Abstract

Analyses of spectra from three current missions have raised a number of questions regarding the accuracy of plasma emission codes currently in use. This session was initiated in order to bring developers of these codes together with the high energy astrophysics community in order to discuss the problems associated with fitting of spectral data. The first group of speakers addressed the following topics: the need to have an appropriate plasma model (e.g., photoionization or collisional); calculations and experiments to provide a more accurate and complete set of atomic data; and the problems with fitting spectra from EUVE, DXS, and ASCA. The code designers had been asked in advance of the meeting to compute a number of test cases in order to make comparisons among the codes. During the early days of the meeting, they met several times in order to make these comparisons and to coordinate a presentation of their results. This report summarizes the discussion at the meeting and outlines a number of areas for future work.

Presentations

Introduction

Introductory Remarks. Wilton Sanders, Chair.

Applicability of Models

The Importance of Photoionization. Tim Kallman.

Sources of Atomic Data

Calculations of Atomic Processes of Astrophysical Interest. Duane Liedahl.

Laboratory Measurements of Atomic Processes of Astrophysical Interest. Daniel W. Savin.

Problems with Astrophysical Spectra

Issues in Coronal Plasma Modeling in the EUV. Bob Stern.

Issues in Plasma Modeling of the Soft X-ray (0.1-0.3 keV) Diffuse Background. Dick Edgar.

Problems Encountered in Modeling Coronal Plasmas in the 0.4-2 keV X-ray Regime. Rob Petre.

Spectral Emission Codes

Overview of Modeling. Nancy Brickhouse

Comparison and Discussion of Four Plasma Codes in Three Wavelength Ranges. Brunella Monsignori Fossi, Nancy Brickhouse, Jelle Kaastra, and Kuni Masai.

Introduction

The radical improvement in spectral resolution and signal/noise provided by spectra from EUVE, DXS, and ASCA has generated tremendous opportunities for better understanding of high energy astrophysical sources. At the same time, a number of problems have arisen in modeling the spectral data from various sources. It is likely that a number of factors have combined to confuse the analyses - uncertainties in the instrumental response functions, inadequacies in the emission models, and overly simplified models of the sources.

The Plasma Codes Workshop at the Napa HEAD meeting was organized with the overall goal of opening lines of communication among data fitters, model makers, and providers of atomic data of astrophysical interest. The presentations gave an overview of the modeling process, and discussed strengths, weaknesses, and limitations of the different models. This report summarizes the presentations at the workshop and focuses on uncertainties in the emission models which undoubtedly contribute in part to difficulties in data analysis. It is not intended as a critical review. A number of issues have arisen as a result of this workshop that need to be addressed in future work.

The Importance of Photoionization

The four plasma codes compared at this meeting are primarily designed for collisional plasmas. The simplest model of an optically thin, collisional plasma is the "coronal equilibrium" model, in which the electron density is low enough that the ion populations are predominantly in the ground state, and electron impact processes dominate the ionization balance and excitation processes that lead to emission lines. Radiative recombination and proton impact processes are generally included. The assumption of low density may be relaxed somewhat in the treatment of multiplet ground states and low-lying metastable states. In principle, it is straightforward to extend the coronal model to the photoionized case by including an additional ionization source term. In practice, the detailed treatment of the ionization and recombination processes generally requires greater complexity in the model ion, and an escape probability treatment of resonance line radiative transfer may be necessary.

Since the photoionized plasma is "over-ionized" relative to the purely collisional case, the dominant means of populating upper energy levels is recombination, rather than collisional excitation. Thus the line spectrum will in general be dominated by different lines, e.g., Fe L-shell lines will be transitions from 3s -> 2p in the photoionized case, rather than 3d -> 2p as in the collisional case (Figure 1). Furthermore, at typical temperatures of 10⁵ K, more ionization stages co-exist than in the collisional case, and the coupling of several ionization stages can become important. From the perspective of spectral fitting, the overlapping between ions makes the temperature and abundance effects difficult to determine, especially in the energy range near 1 keV.

Figure 1: Comparison of photoionized (a) and collisional (b) plasmas (Liedahl et al. 1990b).

The use of photoionization models for comparison of X-ray spectra evolved from the modeling efforts aimed at understanding galactic H II regions, planetary nebulae, and AGN broad line clouds. These have been reviewed recently by Ferland et al. (1995). A model calculation generally consists of the simultaneous determination of the ionization, excitation, temperature, emission and absorption of a gas of specified density (or pressure) and elemental composition, illuminated by a source of ionizing photons with specified spectral shape and luminosity. The computations typically assume the following: that all processes of excitation, de-excitation, ionization, recombination, heating and cooling are in a steady state; that the populations of excited levels are negligible compared with that of the ground level for the purpose of calculating ionization balance (the "nebular" assumption; c.f. Osterbrock 1974); and that the escape of resonance line photons from the emitting gas can be described by an escape probability formalism (e.g. Osterbrock 1962; Hummer & Kunasz 1980). The transfer of continuum photons is usually treated in either a single- or two-stream approximation (Kallman & McCray 1982). The results of model calculations are conveniently parameterized in terms of the shape of the initial spectrum and the "ionization parameter," defined as the ratio of the incident ionizing flux to the gas density.

Such techniques have been used successfully to constrain models of the emission regions near AGN and X-ray binaries by comparing them with observations of the iron K line region (Kallman & White 1986; Marshall et al. 1993), and have been used to model the photoelectric opacity in partially ionized gas near AGN (Krolik & Kallman 1984; Netzer, Turner & George 1994; Netzer 1993; Yaqoob et al. 1989). Recently, models which relax the nebular assumption have been developed by Ko & Kallman (1994), and the atomic rate data for the ions Fe XVII-XXIV from Liedahl et al. (1989; 1990a, b; 1992a, b) have been included. Results show that in the 0.5-10 keV X-ray range there exist a number of strong spectral features, notably the K lines of O, Si, and S, which are relatively stable against changes in ionization parameter. A likely site for the emission of photoionized spectra is in X-ray binaries. Preliminary attempts at fitting such models to data from ASCA observations of XRBs suggest that the simplest models predict excess emission in the strong K lines, indicating possible deviations from cosmic element abundances. Furthermore, in at least one object the relative strengths of the strongest features are not well fitted by simple models (Angelini et al. 1995), suggesting that mechanisms other than recombination and electron excitation in a photoionized gas are at work. However, only a fraction of the data obtained with ASCA on compact objects has been analyzed as yet.

Modeling the spectra of photoionized plasmas deserves high priority, since photoionization is important for a wide range of astrophysical plasmas. More than half the papers at the Napa meeting concern plasmas which are likely to exhibit significant photoionization, such as those found in AGN, CV, and XRB. Users of emission codes must ascertain the applicability of an emission code to the source under consideration.

Sources of Atomic Data

Calculations of Atomic Processes of Astrophysical Interest

The current plasma emission codes contain a mixture of reasonably accurate and highly speculative rates, most of which have not been experimentally verified. Recent advances in computational speed and accuracy are now helping us build more reliable databases and plasma codes. Unfortunately, we are not yet to the point where we can place our full confidence in computer codes to calculate all the details of X-ray spectra. The accuracy of theoretical calculations is dependent upon the complexity of the ion and, in particular, the degree to which an atomic model accounts for all processes that lead to line formation. Ideally, calculations of atomic rates are subjected to experimental verification in the laboratory before being incorporated into plasma emission codes. However, since experimental work is more costly and more time consuming than the calculations, experimental benchmarking lags the calculations and the astrophysical observations by a substantial margin.

Using the HULLAC code (Klapisch 1971; Klapisch et al. 1977; Bar-Shalom, Klapisch, & Oreg 1988), Liedahl, Osterheld, & Goldstein (1995a) find that significant errors exist in the Fe L-shell emission predicted by the current plasma codes. The existing codes overestimate the intensities of n=4 -> 2 transitions relative to 3 -> 2 transitions, at least in Fe XXIII and Fe XXIV (Figure 2). The new calculations by Liedahl et al. (1995a) ameliorate this problem. The improvements derive primarily from direct calculation of previously uncalculated rates - the current generation of plasma codes contain n=4 -> 2 rates which were crude extrapolations of the n=3 -> 2 transitions. Moreover, the 3 -> 2 spectra themselves are discrepant with more recent calculations. Dielectronic satellite lines and the lines produced through cascade following dielectronic recombination, as approximated in these codes, are also in need of revision. Calculations of spectra of the entire Fe L-shell series are underway (Liedahl, Osterheld, & Goldstein 1995b) and are nearly ready for incorporation into revised plasma emission models.

Liedahl (1994) shows that the current generation of codes are likely to have inaccurate Ne, Mg, Si, and S L-shell emission as well. A particularly complex problem exists in the case of the Fe M-shell ions (Fe IX-XVI). These ions are relevant to the interpretation of spectra in the EUV band (for T o(^<,~) 10⁶ K) and in the soft X-ray band (e.g., DXS). It is clear from recent high spectral resolution solar EUV data (e.g., Thomas & Neupert 1994) and from high signal-to-noise EUVE observations of ~ 10⁶ K stars such as Procyon (Drake et al. 1994) and Alpha Cen (Mewe et al. 1995) that the spectra from plasmas in this temperature range are superpositions of complex ions of several elements. The special edition of Atomic Data and Nuclear Data Tables (Lang 1994) provides critical evaluations of the theoretical collision data.

Among the problems associated with implementing L-shell ions of intermediate-Z elements and Fe M-shell ions in user-friendly codes is the need to accommodate the spectral sensitivity to variations in electron density. Unlike Fe L-shell ions, which can often be treated in the coronal approximation, the critical electron densities of the lower-Z L-shell ions and the Fe M-shell ions are lower than those that might be encountered in stellar coronae, CVs, and possibly AGN.

Figure 2: High resolution comparison between SPEX, with Arnaud & Rothenflug (1985) ionization balance, and MEKA for Fe XXII-XXIV. The only difference between the models is the use of Liedahl's (1995a) rates instead of the older rates in MEKA.

Laboratory Measurements of Atomic Processes of Astrophysical Interest

Laboratory astrophysics should play an important role in benchmarking the atomic physics calculations which are incorporated into plasma X-ray emission codes. In the past, measurements of atomic processes which generated X-ray emission were hampered by the difficulty both of producing highly charged ions and of studying them in a controlled environment. As a result, solar observations were often used to benchmark plasma X-ray emission codes. Accurately extracting the underlying atomic physics from solar observations, however, is complicated by astrophysical uncertainties and is subject to potential errors in the background subtraction produced by weak lines.

In the late 1970's measurements on highly charged ions in a reasonably well-controlled environment became possible due to advances in Tokamak technology. Tokamak plasmas are used to study highly charged ions in conditions believed to approach coronal equilibrium (Beiersdorfer et al. 1989; Bitter et al. 1993). Studies have typically been limited to atomic processes which involved excitation of a K-shell electron. The resulting K-shell emission can then be observed, but issues of ion transport and line-of-sight averaging can complicate interpretation of the observed spectra.

In the late 1980's a new type of device, the electron beam ion trap (EBIT), was developed for the study of highly charged ions (Marrs, Beiersdorfer, & Schneider 1994). An EBIT uses a high density beam of nearly monoenergetic electrons to generate and trap highly charged ions. The electron beam is then used to probe the trapped ions. All coupled collisional and radiative transitions from the resulting electron-ion collisions can be observed spectroscopically. EBITs can be used to study highly charged ions under equilibrium and non-equilibrium conditions. A number of astrophysically important electron-ion collision processes have been studied recently with the Lawrence Livermore National Laboratory (LLNL) EBIT. Wavelength surveys have been carried out for Fe X through Fe XVII (Decaux et al. 1995); direct excitation has been measured for Fe XXIV and Fe XXV (Wong et al. 1995); dielectronic recombination resonance strengths have been measured for Fe XXV (Beiersdorfer et al. 1992); inner-shell collisional ionization has been measured for Fe XXIV (Wong et al. 1993); and a lifetime measurement has been made for the metastable ³S0 level in He-like Ne IX (Wargelin, Beiersdorfer, & Kahn 1993). These measurements have focused primarily on studying atomic collision processes that generate K-shell emission.

Work is now under way to extend LLNL EBIT studies to atomic processes which generate L-shell emission. A wavelength survey of all Fe L-shell ions (Fe XVI to Fe XXIV) has recently been completed and experimental work is now focused on measuring Fe L-shell emission line ratios. For example, measurements are being carried out for Fe L-shell 3 -> 2 and 4 -> 2 line emission for which significant errors are believed to exist in current emission codes (Fabian et al. 1994; Liedahl, Osterheld, & Goldstein 1995a). These measurements and future planned measurements will provide needed benchmarks for calculations to be used in new generations of plasma emission codes.

Data Analysis

This section provides a brief overview of problems encountered by data fitters in the three wavebands represented by the EUVE, DXS, and ASCA observations.

Stellar coronae observed by EUVE (70-760 Å ; [[lambda]]/[[Delta]][[lambda]] ~ 200) provide examples of unresolved issues. Lines of Fe VIII-XXIV are observable, allowing a description of the Differential Emission Measure (DEM) over a temperature range from ~ 10^5.6 - 10^7.2 K (e.g., Brickhouse, Raymond & Smith 1995; Monsignori Fossi et al. 1994b, 1995; Stern et al. 1995; Mewe et al. 1995). The continuum emission from higher temperatures is not well constrained by observable ionization states (i.e., there are no Fe XXV or XXVI lines in the EUVE range). For the case of the prototypical binary source Algol (Stern et al. 1995), the EUVE data, when modeled using the Brickhouse, Raymond & Smith (1995) Fe line emissivities and a largely H-He continuum from Mewe, Lemen & van den Oord 1986, require either that most of the emission measure distribution comes from log T > 7.5, which is inconsistent with X-ray data, or that [Fe/H] is about 30% of the solar value. While Algol may be the clearest example of these curiously low Fe abundances, other sources such as [[alpha]] Cen seem to have the same problem, requiring either a physically implausible high temperature tail, or some other mechanism to reduce the apparent Fe "abundance." In the case of [[alpha]] Cen, Schrijver, van den Oord, & Mewe (1994) and Mewe et al. (1995) suggest that resonance scattering of the strongest EUV lines may play a significant role. Others have proposed that the omission of weak lines in the plasma codes could explain these apparent problems, in particular for the spectra of the lower activity stars. In any event, understanding the accuracy of the atomic rates will help to constrain the possibilities. Lower temperature lines from other elements are also observable. He II [[lambda]]304 emission is one of the strongest EUV lines in many coronal sources, and yet its emission is not well understood, since it is likely to be optically thick, and may have contributions from both collisional excitation and photoionization followed by radiative recombination cascades.

The DXS data (44-84 Å [150-284 eV]; [[lambda]]/[[Delta]][[lambda]] ~ 20) clearly demonstrate the presence of lines in the spectrum of the low energy X-ray diffuse background (Sanders et al. 1993; Edgar 1994). This spectral range is rich in Si, S, Mg, and Fe transitions, and the DXS spectra contain many emission lines, but matching specific lines or groups of lines has proven difficult. Since initial efforts to fit a single temperature with plasma models failed, and the RS and MEKA codes give different results, a bootstrapping approach has been taken. This method consists of trying to identify a particular feature by its wavelength, calculating the other lines implied by fitting that one line, and "accumulating" the spectrum by adding one ion at a time. Thus, the spectrum may contain multithermal or non-equilibrium components, constrained by the requirement that the spectrum not be overpredicted at any feature.

The ASCA satellite, described by Tanaka, Inoue, & Holt (1994), has produced a wealth of moderate resolution X-ray spectra, many of which are reported in special issues of Publications of the Astronomical Society of Japan (1994) and the Astrophysical Journal Letters (1994). Fits to many ASCA spectra (0.4-10 keV (1-30 Å); [[lambda]]/[[Delta]][[lambda]] ~ 15) of stars and supernova remnants suggest low abundances for O, Ne, Mg, Si, and Fe compared with those indicated from optical or UV data. The most extreme example of this is the Cygnus Loop, whose optical data suggest near-solar abundances (see Raymond et al. 1988), but for which the ASCA data suggest abundances < 0.1 solar (0.04 for oxygen) (Miyata et al. 1994). In contrast, the inferred abundances for elliptical galaxies seem reasonable. Furthermore, in the stellar spectra, the N abundance is generally < 0.1 solar. Al is absent from the current RS code; the consequences of this are unknown. A number of modelers have found differences in temperatures derived from the RS and MEKA codes below 1.5 keV. The difference in inferred temperature can be as large as 30 percent. The new Fe L-shell atomic rate calculations have not been folded into the current analyses. Use of the old rates lead to fitting problems in the 0.8-1.3 keV band, and can produce erroneous Ne and Mg abundances.

The Plasma Codes

Representatives of four of the plasma codes had agreed before the meeting to prepare test cases to simulate spectra for these three instruments. During the conference three representatives met several times with the session chair to compare the cases. In the interest of time and efficiency at the actual workshop session, they agreed on a mutual presentation, consisting of a set of introductory remarks and the presentation of the test case comparisons. This section is a summary of the group presentation.

What's in these Spectral Codes?

The four spectral emission codes are designed to model hot, optically thin plasmas. Given Ne, Te, and abundances, all the codes compute the power radiated in a given (broad) spectral range. The continuum emission processes include bremsstrahlung, radiative recombination, and 2-photon emission.

Line emission includes collisional excitation and satellite lines. The first step in calculating excitation line emission is to determine the population of a particular ionization state, either by computing ionization and recombination rates, or by assuming ionization equilibrium populations. Codes which compute the rates can, in principle, include additional effects, such as a photoionizing source term or time-dependent heating or cooling.

The second step is to determine the populations of the upper levels of the ion from which the line emission originates. The emission is proportional to that population times the radiative transition probability. For a fully collisional-radiative model, one calculates the statistical equilibrium solution including all collisional excitation and de-excitation and all radiative transitions among all levels. In the "coronal model," most of the population is in the ground state, and statistical equilibrium is determined by a balance between collisional excitations from the ground state to upper levels, and radiative transitions down. One does not need to solve the set of statistical equilibrium equations in this case, as a cascade matrix can be determined from the radiative branching ratios. Some ions in collisional plasmas have two sources of additional complexity - ground states with fine-structure splitting, and metastable levels (often the lowest level in a system other than that of the ground state, e.g., a triplet level with a singlet ground state). The population can build up in these levels as the density increases. Collisional de-excitation of a metastable system may also have to be computed since the radiative transition is weak or forbidden. For codes which do not solve the full set of statistical equilibrium equations, some statistical treatment of the lower level populations is necessary. Radiative recombination to upper levels followed by radiative cascade may also be included.

Satellite lines are generally treated separately. These lines are emitted from radiative decay of excited states lying above the first ionization limit. These upper states can be produced by impact excitation of inner-shell electrons or by dielectronic capture of the incident electron into a highly excited state.

A Brief History

The codes discussed in this section are:

MFL. Landini & Monsignori Fossi (1990; 1991). Monsignori Fossi & Landini (1994a) is a code under development.

MEKA. Mewe, Gronenschild, & van den Oord (1985). (See also Mewe 1991.) SPEX (Kaastra & Mewe 1994) is a new code under development.

RS. Raymond & Smith (1977); Raymond (1988). BRS (Brickhouse, Raymond, & Smith 1995) is a new code under development.

Masai. Masai (1984; 1994a, b).

All of the four codes discussed have their origins in the 1970s, with various revisions, rewrites, and updates since that time (Landini & Monsignori Fossi 1970; Mewe 1972; Raymond & Smith 1977; Kato 1976). Computing in that era demanded that readability and flexibility be sacrificed for memory conservation and efficiency. These codes were not originally intended for high resolution spectra; nor were they intended for distribution. Furthermore, the atomic rate data available at that time were extremely incomplete and inaccurate by today's standards. Approximations which adequately reproduced the old atomic data may no longer provide an adequate representation of the newer results. For example, the older collision strengths were often calculated only at high energies; thus, the extrapolation of these rates to low energies might be extremely inaccurate, even when the rates at collisional temperatures are adequate.

Dramatic improvements in the availability and accuracy of atomic rate data over the last decade are encouraging (see Mason & Monsignori Fossi 1994). For the high temperature (~ 10⁷ K) Fe L-shell [[Delta]]n=0 lines observable with EUVE, some atomic collision rates are accurate to ~10% (e.g., Aggarwal 1991 for Fe XXI). One challenge for high energy spectral analysis is the systematic updating of atomic rates, as ongoing research in both theoretical and experimental atomic physics makes further improvements likely. At the same time, the level of detail required to treat the various atomic processes depends on the anticipated applications and availability of the necessary rate coefficients.

Where do the Current Codes Stand?

The standard user codes, such as XSPEC or EXSAS, necessarily lag behind what the code designers have and use. At a minimum, the updating of atomic rates is a major, ongoing project. Therefore, the remarks regarding the current status of codes refer to what is currently available in the public domain, unless otherwise stated. Both the MEKA and RS codes are being totally rewritten, in addition to incorporating new rates, and the new versions are discussed as well.

The MFL code is available in an updated version (January 1995) via the World Wide Web at the Center for EUV Astrophysics and at Arcetri. This code with DEM fitting routines (Monsignori Fossi & Landini 1991) should also be available with the Solar and Heliospheric Observatory (SOHO) software package. Work is in progress to complete the database of collisional rates and radiative decay probabilities (Dere et al. 1994). The MEKA code will be updated one last time in the next few months to revise ionization balance, include new lines, especially for [[lambda]] > 300 Å, and to include new Fe L-shell data. In about a year the new code of Kaastra & Mewe, called SPEX, will be available for its first distribution. New Fe EUV emissivities of Brickhouse, Raymond & Smith (BRS) are available electronically. This group will provide new Fe X-ray emissivities in a similar format using the new L-shell results, and are planning initial code distribution by 1996. The Masai code is being developed for L-shell lines of Fe and Ni, including aspects of density-dependence and satellites. The ions concerned have multiplet ground states, and their lines can be affected by proton impact (e.g., see Masai & Kato 1987, and reference therein).

The rewrites of MEKA/SPEX and RS/BRS are being designed for distribution, with documentation, version control, and a wide range of input and output options. Both codes will eventually have capabilities for time-dependent ionization and photoionization. In addition, the SPEX code will provide fitting routines for DEM, 1- and 2-temperature, and power law models. On the other hand, the BRS code will include uncertainty estimates in the atomic database, so that these may be included in the goodness-of-fit calculations.

General Comparison of Codes

[[lambda]] (Energy) range:

MFL: 1-2000 Å.

MEKA: <= 300 Å (Update will extend through EUVE range).

RS: 1Å - IR.

Masai: 1-1216 Å.

Ionization Balance:

MFL: Computes rates (Landini & Monsignori Fossi 1990; 1991), similar to Arnaud & Rothenflug (1985), except for Fe from Arnaud & Raymond (1992).

MEKA: Arnaud & Rothenflug (1985). Update will use Arnaud & Raymond (1992) for Fe.

RS: Computes rates; similar to Arnaud & Raymond 1992 for Fe. BRS uses Arnaud & Raymond 1992.

Masai: Ionization based on Lotz (1967; 1968). Radiative recombination calculated with hydrogenic approximation. Dielectronic recombination scaling based on Aldrovandi & Pequignot (1973) and Jacobs et al. (1977).

Elements:

MFL: 30.

MEKA: 15.

RS: 13.

Masai: 30 for ionization and recombination. 15 for lines.

Philosophy:

MFL: Theoretical rates; [[lambda]]obs; compare with observations for assessment. Original emphasis on prediction of broad band flux (EXOSAT, ROSAT). Current emphasis on EUV, UV synthesis.

MEKA: Match observed spectra (emissivity and wavelength), e.g., the solar line list of Doschek & Cowan (1984); theoretical scaling for temperature dependence. Original emphasis on X-ray synthesis based on observables.

RS: Theoretical rates and wavelengths, including flux for weak lines; compare with observations for assessment. Original emphasis on prediction of total broad-band flux. BRS uses [[lambda]]obs.

Masai: Original Kato-Masai code developed specifically for modeling non-equilibrium plasmas. Ionization and recombination rates can be chosen in combinations of the original data set, Arnaud & Rothenflug (1985), and Arnaud & Raymond (1992). Line emission is based on Kato (1976), Stern et al. (1978), and Mewe et al. (1985).

Computation:

MFL: Solve statistical equilibrium equations for Be-, C-, and N-like and Fe ions. Ground/ metastable treatment with cascade matrix currently used for other ions until completion of database compilation.

MEKA: Ground state/metastable treatment with cascade matrix.

RS: Ground state/metastable treatment with cascade matrix; BRS solves statistical equilibrium equations.

Masai: Eigenvalue scheme (Masai 1984; 1994a). Masai (1994b) focuses on density dependence of line intensities.

Comparison of Test Calculations

All calculations use cosmic abundances, Allen (1973). Binning and plotting sizes and units were specified in advance for ease of overlaying. Points of significant disagreement are enumerated here.

I. EUVE test cases. 80-180 Å. [[lambda]]/[[Delta]][[lambda]] ~ 500. There is good agreement overall for Fe; Ni needs revision in all codes, both for collision rates, and for ionization balance. Differences between RS and BRS show the need to split up multiplets for good spectral resolution (Figure 3).

a. Te = 10⁷ K; Ne = 10⁹ cm^-3; log EM =52.65

1. MEKA predicts less Fe XVIII [[lambda]][[lambda]]94/104 and Fe XIX [[lambda]][[lambda]]101/120 by factor of 2.

2. MEKA predicts less Fe XX [[lambda]][[lambda]]119/122 by 60%.

3. MFL omits Fe XXI [[lambda]]124.

4. MFL predicts more Fe XXII [[lambda]]116.

5. MEKA predicts more Fe XXII [[lambda]]156 by factor of 2.

b. Ne = 10⁹ cm^-3; log EM cm^-3 = 0.35 log Te + 43.72

1. BRS predicts more Fe XXII [[lambda]]117 by factor of 2.

2. Fe IX and X (~ 10⁶ K) lines in reasonable agreement.

II. DXS test cases. 40-85 Å. [[lambda]]/[[Delta]][[lambda]] ~ 100.

a. log Te [K] = 5.8; Ne = 10^-3 cm^-3; EM = .005 cm^-6 pc

1. RS includes edges at ionization thresholds that are omitted in others.

2. MEKA predicts some Ar IX and Ne VIII stronger than others by factors of 6-10.

b. log Te [K] = 6.0; Ne = 10^-3 cm^-3; EM = .005 cm^-6 pc

1. MEKA predicts Ar [[lambda]]48, 10 times stronger than others.

2. Masai predicts S 2.5 times weaker than others. Other S and Si differences also apparent, but difficult to untangle.

c. log Te [K] = 6.3; Ne = 10^-3 cm^-3; EM = .005 cm^-6 pc

1. MEKA predicts some of the Fe XVI lines 2-3 times stronger than the others.

2. Fe XV shows large disagreements.

Figure 3: Comparison between RS and BRS for a section of the EUVE SW range, showing the effects of splitting up multiplets.

III. ASCA test cases. 0.1-10 keV. [[Delta]]E = 30 eV.

MEKA (current version of XSPEC) and SPEX are also compared, showing the large differences due to ionization balance and Fe L-shell changes. (Figure 4)

a. kTe = 0.3 keV; Ne = 1.0 cm^-3; EM = 10⁵⁸ cm^-3

1. Fe XVI. SPEX and Masai agree. RS and MFL are lower by factor of 2 to 3.

2. Fe XVII. n=3-2 lines. SPEX larger than others by factor of 2, or RS and SPEX agree, with Masai and MFL 3 times lower.

3. Fe XVII n=4-2 lines. Masai 3 times lower than others.

4. Fe XVII n=5-2 lines. SPEX 2 times larger than RS, with Masai and MFL lower still.

b. kTe = 1.5 keV; Ne = 1.0 cm^-3; EM = 10⁵⁸ cm^-3

1. Fe L complex: Masai sometimes 2 times larger relative to RS and MEKA.

2. But there is factor 2 to 3 difference between MEKA and SPEX due to better atomic calculations by Liedahl and different ionization balance, with RS intermediate.

c. kTe = 6.0 keV; Ne = 1.0 cm^-3; EM = 10⁵⁸ cm^-3

1. Good agreement - mostly continuum.

Figure 4: Comparison of MEKA code (thin line) and SPEX code (thick line).

Conclusions

Overall, the agreement of the codes with each other is at least as good as the agreement of current versions of "old codes" with the newer calculations.

Some of the discrepancies in the codes may be the result of simple errors that can be easily checked. This is particularly true for the wavelength ranges where there have not been sufficient comparisons with data, such as the DXS band. The code representatives have agreed to check the Fe XV and XVI discrepancies in particular.

The ionization balance is a large source of the discrepancy between MEKA and the others. The revised version of MEKA will use the Arnaud & Raymond (1992) Fe rates.

There are still rather large uncertainties in the ionization balance - the best dielectronic recombination rates are uncertain at the 30% level, but some rates in the current codes are probably worse than that. The ionization balance for Ni needs to be revised; intermediate Z element ionization balance may also need reassessment.

The Fe L-shell problem is a high priority, since it dominates the 1 keV X-ray spectrum. New atomic data provided by Liedahl and others will be included in MEKA ; BRS emissivity tables for Fe X-ray emission will be made available as soon as possible.

The L-shell problem for Si, S, and Mg is likely to be analogous to that for Fe. This is critical to the DXS spectrum.

The Fe EUV data relevant to the SW band of EUVE is in good shape. There are a number of strong resonance lines for which the coronal assumption may apply; furthermore, a number of new theoretical calculations are claimed accurate to 10 to 30%. The Ni collision rates for this wavelength range have not been updated for any of the codes.

The test cases at this workshop for EUVE concentrated on high temperature plasmas. It would be useful to conduct a test of a lower temperature plasma (~ 10⁶ K). This would highlight the comparison of lines in the MW band, as well as the shortest wavelength portion of the SW band. For Fe this wavelength range includes lines from intermediate stages of Fe, for which the calculations are expected to be less accurate; many of these lines are blended, increasing the reliance on simulated spectra; lines from abundant elements other than Fe are observed in this spectrometer, and an assessment of their uncertainties would be useful to the study of abundances. The participants have agreed to construct such a test.

Additional Topics which need to be addressed but which were not a part of this Workshop

Spectral fitting. [[chi]]² fits that only include the statistical errors in the data do not reflect uncertainties in the atomic rates or in the response matrix function. Furthermore, weighting by a single global [[chi]]² does not necessarily weight the physical information content. For example, it may overstress hundreds of continuum points relative to the emission lines.

Source models. How complex does the source model need to be to extract the physical information of interest? Simple temperature models may be an adequate description of dominant temperatures, but may still not be appropriate for abundance determinations. DEM models, which are inherently ill-posed, may be constrained by "smoothness" criteria, but may then miss strong features.

Multiwavelength observations. Collaboration between observers on EUVE, which can measure DEM over a wide temperature range, and ASCA, which has unique access to the higher temperatures and important abundance diagnostics, may be critical to understanding both spectra.

Photoionization. Although plans for both BRS and SPEX include the incorporation of photoionization into the spectral emission models, the details of how to do this have not been discussed. Among the issues are (1) radiative recombination rates; (2) assessing the accuracy of the atomic rates at low temperatures; (3) how many levels to include in model ions; (4) how to include an external photoionizing source.

Nonequilibrium effects. Applications of Masai and the general version of RS include time-dependent ionization and recombination and non-Maxwellian distributions. The general version MEKA also includes time-dependent ionization. Certain improvements in capabilities are planned.

Interfaces between the codes and data modelers. The relative roles of HEASARC, MPE, the AXAF Science Center, or other software interface organizations and the code builders in maintaining codes should be discussed. The creation and maintenance of atomic databases for high energy astrophysics applications are critical areas for discussion as well. The accessibility of capabilities in the general codes which are not currently available is another issue for discussion.

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