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EMISSION SPECTRA AND IONIZATION STRUCTURE OF IRON IN GASEOUS NEBULAE AND PARTIALLY IONIZED ZONES

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

Manuel A. Bautista, B.Sc.

*****

The Ohio State University

1997

Dissertation Committee:

Professor Anil K. Pradhan, Adviser

Professor Darren L. DePoy Adviser Professor Richard W. Pogge Department of Astronomy ÜHI Number; 9801640

This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI 300 North Zeeb Road Ann Arbor, MI 48103 © Copyright by

Manuel A. Bautista

1997 ABSTRACT

The emission spectra and the ionization structure of the low ionization stages of iron, Fe I-IV, in gaseous nebulae are studied. This work includes: (i) new atomic data; (ii) detailed study of excitation mechanisms for the [Fe II], [Fe III], and [Fe IV] emission, and spectroscopic analysis of the observed IR, optical, and UV spectra; (iii) study of the physical structure and kinematics of the nebulae and their ionization fronts. Spectral analysis of the well observ^ed Orion nebula is carried out as a test case, using extensive collisional-radiative and photoionization models. It is shown that the

[Fe II] emission from the Orion nebula is predominantly excited via electron collisions in high density partially ionized zones; fluorescence is relatively much less effective.

Further evidence for high density zones is derived from the [O I] and [Ni II] spectral lines, [Fe II]/[O I] and [Fe II]/[Ni II] correlations, and the kinematic measurements of ionic species in the nebula. The ionization structure of iron in Orion is modeled using the newly calculated atomic parameters, showing some significant differences from previous models. The new model suggests a fully ionized H II region at densities of the order of 10^ cm"^, and a dynamic partially ionized H II/H I region at densities of

10'’ — 10' cm~^ . The gas phase iron abundance in Orion is estimated from observed spectra, including recently observed [Fe IV] lines.

11 To Maggie, for all the good and the difficult moments that we have lived and for the

life that we have ahead, together.

in ACKNOWLEDGMENTS

There are several people who contributed very much to my present achievement.

The most influencing have been my parents, Manolo y Gloria, who gave me all their

love and support since I was born. They taught me about the importance of honesty,

hard work, and perseverance. My parents are to me real life heroes and I love them.

I like to recognize also my grandmothers, Ligia y Margot, who also cared for me

so much. They were very important to me during my early years and accompanied

me for a good part of my education.

Various good teachers influenced my life and inspired me to pursue these studies.

-A.mong them, I regard special gratitude and appreciation for Celso Luis Ladera,

Claudio Mendoza, and .A.nil K. Pradhan (my present adviser). Luis was the best

teacher that I had as undergraduate at the Universidad Simon Bolivar. He trusted

me, motivated me, and gave me enough freedom to take my first steps in research. At

the same time, he was a counselor and friend. Claudio introduced me to the scientific areas that I like the most, from the use of computers to atomic physics to spectroscopy and astrophysics. He offered me many opportunities and guided me to take the right decisions, which have led me to this point. Anil has been the best adviser that there is. He is, in addition to a very good scientist, one of the most patient, caring, and generous persons that I have ever met. He has been also a friend since the first day

IV that I arrived to Columbus and he received me in his home and helped me to start a

new life so different and far away from my country.

In addition to good teachers, good collaborators and team mates were also part of

my experience. Sultana N. Nahar and Hongling Zhang encouraged me all along this

work and sheared with me a lot of their expertise and knowledge. They also provided

a very supportive and friendly environment to work. I feel also lucky for having Don

Osterbrock as a collaborator. Don is, without a doubt, one of the greatest astronomers

of this time as well as one of the nicest persons in the field. Don’s com m ents and

suggestions have been fundamental throughout the present work and his words of

wisdom and encouragement were most inspiring.

I am grateful to the faculty and staflf members of the Department of .Astronomy for

their support, instruction, and guidance. I thank in particular Rick Pogge and Darren

DePoy for their many useful discussions and for teaching me almost everything that

I know about observational astronomy.

I thank the entire crew of the Ohio Supercomputer Center for their help and

instruction in the use of supercomputers and massive parallel processors.

Apart from studies and work, my time at the department was filled with pleasant

moments in the company of my graduate students fellows. I especially appreciate all

the help that my compadre Ani Thakar and his family gave me since my arrival to

Columbus. I thank my lunch and soccer partners Cheongho Han and Mark Everett for

their sincere friendship and the good times that we had together, including the arrest

on the Sunset Crater in Arizona. I thank Bob Blum, Glen Tiede, Mark Houdashelt,

Anita Krishnamurthi, Mike Owen, and Solange Ramirez, to mention just a few, for occasional “get-aways”, tea time senseless discussions, soccer, tennis, and softball games, etc. I also thank Joao Santos, Ignaz Wanders, Kevin Uchida, and the rest of

the department’s postdoctoral fellows for many good moments.

Finally, I thank with all my heart my son Manuel Antonio (Mantonio) and my wife

Maggie for all their sacrifices and courage in following me here in chase of my dreams.

Mantonio and Maggie have given me the moral support that took me throughout the

most difficult moments. Maggie has been also my counselor and confident and she

has helped me a lot with her talents and wisdom. Mantonio and Maggie are the most

important people in my life and the source of my happiness. I hope being able to make everything that they have given for me worthy.

Support for this work was provided in part by an educative loan of the Fundacion

Gran Marizcal de .A.yacucho (Venezuela), the Department of .\stronomy of the Ohio

State University, and the U.S. National Science Foundation (PHY-9421898) grant for the Iron Project. The computations were carried out in part on the Cray Y-MP, Cray

T3D, and IBM SP2 at the the Ohio Supercomputer Center (OSC).

VI VITA

May 20, 1968 ...... Bogota - Colombia

1990 ...... B.Sc. Physics, Universidad Simon Bolivar, Venezuela 1990-1991 ...... Research Associate, IBM Scientific Center, Venezuela 1991-present ...... Physics Specialist, Centro Nacional para el Mejoramiento de la Ensenanza de la Ciencia (CENAMEC), Ministery of Education of Venezuela 1993-present ...... Graduate Teaching .Associate, T he Ohio State University

Publications

Research Publications

Nahar, S.N., Bautista, M.A., & Pradhan, A.K., "Total electron-ion recombination of FeF Astrophysical 7., 479, 497 (1997).

Bautista, M. A., “Atomic data from the Iron Project XIX. Photoionization Cross Sections and Oscillator Strengths for Fe I” Astron. and Astrophys. SuppL, 122. 167 (1997).

Bautista, M. A., “Atomic data from the Iron Project XVI. Photoionization Cross Sections and Oscillator Strengths for Fe V” Astron. and Astrophys. SuppL, 119, 115 (1996).

Bautista. M. A., Peng, J.,& Pradhan, A. K., “Excitation of [Nill] and [Fell] lines in gaseous nebulae” Astrophysical J., 460, 372 (1996).

Bautista, M. A. &: Pradhan, .A.. K., “Atomic data from the Iron Project XIV. Electron Excitation Rates and Emissivity Ratios for Forbidden Transitions in Nill and Fell” Astron. and Astrophys. SuppL, 115, 551 (1996).

vii Bautista, M. A.. Nahar, S. N., Peng, J., Pradhan, A. K., & Zhang, H. L.. “The Iron Project: Atomic data for Fel - FeVI” Astrophysics in the Extreme Ultraviolet, eds. S. Bowyer and R.F. Malina (Kluwer Academic Publishers), 577 (1996).

Bautista, M. A., Pogge, R. W.,& DePoy, D. L., “The nebular extinction in the Orion nebula” Astrophysical J., 452, 685 (1995).

Bautista, M. A. & Pradhan, A. K. “Iron to oxygen abundance ratio in the Orion nebula” Astrophysical J. Letters, 442, L65 (1995).

Bautista, M. .A.. & Pradhan, A. K. “Photoionization of neutral iron” J. Phys. B: At. Mol. Opt. Phys., 28, L173 (1995).

Bautista, M. A., DePoy, D. L., Pradhan, .A. K., Elias, J. H., Gregoiy, B., Phillips, M. M., & Suntzeff, N. B. “Near infrared spectra of SN 1987.A: Days 936 to 1445” Astronomical J., 109, 729 (1995).

Bautista, M. .A.., Pradhan, A. K.,& Osterbrock, D. E. “[Fe II] emission from high density regions in the Orion nebula” Astrophysical J. Letters, 432, L135 (1994).

Bautista, M. .A.., Rangel, R. E., k. Taylor P. “Ferromagnetic-Paramagnetic Phase Transitions in a Random-Bond Potts Model” Condensed Matter Theories, eds. L. Blum and F.B. Malik (Plenum Press), vol. 8 , 649 (1992).

Ladera, C. L. & Bautista, M. .A. “Measuring the spatial coherence from an extended quasi-monochromatic source by double-exposure speckle interferometiy” Optics Let ters, 17, 825 (1992).

Bautista, M. A. & Ladera, C. L. “.Algebraic determination of the vibrational quantum numbers of a diatomic molecule” J. Chem. Phys., 96, 5600 (1992).

Fields of Study

Major Field: .Astronomy

Vlll TABLE OF CONTENTS

Page

A b s tra c t ...... ii

D edication ...... iii

Acknowledgments ...... iv

V i t a ...... vii

List of Tables ...... xii

List of Figures ...... xv

Chapters;

1 INTRODUCTION ...... 1

2 ATOMIC DATA FOR Fel-V ...... 1 1

2.1 Theoretical M ethods ...... 14 2 .1 .1 The R-matrix m ethod ...... 15 2.2 The RM.\TRX and the T3DRM packages ...... 16 2 .2 .1 STGl and T3DS1 ...... 18 2.2.2 STG2, T3DS2, and T3DSD ...... 18 2.2.3 STGH and T3DSH ...... 20 2.2.4 STGB, STGBB, T3DSB, and T3D B B ...... 22 2.2.5 STGF, STGFJ, T3DSF, and T 3D SFJ ...... 22 2.2.6 STGBF and T3DSBF ...... 22 2.3 Collision Strengths for Ni II and Fe I I ...... 23 2.3.1 Target data ...... 23 2.3.2 Calculations ...... 26 2.3.3 Results ...... 28

IX 2.4 Photoionization Cross Sections and Oscillator Strengths for Fe I, Fe IV. and Fe V ...... 34 2.4.1 Target expansions ...... 34 2.4.2 Results ...... 42 2.5 Review of Other Atomic D ata ...... 75 2.5.1 Collision strengths and transition probabilities ...... 75 2.5.2 Photoionization cross sections and recombination rate coeffi cients ...... 81

NEAR INFRARED SPECTROSCOPY AND THE NEBULAR EXTINC TION IN ORION ...... 87

3.1 Observations and Data Reduction ...... 8 8 3.2 Optical to Infrared Extinction ...... 94 3.3 Deviations from Case B Recombination ...... 97 3.4 An Empirical Nebular Extinction C urve ...... 99 3.5 .Applications of the Empirical Extinction L aw ...... 103

SPECTR.AL DLAG.NOSTICS FROM Fe II-IV EMISSION SPECTR.A.. . Ill

4.1 Collisional and Fluorescent excitation of Ni II and Fe II ...... 1 1 2 4.1.1 Three level m o d e ls ...... 113 4.1.2 Multilevel model for Ni I I ...... 115 4.1.3 .Atomic Data for Ni I I ...... 117 4.1.4 Multilevel Model for Fe II and Optical Depth Effects .... 119 4.2 [Fe II] Emission from the Orion N eb u la ...... 122 4.2.1 The Optical Lines ...... 122 4.2.2 The IR and Near-IR [Fe II] L in e s ...... 128 4.2.3 Two-Zone Model of [Fe II] E m is s io n ...... 131 4.3 [O I] Diagnostics ...... 135 4.4 [Fe II] to [0 I] and [Fe II] to [Ni II] C orrelations ...... 138 4.5 Diagnostics of PIZ’s in Various Gaseous N ebulae ...... 140 4.6 The [Fe III] lines ...... 143 4.6.1 The [Fe IV] lines ...... 147 4.7 Kinematic .Analysis of the Orion N ebula ...... 153

PHOTOIONIZ.ATION MODELING OF THE ORION NEBULA 162

5.1 Fe Ionization Balance ...... 162 5.2 Modeling of Fe in O rion ...... 170

X 6 THE IRON ABUNDANCE IN ORION ...... 176

6.1 The Fe/0 Abundance Ratio in Orion ...... 176

7 SUMMARY AND CONCLUSIONS...... 185

7.1 Atom ic D ata for Fe I - V ...... 185 7.2 The Nebular Extinction in O rion ...... 187 7.3 Analysis of Forbidden Fe II-IV Emission Spectra and the Iron Abun dance in O rion ...... 188 7.4 Photoionization Modeling of Fe in the Orion Nebula ...... 190 7.5 The Iron Abundance in Orion ...... 191

Bibliography ...... 194

XI LIST OF TABLES

Table Page

2.1 New atomic data for Fe I-IV ...... 13

2.2 Target terms and energies for Ni II ...... 24

2.3 Sample of oscillator strengths for Ni I I ...... 25

2.4 Target terms and energies for Fe I I ...... 26

2.5 Sample of oscillator strengths for Fe I I ...... 27

2.6 Comparison of Maxwellian averaged collision strengths for Ni II . . . 32

2.7 Comparison of T(T = 10“* K) values for Fe I I ...... 33

2.8 Calculated (cal) energy levels of Fe II and comparison with observed (obs) levels from Sugar & Corliss (1985) ...... 36

2.9 Calculated and observed term energies (Rydbergs) for Fe V relative to the 3d‘*(^T>) ground state. The spectroscopic and correlation configu rations for Fe V, and the values of the scaling parameters for each orbital in the Thomas-Fermi-Dirac potential used in Superstructure, are also given ...... 37

2.10 Calculated (cal) energ}^ levels of Fe VI and comparison with observed (obs) levels. The energies (in Rydberg) are relative to the 3d^(^F) ground state. The spectroscopic and correlation configurations for Fe VI, and the values of the scaling parameters A„j for each orbital in the Thomas-Fermi-Dirac potential used in Superstructure are also given ...... 38

X ll 2.11 Correlation functions for Fe I included in the CC expansion. Upper panel: correlations for quintets and singlets: lower panel: correlations for singlets and triplets ...... 40

2.12 Correlation functions for Fe IV included in the CC expansion 41

2.13 Correlation functions for Fe V included in the CC expansion 41

2.14 Comparison of calculated (cal) energy levels with experimentally ob served (obs) levels from Nave et al. (1994) for F e l ...... 44

2.15 Comparison of calculated and corrected ^/-values for Fel with experi mental measurements from Nave et al. (1994) and Fuhr et al. (1988) . 47

2.16 Comparison of the calculated energies for Fe IV, Ecah with the results, Eop- by Sawey k Berrington (1992), and observed energies, Eots, from Sugar & Corliss (1985) ...... 57

2.17 Comparison of calculated p/-values in LS coupling for Fe IV with the calculations by Sawey & Berrington (1992; SB), and the semi-empirical results by Fawcett (1989) using Cowan’s code ...... 61

2.18 Comparison of calculated (cal) energies for FeV in Ry with the re sults by Butler in TOPbase at CDS (Cunto et al. 1993; TOP) an the observed (obs) energies from Sugar k Corliss (1985) ...... 69

2.19 Comparison of ratios of .A.-values for near-IR lines with observations . 78

2.20 Comparison of ratios of A-values for optical lines with observations . 79

3.1 Near-Infrared Emission L in es ...... 92

3.2 Ionic .Abundances ...... 104

3.3 Helium Ionic .Abundances ...... 105

4.1 Two-zone m odel for [Fe II] emission from Orion ...... 134

4.2 Physical conditions of PIZ’s in various nebulae ...... 142

Xlll 5.1 Optical spectrum of oxygen in Orion vs. photoionization models . . . 174

6.1 Fe^‘*'/0'^ abundance ratios in O rion ...... 181

6.2 Fe/O abundance ratios in O rion ...... 183

XIV LIST OF FIGURES

Figure Page

2.1 The RM ATRX Package ...... 17

2.2 Excitation collision strengths for the transitions (^£> 5 /2 - ^ ^ 7/2 ) (a) and (■^T>5 /2 F 3 /2 ) (b) in Ni II vs. incident electron energy. The dashed lines indicate the one point values by Nussbaumer &: Storey (1982). . 29

2.3 Excitation collision strengths for the transitions (®Dg /2 —® D 7/ 2 ) in Fe II vs. incident electron energy from the present computation (a) and Zhang &: Pradhan (b) ...... 30

2.4 \o g g fv plotted against logp/t for transitions between calculated LS terms of Fel ...... 45

2.5 Photoionization cross section (cr (Mb)) of the ground state 3d®4s^ of Fe I: (a) full curve, present result; broken curve, Kelly (1972). Thresholds from all configurations included in present computation are marked, (b) full curve, present result; broken curve, Verner et al. (1993); filled squares, Reilman & Manson (1979). (c) Cross section without coupling of the Z(PAs^ target Fe II terms contributing to the ionization of the inner 3d sub-shell ...... 49

2.6 Photoionization cross section (cr (Mb)) for a sample of excited states of Fe 1...... 53

2.7 Partial photoionization cross sections of the Fe I ground state into the ground and excited states of Fe II ...... 54

2.8 Photoionization of Fel bound state in a Rydberg series showing the PEC resonance features ...... 55

XV 2.9 log g fv plotted against log g fi for transitions between calculated LS terms of FelV ...... 58

2.10 Photoionization cross section (cr (Mb)) of the ground state 3d^(®S) of Fe IV as a function of photon energy (Rydbergs). (a) the cross section obtained with the present 31CC expansion (solid curve); (b) the cross section excluding the 3s^3p^3d® configuration; (c) the cross section with the Ss^Sp^Sd^ target terms of Fe V included explicitly (the Rydberg series P°)nd{^P°) for n=3 to 10 is marked). The dashed curve shows the results of Sawey & Berrington (1992) and the filled dots, those of Reilman & Manson (1979) ...... 62

2.11 Partial photoionization cross sections of some excited states (3d® ‘‘G panel (a); Zd^{^D)Ap ‘^F° panel (b); 3cZ'*(®F2)4p panel (c)) of Fe IV into the ground state of Fe V ...... 65

2.12 Photoionization of FelV bound states in the 3d‘^D)nd{^G) Rydberg series showing PEC resonances ...... 6 6

2.13 log g fv plotted against log g fi for transitions between calculated LS terms for FeV ...... 70

2.14 Photoionization cross section (cr (Mb)) of the ground state 3p‘(^D) of Fe V. In panel (a) the present results (solid line) with the results by Reilman & Manson (1979; dashed line); In panel (b) cross sections by Butler in T O Pbase (Cunto et al. 1993, solid line) and by Reilman & Manson (1979; dashed line) ...... 71

2.15 Partial photoionization cross sections into the ground state and the excited states of Fe VI ...... 73

2.16 Photoionization of Fe V bound states in a Rydberg series showing the PEC resonances features ...... 74

2.17 New recombination rate coefficients for Fe I (Nahar, Bautista, &: Prad han 1997), Fe II (Nahar 1996b), Fe III (Nahar 1996c), and Fe IV (Nahar & Bautista 1997). These are compared with dielectronic plus radiative recombination results by Woods et al. (1981; dashed line) ...... 83

XVI 3.1 OSIRIS cross-dispersed spectra of the OTV region in the Orion Nebula in the J. H, and K spectral windows. Relative flux per unit wavelength is plotted against the observed wavelength in microns ...... 91

3.2 The logarithm of relative strengths of the hydrogen Brackett series emission lines in the near-IR divided by predicted Case B recombina tion emissivities plotted against A^/A j . The slope of the best-fit line gives the total extinction in the near-IR J band, A j ...... 95

3.3 The logarithm of relative strengths of the hydrogen emission-lines in (a) the Balmer series, and (b) the Paschen series divided by predicted Case B recombination emissivities plotted against A^/Av-. The slope of the best-fit line gives the total extinction in the V band. Ay. Data are taken from OTV ...... 96

3.4 Intensities of Balmer, Paschen, and Brackett emission-lines corrected for extinction using our nebular extinction law plotted against principal quantum number of the upper level of the lines (n) ...... 1 0 1

3.5 Extinction magnitudes, A\, plotted as a function of y = (1/A — 1.82). Shown are our nebular extinction curve with A\- = 1.4 and N\- = 0 .1 (solid line), and the interstellar extinction curves with .4v = 1 . 8 6 (dash-dotted line). A y = 1.4 (dotted line), and A y = 1.15 (dashed line). 1 0 2

4.1 Line emissivity ratio Nill A7412(^fs/2 D 3/ 2 )/A 7 3 7 9 (^F7/2 D 5/ 2 ) of Ni II vs. Ng assuming collisional excitation only (solid line), and including fluorescence (dashed line) by a UV field as in the P Cygni circumstellar nebula with Tg =5300 K in panel (a) and Orion with Tg =10000 K in panel (b). The observed line ratios by Barlow et al. (1994) and OTV are indicated by the horizontal lines. The squared dots represents the results of Lucy (1995) ...... 116

4.2 Energy diagram of Fe II with infrared and optical lines considered. . . 121

XVII 4.3 [Fe II] line ratios vs. log Ne (cm~^ ) for Te = 9000 K. The different curves represent pure collisional excitation (solid), collisional and flu orescent excitation without optical depth effects (dotted), collisional and fluorescent excitation including line self-shielding (long dashed), and collisional and fluorescent excitation for a UV field ten times that in Orion (short dashed). Collisionally excited line ratios calculated with collision strengths of the present 23CC calculation (short-dash and dot curves) are also shown. The predicted line ratios by Baldwin et al. (1996) are indicated by square dots. The horizontal lines indicate the observed values by OTV (solid) and Rodriguez (1996; dashed lines). 123

4.4 Optical to near infrared [Fe II] line ratios vs. log iVg (cm“^ ) for Te — 9000 K. Optical measurements by OTV and near-IR observations by Lowe et al. (1979; dotted line) and Bautista et al. (1995; solid line). . 130

4.5 [0 I] AA6300 + 6364 to A5578 line ratio vs. log Ne(cm"^) for T = 5000, 10000, and 20000 K. The value of this line ratios reported by OTV and the upper limits given by Baldwin et al. (1996; HST and CTIO) are represented by horizontal dashed lines ...... 137

4.6 The [Fe II] to [O I] and [Fe II] to [Ni II] correlations ...... 141

4.7 Energy diagram of Fe III with infrared and optical lines considered. . 145

4.8 [Fe III] line ratios vs. log Ne (cm~^ ) for Te = 9000 K. The horizontal lines indicate the observed values by OTV (solid), Greve et al. (1994; dotted lines), and Rodriguez (1996; dashed lines) ...... 146

4.9 Energy diagram of Fe IV with optical and ultraviolet lines considered. 148

4.10 [Fe IV] line ratios vs. log Ne (cm"^ ) for Tg = 9000 K ...... 150

4.11 Line ratio Ng diagnostics from [Fe IV] and [O III] optical lines of high density plasma in the planetary nebula with a symbiotic star core M2-9. Observations by Torres-Peimbert & Arrieta (1996) ...... 152

xvui 4.12 The observed velocities of optical lines in Orion vs. the minimum photon energy required to produce the ionized specie (adapted from Kaler 1967 and Balick et al. 1974). The velocities of the molecular cloud (OMC-1) and the photodissociation region (PDR) are also indicated. The observations are from Kaler (1967; empty squares), Fehrenbach (1977; filled circles), and O’Dell & Wen (1992; filled squares) ...... 157

5.1 Computed physical condition for a constant pressure cloud cis a func tion of the distance from the illuminated face ...... 164

5.2 Sample of ionizing fluxes vs. the photon energy near the illuminated face (a) and near half thickness of the cloud (b). The ionization limits for Fe I-III are also m arked...... 165

5.3 Computed photoionizing rates fro Fe I-III as a function of the distance from the illuminated face of the cloud. The solid curves represent the results using the new photoionization cross sections. These are compared with the results obtained with cross section by Reilman & Manson (1979; dotted curves) and Kelly (1972; dashed curve) ...... 167

5.4 Computed ionization structure of iron in a constant gas pressure cloud as a function of the distance from the illuminated face. The present results (solid curves) are compared with the results from CLOUDY (dotted curves) ...... 169

6.1 The Fe^'^/0'^ abundance ratio in Orion as a function of the assumed temperature and electron density of the region. The line intensities are from OTV for Ipg2+(A4881) and Iq+(A3728) (solid curves) and Io+(A7322) (dashed curves) ...... 180

6 . 2 The Fe^'*‘/0^'*‘ abundance ratio in Orion as a function of the assumed temperature and electron density of the region. The line intensities are from Rubin et al. (1997) for the [Fe IV] 2827 .4line and from OTV for the [O III] 4363 .4 (solid line) and the [O III] 4959 .4 line (dashed line). 182

XIX CHAPTER 1

INTRODUCTION

The spectra, ionization structure, and abundance of iron are valuable indicators of the physical conditions and the chemical evolution of astrophysical objects. First, owing to the relatively high abundance of this element and the complex atomic structure of its ions, a large number of spectral lines are observed across most of the electro magnetic spectrum. Secondly, several ionization stages of iron may be observed from diflferent zones within the same object. The low ionization stages of iron, Fe I-IV, generally span the physical and the ionization structure of gaseous nebulae, from the cool neutral regions and partially ionized zones, to the fully ionized regions close to the ionizing source. For example, since the ionization potential of Fe I (first ionization potential; FIP) is 7.6 eV, compared with 13.6 eV for H I, the Fe II spectrum com monly traces the conditions in partially ionized regions and ionization fronts where

Fe II is partially shielded by H I. Beyond 54.4 eV, the FIP of Fe IV. the photon density from the radiation field of 0 and B stars is too low to produce higher ioniza tion of iron (Osterbrock 1989). Thus, a combined study of Fe I-IV should provide detailed information on the physical conditions, particularly the temperature and the density profiles of the photoionized region (HII region). Thirdly, while iron is pri

1 marily formed in the ISM by supernovae, it is a refractory element and its gas phase

abundance constrains the chemical enrichment of the ISM and the formation of dust

grains.

In terms of its observed abundance, iron is known for been strongly underabun- dant in the interstellar medium (ISM) and in gaseous nebulae compared to the cosmic abundances, i.e. the average solar abundances, normal stellar abundance, and me- teoritic abundances (Olthof and Pottasch 1975). Because it is usually assumed that the presence of star formation regions is nearly accidental and affects only the ion ization and not the abundance of the elements the observed underabundance of iron is normally explained by condensation onto grains.

In HII regions, derived gas phase abundances of iron are typically much higher than in the cold ISM, but still about an order of magnitude lower than the cosmic value. This suggests the presence of some destruction mechanism of dust grains.

However, there are still great uncertainties on the abundance determinations. Current sources of uncertainty for these determinations include: ( 1 ) errors in the atomic data for Fe ions; (2) systematic errors in the determination of abundances from lines well separated in wavelength due to selective extinction effects; (3) preferential excitation of Fe lines trough mechanisms other collisional excitation; (4) errors in the estimated ionic fractions the observed ions of Fe. In addition, recent evidence suggests that

Fe lines used to estimate the abundances of this elements in nebulae may suffer of selective effects related to the actual structure of the H II regions which are not well understood. For instance, we showed (Bautista, Pradhan, k Osterbrock 1994;

B autista k Pradhan 1995; Bautista, Peng, k Pradhan 1996) that the electron density in the emitting region of dipole forbidden lines of ionized Fe ([Fell]) in Orion is much higher that that from previous diagnostics from lighter elements. Also, we found some

evidence that [Fe II] and [Ni II] lines may suffer of different extinction (absorption and

scattering of photons) to dust grains in Orion than lines from other species (Bautista.

Peng, &: Pradhan 1996).

As the best observed diffuse H II region, the Orion nebula (M42) is commonly

used as a ’’benchmark” for nebular studies, on which every observational technique

has been tested and used (e.g. Felli et al. 1993; O’Dell, Wen, &: Hu 1993, end ref

erences therein). The present study aims at an understanding of some aspects of

low-excitation photoionized nebulae through the analysis of the ionization structure

and spectra of Fe I-FV" in Orion based on: (i) new calculations of accurate atomic data for Fe I-IV, necessary for ionization equilibrium and spectral formation compu tations, (ii) spectroscopic obsers’-ations of Orion and study of the nebular extinction corrections of the observed line strengths, (iii) study of ionization balance, excitation mechanisms, and radiative transfer of the spectra of Fe ions; (iv) study of the phys ical structure of nebula including density and temperature variations and kinematic effects.

Despite the importance of low ionization stages of iron in laboratory and astrophysical plasmas, accurate atomic data for these ions were not available until the recent advances by the OPACITY Project (hereafter OP, Seaton et al. 1994) and the

IRON Project (hereafter IP; Hummer et al. 1993). However, the OP calculations of radiative data and photoionization cross sections for the low ionization stages of iron, i.e. Fe I-V, are not sufficiently accurate for modeling and lead to significant discrep ancies with observations (e.g. Pradhan 1996). One of the primary goals of the IP to carry out improved calculations for these ions (Bautista et al. 1996). The IP calcu lations are carried in the close coupling approximation using the R-matrix method

that is presently the most accurate method for the calculation of photoionization, re

combination, and excitation cross sections. The calculations are rather involved, and

computationally intensive, owing to the complex electron-electron correlation effects,

the large number of coupled atomic states of iron ions, and the complex resonance

structures present in the cross sections. A brief discussion of these calculations and

the atomic data is presented in Chapter 2 .

From the observational side, one of the principal sources of systematic error en

countered in spectrophotometry of gaseous nebulae is correctly accounting for the

effects of dust extinction. Traditionally, an extinction correction is derived by assum

ing the standard interstellar extinction law, derived from stars , and then estimating

the amount of extinction required to explain the observed line strengths as compared

with theoretical expectations. At visual wavelengths the most common practice is to

compare the observed relative strengths of the H I Balmer series emission lines with

the predictions of recombination theory for an assumed nebular density and temper

ature (e.g., Osterbrock 1989). A less common approach is to use only those emission

lines of a particular ionic species that are both well-separated in wavelength and arise

from transitions out of the same upper level, making them insensitive to assumptions

about the nebular density and temperature. Particular examples include using the

combination of H I Paschen and Balmer recombination lines (e.g.. Miller & Mathews

1972), and the [S II]A4071 and A10300 emission lines (Allen 1979; Greve et al. 1989).

These alternative extinction diagnostics rely on accurate measurements of very faint emission lines often made by different instruments, and the derived extinction esti mates can have large errors. Even if the problems of choosing appropriate diagnostic lines and making line

measurements of acceptable precision can be solved there remains the fundamental

weakness that the traditional methods relies on the assumption that extinction in

extended gas nebulae behaves in the same way as stellar extinction, where you have

a point source behind a screen of dust. This assumption is motivated by simplicity,

since for a given extinction law the amount of extinction towards the nebula can

be quantified by a single number, the total extinction at 5500Â, (-4^), for example,

without having to solve for the radiative transfer problem in rather complex geome

tries. The typical choice for the extinction law is that derived by Cardelli, Clayton,

&c Mathis (1989).

The extinction due to dust in the Orion Nebula is well known to depart from

the usual interstellar case. The extinction of stars in the Trapezium, has a different

wavelength dependence than the extinction seen in typical OB stars within I kpc

of the Sun (Mathis & Wallenhorst 1981). stars within 1 kpc of the Sun. This has

been interpreted as the result of a different distribution of the sizes of the dust grains

in the nebula as compared with the typical distribution in the interstellar medium

(Mathis &: Wallenhorst 1981). As for the nebular extinction, most of the extinction

appears to rise in a foreground “lid” between the observer and the nebula (Wen &

O’Dell 1995); however, there is evidence for a clumpy distribution of dust on very

small scales (Pogge, Owen, & Atwood 1992; Greve et al. 1989) and for reflection of

radiation off of the backside of the nebula (O’Dell, Walter, & Dufour 1992). Further,

it is also likely that some dust is mixed in with the line-emitting gas in the nebula.

Chapter 3 presents measurements of the relative intensities of the near-infrared

H I Brackett series emission lines in the same region of Orion Nebula recently studied in detail by Osterbrock, Tran, &: Veilleux (1992; henceforth OTV). We have combined

our data with the OTV measurements of the Balmer and Paschen series emission lines,

and use these data, which span a wavelength range of 0.34 to 2.2 fim, to show how the

assumption of an interstellar extinction law leads to significant discrepancies in the

extinction derived for the decrements of each of these emission-line series. We show

that this discrepancy cannot be attributed to deviations from Case B recombination

theory, but is probably a consequence of secondary effects arising because of the

complex distribution of dust in the nebula. We present an empirical approach in

which we introduce an additional wavelength dependence term to the Trapezium

stellar extinction law (M athis & W allenhorst 1981) to derive an effective nebular

extinction law. This nebular extinction law is used to re-analyze the reddening-

sensitive emission-line diagnostics of temperature and ionic abundances observed by

OTV. Finally, we present a case where even this explicitly derived nebular extinction

law may be inadequate to analyze all of the observed emission lines, showing how it

might lead to large systematic errors in the estimation of the gas-phase Fe'"'/H'^ ionic

abundances in the Orion Nebula.

Excitation mechanisms for iron spectra are of particular interest. The forbidden

[Fe II] emission is known to be exceptionally strong in most gaseous nebulae, such as

Orion (e.g. Grandi 1975; OTV), supernova remnants (e.g. Dennefeld & Péquignot

1983; Dennefeld 1986; Henry et al. 1984; Hudgins et al. 1990; Rudy et al. 1994), Seyfert galaxies (e.g. Osterbrock et al. 1990), and circumstellar nebulae of luminous blue variables (e.g. Stahl k Wolf 1986; Johnson et al. 1992). In earlier works we found that the optical [Fe II] emission in Orion is collisionally excited in regions with high electron densities of ~ 1 0 ^ - 10' cm~^ (Bautista, Pradhan, k Osterbrock 1994; BPO hereafter). Further, we presented evidence that [Fe II] emission in Orion stems from partially ionized zones (PIZs), where hydrogen and oxygen are mostly neutral, and collisionally excited [0 I] lines are observed (Bautista & Pradhan 1995). At about the same time, in order to explain the anomalously intense [Ni II] optical emission from a variety of astrophysical objects, Lucy (1995) showed that the [Ni II] emission in Orion and the circumstellar nebula P Cygni could be excited by fluorescence via the background UV continuum, and suggested that [Fe II] optical emission may be similarly affected by UV fluorescence. This photo-excitation mechanism for [Ni II] and

[Fe II], in competition with collisional excitation, was further examined by Bautista,

Peng, & Pradhan (1996), in light of available observations. We concluded that owing to the differences in the atomic structure, fluorescence excitation is not as effective for [Fe II] as for [Ni II]. In contrast, Baldwin et al. (1996) modeled the optical [Fell] emission from Orion and suggested that UV fluorescence is indeed a viable mechanism for the excitation of the [Fe II] lines as opposed to the high electron densities deduced by BPP. They argued that the UV lines of Fe II that dominate the photoexcitation are optically thick and by including self-shielding, a process not considered in BPP, the observed [Fell] spectra could be reproduced at electron densities of ~ 10“* cm~'^

The collisional and fluorescent excitation, including optical depth effects, are further investigated herein (Section 4.1). Our results and those reported by Baldwin et al. are compared in detail with several independent spectroscopic measurements of Orion.

In Sections 4.2 and 4.3 we investigate the excitation of the optical [Fe III] and the

[Fe IV] UV lines, as additional diagnostics of the physical conditions in the emitting regions, as well as to study the ionization structure and the abundance of iron in

Orion. In Chapter 5 various photoionization models of the Orion nebula are presented under static conditions. Some discrepancies between the predictions of current static photoionization models and the observed structure of nebulae are pointed out. Then, the effects of the high density ionization front on the predicted spectra of neutral and low ionization species, e.g. O I and Fe II, are illustrated.

The role of kinematics in the structure and physical properties of photoionized nebulae is discussed in Chapter 6 . In diffuse H II regions, such as the Orion and

M l7, the ionizing radiation from hot stars in the nebular interior drives dissociation

(D) and ionization (I) fronts into a dense molecular cloud on the far side of the nebula. The newly ionized gas is driven away from the front into the nebula by a strong pressure gradient forming the “champagne” effect (Bodenheimer et al. 1979), resulting in a stratification of velocities and the ionization state of the emitting ions in the H II region. Such a correlation was observed by Kaler (1967); it is expected that an ionization model of the nebula would yield an understanding of the observed kinematics. The correlation between expansion velocities and the physical conditions in nebulae and their ionization fronts is shown.

Finally, the gas phase F e/0 abundance ratio is derived spectroscopically for the different emitting regions in Orion (Chapter 7). These estimates take into account the spatial variations of the density and temperature profiles across the nebula. Section

7 summarizes the results and the conclusions. REFERENCES

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1 0 CHAPTER 2

ATOMIC DATA FOR FEI-V

Recent progresses in large scale computations of photoionization cross sections, ra

diative transitions probabilities, collision strengths, and recombination coefficients for

the lowest ionization stages of Iron, i.e. Fe I-V, are reported. This work was car

ried out in collaboration with the Ohio State Atomic-Astrophysics group integrated

by Dr. Sultana N. Nahar, Dr. Honglin Zhang, and myself and directed by Prof.

Anil K. Pradhan. Table 2.1 summarizes the extent of the computed data for Fe I -

Fe V that has been calculated during the course of the present work. These com

putations are part of an international project called the Iron Project (Hummer et al. 1993) and complements or supersedes the radiative data for the iron ions obtained under the Opacity Project (Seaton et al. 1994). These calculations were carried out in the close-coupling approximation using the R-matrix method as developed by the

Opacity Project and the Iron Project.

Reliable ab initio calculations of atomic processes require first of all the compu tation of target wave functions that accurately represent the ionic systems. However, for complex ions such as the low ionization stages of iron the target representa tions involve the inclusion of large numbers of correlation configurations and, as a

11 consequence, very large close-coupling expansions that become computationally in

tractable even on supercomputers. New possibilities towards the computation of these

very large atomic systems, and ab initio calculations in general, are afforded by the

new technology of massively parallel processors (MPP’s). Furthermore, part of the

present work consisted on the adaptation of the Iron Project R-matrix package of

codes (Berrington et al. 1995) to the massively parallel environment, in particular the

Cray T3D and the IBM SP2.

The present results exhibit large differences with respect to data currently in use

and is expected to be of importance in the study of astrophysical objects.

In this chapter, I start by reviewing the theoretical methods used for the present

atomic physics calculations (Section 2 .1 ). In Section 2 .2 the package of codes, RMA-

TRX, used for the present work is presented and the version of this package created as

part of the present work to run on massively parallel machines. T3DRM, is described.

Sections 2.3 and 2.4 present large scale calculations under the present project of col lision strengths for Fell and Nill and photoionization cross sections and transition probabilities for Fel, FelV, and FeV. Section 2.5 presents a review of the rest of the collisional and radiative atomic data for Fel-V that has been used for the present project.

Most of the material presented in this chapter has been reported also in Bautista

(1996; 1997), Bautista & Pradhan (1995a; 1996; 1997a; 1997b), Bautista, Peng, &

Pradhan (1996), and Nahar, Bautista, & Pradhan (1997).

12 Ion Photoionization Recombination Collis. Excitation Transition Prob. Fe I 1 2 - 3 Fe 11 4 5 6 7 Fe III 8 9 1 0 11 Fe IV 1 2 13 14 15 Fe V 16 17 - 18 1. (Tp[ for 563 bound states multiplets (Bautista & Pradhan 1995; Bautista 1996): 2 . olr{T) - recombination rate coefficients (Nahar et al. 1997); 3. A- -coefficients and gf-values for 27,000 LS multiplets (Bautista 1996); 4. api for 745 bound states (Le Dourneuf e t al. 1993; Nahar & Pradhan 1994); 5. oir{T) - Nahar (1997); 6 . T(jT) - for 12,561 fine structure transitions among 142 levels (Zhang & Pradhan 1995); 7. A-coefficients and gf-values for dipole transitions among 19,267 LS multiplets and 234,689 fine structure transitions (Nahar 1995); 8 .

Table 2.1: New atomic data for Fe I-IV

13 2.1 Theoretical Methods

Collisional and radiative effects of atomic systems are calculated from the wavefunc-

tion representations of these systems. These wavefunctions result from the solution

of the time independent Shroedinger equation

^ ^ + 1 $ = (2.1)

where ^ and E are the total wavefunction and total energy of the system. Using

Rydberg units (üq = h = rrie = c = I) the non-relativistic Hamiltonian for the

N-electron target of nuclear charge Z plus a scattering electron is

iV+1 g y iV+1 9 Hh +1 = ^ ( - T-)- (2.2) i=l j>i ^0

For systems with Z less than about 30 relativistic effects can be introduced in the

Breit-Pauli (BP) approximation as

== ffar+i 4- (2.3)

where Hat+i is the non-relativistic Hamiltonian defined by Eq.( 2 .2 ), and H^^y are the mass and Darwin correction terms, and Hf^^y represents the spin-orbit term

that results from the reduction of the Dirac equation to Pauli form. For the present work concerning the lowest ionization stages of Fe only the mass and Darwin terms are considered. These have the advantage that they conserve the Russell-Sanders (LS) coupling symmetry. On the other hand, spin-orbit interactions break the LS terms into fine structure levels of total angular momentum {J = L + S). Such a symmetry representation would result in formidable additional demands to the already huge computations. Moreover, spin-orbit interaction effects for collisional excitation of

14 Fell-IV have been studied by Pradhan & Zhang (1993) and Zhang Pradhan( 1995b;

1995b; 1997) and were found to be relatively unimportant.

2.1.1 The R-matrix method

In the R-matrix theory the configuration space is partitioned into an internal and an

external regions to a sphere of radius a (Burke et al. 1971).

In the external region exchange between the scattered electron and the target can

be neglected. Thus, the potential is approximated by a local multipole potential of

the target and the solution can be obtained with asymptotic expansions of the wave

functions or by using perturbation theory. In the internal region, r < a, electron

exchange and correlation between the scattered electron and the iV-electron target are

important and the (yV-l-l)-electron system is represented by configuration interaction

expansions similar to the case of a bound system.

In order to find solutions in the internal region a wavefunctions basis set is con

structed using the close coupling (CC) approximation of the form

^k[E\ SLn) = . 4 ^ Xidi + X! (2.4) * * j

where y, is the target ion wavefunction in a specific £,• 5, state, 0, is the wave function

for the free electron, are short range correlation functions for the bound (e-f-ion) system, and .4 is the antisymmetrization operator.

.\ccurate CC calculations of atomic processes require, first of all, a good rep resentation of the core ion. Such representation of complex ions has to include a large number of correlation configurations. However, in order for the computations

15 to be computationally tractable, the configuration expansion needs to be as small as

practical.

Target wavefunctions were calculated using the Thomas-Fermi statistical poten

tial as implemented in the atomic structure code SUPERSTRUCTURE (Eissner et

al. 1974, Eissner 1991). This method provides reasonably accurate wavefunction rep

resentations of the target systems and is computationally much more efficient than

other ab-initio methods, e.g. Hartree-Fock (Clementi & Roetti 1974) and configura

tion interaction (Cl) using Slater-type orbital expansions (Hibbert 1975).

2.2 The RMATRX and the T3DRM packages

The RMATRX package of codes was developed by the Opacity Project and Iron

Project for the calculation of atomic processes using the R-matrix method outlined

above. The most recent version of the package was published by Berrington et

al. (1995). This package was written in FORTRAN 77 and consists of nine sepa

rate programs or stages occupying over 60,000 lines of coding plus several extensions.

The structure of the RMATRX package is shown in Fig. 2.1.

The T3DRM package was created as part of the present work and consists on

an adapted version of the RMATRX package to run on massively parallel processors

(M PP’s), particularly on the CRAY T3D. Data parallel, work sharing, and message

passing paradigms are used in T3DRM. Message passing was implemented using

the libraries PVM of CRAY, message passing libraries (MPL) of IBM, and message passing inter-phase (MPI). The former set of libraries has became the standard for parallel computers, so it provides portability of the codes among most platforms.

1 6 CIV3 SUPERSTRUCTURE

STGl STGIR

STG2RSTG2

STGH

STGB STGF(J) STGD

STGBB STGBF STGFF

ENERGY FREE-FREE COLLISION DAMPING fVALUES PHOTOIONI LEVELS ZATION CR OPACITY STRENGHTS CONSTANTS

INTFACE

BE BF

EOS. OPAC

RECOMBINATION OPACITIES COEFFICIENTS

Figure 2.1: The RM ATRX Package.

17 The T3DRM package has been fully tested and at least three large scale calcu

lation have been carried out with these codes, i.e. collision strengths and excitation

rate coefficients for Fell and Nill (Bautista & Pradhan 1996) and photoionization

cross sections and oscillator strengths for FeV (Bautista 1996). Most modules in the

T3DRM package exhibit speed-ups with respect to the serial version that are nearly

linear with the number of processors in the partition, reaching computing speeds that

are orders of magnitude greater than in serial processing on the Cray Y-MP. .A.lso, by

sharing the largest arrays in the codes among the multiple processors RAM memories

over 250 Mega words have been obtained. The parallelization on MPP’s affords new

opportunities for ab initio computations.

2.2.1 STGl and T3DS1

The STGl module is the first stage in RMATRX. It calculates the orbital basis and

all radial integrals in the internal region. T3DS1 is the version for the T3D of STGl.

This code remains in the serial form since it normally takes very short time and uses

little memory. Some changes, though, were made to this program to fix small coding errors and to properly initialize variables. These are minor problems that have no effect when running on most supercomputers but cause the program to fail when working with the current verv" sensitive FORTRAN compiler of the T3D.

2.2.2 STG2, T3DS2, and T3DSD

STG2 is the second stage in RMATRX. It calculates the LS-coupling elements of the

Hamiltonian and Dipole matrixes in the internal region. The Hamiltonian matrix

1 8 elements have the form

Hij = < ^i\H \’^j > (2.5)

where H is the Hamiltonian operator and é represents a single configuration in the

CC expansion of Eq.(2.4). In practice these matrix elements are calculated within

nested loops over the total (LS tt) symmetries of the (N -l- l)-electron system and

the Xi target states in the CC expansion. In a separated section of STG2 the dipole

matrix elements of the form

D m n =< > (2.6)

are evaluated. Here 0 denotes antisymmetric basis functions in the internal region

and D represents both length and velocity forms of the dipole operator:

iV + l V + l Q and D y = (2.7) fi=l n=l

For parallel computations it results convenient to separate the calculation of

Hamiltonian and dipole elements into two different modules which were called T3DS2

and T3DSD respectively.

The computation of Hamiltonian elements in T3DS2 was parallelized according to total S L tt sym m etries of the [N + l)-electron system. For this, the first processing element (PE) of the parallel partition is used as a “master” PE which distributes the work among all the other PE’s included in the task (“slaves”) in the partition. In this approach the load balance is controlled dynamically by the master PE that passes a new S L tt to each slave as it finishes its computation.

The input file for T3DS2 is similar to that used for STG2. The only changes are that T3DS2 has the I/O units defined within the code so card 2 of the input for

19 STG2 is no longer used. The other difference is that the parameter IPOLPH that indicates when the dipole matrix is to be calculated is no longer necessary and should be removed of the input file.

T3DS2 produces a large number of output files that trace the work done by each

PE. These files are named stg2nn.out, where nn is equal to (10 4- the PE number), for example, stg210.out is the output of PE=0, stg211.out corresponds to PE=I, etc.

There is also a number of files that contain the elements of the Hamiltonian for each

S L t t and they are named STG2Hmm.DAT, where (mm = 1 0 + the S L t t number).

The SL?r number goes from 1 to the total number of SLyr’s (parameter IN AST in the input) and is assigned to each S L tf in the same order in which they are given in the input file.

T3DSD is the version for T3D of the module of the STG2 code that calculates the dipole matrices. This code looks for dipole couplings between the symmetries included in the calculation and then distributes the coupled pairs over all the PE’s. One advantage of this approach over that used in T3DS2 is that since there is no MASTER

PE distributing the work through the partition. The disadvantage, however, is that the load balance can not be warranted.

The input file for T3DSD is exactly the same as for T3DS2. T3DSD creates output files in the same way as in T3DS2 with one stg2nn.out for each PE in the calculation and STG2Dmm.D.4T, where (mm = 1 0 + the SLtf pare number).

2.2.3 STGH and T3DSH

The module STGH diagonalices the Hamiltonian matrix and processes the dipole matrix from STG2. STGH takes relatively short time to execute but, it presents

2 0 the difficulty that it requires a lot of memory, which often exceeds the capabilities of

current supercomputers.

T3DSH is the parallel version of STGH. In T3DSH the largest arrays are dis

tributed over the memory of all the PE’s in the parallel partition. Then, the total

memory available to the job is scaled linearly with the number of PE’s in the partition

requested.

T3DSH requires that all the symmetries and the pairs of coupled symmetries to be

specified in the input. Thus, the total number of symmetries most be specified with

IN.A.ST on card 5 and the number of symmetry pairs is specified with a new variable

IDIP on card 4 right after IPOLPH. The symmetries are given in the input file after

the target energies as LL, SPN, PARITY, INDEX, where INDEX is the number of

the STG2H file where this particular symmetrv' can be found. The list of symmetry

pairs is given as NFINAL, NINITIAL. INDEX, where NFINAL and NINITIAL are

the numbers of the final and initial symmetric of the pair and INDEX is the number

of the STG2D file for the pair. The INDEX numbers of the symmetries and the pairs

can be easily figured out from the STG2 or T3DS2 input files.

One problem when running T3DSH on the T3D is that this code is less efficient

than the original STGH program on a CR.A.Y YMP. This seems to be due to the very limited CACHE space for remote memory accessing of the T3D compared with that of the YMP. For this reason, an additional version of T3DSH without distributed memory was created to run on the YMP for computations less memory demanding.

It is important to notice that T3DSH reads the STG2H and STG2D files created on T3D which uses a different format than YMP, therefore the assign command most be used to transform the files between the formats of the two architectures.

2 1 2.2.4 STGB, STGBB, T3DSB, and T3DBB

STGB reads the (iV + 1)-electron Hamiltonian matrix and calculates energies for bound states. It also produces datasets B required for bound-bound and bound-free radiative calculations. T3DSB is the T3D version of this program and is parallelized over the SLtp’s included in the calculation.

STGBB reads the datasets B and the dipole matrix to calculate oscillator strengths for bound-bound transitions. The T3D version of this program, T3DSBB, is paral lelized over the coupled pairs.

2.2.5 STGF, STGFJ, T3DSF, and T3DSFJ

STGF and STGFJ read the Hamiltonian and calculate collision strengths for inelastic collisions in LS-coupling or in fine structure. STGF also writes datasets F needed in the calculation of photoionization cross sections. In practice, these collision strengths need to be computed for thousands of energies; therefore, new versions, T3DSF and

T3DSF.I, parallelized over the entire energ}' mesh were created.

2.2.6 STGBF and T3DSBF

STGBF reads the B and F datasets and the dipole matrix and calculates photoion ization cross sections. These cross sections must be calculated for large numbers of photon energies. Therefore, T3DSBF distributes the number of energy points on which the cross sections is calculated among the PE’s in the partition.

2 2 2.3 Collision Strengths for Ni II and Fe II

Collision strengths and electron impact excitation rates were calculated for Nill and

Fell. In the Nill case the lowest 7 LS terms were included, which result in 17 fine

structure levels and 136 transitions. Coupling effects and resonance structures con

sidered in the present calculations result in differences of up to a factor of two with

the earlier distorted wave calculations by Nussbaumer &: Storey (1982), although

reasonable agreement is found for the line diagnostics of some strong transitions in

Ni 11. The Fell calculation includes 23 LS terms giving 74 fine structure levels and

2701 transition. This dataset complements earlier calculations by Zhang k Pradhan

(1995a).

2.3.1 Target data

The 7-term LS expansion for Ni 11 considered here is a subset of a larger wave func tions representation of the ion that includes the lowest 30 even and odd parity terms, i.e. all the levels up to 0.7224 Rydberg above the ground state. This larger represen tation of the target is dominated by the configurations 3cP, 3d® 4s, 3d® 4p and 3cf 4s^; however, the 7-term LS expansion used in this calculation is dominated by the con figurations 3d^ and 3d® 4s only. We have optimized the target expansion over all the configurations, for configuration interaction as well as for future work involving the odd parity levels. The calculated and the observed target term energies for the terms relevant to the present calculation averaged over the fine structure are presented in

Table 2.2. The observed energies are taken from Sugar & Corliss (1985). The earlier target energies obtained by Nussbaumer & Storey are also given and it is seen that the

23 present calculated energies are in much better agreement with the observed values,

within about 5 - 10%. Another indication of the accuracy of the target wave function

is the reasonably good agreement obtained (~ 10 — 30%) between calculated length

and velocity f-values, as shown in Table 2.3.

Term E (observed)" E (present) E (NS)" 3d^ ’^D 0.0000 0.0000 0.0000 3d«(^F)4s 4F 0.0798 0.0740 0.0314 3d®(^F)45 2 F 0.1236 0.1234 0.0776 3d^CP)4s 4p 0.2128 0.2556 0.2114 3dH^D)4s 0.2181 0.2439 0.1985 3d^(^P)4s 0.2610 0.3065 0.2605 3d\^G)4s 2 G 0.2908 0.3283 0.2824 “ Sugar Corliss (1985) * Nussbaumer &: Storey (1982)

Table 2.2: Target terms and energies for Ni II.

For Fe II we use a subset of an accurate and more extensive target wave function

representation (52 LS terms) that has been used to compute radiative data, photoion

ization cross sections, and transition probabilities for Fe I (Bautista & Pradhan 1995a:

Bautista 1997). The expansion considered for the present calculation consists of the

lowest 18 LS even parity terms plus the 3d®4p z z z z ■*F°, and z ^D°

terms. Table 2.3 gives the target symmetries included and their calculated energies, compared with those obtained with the target calculated by Pradhan & Berrington

(1993) and used by Zhang & Pradhan (1995a). The present target energies compare

24 Transition gfi gfv a '^D-z '^F° 0.70267 0.59782 a^D-z 1.59759 1.28159 a^D-y 0.49559 0.40461 a^D-z 0.37276 0.26010 a ^F-z^D'’ 5.41323 3.86574 a^F-z ^G° 10.4175 15.7351 a^F-z •‘F ° 7.75346 7.76380 a^F-z 2G° 4.60849 7.93458 a^F-z ^F° 3.63620 4.31824 a'^F-z ^D° 2.61489 2.39635 a^F-y ^D° 0.10583 0.11570 b^D-z 0.04774 0.04222 b^D-y ^D° 2.74048 2.97062 b-D-z 3.59285 5.18373 a^P- z ^D° 0.11126 0.23252 a^P-z ^P° 3.34886 3.38832 a^P-z 2p° 0.25738 0.29348

Table 2.3: Sample of oscillator strengths for Ni II

well, i.e. within about 10%, with experimental values. The calculated length and ve locity /-values also show good agreement with each other and also with the observed values (Fuhr et al. 1988) and the theoretical values by Nahar (1995) calculated for the

Opacity Project. The present f-values seem to agree better with the observed values than those by Pradhan & Berrington (1993), as shown in Table 2.5.

25 Term E (observed)" E (present) E (PB)'’ 3d®("T>) 4s a ®D 0 . 0 0 .0 0 . 0 SdJ Q ‘‘F 0.0186 0.0182 0.0518 3d^{^D) 4s a W 0.0953 0.0720 0.0907 3d' a ^P 0.1302 0.1203 0.170 ZcC a 0.1604 0.1427 ZdJ a 2 p 0.1737 0.1651 3d^ a 0.2146 0.1835 3d^ a ^ D 0.1934 0.1861 3d®(3p)4s b ‘‘P 0.2303 0.1914 0.246 3cf{^H)As a 0.2242 0.1918 0 . 2 2 1 3d=(^F)4s b "F 0.2452 0.2040 0.249 3d^ 4s^ a ®S 0.2461 0.2087 3d®(^G)4s a 0.2761 0.2310 0.274 3d®(3p)4s b 2 p 0.2861 0.2347 3d®(3p)4s b 0.2808 0.2354 3d® (3 F) 4s a -F 0.2663 0.2463 3d®(^G)4s 0.3330 0.2746 3d®(^D)4s b^D 0.3480 0.2825 0.349 “ Sugar &: Corliss (1985) ^ Pradhan &; Berrington (1993)

Table 2.4: Target term s and energies for Fe II

2.3.2 Calculations

Pradhan & Zhang (1993) and Zhang &: Pradhan ( 1995a,b) showed that that the

Breit-Pauli effects are not significant for the low-lying fine structure transitions in

ions such as Fe II and Fe III. Therefore, we carried out calculations of the scattering

matrixes in the LS coupling scheme, introducing only the mass and Darwin relativistic corrections (Eq. 2.3). The fine structure collision strengths were obtained by an

2 6 Transition afi 9Îv ^//(PB)“ 17/.(PB)“ gf{ohs.)^ a^D-z ^D° 9.18 8.60 10.2 9.9 9.86 7.76 a^D-z 12.86 14.36 14.4 14.1 14.3 11.3 a^D-z 5.01 5.11 6.3 6.0 6.19 3.87 a^F-z 2.04 0.80 2.05 1.37 a^F-z ^F° 1.02 0.39 1.04 0.87 a^^D-z 4.74 7.34 5.8 7.6 6.67 4.36 a^D-z ■‘F" 6.65 11.93 8.2 10.8 9.23 6.61 a^D-z ■‘F° 2.87 4.46 3.8 4.2 4.11 2.63 a^F-z 0.27 0.16 0.30 0.20 a^P-z 0.85 0.44 0.97 0.79 Pradhan & Berrington (1993) ^ Fuhr et al. (1988) Nahar (1995)

Table 2.5: Sample of oscillator strengths for Fe II

algebraic transformation of the scattering matrices to the pair coupling scheme using

a parallelized version of the code STGFJ. Partial wave contributions are included from

total angular momenta ( J = 0 — 9) for the case of Ni II, and ( J = 0 — 14) for Fe II.

We considered 88 SL-k symmetries (that denote the total spin, angular momenta, and parity of the e4-ion system) for Ni II with {L < 10), (25' -f-1 = 1,3,5, 7), and (tt = even and odd). The Fe II calculations included 128 SL tt symmetries with {L < 15),

(25 4- 1 = 1,3,5, 7), and ( t t = even and odd).

The collision strengths for both Ni II and Fe II were calculated for nearly 2000 energies ranging from 0 to 1 Rydberg. The energy mesh was chosen carefully as to

27 ensure that the resonance structures, particularly near the excitation thresholds, are resolved well enough to calculate accurate Maxwellian averaged rate coefficients.

2.3.3 Results

In this section we compare our results with those by Nussbaumer &c Storey (1982) and Zhang k Pradhan (1995a) for Ni II and Fe II respectively. We find that although

Nussbaumer k Storey did not calculate collision strengths as a function of electron energy for Ni II, their single point values for the strongest transitions appear to approximate the average of our results. For weaker transitions however (smaller collision strengths), their values differ significantly from the present results owing to the coupling and the resonance effects not included in their calculation. Figs. 2.2 (a) and (b) show the present collision strengths for Ni II, along with the single collision strength calculated by Nussbaumer k Storey, for some of the stronger transitions. It is noted that the presence of resonance structures in the present collision strengths would enhance the Maxwellian averaged values, although the resonances appear to be weak.

Comparing the present collision strengths for Fe II with those by Zhang k Pradhan we find that in general the background of the collision strengths in both sets of data are similar and the differences are mostly in the positions and strength of the resonances.

Fig. 2.3 compares our results for the (^Dg/2 —® D 7/2 ) transition in Fe II with the results by Zhang k Pradhan. It is noticed that both calculations give very similar background for the cross sections; however there are differences in the structure of the resonances. We expect the present results to be more accurate in the position of

2 8 1.4

1.2

o ' a .8

LL I .2

1 .2 .3 .4 .5 6 E (Rydbergs)

Figure 2.2: Excitation collision strengths for the transitions (^£> 5 /2 F 7/2 ) (a) and (^Dq /2 F5/2 ) (b) in Ni II vs. incident electron energy. The dashed lines indicate the one point values by Nussbaumer & Storey (1982).

29 Q CO I

P a

g 8

0 0 1 .2 .3 .4 E (Rydberg)

Figure 2.3: Excitation collision strengths for the transitions ^ ^ 7/2 ) in Fe II vs. incident electron energy from the present computation (a) and Zhang & Pradhan (b).

30 the resonances than those Zhang & Pradhan because of our better representation

of the target. However, the extend and high of some resonance structures may be

underestimated in the present computation because of the small number of odd parity

terms included in this expansion. New calculations for a much larger number of states

and improved wavefunction expansion are in progress.

Maxwellian averaged effective collision strengths are given by

Tij = (2.8)

Here, is the collision strength corresponding to the transition from level i to level

y, Ej is the energy of the incident electron with respect to the excitation threshold of

the level j, and T is the tem perature.

Tables 2.6 and 2.7 present samples of Maxwellian averaged collision strengths at

10,000 K for Ni II and Fe II, and compare them with previous results by Nussbaumer

& Storey and Zhang & Pradhan respectively. Table 2.7 includes also the results

obtained with a smaller 18-term calculation that excludes the odd parity terms. Our

results agree well (10 - 20%) with the single point collision strengths by Nussbaumer

& Storey (1982) for the transitions that give rise to some of the strongest lines,

e.g. ^Z? 5 /2 —^ Ft/2- However, for other transitions the differences rage from 30% to

more than a factor of two. When comparing our results with those by Zhang &

Pradhan, the overall difference is about 30%, being systematically smaller for the

stronger transitions and greater for the weaker ones. The present 23CC results are

well correlated with those of Zhang & Pradhan particularly for transitions from the

levels of the ground (a ^D) and first excited (a multiplets which dominate the collisional excitation of the ion. These differences still present may be due in part to

31 the more extensive resonance structure obtained by Zhang & Pradhan owing to their inclusion of many more odd parity terms. Two exceptions to this are the transitions a ^Di — a ‘^Fj and a ^Fi — b '^Fj for which the collision strengths differ by factors of two to three. This suggests that there may be some difHculties in representing the states of Fell with 3dJ configuration, which would require a more extensive target basis set than used so far. However, this has only a small effect on the near-IR and optical line ratios.

Transition T(10‘‘A') [present] T(IO-'K) [NS]“ ■^^5/2 T>3/2 0.113 0.148 "A5/2 —^ Fg/2 0.165 0.230 "^5/2 —^ F7 /2 0.088 0.144 ^•^5/2 F^/2 0.041 0.062 ^^5/2 — -^3/2 0.015 0.024 "^5/2 —^ Fy/2 0.749 0.777 ^D s/2 — ^ ^5/2 0.135 0.174 ^^5/2 “ * P0/2 0.042 0.088 "^5/2 —^ F 3 /2 0.021 0.049 ^T),5/2 —^ P1/2 0.009 0.022 ^^5/2 — 6 ^^3/2 0.046 0.167 ^D^/2 — b ^Dsf2 0.140 0.095 ^T>5/2 — ^ F3 /2 0.184 0.132 0.054 0.049 ^£>5/2 Pl/2 0.054 0.049 ^Pâ/2 —^ Gg/2 0.184 0.215 ^Dâ/2 G7/2 0.050 0.114 Nussbaumer & Storey (1982)

Table 2.6: Comparison of Maxwellian averaged collision strengths for Ni II

32 Transition Present (23CC) (18CC) ZP°(38CC)

^Dg/o9/2 — J^7/2 5.260 4.65 5.52 - ^D s/2 1.300 1.29 1.49 - ^D z/2 0.641 0.813 0.675 - ^D i/2 0.297 0.433 0.284 - 'F o 9/2 1.49 1.31 3.60

'F 7 / 2 0.566 0.614 1.51 - ' a5/2 / 0.120 0.135 0.497 - ^D-/2 8.040 14.30 10.98 - 'D s5/2 / 0.445 0.572 0.560 -'F,3/2 0.167 0.386 0.191 - 'a /2 0.722 0.542 0.948 3/2 0.404 0.319 0.502 - 6 'a5/2 , 0.273 0.215 0.308 - ' a 13/2 0.543 0.196 0.631 - '^11/2 0.256 0.196 0.311 — b 'i / 9 /2 0.420 0.081 0.402 — b 'F 7 /2 0.188 0.039 0.216 - ®5'ô/2 0.857 0.399 — - 'G ii/2 0.435 0.373 0.344 ~ '

Table 2.7: Comparison of T(T’ = 10 K) values for Fe II

33 In terms of the calculated line intensities and emissivity ratios for Nill under

collisional excitation conditions both, Nussbaumer & Storey and the present, data

sets yield similar results for observable lines as shown in Bautista &c Pradhan (1995a).

Also, forbidden Fell line ratios for optical and near-IR lines calculated with either

Zhang & Pradhan or the new data are very similar, as shown in Figs. 4.3 and 4.4.

Effective collision strengths are obtained for all the transitions calculated in this

work for temperatures ranging from 500 K to 20,000 K.

2.4 Photoionization Cross Sections and Oscillator Strengths for Fe I, Fe IV, and Fe V

Photoionization cross sections and dipole transition probabilities for Fe I, Fe IV,

and Fe V were calculated. The computations were carried out in the close coupling

approximation using the R-matrix method including 52 LS terms dominated by the

configurations 3d®4s, 3dJ, 3d®4p, 3d^4s^, and 3d®4s4p of the target for Fel, 31 LS terms

with multiplicity (25 -f 1) = 3 and 5 owing to the configurations 3cf^, 3cf 4s, and

3d^ 4p of the target for FelV, and 34 LS terms dominated by the configurations

3d^, 3(P 4s, and 3cP 4p of the target for FeV. The present results differ by up to several orders of magnitude from earlier data from central field type approximations.

2.4.1 Target expansions

Accurate computations for low ionization stages of iron must allow for channel cou pling among many states of the target ions for at least three reasons. First, the con figuration interaction (Cl) between the numerous low lying LS terms is important.

Second, strong dipole couplings between opposite parity terms within the target ion

34 give rise to large photoexcitation-of-core (PEC) resonances at corresponding incident

photon frequencies (Yu and Seaton 1987). Third, the photoionization channels corre

sponding to the ionization of the open inner shells are likely to contribute considerably

to the total cross section. This means that in the case of Fel, for instance, terms dom

inated by the configurations and 3d^4s4p of Fe II should also be included. For

the present work the photoionization of Fe I, FelV, and FeV are considered as

hu -f- Fel —ê + FeII{Z(fAs, 3(f, SdÂp, 3d°As^, 3dÂsAp) (2.9)

hu -h F elV -4-6 + FeV{3d\ 3d^ As, 3(f 4p) (2.10)

hu A- FeV —> e + FeVI{3d^, 3d^ 4s, 3d} Ap) (2.11)

The atomic structure code SUPERSTRUCTURE (Eissner et al. 1974, Eissner

1991) was used in the present work to compute eigenfunctions of 52 states of the

Fel target system (Fell), 31 states of the FelV target (FeV), and 34 states of the FeV

target (FeVI). Tables 2.8-10 present completes list of list of configurations included in

the target, as well as a comparison between the calculated target term energies and

the observed energies, averaged over the fine structure, taken from Sugar & Corliss

(1985). These tables also present complete lists of correlation configurations included

and the values of the scaling parameters for the Thomas-Fermi potentials for each ion.

The agreement between the calculated and laboratory energies is very good, generally

within 10% for Fell and 2% for FeV and FeVI. A further indication of the accuracy

of the target wavefunctions is the good agreement (< 10%) between the length and

the velocity forms of the dipole oscillator strengths between opposite parity terms of each ion.

35 Level Ecal Eobs Level Ecai Eobs 3d®(’D) 4s a 0.0 0.0 3(P{^D)Ap 2 6“PÛ 0.3798 0.3886 3d^ a '‘F 0.0186 0.0182 3(f(=D)4p 2 ‘*F° 0.3872 0.4037 3dP(^D) 4s a -*D 0.0953 0.0720 3tf(=D )4p 2 ‘‘D° 0.3807 0.4039 3dJ a •‘F 0.1302 0.1203 3(P{^D)Ap 2 ‘P° 0.4012 0.4265 3dt^ a ^G 0.1604 0.1427 3(f{^S)AsAp 2 8P° 0.5667 0.4762 3d^ a 0.1737 0.1651 3d^ As^ b^G 0.5462 0.4907 3d^ a 0.2146 0.1835 3d^ As^ d^F 0.5961 0.5199 3d^ a 2 d 0.1934 0.1861 3cP{^F)Ap 2^S ° 0.5762 0.5399 3(f(^P)4s b 0.2303 0.1914 3d^ As^ c-‘D 0.6237 0.5463 3d^{^H)As a 0.2242 0.1918 3d=(3p)4p y^P° 0.5805 0.5504 3d®(V)4s b 0.2452 0.2040 3cP{^H)Ap z^G° 0.5729 0.5504 3d^ 4s^ a 0.2461 0.2087 3d\^H)Ap 2 -‘//° 0.5760 0.5516 3(f(3G)4s a ^G 0.2761 0.2310 3(f(^P)4p z^D " 0.5850 0.5567 3d®(3p)4s b 2P 0.2861 0.2347 3d^{^H)Ap 2 0.5756 0.5565 3(f{^H)As b 2/7 0.2808 0.2354 3(PCF)Ap p^D ° 0.5849 0.5646 3d^{^F)As a 2p 0.2663 0.2463 3cF{^H)Ap z^D " 0.5801 0.5629 3d^{^G)As b'^G 0.3330 0.2746 3d^{^F)Ap I/"F« 0.5955 0.5625 3d^l^D)As b ‘‘D 0.3480 0.2825 3cFI^S)AsAp ^6pO 0.6379 0.5620 3dJ b 2 p 0.3279 0.2871 3cFCH)Ap z ^ /o 0.5816 0.5654 3(f(V )4s a 2/ 0.3475 0.2959 3cF{^F)Ap X -‘D° 0.6002 0.5722 3é{^G)As c 2G 0.3608 0.3013 3cP{^F)Ap 0.6020 0.5791 3d^CD)A.s 6 2D 0.4059 0.3261 3cFCF)Ap 2 2P0 0.6025 0.5826 3(fi{^S)As a 2 5 0.4145 0.3354 3d^{^F)Ap 0.6096 0.5881 3d^CD)As c 2 d 0.4115 0.3442 3(f(^P)4p Z^P« 0.6015 0.5869 3d^{=D)Ap z= D ° 0.3515 0.3490 3cF{^H)Ap z W 0.5983 0.5926 3d^{^D)Ap z « F ° 0.3732 0.3805 3(f 4s2 V 0.7699 0.6656

3s‘ 3p® ZdJ 4p, 35^ 3p® 3d^,3p^ 3rf^,3s^ 3p^ 3cf 4s, 3p® 3(f 4s^,3s^ 3p® 3d' 4s, 3s^ 3p^ 3rf® A„/: 1.33166 (Is), 1.23525 (2s), 1.07709 (2p), 1.0 7885 (3s), 1.05515 (3p), 1.05113 (3d), 1.03293 (4s), 0.88831 (4p), 1.40563 (4d)

Table 2.8: Calculated (cal) energy levels of Fe II and comparison with observed (obs) levels from Sugar &: Corliss (1985).

36 Level Eca/ Level Eo6s EcaZ 3d“ 0.000000 0.00000 Zd^(^F)As J p 2.12336 2.161109 Zd^ 3 p 0.227038 0.232252 3d=(V)4p 2.33251 2.355847 3d^ 0.223059 0.259441 3d=(V)4p 5pO 2.35148 2.386004 3cM 3 p 0.237769 0.261593 3d=(^Dl)4s 2.34905 2.419861 Zd^ 0.267818 0.309157 Zd^*F)Ap 5pO 2.36577 2.391652 3d'* 0.327553 0.379240 3d^(V )4p 3p0 2.36838 2.397309 3d^ 3p 0.561290 0.618696 Zd^*F)Ap Zq Q 2.40378 2.440669 3d-» 3p 0.560546 0.618706 3d^(V )4p 3pO 2.42943 2.469158 3d^CF)4s 5p 1.70206 1.695583 Zd^-^P)Ap 5 pO 2.49342 2.534489 Zd\^F)As 3p 1.78024 1.782194 Zd^{^P)Ap 5p0 2.51746 2.556067 Zd\^P)As 5p 1.86264 1.874768 Zd^‘^P)Ap 3pO 2.50752 2.551853 3(f(^G)4s 1.89927 1.910388 ZdH^G)Ap 3p0 2.52243 2.558687 Zd^{^P)As 3p 1.93610 1.963195 Zd^^G)Ap 3gO 2.54016 2.585237 3d^(2p)4s Zp 1.94802 1.975859 Zd^(^G)Ap 3pO 2.54951 2.597140 3d^(^D)4s 1.96486 1.984966 Zd^{^P)Ap 3 pO 2.60523 2.623293 Zd^{^H)As 1.96974 1.985141

oA O O J O O - i o_4 o j 6 nA o_6 oj-2 i_2 0 .1 o_6 o j 4 1 - -5 ... 1 o _ 6 o j 4 I _ 3p® 3p^ Zd^ 4s, 3p® 3^^* 4s^, 3s^ 3p® ZS 4s 4p, 3s^ 3p® Z(fi 4s Ad A„,: 0.92092(ls), 1.12967(2s), 1.30081(2p), 1.301 77(3s), 1.10895(3p), l.G8238(3d), 1.08360(4s), 1.08238(4p), 1.19316(4cl)

Table 2.9: Calculated and observed term energies (Rydbergs) for Fe V relative to the Zd‘^{^D) ground state. The spectroscopic and correlation configurations for Fe V, and the values of the scaling parameters A„/ for each orbital in the Thomas-Fermi-Dirac potential used in Superstructure, are also given.

37 Level E 065 Eca/ Level Eo 6s Eca/ 2 p 0 3d^ 0 . 0 0 0 0 0 0 0 . 0 0 0 0 0 0 3d"(^P)4p 3.11654 3.157376 3d* 4p 0.164747 0.169518 3d=('*P)4p 4do 3.12830 3.163145 3d* 2 G 0.180803 0.193499 3d2(3p)4p 2 d 0 3.13696 3.168952 3d* 2 p 0.229137 0.232475 3d*(^P)4p 2G° 3.17472 3.219006 2 5 0 3d* 2 d 0.249488 0.242133 3d2(3p)4p 3.19529 3.241274 4 5 0 3d* 2 /f 0.253531 0.281387 3d=(^P)4p 3.23038 3.283241 2 pO 3d^ 2 P 0.412069 0.435277 3 (f('D )4 p 3.25359 3.299941 2 p 0 3d* 2 D 0.644089 0.655111 3d^('D)4p 3.26285 3.314892 3(f(3F)4s 4p 2.38728 2.328184 3(f(^P)4p 4d 0 3.27922 3.322854 3d2(3f)4s 2 P 2.44996 2.414726 3(f(*D)4p 2 pO 3.29096 3.346683 4 pO 3d*(*D)4s 2 D 2.55031 2.516728 3cF(3p)4p 3.31433 3.362279 3d2(3p)4s 4p 2.56282 2.518222 3d^(*G)4p 2 ^ 0 3.31718 3.356075 3d2(3p)4s 2 P 2.61748 2.600714 3tF(^P)4p 2 D° 3.36622 3.442309 2 p 0 ZcPCG)4s 2 G 2.65322 2.604507 3(f(*G)4p 3.38819 3.421722 2 p 0 3d*(3F)4p 2 5 3.06587 2.95662 3d*(3p)4p 3.40039 3.477487 3d2(3p)4p 4(J0 3.09326 3.117651 3(f(*G)4p 2 p 0 3.43794 3.487353 3d2(3p)4p 4 pO 3.09926 3.128948 3cf^('5)4p 2 pO 3.72251 3.788938 Correlation: 3a- 3p^ 3 d ', 3s^ 3p‘ 3d^ 3s 3p® 3 d \ 3p® 3d^ 3p® 3d'' 4s, 3s^ 3p® 3cP Xni: 1.1024 (Is), 1.0867 (2s), 1.4669 (2p), 1.4669 (3s), 1.1000 (3p), 1.0640 (3d), 1.1655 (4s), 1.0968 (4p) , 1.2287 (4d)

Table 2.10: Calculated (cal) energy levels of Fe VI and comparison with observed (obs) levels. The energies (in Rydberg) are relative to the 3d^(^F) ground state. The spectroscopic and correlation configurations for Fe VI, and the values of the scaling parameters for each orbital in the Thomas-Fermi-Dirac potential used in Superstructure are also given.

38 The present calculations were carried out in LS coupling, since the relativistic

effects in photoionizing the low ionization stages of iron should be small. Although,

they might be significant for some types of transitions in Fe IV, it would be impractical

at this stage to carry through a large-scale relativistic calculation involving a number

of channels several times larger than the already huge value used in the LS coupling

case. Also, the inclusion of fine structure has only a marginal effect on the calculation

of the Rosseland or the Planck mean opacities (Seaton et al. 1994).

The second summation in the CC expansion (Eq. 2.4) represents short range cor

relation functions. These functions are very important in obtaining accurate (e + ion)

wavefunctions, but may cause pseudo-resonances, particularly if the two summations

in Eq. 2.4 are inconsistent (Berrington et al. 1987; also discussed later). Owing to

the magnitude of the calculations, the sets of functions were optimized to include

only the minimum number of correlation functions that have important effects on

the bound states energies and bound-bound oscillator strengths. Nonetheless, these

components of the close coupling expansion are large (Tables 2.11-13).

For Fel the total state of (N-i-l)-electron functions had to be truncated in view

of our present computational capabilities on the Cray Y-MP with 64 MW memory

and 2 Gb disk space limit for the diagonalization of the dipole matrix in STGH.

This computational constraint affected the accuracy of the results for the singlet and

the triplet symmetries. The present calculation for quintets and septets included a

total of 56 (N-l-l)-electron functions which produced nearly 1650 configurations, 150 channels, and a Hamiltonian matrix with a maximum dimension of nearly 2000. For singlets and triplets 65 (N-f-l)-electron functions were included which gave rise to

39 3s^3p®3d®, 3s^3p^3d^4s, 3s^Sp^3dJ4p, 3s^3p^3cf4d, 3s^3p®3d®4s4p, 3s^3p^3rf®4s, 3p^3(fi4s^, 3p^3(f 4a, 3s3p®3c^, 3s3p®3rf*4s, 3p®3d^4p, 3s^3p®3d®4p^, 3s^3p‘*3rf^4s4p^, 3sZp^3dJAsÂp, ZsZp^ZdJAs^, Zs^Zp^ZdÂp, Zs^Zp^ZdÂsAp^, ZsZp^ZcfAsAp^., 3s^3p^3d®4s4p^, 3s^3p'*3d®4s^4p^, 3p®3c/®4s^4p^, 3a^3p‘*3rf^°, 3p®3rf^°, Zs^Zp^ZdJAp^^ Zs^Zp^ZdÂs^, ZsZp^ZdJAp^, Zp^ZdÂsÂp, Zp^ZdÂp^, Zp^ZdJAsAp^, Zs^Zp^ZdÂsAd, Zs^Zp‘^ZdÂd, 3s^3p‘*3cP4a, 3s^3p‘*3

Zs^Zp^Z(fi, Zs^Zp^ZdÂs, Zs^Zp^ZdJAp, Zs^Zp^ZdJAd, Zs^Zp'^ZdJAsÂp, ZsZp^ZdÂp", ZsZp^ZcPAs^, Zs^Zp^ZdPAs^, Zs^Zp^ZdÂsAp, Zs^Zp^ZdÂs, Zp^ZdJAsÂp, Zs^Zp^ZcÂs, Zp^ZdÂs^, ZsZp^ZcP, ZsZp^ZdÂs, Zs^Zp^ZdÂsÂp, Zp^Z(fAp, Zs^Zp^ZdÂp^, Zs^Zp^ZdJAsAp^, ZsZp^ZdJAsÂp, ZsZp^ZdJAs^, Zs~Zp^ZdÂp, Zs^Zp^ZdÂsAp^, ZsZp^ZdÂsAp^, 3s^3p^3rf®4s4p^, 3s^3p‘‘3d®4s^4p^, Zp^ZdÂsÂp^, Zs^Zp^Zd^'^, Zp^Zd^°, 3s^3p’3

Table 2.11: Correlation functions for Fe I included in the CC expansion. Upper panel: correlations for quintets and singlets; lower panel: correlations for singlets and triplets

40 3p®3(i", 3s3p^3(f, 3p^rf^4s, 3p^(f4p, 3p^d'^4d, 3s^3p'^3cf, 3s3p‘*3rf^4s, 3s3p‘^3d^4p, 3s3p'*3d^4d, 3p^3d^4s^, 3p‘*3d'4p^, 3p‘*3d®4s4p^, 3s^3p^3d^, 3s‘^3p^3d‘^4s, 3s^3p^3d^4p, 3s^3p^3(f, 3s^3p^3d^4s, 3s^3p^3dHp, 3s'^3p^3dHd, 3p®3d«4s, 3p®3d®4p, 3p^3(f4d, 3pV 4s^, 3p®3d^4p2, gpGg^s^g^p 3p^3d^4s4d, 3s3p®3d'^4s^, 3s3p^3d^4p^, 3s3p^3d^4s4d, 3s^3p^3d‘^4s4d, 3p^3cf4s4d, 3s3p®3d®, 3p®3rf“4s24rf, 3p®3d‘'4s4p^, 3s^3p^3d^4p^, 3s‘^3p^3d^4s'^, 3s3p^3d^4s, 3p^3dJ, 3s^3p^3d^4s^, 3s^3p^3rf‘*4p^, 35^3p^3rf'*4s4p, 3s^3p^3d^Ap4d, 3s3p®3d®, 353p®3c/‘‘4s^, 3s3p^3d^4p'^, 3s3p^3d^4s4d, 3s3p^3d^4p4d, 3s^3p^3d^, 3s^3p^3d^4s, 3s^3p*3d^4s^, 3s^3p^3d^4p^, 3s^3p‘^3d^4s4d, 3s^3p'^3d^4s4p^, 3s^3p^3d^4d, 3s3p^3d^4s4p, 3p^3d^4s^4p, 3s3p^3d^4d. 3s^3p^3d^4s4d, 3s3p®3rf‘*4s4p, 3s~3p‘^3d^4d, 3s3p^3d^4s^4p^

Table 2.12: Correlation functions for Fe IV included in the CC expansion

3s^3p^3d^, 3s^3p^3d^45,3s'^3p®3d^4p, 3s~3p^3d^4d, 3s^3p^3d^, 3s^3p^3d‘^4s, 3s^3p^3d‘^4d, 3s^3p°3d^4s4d, 3p^3d^4s4d, 3p^3d®, 3p®3d^4p, 3s^3p^3d®, 3s^3p*3d^4p, 3s3p^3d^4s4d, 3p^3d^4s^4d, 3p®3d^4s4p^, 3s^3p'*3d‘*4p^, 3s^3p‘‘3d‘*4s^, 3s3p^3d^4s, 3s3p^3d‘^4d

Table 2.13: Correlation functions for Fe V included in the CC expansion

41 almost 2900 configurations and 152 channels: the dimension of the Hamiltonian matrix

was nearly 3000.

The overall calculations for each ion were divided into groups of total (e + ion)

symmetries SLtt according to their multiplicity, i.e. (2S+1) =1, 3, 5, and 7 for Fel and

FeV and (2S+1) = 4 and 6 for FelV. Because of memory and disk space constrains

(several tens of gigabytes) it was not possible to calculate the doublet symmetry states of FelV. These states, however, are not coupled to the ground state of the

ion thus, they are relatively unimportant. On the other hand, a calculation with a

reduced number of terms would probably yield results similar to those of Sawey &

Berrington (1992) who included only the 3d^ term in their calculations under the

Opacity Project.

2.4.2 Results

Three sets of data are calculated: (a) energy levels, (b) oscillator strengths, and (c) total and partial photoionization cross sections.

The effects of these parameters on the ionization structure and spectra of iron in nebulae are discussed in Chapter 5.

F el

.A. total of 1,117 states in LS coupling were found up to n < 10 for Fel. Table 2.14 compares a small sample of the computed energy levels separately for septets, quintets, triplets, and singlets with experimental values from Nave et al. (1994). The agreement for septets is good even for highly excited multiplets, the overall error of calculated energies with respect to observed values, weighted over the energy of the multiplet

42 (cT^ = Yl^obsi^obs - ^caiŸ/^lbs îs about 1.9%. The agreement for quintet states can be regarded as satisfactor}', particularly for terms with absolute energies greater than

0.2 Ry. It is noticed that the calculated energy for the a ground state of Fe I agrees with the observed energy to about 1.2%, and the averaged difference between calculated and observed energies weighted over the multiplet energies is about 4.4%.

As expected, the results for the calculated energies of the triplets and singlets present the largest discrepancy with experiment. The overall difference with observed energies for triplets is about 8.9%. Calculated energies for singlet are in reasonable agreement with experiment for terms with absolute energy greater than 0.2 Ry; however, greater discrepancies are observed for higher excitation terms and the averaged difference with experiment is about 10.6%.

Dipole oscillator strengths (/-values) for 32,316 transitions among the calculated states of Fe I were obtained in LS coupling. This set includes transitions when the lower state lies below the first ionization threshold and the upper state lies above.

These transitions are important because they might contribute to the total photo absorption, but do not appear as resonances in the photoionization cross sections.

There are two criteria commonly used in assessment of the accuracy of oscilla tor strengths. First, both length and velocity forms of the oscillator strengths are calculated and compared with each other. This provides a check on the accuracy of the wavefunctions and, therefore, on the accuracy of the /-values (Berrington et al. 1987). Fig. 2.4 shows the log of the absolute value of the velocity form of the g/-values, plotted against the log of the length form of the g/-values separately for septets, quintets, triplets, and singlets. In each panel the statistical dispersion of the plot for gf[^ > 0.01 is indicated. It is observed that dispersion in the g/-values for

43 Conf. Term -Eca! -E o6s Conf. Term -Eca! -Eofcs 3d^{W)4s4p z‘^D° 0.4130 0.4020 3(P{^D)4s4p z‘F° 0.3850 0.3719 3(f{^D)4s4p z‘P° 0.3750 0.3616 3d^{^S)4sHp /P° 0.2130 0.2139 3(f{^D)4s5s e-^D 0.1850 0.1869 3cP{^D)4sop 7^0 0.1260 0.1283 3d^l^D)4s4d e^P 0.1200 0.1196 3cP{=D)4s4d PD 0.1210 0.1185 3d^4s^ a=D 0.5700 0.5771 3d^{^F)4s P f 0.5290 0.5128 3d^(“P )4 s a^P 0.4280 0.4197 3(P{^D)4s4p z^D° 0.3620 0.3425 3d®(^D)4s4p z^F° 0.3470 0.3328 3cP{^D)4s4p Zopo 0.3320 0.3135 3é{^F)4p y-D° 0.2810 0.2755 3dJ{^F)4p y-opo 0.2770 0.2699 3(f{^F)4p z^G° 0.2660 0.2606 3(P{^D)4s4p ySpO 0.2420 0.2434 3d^i^D)4s4p x^D° 0.2190 0.2166 3(P[^D)4s4p x^F° 0.2190 0.2104 3d^CP)4s4p z^S° 0.2000 0.2081 3(P{^P)4s4p x^P° 0.1770 0.1912 3d^{^P)4s4p w'^D° 0.1730 0.1807 3(P{^F)4s4p -opo 0.1540 0.1770 3d^l^D)4s5s e^D 0.1660 0.1703 3dP{^F)4s4p 0.1390 0.1637 3dJ{^F)0s e^F 0.1460 0.1479 3(P{^G)4s4p w'^G° 0.0810 0.1477 3(P{=D)4s4d PD 0.1260 0.1198 3d^{^D)4s4d 0.1250 0.1173 3d®(^D)4s5p vPF° 0.1120 0.1122 3(P{^D)4s4d p F 0.1160 0.1121 3d"(“F )4 s a? F 0.4730 0.4677 3d^4s^ o»P 0.3880 0.4081 3d^4s^ a?H 0.3490 0.4024 3d^4s^ 6»F 0.3490 0.3911 3d^^G)4s a^G 0.3690 0.3808 3d^^P)4s 6»P 0.3600 0.3721 3d®4s^ b^G 0.2970 0.3617 3d'{^P)4s c»P 0.3460 0.3570 3dJ(^H)4s b^H 0.3160 0.3409 3d'^(^D2)4s a^D 0.3290 0.3403 3d®4s2 b^D 0.2440 0.3133 3d®('’D)4.s4p z»D° 0.3070 0.2932 3d®(^D)4s4p z^F° 0.2970 0.2922 3d» c»F 0.2080 0.2777 3d®(^D)4s4p zZpo 0.2810 0.2696 3d"(-‘F)4p z»G° 0.2590 0.2556 3dJ{^F)4s d^F° 0.0940 0.2437 3d"(-‘F)4p p"F° 0.2430 0.2432 3d\^F)4p 0.2270 0.2299 3d» 3p 0.0380 0.2071 3(f{^P)4s4p 0.1260 0.1562 3d»(»P)4.s4p p3po 0.1400 0.1545 3d^[^F)4s4p 3 po 0.0570 0.1522 3d^(‘‘P)4p 0.1190 0.1475 3d^{^P)4p X^P° 0.1180 0.1398 3d"(-‘P)4p 0.1190 0.1475 3d^(-G)4s a^G 0.3470 0.3569 3d^(^P)4s a^P 0.3330 0.3298 3d'(^D2)4s a^D 0.3170 0.3201 3d^(2p)4s a^H 0.2930 0.3182 3d^4s^ a^I 0.2830 0.3137 3d»4s2 b^G 0.3000 0.3093 3(P4s^ FD 0.2540 0.2652 3d»(^P)4s4p Ipo 0.1370 0.1487 1 po 3d^{^H)4s4p %/'G° 0.1100 0.1370 3d»(»F)4s4p 0.1080 0.1322

Table 2.14: Comparison of calculated (cal) energy levels with experimentally observed (obs) levels from Nave et al. (1994) for Fel

44 Septets Quintets 2 2

0 = 11% 1 1

0 0

1 1

a> O) o 2 2 2 1 0 1 2 2 1 0 1 2 Triplets Singlets 2

0 =51% 0 =2 7 % 1

2 -2 2 1 01 2 ■2 1 0 1 2

log lgf,l

Figure 2.4: loggfy plotted against loggfi for transitions between calculated LS terms of Fel.

45 each symmetry is consistent with the differences found between the calculated ener gies and the experimental ones. Septets, whose calculated energies agree well with experiment, exhibit the lowest dispersion in the ^/-values of only 11%. Transitions among quintet terms have a greater dispersion of about 20%.

Triplets present the largest dispersion (~ 51%) consistently with the discrepancies found for the energy levels; however, for transitions with gfi >0.1 the dispersion is about 22%. The dispersion for transitions among singlet states is about 27%.

The second accuracy evaluation is the comparison of a limited number of individual gf values with those observed experimentally by Nave et al. (1994), and those in the critical compilation of transition probabilities by Fuhr et al. (1988). For this comparison, presented in Table 2.15, the fine structure g f values presented by Nave et al. and Fuhr et al. were summed, though for some multiplets the experimental data is incomplete. Some improvement to the accuracy of the calculated g f values can be obtained by correcting the calculated energy difference for the transitions with experimental energies, i.e.

gfijicor) = ^ X gfijical), (2.12) where gfij{cor) and gfij{cal) are the corrected and calculated ^/-values respectively and {Ej—Ei)exp and {Ej—Ei)cai are the experimental and calculated energ}' differences between the levels.

Table 2.15 shows significant differences between the two sources of experimental data. In most cases these differences arise from incompleteness of the set of fine structure /-values, measured within an LS multiplet, in the the earlier compilation by Fuhr et al. as compared to the more complete work by Nave et al. In some other

46 Transition Present^ Present^ Nave et al. Fuhr et al. z^D° - e^D 5.44 5.13 4.32 3.47 * oPD - z^D° 0.689 0.611 0.575 0.566 aPD - z^P° 0.598 0.540 0.611 0.162* aPD — y^D° 3.67 3.52 3.29 2.28* aPD — y^F° 1.56 1.49 1.46 1.41* aPD - x^P° 0.0739 0.0753 0.110 0.190* aPD - x^F° 15.9 15.2 15.5 14.2* aPD - x^D° 8.26 8.04 7.05 7.63* a^F — z^D° 0.243 0.238 0.174 0.166* a^F - z^F° 0.0223 0.0221 0.0121 0.0115* aPF - y^D° 4.70 3.86 3.62 3.60 * aPF - y'^F° 8.14 7.85 6.75 6.75 a^P - z^P° 0.233 0.258 0.196 0.137* aPP - z^S° 0.686 0.636 0.325 0.316 aPP - x^P° 0.282 0.256 0.213 0.245 a^F - z^F° 0.0385 0.0383 0.0444 0.0400* a^D - y^F° 6.17 6.98 5.15 5.25 a^F - z^D° 0.270 0.283 0.206 0.100* a^F - y^D° 5.24 5.11 4.44 4.68* a^P - z^P° 0.0664 0.0494 0.0252 0.025 a^G - 0.282 0.261 0.173 a^G -z^G ° 0.618 0.578 0.186 0.158 a^G-y^G° 0.616 0.587 0.631 a^G-z^H° 2.19 1.58 1.44 1.78 a^G-z^F° 0.224 0.210 0.575 0.724 a^G-y^G° 0.616 0.572 0.631 a^G-x^G° 0.802 0.747 0.468 0.562 a^G-x^F° 0.639 0.512 0.316 0.347 a^P — w^D° 0.324 0.274 0.170 0.170 a^D - z^F° 0.158 0.136 0.0978 0.166 a^D — y^D° 0.159 0.137 0.158 0.11 a^DP° 0.0616 0.0646 0.0537 0.0457 ^ calc, with theoretical energies ^ corrected with obs. energies * incomplete multiplet

Table 2.15: Comparison of calculated and corrected ^/-values for Fel with experi mental measurements from Nave et al. (1994) and Fuhr et al. (1988)

47 cases, however, differences up to 40% come from the experimental measurements

themselves. It is also noted that the effect of correcting the calculated ^/-values

using experimental energy differences is quite significant, and in most cases seems

to bring the ^/-values closer to those measured experimentally. Unfortunately, it is

difficult to derive conclusions regarding the accuracy of the g /-values for transitions

among septets since there seems to be no complete experimental data for any multi

plets. Thus the values given in Table 2.15, summed over the available fine structure

components, should be considered as lower limits to the total LS multiplet strength.

Oscillator strengths for quintets compare reasonably well with experiment, the differ

ences being within 10-20% with only two exceptions. Once again, triplets and singlets

present the largest discrepancies with respect to observed values, though most values

are in good agreement, 10-20%, with experiment.

The dispersion between length and velocity forms of the oscillator strengths and

the comparison of a sample of values with experimental measurements suggests that

for septets and quintets the present g f may be accurate to the 10-20%, ^/-values for

singlets to about 30%, and for triplets to about 30-50%. The present ^/-values could

be considerably improved if corrected using experimental energy separations; this is

recommended for practical applications.

Fig. 2.5(a) and (b) show the photoionization cross section for the 3d®4s'^(^D)

ground state up to photon energies above all ionization thresholds of Fe II included

in the CC expansion. Fig. 2.5(c) presents the same cross section from another

calculation excluding the G f D and ‘‘F) terms of Fe II that correspond

to the ionization of the inner 3d shell. In Fig. 2.5(a) the thresholds of the first term dominated by configurations ZdfAp(fD°),ZdfAs^{^G) and 3d^4s4p(®P®) are marked.

48 2

2 m ill -3

.6 .8 1 1.2 1.4

1 .6 .8 1 1.2 1.4 2

1 .6 .8 1 1.2 1.4 Photon Energy (Ry)

Figure 2.5; Photoionization cross section (cr (Mb)) of the ground state ’D of Fe I: (a) full curve, present result; broken curve, Kelly (1972). Thresholds from all configurations included in present computation are marked, (b) full curve, present result; broken curve, Verner et al. (1993); filled squares, Reilman & Manson (1979). (c) Cross section without coupling of the 3d^4s^ target Fe II terms contributing to the ionization of the inner 3d sub-shell.

49 There is strong enhancement in both the background and the resonances structures

with the onset of additional inner shell ionization channels into 3d^4s^ terms of Fe II.

In particular, the presence of large resonances just above the 3d®4p(®D°) term is

noted; this is due to strong coupling to the terms corresponding to the ionization of

the 3d shell.

The present ground state cross section is compared with that of Kelly &: Ron

(1972) and Kelly (1972) (Fig. 2.5(a)). The first of these papers concerns the small

range of energy from the ionization threshold to 10 eV (~0.735 Ry), and the sec

ond paper deals with the cross section for a more extended range of energies. The

agreement between the present work and both of these cross sections is remarkably

good below 0.73 Ry, where the cross section is dominated by correlations involv

ing the terms of the core ion 3d®(^D)4s a ®D, 3d' a '*F,3d®('’D)4.s a ‘‘D, and 3d"

a ■’P. Beyond this energy Kelly’s calculations underestimate the actual cross sec

tion; most likely due to missing correlations from the 3d®(^P)4s ■'P. 3d®(^P)4.s ‘‘P,

3d®(^P)4s ■’P, 3d®(^G)4s and 3d®(^D)4s terms. Nevertheless, Kelly included

contributions from 3d'’4s^(®S) that produce a sharp jump of the cross section near

0.79 Ry. An interesting feature in Kelly’s cross section is the series of resonances

due to Zd^As^np ’^P,” P autoionizing states (see Fig. 7 of Kelly & Ron 1972).

The position of the strongest set of these resonant obtained by Kelly was about 0.89

Ry while the actual structure of the peak and its hight were rather uncertain. The

present calculations reproduce such a feature but at 0.94 Ry and it is considerably

higher than in Kelly’s results. Some other resonances of this series found by Kelly are also seen in the present cross section. Another important characteristic of the cross section is its sharp jump at the position of the thresholds for ionization of the inner

50 3d sub-shell. Kelly’s calculations give a single edge at 1.16 Ry for all the contribu

tions due to 3c/^4s^ D / F, and ‘‘G. In the present calculation separate edges are

obtained for each of these thresholds, as well as for those of 3d®(®D)4s4p and

which were not considered by Kelly. Finally, Kelly’s cross section at high ener

gies (above the thresholds associated with 3d inner-shell ionization) agrees well with

both the present results and those from central field type approximations (Reilman

& Manson 1979; Verner et al. 1993).

Fig. 2.5(b) also shows a comparison with the results of Reilman and Manson

(1979) in the central field approximation, and the more recent calculations of Verner

et al. (1993) in the Dirac-Hartree-Slater approximation. The results of Reilman &

Manson and Verner et al. neglect the complex correlation effects, such as inter-channel

coupling, that are responsible for the large cross sections in the near threshold region.

The present coupled channel results are up to several orders of magnitude higher

in the energy region below about 1 Rydberg. The two earlier result agree very well with each other. .A. remarkable feature of the comparison in Fig. 2.5(b) is the large discontinuous jump in the earlier results, over 3 orders of magnitude, due to the on set of inner shell ionization of the 3d sub-shell. The present results exhibit no such discontinuity since the ionization thresholds up to inner-shell ionization are explic itly coupled together. The total photoionization cross section is therefore continuous across all thresholds in the eigenfunction expansion. This might be regarded as a general feature of photoionization cross sections in the high energy regime, in that the inner shell photoionization “edges” often seen in the central field type cross sec tions should not in fact be sharp discontinuities, but should consist of a relatively smoothly varying background superimposed with autoionizing resonances, if the ap

51 propriate thresholds belonging to the high lying states are considered. It is clear from

Fig. 2.5(b) that the amount of photoabsorption missing from the earlier works is con siderable, and the integrated photoionization rate (as inferred from the area under the solid and the dashed curves) would be in substantial error. The sharp ionization edges are thus artifacts introduced in the cross sections owing to the neglect of cou pled states in the high energy region. In practice, however, it is computationally very expensive to couple a very large number of excited states for heavy atoms so as to avoid these inner shell discontinuities. On the other hand, the magnitude of the jumps decreases with energy (i.e. successive inner shell ionizations) and is usually much less than the large one seen for Fe I in Fig. 2.5(b) (Verner et al. 1993). Furthermore, at higher photon energies ( > 1 Rydberg), when the coupling of the ejected electron with the core ion is weak, the central field results approach the present cross sections.

The convergence of all results in the high energy region, where one would expect the central field approximation to yield reasonably accurate cross sections, also indicates that the close coupling results have converged (this is not the case in Fig. 2.5(c) where the discrepancy with previous works at high energies is considerably larger).

Photoionization cross sections were calculated for all computed bound states with energy below the first ionization potential of Fe I. In order to delineate in detail the autoionization resonances near the ionization thresholds a very fine mesh of energies, typically about 2000 points, was used in the range of up to 0.3 Rydberg above the threshold. Fig. 2.6 shows the photoionization cross sections for some excited terms of Fe I.

In practical applications, particularly non-LTE spectral models, it is important to determine accurately the level population in the excited levels of the residual ion

52 Z5 2

1 .6 .8 1 1.2 1.4 .4 .5 .6 .7 8 9

3 d T F )4 s a T 1.5

O) o

1.2 1.4 .4 .6 .8 1 1.2

2 ad'c'F

1.5 1

•1 .4 .6 .8 1 1.2 1.4 2 .4 .6 8 Photon Energy (Ry)

Figure 2.6: Photoionization cross section (a (Mb)) for a sample of excited states of Fe I.

53 2

-2 2

3d® 4s (“D)

O) o

-2

3d' (T)

3d® 4s (®D)

Photon Energy (Ry)

Figure 2.7: Partial photoionization cross sections of the Fe I ground state into the ground and excited states of Fe II.

54 Fe°. 3d®(®D)nd

4s4p (®P°) 1 9d

- — ______j-

-4 4 5

O' oi o -4 4

-4 4

-4 .5 Photon Energy (Ry)

Figure 2.8: Photoionization of Fel bound state in a Rydberg series showing the PEC resonance features.

0 0 following photoionization. Therefore, partial cross sections for photoionization of the ground state of Fe I into the ground and excited terms of Fe II have been calculated.

A few examples of these partial cross are shown in Fig. 2.7. Some examples of the so called photoexcitation-of-core (PEC) resonances in photoionization cross sections along Rydberg series of Fe I are shown in Fig. 2.8. Such PEC resonances result from strong dipole couplings between opposite parity terms within the target ion (Yu

& Seaton 1987). The present work entails the full set of calculations for all 1,117 bound states, including partial cross sections into the ground and excited states with multiplicity (2£ 4-1) = 5 and 7 of Fe II.

FelV

Energies for 746 LS terms of Fe IV corresponding to all possible bound states with principal quantum number n < 10 were calculated. In Table 2.16 we compare the computed energies for these terms with those calculated by Sawey & Berrington

(1992) and experimental values from Sugar & Corliss (1985). The energies obtained in the present work, especially those for the low lying st states, agree typically within

2% with the experimental values. This level of agreement, for most terms, is better than the results of Sawey & Berrington.

Dipole oscillator strengths (/-values) for 34,635 transitions among the calculated states of Fe IV were obtained in LS coupling. This set includes transitions for which the lower state lies below the first ionization threshold and the upper state lies above.

These transitions can be important in opacity calculations because they contribute to the total photo-absorption, but do not appear as resonances in the photoionization

56 Conf. Term Eca/ Eop E065

3d^ -3.984 -3.961 -4.028 3d^ -3.665 -3.640 -3.734 3(f 4p -3.660 -3.585 -3.706 3d^ -3.613 -3.563 -3.674 3d^ ‘‘F -3.485 -3.426 -3.548 3d\^D)4s -2.941 -2.774 -2.857 3d‘^{=D)4s -2.795 -2.685 -2.767 3d\^P2)4s 4p -2.648 -2.531 -2.616 3d-^{^H)4s -2.618 -2.531 -2.620 3d\^F2)4s 4p -2.613 -2.516 -2.605 3d‘^CG)4s ‘‘G -2.580 -2.488 -2.578 3d\^D)4s -2.523 -2.427 -2.519 3d\=D)4p 6 po -2.275 -2.256 -2.303 3d\^D)4p 6 p o -2.267 -2.250 -2.296 3d‘^CPl)4s 4 p -2.280 -2.194 -2.292 3d\^Fl)4s 4p -2.270 -2.198 -2.293 3d‘*CD)4p 4 p o -2.226 -2.224 -2.274 3d*(^D)4p 6 DO -2.229 -2.214 -2.266 3dH^D)4p 4 p o -2.184 -2.189 -2.237 3d\^D)4p ipo -2.115 -2.135 -2.184 3d\^H)4p 4 p o -2.005 -2.035 -2.090 3(f(^P2)4p 4po -1.971 -2.024 -2.075 3d\^F2)4p 4QO -1.967 -2.035 -2.065 3d\^H)4p 4 JO -1.972 -2.006 -2.058 3d\^P2)4p 4 p o -1.936 -1.997 -2.048 3d\^F2)4p 4 p o -1.932 -1.987 -2.038 3d\^H)4p 4g o -1.949 -1.988 -2.040 3d\^F2)4p 4 DO -1.910 -1.970 -2.026 3j4(3G)4p 4 R O -1.906 -1.956 -2.010 3d4(3G)4p 4 p o -1.902 -1.959 -2.012 3d4(3G)4p 4g o -1.877 -1.929 -1.982 3d\^D)4p 4 DO -1.819 -1.900 -1.959 3d\^D)4p 4 p o -1.816 -1.895 -1.947 3d\^D)4p 4 p o -1.806 -1.882 -1.939

Table 2.16: Comparison of the calculated energies for Fe IV, Ecai, with the results, Eop, by Sawey & Berrington (1992), and observed energies, Eoôs, from Sugar & Corliss (1985) 57 2

1.5

O) O) .5

1 1 5 0 5 1 1.5 2 log gf,

Figure 2.9: log gfy plotted against log gf^ for transitions between calculated LS terms of FelV.

58 cross sections (strictly speaking, the upper bound state does autoionize if departure from LS coupling is considered and fine structure continua are explicitly allowed). In the absence of experimental /-values it is diflScult to ascertain the overall accuracy of the data. However, a comparison of length and velocity oscillator strengths provides consistency check on the accuracy of the wavefunctions and, therefore, on the reliabil ity of the /-values. In Fig. 2.9 we plot log g fv vs. log gf^. We have included all the symmetries since each exhibits roughly the same dispersion. The dispersion between length and velocity values with gf’s greater than unity < 13% for the quartets, and

< 22% for the sextets. This, added to the good agreement between the calculated energies and those observed experimentally, suggests that the overall uncertainty for such transitions should be 20% or less. However, weaker transitions are likely to have greater uncertainties.

Table 2.17 presents a comparison of the present ^/-values with those of Sawey &

Berrington (1992) and Fawcett (1989) for a small sample of transitions. Fawcett’s work is based on a semi-empirical adjustment of Slater parameters in the relativistic

Hartree-Fock code by Cowan (1981) to minimize the differences between calculated and observed wavelengths. Very good agreement between the present results and

Fawcett’s values is observed for most transitions.

Photoionization cross sections were calculated for all 746 bound states of Fe IV considered here. These cross sections include detailed autoionization resonances re sulting from the coupling to states dominated by 3d*, 3d^4s, and 3d^4p configurations in the core ion. Fig. 2.10(a) shows the photoionization cross section of the 3d^ (®S) ground state of Fe IV. In the same figure we have plotted the results of Reilman &

Manson (1979) and those of Sawey & Berrington (1992). One interesting feature in

59 the present cross section is the huge resonance, more than 1 Ry wide and two orders of magnitude higher than the background, just above the ionization threshold. Such a feature should have a large effect on the ionization rate and the opacity of Fe IV: thus a careful and detailed study of this resonance is worthwhile.

The first thing to investigate is what electron configuration of the Fe IV system is responsible for the resonance, and whether this is possibly a pseudo-resonance that sometimes arise in close coupling calculations owing to inconsistencies between the two summations in Eq. 2.4. Pseudo-resonances can arise if the first summation involving all channels coupled to the target terms does not explicitly include the parent configurations of some {N + l)-electron correlation configurations included in the second summation. Such configurations then do not have corresponding thresholds for the Rydberg series of resonances in the target expansion. These manifest themselves as large pseudo-resonances, which in a sense represent the entirety of resonance series belonging to the missing thresholds. In order to rule out this possibility, the ground state cross section was calculated several times with different subsets of the (iV + 1)- electron correlation configurations listed in Table 2.12.

It appears that the configuration 3s^3p^3d® gives rise to the particular resonance.

Fig. 2.10(b) shows the cross section obtained when this configuration is excluded.

The 3s^3p'’3d® configuration of Fe IV corresponds directly to the 3s^3p^3d^ correla tion configuration in the expansion for the Fe V core ion. Thus, this resonance appear to be real. In addition, the term energies for Fe IV calculated with an accurate Cl expansion that includes the 3s^3p^3d® configuration, using the code SUPERSTRUC

TU RE (Eissner 1991), indicates that an autoionizing 3s^3p^3d®(®P°) state is indeed

60 Configuration Transition Present SB Fawcett

3d\^D)As - 3d^{^D)Ap 6 ^ _ G po 6.11 5.92 6.11 _6 £)0 10.2 9.83 8.49 6/) _6 po 13.8 13.3 13.9 if) _4 po 3.77 3.64 2.20 ad - i D° 7.02 6.67 6.57 if) po 9.17 8.79 8.75 3d\^H)As - 3d^{^H)Ap AR _4 ffo 12.7 11.5 12.0 i R f° 17.5 16.6 16.9 3d\^F)As-3d^{^D)Ap i p - i po 0.11 0.08 0.10 3dH^G)As - 3d‘^i^D)Ap iQ _A po 0.11 0.08 0.10 3dH^G)As - 3d\^H)Ap AG _ 4 RO 1.90 2.24 1.94

Table 2.17: Comparison of calculated ^/-values in LS coupling for Fe IV with the calculations by Sawey k. Berrington (1992; SB), and the semi-empirical results by Fawcett (1989) using Cowan’s code.

expected at about 4.58 Ry above the ground state. That the energy of this state agrees well with the position of the resonance adds weight to our identification.

As this resonance arises from the configuration in Fe IV, one might expect that explicit inclusion in the calculation of the thresholds due to the 3s^3p^3d^ parent configuration in the Fe V target would change the shape of the resonance and even break it into a series of narrow Rydberg resonances. The list of term energies for

Fe V in the present target expansion shows that above these 31 terms the next higher terms coupled to the ground state of Fe IV are 3s^3p^3d^ ("F°), (^P°),

61 3

0 34 5 6 7 8 9 10

a S 3 i

0 34 5 6 7 8 g 10

3 5 6 78910 - 3p'3d‘('P°)nd (‘P°) I

0 34 56 7 8 9 10 Photon energy [Ry]

Figure 2.10: Photoionization cross section (cr (Mb)) of the ground state 3d^(®5) of Fe IV as a function of photon energy (Rydbergs). (a) the cross section obtained with the present 31CC expansion (solid curve); (b) the cross section excluding the 3s^3p“3d® configuration; (c) the cross section with the 3s^3p^3d^ target terms of Fe V included explicitly (the Rydberg series P°)nd{^P°) for n=3 to 10 is marked). The dashed curve shows the results of Sawey & Berrington (1992) and the filled dots, those of Reilman & Manson (1979).

6 2 Therefore, the ground state cross section was re-calculated including these states; the

result is shown in Fig. 2.10(c). A large number of narrow resonances converging on

to the new thresholds are present: however, the large resonance under investigation

remains unchanged.

The more extended calculation also allows for a better identification of the origin of

the resonance, which seems to belong to the P°)nd{^P°) Rydberg series,

as indicated in Fig. 2.10(c) for n = 3 to 10. An alternative series could be the

3s^3p^3(P{^P°)nd{^P°); however, the percentage channel contribution with the

parent is smaller.

Thus, the nature of the large resonance in the ground state cross section seems

to be understood, and its identification as the autoionizing equivalent electron state

3s^3p^3(P{^P°) explains in large part the broadness of the feature. Nevertheless, one

should be aware that the position of the resonance may be uncertain in the absence

of experimental data for the 3s^3p"^3d^ thresholds in Fe V. Also, the position of the

resonance in the present calculation relies entirely on the accuracy of the 3s^3p^3d^

wavefunctions, which is rather difficult to assess.

The failure of other authors to obtain resonance structures in the cross sections is due to the absence of the relevant electron correlations in those calculations. This is always the case for the central field approximation used by Reilman & Manson

(1979). The close-coupling calculation by Sawey k. Berrington included only the 16 states of the target ion dominated by the 3d^ configuration. This means that only contributions from the 3d^{^D) ground state of the Fe V core ion were included in the photoionization cross sections of states with multiplicity (25 +1) = 6 . Therefore,

63 all coupling effects for the cross sections of these states and, in particular, of the the ground state of Fe IV, were also missing.

We have obtained the partial cross sections for photoionization of the states of

Fe IV into at least the lowest few (particularly the metastable) terms of Fe V. These partial photoionization cross sections are also necessary in the calculation of unified electron-ion recombination rate coefficients (Nahar Pradhan 1994; Nahar, Bautista,

& Pradhan 1997b). Fig. 2.11 presents these partial cross sections for photoionization of some excited states of Fe IV into the ground state of Fe V.

The PEC features are prominent in the photoionization of excited bound states along a Rydberg series, as the outer electron is weakly bound and photo-excitation takes place within the ion core - the PEC process is thus the inverse of the di-electronic recombination process with the outer electron as a “spectator” (Nahar and Pradhan

1992; 1994). Such PEC resonances are seen in Fig. 2.12 which displays the photoion ization cross sections of Fe IV bound states in the Rydberg series Zd^{^F)nd{^D) with n = 5-9. .A.t the Fe V target thresholds Zd^Ap{z'^F°,z^D°,z^S°), the incident photon energies equal those of the strong dipole transitions from the ground state 2d^{a^F) and large PEC autoionizing resonances are formed, enhancing the effective cross sec tion up to several orders of magnitude above the background. The prominent peaks shown in Fig. 2.12 correspond to these dipole transition energies a^F —> z^F°, z^D°.

64 3

1 3.5 4 4.5 5 5.5 6

1 2 ’’"ô7 g 0

1 2 2.5 3 3.5 4 4.5 5 5.5 6

I I “i T”T m TT I i" r I I n n | i i i r

(c)

■ I I I I i i M I I i 3.5 4 4.5 5.5 6 photon energy [Ry]

Figure 2.11: Partial photoionization cross sections of some excited states (3cfi panel (a); 3d^{°D)4p '^F° panel (b); 3d‘^{^F2)4p ^G° panel (c)) of Fe IV into the ground state of Fe V.

65 -2

-2

O) o 2

■2 2 2.2 2.4 2.6 2.8 3 photon energy [Ry]

Figure 2.12: Photoionization of FelV bound states in the D)nd{^G) Rydberg series showing PEC resonances.

66 Fe V

A total of 1812 states in LS coupling were found up to n < 1 0 . In Table 2.18 we compare the computed energies for these terms with the few experimental values available (Sugar & Corliss 1985). The overall agreement is of about 1 .6 %: the dif ference for the 3(P (^D) ground state is only of 0.85%. In the same table we also present the unpublished results computed by Butler under the Opacity Projects in

TOPbase at CDS (Cunto et al. 1993) using a 15 CC expansion. These values differ from the observed energies by about 2.5% which is slightly worst than for the present results. Dipole oscillator strengths (/-values) for 129,904 transitions among the cal culated states of Fe V were obtained in LS coupling. This set includes transitions for which the lower state lies below the first ionization threshold and the upper state lies above. These transitions are important because they might contribute to the total photo-absorption, but do not appear as resonances in the cross sections.

In the absence of experimentally measured /-values it is difficult to ascertain the overall accuracy of the data. However, a comparison of length and velocity oscillator strengths provides us with a check on the accuracy of the wavefunctions and, therefore, on the reliability of the /-values. In Fig. 2.13 we plot log gfv vs. log gf^. In this plot we have included all the symmetries since each of them exhibits roughly the same dispersion. The agreement between length and velocity /-values is quite satisfactory, especially for g f values greater than unity. We note that for g f > 0.1 the overall dispersion is about 16% which, added to the good agreement between the calculated energies and those observed experimentally, suggests that the data for most such transitions should be accurate to about 1 0 - 2 0 %.

67 Photoionization cross sections were calculated for all 1812 bound states of Fe V. obtained in the present calculations, including detailed autoionization resonances re sulting from the coupling to states dominated by 3d^4s, and 3(f4p configurations in Fe VI. Fig. 2.14(a) shows the photoionization cross section of the Sd'* (5D) ground state of Fe V. In the same figure we have plotted the results of Reilman & Manson

(1979) in the central field approximation. Both of these approximations neglect the complex correlation effects, such as the inter-channel coupling to inner shells, which result in cross sections in the near threshold region with erroneously small values.

The earlier results by Reilman and Manson (1979) underestimate the photoionization cross section of the ground state of Fe V, for energies below about 10 Ry, by up to a factor of four. Beyond 1 0 Ry the present cross sections converge well toward the results by Reilman and Manson as might be expected since the electron correlation effects get weaker with increasing energy. It is worth to emphasize that the differ ences between the present CC calculations and the previous works stems primarily from the inclusion of full coupling to the dominant states of the core ion, particularly those including the inner 3d shell, that manifest themselves well below the onset of the 3d-shell ionization through autoionizing resonances and resulting enhancement of the effective background cross section.

Fig. 2.14(b) shows the earlier 15 CC results (obtained from TOPbase; Cunto et al. 1993), which also underestimate the cross section for the ground state of Fe V by nearly a factor of two in the energy range of interest and neglect much of the resonance structures in the near-threshold region. This difference arises from the much smaller number of target states in the previous Opacity Project calculations for Fe V.

6 8 Conf. Term Eca/ Etop E[j6s 3d-* -5.557 -5.440 -5.510 z é 3p -5.342 -5.183 -5.283 -5.318 -5.212 -5.287 3d‘* 3p -5.314 -5.176 -5.272 3d^ -5.272 -5.151 -5.242 3(M -5.217 -5.074 -5.184 3d^ -5.203 -5.064 -5.182 3d“ V -5.197 -5.175 3(^ -5.188 -5.009 -5.156 z é -5.149 -4.988 -5.095 3(f* ^F -5.059 -4.915 -5.037 Zd^ 3p -4.980 -4.814 -4.949 3d‘* 3p -4.982 -4.823 -4.949 3cM ^G -4.895 -4.741 -4.868 Zd^ -4.673 -4.494 -4.662 Zd^ -4.446 -4.215 -4.413 3d^(‘‘F )4s 5F -3.748 -3.753 -3.808 3 d ^^F )4 s 3p -3.663 -3.674 -3.730 3d^(^F)4s 5p -3.575 -3.559 -3.647 3(f(^G )4s ^G -3.543 -3.535 -3.611 3d3(“P )4 s 3p -3.495 -3.484 -3.574 3d^(^G)4s ‘G -3.503 -3.495 -3.571 3d^(2F)4s 3p -3.482 -3.472 -3.562 Zd^(^D)As -3.467 -3.446 -3.545 Zd^(^H)As -3.471 -3.470 -3.540 3rf3(2p)4s ‘p -3.446 -3.434 -3.517 Zd^{^D2)As -3.429 -3.406 -3.507 Zd?{^H)As -3.431 -3.430 -3.500 Zd^{^F)As 3p -3.302 -3.280 -3.387 Zd^{-F)As ‘F -3.268 -3.243 -3.351 3rf3(4p)4p 5G° -3.181 -3.135 -3.178 Zd^{^F)Ap 5p0 -3.152 -3.110 -3.159 Zd^[^Dl)As 3p -3.038 -3.021 -3.161 Zd\^F)Ap 5p0 -3.142 -3.099 -3.144 Zd^{^F)Ap 3 DO -3.142 -3.102 -3.142

Table 2.18: Comparison of calculated (cal) energies for FeV in Ry with the results by Butler in TOPbase at CDS (Cunto et al. 1993; TOP) an the observed (obs) energies from Sugar & Corliss (1985) 69 2

1.5

1 .5 0 5 1 1.5 2 loglf.l

Figure 2.13: log gfv plotted against log gfc for transitions between calculated LS terms for FeV.

70 3

3d^ 4p3(f

oO) 1

0 5 6 78 9 10

g 1

0 5 6 7 8 9 10 Photon Energy (Ry)

Figure 2.14: Photoionization cross section (cr (Mb)) of the ground state 3p"‘('’D) of Fe V. In panel (a) the present results (solid line) with the results by Reilman & Manson (1979; dashed line); In panel (b) cross sections by Butler in TOPbase (Cunto et al. 1993, solid line) and by Reilman & Manson (1979; dashed line).

71 For practical applications regarding non-LTE spectral models it is of interest to obtain the partial cross sections for photoionization of the ground state of Fe V into at least the lowest few (particularly the metastable) terms of Fe VI. Fig. 2.15 presents these partial cross sections for photoionization of the ground state of Fe V into the lowest coupled terms in Fe VI. i.e.

hu + FeV[Zd\^D)\— ^ (2.13)

e + FeVI[M\^F), ^ P ) , ZdHs{^F), (‘‘P)].

One interesting feature observed in the photoionization cross sections are the so called photoexcitation-of-core (PEC) resonances that result from strong dipole couplings between opposite parity terms within the target ion (Yu k. Seaton 1987).

Such PEC resonances are seen in Fig. 2.16 which displays the photoionization cross sections of Fe V bound states in the Rydberg series Zd^[^F)nd{^D) with n = 5-9.

.\t the Fe VI target thresholds 3d^4p(z‘‘F°, z^S°), the incident photon energies equal the energies of the strong dipole transitions from the ground state Zd^{a^F), and large PEC autoionizing resonances are formed, enhancing the effective cross section up to several orders of magnitude above the background. The prominent peaks shown in Fig. 2.16 correspond to these dipole transition energies cl^F —>• z^F°,

72 -2 II — f i l li 1 Ihlp ------— _

-4 1 L 1 .i 1 1 1 i 1 1 1 _ 1 1. 1 , 1 , 0

-1 3d"4s ("F)

-2

-3

-4 J L I I I I I 2

o ’ 05 0 O

2.5

It—

0 1 2 3 4 Photon Energy (Ry)

Figure 2.15: Partial photoionization cross sections into the ground state and the excited states of Fe VI.

73 FeV, 3dfF)nd"D

6 4

0 -2

-2

b0 . m o -2

-2

-2 2.8 3 3.2 3.4 3.6 Photon Energy (Ry)

Figure 2.16: Photoionization of Fe V bound states in a Rydberg series showing the PEC resonances features.

74 2.5 Review of Other Atomic Data

With the exception of experimentally measured energy levels (compiled by Sugar

and Corliss 1985) and oscillator strengths for dipole allowed and intercombination

transitions in Fell, all other atomic data for iron ions for the present project are

computed theoretically. Then, a review of these data, which was not calculated

within the present project, is presented below.

2.5.1 Collision strengths and transition probabilities

The collisional-radiative models used in the present study employ the Maxwellian

averaged effective collision strengths and transition probabilities for forbidden tran

sitions obtained as described below.

F ell

Recently, collisional data for electron impact excitation of Fe II were provided by

the close-coupling calculations of Pradhan and Zhang (1993) and Zhang and Prad

han (1995a). Collision strengths and rate coefficients were given for 10,011 transi

tions among 142 fine structure levels of 38 LS terms dominated by the configurations

3d® 4s, 3d^, and 3d® 4p. For the present work we construct a 159 level system for Fe II

that uses data for the 142 levels in Zhang & Pradhan, and the results from the present calculation (Section 2.3) including 23 states. However, the line ratio diagnostics with either set of data for the near-IR lines are nearly identical, and for the optical lines the diagnostics differ only marginally.

Accurate transition probabilities for forbidden transitions are difficult to calculate because very accurate wavefunctions are needed to obtain the weak relativistic electric

75 quadrupole and magnetic dipole probabilities with very small Einstein A-coefBcients.

For Fe II such computations are especially challenging owing to the number of al gebraic terms involved. The first A-values for the [Fe II] IR and optical lines were reported by Garstang (1962). Nussbaumer & Storey (1988) provided a more accurate set of IR A-values for transitions among the 16 fine structure levels of the first 4 LS terms, a®D, a^P and 3dJ a^F, a'^D, using the program SUPERSTRUCTURE

(Eissner et al. 1974). Recently, Quinet et al. (1996) have reported more extensive calculations for the [Fe II] transitions, using SUPERSTRUCTURE and the semi- empirical code by Cowan (1981). The differences between these data and that of

Nussbaumer & Storey and Carstang’s is small, a few percent, for most transitions but it reaches up to a factor of two for some transitions. Computational limitations restricted Quinet et al. (1996) from explicitly including some important configurations that were included earlier by Nussbaumer and Storey (1988), such as the 3d^4d^ and

3d^4/~, in the configuration interaction expansion. The effect of excluding these con figurations was estimated to be approximately 25-30% for many transitions (Quinet et al. 1996; private communication).

Some indication of the accuracy of the difierent A-value calculations may be ob tained by comparing with observations for pairs of lines that originate with the same upper level; for then the intensity ratio depends only on the known energy differ ences and the .A.-values. In Tables 2.19 and 1.20 we compare such line ratios, for

IR and optical lines respectively, with selected observations of the Herbig-Haro ob ject, HHl, which exhibit particularly strong [Fe II] emission in both optical and IR wavelengths, while emission from HI and Hel are inhibited. These comparisons have been confirmed with spectra of various nebulae and supernova remnants. Table 2.19

76 reveals very good agreement, within ~ 5% for most line ratios, between the data by

Nussbaumer &c Storey and the observations, but the data by Quinet et al. yield sig

nificant discrepancies. One particularly interesting ratio is the I(1.257//m )/(1.644)um

), comprising the strongest [Fe II] lines in the near-IR region. This ratio is useful, for

example, in the diagnostic of dust extinction (e.g. Dennefeld 1982, 1986; Bautista,

Pogge, & DePoy 1995). The observed ratio of about 1.34 agrees within 2% with

the expected value from the Nussbaumer & Storey data, while the Quinet et al. data

yield a ratio nearly 30% lower. The line ratios comparison for optical lines in Table

2.18 shows some differences between observations and Garstang’s data, ~ 30%. The

differences with respect to the data by Quinet et al. are somewhat larger.

Based on these comparisons we adopt the data by Nussbaumer & Storey for the IR

transitions, and Garstang’s data for the rest. We estimate that these data sets may

be uncertain to the 5-10% and 30-40% levels respectively. It seems clear, nevertheless,

that more calculations of transition probabilities for the optical [Fe II] transitions are

needed.

F e lll

Recently, Zhang & Pradhan (1995b) and Zhang (1996) reported an extensive set of collision strengths for transitions among 83 LS terms and 219 fine structure levels.

They investigated and found the relativistic effects on the collision strengths for the low-lying forbidden transitions to be small, but the effects of resonances and

77 Line ratio Transitions Wavelength(^m) Observed" N &; S* QLZf **P. 9/2 1.257 1.34 1.36 1.04 “ '*^7/2~“ '‘f’9/2 1.644 a ^D-^/n—a ®/?7/2 1.298 0.38 0.36 0.23 “ '*^7/2~“ ^fg/2 1.644 1.677 0.13 0 . 2 0 0.41 a ''O7/ 2—Q '"fg/2 1.644 “ ^^5/2~o *Pg/2 1.534 0.84 1.06 1.33 “ ■*^5/2~“ ®£*5/2 1.295 “ ^^5/2~“ ®^3/2 1.328 0.54 0.61 0.58 “ *0^/2—a ®Ds/2 1.295 “ ^D s/2-0. '‘F7/2 1.677 0.80 0.77 0.97 “ ■*^5/2~“ ®Ds/2 1.295 “ ''D3/ 2-Q ®D3/2 1.279 0.72 0 . 8 6 0.73 “ ^^2/2-0. ■'F7/2 1.599 “ ^03/ 2—a ®Di/2 1.298 0.51 0.38 0.32 “ ■*D3/2~“ ''F7/2 1.599 “ ''O3/ 2—Q ''F5/2 1.712 0.25 0.26 0.26 “ *D2/2~°- ■'F7/2 1.599 “ ^®l/2~“ ^F;/2 1.644 0.64 0.98 1.38 0 *Di/ 2-a ®£*1/2 1.271 “ Near-IR spectra of HHl by Everett & Bautista (1996; unpublished) * Nussbaumer & Storey (1988) Quinet et al. (1997)

Table 2.19: Comparison of ratios of A-values for near-IR lines with observations

78 Line ratio Transitions Wavelength (A) Observed® G92* QLZ® 4 3 7 2 .4 0.83 0.52 0.51 ® ■'F5/2 4 3 1 9 .6 a ■ 'G g/o—0 ^Pt/2 4 2 9 6 .9 1.70 2.13 2 .2 1 a ■*Fs/2 4 3 5 2 .8 “ *Gg/2—a '*Fj /2 4 2 7 6 .8 2 . 1 2 4.53 3.98 ® ■‘F9/2 4 1 7 7 .2 a *Gg/2~ ^F s/g-a ■‘Fs/2 4 9 7 3 .4 0.50 0.84 1.08 6 ‘*Fs/ 2 —“ '’D 5/2 4 4 8 8 .8 6 *F^/ 2—0- ^F g/2 5 0 7 3 .4 0.50 0.39 0.56 6 ^Fs/2—a ®£>5 /2 4 4 8 8 .8 6 '*F g/2—a *Fg/2 4 8 1 4 .6 5.50 6 . 2 2 7.60 6 ■’F g /2 —a ®Ds/2 4 4 9 2 .6 a ^Hg/2~a ■’F7/2 5 2 2 0 .1 3.40 4.86 5.15 a ^ffg/2—O- *Fg/2 5 0 7 2 .4 a *Hg/2~0- ^ F s/2 5 3 3 3 .7 9.40 1 1 . 2 12.4 a ■‘fTg/g—a ■‘Fg/2 5 0 7 2 .4 6 'P 5 / 2 —a ^Dt/2 4 8 8 9 .6 3.20 3.69 2.51 b * Ps/ 2—a *Fj /2 5 4 3 2 .2 6 ^ ^ 3 / 2 “ “ ® ^ 3 /2 4 7 7 4 .7 0.072 0.094 0.065 b ■*F3/2~“ '' F7/2 5 1 5 8 .8 a ‘* P i i / 2 ~ a ■'F7/2 5 2 6 1 .6 2.70 3.01 3.24 a ■ * P ii/2 ~ a ■*Fg/2 5 1 1 1 .6 a ^ P s /2 —a ■*p7/2 9 0 5 1 .9 0 . 2 1 0.23 0.24 a ^ P s /2 —a ■•F9/2 8 6 1 7 .0 a '*P3/2“ “ ''F3/2 9 4 7 0 .9 0.13 0.15 0.16 a ■’P 3 /2 ~ a ■*F7/2 8 8 9 1 .9 a ■*P 1/2 —a ■'F3/2 9 2 6 7 .5 1.40 1.26 1.29 “ Optical spectra of HHl Bohm & Solf (1990) * Garstang (1962) ® Q uinet et al. (1997)

Table 2.20: Comparison of ratios of A-values for optical lines with obser\^ations

79 channel couplings to be considerable. They also reported good agreement between

a much smaller 7-term calculation with that of an earlier calculation by Berrington

et al. (1991), but differences in the T-values of up to a factor of two, with respect

to the full 83-term results, owing to resonances converging on to the higher lying

energy levels omitted from the smaller eigenfunction expansions. .\s part of the Iron

Project series of publications, Zhang (1996) has provided the complete dataset of the

Maxwellian averaged T-values for the 23,871 transitions among 219 levels in Fe III.

Only two calculations of transition probabilities for [Fe III] lines have been re

ported. The first calculation was carried out by Garstang (1957). More recently,

Nahar & Pradhan (1996) have presented new A-values for a larger set of forbidden

transitions than the Garstang’s work, as well as for a large number of dipole allowed

transitions. In general, the result of Nahar &: Pradhan agree within ~ 30% with those

of Garstang for the transitions common in the two datasets, with some differences of

factors of two or higher. The differences are sufficient to affect significantly several

diagnostic line ratios; a comparison with available spectroscopic observations (line

ratios) shows that the new forbidden A-values of [Fe III] should be preferred (Nahar

and Pradhan 1996).

F elV

The latest collisional calculation for Fe IV has been carried out by Zhang & Pradhan

(1997). This work includes transitions among 49 LS terms, and 140 corresponding

fine structure levels, dominated by the 3d®, 3d'*4s and Zd^Ap configurations. Zhang

& Pradhan also did a 5-term calculation whose results compare very well, within

~ 5% or better, with the earlier 4-term (3d® : ®5,"* G,^ P, and ^D) calculation

8 0 of Berrington & Pelan (1995; some of these values were subsequently revised in an

Erratum by Berrington & Pelan 1997). However, Zhang and Pradhan (1997) find that

with the larger 49-term expansion, including the couplings to the 3d^ Ap odd parity

terms leads to resonance structures that enhance the T-values by 20 to 50% for many transitions over the Berrington and Pelan data. We expect the overall uncertainties in the Zhang and Pradhan data to be 10-30%.

The only calculation of A-values for [Fe IV] lines that has been reported is that of

Garstang (1958). Spectroscopic observations of these lines are very scarce. Therefore, no checks on the reliability of these data can be made. New calculations of forbidden transition probabilities that take into account important spin-orbit and spin-spin relativistic perturbations are needed.

2.5.2 Photoionization cross sections and recombination rate coefficients

The photoionization models depend on the accuracy and consistency of the photoion ization and the recombination data. During the past few years, the close coupling approximation, as implemented via the R-matrix method to compute collisional and radiative atomic parameters, has been extended to a unified treatment of electron- ion recombination that includes both the radiative and the dielectronic recombina tion processes (Nahar and Pradhan 1992, 1995a,b). Further, since the same target eigenfunction expansion is employed for the photoionization and the recombination calculations, the photoionization/recombination data are self-consistent. Photoion ization cross sections and the unified electron-ion recombination rate coefficients have been computed for all iron ions of interest herein: Fe I - IV.

8 1 Photoionization cross sections for Fell and Felll were calculated by Nahar k

Pradhan 1994 and Nahar 1995). These results differ by up to one to two orders of magnitude from the central field type calculation of Railman & Manson (1979) and

Verner et al. (1993).

Unified and total electron-ion recombination coefficients have been recently cal culated for Fe I (Nahar et al. 1997), Fe II (Nahar 1996a), Fe III (Nahar 1996b), and Fe IV (Nahar, Bautista, & Pradhan 1997; to be submitted). The computa tions employ the same close coupling expansions and wavefunctions as used in the photoionization calculations. This enables, for the first time, complete consistency between photoionization and recombination data in the photoionization models. The new recombination rates for Fe I - IV are shown in Fig. 2.17, and compared with previous results by Woods et al. (1981). It is noticed that the new rates for Fe I and

Fe II are about a factor of 5 higher in the temperature range of maximum abundance,

10^ to 10"* K, than those by Woods et al.. For Fe III the differences are about a factor of 2 at T = 10“* K. An interesting feature of the new, unified rates is that at high temperatures, where dielectronic recombination dominates the total recombina tion (around the large ‘bump’), the present rates are substantially lower than the rates derived from the Burgess General Formula (used by Woods et al. ) that is often employed in astrophysical and plasma models. This large reduction is due to auto ionization into the numerous excited states of the target ion, not considered in the

Burgess formula, which can be thereby inaccurate by a considerable factor.

8 2 Fel Fell

-10 -1 0

- 10.5 - 10.5

-11 -11

- 11.5 - 11.5

-1 2 -1 2

- 12.5 - 12.5 1 2 S 6 1 2 5 6

-1 0 -9

- 9.5

I - 10.5 cc a -1 0 o ocn - 10.5

- 11.5

-1 2 -1 2

- 12.5 - 12.5 1 2 3 54 6 1 2 3 4 5 6 log,o(T)(K)

Figure 2.17: New recombination rate coefficients for Fe I (Nahar. Bautista, & Pradhan 1997), Fe II (Nahar 1996b), Fe III (Nahar 1996c), and Fe IV (Nahar &: Bautista 1997). These are compared with dielectronic plus radiative recombination results by Woods et al. (1981; dashed line). 83 REFERENCES

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8 6 CHAPTER 3

NEAR INFRARED SPECTROSCOPY AND THE NEBULAR

EXTINCTION IN ORION

We examine the nebular extinction in the Orion Nebula using a combination of new near-infrared (1.2 — 2.4 //m) and previously published optical (0.34 — 1.0 ^m) spec trophotometry. Using the emission lines of the H I Baimer, Paschen, and Brackett recombination series, and assuming Case B recombination and the stellar extinction law, we obtain discrepant estimates of the total extinction, Av, in which the derived

.4v' increases with the wavelength of the series being considered. This discrepancy is inconsistent with expected small deviations from Case B recombination theory. We suggest instead that it is mostly a consequence of optical effects due to the complex distribution of gas and dust in the nebula. We derive an empirical effective nebular extinction law for the ionized hydrogen zone of the nebula and use this extinction law to deredden the observed emission-line ratios to assess the impact of our neb ular extinction treatment on dust-sensitive emission-line diagnostics of temperature and ionic abundances. Finally, we present a case were even this nebular extinction law may be inadequate to analyze all of the observed emission lines, showing how it

87 might lead to large systematic errors in the estimation of the gas-phase Fe'^/H'*' ionic abundance in the Orion nebula.

The work presented in this chapter weis carried out in collaboration with Profs.

Richard W. Pogge and Darren L. Depoy and was published as Bautista, Pogge, &:

DePoy (1995).

3.1 Observations and Data Reduction

For this work we have observed the relatively non-descript region of the Orion Nebula located 5” North and l . ” 8 East of the brightest Trapezium star (Û^C Orionis) that was the subject of study by Osterbrock, Trans, &: Viellux (1992; OTV hereafter). OTV used the Lick 3 m Reflector and grating spectrograph with a 47” long slit centered on this location and oriented East-West. They used two slit widths: 2” wide in the wavelength region AA3000-7000 A, and 3” wide for AA7000-11000 A. These spectra provide us with measurements of the H I Balmer and Paschen series emission lines, as well as with the forbidden lines used as diagnostics of the nebular conditions discussed below.

We observed this region on 1994 January 27 from the Cerro Tololo Inter-.American

Observatory with the 1.5 m telescope and the Ohio State Infrared Imager/ Spectrometer

(OSIRIS; DePoy et al. 1993; .Atwood et al. 1995). OSIRIS was used in its cross dispersed spectrographic mode, which provides simultaneous coverage of the entire

J, If, and A' atmospheric windows between 1.18 and 2.36 /im at a spectral resolu tion (A/AA) of ~570. We used a 3” wide by 39" long slit oriented East-West and centered on the OTV region of Orion. .A total of 14 spectra at the OTV location

88 were taken, each with an exposure time of 100 seconds. Before and after each of the

object spectra, night-sky spectra were obtained by offsetting the telescope 7’ towards

either the north or the south of the region. Flat field frames were built up from sev

eral exposures of a “white spot” attached to the interior of the dome. The standard

star HD40335 was observed at the same airmass as the Orion Nebula observations to

provide both a flux calibration and atmospheric absorption correction.

Reduction of the cross-dispersed spectra was done following the basic techniques

outlined by .A.twood et al. (1995) using the OSU im plem entation (version 4.2.2) of the

Lick Observatory VISTA Image Processing Package (Stover 1988). The 14 spectra

were added together, and the summed sky frame subtracted. The sky subtracted

spectrum was then flat fielded using the dome flats. The standard star frame was

reduced in a similar fashion, and then extracted from the cross-dispersed spectra using

a standard spectrum following algorithm to trace the curved spectra in each cross

dispersed order across the detector. The hydrogen absorption lines were removed by

interpolating between adjacent continuum regions on both sides of the lines. These

spectra were used to divide out the atmospheric absorption lines from each of the

Orion spectra. Residual hydrogen absorption lines in the standard star were less

than ~ 3.4 equivalent width, much less than the equivalent widths we measure in our

nebular spectra (see Table 3.1).

The spectra were extracted from the images using the SPECTROID routine in

VISTA. Our effective aperture on the sky is 3"5x22", oriented East-West like the OTV aperture. Our efféctive aperture is shorter than the OTV aperture (22"compared to

47"). Although images of this region show no complex nebular structure, or obvious changes in the local extinction (e.g., Pogge, Owen, & Atwood 1992). We do not

89 attempt to merge our spectra with the OTV spectra. The wavelength scale was determined from a quadratic fit to night-sky lines and prominent H I recombination lines in our spectra. The final spectra were put on a relative flux scale (in units of ergs s"^ cm"^ ^m"^) by assuming the standard star has the spectral shape of a 10** K blackbody. We do not estimate absolute fluxes.

Our final near-IR spectra of the OTV region are shown in Figure 3.1, where we plot each of the JHK spectral windows separately, and have identified the principal emission lines. In the J and K spectra, we have chosen the Y-axis limits to emphasize the faint lines, cutting off the tops of the very bright Bry and Pa/5 emission lines.

.411 emission lines were measured using the LINER interactive spectral line analysis program developed at Ohio State. Closely blended lines were decomposed by fitting

Gaussian profiles to the lines using a nonlinear least-squares algorithm. We only attempted to deblend lines if their separation satisfied the criterion that the "valley" between the peaks of the lines was ~ 1 0 % below the peak of the faintest of the two lines, allowing unambiguous identification of the two components.

The intensities relative to Bry and equivalent widths (Wa) of the lines detected are given in Table 3.1. The primary sources of uncertainty in the measured line fluxes comes from errors in the determination of the continuum level and the line fitting procedure, respectively, and thus is formally estimated from the maximum deviations we obtain by a combination of the results of choosing different continuum levels and the statistical errors from the numerical fits. For the strongest H I and

He I recombination lines, line flux ratios relative to I{Brj) are uncertain by about

±5%. For most of the other emission lines the uncertainty is about ±10%, while the faintest lines (with Ifl(B rj) ^ 0.05) are probably uncertain by about ±20%.

90 .01 PP + Hel 1.279 CO .008 CO

.002

1.24 1.28 1.31.26 1.32 1.34 Wavelength (urn) .008

.006 - + ^ to w m ur.0O4 [L §2 a a a a

.002 w u l u j u

-I I I. ■ 1 -J I I t_ -I I I L. I I L J I I L 1.55 1.6 1.65 1.7 1.75 Wavelength (nm) .008

Hel 2.06 Bry CM .006 - 2i K(1.0)8(1)

CM u ." .0 0 4 CM

.002

2.05 2.1 2.15 2.2 2.25 Wavelength (pim)

Figure 3.1: OSIRIS cross-dispersed spectra of the OTV region in the Orion Nebula in the J, H, and K spectral windows. Relative flux per unit wavelength is plotted against the observed wavelength in microns.

91 ^obs Specie Transition Aeip III{B n ) Wxlpm X 1 0 ] 1.253 He I 4p - 3s 1.2528 0.096 0.0188 -h[Fe II] o-^D\/2 — n^Dz/z 1.2521 +[Fe II] O.^Gtj2 — O.^D^/2 1.2535 1.256 [Fe II] a ^D-/2 — a ^Dg/2 1.2567 0.092 0.0164 1.263 Hz v = 2-0Q{o) 1.2614 0.061 0 . 0 1 2 1 1.269 [Fe II] 0‘‘^D iI2 — CL^D i/2 1.2703 1.279 He I 1.2788 0.231 0.0458 4-He I - M ^ D 1.2790 1.282 H I Paschen-,/? 1.2818 4.367 0.870 1.298 [Fe II] a ‘^Dz/2 ~ o ®L>i/z 1.2978 0.037 0.0115 “h, 9 : 1.316 0 I A s^S°-3p^P 1.3167 0 . 1 0 0 0.0223 1.320 [Fe II] a ‘^Djf2 — a ^Dt/2 1.3206 0.031 0.0070 1.520 H I Brackett 20 1.5192 0.035 0 . 0 1 1 2 1.526 H I Brackett 19 1.5261 0.057 0.0187 1.535 H I Brackett 18 1.5342 0.052 0.0172 +[Fe II] O'^D ô/2 ~ G^fg/z 1.5339 1.544 H I B rackett 17 1.5439 0.061 0.0198 1.556 H I B rackett 16 1.5556 0.070 0 . 0 2 2 0 1.571 H I Brackett 15 1.5701 0.070 0.0218 1.588 H I B rackett 14 1.5880 0.109 0.0352 1.611 H I B rackett 13 1.6109 0.031 0.0461 1.641 H I Brackett 12 1.6407 0.271 0.0906 4-[Fe II] Û ^Dt/2 — a ‘‘Fg/z 1.6435 1.680 H I Brackett 11 1.6806 0.245 0.0813 -f[Fe II] Ü ^Dâ/2 — a^fy/z 1.6773 1.700 He I Ad^D-Zp^P° 1.7007 0.096 0.0325 1.736 H I Brackett 10 1.7362 0.284 0.0954 1.749 Hz n = 1 - 0 5(7) 1.7485 0.048 0.0167 +[Fe II] a '*L)i/z — a ^p3/2 1.7449

Continued

Table 3.1: Near-Infrared Emission Lines

92 Table 3.1: (continued)

^obs Specie Transition ^exp I /I { B n ) Wxlfim X 10] 2.032 H2 u = 1 — 0 5(2) 2.0332 0.057 0.0178 +[Fe III] a — a ^ (? 3 2.0217 2.057 He I 4p^P° - 2s^S 2.0581 1.048 0.321 2.071 H2 u = 2 — 1 5(3) 2.0729 0.048 0.0153 2 . 1 1 1 He I 4s"5-3p"P° 2.1126 0.052 0.0166 +He I 4s‘5-3pip° 2.1138 2 . 1 2 0 H2 y = 1 — 0 5(1) 2 . 1 2 1 2 0.170 0.0564 2.165 H I Brackett- 7 2.1656 1 . 0 0 0 0.306 2.218 [Fe III] a ^Hs ~ a, 2.2184 0 . 0 2 2 0.0054 2 . 2 2 2 H2 V = 3 — 2 5(0) 2 . 2 2 0 0 0.057 0.0159 2.242 [Fe III] a ^ H4 — a ^G^ 2.2427 0.013 0.0039 2.247 H2 V = 2 — 1 5(1) 2.2471 0.026 0.0077

93 3.2 Optical to Infrared Extinction

In this section we follow the traditional method of calculating the visual extinction,

Ay, using the H 1 emission lines and using the interstellar extinction law. We compute

Ay separately for each of the Balmer, Paschen, and Brackett series emission lines

by assuming Case B recombination emissivities and the COM extinction curve with

Ry = 5.5 as found by Mathis & Wallenhorst (1981).

At infrared wavelengths longward of 1.2 ^m, the COM extinction curve is nearly

independent of the assumed value of Ry, so can derive an estimate of the extinction

by plotting the logarithm of the ratio of the observed to predicted H 1 Brackett

emission-line intensities against the ratio (A^/Ay) as shown in Figure 3.2. In this

plane, the slope of the line is —0.4Ay. We have assumed Case B recombination

emissivities interpolated to Ng = 4000 cm~^ and T=9000 K as found by OTV for this

region, using data obtained from the INTRAT data server (Storey k Hummer 1995;

access to INTRAT was kindly provided by Dr. D. Hummer). The slope of the line

in Figure 3.2. gives Ay = 0.62 ± 0.06. For Ry = 5.5 this yields Ay = 1.86 ± 0.18

(assuming a smaller value of Ry would increase the value of Ay).

A similar treatment of the OTV measurements of the H 1 Balmer and Paschen series emission lines is shown in Figures 3.3a and b, where we have chosen only the unblended lines for our analysis following OTV. Since these lines have wavelengths blueward of 1 . 2 ^m, we have plotted line strengths measured relative to B.0 against

Ay/A\ instead of Ay, and we assume Ry = 5.5 as above. We find Ay = 1.22±0.10 for the Paschen series lines, and A y = 1.03 ±0.05 for the Balmer series. By comparison,

OTV estimated the visual extinction using selected H 1 Balmer and Paschen lines

94 1.5 T'“ i r I '1 ■ l' T 'I 1 n I I 1 I I '1 I I I I I 1 1 I I 11 I I I r

1.45 Bracket Series

CO c o 1.4 ü

\ r u_I

u. 1.35 D) O

1.3

1 2 5 L l - L 1 J - I I L - l - I l - l - I I I - I. I I I I I I I I t I I I I I I I I .4 .5 .6 .7 .8 .9 1

Figure 3.2: The logarithm of relative strengths of the hydrogen Brackett series emis sion lines in the near-IR divided by predicted Case B recombination emissivities plotted against Ax/Aj. The slope of the best-fit line gives the total extinction in the near-IR J band, Aj. 95 .1 (a) Balmer Series

u f 0 O) o

-.1

8 9 1 1.1 1.2 1.3

.32 (b) Paschen Series

LL << U_ .28 O) o .26

.24

.58 .59 6 .61 .62 A/A,

Figure 3.3: The logarithm of relative strengths of the hydrogen emission-iines in (a) the Balmer series, and (b) the Paschen series divided by predicted Case B recombina tion emissivities plotted against A^/Av-. The slope of the best-fit line gives the total extinction in the V band, Ay- Data are taken from OTV. 96 taken together and found Ay = 1.15 ± 0.12, consistent (and between) our estimates

using the series independently. These estimates of .4v are about 4cr smaller than

.4y = 1.86 ±0.18 derived above from the Brackett emission lines. We could force the

derived Ay estimates from all of these series into agreement by adopting Ry %9:a

value that is much larger than permitted by the observations of the Trapezium stars.

What is most striking is that the value of .4^ derived for a given series increases systematically with the mean wavelength of that series.

One immediate possibility is that we are seeing the effects of deviations from the

assumption of Case B recombination emissivities. We find, however, that this does

not work, as we discuss in the next section.

3.3 Deviations from Case B Recombination

In the standard treatment of H I recombination (Osterbrock 1989), there are two simple cases; Case .A. and Case B. In Case .4 the nebula is optically thin to all line emission from the recombining atoms, whereas in Case B the nebula is optically thick to the Lyman series photons, but optically thin to all other series photons. In a Case

B nebula, a Lyman series photon emitted by a recombining atom will be immediately absorbed by another H I atom in the vicinity and then re-emitted. After a few such resonant scattering, the excited electron makes a less-probable allowed transition into a lower energy level with n > I and emits a lower-series photon, plus either a Lya photon or two-photon continuum emission. This “degrading” of the Lyman series photons into lower series photons has the effect of increasing the observed emissivities of the lower-series emission lines over the values expected from Case A. Because dust

97 grains have a high ultraviolet absorption eflRciency, if dust is present in a Case B nebula

it will absorb some of the Lyman series photons before they can be degraded into

lower-series photons, thus driving the observed emissivities back towards their Case

A values. Unlike the Case A and B situations where radiative transfer is relatively

unimportant, computing dust-modified emissivities requires a formal treatment of

radiative transfer (Cota & Ferland 1988; Hummer &: Storey 1992).

Hummer & Storey (1992) have shown that the relative emissivities of the Balmer

series lines arising from low-lying (n < 6 ) upper levels vary by less than 1 0 % due

to the effects of dust absorption. In particular, the Ha/H/3 ratio used most often to

estimate extinction does changes by less than 5%. For the infrared lines, the effect is

of similar magnitude, and in the same direction. In Figure 3.2, the two most extreme

points on the plot correspond to Pa/d A1.2818//m and Br 7 A2.1655//m. .An upper

limit to the effect of dust optical depth on the line ratio Pa/d/Br^ can be found by considering how this line ratio changes between the two extremes of the Case B and

Case .A approximations. The difference in the predicted line ratios from the two recombination models is less than 6 %. This difference in the line ratio would yield a visual extinction of at least Av = 1.5, still greater than that derived from the optical emission lines. Similar arguments apply to the other emission lines plotted in Figure 3.2. For example, the upper limits to the Case B deviations of the ratios

B rll/B r 7 and Br2 0 /B r 7 are 2% and 4% respectively. Dust UV absorption effects, while undoubtedly affecting the assumed recombination-line emissivities, still have only a small effect overall, and it is similar in effect for all of the line series.

Even if deviations from Case B due to dust UV optical depth effects were large, they could not account for the observed discrepancies in the values of Ay derived

98 separately for each of the different emission line series. The predicted deviations

from Case B would aflfect the extinction estimates in both the optical and IR lines

in the same direction; deviations from Case B resulting in an overestimate of Tv- from the Brackett lines would yield a similar overestimate of .4v- from the Balmer lines. Therefore the difference in the extinction estimated from the optical and IR measurements cannot be accounted for by these effects.

3.4 An Empirical Nebular Extinction Curve

We have shown above that the value of Ay estimated using the lines of a given recombination-line series increases with the mean wavelength of that line series: the near-IR Brackett lines give a larger estimate of .4v- than the visual Balmer lines. This departure from the assumed interstellar law might be explained by optical effects in the rather complicated dust geometry of the nebula. Although most of the extinction appears to be due to a foreground lid (Wen k O’Dell 1995), there is evidence of reflec tion of radiation off of the backside of the nebula, and inhomogeneity of the extinction on small scales (Pogge, Owen, & Atwood 1992; O’Dell, Walter, & Dufour 1992). The effect we see, however, is still somewhat subtle. If we did not have the Brackett line series data, we would not be compelled to treat the difference between the Ay derived from the Balmer and Paschen series lines as particularly significant. This suggests that instead of a detailed model calculation, a semi-empirical treatment of the prob lem may be more practical from an observational standpoint, and may be applicable in general to the study of nebulae. A more detailed study of radiative transfer in

Orion in particular is beyond the scope of this work. The method described below

99 derives empirically an effective “nebular” extinction law from the hydrogen emission

lines appropriate to the place that we are measuring in the nebula. This method may

also be applicable for other places in Orion and for other objects, although the values

of the parameters involved are likely to vary.

We start with the observed stellar extinction law and introduce an additional

wavelength dependence as follows:

-■^A — (~7^\ y)» (3.1) ' - ■ I V ' / R y

where the quantity in ()'s is the mean interstellar extinction curve for a given Ry,

y = (1/A — 1.82) following CCM ’s notation, and Ay is the effective extinction at

A = 0.55 )Lim to be derived from observed emission lines. The new term we have

introduced, Ny, is a constant that embodies the first-order optical effects due to dust

in the nebula, and may be found by a fit to the observed emission-line strengths.

Adopting the CCM mean interstellar extinction curve, which is an e.xcellent fit to the

observed stellar extinction in Orion, we find Ay = 1.4 ± 0.1 and Ny = 0.10 ± 0.02.

Note that the foreground extinction is included in Ay.

In Figure 3.4 we show the results of the dereddening procedure for the H I lines.

We have obtained an excellent fit across the entire 0.3-2.2 ^m wavelength range. In

Figure 3.5 our nebular extinction curve is plotted as .4;^ a function of y along with the standard interstellar extinction law for different values of Ay. The nebular extinction curve differs from the mean interstellar extinction law for the adopted Ry by having an additional wavelength dependence parameterized by the constant, Ny. The total departure of the nebular extinction curve for Ay = 1.4 and Ny = 0.10 from the predictions of the CCM interstellar curve with the same Ay are greater than 30%.

100 1-2 I I I I I I I I I I I I I I I I I r

1.1 —

1 ----- "O p o o o I .9 —

# Balmer series -

.8 — Paschen series

^ Brackett series-

7 t I I I I I I I I I I I I I I I I I I 1 I J - I L _ 1 0 5 10 15 20 25 n

Figure 3.4: Intensities of Balmer, Paschen, and Brackett emission-lines corrected for extinction using our nebular extinction law plotted against principal quantum number of the upper level of the lines (n).

101 3.0

Nebular (A^=1.4, N^=0.1) Interstellar (Ay=1.4) 2.5 Interstellar (A^=1.15) Interstellar (A^=1.86)

2.0

1.0

0.5

0.0 -2 1 0 1 2 y = (1/A.-1.82)

Figure 3.5: Extinction magnitudes, .4a, plotted as a function of y = (1/A — 1.82). Shown are our nebular extinction curve with .4v = 1.4 and Ny = 0 .1 (solid line), and the interstellar extinction curves with Ay = 1.86 (dash-dotted line), .4y = 1.4 (dotted line), and .4y = 1.15 (dashed line). 102 What is most important, however, is the variation of the extinction with wavelength.

The nebular extinction curve exhibits similar behavior to the CCM curve in the IR

region, specially compared to that with .4^ = 1.4, but changes appreciably below

A ~ 7580À. Blueward of ~ 3500A, we are extrapolating from the weak Balmer series

lines, and do not know how well our empirically-derived extinction law works for

shorter wavelengths.

3.5 Applications of the Empirical Extinction Law

How does our elective extinction determination affect the results that were previously

obtained by OTV using the standard extinction law? We have re-derived the relative

abundances of several ionic species (He, N, O, Ne, S, Cl, and Ar) using OTV’s line

observed line strengths, and compare these with the values given in Table 10 of OTV.

We have adopted the same densities derived by OTV as these should not be strongly

affected by extinction because the diagnostic emission lines are very close in wave

length. Temperature diagnostics, on the other hand, often involve widely separated

lines (e.g., [S III]/(A9069-H A9531)//(A6312) and [Ar IH]/(A7136-f A7751)//(A5191)), and must be recomputed using our extinction law. We used five-level atom models with the collisional data compiled by Pradhan & Peng (1994) for these ions. We find that applying our nebular extinction corrections results in T (5‘^"^) = 10000 K and T(-4r= 8400 K, somewhat closer to the mean value of T = 9000 K than the results of OTV, who derived T = 8300 K for both ions. We note, however, that part of the discrepancy in the [S III] temperature seems to come as much from the use of different atomic parameters than OTV as from our different extinction law, though

103 N{X^)/N{H+) Ion Ratio OTV This work Diff (%)“ \T-}“ /iA b o 4 o -h A b o o j; - 5 - 5 f{Ha) 1.60 X 1 0 - 1.60 X 1 0 - 0 . 0 /(A3726-fA3729) -4 -4 ^ l{Hi) 1.48 X 1 0 - 1.45 X 1 0 - 2 . 0 Q+ /(A3726+A3729) -4 -4 ^ l(H6) 1.46 X 1 0 - 1.43 X 1 0 - 2 .1 -4 -4 Mean 1.47 X 1 0 1.44 X 1 0 2 . 0 Q++ /(A4959+A5007) -4 -4 X 1 0 X 1 0 0 . 0 ^ I(H3) 1.57 - 1.57 - Mp++ /(A3869) -5 -5 2.54 X 1 0 - 2.51 X 1 0 - 1 .2 yr + + /(A 3 8 6 9 ) -5 -5 X 1 0 X 1 0 0 . 8 7 ( //5 ) 2.52 - 2.50 - -5 -5 Mean Ne'*"'" 2.53 X 1 0 - 2.50 X 1 0 - 1 .2 q+ 7(A6716+A673l) -7 -7 l{Ha) 4.55 X 1 0 - 4.54 X 1 0 - 0 . 2 c+ /(A4069+A4076) -7 -7 ^ HHS) 5.52 X 1 0 - 5.51 X 1 0 - 0 . 2 -7 - 7 M ean S"^ 5.04 X 1 0 - 5.02 X 1 0 - 0.4 q++ /(A9069+A9531) -6 -6 ^ {{Ha) 8.69 X 1 0 - 7.89 X 1 0 - 9.2 q++ 7('A9069+A953l) -6 -6 X 1 0 X 1 0 2 .1 ^ /(PolH-Pal2+Pal3) 7.72 - 7.56 - -6 -6 Mean S"*"^ 8 . 2 1 X 1 0 - 7.72 X 1 0 - 6 . 0 /(A8579+A9124) -8 -8 I{Ha) 2.13 X 1 0 - 1.98 X 1 0 - 11.7 PI+ /(A8579+A9124) -8 -8 X 1 0 X 1 0 /((Pall + Pal2+Pal3) 1.91 - 1.92 - -0 .5 -8 -8 Mean Cl'*’ 2 . 0 2 X 1 0 - 1.95 X 1 0 - 3.5 / ( A5518+A5538) -7 -7 1{H0) 1 .0 1 X 1 0 - 1 .0 0 X 1 0 - 1 .0 PI++ /(A5518+A5538) -7 -7 1 .0 1 X 1 0 X 1 0 - - 2 . 0 ^ {{Ha) - 1.03 ■7 -7 Mean C1++ 1 .0 1 X 1 0 - 1 .0 2 X 1 0 - - 1 .0 A _++ 7(A7136+A775I) ■7 ■7 1.92 X 1 0 - 1 .8 8 X 1 0 - 2 .1 ______{{Ha)____ “ Percent difference of column 4 relative to column 3.

Table 3.2: Ionic Abundances

104 #(#e+)/#(#+) Ratio O TV This work 4471/#,# 0.0899 0.0901 4 4 7 1 /# 7 0.0924 0.0926 4 9 2 1 /# # 0.0825 0.0825 5 8 7 6 /# # 0.0904 0.0891 5876/#a 0.0925 0.0941 6678/Ha 0.0887 0.0887 Mean 0.0894 0.0895 ±0.0017 ±0.0018

Table 3.3: Helium Ionic Abundances

this is not the case for the [Ar III] temperature. For our ionic abundance analysis we will adopt a temperature of T = 9000 K, the same as that used by OTV.

The detailed comparison of our ionic abundances and OTV’s is given in Table 3.2, where we list our newly computed values using our nebular extinction law along side the OTV values. We find that abundance ratios derived using the new extinction corrections are systematically lower than those computed by OTV (see their Table

10), although only by a few percent. In general, the differences amount to ~ 1% for abundances estimated from optical lines (e.g., = 1 . 0 1 x 1 0 ~" com pared to 1.02 X 10“' derived by OTV), but it can be nearly 10% for those abundances derived from near-IR lines (e.g. S++).

We can also compare estimates of the He'^/H'^ ratio made using OTV’s data and our new near-IR He I emission-line observations in Table 3.3. This provides not only a

105 test of our procedure, but with a better estimate of the optical to near-IR extinction,

we can test the reliability of the theoretical line emissivities for He I. By using the

He IAA4471, 4921, 5876, and 6678À lines, and following exactly the same procedure described by OTV (except for the extinction correction) we find an average value of = 0.0895 ±0.0018, which is not statistically different from the value of 0.0894 ± 0.0017 computed by OTV. Nevertheless, if we derive the He^ ionic abundance from our observations of the He IA2.058/im (2^P — 2^5) emission line using the Smits (1991) emissivities, we find N{He'^)/N{H'*') = 0.054 ± 0.004, which is 40% lower than what is derived from the optical He I lines.

A similar discrepancy was noticed by DePoy & Shields (1994) in their observations of this line in a sample of planetary nebulae. They proposed that the discrepancy between their model predictions and their observations may be due to either pho toionization of neutral helium atoms in the metastable state 2 ^S, or due to velocity stratification in the planetary nebula envelopes.

There are other He I lines of interest in these spectra. One is the He I A1.083 ^m

(2 ^S—2 ^P) emission line that OTV found to be about 50% weaker than the prediction based on the Smits emissivities. Similar disagreement has been found by Peimbert k

Torres-Peimbert (1987a,b), Clegg k Harrington (1989), Ferland (1992), and others in different objects. Since this line is primarily excited by collisions, it has been suggested that the collision strengths had been overestimated by as much as a factor of two. The more recent and extensive calculation of collision strengths by Savvey k Herrington

(1993), however, gives collision strengths for this particular transition that are very similar to those of the previous calculations. It is likely that the observed discrepancy is due to destruction of this line by dust as suggested by Ferland (1992) and Baldwin

106 et al. (1991). Finally, of potential interest is the He I A1.70 /rm emission line that is

typically strong in H II regions (see Figure 3.1b), and that is well-placed in the H-

band window for observation with emerging infrared spectrophotometric techniques.

At present there are no calculated emissivities available for this line. A new and

thorough calculation of He I recombination line strengths is badly needed before

further progress can be made. Recently we learned that Smits has recomputed the

He I emissivities (Smits 1994) and these data have been used by Kingdon & Ferland

(1995) to calculate the contribution of collisional excitation to the emissivities of the

recombination lines using the latest collisional data by Sawey & Herrington (1993).

Kingdon & Ferland find that the discrepancies exhibited by some of the lines, as we

have discussed, remain unexplained.

In the preceding discussion, we have assumed that the nebular extinction law

derived from the hydrogen recombination line strengths applies to the collisionally

excited metal-ion lines. Implicit in this assumption is that the ionic line-emitting

regions are spatially co-extensive with the ionized hydrogen zone. Such an assumption

is not valid for some ionic species, like [Fe II], which arise in the partially ionized zone

which is disjoint from the ionized hydrogen zone (Bautista &: Pradhan 1997b; and

references therein). If the partially ionized zone is located at the far edge of the blister

and is much thinner than the ionized region we may expect the the dust effects to

affect these lines in a different way than as observed for lines arising in the ionized

hydrogen zone.

By using pairs of [Fe II] emission lines that arise from the same upper level, we can estimate the amount of total visual extinction towards the [Fe II] line-emitting region. One of these lines pairs are the AA7452 and 7155À lines observed by OTV

107 (arising from the a ^Gg/2 upper level). Using the CCM interstellar extinction curve

with Rv = 5.5 and transition probabilities for these lines from Garstang (1962), we

find Av = 2.6 ±2.2, assuming a 10% uncertainty on the measured line ratio. .A.nother

pair of emission lines that we can use are A1.257 /j,m and A1.644 /L/m lines observed in

our near-IR spectra, although the latter of these two lines is strongly blended with

the Brackett-12 recombination line of hydrogen. In order to estimate the strength of

the 1.644/Lfm line we use the predicted Case B emissivities to determine an average

intensity of the Brackett-12 line from the adjacent, unblended Brackett series lines,

and then subtracted this value from the total flux measured for the line blend. Using

the transition probabilities of Nussbaumer &: Storey (1988), the total visual extinction

we derive for this pair is , 4 y = 3.7 ± 1.4. The values of Av for the [Fe II] lines derived

in this way, while larger than the hydrogen recombination line estimates, are very uncertain; the difference is only at 2cr-level. More accurate measurements will be necessary in order to reduce the uncertainty in the extinction for [Fe II] lines, and to test our suggestion that these lines are indeed subjected to a greater amount of extinction than lines arising in the ionized hydrogen region of the nebula.

108 REFERENCES

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110 CHAPTER 4

SPECTRAL DIAGNOSTICS FROM FE II-IV EMISSION

SPECTRA

The excitation mechanisms for the [Fe II], [Fe III], and [Fe IV] emission from nebulae are studied and spectroscopic analysis of the observed IR, optical, and UV spectra of gaseous nebulae are carried out. It is shown that the [Fe II] emission from the

Orion nebula is predominantly excited via electron collisions in high density partially ionized zones; radiative fluorescence is relatively much less effective. Further evidence for high density zones is derived from the [O I] and [Ni II] spectral lines. It is also shown that optical [Fe II], [Ni II], and [O I] emission are well correlated throughout nebulae which indicates that these lines are formed in the same partially ionized zones.

Most of the work presented here has been published in Bautista, Peng, & Pradhan

(1996), Bautista &: Pradhan (1995b; 1997), and Bautista, Pradhan, & Osterbrock

(1994).

Ill 4.1 Collisional and Fluorescent excitation of Ni II and Fe II

For each bound level z, with population n, and energ>* the equations of statistical equilibrium under optically thin conditions is

^ 1 Rij — ^ 1 TljRji (d.l) j j where the sums are over all other bound levels j. The rate coefficient R i/is given by

Rij — Cij + Aij Ei > Ej (4.2) or

Rij = Cij Ei < Ej

Here Cij is the collisional excitation or deexcitation rates; Aij is the spontaneous rate.

In the optically thin case there is no radiative transfer included. The above model does not consider fluorescence due to background continuum radiation of an external source. The line emission photons created by the ions are also assumed to escape without absorption.

We consider continuum fluorescence in the model by assuming a thermal contin uum radiation pool in which all ions can be excited by photon pumping or deexcited by the induced emission. The thermal radiation field is a black body at temperature

T. The rate coefficient Rij then becomes

Rij = Cij 4- Aij -I- UuBij {Ei > Ej), (4.3) or

Rij = Cij 4- b\Bij [Ei < Ej),

112 and

hu = \Ei — Ej\. (4.4)

Here Bij is the Einstein coefficient and Uu is the radiation density. If we assume a black body radiation field with temperature we have

exp{hu ! kT r) — V where w is the geometrical dilution factor.

As in Lucy (1995), we begin by analyzing simplified three level models for Ni II and Fe II which enable a qualitative understanding of the problem.

4.1.1 Three level models

The 3-level model of Ni II described in Fig. 1 of Lucy entails fluorescence excitation of the level a that gives rise to the A7379 line produced by a UV radiation induced dipole transition from the ground state of the ion a -D 3 /2 (level 1 ) to the excited

2 (level 3), followed by spontaneous decay to the a ~F-/2 level (level 2).

In this model the population of the level 2, N2, with respect to th a t of the level

1 , Ni is given by (Eq.(l) in Lucy)

■V2 _ A/egl 2 + bz2BizJ\Z .

■Vi *VgÇi2 + A21 + 631^23 J23, where A2 1 , B 13. and S 23 are the Einstein coefficients, qi2 and are the Maxwellian averaged collision strengths, J 13 and J 23 are the intensities of the continuum at the frequencies of the 1 3 and 2 —> 3 transitions, and 632 is the branching ratio defined by

632 = 1 - 613 = , . • (4.7) . 4 3 2 + -431

113 From Eq.4.6 a critical electron density for fluorescence (iVj/) can be defined,

Y _ 6 3 2 ^ 1 3 93 -da 1,432 ^ 9i 2 2/11^13 gi .431 + A32 9i2

such that if Ne in the plasma is lower than Ncf the emission is dom inated by fluores

cence. Conversely, if Ng > the line is predominantly excited by electron collisions.

In this equation 1/13 is the frequency of the 1 -> 3 transition and ^ 3 and are the

statistical weights of the levels 1 and 3 respectively. Ncf decreases as i/î^ and only the

lowest odd parity terms of the ion coupled to the ground state are likely to contribute

significantly to the fluorescence excitation mechanism (in the case a black body ra

diation field, the dependence of Ncf cancels out and it drops exponentially with

1^13) ■

Eq.4.3 can be evaluated for a given set of condition of the plasma and the intensity of the radiation field. Using the values corresponding to P Cygni given by Lucy, we obtain Ncf = 9.1 x 10^ cm~^. In th e case of the Orion nebula, the conditions given by Lucy yield Ncf = 1.1 x 10'' cm“^. These values are obtained using the collision strength for the transition 2 —»1 by Nussbaumer k Storey (1982). If the new Ni II collision strengths given in Bautista & Pradhan (1996) are used then we obtain similar values, Ncf to be 9.6 x 1 0 ^ and 1 . 2 x 1 0 '* cm"^ are obtained for P Cygni and Orion respectively.

For Fe II the fluorescence excitation of either the IR or the optical lines is expected to be less important than in Ni II because nearly all of the lines observed in these spectral ranges correspond to transitions among quartet and doublet levels, which can not be pumped by dipole allowed transitions from the ground state. .Also,

Intercombination transitions from the ground state to quartets are relatively inefficient

114 as their transition probabilities are at least one to two orders of magnitude smaller than for the dipole transitions. Perhaps, the greatest fluorescence effect may be seen for the level a ^Si/2 that gives rise to the A4287 line. Photoexcitation of this level could occur via pumping of the z levels from the ground term; however, inspection of the energy of the z multiplet relative to the ground state, and of the A-values for the transition involved in the process, indicates that the critical fluorescence densities in Fe II should be about an order of magnitude lower than those for Ni II, and hence collisions would be that much more dominant compared to fluorescence.

4.1.2 Multilevel model for Ni II

Generalizing the model to calculate line emissivities in a multilevel system including photoexcitation, we adopt a model similar to Lucy (1995) for Ni II. The presentation of the results is followed by a brief discussion of the atomic data.

Fig. 4.1(a) shows the ratio [Ni II] A7412/A7379 vs. Ng, with and without fluores cence for the radiation fields of P Cygni. The line ratio calculated Lucy is also shown.

In the same figure we plot the flux ratios of these lines as measured in P Cygni by

Barlow et al. (1994). The same line ratio is shown in Fig.4.1(b) but, for a radiation field similar to that of the Orion nebula. The observed line ratio here is taken from

Osterbrock, Tran, & Veilleux (1992; OTV hereafter). It is noted that our results for the [Ni II] A7412/A7379 ratio are higher than those by Lucy by about 15%. This difference seems to come from the different sets of atomic data adopted, particularly the A-values for allowed transitions. We have compared our results for line ratios with those given in Table 1 of Lucy and we find differences typically about 10 - 15%.

115 .5 .5

T =5300K T^=10,000K

.4 .4

en .3 .3 CO

CJ <- Fluorescent exc. .2 .2

Collisional/exc. .1 .1

0 0 2 4 6 8 24 6 8 log N,

Figure 4.1: Line emissivity ratio Nill A7412(^F^/2 —^ £>3/2)/A7379(^Fr/2 D 3/2 ) of Ni II vs. Ne assuming collisional excitation only (solid line), and including fluorescence (dashed line) by a UV field as in the P Cygni circumstellar nebula with Te =5300 K in panel (a) and Orion with Tg =10000 K in panel (b). The observed line ratios by Barlow et al. (1994) and OTV are indicated by the horizontal lines. The squared dots represents the results of Lucy (1995). 116 Nevertheless, it appears that fluorescence of [Ni II] lines may be important in both

P Cygni and Orion.

By contrast, Lucy showed that the UV radiation field in the Crab nebula is too weak to effectively pump [Ni II] lines, and even less the [Fe II] emission. This is expected to be the case for most old Type II SNRs which exhibit relatively weak s}"nchrotron radiation. However, The situation is likely to be quite different during early phases of Type I or Type II supemovae (Ruiz-Lapuente and Lucy 1992, Li and

M cCray 1995).

4.1.3 Atomic Data for Ni II

The primary difference between Lucy’s model for Ni II and ours is the atomic data.

We find that the differences in the collisional data, while significant for the weaker transitions, are not important for the photoexcitation case. However, the radiative data is quite different. Whereas the recent .^.-values tabulated by Kurucz (1992) are employed in Lucy (1995), we have carried out new calculations for Ni II .A.-values using the SUPERSTRUCTURE program by Eissner, Jones, and Nussbaumer (1974), and a variation thereof by W. Eissner and C. J. Zeippen (private communication) that deals with the relativistic El, E2, and Ml .^.-values.

The most important multiplet in the photoexcitation case is the (^Dj —^F°,). For the J = 5/2 and J’ = 7/2, our value for log(gf) is -0.44, and agrees fairly well with

-0.42 obtained by Kurucz. However, Fuhr et al. (1988) in their critical compilation of transition probabilities for iron peak elements give a value that is nearly half, -

0.75 (no other transitions within this multiplet are listed). Interestingly, the Fuhr et al. value is derived from that of Kurucz and Peytermann (1975) value normalized to

117 the lifetime of the 3rf®(^F)4p^F°/2 level. For the other two transitions in the multiplet our values differ significantly from Kurucz; the A-values are 1.03 and 1.57 (in units of

10® sec" ^ ) respectively for the .1 = 5/2 = .J’ transition, and 0.92 and 0.43 respectively for the J = 3/2, .1’ = 5/2 transition.

For the transitions among the (‘‘F — D°), G°), and (“'F —^ F°) multiplets listed in Fuhr et al., our calculations are in better agreement, to about 10% overall, with theirs than the values by Kurucz. But our values show poor agreement (up to a factor of two or worse) for the intercombination multiplets (these however do not contribute to a large extent), and for the (^F —^ F°) multiplet; the Kurucz values agree much better with Fuhr et al. for these multiplets than ours. The compilation by

Fuhr et al. is largely based on the relative oscillator strength data of Bell et al (1966), normalized to an absolute scale by Lawler and Salih (1987) through measurements of radiative lifetimes of twelve levels of Ni II by the laser-induced fluorescence technique.

While the uncertainty ratings assigned to the Fuhr et al. values ranges from ‘B’ to ‘C’

(i.e. up to only 25%), the measured values are not absolute per se; as such we feel that the true uncertainties may well be larger. Also, given the dispersion in the theoretical data, and a fairly large number of transitions considered in the models, the situation with respect to the A-values remains uncertain to a significant degree. Nonetheless, our results show that the uncertainties in the A-values do not qualitatively affect conclusions regarding the nature of the photoexcitation process at low densities, and competition with collisional process at high densities, in the formation of the lines under consideration in this work. The quantitative differences with Lucy (1995) are found to be less than 15% in the line ratios for Ni II.

118 4.1.4 Multilevel Model for Fe II and Optical Depth Effects

For the present work we have constructed an extended 159-level CR model for Fe II that combines the 142 quartet and sextet levels included in the calculation by Zhang &

Pradhan (1995) with the lowest doublet levels (a ^Gj, a -Pj, a a b ^Fj, b "^Hj, a “^Fj, and b ^Gj), and the 4s^ ^85/2 level. Dipole allowed and intercombination transi tion probabilities, necessary for fluorescent excitation, are taken from the compilation of experimental and solar data by Giridhar & Ferro (1995), when available, and from

Nahar (1995) for the rest of the transitions. An energy level diagram for Fe II is shown in Fig. 4.2. Many of the lines observed in Orion’s optical and near-IR spectra are also marked in this figure.

As discussed above, unlike the case of Ni II (Lucy 1995) where all levels par ticipating in fluorescent excitation have the same spin multiplicity (doublets), pho toexcitation of Fe II is a relatively inefficient mechanism and the critical densities for fluorescence of most lines are much lower than 10® cm~^ for the radiation field in Orion. This is because the ground multiplet of Fe II is a while most of the observed lines involve the quartet multiplets. Thus, photoexcitation of quartet levels must occur via intercombination transitions which are generally much weaker than the dipole ones in low-ionization atomic species where relativistic spin-orbit mixing is weak. This is the case for Fe II, as revealed by inspection of the A-values. In

Bautista, Peng, & Pradhan (1996) we found that photoexcitation of Fe II could not explain the observed relative intensities of optical [Fe II] lines.

In terms of the atomic data, the present fluorescent excitation model should be quite accurate since we use experimental .^.-values for most dipole and intercom

119 bination transitions. Also, the efficiency of the photoexcitation by UV continuum radiation mechanism drops rapidly with the energy of the odd parity levels, thus the number of energy levels included in the present model should be sufficient.

Baldwin et al. (1996) have suggested that the UV lines dominating the pumping are optically thick and this would affect fluorescent excitation. The line center optical depth for a transition u — l, where u and / are the upper and lower levels respectively, is given by

dTui = — (n/ - nugi/gu)Nidr (4.9) mcv where v is the linewidth (~ 13 x lO'^ cm s“^ for Orion), gi and g^ are the statistical weights of the levels, ni and are the population fractions for the levels, and Ni is the number density of the ion i being considered (Mihalas 1978). In plane parallel geometry the probability that a line photon will escape from the absorption layer is given by

1 — T’esc('Tuj) = ------. (4.10)

W ith this expression for the Pesc one can compute the emissivity of the lines in NLTE, including the effects of line self-absorption, by replacing the .Vvalues by effective transition probabilities,

= AjtiPosciTui)- (^-II)

Here, the total r„/ along the line of sight can be evaluated from Eq. 4.9 by adopting some reasonable column density of Fe II ions.

To calculate theoretical emissivities and line ratios for the ion it is necessary to solve simultaneously the coupled equations of radiative transfer and statistical equilibrium in an iterative manner.

120 Fell

z‘S°

z'P"

z'P z*P zV z 'P = z'D°

z’D‘

5169 Œ IXi a ‘G

4244 a ‘H a ‘S 4277

■4815

a 'P 5 3 3 4 4287J

889i 5262

4359 a*D 7475 8 6 1 5159 7155

1 2 5 1

a'D 16436 a 'F

Figure 4.2: Energy diagram of Fe II with infrared and optical lines considered.

121 4.2 [Fe II] Emission from the Orion N ebula

4.2.1 The Optical Lines

As a first step, we identify and study particular transitions that are relatively in sensitive to fluorescence and which afford reliable density diagnostics. To that end, we compared the population of all the 159 levels in our Fe II model for both the collisional and fluorescence models under conditions of Tg =10“* K, Ne =4000 cm“'^ , and a radiation field as considered above. Then, we identified the levels that give rise to observed lines in the optical which are least affected by fluorescence. As expected, among these levels are those with multiplicity two (e.g. a ^Gg/2 which gives rise to the 7155 and 7452 .4 lines), since they are not directly coupled to the sextet ground state. Other levels nearly insensitive to fluorescence are a ^Dj,a ^Fj,a ^Dj, and a ‘^Pj levels, which yield all the IR and the near-IR lines, as well the 8617 and 8892

Â lines.

Emissivity line ratios for lines insensitive to fluorescence are shown in Fig. 4.3(a)-

(c), together with the observed ratios by OTV and Rodriguez. Several other line ratios are shown in Figs. 4.3(d)-(l). Here, the different curves represent pure collisional excitation, collisional and fluorescence excitation with the radiation field expected in Orion with and without optical depth effects, and fluorescence excitation by a radiation field ten times more intense than in Orion. The observed line ratios are represented by horizontal lines. Also in these figures, the line ratios predicted by the three models of Baldwin et al. (1996) are shown as filled squares.

122 Figure 4.3: [Fe II] line ratios vs. log Ng (cm~^ ) for Te = 9000 K. The different curves represent pure collisional excitation (solid), collisional and fluorescent excitation with out optical depth effects (dotted), collisional and fluorescent excitation including line self-shielding (long dashed), and collisional and fluorescent excitation for a UV field ten times that in Orion (short dashed). Collisionally excited line ratios calculated with collision strengths of the present 23CC calculation (short-dash and dot curves) are also shown. The predicted line ratios by Baldwin et al. (1996) are indicated by square dots. The horizontal lines indicate the observed values by OTV (solid) and Rodriguez (1996; dashed lines).

123 2 0 I I I I 1 I I I I I I ~ i I I I I 1 I I 1 I I I 5

4 I 1 5 h (a) Observed 3 10 A 2 ■n % 5 — 1

.L l_l_l I I I I I I I I I I I I I I I I 0 3 4 56 7 3 4 5 6 7

3 3

2 tv

S 1 1

0 0 3 4 5 6 7

1 8

.5 4

0 0

log N,

Figure 4.3: Continued

124 Figure 4.3: (continued)

4 1 I 3

2 § .5

1 i 0 0 3 4 5 6 7

1.5

m 5 1

1.4 10 1.2 8 1 tÔ 6 m+ 4

log N,

125 Several conclusions can be derived from these figures. First, the calculated line

ratio curves with and without optical depth effects for the UV lines are nearly in

distinguishable. Therefore, optical depth effects under the conditions of Orion are

negligible for the fluorescent excitation of the optical [Fe II] emission. Second, op

tical [Fe II] line ratios are consistent with high densities (10^ — 10^ cm“^ ). This is

particularly the case for line ratios unaffected by fluorescence, which at Ng =4000

cm"^ would yield line ratios different from the observed ones by more than a factor

of two. Among the line ratios that are affected by fluorescence, only a few seem to

agree with observations, while a majority exclude this excitation mechanism. This is

also the case for the line ratios considered by Rodriguez (1996), e.g. 1(7155)/I(8617)

(Fig. 4.4(c)). I(4287)/I(8617) (Fig. 3.4(j)), and I(5262)/I(8617) (Fig. 3(b) in BPP

and Fig. 4(c) in BP96).

For several of the line ratios (Figs. 4.4(e-l)) the present model agrees reasonable

well with the different models presented by Baldwin et al. However, their model of the

cloud entails a mean density for the fully ionized zone (FIZ) of ~ 10“^ cm"^ , which

is more than twice the density (4000 cm~^ ; OTV) normally derived from [O II] and

[S II] line ratios along the line of sight. This has the effect on the model of reducing

the depth of the FIZ and the geometrical dilution of the radiation which is inversely proportional to the square of that depth. The higher density in their model should lead also to an overestimation of the optical depths. An unexplained discrepancy between our results and those of Baldwin et al. appears in the fluorescent pumping of the 4277 .4(a ■‘F 7 /2 — a ‘‘Gg/ 2 ) line. In general, it is found that both our present fluorescent model and those of Baldwin et al. fail to reproduce the observed line ratios regardless of any possible enhancement of the stellar radiation fleld.

126 Recently, Rodriguez (1996) compared observed [Fe II] line ratios from twelve dif ferent positions in Orion and sixteen positions in six other H II regions, with the ratios expected under collisional excitation conditions. Rodriguez reported consider able scatter for the line ratios and the predictions from B PP’s collisional model. This scatter may correspond to a variety of causes. One is the combined uncertainties in atomic data and observations. It is noted that Rodriguez applied the same extinc tion correction for every spectrum; however, the extinction in Orion is known to vary widely on small spatial scales (e.g. OTV; Pogge, Owen, Atwood 1992; Bautista,

Pogge, & DePoy 1995). In addition, uncertainties from individual line intensity mea surements themselves may be large and should also be considered. Another source of dispersion comes from the fact that a single temperature was assumed in trying to match the observations for twelve different positions in M42 and nine observations of other objects; but the ratios presented are temperature sensitive, particularly at den sities of ~ 10® cm~^ and higher. For instance, the I(5262)/I(8617) ratio at Ne =10® cm“^ varies by more than a factor of two between 5000 and 10000 K (see Fig. 4.4(c) in BP). One more reason for the observed scatter, and perhaps the most important, is that if the PIZ is a thin transition region it is expected that the physical conditions vary rapidly within it, as suggested in Bautista & Pradhan 1995. Then, a single set of Te and Ne may not fit all the line ratios simultaneously. Nevertheless, every line ratio reported by Rodriguez indicates electron densities between 10® and 10~ cm'® , while no definitive dependence on fluorescent excitation is found.

Additional spectroscopic evidence against fluorescent excitation of Fe II lines in

Orion is the absence of some allowed emission lines in the observed spectra. If the pop ulation of the levels that give rise to the forbidden lines were dominated by cascades

127 from the odd parity levels, the allowed transitions that result from these cascades,

some of which lie in the optical region, should be seen. That is the case, for instance,

for the 5169.0 A [z ®P°/2 — a line that could arise due to the fluorescent exci

tation of the ^8 5 /2 level, via the sequence ®/)g /2 —® ^ 7 /2 —^ •S'5 /2 - Then, the strength

of this line should be directly related to the strength of the 4287 A {^8 5 / 2 —® £>9/ 2 )

feature and, under the conditions in Orion, the intensity of the 5169.0 A line should

be of about 70% of that at 4287 A. Other allowed transition of similar intensity are

at 3227.73 A (z '^Dy2 ~ ° ^^5 /2 ) and 3259.05 A (y ‘‘Fg/ 2 — 6 ‘^0 7 /2 )- None of these

lines has been observed in Orion. Moreover, recent echelle observations by Peimbert

et al. (1996) establish an upper limit to the Ipe //(A5169)//[f’g //](A4287) of about 0.1.

given by the sensitivity limit of their spectra. This indicates that less than 20% of the

total intensity of the [Fe II] 4287 A line in Orion could be explained by fluorescent

excitation by UV continuum radiation.

In contrast with Orion and other diffuse H II regions, circumstellar nebulae and the

subclass of bipolar planetary nebulae with symbiotic star cores do exhibit rich Fe II

spectra, in addition to the forbidden [Fe II] lines, particularly in their core regions,

e.g. Eta Carinae (Hamann DePoy 1994), IRAS 17423-1755 (Riera et al. 1995), He2-

25, Th2-B, and 19W32 (Corradi 1995), and M2-9 (Torres-Peimbert &c Arrieta 1996).

Preliminary comparisons indicate good agreement between our fluorescent model and

the observations of these objects.

4.2.2 The IR and Near-IR [Fe II] Lines

The strength of near-IR [Fe II] lines with respect to the optical lines also indicates the presence of high density regions. The 12567 A (a ®Dg /2 — a '*£>7/2 ) line from Orion

128 was measured by Lowe et al. (1979) using a large circular aperture (2’ in diameter) that contains the region studied by OTV. More recently, we also measured this line

(Bautista, Pogge, and DePoy 1995) centered at the same location as OTV, although the effective aperture was only about half of that of OTV. Because of the large changes in local extinction at small scales in Orion (e.g. Pogge et al. 1992) near-IR to optical line ratios from independent observations covering unequal areas maybe unreliable.

Baldwin et al. (1996) used the intensity ratio between the 8617 A from OTV and the

12567 A line from Lowe et al. as evidence against the high density regions. This and other ratios of optical lines to the 12567 A line are shown in Figs. 4.4(a)-(d). Two sets of observed line ratios are given here according to the 12567 A intensities from

Lowe et al. and Bautista et al. (about 30% greater). While the I(12567)/I(8617) ratio seems consistent with about 10*^ cm“^ , all other optical to near-IR line ratios yield densities greater than 10^ cm“^ . As for the optical line ratios, neither the fluorescent models of Baldwin et al. (1996) nor ours can reproduce the majority of the observed line ratios. Future analysis of IR and near-IR [Fe II] lines would depend on accurate spectroscopic observations of the nebula with sufficiently high resolution as to separate most of the [Fe II] lines from the much stronger H I emission.

In conclusion, while the intensity of near-IR lines with respect to the optical lines is also consistent with the existence of high density regions in the Orion nebula, some systematic differences between optical and IR lines may exist as pointed out in BP95a and now indicated by the I(12567)/I(8617) line ratio. Such differences are expected if the PIZ is a thin transition region between the low density, fully ionized medium

129 1 4 I I I I I |~i 'I r I I r I I I I I I I I

0 3 54 6 7 3 5 6 74 log N,

Figure 4.4; Optical to near infrared [Fe II] line ratios vs. log iVg (cm~^ ) for Tg = 9000 K. Optical measurements by OTV and near-IR observations by Lowe et al. (1979; dotted line) and Bautista et al. (1995; solid line).

130 and the high density neutral medium. Then, the higher excitation optical emission would come preferentially from the highest densities zones, while IR lines, with much lower critical densities, may arise from the more extended lower density gas, as dis cussed in the next section.

4.2.3 Two-Zone Model of [Fe II] Emission

The analysis of optical [Fe II] emission from Orion led to the discovery of high density

(iVg =10^ — 10' cm~^ ) PIZ’s, but the approximation of a single temperature-density in the emitting region may be responsible for some of the observed dispersion between different line ratios, as well as between the optical and IR lines. Moreover, it is possible that some fraction of the lower excitation lines may originate from the PIZ.

A more realistic model of the PIZ should take into account that this is probably a thin transition region between the low density fully ionized and the high density neutral media, and therefore may vary rapidly in physical conditions. In this section we construct a two-zone model for the [Fe II] emitting region to illustrate how its inhomogeneity could lead to the observed Ne dispersion.

Assuming the dominant [Fe II] optical emission from the PIZ with {Ne ,Te )=(10® cm~^ ; 10,000 K), 50% of the gas ionized, and nearly all iron as Fe'*’, the intensity of the 4277 A line, for instance, with respect to H/?, may be expressed as

/(Fe r/](4277) _ i(4277) NpizjFe^) lp,z jcffi 7Vf,,z(jsr+) If.;, ' I ' where j is the absolute emissivity of the line per ion, N piz and Nprz indicate densities in the PIZ and FIZ respectively, and Ip iz/h iz is the mean ratio of the column lengths of the two media. From the measured intensity of the 4277 .4 line with respect to

131 H/?, as 4.3x10 ^ (OTV 1992), and the FIZ density of 4000 cm ^ , the depth of the

PIZ is of the order of

= 10'® - 10'". (4.13) i-FIZ

Thus, the PIZ appears to be a very thin region compared with the extent of both the FIZ and the ionization-dissociation front. .A. consequence of this is that a very- small fraction of Fe"*" in the FIZ could be sufficient to dominate the emission of lines with low critical densities. For instance, for the 12567 k line, with a critical density of the order of 10^ cm'^ , an increase in iVg from 4000 to 10® cm '^ enhances its emissivity by a factor of only 10.4, much less than the factor of ~ 250 for the optical lines. Therefore, even if only ~ 2% of the iron in the FIZ is in Fe"*", one can express the intensity of this line by

7(12567) = (i(12567)V(Fe+)/)p,z + (;(12567);V(Fe+)/)p/z, (4.14) to obtain 7(12567) = (j(12567)jV (F e+ )Z )x (1+0.1), (i.e. with the contribution of the PIZ about one tenth that of the FIZ). The 12567 k line, and the IR and near-IR lines with similarly low critical densities, should originate preferentially from the FIZ, unlike the optical lines. Two predictions may be made from such a scenario: (1) line density diagnostics with IR lines may behave differently than those with optical lines and would be consistent with the conditions of the FIZ, e.g. {Ne .Te )% (4000 cm '^

, 9000 K): (2) there should be clear kinematic differences between the IR and the optical lines, i.e. the velocities measured from the IR [Fe II] lines should be similar to those of the nebular [S II] emission, unlike the velocities from optical [Fe II] lines which are close to those of [0 I] at the ionization front (see Chapter 4).

132 Table 4.1 shows the relative intensities of the optical and near-IR lines calculated with a model that combines a FIZ and a thin high density PIZ. The conditions in the

FIZ are: (Tg , iVg )=(9000 K, 4000 cm~^ ), a thickness of 0.13 pc, and Fe^ ionization fraction of 2%, and the conditions in the PIZ are: {Te , N e) = (10'* K, 2x10® cm“^

), thickness of 3x10"® pc, and Fe"*" ionization fraction of 80%. Fluorescent excitation for conditions similar to those of Orion is also included. This mechanism may only affect the emission from the FIZ where the electron density is lower than the critical density for fluorescence. The present results are also compared with observations of

Orion by OTV, and with the models by Baldwin et al. (1996).

The results in Table 4.1 show that the observed optical and near-IR spectra can be reasonably well explained by this simple two-zone model, while serious discrep ancies exist when the contribution from the PIZ is neglected. For instance, it can be seen that in the absence of the PIZ the observed intensity of the A5262 line with respect to the A8617 differs by factors of two to three from theoretical models that include fluorescence (present model III and models A, B, C of Baldwin et al. ). This

I(5262)/I(8616) ratio is one of the ratios considered by Rodriguez (1996). On the other hand, by including the contribution of a thin high density PIZ (present models

I and II) good agreement is found for most lines including the near-IR lines. The mean dispersions (cr) between observations and the various models are also indicated in Table 4.1. This also shows that the models presented here are in much better agree ment with the observations than those of B96 et al. Moreover, model (II) of Table

5 that neglects fluorescent excitation in the FIZ seems to be better than model (I).

This may suggest that the contribution of fluorescence to model (I) is overestimated.

On the other hand, model (III) and models (A), (B), and (C) of B96, which

133 Observed Present® B96 A (A) 1/1(8617)“ (I) [PIZ%]/ (II)[PIZ%]/ (III) (A) (B) (C) 8892 0.19 0.31 [32%] 0.33[33%] 0.27 0.31 0.31 0.36 7452 0.51 0.22[60%] 0.26[61%] 0.12 ——— 7155 1.47 0.73[60%] 0.84[61%] 0.39 ——— 5159'' 1.3 2.3[37%] 1.4[69%] 1.8 1.7 1.9 1.1 5262 0.81 0.90[47%] 0.64[77%] 0.61 0.28 0.31 0.26 5334 0.33 0.43[69%] 0.40[87%] 0.18 0.22 0.24 0.21 4815'’ 0.94 0.61 [48%] 0.48[72%] 0.41 1.1 1.2 0.71 4245 0.87 2.0[23%] 0.69[79%] 2.0 2.1 2.4 1.3 4277= 0.64 0.52[46%] 0.34[84%] 0.36 0.46 0.50 0.37 4287 1.29 0.31 [67%] 0.31 [79%[ 0.13 —— — 12567^ 3.3-4.2 3.2[04%] 3.4[04%] 4.1 3.5 3.4 2.6

O'.... 0.65 0.40 0.63 0.69 0.80 0.53 “ Line intensities corrected for extinction from OTV except for the 12567 A line. * Unresolved [Fell] blends. Possibly blended with O il A4275.6 and 4276.8 A. Measurements from Lowe et al. (1979; lower value) and Bautista et al. (1995; higher value). ^ (I) PIZ and FIZ with fluorescence; (II) PIZ and FIZ without fluorescence; (III) only FIZ with fluorescence. ^ The percentage contribution of the PIZ to the total intensity of the line is indicated brackets. The contributions of the PIZ to the 8617 A line are 24% in model (I) and 28% in (II).

Table 4.1: Two-zone model for [Fe 11] emission from Orion.

134 neglect the contributions from the high density zone differ from the observed line ra tios by 53-80%. Notice also that in models (I) and (II) which best fit the observations the contributions of the PIZ dominate the total intensity of the optical lines, partic ularly in model (II) where the PIZ is responsible for 70-80% of the optical emission.

A better representation of the [Fe II] nebular emission would require radiative and hydrodynamic modeling of the structure of the PIZ, which exceeds the capabilities of current photoionization modeling codes.

4.3 [O I] Diagnostics

In the optical region of the spectrum there are three collisionally excited [O I] lines some times detected in H II regions; these are due to transitions ^ Dg Pg, and ^Sq D2 at A A 6363, 6300, and 5577 respectively. All three lines were reported by OTV, and were also measured by Baldwin et al. (1991) at twenty one different positions in Orion. In Fig. 4.5 we plot the line ratios /(AA6363 4- 6300)//(5577) vs.

Ne for temperatures of 5000, 8000, 10000, 12000, and 20000 K. The line ratios are calculated using a five level collisional-radiative model for 0 I with atomic data com piled by Pradhan & Peng (1994) including excitation rates by Berrington & Burke

(1981) and Le Dourneuf Sz Nesbet (1976). It is seen that for any reasonable temper ature the Ne in the [O I] line formation region is much higher than the density in the ionized region of the nebula, which is of the order of 10^ cm~^. At 10000 K the electron density obtained from the [0 I] observations is about 10® cm"®, in agreement with the [Fe II] diagnostics. The [O I] line ratios from the twenty one different spec tra reported by Baldwin et al. (1991) also indicate similar densities, between 10® and

135 10^ cm“^ at 10000 K. Other previous measurements of the [O I] A 6300 by Peimbert

and Torres-Peimbert (1977), at twelve different positions, agree with OTV to within

about 50 %. The [O I] measurements may suffer to varying degree from uncertainties

due to night sky contamination; hence one should allow for at least a factor of two

error in the line ratios.

Recently, Baldwin et al. (1996) carried out observations of the [O I] emission from

Orion using the Faint Object Spectrograph (FOS) on the Hubble Space Telescope (HST)

and Cassegrain echelle spectrograph on the 4 m telescope of the Cerro Tololo Inter-

American Observatory (CTIO). Baldwin et al. report no detection of the [0 I] 5577

Aline, for a position in Orion different from that of OTV. Baldwin et al. suggest

that previous measurements of the [O I] 5577 Aline were contaminated by telluric

emission and did not represent actual emission from Orion. The upper limits set

by the sensitivity limit of their observation establish upper limits to the averaged

electron density of the emitting region of 10® and 2 x 10® cm"® respectively for Tg =

lO"* K. If a temperature of 8000 K were adopted instead the Ne upper bounds would be 2 X 10^ and 5 x 10®.

Furthermore, we find no contradiction between the present [O I] line ratio mea surements in Orion and the results of the diagnostics with optical [Fe II] lines (iVg

% 10° — 10^ cm"® ), contrary to the conclusions of Baldwin et al. Better observations of the [01] optical emission from Orion are needed.

136 3.5 T = 5 0 0 0 K

2.5

ïôôoa CTI CO CD CO ? 20000 K 1.5 HST I OTV s O) o

- .5 3 54 6 7 log (N j

Figure 4.5: [O I] AA6300 + 6364 to A5578 line ratio vs. log Ne(cm~^) for T = 5000, 10000, and 20000 K. The value of this line ratios reported by OTV and the upper limits given by Baldwin et al. (1996; HST and CTIO) are represented by horizontal dashed lines. 137 4.4 [Fe II] to [O I] and [Fe II] to [Ni II] Correlations

The [Fe II] to [O I] correlation for SNR, Seyferts, and starburst galaxies has been

previously established by Mouri et al. (1990), Mouri, Kawara, &: Taniguchi (1993),

and Goodrich, Veilleux, & Hill (1994). They propose that this correlation is due

to the fact that both species are mainly coincident within partly ionized zones, and

their dominant ionization stages result in enhanced [O I] and [Fe II] emission. This

suggestion naturally follows the ionization structures of supernova remnants and H II

regions modeled by Oliva, Moorwood, & Danziger (1989). One problem, however,

in the [Fe II] to [O I] correlation plot by Mouri et al. (1990) is that the point corre

sponding to Orion lies away from the linear fit, towards lower [Fe II] 1.644 (xm line

strength. This problem is exacerbated by their use of inaccurate atomic data for Fe II

and an assumed electron density in the PIZ which is much lower (~ 10^ cm“^) than

the one obtained by BPO. Thus Mouri et al. obtain a low value for Fe/0 in Orion,

which they interpret as the result of depletion into grains.

.A.lthough the [Fe II] to [O I] correlation that Mouri et al. notice is real, their

deduced value for the line ratio [Fe II] 1.644/im/Br7 (IR lines) vs. [0 I] 0.63^m/Ho

(optical lines) in Orion may suffer particularly from the fact that the critical density

(Ncrif) of the [Fe II] 1.644 /j,m line is only about 10'' cm~^, which is lower than the

density in the PIZ of Orion, about 10® cm'® (BPO); this prevents the line from

increasing in intensity unlike the [O I] 0.63/im line with a higher Ncru ~ 2 x 10~

cm'®. Other possible problems may be random errors in the IR and optical line ratios

from different sets of observations, and some uncertainty as to how Br 7 and Hor are correlated because of effects like extinction, deviations from Case B recombination.

138 selective reflection effects, etc. For instance, Oliva et al. (1989) pointed out that

IR and optical spectra of supernova remnants can not easily be compared because

of what they term the ”H/?/Br 7 ” problem. .\lso, O’Dell, Walter, & Dufour (1992)

showed that in Orion there is great dispersion when correlating radio to H/? emission

due to reflecting dust slabs at the front and back edges of the ionized region.

We reduce these diflBculties by establishing a similar [Fe 11] to [0 1] correlation as

Mouri et al. (1993), but based on the optical/H/3 ratio for both [Fe 11] and [O 1]. In

Fig. 4.6(a) we show the line ratios [Fe 11] A5159/H/Î vs. [O 1] A6300/Hd (we employ

the line intensities from OTV; [Fe 11] A5159 was not measured by Baldwin et al.).

For this plot all three lines are observed in the optical region and were taken from the

same observation in each case (references as in Mouri et al. 1990 and 1993). .Also, it is

important to note that both the [Fe 11] and [0 1] lines have similar critical densities,

and the excitation energies of the Fe and 0 lines are close: AE([Fe 11]A5159) = 2.4

eV, and A£'([0 1] A6300) = 2 eV. From Fig. 4.6(a) it can be seen that the [Fe 11] to

[O 1] correlation, from all objects including Orion, is very good, with relatively little

scatter.

The ionization potentials of Fe and Ni are similar, 7.9 and 16.2 eV for Fe“ and

Fe"^ respectively, and 7.6 and 18.2 eV for Ni° and Ni"*". Thus one might expect Fe"^

and Ni"*" to coexist in the PlZs.

In Fig. 4.6(b) we plot observed values of [Ni 11] A7379/Ha vs. [Fe 11] A8616/Ha

for as many objects as we could find measurements for these lines in literature, again

including H 11 regions, SNRs, Seyferts, circumstellar nebulae, and Herbig-Haro ob jects. References to the observations are as in Table 4.2 of the present paper, and

Table 3 of the work by Dennefeld (1986); an additional reference is that for Seyfert

139 galaxies by Osterbrock et al. (1990). From Fig. 4.6(b) it can be seen that the corre

lation is very strong, with the conspicuous exception of the point that corresponds

to the Crab nebula giving the average value over its bright [Ni II] filaments. This

extremely high luminosity of [Ni II] lines in the Crab is still, therefore, unexplained.

In the correlation shown in Fig. 4.6(b) it is important to note that both the [Fe II]

and [Ni II] lines employed have critical electron densities well above 10® cm~^, and that

their excitation energies are very close: A£'([Fe II]A8616) = 1.67 eV, and A£'([Ni II]

A7379) = 1.68 eV. .A.lso, both lines are close in wavelength which diminishes any

uncertainty with respect to extinction corrections.

4.5 Diagnostics of PIZ’s in Various Gaseous Nebulae

Line ratio diagnostics of high density PIZ’s using [Fell], [Nill] and [OI] lines have been extended to a sample of gaseous nebulae including supernova remnants, H II regions, Seyfert galaxies, Herbig-Haro object, and starburst galaxies. The results are presented in Table 4.2. References to the observed sources are given, along with the conditions in the region obtained by those authors from line ratios of other atomic species (e.g. [0 II], [0 III], [S II], etc.). It is noticed in Table 4.2 that in all cases the electron densities derived in the present work are considerable higher, by one to three orders of magnitude, than those obtained from other species present mainly in fully ionized regions.

140 0

-.5

-.4

-.6 -1.5 O) —.8 o -2 o» o g* - 1.2 ■SNRs

-2.5 -1.4 OSeyfert OSeyfert

- 1.6 ■SNR oHH —3

- 1.8 •Orion •Orion

-2 -3.5

- 2.2

-3 -2 1 0 -3 2 1 0 log ([Fe ll]X5159/Hp) log ([Fe ll]X8616/HJ

Figure 4.6; The [Fe II] to [O I] and [Fe II] to [Ni II] correlations.

141 '-pa Object lines used log Ne Te log N“ '*■ e Ref. Orion [Fe II], [O I] 6.3 10,000 3.6 9000 1 Crab (FKIO) [Fe II], [Ni II] 4.1 ± 0 .3 5000 3.4 13000 3 C rab (FK6) [Ni II] 4.5 ± 0 .3 3.4 13000 3,4 Kepler [Fe II] 4.0 ± 0.3 8000 > 3 5000-10000 5,6,7 N49 [Fe II] 3.8 ± 0 .2 ~ 5000 3.0 ± 0 .2 8000-9100 6,8,9 RCW103 [Fe II] 3.4 ±0.2 3.1 ±0.1 5,8,11 N63A [Fe II] 3.6 ± 0.2 3.3 ±0.2 6,8,9 N103B [Fe II] 3.8 ±0.5 3.9 6,9,10 N132D [Fe II] 4.3 ± 0 .3 3.4 13200 9 RCW86 [Fe II] 4.4 ±0.2 ~ 3 5,10 IC443 [Fe II] 4.0 ±0.4 100-500 8000-12000 12 NGC 4151 [Fe II] 4.4 ± 0 .4 13 HH 1 [Fe II], [O I] 5.9 ±0.2 ~ 3.7 10000 14 Conditions determined from [S II] lines. (l)Osterbrock et al. 1992; (2) Barlow et al. 1994; (3)Rudy et al. 1994; (4) G raham et al. 1990; (5) Leibowitz &: Danziger 1983; (6) Oliva et al. 1989; (7) Dennefeld 1982; (8) Vancura et al. 1992; (9) Danziger & Leibowitz 1985; (10) Dennefeld 1986; (11) Fesen & Kirshner 1980; (12) Osterbrock et al. 1990; (13) Brugel et al. 1981.

Table 4.2: Physical conditions of PIZ’s in varions nebulae

142 4.6 The [Fe III] lines

Forbidden [Fe III] lines are expected to be collisionally excited. Fluorescent pumping of these lines by continuum radiation is unlikely because of the large energy difference

(more than 1 Rydberg) between the ground state of the ion and the first odd parity levels. Moreover, the stellar continuum radiation in this energy range is absorbed for the most part by hydrogen.

We use an 34-level CR model for Fe III with collision strengths from Zhang (1996) and transition probabilities from Nahar & Pradhan (1996). .A.n energy level diagram for the Fe III system is shown in Fig. 4.7, where the most important lines under nebular conditions in the optical and near-IR regions are indicated. One interest ing characteristic of the Fe III system is that the near-IR emission originates from higher excitation levels (^Gj) than the optical lines (levels ^Fj, and ^Pj), which explains why the near-IR [Fe III] emission is usually very weak in gaseous nebulae.

Also, the maximum energy difference between the levels that give rise to the optical lines is only of about 0.02 Ry (~ 3000 K), which makes the relative line intensities of these lines insensitive to small temperature variations.

Some line ratios among optical and near-IR lines are shown in Figs. 4.8(a)-(j) at Te = 9000 K. Optical observations of Orion are from OTV (solid lines), Greve et al. (1994; dotted lines), and Rodriguez (1996; dashed lines) and near-IR observations are from DePoy k. Pogge (1994; dashed line) and Bautista et al. (1995; dotted line).

The observation by Greve et al. and Rodriguez include several positions; here we present the entire ranges of their measured line ratios. The observed [Fe III] line ratios in Orion agree well with the diagnostics using lines of species such as [S II],

143 that indicate Ne of a few times x 10^ cm"'^ . The line ratios from Kaler et al. seem to indicate densities greater than those of OTV by about 0.2 dex, although this difference could be entirely accounted for by the observational uncertainties. Greve et al. observations indicate densities between a few times 10^ to almost 10“* cm“^ , with the lowest iVg near the Trapezium and highest towards the edges of the nebula.

The observations of Greve et al. also reveal variations in the intensities of the [Fe III] lines with respect to H/3 along six consecutive positions on a North to South line centered at ~ 20’ W of 0^ Ori A. Here, the intensity of the [Fe III] emission seems to have a minimum near the Trapezium region and increases toward the edges of the nebula, particularly in the North direction. This behavior seems correlated with the

[N II] and [O II] emission and is anticorrelated with that of He I, [O III], [S III], and [Ne III]. These correlations between the [Fe III] emission and the low ionization species is consistent with a drop in the ionization of the plasma towards the edges of the nebula.

144 Felll

21457 22427 22184 23485

>. çc

Figure 4.7: Energy diagram of Fe III with infrared and optical lines considered.

145 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 -1 1 1 1 1 1 1 '1 1 1 1 (a) (b) - - /—S

_ cnT 3 - - S - I g -- 5 6 2. 2 - - -

_I_U 1 1 1 1 1 r 1 1 1.1-1 1 IJ 1 1- 1 _l J. 1 I 1 t p r 1 r 1 r r 1 r p r p 2 3 4 5 6 6

5 1.2

CM S 4 3“5

3 I

1 6 2 3 4 5 6 2.5

I I 1.5

2 3 4 5 6 log N.

Figure 4.8: [Fe III] line ratios vs. log Ne (cm"^ ) for Te = 9000 K. The horizontal lines indicate the observed values by OTV (solid), Greve et al. (1994; dotted lines), and Rodriguez (1996; dashed lines).

146 4.6.1 The [Fe IV] lines

We use a 33-level CR model of Fe IV that includes the collisional rate coefficients from Zhang & Pradhan (1997) and A-values from Garstang (1958). An energy level diagram for the Fe IV system is shown in Fig. 4.9, which illustrates the lowest metastable levels "‘Gy, and ^Dy that give rise to lines in the UV. Emission lines in the optical from higher excitation levels, about 0.5 Ry (~ 6 .8 eV) above the ground state, are expected to be weak unless relatively high densities and/or temperatures are present. Fluorescent excitation by a stellar radiation continuum seems unlikely, as photons with energies higher than 1.7 Ry (~23 eV) are required to excite the lowest odd parity levels. We identify the strongest [Fe IV] transitions for condition of Ne = 4000 cm"^ and Tg = 9000 K. These, in decreasing order of intensity, are:

2835.7 .4 («^5/2 ^ /2 ), 2829.4 À (=%/2 /^/g), 2567.6 .4 (=. 9 5 /2 D 5 /2 ), 2567.4

(^■S'5/2 —^ 7 )3/2 ), &nd 3101.7 .4 {^Ss/2 Gn/2).

Recently, the detection of the [Fe IV] 2835.7 A line in Orion was reported by

Rubin et al. (1997) using the GHRS/HST spectrograph. No other [Fe IV] line could be measured. Based on the observed 2835.7 Aline and their models, Rubin et al. have derived the Fe/H abundance ratio in Orion to be lower than the solar by a factor between 70 and 200, much lower than any previous estimate from [Felll] or

[Fell] lines. reexamination of this result is presented in Section 4.5.

147 FelV

5 4198 4907 ^ >. 415: çc 4900 .4 4903 m 4869 5233 5034 3 2835.7, 2829.. 2567.1 .2 2567..

3101.7 1

Figure 4.9: Energy diagram of Fe IV with optical and ultraviolet lines considered.

148 In the optical region the strongest [Fe IV] features are those at 4906.6 A(‘‘Gn /2 —^

F9 /2 ), 4900.0 A (‘*Gg /2 ^ 7/2)7 4903.1 A(‘*G 7/ 2 — 4198.2 A(‘*Gn /2 —^//g/ 2 ), and

4152.3 A (‘‘Gg /2 —^ ^ 11/2 )- But the strength of the 4906.6 Aline with respect to the

2835.7 UV feature is only about 0.014. Similarly, the strength of the 4906.6 A line with respect to the nearby [Fe III] 4881 A line is about 0.012xiV(Fe^‘^)/iV(Fe^'^).

In principle these [Fe IV] features maybe suflSciently strong to be detectable with modern high sensitivity spectrographs, but they have not been reported. Careful observational search of these [Fe IV] lines in Orion and other gaseous nebulae would provide important information about the ionization structure of iron and the excita tion mechanism of Fe IV. Some potentially useful Ne and Te sensitive line ratios with

UV and optical lines are shown in Figs. 4.10(a)-(h).

Surprisingly, strong optical [Fe IV] emission is seen in planetary nebulae with symbiotic cores like M2-9 (Balick 1989: Torres-Peimbert & Arrieta 1996). The reason for this is likely the high Ng (~ 10^ cm“^ ) in the nebular core. Fig. 4.11 compares the density diagnostic results from [Fe IV] and [O III] lines as measured by Torres-

Peimbert Arrieta. The very good agreement between both diagnostics provides observational support for the accuracy of the atomic data and the present excitation model for Fe IV.

149 1.5

I O 0 0 § I

2 4 6 8 2 4 6 8

1.2 1.5 o

1 i

.5 2 4 6 8 2 4 6 8

1.4 0 1 1.5 g 1.2 ? I I 1

2 4 6 8 2 4 6 8 log N,

Continued Figure 4.10: [Fe IV] line ratios vs. log Ne (cm ^ ) for Te = 9000 K

150 Figure 4.10; (continued)

.4 4

O (O cô S .3 2 (O + .2 s CM i 1 0 0 2 4 6 8 2 4 6 8

4 3 0 o S 2 55 1 2 S 1 I 0 0 1

2 4 6 a 24 6 a log N,

151 [FelV ] [O III] 2.2

T .=7000lt aoooif

o 9000K— • § 10000K -

% O bserved g 1.4

1.2 O bserved

4 5 6 7 8 9 4 5 6 7 8 9

Figure 4.11: Line ratio Ne diagnostics from [Fe IV] and [O III] optical lines of high density plasma in the planetary nebula with a symbiotic star core M2-9. Observations by Torres-Peimbert & Arrieta (1996).

152 4.7 Kinematic Analysis of the Orion Nebula

Although photoionization models generally assume static conditions, the differential expansion of nebulae is known. For example, Kaler (1967) presented radial velocities for a variety of ions taken from spectroscopic observations of Orion by Kaler, Aller,

& Bowen (1965). This study includes the expansion velocity of Fe^ as obtained from

[Fe II] lines. Fehrenbach (1976) reported additional measurements of three different positions in Orion which included the velocities from forbidden emission of Fe II. Ni II, and S II. It was pointed out in this work that there is a large separation in expansion velocity between these low ionization species and the higher ionization ions, e.g. and O^"*". The most recent kinematic studies of Orion have been presented in several papers by Castaneda, O'Dell, and Wen. In particular, O’Dell &: Wen (1992) measure the expansion velocities with the [0 I] A6300 A for several arcminutes across the core of the nebula. Fig. 4.12 shows the measured expansion velocities of various ions from Kaler (196 7), Fehrenbach (1976), and O’Dell &: Wen (1992) against the energy- necessary to form them. This figure is adapted from plots previously presented by

Kaler (1967) and Balick, Gammon, & Hjellming (1974). The ordinate on the right represents the observed velocities in the heliocentric system, and the ordinate on the left gives the velocities with respect to the molecules in the OMC-1 (+27 Km s“ ^). The data by Fehrenbach corresponds to the position G A417 in Table 3 of his paper. One difficulty with these data is that only statistical dispersions for the mean velocities are given, without including the instrumental errors which dominate when the number of lines observed is small. We have estimated error bars for these measurements by taking the ratio of the instrumental error (~ 3 Km s~^) by the square root of the

153 number of lines measured. The data from O’Dell & Wen corresponds to that given in Table 5 of their paper which includes measurements by O’Dell et al. (1991) and

Castaneda (1988).

The first thing to notice from this figure is the strong, systematic dependence between the velocities of the ions and their formation energies. In particular, there is a sharp division in velocity between ions that require photon energies greater than

13.6 eV (1 Ry), indicated by the vertical dashed line, and neutrals and ions with lower first ionization potential, such as 0°, Fe"^, and Ni'*’. This velocity stratification in Orion has been previously pointed out by several authors, e.g. Kaler (1967) and

Balick et al. (1974). It is also clear from the figure that forbidden emission from O I.

Fe II, and Ni II should stem mostly from the same PIZ at the ionization front, as predicted by photoionization models (Baldwin et al. 1996) and seen from the [O I]/

[Fe II] and the [Ni II]/[Fe II] correlations (Chapter 4 and references therein). The velocities associated with [S II] emission, on the other hand, lie in between those of the ionization front and the fully ionized zone. This is because, although S'*" requires only 10.4 eV to be created, its emission region extends up to 23.3 eV. By contrast, Fe'*' ionizes to Fe'*"*' at 16.2 eV and, in addition, Fe'*' ionizes to Fe'*"*' by charge exchange with H'*' (Neufeld & Dalgarno 1987). Furthermore, spectroscopic diagnostics from

[S II] should sample mostly the region in the FIZ right behind the ionization front, and may not agree with the results from [Fe II] lines.

Another thing to notice from Fig. 4.12 is that the velocities of species in the

PIZ are similar to those of the photo-dissociation region (PDR) and the molecular cloud. This has important implications for constraining the gas densities in that zone.

The continuity equation for the flow co-moving with the ionization front implies that

154 any two points along the gas flow with similar bulk velocities should have about the

same densities, like in the case of the PIZ and the PDR and molecular cloud. With

pv = constant, one can establish limits on the density of the PIZ by estimating the

velocity of the ionization front from known densities and velocities of the PDR and,

for instance, the [O II] em itting zone. Thus,

(lO^cm"^) X (26.lATms"^ — Us) = (4000cm“^) x (13.8R'ms~^ — «*) (4.15)

yields a heliocentric velocity for the ionization front of about 26.6 Km s~^ From this

we have

where 10^ cm“^ is the estimated density of the PDR (Tielens & Hollenbach 1985)

and 26.1 Km s“^ is the flux averaged velocity of the PDR measured from radio CII

emission (Goudis 1982). Therefore, the density of the [O I], [Fe II], [Ni II] zone should

be at least ten times greater than that at the [O II] emitting region (FIZ). No upper

limit on the density of the PIZ can be obtained given the present uncertainties in the expansion velocities.

.Additional information about the structure of the PIZ may come from the kine matic study of the [O I] 6300 A. line of O’Dell & Wen (1992). They found that this line may be formed by two different components separated by a few Km s " \ the component with higher heliocentric velocity being narrower than the other. Both components average out to have similar fluxes across most of the region studied. It is possible, though, that the two components in the line profile are artifact of Gaussian fits to a line th a t is intrinsically asymmetric, as pointed out by O’Dell & Wen. Nev ertheless, either the multicomponents or the asymmetries of this line seem to suggest

155 that the PIZ is complex in its structure with rapid changes in density. The narrow component of the [0 I] line with an average heliocentric velocity of 27.4 ±2.0 Km s~^ very close to the 27 Km s"^ of the OMC-1, could reach high densities of the order of

10® - 10^ cm-3 .

156 HI H ll ------Hel , Hell 1 “ 10 — SI Sll . Sill . SIV I II OI Oil . Olll 1I 1 35 - Nil .Nill , NIIII , NIIV 1 1 1 Fel Fell 1 Felll FelV

OMC-1— > < PDR ^ I (Ji 25 I

s —5 — (FIZ) 3 (/) 20 SIVT m —10 —

Felll 15 Neill _ []

-15 — Gill -- Sill 10

-20 I I I I I I I I J I I I I L 10 20 30 40 IONIZATION POTENTIAL (eV)

Figure 4.12: The observed velocities of optical lines in Orion vs. the minimum photon energ\' required to produce the ionized specie (adapted from Kaler 1967 and Balick et al. 1974). The velocities of the molecular cloud (OMC-1) and the photodissociation region (PDR) are also indicated. The observations are from Kaler (1967; empty squares), Fehrenbach (1977; filled circles), and O’Dell & Wen (1992; filled squares).

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161 CHAPTER 5

PHOTOIONIZATION MODELING OF THE ORION NEBULA

The new atomic data for Fe I-V provides, for the first time, the possibility of an

accurate calculation of the ionization structure of Fe in low ionization nebulae. It

is important to notice that iron has only a minor effect on the cooling of the fully

ionized region, thus changes in the ionization of this element would not alter the

conditions in the nebula. Therefore without lost of accuracy one can compute the

temperature, electron density, and ionizing radiation flux at every point in the nebula

using presently available photoionization modeling codes, and then use these results

for the calculation of the ionization-recombination balance of iron separately.

The work presented in this Chapter forms part of a the paper (Bautista &: Pradhan

1997).

5.1 Fe Ionization Balance

In the present work we use the computer code CLOUDY (Ferland 1993) for photoion ization modeling, but incorporating the new atomic data for the Fe ions (Table 2.1).

Stellar continuum radiation, dust content, and turbulence velocities were taken to be similar to those in Baldwin et al. (1991). We assume mean chemical abundances

162 for the Orion nebula as in Ferland (1993), which are based on results from Baldwin et al., Osterbrock et al. (1991; OTV), and Rubin et al. (1991a). The structure of the nebula in this section is assumed as that given by the condition that the total

(gas and radiation) pressure remains constant through the cloud. The mean density throughout the cloud is ~ 10"* cm~^. This model allows us to study the effects that the new atomic data have on the calculated ionization structure of iron in the nebula.

However, as we shall see later, this model seems unable to reproduce the observed spectra of high and low ionization species simultaneously with the observed depth of the ionized region.

In Fig. 5.1 we show the physical conditions (N , Tg , ) in the cloud, as obtained from the model. In Fig. 5.2 we present examples of the ionizing radiation flux at two different zones in the cloud (a) at the near side to the ionizing star and (b) near the ionization front. The ionization thresholds of Fe I - III marked in Fig. 5.2 reveal the correlation with the photoionization cross sections near the ionization thresholds as they affect the total photoionization rate. For instance, in the photoionization of Fe I the ionizing flux per photon energy unit is maximum between its ionization threshold ~ 0.55 Ry (7.5 eV) and 1 Ry (13.6 eV), beyond which most of the photons are absorbed by H I ionization. This is the same energy interval for which the previous photoionization data (Verner et al. 1993; Reilman & Manson 1979) underestimates the Fe I cross section by up to three orders of magnitude. A similar situation applies to Fe II whose ionization potential (1.18 Ry) lies below that of neutral He (1.81 Ry).

-A.S one goes deeper in the cloud fewer photons with energies greater than 1.81 Ry are available and the photoionization of Fe II is dominated by the flux in the near threshold region, where it is heavily attenuated by extensive resonance structures.

163 15000

7 10000 I

5000

0 2x10" 2.5x10"

15000

10000 7 Eü

5000

12000

11000

10000

9000

8000

7000 0 Distance from Ionizing star [cm]

Figure 5.1: Computed physical condition for a constant pressure cloud as a function of the distance from the illuminated face.

164 12

6 Fel Fell Felll

■D 2 0 .5 1 1.5 2 2.5 3 3.5 4

I(0 m Q. 12 (0 c o o a . 10 O) o

6 Fel Fell Felll

2 0 .5 1 1.52 2.5 3 3.5 4 Photon energy [Rydbergs]

Figure 5.2: Sample of ionizing fluxes vs. the photon energy near the illuminated face (a) and near half thickness of the cloud (b). The ionization limits for Fe I-III are also marked.

165 We calculate the photoionization rate of Fe I - IV by integrating the new pho

toionization cross sections over the ionizing flux at every point of the nebula. At high

photon energies where the R-matrix data is not available, we use the central field data by Reilman & Manson which should be reasonably reliable at high energies, as seen by the relatively small differences with the close-coupling results. Photoionization from excited states of Fe ions was found to be negligible and was not considered.

Fig. 5.3 shows our results for the photoionization rates as a function of distance from the ionizing star, with those obtained using cross sections by Reilman & Manson.

It is seen that the ionization rates for Fe I - III calculated with the new data increase by nearly a factor of two for Fe I and Fe II, and about a factor of five for Fe III with respect to those using cross sections of Reilman &c Manson. Near the ionization front the differences become much larger and are of about an order of magnitude for Fe I and Fe II. This is because deeper in the cloud the ionization becomes dominated by photons below the ionization thresholds of H I for Fe I, and He I for Fe II, where the discrepancies between the two sets of cross sections are greater. It is emphasized that the resonance structures are physical features and their effect on the effective photoionization cross section should be taken into account, and that there can be a significant loss of accuracy in using fits of only the background cross sections.

Before computing the ionization structure of iron in the nebula one must also include the effects of charge exchange of Fe ions with other species in the FIZ. The most important of these reactions are

4-^ # Fe+ 4- (5.1)

166 Fe 13

12.5

11.5

1 0 5 1— 1 I I ____I— I______I I I I I I I — I 1_ 1____I______I______I______I______I i l l I______i_ 0 5x10" 10" ^ 1.5x10’' 2x10’' 2.5x10"

I 12 c 0 1 11 c o O) 10 o

9 0 5x10’* 1.5x10’' 2.5x10’' Fe

6 0 5x10’* 10’' 1.5x10’' 2.5x10’' Distance from Ionizing star [cm]

Figure 5.3; Computed photoionizing rates fro Fe I-III as a function of the distance from the illuminated face of the cloud. The solid curves represent the results using the new photoionization cross sections. These are compared with the results obtained with cross section by Reilman Manson (1979; dotted curves) and Kelly (1972; dashed curve). 167 The rate coefficients for these reactions were calculated by Neufeld and Dalgarno

(1987) using the Landau-Zener approximation and might be highly uncertain for

complex atomic systems such as the Fe ions. This is therefore the main source of

uncertainty for the Fe II/Fe III ionization balance as far as the atomic data is con

cerned. For example, changes in the rates by the estimated uncertainty of a factor

of three varies the ionic fractions of Fe I and Fe II by up to 20% (Fe III and Fe IV

remain almost unaffected). However, the uncertainties on the rates could be much

higher than a factor of three, and very elaborate calculations are needed to obtain

precise values. Charge exchange ionization an recombination between Fe"*" and Fe

are very important in limiting the physical extent of Fe II emitting region.

Fig. 5.4 shows our results for the ionization fractions of Fe I-IV in the nebula.

These results are compared with those obtained with the earlier atomic data in the code CLOUDY; which uses the tabulated cross sections from Reilman & Manson, extrapolated to the ionization threshold. For Fe III for example, CLOUDY includes a value for the cross section at 2.2 Ry of 8.8 Mb which is about four times higher than the background cross section from the new data (Nahar 1996). That overestimation of the cross section compensates in part for the missing contribution of the reso nance structures. In addition, the code uses recombination coefficients from Woods et al. (1981) which are about a factor of two too low at Tg around 10^ K. Therefore the agreement between the CLOUDY predictions and the present results is somewhat fortuitous.

168 1

FelV ,8

.6 o (0 o 'o c

.2 Felll Fel -

Fell

0 0 Distance from star [cm]

Figure 5.4: Computed ionization structure of iron in a constant gas pressure cloud as a function of the distance from the illuminated face. The present results (solid curves) are compared with the results from CLOUDY (dotted curves).

169 5.2 Modeling of Fe in Orion

In addition to atomic data, the main source of uncertainty in calculating the ion ization structure of Fe in nebulae is the assumed structure for the cloud. Different assumptions about the radial density dependence (constant , exponential, or power law), or constant thermal and/or radiative pressure, constant temperature etc. result in significant differences in the ionization structure of Fe and other ions. For instance,

Baldwin et al. (1991) assumed a mean gas density for Orion of ~ 10 * cm~^ , and con stant gas pressure, and obtained Fe ionic fractions averaged over line of sight of (Fe'*’

/ Fe^"^ / Fe^"*" ) = (0.01/0.24/0.74). On the other hand, Rubin et al. (1991b) used an exponential density profile, as a function of radius, up to a maximum of 5000 cm~^ and a “plateau” beyond, to obtain (0.05/0.41/0.53). Some differences between these two models for the ionic fractions for other elements are also present, e.g. He. One might therefore expect an uncertainty of about a factor of five in an iron abundance estimate based on [Fe II] lines and ionization corrections from photoionization mod els. If [Fe III] lines are used instead, the uncertainty would be of about a factor of two. Rubin et al. (1997) have recently estimated the iron abundance in Orion from

[Fe IV] lines and obtained values that differ by nearly a factor of three when using the Baldwin et al. and Rubin et al. (1991b) models.

Another difficulty with modeling the ionization structure of iron, and particularly the ionic fraction of Fe+, is the inadequacy of the physics of ionization fronts in photoionization models that assume static conditions everywhere in the cloud with the ionization front at a distance where all ionizing photons have been absorbed.

However, real photoionization fronts are highly dynamic and travel away from the

170 ionizing star into the molecular cloud. More realistic models of blister H II regions,

like Orion, should consider the effect of ionization fronts at a distance from the ionizing

star where enough photons are available for ionizing new neutral material as the front

travels into the cloud. One should also take into account the radiation energy that

is used to accelerate the gas away from the ionization front into the fully ionized

zone. This difficulty with the thickness of the cloud and the location of the ionization

front is readily noticed by comparing the Rubin et al. (1991a) and the Baldwin et

al. models. The model of Rubin et al. uses an exponentially increasing gas density

with a peak value of 5000 cm”^ and predicts a distance to the He ionization front of

0.277 pc. By contrast, the estimated mean thickness of the emitting region from the

surface brightness of the Ha emission is only 0.13 pc (Wen &c O ’Dell 1995). Perhaps,

the extent of the ionized region in the Rubin et al. model could be reduced by

decreasing the number of ionizing photons in the model (Q), but that would conflict

with direct measurements of Q-values from radio continuum flux density. The Baldwin

et al. model, on the other hand, gives a thickness for the ionized region of about 0.07

pc, closer to observations, but the adopted density is ~ 10“* cm"^ . Such a density

is considerable higher than what is observed in the nebula for the most part, with

the only exception of a region immediately south-southwest of the Trapezium. If a

lower density had been adopted, like that in Rubin et al., a much thicker ionized zone

would have been obtained.

In modeling the ionization structure of the Orion nebula we constructed a simple

model of the nebula that uses a constant density of 4000 cm“^ , based on long estab

lished [S II] and [O II] line diagnostics, until a maximum distance from the star where a high density ionization front is encountered. The position of the front is optimized

171 to match the observed relative intensity of the [O I] 6300 A line with respect to without significantly affecting the intensities of [0 II] and [O III] lines. Two models were calculated for peak particle densities of the ionization front at 10® cm~^ and 10~ cm~^ . Other conditions such as turbulent velocity, stellar temperature, and number of ionizing photons are as in Baldwin et al. (1991). It might be noted that there is no explicit control over the electron density, temperature, and depth of the PIZ, and they are calculated in the model according to photoionization-recombination equilibrium which depends only on the particle density and position of the ionization front. The results of these calculations are shown in Table 5.1, also showing three different sets of observations, columns 3-5, from OTV, Baldwin et al. (1996), and Greve et al. (1994).

The results reported by Baldwin et al. (1996) are shown in columns 6-8. The results for five different models calculated here, (I) to (V), are given in columns 9-13.

Inspection of Table 5.1 reveals the difficulty in reproducing the observed spec trum with current photoionization models and, in particular, the problems in trying to match simultaneously all the observed ionization stages of a given element, e.g. oxygen. Model (I) in the present work was calculated assuming constant gas pressure conditions with a mean density of ~ 10“* cm~^ , as in Baldwin et al. (1996). When comparing these results with obser\^ations one finds that the models systematically overestimate the intensity of [O II] and [O III] from a few percent to over a factor of two. On the other hand the [O I] emission is underestimated by up to a factor of three. Models (II) and (III) were calculated with constant gas pressure conditions but with a mean density of ~ 4000 cm~^ determined by spectroscopic diagnostics. The difference between models (II) and (III) is that the former uses the LTE stellar contin uum flux from Kurucz (1979), while model (III) uses a NLTE stellar continuum from

172 Sellmaier et al. (1996). Clearly, adopting a lower density for the cloud and the use

of accurate NLTE stellar continuum fluxes improve the results for [O II] and [O III]

emission with respect to observations. However, the discrepancies for the [O I] lines

increase to about a factor of five or more. This is because lowering the mean density

of the cloud has the general the effect of increasing the ionization and reducing the

fractions of neutrals. The same conditions as in model (III) were used for (IV) and

(V), together with the high density ionization fronts (in the PIZ). Model (IV) uses a

front with peak density 10® cm~^ at a depth in the cloud of 6.5 x 10^' cm (= 0.21 pc),

and model (V) has a front with peak density 10^ cm“^ at a depth of 6.9 x 10^^ cm

(=0.22 pc). [O II] and [O III] lines in both of these models remain nearly unaltered

with respect to model (IV) and in reasonable agreement with observations. However,

the [O I] lines are considerably enhanced, close to the observed levels, as a result of

the contribution from the PIZ within the front.

Table 5.1 clearly shows the effect of the assumed density structure of the cloud on the predicted spectrum from photoionization modeling. The table also shows that

there is a significant contribution to the emission from neutral and low ionization species from the high density PIZ. It must be pointed out, however, that the models presented in Table 4.1 are still illustrative, and accurate modeling of ionization fronts requires a detailed radiative-hydrodynamic treatment.

173 line Observed** Baldwin et al. ( 1996) P re sen t' Ion (A) OTV B96“ (A) (B) (C) (I) (11) (III) (IV) (VI

[O 1] 6300 0.959 0.722 0.341 0.336 0.699 0.34 0.20 0.17 0.75 0.91 [O I] 5.577 0.058 < 0.014 0.004 0.004 0.01 0.004 0.002 0.002 0.006 0.009 [Q III 3727 146 94 188 188 149 186 209 145 126 132 7320 6.21 ———— 13.8 7.86 4.44 11.6 9.19 7330 5.47 ——-— 11.2 6.35 3.56 9.10 7.45 [O III] 1363 1.39 ———— 1.93 2.39 0.74 0.69 0.79 4959 100.2 ———— 132 169 87.8 75.9 87.6 5007 302 343 465 460 379 395 507 263 228 263

“Baldwin et al.(1996)

•’Intensity relative to Hiï times 100. 'Results from present photoionization models including the contribution from a high density ionization front (see text for an explanation of the different models)

Table 5.1; Optical spectrum of oxygen in Orion vs. photoionization models

174 REFERENCES

Baldwin, J.A., Ferland, G.J., Martin, P.G., Corbin, M.R., Cota, S.A., Peterson, B.M.,

Slettebak, A. 1991, A pJ, 374, 580

Baldwin, J.A., et al. 1996, ApJ, 468, L115

Bautista, M.A., & Pradhan, A.K. 1997, -A.pJ, in press

Ferland, G.J. 1993, University of Kentucky Department of Physics and .A.stronomy

Internal Report.

Kelly H.P. 1972, Phys Rev A 6, 1048.

Kurucz, R.L., 1979, .4.pJS, 40, 1.

Nahar, S.N. 1996, Phys. Rev. A, 53, 2417

Neufeld, D. A. & Dalgarno, A. 1987, Phys. Rev. 35. 3142

Osterbrock, D.E., Tran, H.D., &Veilleux, S. 1992, .A.pJ, 389, 305 (OTV)

Reilman, R.F. & Manson, S.T. 1979, .A.pJS, 40, 815

Rubin, R.H., Simpson, J.P., Haas, M.R., & Erickson, E.F. 1991a, 374, 564.

—, 1991b, PASP, 103, 834.

Rubin, R. H., et al. 1997, .\p J, 474, L131.

Sellmaier, F.H., Yamamoto, T., Pauldrach, .A..W..A.., Rubin, R.H. 1996, .4.&A, 305,

L37.

Verner, D. A., Yakovlev, D. G., Brand, I. M., Trzhaskovskaya, M. B. 1993, ,A.t. Data

Nucl. Data Tab. 55, 233.

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Woods, D.T., Shull, J.M., and Sarazin, C.L. 1981, -A.pJ, 249, 399

175 CHAPTER 6

THE IRON ABUNDANCE IN ORION

In addition to study the emission spectra of iron ions and derive the physical condition of the emitting regions it also the aim of this work to try to estimate the gas phase abundance of iron in nebulae, and particularly in Orion. In this chapter the relative abundance of iron with respect to oxygen is calculated.

The calculations presented here have been reported also in Bautista & Pradhan

1997).

6.1 The Fe/O Abundance Ratio in Orion

There are two basic approaches typically used to estimate gas phase abundances in gaseous nebulae. The first one consists of estimating the ionic abundances, normally relative to hydrogen, directly from spectra assuming mean density and temperature derived from line ratio diagnostics. Then, the abundances of all observed ions of the same element are added to yield the total gas phase abundance of the element.

Few prior assumptions need to be made about the structure of the cloud, but the method has the disadvantage that it neglects any temperature and density variations along the line of sight, as predicted from photoionization models (e.g. Fig. 4.1).

176 Additional temperature fluctuations, different from photoionization models, have also been studied by Peimbert (1967; 1995, and references therein). The second approach consists of photoionization modeling to reproduce the conditions in the cloud, and the abundance of elements adjusted to match the observed spectrum. The results, then, depend on the initial assumptions about the structure of the nebulae and may be subject to large uncertainties in the model.

Relative ionic abundances should be most accurate when calculated for ions that are closely coexisting in the nebula and whose lines are produced by the same mech anism, e.g. collisional excitation or recombination. Lines excited by fluorescence are difficult to interpret as they generally involve a large number of levels and depend on the nebular photoexcitation emission.

For Orion we calculate the abundances of Fe'*', Fe^"*", and Fe^"^ relative to 0°,

0'"', and 0-""" respectively, and derive the total N(Fe)/N(0) from each of the ionic ratios using calculated ionic fractions. The abundance ratio N(Fe‘"'')/N(Q-^‘'") can be obtained from the observed line intensities T, and the calculated emissivities j ’, as

iV(Fe''^) /fe'+ ioj+ (6 . 1) vV(0;+) Iq]+

The total N(Fe)/N(0) abundance ratio is

N{Fe) ^ ,V(Fe'+) A'(Q;+) jV(0) ^V(0;+) %(Fe'+)' ^ where % is the calculated ionic fraction in the nebula.

We fist calculate the N(Fe‘*')/N(0°) ratio from the intensity ratio measured by

Osterbrock, Tran, k Veilleux (1992; OTV), /fe+(A8617)//oo(A6300) = 0.069. The particular advantage of ratios of the optical [Fe II] lines and the [O I] 6300 line is

177 that the excitation energies are similar, as are the critical densities > 10^ cm“^ .

These ratios are therefore insensitive to uncertainties in and . Assuming a density for the emitting region of 10® cm“^ ones gets N(Fe'^)/N(0°)=0.069x 1.08

=0.075. If an electron density of 4000 cm“^ were adopted instead, the abundance ratio would be N(Fe'^)/N(0®)=0.069x 0.80 = 0.055, which differs by less than 30% from the previous value. Similar results can be obtained using other optical [Fe II] lines. A calculation of the total N(Fe)/N(0) ratios from Fe"*" and O® depends on the ionic fractions. Assuming most of the emission from the PIZ, where Fe^ and 0° are the dominant ionization stages, the ratio of the ionic fractions would be about unity and the N(Fe)/N(0) ratio (as derived in Bautista& Pradhan 1995 and Bautista et al. 1996) should be close to the solar value of 0.048 (Aller 1987) or 0.044 (Seaton et al. 1994). If the emission originated mainly from the FIZ the ratios would be 0.16,

0.27, 0.35 respectively, from photoionization models from the present work (Model

III in Table 5.1), Baldwin et al. (1991), and Rubin et al. (1991a; 1991b). This yields lower bounds to the total N(Fe)/N(0) between ~ l/4 and 1/2 of the solar value.

Fe^"*" and 0'*’ are expected to be mostly coexisting; one can therefore calculate

Fe^'^/0'*' with good accuracy. In Fig. 6.1 we plot this abundance ratio as a function of electron temperature and density. This was calculated according to Eq. 6.1 using line intensity ratios from OTV for Ipe2+(A488l) and Iq+(A3728) (solid curves), and

Io+(A7322) (dashed curves). In principle, one should obtain the same relative abun dance ratio from every line, thus the actual conditions of the emitting region and the abundance ratio are given by the point where the different curves intersect. In that sense. Fig. 6.1 shows that if the temperature of the region were 9000 K, the electron density should be about 2500 cm"^ . Similarly, a density of 4000 cm"® , as adopted

178 by OTV, would yield a temperature close to 7000 K. We adopt mean conditions for

the Fe^'*' and O'"" emitting region of Ne = 3000 cm"^ and Te =8000 K. Table 6.1

presents the abundance ratios derived from individual [Fe III] lines observed in Orion by OTV. The mean abundance ratio is N(Fe^^)/ N {0''") = 0.011 ± 0.003, where the error comes from the statistical dispersion (the value from the blend of lines at 4986

Â was excluded since it is more than two sigma away from the mean). The ratio of the ionic fractions, X{0'^)/X{Fe^'^), according to any of our present models (III),

(IV), or (V) is about 1.1, which yields an iron to oxygen abundance ratio by number of about 0.012± 0.003 or 1/(3.7 ± 1.0) of the solar value. Notice that the ratio of the ionic fractions from the models of Baldwin et al. (1991) and Rubin et al. (1991a;

1991b) are higher than the present value, 1.75 and 1.39 respectively, and they would yield abundance ratios of about half solar to about 35% lower than solar.

The iron to oxygen abundance ratio in the Fe IV emitting region can be calculated from the [Fe IV] and [0 III] lines. We use the intensity of the [Fe IV] 2827 Aline with respect to H/J, as measured by Rubin et al. (1997), and OTV’s observations of

[O III] lines also with respect to HP. Fig. 6.2 shows the calculated N{Fe^'^)/N{0^'^) abundance ratios as a function of temperature for several Ne . Here the solid curve represents the abundance ratio from the [O III] 4363 A line and the dashed curve indicates the ratio obtained with the [0 III] 4959 X feature. .\s before. Te , Ne , and the abundance ratio are given by the crossing points of the two curves. We find the

179 .02

.018 2000 cm

.016

.014

012 3000

b z

4 0 0 0 z .008

6 000 006

10000 004

002

6000 7000 8000 9000 10000 Te(K)

Figure 6.1: The Fe^'^/O'^ abundance ratio in Orion as a function of the assumed temperature and electron density of the region. The line intensities are from OTV for I/Te2+(A4881) and Io+(A3728) (solid curves) and Io+(A7322) (dashed curves).

180 A(A) Transition W+(A)//o+(3727) iV(Fe2+)/7V(0+) 5412 a ^ D \ — a 2.4 X 10-“ 0.0084 5270 a ^ Dz — o ^ p 2 3.7 X 10-3 0.012 4987 a ^ D i — a ^ 2.3 X lQ -“ 0.003 + a ^D'i — a 4881 a — a 2.9 X 10-3 0.0092 4658 a — a 9.2 X 10-3 0.036 4702 a — a 1.7 X 10-3 0.0099 4734 a ® ^ F z 5.6 X 10-“ 0.0095 4607 a — a ^ F ] 4.2 X 10-“ 0.013 4755 a — a ^Fj 1.2 X 10-3 0.012 4769 a — a ^Fî 6.3 X 10-“ 0.011 4778 a '^Z?i — a ^ F2 4.0 X 10-“ 0.016

Table 6.1: Fe^^/O"^ abundance ratios in Orion

181 .0 0 4

.0035

.003

.0025 N. = 4000 cm

.002

.0015

.001

.0005

7000 8000 9000 10000 11000 12000 T.(K)

Figure 6.2: The Fe^'^/O^'*' abundance ratio in Orion as a function of the assumed temperature and electron density of the region. The line intensities are from Rubin et al. (1997) for the [Fe IV] 2827 .4.1ine and from OTV for the [O III] 4363 .4. (solid line) and the [O III] 4959 A line (dashed line).

182 Zone Fe‘+/QJ+ F e /0 (Fe/0)/(Fe/O)O Fe+-0“ 0.065 0.010 - 0.065 1/4 - 3/2 Fe2+-Q+ 0.014± 0.004 0.015± 0.005 1/(3.7±1.0) Fe3+.Q2+ Q.0020± 0.0006 0.0017± 0.0005 1/(26 ± 8 )

Table 6.2: Fe/0 abundance ratios in Orion

conditions for the Fe^'*' - O^'*' emitting region of about Te = 10500 K and iVg = 4000 cm~^ , and N{Fe^'^)/ N {0 ‘^'^) abundance ratio of 0.002. The uncertainty in this

value from errors in the assumed conditions is less than 10%, as seen from Fig. 6.2.

The X { 0 ‘^'^)/X{Fe^'^) ionic fractions ratio from our present model (III), (IV), or (V) is 0.96, which yields a total N {F e)/N {0) of 0.0017 or 1/26 of the solar value. If ionic fractions from Baldwin et al. (1991) or Rubin et al. were used, one would get a total abundance ratio of about 1/30 of the solar value. This result is between 1.2 and 3.3 times higher than the values derived by Rubin et al. (1997), if one assumes a

N {0 )/N {H ) ratio for Orion of about 1/2 solar. Nevertheless, the present gaseous iron abundance from the Fe^"^ lines is about a factor of ten lower than our results from Fe'*" and Fe^"*". This large discrepancy seems to exceed the combined uncertainties of the observations and the atomic data and remains unexplained. A summary of the ionic and total Fe/0 abundance ratios estimated for different ionization zones in Orion is presented in Table 6.2.

183 REFERENCES

Aller, L.H. 1987, In: Spectroscopy of Astrophysical Plasmas, ed. A. Dalgarno & D.

Layzer (Cambridge: Cambridge Univer. Press), 89.

Baldwin, J.A., Ferland, G.J., Martin, P.G., Corbin, M.R., Cota, S.A., Peterson. B.M.,

Slettebak, A. 1991, ApJ, 374, 580

Bautista, M.A., Peng, J., & Pradhan, A. K. 1996, ApJ, 460, 372

Bautista, M.A., & Pradhan, .A..K. 1995, ApJ, 442, L65

Osterbrock, D.E., Tran, H.D., &Veilleux, S. 1992, ApJ, 389, 305 (OTV)

Peimbert, M., 1967, ApJ, 150, 825.

Peimbert, M., 1995, in: The Analysis of Emission Lines, ed. R.E. Williams, Cam

bridge University Press.

Rubin, R.H., Simpson, J.P., Haas, M.R., & Erickson, E.F. 1991a, 374, 564.

— 1991b, PASP, 103, 834.

Rubin, R. H., et al. 1997, ApJ, 474, L131

Seaton, M.J., Yu Van, Mihalas, D., & Pradhan, A.K. 1994, MNRAS, 266, 805.

184 CHAPTER 7

SUMMARY AND CONCLUSIONS

7.1 Atomic Data for Fe I-V

Extensive radiative data have been calculated: energy levels, dipole oscillator strengths, and partial 1 and total photoionization cross sections for Fe I, Fe IV, and Fe V using the close-coupling theory in the R-matrix approximation. Most of these data were calculated for the first time and are expected to provide a reasonably complete dataset for these ions to be used in photoionization models and stellar opacities calculations.

Total and partial photoionization cross sections for all bound states of Fe I, Fe IV, and Fe V were obtained, carefully delineating the autoionizing resonance structures.

The present ground state cross section for these ions differ by more than three orders of magnitude in the case of Fe I and up to an order of magnitude for Fe IV and Fe V with respect to previous calculations in using central filed type approximations. By contrast, the present ground state cross section for Fe I agrees well with the results by Kelly &c Ron (1972) and Kelly (1972) using the many-body perturbation theory.

185 Collision strengths and Maxwellian averaged excitation rates for Ni II and Fe II

using the close-coupling theory in the R-matrix approximation as developed by the

Opacity Project and the Iron Project.

It is found that the present collision strengths for Ni II differ considerably for some transitions from those reported by Nussbaumer & Storey (1982). However, for the strongest transitions, which give rise to some of the observable lines in nebular spectra, the agreement between both sets of data is reasonably good. This suggests, in particular, that the accuracy of the atomic data may not be responsible for the longstanding nickel-to-iron abundance problem as suggested by Henry &: Fesen (1988).

New calculations of collision strengths for Ni II are currently in progress with a larger close-coupling expansion that includes states with 3d® 4s configuration.

The data presented here for Fe II complements the set of transitions computed by Zhang Sc Pradhan (1995), by including the doublet and sextet states that were excluded from their computations. The calculated emissivity ratios from both sets of data also agree reasonably well for transitions common to both sets.

Some of the present atomic calculations were carried out with a parallelized version of the RMATRX package of codes developed by the Opacity Project and the Iron

Project (Herrington et al. 1995). Most modules in the T3DRM package exhibit speed- ups with respect to the serial version that are nearly linear with the number of processors in the partition, reaching computing speeds that are orders of magnitude greater then in serial processing on the Cray Y-MP. .A.lso, by sharing the largest arrays in the codes among the multiple processors RAM memories over 250 Mega words have been obtained. The parallelization on massively parallel processors affords new opportunities for ab initio computations.

186 7.2 The Nebular Extinction in Orion

Using the hydrogen recombination lines from the Balmer, Paschen, and Brackett se ries spanning the wavelength region of 0.36 — 2.2^m, we have estimated the nebular extinction in a selected, well-studied region of the Orion Nebula. If we assume all of the extinction is due to a foreground dust screen, we encounter discrepancies be tween the predicted and observed emission-line ratios. This discrepancy is resolved when we apply a first-order empirical correction term to the stellar extinction law to derive an effective “nebular” extinction law. We apply this nebular extinction curve to diagnostic emission-line ratios used to estimate density, temperature, and ionic abundances.

In the part of the Orion Nebula that we are concerned with, we find that the departures from the stellar extinction law are subtle. If we were to consider only those emission lines that lie within the wavelength region spanned by a given hy drogen recombination-line series (e.g., the [O III] lines that are intermingled with the Balmer series lines), there would be only a negligible difference between the extinction-corrected line ratios obtained by using a traditional estimate of .4v from the lines of that series, and those derived using our nebular extinction technique.

However, when we consider those lines that are widely separate in wavelength from the hydrogen lines used to estimate A y (e.g., [S III] A9532À and Ho A6563Â) that the differences between the results of the two methods become significant and system atic. When we try to merge optical and near-IR spectra we find that the traditional method breaks down. These results should serve to alert observers to the fact that for spatially extended dusty objects where radiative transfer effects become important,

187 the extinction law, as derived from stars, cannot be applied uniformly to all emission-

lines at all wavelengths to correct for extinction. Unlike the stellar case, each nebula

(and each position within that nebula) has irreducible differences that could require a

unique nebular extinction correction to tie the visual and near-IR spectrophotometry-

together into a common system.

The method of deriving a nebular extinction curve for a particular region in a dusty emission-line nebula that we have described should be generic, provided that one

has the necessary visual and near-IR spectrophotometry, and that one can eliminate or mitigate the problems of beam-matching between the two different instruments.

While Orion can serve as an excellent test case in a well-observed nebula, the effect we find in Orion is still subtle. We expect that in other, much more dusty nebulae this effect may become important. Future observations should help to bear this out.

7.3 Analysis of Forbidden Fe II-IV Emission Spectra and the Iron Abundance in Orion

The study of forbidden optical emission spectra of [Fe II], under nebular conditions including the effects of collisional excitation, fluorescent excitation by UV continuum, and line self-absorption, reveals fluorescence as relatively inefficient and optical depth effects are generally negligible. The [Fe II] emission from H II regions like Orion forms in high density partially ionized zones (PIZ’s) within the ionization front. This conclusion is derived from numerous density line ratio diagnostics, some of which are insensitive to fluorescent excitation. These line ratios should also be useful for diagnostics of plasmas even when the radiation field is sufficiently intense to affect

188 some of the [Fe II] lines. Moreover, under fluorescent excitation the optical [Fe II]

emission should be accompanied by observable dipole allowed Fe II lines that are

absent in H II regions like Orion, but are observed in circumstellar nebulae and the

subclass of bipolar planetary nebulae with symbiotic star cores (a more detailed study

is in progress).

Unlike the optical emission, the [Fe II] near-IR and IR lines can be easily excited

at low iVe , while they are collisionally de-excited at the high densities in the PIZ.

These lines should therefore originate from a region that extends within the lower density fully ionized zone. Observational studies of the relative intensities of the near-IR [Fe II] lines and their expansion velocities are proposed.

The presence of high density PIZ’s, as in the Orion nebula, appear to be present wherever optical [Fe II] emission has been detected. Other H II regions (M43, M8,

M16, M l7, M20, and NGC7635 observed by Rodriguez 1996) also show similar con ditions. Furthermore, high density regions appear to be located within the ionization fronts and form a general characteristic of these.

The [Fe III] emission lines are primarily collisionally excited and the observed line ratios are consistent with the conditions (Tg and Ne ) of the FIZ. As expected from the modeled ionization structure of nebulae, there is a correlation between the observed [Fe III] emission and th e emission from low ionization species like N"*" and

0+.

The theoretical [Fe IV] emission spectrum was studied in detail. Under nebular conditions most of the emission lies in the UV, as recently observed (Rubin et al. 1997), while the optical emission is formed only by rather highly excited levels that are difficult to populate. Optical [Fe IV] lines have been identified in only a handful of

189 objects including the bipolar nebula M2-9 (Torres-Peimbert & Arrieta 1996). The presence of these lines indicates unusual nebular conditions: electron densities up to

10^ cm”^ and a high degree of ionization.

The observed kinematics of the Orion nebulae seem to be well correlated with the physical conditions derived from the iron spectra. There is a distinction in the observed expansion velocities for different species and their degree of ionization. In particular, neutrals and ionized species of low ionization potential, like 0°, Fe"^, and Ni'*', which are expected to emit predominantly from the neutral and partially ionized zones, are distinctly separated by about 13 km s~* from the fully ionized gas.

Moreover, the expansion velocities of optical emission from 0°, Fe'*', and Ni'*" are remarkably similar to those of the FDR and the molecular core. This also provides strong evidence for the high densities in the PIZ. Similar kinematic analysis of other

H II regions is proposed.

7.4 Photoionization Modeling of Fe in the Orion Nebula

Photoionization modeling of Fe emission in Orion with the new atomic data indicates that the main source of uncertainty to be the assumed structure, for example the assumption of static conditions and an ad hoc density profile. Particularly problematic is the region near and within the ionization front with neutrals and low FIP ions. We illustrate this difficulty by modeling all ionization stages of oxygen (0 1 - III) in

Orion simultaneously. It is found that high densities are required at the I-front for the observed [0 I] emission from Orion to be reproduced. More realistic models of photoionized nebulae would require radiative-hydrodynamic modeling. Also, the

190 roles of enhanced electron and proton impact destruction of grains, particularly in

the high density PIZ, and the precise role of charge exchange processes, remains to

be explored.

7.5 The Iron Abundance in Orion

The relative gas abundance of Fe/0 in Orion is determined spectroscopically from

[Fe II], [Fe III], and [Fe IV] emission separately. Ionic fractions of Fe and O ions that co-exist are employed and the physical conditions {Te , Vg ) in each emitting region is estimated individually. This approach should be accurate and takes into account temperature and density variations across the nebula. The Fe/O abundance ratio in the PIZ is thereby found to be between near-solar values down to a conservative lower limit of 1/4 solar. Taking account of the uncertainties, this is generally consistent with our previous determinations in Bautista & Pradhan (1995) and Bautista et al. (1996).

The Fe/0 ratio derived from [Fe III] lines is about 1/(4 ± 1). For 0/H in Orion of about half of the solar ratio, this result agrees with most previous determinations by other researchers of Fe/H about a tenth of the solar value (e.g. OTV). In contrast, the Fe/0 ratio obtained from [Fe IV] emission is about 26 times lower than solar.

Although considerably higher than the values derived by Rubin et al. (1997), it is still much lower than the determinations from other iron ions. This apparently differential iron gas phase abundance across Orion obtained from different ions is puzzling. It seems unlikely that the emissivities for the [Fe IV] UV lines could be overestimated by as much as a factor of six, unless the Garstang A-values are in substantial error

(work is in progress to check these). However, for conditions in Orion, all of the

191 emission from Fe IV depends mostly on the collision strengths and only marginally

on the A-values (in the low limit). It is noted that the and terms that

give rise to the strongest [Fe IV] UV lines are populated predominantly via collisional

excitation from the first excited state which is highly metastable. Thus, one may

expect that the emissivity of the observed lines would be very sensitive to radiative

depopulation of the state to the ground state yet, we observe that an increase

of the A(‘*Gy — ®5ô/2) values of three orders of magnitude reduces the emissivity of

the 2836.6 Â line by less than a factor of two. On the other hand, the new collision

strengths should be accurate, as discussed in sections 2 and 3.5. .Another possibility

would be that the ionic fractions for the iron ions are in error. If the iron abundances

from Fe^"*" and Fe^+ were to be reconciled in this way the X{Fe^'^)/X{Fe^'^) ionic

ratio would be about 0.27 instead of the value of 1.8 expected from our present model,

3.4 from Baldwin et al. (1991), and 1.3 from Rubin et al. (1991b); the actual gas phase

Fe/0 would then be about 1/14, or Fe/H~l/28, of the solar ratios. But such a low

ratio for the ionic fractions would require a combined error from the photoionization cross sections and recombination coefficients of nearly an order of magnitude. This appears rather unlikely, especially since the unified recombination coefficients in the present work are calculated using the same ab initio close-coupling method as the photoionization data, ensuring self-consistency and minimizing the possibility of any large errors in relative ionic fractions. Alternatively, if the stellar radiation field were adjusted to reproduce this low ionic ratio, the ionic fractions for all other elements, e.g. C, N, O, S, etc., would also be affected. It seems, then, rather difficult to reconcile the abundances derived from each ion, which suggests a gradient in the gas phase iron abundance in Orion via some unknown mechanism.

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