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The Mewe et al. Plasma Emission Code

1. Introduction

During the past decades, a sequence of X-ray missions with ever increasing sensitivity and spectral and spatial resolution has been launched. These missions showed in many cases the existence of thermal X-ray radiation from hot astrophysical plasmas for a broad class of astrophysical sources (e.g. solar and stellar flares, solar and stellar coronae, hot components of the intragalactic medium, supernova remnants, clusters of galaxies, etc.). Motivated by these observations, several computer codes have been developed in the past in order to explain the observed X-ray emission and to understand the physics of the emitting objects. A review and short discussion on many of these models was given by Drake (1992). In this contribution we will focus our attention to the code of Mewe et al. After giving a short historical overview on the development of this code, we will discuss the currently available code. We will give a few examples on the use of it. Finally, we discuss the future developments of the code.

2. Historical background: the 1985 code

Starting in the early seventies, R. Mewe (1972, 1975, Papers I & II) and collaborators at SRON-Utrecht and SRON-Leiden developed a scientific computational package for the calculation of X-ray spectra from hot, optically-thin plasmas. Its scope was to determine the physical parameters of hot astrophysical and laboratory plasmas and to compare them with astronomical space-based observations. The final stage of the software is often called the Mewe-Gronenschild-van den Oord code. It is essentially based upon the work of Mewe and Gronenschild (1981, Paper IV) and Mewe, Gronenschild & van den Oord (1985, Paper V) for the line emission and includes 2167 lines from 15 different chemical elements, covering the wavelength region 1-300 Å. These lines are produced by excitation from electron impact, radiative and dielectronic recombination and by innershell excitation and ionization. In addition to the lines the code calculated the contributions from continuum radiation due to free-free, free-bound, and two-photon emission following Gronenschild and Mewe (1978, Paper III), Mewe, Lemen & van den Oord (1986, Paper VI).

This code has been applied on many occasions to optically thin plasmas, both in steady-state equilibrium (e.g. stellar coronae) and for a time-dependent ionization balance (e.g. supernova remnants).

The code allows the user to vary several quantities independently, such as the electron temperature, electron density, elemental abundances and, for a few helium-like spectral lines, the incoming, diluted blackbody radiation field. The collisional ionization equilibrium version of this code has been used to construct table models for XSPEC and is available (for a restricted set of free parameters, however) as the XSPEC model `Mewe'.

3. Recent developments: the 1992 code

In the last five years many improvements and extensions to the 1985 code have been made. First, the structure of the subroutines has been changed, sometimes drastically, in order to allow all input/output variables to be transmitted as subroutine arguments. Due to historical reasons, this was not always the case in the 1985 code. Further, the speed of the code has been increased significantly by several optimizations, and many improvements and extensions in the modeling of the physical processes have been made.

3.1. Ionization balance

The transition rates (direct ionization, excitation-autoionization, radiative recombination and dielectronic recombination) are now taken from the work of Arnaud & Rothenflug (1985). These transition rates, in general, agree well with laboratory experiments; however sometimes deviations of 10 % occur at particular energies. Another approximate estimate of the systematic uncertainties present in the transition rates can be made by comparing the results obtained by using the transition rates as given in paper IV, for example. The resulting equilibrium population of the ionization states obtained by using the respective sets of transition rates are always consistent to within 20 %.

In the ionization balance as well as in the spectral calculations, all ions of the 15 most important chemical elements are included: H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe and Ni. As the "standard" abundances we adopt the recent compilation by Anders & Grevesse (1989) as listed in Table 1.

The speed of the computations of the ionization balance in non-equilibrium ionization situations was also enhanced significantly, e.g. by replacing the fourth-order Runge-Kutta scheme to solve the coupled system of first-order differential rate equations by a matrix inversion; for details see e.g. Jansen (1988) and Kaastra & Jansen (1993).

			Element 	Abundance 

			H		1 
			He		.0977 
   			C 		3.63 x 10-4 
			N		1.12 x 10-4 
			O		8.51 x 10-4 
			Ne		1.23 x 10-4 
			Na		2.14 x 10-6 
			Mg		3.80 x 10-5 
			Al		2.95 x 10-6 
			Si		3.55 x 10-5 
			S		1.62 x 10-5 
			Ar		3.63 x 10-6 
			Ca		2.29 x 10-6 
			Fe		4.68 x 10-5 
			Ni		1.78 x 10-6

3.2. Continuum emission

As soon as the ion concentrations are known it is possible to calculate the X-ray spectrum, consisting of continuum and line emission. The continuum emission was described by Mewe and Gronenschild (1978) and Mewe, Lemen & Van den Oord (1986, Paper VI), and consists of free-free emission, free-bound emission and two-photon emission.

Paper VI used an approximate formula for the free-free Gaunt factor based upon a correction to the non-relativistic Born approximation. Since this requires the evaluation of modified Bessel functions for each energy at which the spectrum is calculated and for each ion present, the total amount of CPU time required becomes large for systems such as a supernova remnant with many shells. Therefore, Kaastra (1992) applied the exact Gaunt factors as calculated first by Karzas & Latter (1961) and tabulated on a two dimensional grid by Carson (1988), and interpolated bilinearly and logarithmically on Carson's grid. This yields the true Gaunt factor within 1%. A relativistic correction at high temperatures and energies was also applied (equation B4 of Kylafis & Lamb, 1982).

In paper VI the free-bound Gaunt factor was approximated by assuming that the individual Gaunt factors for each excited state with principal quantum number n did not depend upon energy, and that the edge energies of the higher excited states are equal to the edge energy of the first excited state. In the new code we take into account the full energy dependence of these partial Gaunt factors and the correct edge energies of the excited states in the hydrogenic approximation, using a fit to the tabulated Gaunt factors of Karzas & Latter (1961).

We did not use the square root of a cosine (paper III) for the two-photon emission Gaunt factor. Instead, we adopted the more exact values derived from Spitzer & Greenstein (1961) for hydrogenic ions, and Dalgarno & Drake (1969) for the helium-like ions.

3.3 Line emission

The 1985 code included 2167 lines of the 15 elements mentioned before, produced by excitation, radiative recombination, dielectronic recombination and innershell ionization.

The 1992 code now consists of 2409 lines. Additions originate from the splitting of some lines into doublets (Lyman alpha, for instance) and the addition of about 250 dielectronic recombination and innershell excitation satellite lines of the helium- and hydrogen-like resonance lines from Fe and Ca between 4-7 keV. For several lines (e.g. helium-like lines from C V to S XV and lines from Fe IX-XIV, Fe XVIII-XXIII, cf. Mewe et al. 1991), the electron density dependence is taken into account. In a few cases we slightly changed the energies of a number of lines around 1 keV, based on a comparison with measurements of the Flat Crystal Spectrometer on the Solar Maximum Mission (K. T. Strong, private communication).

4. Applications of the 1992 code: XSPEC model MEKA (Mewe-Kaastra)

The collisional-equilibrium emission code has been installed as an XSPEC model in the latest release of XSPEC (version 8.23). The model is called MEKA. Free parameters are the electron temperature (keV), the Hydrogen density (cm^-3) and the abundances of 14 elements from He to Ni. The abundances are defined with respect to the standard solar abundances mentioned in section 3.1. Note that in this definition Hydrogen has always abundance 1, and therefore the Hydrogen abundance is not a free parameter. The normalization of the model is the quantity A, defined by

A = ne V / (nH d2)					(1)

in units of 10⁵⁰ cm³ pc^-2 (=1.0503 x 10¹¹ m) where n_e and n_H are the electron and Hydrogen density of the plasma, d the distance to the source and V the volume of the source. Since one of the other input variables is the Hydrogen density, the usual reduced emission measure C as used in the 1985 code is

C = ne2 V / d2 = A nH2 f,      				 (2)

The model is valid for temperatures in the range of about 10⁴ K to 10¹⁰ K. At low temperatures, the plasma becomes nearly neutral and then effects of charge transfer reactions (not included in the code) alter the ionization balance; at extreme high temperatures the relativistic corrections become too large. Correspondingly, the valid energy range for the code is for the continuum 0-~500 keV; for the lines the valid energy range is 0.041-10 keV. (At higher energies, there are no lines; at lower energies, we did not include lines.) The density range is typically from 0 to 10¹⁴ cm^-3, depending slightly upon the transition; in our code we assume that the population of excited atomic levels is negligible. Also we are in the optically thin limit, i.e. no photo-ionization or photo-excitation effects are taken into account.

As an example we show below a simulation of the spectrum of AR Lac, with the parameters adopted from a two-temperature fit to SSS data with a Raymond-Smith (1977) spectrum made by Drake et al. (1992). The simulation is done for the planned XMM reflection grating spectrometer (XMM-RGS) and use is made of the fake-option of XSPEC. An integration time of 10000 s was used. Figure 1 shows a part of the spectrum near the Fe-L complex, between 0.8 and 1.2 keV. Many spectral lines are visible. Figure 2 shows the model spectrum of the soft component only. Many spectral lines and the free-bound emission edge of O VIII near 0.87 keV are clearly visible.

Fig. 1. Simulation of an XMM-RGS spectrum of AR Lac for 10⁴ s integration time with parameters adopted from Drake et al. (1992).

Fig 2. The soft X-ray model component only of the spectrum shown in Fig. 1.

5. Future developments: SPEX

The 1992 code presented here is an end-product. We do not intend to extend or improve it further, since we have started work on a code with a completely new design and much more powerful application possibilities: the SPEctral X-ray and UV modeling and analysis package (SPEX) is now under development at SRON-Utrecht and at SRON-Leiden.

Scope of the new work is to include a wide range of astrophysical situations which can be analyzed with one software package.

Current and future developments are pointed to extend the work to nebular-type, photo-ionized plasmas (cf. Kaastra and Mewe, 1992a,b). This will be needed since it has become evident that photo-ionized plasmas play an important role in accretion-powered X-ray sources (X-ray binaries, cataclysmic variables, and active galactic nuclei) where a central X-ray emitting region is surrounded by a cooler, partially ionized medium, and in early-type stars where X-rays produced in shocks are transferred through a stellar wind.

Moreover, atomic physics has improved considerably during the last decade, and the advent of a new series of satellites with high sensitivity and spectral resolution like EUVE, ASCA, SAX, AXAF, and XMM strongly demand the availability of spectral codes with higher accuracy and more detail.

SPEX will encompass a number of subroutines for the computation of emergent spectra of optically thin plasmas such as stellar coronal loop structures and supernova remnants (also including transient ionization effects), as well as photo-ionized and optically thick plasmas.

A spectral fitting mode and a subroutine for Differential Emission Measure modeling will also become available. Depending on the various applications to possible source configurations we will deal with a number of cases, such as:

• Multi-temperature plasma (optically thin, steady state, Differential Emission Measure (DEM) modeling)

• SuperNova Remnants (SNR) (optically thin, multi-temperature structure, transient state)

• Solar flare plasma (optically thin, transient state)

• Active Region Loop Spectrum (ARLS) (optically thin, multi-temperature structure, steady state)

• Photo-ionized plasma (nebular type)

At the moment, updating the atomic physics is in progress. The current experimental version of SPEX now contains nearly 2800 spectral lines between 1-2000 Å. About 300 far UV lines between from the work of Landini and Monsignori Fossi (1990) and about 60 dielectronic recombination lines to the helium-like Mg lines at 1.3 keV have been included.

Several dielectronic and innershell excitation satellite lines which were lumped together in the 1985 and 1992 code are split now in the new code and more than 1000 dielectronic recombination (DR) satellite lines and 400 K-alpha and K-beta lines between 0.3 and 10 keV will be inserted. A major revision of the atomic data parameters and line wavelengths has been started now on the basis of a search through the literature on excitation cross sections and spectral line compilations. After completing the H- to Be-iso-electronic sequences (including the element P with abundance 2.82 x 10^-7) and inserting the DR lines, the database will contain more than 5000 lines from 16 elements. Moreover, all ions of the 14 cosmically less abundant elements with atomic number Z < 31 will be included to complete the 16 elements in the current code.

Some preliminary results obtained with the code extended by Kaastra towards photo-ionized plasmas have been presented by Mewe (1992), but this part of the code is still under development.

At the moment, various documents are in preparation in order to give a detailed description of the software package SPEX including the physical background and examples of results of spectral calculations.

It is our intention that older versions of SPEX will be continuously updated and collected into an increasingly more complete package and maintained in order to reflect the state of the art on X-ray and UV spectral modeling. All software is completely documented. At the moment we are investigating the possibilities and conditions for future distribution of the new code.

References

Anders, E., Grevesse, N., 1989, Geochimica et Cosmochimica Acta 53, 197
Arnaud, M., Rothenflug, R., 1985, Astr. Ap. Supp. 60, 425.
Carson, T.R., 1988, Astr. Ap. 189, 319.
Dalgarno, A., Drake, G.W.F., 1979, Les Congrès et Colloques de l'Université de Liège, Belgium, Vol. 54, p.69.
Drake, S.A., 1992, Legacy 1, 59.
Drake, S.A., Arnaud, K.A., White, N., 1992, Legacy 1, 43.
Gronenschild, E.H.B.M., Mewe, R., 1978, Astr. Ap. Supp. 32, 283 (Paper III).
Jansen, F.A., 1988, Ph. D. Thesis, Leiden University.
Kaastra, J.S.: 1992, An X-ray spectral code for optically thin plasmas, internal SRON-Leiden Report, updated version 2.0 dd. 12-03-1992.
Kaastra, J.S., Jansen, F.A.: 1993 Astr. Ap., in press.
Kaastra, J.S., Mewe, R., 1993a, Astr. Ap. Supp. 97, 443.
Kaastra, J.S., Mewe, R., 1993b in Proc. 10th Int. Colloquium on UV and X-ray spectroscopy of astrophysical and laboratory plasmas, eds. E.H. Silver and S.M. Kahn, Cambridge Univ. Press, in press.
Karzas, W.J., Latter, R., 1961, Ap. J. Supp. 6, 167.
Kylafis, N.D., Lamb, D.Q., 1982, Ap. J. Supp. 48, 239.
Landini, M., Monsignori Fossi, B.C., 1990, Astr. Ap. Supp. 82, 229.
Mewe, R.: 1972, Solar Phys. 22, 459 (Paper I).
Mewe, R.: 1975, Solar Phys. 44, 383 (Paper II).
Mewe, R.: 1992, in Proc. Workshop of UK SERC's Collaborative Computational Project No 7 (CCP7) on The physics of chromospheres, coronae and winds, eds. C.S. Jeffery and R.E.M. Griffin, Cambridge University Printing Service, p. 33.
Mewe, R., Gronenschild, E.H.B.M., 1981, Astr. Ap. Supp. 45, 11 (Paper IV).
Mewe, R., Gronenschild, E.H.B.M., van den Oord, G.H.J., 1985, Astr. Ap. Supp. 62, 197 (Paper V).
Mewe, R., Lemen, J.R., van den Oord, G.H.J., 1986, Astr. Ap. Supp. 65, 511 (Paper VI).
Mewe, R., Lemen, J.R., Schrijver, C..J., 1991, Ap. Space Sci. 182, 35.
Karzas, W.J., Latter, R.; 1961; Ap. J. Supp. 6, 167.
Raymond, J.C., Smith, B.W., 1977, Ap. J. Supp. 35, 419.
Spitzer, L., Greenstein, J.L., 1951, Ap. J. 114, 407.

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