the dominant excitation process for most of the excited levels of an ion, resonance excitation, produced by the two-stage process of dielectronic capture followed by autoionization leaving the ion in an excited state, is important for certain transitions, e.g., intersystem and forbidden transitions, for which direct electric dipole collisional excitation is weak or zero. Proton excitation is sometimes important for transitions within the ground conðguration. We choose atomic data which contain these additional excitation processes whenever possible. In a few cases we have augmented the data with our own calculations (by one of us [J. M. L.]) of resonance excitation and proton excitation when these processes are not included in the basic data set for a particular ion. The ions and wavelengths that we consider are given in Table 2. The temperatures of maximum ion concentration in ionization equilibrium are also given (Arnaud & Rothen- Ñug 1985). We obtained what we regard as the best atomic data (and sometimes the only atomic data) for the ions and lines in Table 2 from a number of sources, listed in Table 3. Some of the data we use are di erent from those currently adopted for the CHIANTI database, and we discuss some of the di erences in 5. The atomic data in the sources given in Table 3 were used to obtain level populations using equation (1). A line intensity I is proportional to n A. ij j ji 4. RESULTS We measured the intensities of the lines in Table 2 as described in 2 and formed intensity ratios for comparison with theoretical ratios. The intensities of the lines marked with an asterisk in Table 2 were selected to be used in the denominator of each intensity ratio for several reasons. These lines are all strong, easily identiðed, and not densitysensitive for the quiet Sun. In addition, we picked lines for the denominators with wavelengths longer than the H I Lyman limit (near 912 A ) when possible. As will be described below, this allowed us to estimate the e ect of Lyman continuum absorption on our intensity ratios. TABLE 3 ATOMIC DATA REFERENCES Ion References C II... Blum & Pradhan 1992 N III... Sta ord, Bell, & Hibbert 1994 N IV... Keenan et al O III... Lennon & Burke 1994 O IV... Zhang, Graziani, & Pradhan 1994 O V... Keenan et al S III... Tayal 1997 S IV... Klapisch et al. 1988; Goldstein et al. 1988; Dufton et al S V... Pradhan 1988

6 914 DOSCHEK ET AL. Vol. 518 Some intensity ratios are subject to variations due to solar rotation and possible intensity Ñuctuations with time, although this problem does not exist for a line ratio formed from two lines observed in the same spectrum, i.e., within the 44 A wavelength interval of an individual spectrum. We carried out several procedures to estimate the size of intensity ratio variations due to spatial and temporal e ects, and to mitigate their e ects on the line ratios. As mentioned earlier, to lessen e ects due to spatial variations and also improve counting statistics, every line we measured was summed over the entire slit. In order to investigate the e ect of a time delay between the measurement of two line intensities on the value of an intensity ratio, either because of temporal and/or spatial intensity changes, we measured the intensities of a few lines (not many are available in the relevant temperature regions) in both Ðrst and second orders. The intensity of the second-order line should be the same as the Ðrst-order intensity if there are no changes due to temporal or spatial e ects. For example, we measured two O III lines in both Ðrst and second order. Their Ðrstorder wavelengths are and A, and in Ðrst order they are blended. In second order these lines are blended with a S IV line at A. Using a Gaussian deconvolution program, we determined the three individual intensities and then compared the O III intensities with those found for the blended O III lines in Ðrst order. As a further check, we measured the second-order intensities of the two O III lines in spectra for which they are on the bare portion of the detector. In this case the Ðrst-order S IV line is much weaker on the bare part of the detector than on the KBr section, whereas the two second-order lines are as strong as they appear on the KBr portion of the detector. In all cases we found the second-order intensities of the O III lines to be within 20% of the Ðrst-order intensities. Because the S IV lines near 1400 A are interesting in themselves, an example of the three deconvolved lines near 1406 A is shown in Figure 2. ANIII line at A was also measured in both Ðrst and second order. Its Ðrst- and second-order intensities also agree to within 20%. Thus, within a particular quiet-sun region the time di erence between spectra does not signið- FIG. 2.ÈFeature near 1406 A in the 1996 October 1 quiet-sun spectrum shown in histogram format. The data are integrated over the slit length. Also shown is the Gaussian deconvolution of the feature into two O III second-order lines and one Ðrst-order S IV line, with the continuum removed. The dotted curve is the three-gaussian convolution. cantly a ect our results. This conclusion is generally supported by the results discussed in the next section, i.e., the di erences in the line ratios among the three di erent regions are usually not large, as is expected if all the regions are quiet-sun regions with similar characteristics. Our results are given in Table 2, which includes a list of the ratios we found for each solar region observed, the ratios averaged over the three regions, and the predicted ratios based on the atomic sources given in Table 3, along with the additions for certain ions, such as resonances, discussed in 3. The uncertainties of our measured line ratios depend on the intensities of the lines, blending of lines in some cases, instrument calibration, and intensity variations from the Sun in time and in solar location. Although we have shown that these latter two e ects are not large, we cannot conclude that there is no error due to them. Instrument calibration uncertainties are probably 20% or less. The best method for estimating overall uncertainties in the line ratios is to compare the ratios for each of the regions. From this comparison, in general we conclude that the overall uncertainties are a factor of 2 or less. 5. DISCUSSION AND CONCLUSIONS 5.1. E ects of the Solar Atmosphere on the Results The predicted ratios in Table 2 are the ratios calculated assuming an isothermal plasma at the temperatures given for each ion in the table. These ratios do not include the fact that the typical quiet-sun plasma is multithermal, with a distribution of emission measure as a function of electron temperature, i.e., a di erential emission measure (DEM). A typical DEM is given in Raymond & Doyle (1981). Qualitatively, the DEM has a minimum near 105 K. We always form our intensity ratios in such a way that the line in the numerator has nearly the same excitation energy or a higher excitation energy line than the line in the denominator. Consequently, if the excitation energies are not nearly the same, the predicted quiet-sun ratio including the quiet- Sun DEM will be slightly smaller than the isothermal prediction for temperatures less than 105 K, and slightly higher for lines formed at temperatures greater than 105 K. The largest di erence occurs for the shortest wavelength lines of S III, which is about the same as that found by Doschek et al. (1997) for Si IV, and is a factor of about 1.4. That is, if the DEM is included, the predicted S III ratios involving the lines near 680 A should be reduced by about a factor of 1.4. The e ect is smaller for the longer wavelength S III lines. In the next section we will see that this is not a large factor compared with the largest di erences found between measured and predicted ratios for S III. We have not included the DEM speciðcally for each ion in Table 2 because we actually do not know the precise shape of the DEM for the individual quiet-sun regions we have examined. Suffice to say that the e ect of the DEM on the line ratios is not large and that the predicted ratios do not contain a solar-speciðc DEM adjustment that would only be approximate if a typical DEM were used. The given theoretical ratios in Table 2 are applicable for any astrophysical plasma governed by collisional processes where photoionization and photoexcitation can be ignored. Although we have tried to choose lines that are not a ected by electron density and temperature, some of the ratios in Table 2 are somewhat sensitive to the temperature.

7 No. 2, 1999 MEASURED AND CALCULATED SOLAR EUV INTENSITIES 915 We have compared our measurements with theoretical predictions assuming the temperatures of maximum emitting efficiency in ionization equilibrium, determined from Arnaud & RothenÑug (1985). We can estimate the e ect on our ratios that results from adopting a di erent temperature by realizing that in a line ratio the e ect of temperature is primarily in a ratio of exponential factors that appear in the collisional excitation rate coefficient in equation (2), i.e., exp ([de/kt ), where de is the energy di erence between the two excitation e energies of two lines in a line ratio. Most of the temperature dependence in a line ratio is in this exponential factor. We have determined the maximum e ect of temperature on our line ratios for each ion in Table 2 by calculating the exponential factor for each line using the starred lines in the table as one line (except for the O III ion), and the line with the maximum wavelength di erence from the starred-line wavelength as the other line. This maximizes de in the exponential factor, and therefore gives the maximum possible e ect of temperature on a line ratio. For O III we have used the longest and shortest wavelength lines in Table 2 because all the lines are rather close in wavelength. These exponential factors are shown in Figure 3. The temperatures at which we expect the lines of each ion to be emitted in ionization equilibrium are marked on the curves with asterisks. Where the ionization equilibrium temperatures are the same for di erent ions, the asterisks alone cannot distinguish among di erent ions, and therefore curves with the same ionization equilibrium temperature are distinguished as shown in the Ðgure. Thus, for each ion, varying the temperature by a given percentage will produce a change in line ratio that is equal to or less than the change in the ionïs exponential factor shown in Figure 3. For each ion the e ect of temperature could be reduced further by comparing all lines to a line with a wavelength that is as close as possible to the average wavelength of the lines, rather than with the starred wavelength lines in Table 2. We chose the starred lines because these lines fall on the long-wavelength side of the H I Lyman limit at 912 A (except for O III, for which there is no line within the SUMER wavelength range longer than 912 A ), and therefore only one line in a line ratio could be a ected by the photoionization e ect discussed in the paragraph below. Figure 3 is somewhat complicated, and therefore we give an example of its use. Suppose we wish to investigate the temperature sensitivity of the S IV lines in Table 2. In this case we use the dotted curve in Figure 3 and note that in ionization equilibrium S IV is emitted at a temperature of 1 ] 105 K, as indicated by the asterisk on the curve. The curve applies to the ratio of the intensity of the shortest wavelength S IV line in the table, the line at A, to the intensity of the starred S IV wavelength line in Table 2 ( A line). The exponential factor at the ionization equilibrium temperature is If the S IV lines were actually emitted at a temperature twice as high as the ionization equilibrium temperature, then from Figure 3 we see that the exponential factor would increase to 0.66, and the ratio of this factor to the ionization equilibrium factor of 0.44 would be Therefore, the / intensity ratio would increase by the same factor. The intensity ratio of the A line to any of the other S IV lines in Table 2 with longer wavelengths than A would change by a FIG. 3.ÈThe exponential factor described in the text. The asterisks mark the temperatures of maximum ion formation in ionization equilibrium (Arnaud & RothenÑug 1985) and can be used to identify the ions corresponding to the curves by comparing the marked temperatures with the temperatures in Table 2. Some of the curves that have the same marked temperature have been speciðcally labeled to distinguish them from each other.

8 916 DOSCHEK ET AL. Vol. 518 factor less than 1.5. Of course, for lines very close to the A line the change would be nearly the same as for this line. Similarly, if the temperature were reduced over the ionization equilibrium temperature by a factor of 2, the / intensity ratio would decrease by a factor of about 2.3 (0.44/0.19), but changes in the ratio of the A line to any of the other lines in Table 2 would decrease by less than this amount. For the particular case of S IV, an emitting temperature less than the ionization equilibrium temperature has a greater e ect on the intensity ratios than an emitting temperature greater than the equilibrium temperature. We have discussed the exponential factor for particular ratios where it is maximized, but the reader can easily calculate the factor for a speciðc ratio if desired. We consider the temperature dependence of line ratios further in the discussions of the results for individual ions. Another possible e ect on the ratios is photoionization in clouds of neutral hydrogen that might be present in the solar atmosphere (e.g., Schmahl & Orrall 1979; Kanno 1979; Doschek & Feldman 1982). Doschek & Feldman (1982) concluded from an analysis of Skylab spectra that the intensities of lines that fall at wavelengths less than the Lyman limit at 912 A are attenuated by no more than a factor of 2 by this e ect. The data we discuss are considerably better for investigating Lyman absorption than the data used in the above-mentioned papers. If di erences that we Ðnd between measurement and theory are due to attenuation of lines shortward of the Lyman limit due to photoionization in hydrogen clouds, then we expect a wavelength dependence for the discrepancies that scales approximately as j3. In contrast to this expectation, we Ðnd no wavelength dependence in our data for the discrepancies between theory and measurement to be discussed below. Our data for C II, which are ideal for a Lyman absorption investigation because the C II lines shortward of the Lyman limit are very close to the limit, thereby maximizing the e ect, give an average decrease in measured ratios of a factor of 1.9 that might be due to Lyman attenuation. However, the same and much larger factors are found for shorter wavelength lines of other ions. It is true that most of the di erences between theory and experiment that we found are in the proper sense to be interpreted as the result of Lyman absorption. But since no wavelength dependence is observed, it seems more likely that problems with the atomic physics will be found to be the cause of the discrepancies discussed below. From the C II data we can conclude that the e ect of Lyman attenuation on line ratios is no larger than a factor of 1.9 at 904 A. If this is the case, then the e ect of the Lyman continuum should be unimportant at wavelengths of 700 A and less. We note that in the above discussion we have only considered attenuation due to photoionization of neutral hydrogen. We have not considered possible e ects of other cool absorbers Comparison of T heory and Measurement C II Except for the / ratio, the measured ratios and predictions agree to better than a factor of 2. The / ratio di erence is a factor of 2.9, which is uncomfortably large. Most of the ratios from the di erent quiet-sun regions agree reasonable well with one another. All the lines are close in wavelength, so the ratios are not sensitive to the precise value of the temperature. All of the ratios for lines less than the Lyman limit are smaller than the predicted ratios, which is consistent with a Lyman absorption e ect and essentially deðnes an upper limit for the e ect in the quiet Sun near the Lyman limit. A possible explanation for the observed C II discrepancies with theory that should be considered is optical depth in the lines. The C II lines are formed in the chromosphere where densities are high, and carbon is an abundant element in the Sun. At solar densities the two levels of the ground conðguration (2s22p 2P ) are statistically populated. The e ect of opacity on 1@2,3@2 altering line intensities depends on the absorption oscillator strengths of the transitions. These are the same for the and A transitions from the upper 2s2p2 2S level. However, the opacity of the A line terminating 1@2 on the J \ 3/2 ground conðguration level will be twice that of the A line terminating on the J \ 1/2 ground conðguration level because the population of the J \ 3/2 level is twice as large as the population of the J \ 1/2 level. This might help explain the discrepancy in the / line ratio, because the e ect of multiple photon scattering will be to transfer intensity from the A line to the A line, thereby increasing the / ratio. The situation for the transitions near 900 A arising from the upper 2P levels is more complex because of blending. However, opacity might also a ect line ratios involving these lines. The precise values for these intensity ratio modiðcations due to opacity depend on too many factors to consider in detail here N III and N IV For N III all the measured ratios except the / ratio are smaller than the predicted ratios by factors that are quite close to 2. The / ratio agrees to within 5% with predictions. In principle these di erences could also be caused by Lyman absorption, except that the di erences are slightly larger for N III than for C II but instead should be very small or undetectable based on our results for C II (because of the wavelength dependence of Lyman absorption). We note that the agreement between measurement and theory is excellent for line ratios involving only lines that originate from the 2P and 2S states; it is the comparison of these lines with the two lines from the 2D level that gives the factor of 2 di erences. For temperature to be completely responsible for a factor of 2 di erence, the ionization equilibrium temperature would have to be less than 5 ] 104 K, which seems too large an uncertainty in the ionization balance calculations. For N IV the only line ratio measured is in excellent agreement with the theoretical prediction O III,OIV, and O V The O III measured and predicted ratios are in excellent agreement with theory. The O IV measured and predicted ratios agree to just within a factor of 2, with the measured ratios less than the predicted ratios as found for the C II and N III ratios involving lines less than the Lyman limit. The / ratio is in excellent agreement with theory. The O V measured and predicted ratios are di erent by factors that are very close to 2.5 for all lines, and the measured ratios are less than the predicted ratios. However, excluding the A intersystem line, ratios formed by other combinations of O V lines are in excellent agreement with theory. We note that the CHIANTI database does not

9 No. 2, 1999 MEASURED AND CALCULATED SOLAR EUV INTENSITIES 917 contain atomic data for O V that include resonance excitation for the A line. As a result, instead of an average di erence of 2.5 in line ratios involving the intersystem line, the CHIANTI average di erence is S III,SIV, and S V For S III the agreement between measured and predicted ratios is generally not good. Only S III excitation rate coefficients for transitions between multiplets are published. One of us (J. M. L.) computed excitation rates between individual levels of the multiplets from the total rate coefficients. Di erences between predictions and measurements ranging from factors of 1.5 to factors of 8 occur. Ratios of lines involving only one upper term, i.e., within a multiplet, agree much better with one another. Temperature cannot account for all of the problems, since the discrepancies for the two lines arising from upper 3S levels are worse than those arising from the 3s23p3d conðguration, even though their wavelengths are longer than the 3s23p3d conðguration wavelengths. Several of the S III lines are quite weak, and there are also several blends, but these difficulties still seem inadequate to account for the observed discrepancies. For S IV the measured and predicted ratios also disagree by large factors that range to almost 6. As found for S III, however, line ratios formed only from lines arising from upper levels belonging to the same term are in good to excellent agreement with theory. In the case of S IV, we have used data calculated by us with the HULLAC code, except for the 1406 A line. However, we note that this code performs optimally for systems more highly ionized than S IV and also does not include resonances. The atomic data used in CHIANTI are from Dufton et al. (1982), Bhadra & Henry (1980), and Bhatia, Doschek, & Feldman (1980). The CHIANTI data are in excellent agreement with the HULLAC results for the / and / intensity ratios. For the shorter wavelength lines the average HULLAC ratios are about 1.6 times less than the CHIANTI ratios and are therefore in better agreement with the observations. However, this may be fortuitous, i.e., the addition of more conðgurations to the HULLAC calculation might not give a better agreement because S IV is not very highly ionized. For the 1406/1072 ratio we used the CHIANTI value, since the Dufton et al. (1982) calculations include resonances. The average measured ratio is in good agreement with this CHIANTI value. The only line ratio available for S V is in poor agreement with theory Concluding Comments An interesting feature of our results for C II, N III, O IV, and O V is the persistent Ðnding that the measured ratios (which involve the intersystem lines) are less than the predicted ratios. If this discrepancy is due to Lyman absorption, we can state that the upper limit for the e ect on a line ratio for any of the ions we consider is a factor of 2. The apparent inconsistency with this interpretation, i.e., no wavelength dependence of the discrepancies, may be the result of remaining uncertainties in atomic excitation rates which might mask the wavelength dependence. Alternatively, although resonance excitation has been included in some of the atomic data we use, perhaps it is still the source of some of this discrepancy, i.e., the theoretical resonance excitation rates may be too small. We remind readers that atomic databases such as CHIANTI represent compilations of atomic data obtained from a wide variety of sources. These data are continually being improved and updated. Readers should check carefully the particular atomic data used for an ion in a database if a large discrepancy is found between observation and predictions using the database. Progress in calculations of atomic data for ionized atoms has improved enormously because of the impetus of astrophysics from space experiments and the worldwide nuclear fusion programs that have promoted the study of ionized atoms in the laboratory. Nevertheless, the above results show that in some cases substantial discrepancies still exist between the best available calculations and observations. We encourage continued improvement in atomic data calculations; speciðcally, this paper indicates that improvement is needed for the ions S III,SIV, and S V. This work was partly supported by NRL/ONR basic research funds. One of us (G. A. D.) was also supported by a NASA Supporting Research and Technology grant (W ). E. E. D. and the NRL group thank the SUMER/ SOHO team for their e orts in obtaining the observations. The SUMER project is Ðnancially supported by DLR, CNES, NASA, and the ESA PRODEX program (Swiss contribution). 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