THE SPECTRUM OF Fe ii

The title of Sveneric Johansson's last paper, "A Half-life of Fe ii" (Johansson 2009), accurately describes his association with the spectrum during his career. He began work on the spectrum as a graduate student of Edlén, with papers on new energy levels (Johansson & Litzén 1974) and a comprehensive analysis of the spectrum (Johansson 1978). Much of his subsequent work focused on the discovery of new energy levels, identification of Fe ii lines in astrophysical spectra, and their use for diagnostics, including the discovery of stimulated emission from Fe ii in η Carinae (Johansson & Letokhov 2004). This work continued for the rest of his life, with his final paper on new energy levels in Fe ii observable solely in stellar spectra (Johansson 2009), completed just days before his death in 2008.

In 1987, I began working on the spectrum of Fe i at Imperial College, London, UK (IC), using Fourier transform (FT) spectra of iron–neon and iron–argon hollow cathode lamps recorded at Kitt Peak National Observatory (KPNO) and IC. This work resulted in two papers on precise wavelengths in Fe i and Fe ii (Nave et al. 1991, 1992). In 1992, I went to Lund University and began work with Sveneric to combine the FT spectra from IC with grating spectra recorded by him in 1988 on the 10.7 m normal incidence spectrograph at the National Institute of Standards and Technology (NIST). The combined data were used to produce a line list of about 34,000 spectral lines covering wavelengths from 833 Å to 5 μm. Roughly 9500 of these lines are due to Fe i, and these were used to produce optimized energy levels and a new Fe i multiplet table (Nave et al. 1994). About 15,000 of the remaining lines belong to Fe ii. After completion of the work on Fe i, I continued to collaborate with Sveneric on the spectrum of Fe ii, with the aim of preparing a comprehensive analysis and line list for Fe ii. However, progress was slow due to competing work and his subsequent illness. Consequently, this work remained uncompleted when Sveneric died in 2008 October.

This paper is my best attempt to complete the analysis of Fe ii in the way that Sveneric was unable to do. It has benefited from unpublished line lists and energy levels that he gave me while I was working in Lund and from the insights into the spectra of iron-group elements that I gained while there. However, the loss of Sveneric's knowledge and lack of access to some of the original data behind the unpublished line lists have resulted in some inconsistencies in the analysis. In particular, it has proven to be impossible to put the intensities on a consistent scale over the whole wavelength region. Since I do not have the original data behind the unpublished line lists, I was also unable to verify all of the lines in these lists in a way that I would have done otherwise. However, these lists appear to be reliable, and I have no reason to doubt that Sveneric prepared them well. Although Sveneric's considerable contributions of lines and energy levels make him a co-author of this paper, the final selection of lines and energy levels in the tables is solely mine.

Gillian Nave.

The iron-group elements have complex spectra with thousands of lines from the VUV to the infrared (Johansson 1978). They are important in the absorption spectra of many astrophysical objects including the interstellar medium, hot and cool stars, gaseous nebulae, galaxies, and quasi-stellar object absorption line systems. Lines from Fe ii in particular account for as many as half of the absorption features in A- and late B-type stars in all wavelength regions (Brandt et al. 1999). They also form prominent emission lines from a wide variety of objects including chromospheres of cool stars (Dupree et al. 2005), active galactic nuclei (Hamann & Ferland 1999), and nebular regions around massive stars.

Problems in modeling stellar spectra in the UV and VUV often can be traced to the lack of adequate data for iron-group elements, particularly for very highly excited levels of these elements. The importance of these highly excited levels has been demonstrated in observations of the Bp star HR6000 made with the HIRES spectrograph on the Very Large Telescope. Castelli et al. (2009) found it possible to identify strong lines in the region around 5178 Å as transitions of the 3d⁶(³H) 4d–4f array due to unpublished energy levels of Fe ii. The upper levels of this transition array are located around 128,000 cm⁻¹ (15 eV) and are the highest known levels of Fe ii.

Previous papers on Fe ii containing substantial numbers of lines or energy levels are summarized in Table 1. The last comprehensive publication on Fe ii was in 1978 (Johansson 1978). It contained classification of 3272 lines from 576 energy levels, covering the wavelength range 900 Å to 11 200 Å. The wavelength uncertainty of the best lines was 0.02 Å. Since then, precise wavelengths of Fe ii in the UV (Nave et al. 1991; Nave & Sansonetti 2004) and VUV (Nave et al. 1997a) have been published. Additional Fe ii wavelengths have been reported by Adam et al. (1987), Rosberg & Johansson (1992), Johansson et al. (1995), Biémont et al. (1997), Aldenius et al. (2006), Aldenius (2009), Castelli et al. (2009), and Castelli & Kurucz (2010). These publications contain approximately 500 new spectral lines. Studies by Adam et al. (1987), Johansson & Baschek (1988), Rosberg & Johansson (1992), Biémont et al. (1997), and Castelli & Kurucz (2010) account for an additional 301 new energy levels.

The laboratory spectra used here are the same as those in our previous studies of Fe i and Fe ii (Nave et al. 1991, 1992, 1994, 1997a). The spectra were obtained on four different instruments: the f/55 IR–visible–UV Fourier transform (FT) spectrometer at the Kitt Peak National Observatory (KPNO), Tucson, AZ for the region 2000 cm⁻¹ to 35 000 cm⁻¹ (5 μm to 2900 Å); the f/25 vacuum UV FT spectrometer at Imperial College, London (IC) for the region 33,000 cm⁻¹ to 67,000 cm⁻¹ (3000 Å to 1500 Å); the f/25 UV FT spectrometer at Lund University, Sweden for the region 31,900 cm⁻¹ to 55,000 cm⁻¹ (3135 Å to 1820 Å); and the 10.7 m Normal Incidence Grating Spectrograph at NIST for high-dispersion grating spectra above 30 770 cm⁻¹ (<3250 Å).

3.1. Fourier Transform Spectra

3.2. Grating Spectra

The initial identification of the lines was performed solely in the FT spectra. These line identifications were carefully examined to eliminate spurious coincidences of lines and energy level differences and were then used to obtain optimized values for many of the energy levels. The remaining levels were found using unidentified lines in the FT and grating spectra and the identifications were again examined to eliminate spurious coincidences. Finally, both the FT and grating spectra were used to obtain optimized energy level values and Ritz wavelengths and wavenumbers. The full procedure is as follows.

About 28,000 lines were measured in the FT spectra. Known lines that belong to species other than Fe ii were identified by comparison to previously published wavelengths in Fe i (Nave et al. 1994), Ar i–ii (Whaling et al. 1995, 2002), Ne i–iii (Sansonetti et al. 2004; Saloman & Sansonetti 2004; Kramida & Nave 2006), and various impurities present in the spectra (Ralchenko et al. 2012). An initial identification of Fe ii lines was made by comparison with Ritz wavelengths calculated from Fe ii energy levels taken from the references in Table 1. Many of these levels had large uncertainties as they were obtained from grating spectra of lower resolution and accuracy than our FT spectra. Setting a large tolerance window for the agreement between the Ritz and experimental wavelengths leads to many spurious identifications of lines from these levels. A better approach is to use a few lines known to combine with these levels to obtain a better value for the energy level. The energy levels then have low uncertainties and the tolerance window can be set lower, leading to fewer spurious identifications.

Roughly 10,000 lines in the FT spectra matched energy level differences in Fe ii. About 1/3 of these lines had more than one possible identification. The identifications of all lines were checked to ensure that very few spurious identifications contributed to the energy level optimization, as even a small number of misidentified lines can have a significant effect on the optimized energy levels. This task was aided by the small uncertainty of the wavenumbers obtained from an FT spectrometer, and by predicted intensities from the atomic structure calculations of Kurucz (2010). Although the accuracy of these calculations is limited by strong configuration interaction in Fe ii, they were useful for locating lines in FT spectra from levels that had been found using less accurate data from grating spectrographs. After eliminating spurious identifications, the total number of Fe ii lines in the FT spectra was 8930, of which 798 had more than one plausible identification.

The lines measured in FT spectra were used to derive optimized energy levels and Ritz wavenumbers using the computer program lopt (Kramida 2011). Values for 942 energy levels of Fe ii were derived from 8930 lines covering wavenumbers from 2008 cm⁻¹ to 67,851 cm⁻¹. The line uncertainties assigned for use in the level optimization omit the calibration uncertainty (see Section 3.1). The statistical uncertainty, estimated as described in Section 3.1, was added in quadrature to a minimum estimated uncertainty of 0.001 cm⁻¹. This value was chosen to ensure that the level optimization was not dominated by the infrared region, where narrow linewidths give very precise wavenumbers, but the calibration uncertainty of the spectra is higher as many overlapping spectra are required to reach the Ar ii standards. Weights were then assigned proportional to the squared reciprocal of the estimated uncertainty of the wavenumber of the line. Lines with more than one possible classification, lines that were blended, and lines with a large difference between the observed and Ritz wavenumber were assigned a low weight so that they did not significantly affect the values of the optimized energy levels.

The optimization was performed in three different steps. The first step was designed to obtain accurate values and uncertainties for the ground term, a⁶D. The values for the a⁶D intervals can be determined from differences between lines close to one another in the same spectrum sharing the same calibration, hence the calibration uncertainty does not contribute to the uncertainty in the relative values of these energy levels. An optimization was thus performed with a set of lines connecting the lowest a⁶D term to higher 3d⁶ (⁵D)4p levels. These lines were assigned a weight proportional to the squared reciprocal of the statistical uncertainty of the wavenumber. The minimum estimated uncertainty of 0.001 cm⁻¹ was omitted as all the lines are in the same spectral region. In the second step, the a⁶D levels were fixed to the values and uncertainties determined from the first step. The weights of all the lines in the FT spectra were assigned by combining in quadrature the statistical uncertainty and the minimum estimated uncertainty of 0.001 cm⁻¹ in order to obtain accurate uncertainties for the 3d⁶ (⁵D)4p and higher levels.

After the second step of the level optimization, a further 86 energy levels that had not been optimized with the FT spectra were added. Most of these were from Biémont et al. (1997) and Castelli & Kurucz (2010). Roughly half of the levels in Castelli & Kurucz (2010) could not be matched definitively to lines in the FT spectra. Levels were adopted from Castelli & Kurucz (2010) if they had strong transitions that matched at least two lines in the FT spectra. All the energy levels were then used to identify additional lines in both the FT and grating spectra. The final optimization step derived values for 1027 energy levels from 13,653 transitions in both FT and grating spectra, again fixing the values of the a⁶D levels to the values obtained in the first step. An uncertainty of 0.005 Å was assigned to all grating lines. The energy level uncertainties from this iteration were added in quadrature to a global calibration uncertainty of 4 × 10⁻⁸ times the value of the energy level.

The 1027 energy levels is given in Table 3. The configurations and terms in Columns 1 and 2 are taken from the NIST Atomic Spectra Database (Ralchenko et al. 2012), the papers in Table 1, or the calculations of Kurucz (2010). Many of the levels between 114,212 cm⁻¹ and 114,673 cm⁻¹ have not been assigned to configurations. The levels in this region are from the two overlapping configurations 3d⁶(⁵D)6d and 3d⁶(³D)4d. The energy level values are given in Column 4. The uncertainties with respect to the ground term are given in Column 5 and represent one standard uncertainty. They were obtained from the lopt program by combining the uncertainties derived from the level optimization in quadrature with a global calibration uncertainty of 4 × 10⁻⁸ times the level value. The last column lists the number of observed lines that combine with the level.

The table of observed Fe ii lines (13,653 transitions) is given in Table 4. The intensities in Column 1 depend on the source conditions and method of measurement. The wavenumbers and intensities of all of the lines above 3250 Å were taken from a weighted average of up to nine individual measurements in the FT spectra. Since these intensities were measured using several different source conditions, they are useful only as a guide to the approximate strength of the line and should not be relied upon for accurate intensity measurements. Wavenumbers and intensities of lines below 3250 Å that are marked with an "F" in Column 11 were also taken from FT spectra. The wavelengths and intensities of lines marked "G" in Column 11 are from the grating spectra of the pulsed iron–neon hollow cathode lamp listed in Table 2. The intensity scale of the grating lines is different from the intensity scale of the FT spectra and is given as decimal numbers in Table 4. Strong lines that saturate the photographic plate are indicated with an "S" in Column 11. Wavelengths and intensities of lines taken from the additional line lists are indicated with "N" in Column 11 if taken from the pulsed iron–neon hollow cathode, "A" if taken from the pulsed iron–argon hollow cathode lamp. The intensities are visual estimates of the photographic density and are also given as decimal numbers, ranging from 0 to 5 for most lines. The intensity scale is different from both the lines in the FT spectra and the grating spectra lines marked with a "G." Lines marked "b" are broad, those marked "0d" are faint and diffuse and those marked "0d?" are hardly detectable from the background. Lines below 1600 Å taken from the line lists given to G. Nave by S. Johansson have uncertain intensities as they are all weak or blended. They have been assigned an intensity of "00" and indicated with "L" in Column 11.

The wavelength in Column 2 was derived from the wavenumber in Column 4 for lines taken from the FT spectra. Air wavelengths, given for lines between 2000 Å and 2 μm, were derived from the five parameter formulae in Equation (3) of Peck & Reeder (1972). The wavelengths were measured directly in the grating spectra and the wavenumbers derived from them. The corresponding one standard uncertainties in Columns 3 and 5 include contributions from the statistical uncertainty in the measurement of the position of the line and the calibration uncertainty for the spectrum. The one standard uncertainty of lines taken from grating spectra has been estimated at 0.005 Å. Ritz wavelengths and their statistical uncertainties were obtained from lopt and are given in Columns 6 and 7, respectively. The uncertainties were derived by adding the uncertainties from lopt to a global calibration uncertainty of 4 × 10⁻⁸. The classification of the line is given in Column 10, with the values of the lower and upper energy levels in Columns 8 and 9, respectively. In addition to the codes indicating the source of the data, Column 11 also indicates if there are any other identifications for the line.

Johansson (1978) obtained an estimate of 130 563 ± 10 cm⁻¹ for the ionization energy of Fe ii by using a two-parameter fit to the highest J-value levels of the lowest three 3d⁶(⁵D)ns configurations and comparing the value to similar terms in other singly ionized iron-group elements. A better estimate can be obtained by using highly excited levels that are well described by the J_cK coupling scheme.

We have used the quadrupole-polarization model of Schoenfeld et al. (1995) to obtain the ionization energy from the 3d⁶(⁵D)4f, 3d⁶(⁵D)5g, and 3d⁶(⁵D)6h levels. The outer electron in these levels is weakly bound to the core and the levels form five groups, separated by the fine structure intervals of the 3d^6 5D term of Fe iii. Within each group the levels form pairs and the energy of the center of gravity of the pairs, E(nlJ_cK), can be described by

$$\begin{eqnarray} E(nlJ_cK) &=& {\rm IE} +E(J_c)- R_{{\rm Fe}}Z_c^2\Big(1/n^2+\alpha \langle r^{-4}\rangle _{nl}\nonumber\\ && -\frac{AB}{D} Q\langle r^{-3}\rangle _{nl}\Big), \end{eqnarray} \tag{ 1 }$$

where IE is the ionization energy, E(J_c) is the energy of the $3d^6\,^5 D_{J_c}$ level in Fe iii, R_Fe is the Rydberg constant for Fe ii (109 736.248 cm⁻¹), Z_c is the effective charge of the core (2 for Fe ii), 〈r⁻³〉_nl and 〈r⁻⁴〉_nl are hydrogenic radial expectation values in atomic units given by Equations (3) and (4) of Schoenfeld et al. (1995), and A, B, and D are given by Equation (5) of Schoenfeld et al. (1995). The dipole polarizability α of the core and its quadrupole moment Q in atomic units are obtained from the experimental energy levels. By plotting E(nlJ_cK)  +  R_FeZ²_c/n²  −  E(J_c) for each configuration against R_FeZ²_c(AB/D)〈r⁻³〉_nl, a straight line of slope Q and intercept IE − αR_FeZ²_c〈r⁻⁴〉_nl is obtained. This is shown in Figure 1. The ionization energy and α can then be obtained by simultaneously solving the equations for the intercepts for pairs of configurations.

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The values of Q obtained from the slopes in Figure 1 are 0.99 ± 0.08 ea²_o (where e is the elementary charge and a_o the Bohr radius) for the 3d⁶(⁵D)4f levels, 1.05 ± 0.02 ea²_o for the 3d⁶(⁵D)5g levels, and 1.098 ± 0.008 ea²_o for the 3d⁶(⁵D)6h levels. By solving the two equations for the intercepts for the 4f and 5g levels, an ionization energy of 130 660 ± 5 cm⁻¹ is obtained with α = 17.0 ± 0.3. For the 5g and 6h levels, the ionization energy obtained is 130 655.4 ± 0.4 cm⁻¹ with α = 15.0 ± 0.2 a³_o. The 4f levels are not well described by the quadrupole-polarization model as the centers of gravity of the pairs show a large scatter around a straightline as shown in Figure 1. We thus recommend the value 130 655.4 ± 0.4 cm⁻¹ obtained from the 5g and 6h levels.

Table 4 contains 12,887 spectral lines from 13,653 transitions in Fe ii, over a factor of three more than the number of previously published lines in Fe ii. About 900 of these lines have alternate plausible identifications due to Fe i, Fe iii, Ne, Ar, or other Fe ii transitions. These lines come from a total list of about 37,000 lines. Roughly 11,500 of the lines in this total list remain unidentified, and about 460 of these lines are present in the FT spectra with an S/N > 50. About half of these strong unidentified lines are in the infrared region and are probably due to highly excited levels in Fe i or Fe ii that have yet to be identified. The uncertainties of the strongest lines in Table 4 vary from 0.0001 cm⁻¹ in the infrared to 0.001 cm⁻¹ in the ultraviolet, and are more than an order of magnitude lower than the best lines in Johansson (1978).

G. Nave thanks Craig J. Sansonetti for many invaluable discussions on wavelength calibration, spectral analysis, and on the best way to approach and present a project of this size. She also thanks Robert L. Kurucz and Alexander E. Kramida for their assistance in finding errors in the tables. James W. Brault, Richard C. M. Learner, Victor Kaufman, and Anne P. Thorne took or assisted with taking many of the spectra used in this paper. Some of these spectra are available in the National Solar Observatory digital Library (Hill & Suarez 2012). This work was partially supported by the National Aeronautics and Space Administration under the inter-agency agreement NNH10AH38I.