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Astronomical Data Analysis Software and Systems VI ASP Conference Series, Vol. 125, 1997 Gareth Hunt and H. E. Payne, eds.

Numerical Simulations of Plasmas and Their Spectra
G. J. Ferland, K. T. Korista, and D. A. Verner Physics & Astronomy, University of Kentucky, Lexington, KY 40506 Abstract. This review centers on the development and application of Cloudy, a large-scale code designed to compute the sp ectrum of gas in photoionization or collisional balance. Such plasma is far from equilibrium, and its conditions are set by the balance of a host of microphysical processes. The development of Cloudy is a three-pronged effort requiring advances in the underlying atomic data base, the numerical and computational methods used in the simulation, culminating in the application to astronomical problems. These three steps are strongly interwoven. A complete simulation involves many hundreds of stages of ionization, many thousands of levels, with p opulations determined by a vast sea of atomic/molecular processes, many with accurate cross sections and rate coefficients only now b ecoming available. The scop e of the calculations and the numerical techniques they use, can b e improved as computers grow ever faster, since previous calculations were naturally limited by the available hardware. The final part is the application to observations, driven in part by the revolution in quality of sp ectra made p ossible by advances in instrumentation. The galactic nebulae represent lab oratories for checking whether the physics of nebulae is complete and for testing galactic chemical evolution theories, and can validate the analysis methods to b e used on the quasars. Models of ablating molecular clouds, the likely origin of some gas in quasars, are tested by studies of the Orion complex. Finally, the quasars themselves present the ultimate challenge: to deduce the comp osition of their emitting gas from the sp ectrum, determine the dep endencies of this sp ectrum on the shap e of the ionizing continuum, correlating this with observed changes in the sp ectral energy distribution, and finally to understand its dep endencies on luminosity (the Baldwin effect). Once the emission line regions of quasars are understood, we will have a direct prob e of the z 5 universe. Cloudy is widely used in the astronomical community, with roughly 50 pap ers p er year employing it. The code is a general sp ectroscopic tool whose development has an impact well b eyond out sp ecific studies.

1.

Introduction

The quasars are the most luminous ob jects in the universe and the highest redshift ob jects we can observe directly. Understanding their emission lines has a cosmological imp erative, since their sp ectra dep end on luminosity (Baldwin 1977; Boroson & Green 1992; Osmer et al. 1994). Once we can directly measure their luminosity, the quasars will gauge the expansion of the universe at redshifts 213

© Copyright 1997 Astronomical Society of the Pacific. All rights reserved.


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z 5. At the same time, the origin of the chemical elements remains a central theme across much of stellar, galactic, and extragalactic astrophysics. Quasars prob e early ep ochs in the formation of massive galaxies and their emission lines can reveal the comp osition of the interstellar medium (ISM) when the universe had an age well under a billion years. Within our galaxy, HI I regions and planetary nebulae define the end p oints of stellar evolution. Detailed analysis of their emission line sp ectra can reveal b oth the nebula's comp osition and the luminosity and temp erature of the central star(s), and can validate the analysis methods to b e used for the quasars. Deducing reliable abundances and luminosities of galactic and extragalactic emission line ob jects is the central theme of the development of Cloudy. Emission lines are produced by warm (104 K) gas with moderate to low density (n 1012 cm-3 ). Such gas is far from equilibrium, and its physical conditions cannot b e known from analytical theory. Rather, the observed sp ectrum is the result of a host of microphysical processes which must b e simulated numerically. The ionization, level p opulations, and electron temp erature are determined self-consistently by solving the equations of statistical and thermal equilibrium. Lines and continua are optically thick and their transp ort must b e treated in detail. Predictions of the intensities of thousands of lines and the column densities of all constituents result from the sp ecification of only the incident continuum, gas density, and its comp osition. By their nature, such calculations involve enormous quantities of atomic/molecular data describing a host of microphysical processes, and the codes involved are at the forefront of modern computational astrophysics. Although the task is difficult, the rewards are great, since numerical simulations make it p ossible to interpret the sp ectrum of non-equilibrium gas on a physical basis. Cloudy has b een develop ed as an aid to this interpretation, much as an observer might build a sp ectrometer. The next few years will witness first light of a large numb er of new optical to infrared observational facilities, and we will b e in a p osition to obtain sp ectra of faint ob jects with unprecedented precision. The basic atomic data base is growing in b oth precision and size, and high-end workstations have the p ower of yesterday's sup ercomputers--large scale numerical simulations and sp ectral synthesis can now b e done with unprecedented precision and facility. Cloudy is op enly available, and other astronomers use it to publish roughly 50 refereed pap ers p er year. It is a general sp ectroscopic tool whose development has an impact well b eyond the sp ecific studies undertaken here. 2. 2.1. Development of Cloudy Web Access

Cloudy's source (ab out 110,000 lines of fortran) and its documentation Hazy, a Brief Introduction to Cloudy (UK Physics Internal Rep ort, 461 pages), are freely available on the Cloudy home page.1 This Web page also has group preprints, and Dima Verner's Atomic Data for Astrophysics2 (ADfA) Web page provides public access to the numerical forms of the atomic data used by Cloudy.
1 2

http://www.pa.uky.edu/gary/cloudy http://www.pa.uky.edu/verner/atom.html


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1200 1000

W (CIV) е

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Figure 1. CIV 1549 equivalent width for a wide range of densities and flux of photons.

2.2.

Cloudy's Stability

A ma jor use of sp ectral synthesis calculations is to deduce the conditions and abundances in the matter producing a sp ectrum. There is always a question of uniqueness since there may b e more than one way to get any particular result, and we must work backwards to deduce the question (prop erties of the ob ject) from the answer (the sp ectrum). Examining predictions over the very broadest p ossible range of physical parameters is vital to really understand what a sp ectrum is telling us. Today we usually use the code to generate very large grids, involving thousands of complete simulations, to generate contour or 3-D plots like that shown in Figure 1. This is an example, based on Baldwin et al. (1995), showing that one of the strongest quasar emission lines is most efficiently produced over a very narrow range of conditions. The p eak visibility occurs for the parameters long ago deduced as "standard" quasar conditions. We argued that this is just a selection effect. A major effort has gone into making it p ossible to generate such large grids on a routine basis. Issues include the following: The code must have enough intelligence to autonomously converge for models with very different conditions, without user intervention. This goal has largely b een realized. All of the predictions shown here are the result of fully autonomous calculations with no outside intervention. The code must resp ond appropriately, no matter what conditions it is asked to compute. It goes to the Compton, molecular, ISM, and LTE limits. The temp erature limits are 2.8 K

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100K

Lines of Fortran

80K 60K 40K 20K 0K

Cloudy's size vs time

1980

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Figure 2. Cloudy's size as a function of time. This shows only the numb er of executable lines of fortran. The total distributed source now constitutes 110,000 lines of code. tial core features--vital if very large grids are to b e computed reliably. Each simulation ends with a summary of all remarkable or surprising features, an analysis of any convergence problems, and checks that the range of validity was not exceeded. One sp ecific example of these internal checks is that the code now tracks timescales for all heating-cooling and ionization-recombination reactions. At the end of the calculation the code will identify the longest timescale. A warning is produced if the time-steady assumption is not valid. 2.3. Completeness of the Simulations

The code includes 104 resonance lines from the 495 p ossible stages of ionization of the lightest 30 elements--an extension that required several steps. The charge transfer data base was expanded to complete the needed reactions b etween hydrogen and the first 4 ions and fit all reactions with a common approximation (Kingdon & Ferland 1996). Radiative recombination rate coefficients were derived for recombination from all closed shells, where this process should dominate (Verner & Ferland 1996). Analytical fits to Opacity Pro ject (OP) and other recent photoionization cross sections were produced (Verner et al. 1996). Finally, rescaled OP oscillator strengths were used to compile a complete set of data for 5971 resonance lines (Verner, Verner, & Ferland 1996). Many other improvements are summarized in Ferland et al. (1997). Figure 2 shows a partial indicator of the scop e of this activity, the numb er of lines of executable fortran, as a function of time. The growth of the code in the past few years has b een explosive, thanks to modern workstations. 2.4. Reliability in the Face of Complexity

This is the central difficulty in any large simulation since analytical answers are seldom known. Predictions are affected by the numerical approximations and atomic data used, as well as the presence of bugs which are certainly present in any large program. The b est way to verify results is to compare completely indep endent calculations. We organized a workshop in 1994 to bring together researchers who have develop ed nebular codes. The result was the set of b enchmarks published in the STScI Osterbrock-Seaton commemoration (Ferland et


Numerical Simulations of Plasmas and Their Sp ectra
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Figure 3.

Refereed pap ers acknowledging Cloudy.

al. 1995). These b enchmarks provide reference p oints to aid validation of any plasma code. We also make a continuous comparison of Cloudy with another indep endently written photoionization code, LineSp ec (Verner & Yakovlev 1990). 2.5. Community Use analysis and theory of sp ectroscopic of refereed pap ers acknowledging the pap ers were published in 1993­1995. pro jects, the code did play some role

Cloudy is widely used by others in their observations. Figure 3 shows the numb er use of Cloudy through 1995. At least 138 Although I was not a co-author on these in their execution. 3. Future Development of Cloudy

The long-term goal is for the ionization and thermal equilibria of all sp ecies and the radiative transfer of continua and lines to b e exact for all conditions. By this standard, the code is well over half-way complete. 3.1. The Underlying Atomic Data Base

A ma jor effort has gone into Verner's Atomic Data for Astrophysics (ADfA) database. The results of any fully non-equilibrium calculation are no b etter than the underlying atomic data. New data app ear throughout the physics and chemistry literature; maintaining the data base is a ma jor ongoing effort, but one that does not directly result in publications. The ADfA contains basic atomic data required for calculation of the ionization state of astrophysical plasmas and for quantitative sp ectroscopy. The home page had more than 3000 visits and more than 4000 data files were retrieved during Octob er 1995­Octob er 1996. The contents of ADfA are driven by Cloudy's needs, which are defined by the sp ectroscopic problems. Because of this, and the public access we provide to our data, it has broad application to anyone working in quantitative sp ectroscopy. 3.2. Photoionization Cross sections, Recombination Coefficients

We have placed a great deal of effort into deriving accurate fits to the b est photoionization cross sections (Verner et al. 1996), the corresp onding radiative


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recombination coefficients (Verner & Ferland 1996), and incorp orating them into Cloudy. This effort is continuing, with the eventual goal of a complete photoionization cross section database, for all energies, of all atoms and ions of the first thirty elements. We plan the following developments: · For some elements, accurate exp erimental data on the ground-state photoionization cross sections are only now b ecoming available. We are replacing the fits to the smoothed Opacity Pro ject (OP) data by the fits to exp erimental data for such sp ecies. · Some photoionization cross sections include strong and wide resonances which cannot b e smoothed, and energy p ositions of these resonances are accurately known by exp eriment. We are extending the treatment of such resonances in our fits. · We are improving our current photoionization fits for the outer shells of non-OP elements up to zinc (Z = 30) by use of isoelectronic interp olation of the fits for the OP elements. · Our current fits reproduce theoretical non-relativistic high-energy asymptotes which cannot b e applied for energies ab ove 50 keV. We plan extensions to relativistic cross sections based on available X-ray exp erimental data (see, e.g., Veigele 1973). · We are creating fits for excited shell photoionization cross sections of atoms and ions based on the OP data near thresholds, and on new Hartree-DiracFock calculations far from threshold. The new data are b eing calculated by Band and Trzhaskovskaya (St. Petersburg). This is needed for dense environments, and for accurate radiative recombination rate coefficients. We have calculated radiative recombination rates for all H-like, He-like, Li-like and Na-like ions of elements from H through Zn, and fitted them with convenient analytical formulae (Verner & Ferland 1996). Using our new fits to the excited shell photoionization cross section data describ ed ab ove, we shall complete the calculations of radiative recombination rates for ions of all isoelectronic sequences of all elements up to zinc (Z = 30), and fit them by analytical formulae. This requires partial cross sections, and cannot b e done with total cross sections, such as those available from the Opacity Pro ject. 3.3. The Line Data Base

The ma jority of the 104 heavy element lines now use collision strengths from g-ap Ї proximations (Gaetz & Salp eter 1983; Mewe 1972). These can b e computed on the fly for any line, but should only b e used for transitions with no quantal calculations. The Iron Pro ject (IP; Hummer et al. 1993) is producing large numb ers of collision strengths which must b e fitted and incorp orated, if this remarkable data set is to b e exploited. We will fit the IP data with a procedure drawing on our previous work on photoionization cross sections (Verner et al. 1996) and the asymptotic limits of Burgess & Tully (1992). We will develop a generalized scheme to represent the full temp erature dep endence in terms of analytical fits, with coefficients that can b e stored along with other line information.


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We have compiled accurate wavelengths, energy levels, and atomic transition probabilities for the p ermitted resonance lines of all ionization states of astrophysically imp ortant elements (Verner, Verner, & Ferland 1996), and these data are in Cloudy. Thus, the resonance line list is fairly complete. However, the set of forbidden and intercombination lines is not complete, esp ecially for high ionization transitions of 3rd row and higher elements. Using our compilation of exp erimental energy levels, we will calculate accurate wavelengths for a complete list of forbidden and intercombination transitions b etween the lowest levels of all ions and elements included in Cloudy. We will compile atomic transition probabilities and collision strengths for them from literature and from available atomic databases, including the very recent database CHIANTI (Dere et al. 1996). All the collision strengths will b e averaged over Maxwellian electron distribution, checked for asymptotic b ehavior by use of the Burgess & Tully (1992) method, and fitted over temp erature with analytical formulae. 4. 4.1. Applications to Quasars The LOC Approach

The "Locally Optimally-emitting Clouds" (LOC) model is outlined in Baldwin et al. (1995). The homogeneity of AGN sp ectra was long a mystery (Baldwin & Netzer 1978). Baldwin et al. (1995) showed that the average quasar sp ectrum can b e produced by simply integrating over all p ossible clouds. Selection effects due to the line visibility function (Figure 1) ensure that most quasars will have very similar sp ectra even if their distributions of cloud prop erties are different. The new asp ect of this approach is allowing a range of cloud prop erties at a given radius, including ranges in column density and gas density. This seems much more realistic than just single-valued functions. Clouds of different gas densities could exist side-by-side for several viable confinement mechanisms (magnetically or shock confined, or dissipating clouds). These integrations have b een carried out over the full range of p ossible parameters. The line visibility functions are so strongly p eaked that the sp ectrum of a typical quasar can b e easily matched. This is not an entirely p ositive conclusion--we want to b e able to deduce conditions in the quasar from the observations. The advantage is that there is no longer any hidden hand needed to adjust cloud parameters--we are dealing with a known, calculable, set of line visibility functions, which introduce p owerful selection effects. Two approaches are b eing taken. First we set up sp ecific "straw man" distribution functions, compute the resulting sp ectrum, and compare this with observations. As an example, Broad Line Region (BLR) clouds could b e radiatively driven outflows; we find that this can drive mass from main sequence stars near quasars. Such winds are Rayleigh-Taylor unstable, and they should cut off at an optical depth of unity in the Lyman continuum. We have carried out such an LOC integration, and find that the predicted lines can match observations. Radiatively driven winds are consistent with the observations. The second approach is to use observations to try placing limits on p ossible distribution functions. We are working with Keith Horne (St. Andrews) to adopt our LOC grids, Keith's maximum entropy techniques (Horne 1994), and Jack Baldwin's line profile observations, to deduce the cloud distribution function. An integration over the full LOC plane produces results which are in


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good agreement with "typical" sp ectra of quasars (Baldwin et al. 1995). There is a large disp ersion from ob ject to ob ject ab out this mean, which, together with detailed line profile studies, suggests that this plane is not necessarily fully p opulated in a given ob ject. A goal is to determine observational limits to the cloud distribution functions. The combination of Keith's methods, Jack's observations, and our cloud simulations makes it p ossible to quantify which p ortions of the plane are p opulated, and whether this dep ends on luminosity. For b oth approaches, we will first generate large data cub es containing predicted line equivalent widths as a function of gas density, column density, and flux at the illuminated face of the cloud. There will b e a large numb er of these data cub es, with various continuum shap es and metallicities. Each will b e incorp orated into an interp olating routine, so that arbitrary parameters can b e sp ecified and the resulting sp ectrum obtained. Calculations of this core set of predictions is now underway and an initial atlas has b een produced (Korista et al. 1997). Our goal in these data cub es is to explore the implications of the LOC. However, this work has application well b eyond our sp ecific LOC models. Any other model of the BLR is only a subset of the LOC. Our grids will b e made publicly available, so it will b e p ossible for anyone to predict the sp ectrum resulting from a favored kinematic-spatial-magneto-hydrodynamic model, without b ecoming involved in the details of photoionization modeling. 4.2. Quasar Luminosity, Continuum Shap e, and Metallicity Correlations

The long-term emphasis is to use luminous quasars to prob e the high redshift universe. The basic problem is to understand luminosity correlations such as those in Baldwin, Wampler, & Gaskell (1989), and Osmer et al. (1994), on a physical basis. Luminosity-line correlations are complicated by other correlations, such as luminosity with continuum shap e, most obviously ox (Avni & Tananbaum 1986; Worrall et al. 1987; however LaFranca et al. 1995 find no dep endence, and Avni, Worrall, & Morgan 1995 find a complicated dep endence). The NV/CIV relation discussed by Hamann & Ferland (1992, 1993) suggests a metallicity-luminosity correlation (Ferland et al. 1996; Korista et al. 1997). The LOC data cub es will b e generated for many different continuum shap es, which we characterize by a Big Bump temp erature, ox , and slop es for the bump and X-ray continuum. From this set, we can search for line ratios more sensitive to the continuum shap e than to the LOC integration or metallicity. The large data sets available from CTIO will b e used, together with our theoretical data sets, archival X-ray and IR observations, to establish constraints on the change in the continuum shap e. The CIV/Ly ratio is an example of lines that are sensitive to changes in the 30 eV continuum (Clavel & Santos-Lleo 1990). For the high redshift quasars, the high energy end of the Big Bump is a more imp ortant ingredient than the X-rays, and we can make explicit predictions for how line equivalent widths change with continuum shap e. This work will b e extended using cloud distribution functions, and the absence/presence of Baldwin effects in various lines, to quantify changes in the Big Bump with luminosity. Acknowledgments. The development of Cloudy would not have b een p ossible without the continued supp ort of NASA and the NSF.


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