IMPROVED log(gf ) VALUES OF SELECTED LINES IN Mn i AND Mn ii FOR ABUNDANCE DETERMINATIONS IN FGK DWARFS AND GIANTS

This experiment, like the recent work by Blackwell-Whitehead et al. (2005c) and Blackwell-Whitehead & Bergemann (2007), relies primarily on FTS data for the measurement of emission branching fractions. The high spectral resolving power and superb wavenumber accuracy of data from FTS instruments are major advantages for branching fraction measurements in complex spectra. The broad spectral coverage, large etendue, high data collection rates, and ability to record an entire spectrum in parallel are additional advantages. As in most of our earlier work, we use data from the 1.0 m FTS at the National Solar Observatory (NSO) on Kitt Peak for Mn i and Mn ii branching fraction measurements (Brault 1976). Although we are working over relatively small spectral ranges, radiometric calibration is necessary. We rely on the calibration provided by overlapping sets of Ar i and Ar ii lines, which are internal to the Mn/Ar hollow cathode discharge (HCD) lamp spectra. The Ar line method captures the wavelength-dependent response of detectors, spectrometer optics, lamp windows, and any other components in the light path or any reflections which contribute to the detected signal (such as due to light reflecting off the back of the hollow cathode). This calibration technique is based on a comparison of well-known branching ratios for sets of Ar i and Ar ii lines widely separated in wavelength, to the intensities measured for the same lines. Sets of Ar i and Ar ii lines have been established for this purpose in the range of 4300–35000 cm⁻¹ by Adams & Whaling (1981), Danzmann & Kock (1982), Hashiguchi & Hasikuni (1985), and Whaling et al. (1993). Measurements from an echelle grating spectrometer in our lab are used to supplement and improve results from the FTS data for a few lines.

Five FTS spectra from the NSO electronic archives are used in this study.⁶ The first two of these are serial 2 and 3 recorded on 1980 September 4 using Mn/Ar HCD lamps operated at 150 mA. Spectrum 2 covers the region from 7965 to 40751 cm⁻¹ with a limit of resolution of 0.061 cm⁻¹. Spectrum 3 covers the region from 14975 to 37584 cm⁻¹ with a limit of resolution of 0.048 cm⁻¹. Both spectra have eight co-adds and both were recorded using the UV beam splitter. The Super Blue silicon photodiodes with Corning 9–54 dye filters were employed to record spectrum 2, while the midrange silicon photodiodes with CuSO₄ and WG295 filters were employed to record spectrum 3. Spectrum 3 has slightly better signal-to-noise ratio (S/N) in the visible and UV from suppression of the multiplex noise due to strong near-IR lines of Ar i, but both spectra have high S/N for all but weak lines in this study.

A series of three spectra, serial 2–4, recorded on 1985 July 22 from an inductively coupled plasma (ICP) source with the Mn content stepped from 1 to 10 to 100 ppm are also used in this study. All three spectra in this series have four co-adds and cover the region from 14886 to 36998 cm⁻¹ with a limit of resolution of 0.071 cm⁻¹. The midrange silicon photodiodes with CuSO₄ filters were employed to record the series. These ICP spectra are valuable for addressing concerns about possible optical depth errors since they cover such a large range of Mn density. These spectra do not have Ar emission lines and thus were radiometrically calibrated using another method. A calibration is established over narrow spectral regions from other archived spectra recorded a short time after the Mn spectra using the exact same FTS configuration.

The results of our FTS branching fraction measurements are given in Table 2. Each multiplet included in this study is discussed below in some detail. Table 2 also compares our branching fractions to other recent FTS measurements or to LS coupling theory. The other experiments to which we compare use similar instruments and technique but represent different sources of data than ours. Figure 2 shows the percent difference between our branching fractions and others (in the sense (others − ours)/ours) versus our branching fractions. The circled data points are weak lines (discussed below) which have been left out of the final recommended log₁₀(gf) results because of their large uncertainties. The goal is a set of branching fractions which have uncertainties <±5% with high confidence.

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The first of the Mn i multiplets in this study is the 3d⁵4s(⁷S)4d e⁸D decaying to the 3d⁵(⁶S)4s4p(³P) z⁸P in the wavelength range around 3540 Å. This multiplet is special for a number of reasons. High-spin terms in Fe-group atoms and ions often have pure, or nearly pure, LS coupling as do the upper and lower terms of this multiplet. Leading percentages of the z⁸P term in the NIST Atomic Spectra Database are listed as 100%. No percentages are listed for the e⁸D term, possibly because the term was not included in the earlier parametric study of the energy levels. An inspection of nearby levels indicates that minimal mixing of e⁸D levels is expected. The measured branching fractions are consistent with perfect LS coupling. Besides the z⁸P, the only other octet term of odd-parity below the e⁸D is the 3d⁵4s(⁷S)5p y⁸P. The energy gap between the e⁸D and y⁸P is so small that the far-IR lines of the multiplet will have completely negligible branching fractions. No earlier measurements on this multiplet were included in the NIST critical compilation of atomic transition probabilities (Martin et al. 1988). For comparison to our branching fraction measurements on this multiplet we have computed LS branching fractions with a frequency-cubed correction. This correction or scaling is equivalent to assuming that the dipole matrix elements have perfect LS values, but it has little effect since the wavelength spread of the multiplet is so small.

The e⁸D–z⁸P multiplet near 3540 Å is in a wavelength range near one of the few Mn ii multiplets accessible to ground-based astronomy near 3470 Å. This proximity is valuable since it can be used to set or check continuum levels or other wavelength dependent effects during the analysis of stellar spectra. Furthermore, there is another perfect LS multiplet, discussed below, with the same lower z⁸P term in the wavelength range around 4800 Å. Because of the common lower term, lines from these two multiplets should yield the same abundance in LTE analyses regardless of whether the Mn lower levels satisfy LTE. If the abundances do not agree, it would indicate that additional factors in line formation processes need to be considered.

The next of the Mn i multiplets in Table 2 is the resonance (E.P. = 0) 3d⁵(⁶S)4s4p(³P) z⁶P decaying to the ground 3d⁵4s² a⁶S in the wavelength range around 4030 Å. Lines of this multiplet are significantly saturated in all but the lowest metallicity stars. We have included this multiplet in our study partly because earlier lifetime measurements on z⁶P levels (Marek & Richter 1973; Marek 1975) were used to establish the absolute scale of the Oxford absorption measurements on Mn i (Blackwell & Collins 1972; Booth et al. 1984). The z⁶P levels all have one dominant, >0.90, branch to the ground a⁶S level, and weak branches to the 3d⁶(⁵D)4s a⁶D in the IR. These weak IR branches near 13000 Å were not measured in the Oxford lab study, but their strength was assessed using Solar spectra. Booth et al. found that the near-IR branching fractions from the z⁶P J = 7/2 level total about 0.03. This contribution is consistent with frequency-cubed scaling of the Einstein A-coefficients assuming similar dipole matrix elements for the z⁶P–a⁶D and z⁶P–a⁶S multiplets. It is actually rather difficult to directly measure the branching fractions of the near-IR lines, because they fall beyond the limit of Si detectors and there are no ''bridge lines'' from the same upper levels in the red. Bridge lines in this case would be used to connect the intensity calibration of two spectra recorded using a Si detector and an InGaAs detector. There is a long tradition of finding transition probabilities from lines in the solar spectrum (e.g., Thevenin 1989, 1990). The Solar method is generally not as accurate as modern lab methods due to a variety of effects, but in the case of these near-IR lines very accurate measurements are not needed. Even if one assumes a large fractional uncertainty for the estimate of the IR branching fractions, 0.03 ± 0.02, the final uncertainty of the log(gf) values of the dominant resonance z⁶P–a⁶S multiplet is scarcely affected, since it is still about ±3% or 0.014 dex from the lifetime measurements.

The next Mn i multiplet in this study is the 3d⁶(⁵D)4p z⁶D decaying to the 3d⁶(⁵D)4s a⁶D in the wavelength range around 4050 Å. The lower a⁶D term has pure LS coupling according to the NIST Atomic Spectra Database,⁷ but the upper z⁶D term is somewhat mixed with a higher ⁶D term. The most important comparison of our new measurements is against recent branching fraction measurements by Blackwell-Whitehead et al. (2005c) and Blackwell-Whitehead & Bergemann (2007) from FTS data. Blackwell-Whitehead et al. (2005c, 2007) included comparisons of their work to older measurements by Blackwell & Collins (1972), Booth et al. (1984), and Woodgate (1966) which will not be repeated here. We note that a small (0.003) residual correction for spin-forbidden lines has been made to our branching fractions based in part on measurements by Blackwell-Whitehead et al. This correction is less than one-tenth of the lifetime uncertainty and thus has little effect on our final transition probabilities. The comparison in Table 2 reveals generally very good agreement. Table 2 includes the original Blackwell-Whitehead et al. (2005c) branching fractions from z⁶D J = 7/2 level which we believe to be correct, and not the results listed by Blackwell-Whitehead & Bergemann (2007) which appear to have branching fraction values transposed for the lines at 4018 Å and 4083 Å. The branching fraction measurement of the weakest line at 4068 Å of this multiplet from the z⁶D J = 3/2 level is affected by blending with an unknown Mn line in our spectra. This blend was separated by fitting the line profile to the known hyperfine structure pattern, but the result is not highly reliable. The line at 4068 Å is too weak for most abundance studies. Our effort to measure this weak line was motivated by the desire to get accurate branching fractions for the other lines from the common upper level. The uncertainties on the branching fraction measurements by Blackwell-Whitehead et al. (2005c) appear to be overly pessimistic for a dominant multiplet with a small wavelength spread. Conversely, the four digit branching fractions reported by Blackwell-Whitehead & Bergemann (2007) suggest an overly optimistic uncertainty, but the four digits were likely included to avoid rounding errors in the transition probability determination. We suggest that both of these sets of branching fractions from FTS measurements have uncertainties similar to our FTS measurements.

Next we consider the upper 3d⁶(⁵D)4p z⁴F term decaying to the 3d⁶(⁵D)4s a⁴D around 4750 Å, which is the dominant multiplet from this upper term, and the same upper term decaying to the 3d⁵4s² a⁴G around 5200 Å. This upper term decays via some weak, spin-forbidden, UV branches which we measured, but dropped from Table 2. Simple LS theory is not applicable to either spin-allowed multiplet from this upper term, but there are recent FTS measurements of the branching fractions by Blackwell-Whitehead & Bergemann (2007). Generally there is very good agreement between our branching fraction measurements and those by Blackwell-Whitehead & Bergemann. The exceptions are some weak branches, <0.1, and the very weak branches, <0.01. There is no obvious explanation for the disagreement between our measurements and Blackwell-Whitehead & Bergemann's measurements on the weak branches at 5255 Å and 4701 Å. Because the differences are −5.8% and +11.5% for these two weak branches using ours as the reference, it is unlikely that optical depth problems in one experiment were the cause, else the differences would be both positive or both negative. Similarly, the differences on the very weak branches at 5260 Å, 5197 Å, and 5149 Å, which are −25%, −15%, and +17% respectively, show both positive and negative deviations. Very weak branches tend to have poor S/N in FTS data and are more vulnerable to hidden blends than stronger branches. Poisson statistical noise from all lines is multiplexed or evenly distributed throughout an FTS spectrum. These very weak lines have such poor S/N in our FTS data that we performed additional measurements using an echelle grating spectrometer equipped with a detector array. A dispersive spectrometer has an advantage over an FTS for measurements on very weak lines, since the multiplex noise is suppressed. Even with additional echelle measurements we were not able to achieve agreement with Blackwell-Whitehead & Bergemann's measurements on the very weak lines.

The next of the Mn i multiplets in Table 2 is the 3d⁵4s(⁷S)5s e⁸S decaying to the 3d⁵(⁶S)4s4p(³P) z⁸P multiplet in the wavelength range around 4800 Å. The upper and lower terms of this multiplet are both perfect LS terms as is common for high-spin terms in the Fe-group. Our branching fraction measurements, recent FTS measurements by Blackwell-Whitehead & Bergemann (2007), earlier absorption measurements by Booth et al. (1984), and LS calculations are all in agreement.

The next multiplet of this study is 3d⁵4s(⁷S)5s e⁶S decaying to 3d⁵(⁶S)4s4p(³P) z⁶P in the wavelength range around 6020 Å. The upper and lower terms of this multiplet are nearly pure LS terms according to the NIST Atomic Spectra Database.⁷ We have adjusted our branching fractions for the weak (total branching fraction <0.038) IR multiplet near 17600 Å from the e⁶S upper term to the 3d⁵(⁶S)4s4p(¹P) y⁶P term as reported by Blackwell-Whitehead & Bergemann (2007). An assumption of similar dipole matrix elements for both multiplets with the usual frequency-cubed scaling leads to an estimate that the IR multiplet should be about 25–30 times weaker than the red multiplet. Uncertainty in branching fractions of the IR multiplet contributes little to the final uncertainty of transition probabilities for the red multiplet which is dominated by the ±3% or 0.014 dex lifetime uncertainty. This multiplet with a relatively high E.P., ∼3 eV, is ideal for Mn abundance determinations in high metallicity stars (Sobeck et al 2006).

The two Mn ii multiplets decaying from the 3d⁵(⁶S)4p z⁵P appear next in Table 2, organized by upper level. This term decays primarily to the 3d⁵(⁶S)4s a⁵S in the wavelength range near 2940 Å, with weaker branches to 3d⁶ a⁵D in the wavelength range near 3470 Å. This situation places special requirements on branching fraction measurements. The weaker of these two multiplets, which is the one accessible to ground-based astronomy, is sensitive to optical depth errors as well as possible radiometric calibration errors. Fortunately, there has recently been some high quality work on both multiplets by Kling & Griesmann (2000). Kling & Griesmann were careful to measure and eliminate optical depth errors in their study, and they used several independent radiometric calibrations. Uncertainties on their branching fractions in Table 2 were reconstructed from uncertainties on their final transition probabilities and radiative lifetimes. We made use of the sequence of ICP spectra with the Mn content stepped by factors of 10 to verify that optical depth effects were under control in our work. Our measurements confirm the branching fraction measurements by Kling & Griesmann as shown in Table 2. Furthermore, the relative strength of lines inside the 3d⁵(⁶S)4p z⁵P–3d⁶ a⁵D multiplet are consistent with LS branching fractions. This is not surprising, but it provides additional confidence. The relative strength of the 3d⁵(⁶S)4p z⁵P–3d⁵(⁶S)4s a⁵S to the 3d⁵(⁶S)4p z⁵P–3d⁶ a⁵D multiplet is the same for all upper levels in the 3d⁵(⁶S)4p z⁵P term, which is also reassuring. The LS calculations in Table 2 used a single adjustable parameter of 2.58 for the ratio of the dipole matrix elements squared for the 3d⁵(⁶S)4p z⁵P–3d⁵(⁶S)4s a⁵S to the 3d⁵(⁶S)4p z⁵P–3d⁶ a⁵D multiplet, and reproduced the measurements quite well. Finally, we note that measurements by Kling & Griesmann on the weak spin-forbidden 3d⁵(⁶S)4p z⁵P–3d⁵(⁶S)4s a⁷S lines from the z⁵P J = 3 and 2 levels were used to adjust our branching fractions. These deep UV lines around 2300 Å have such small branching fractions, 0.0060 ± 0.0006 and 0.0035 ± 0.0009 for the upper z⁵P J = 3 and 2 levels, respectively, that they have almost no effect on the final uncertainty of the important 3d⁵(⁶S)4p z⁵P–3d⁶ a⁵D multiplet.

The Mn ii multiplet from the 3d⁵(⁶S)4p z⁷P term decaying to the ground 3d⁵(⁶S) 4s a⁷S in the wavelength range near 2590 Å is the last multiplet of Table 2. These resonance lines have branching fractions >0.997. Kling & Griesmann (2000) were able to measure two very weak spin-forbidden branches from the z⁷P₃ to the a⁵S and a⁵D terms as well as two similar very weak spin-forbidden branches from the z⁷P₂. We observed the very strong resonance multiplet and the very weak spin-forbidden branches. Unfortunately we were not able to get satisfactory measurements on the very weak branches due to both calibration and optical depth problems. In consideration of the very high purity of the low septet levels, we have adopted Kling & Griesmann's branching fractions for the resonance lines. Kling & Griesmann's branching fraction uncertainties of less than 0.1% for the resonance lines contribute almost nothing to the uncertainty of the transition probabilities for the resonance multiplet due to radiative lifetime uncertainties in the 2%–3% range.

In this section, we summarize the averaging of our data with other FTS data and in some cases LS theoretical values to arrive at the final recommended branching fractions presented in the last column of Table 2. Our recommended branching fractions for e⁸D decaying to the z⁸P multiplet are an unweighted average of our FTS measurements and LS theoretical values. Inclusion of the LS theoretical values has little effect except on the weakest line of the multiplet. The averaged value for the weak 3570 Å line differs from our FTS measurement by <4%. We recommend using 0.970 branching fraction for all three lines of the resonance z⁶P decaying to the a⁶S multiplet. This result is primarily from Booth et al. (1984) observations on the weak IR branches near 13000 Å from the upper z⁶P levels. Recommended branching fractions for the Mn i z⁶D decaying to the a⁶D, z⁴F decaying to the a⁴D, z⁴F decaying to the a⁴G, e⁸S decaying to the z⁸P, and e⁶S decaying to the z⁶P multiplets are unweighted averages of our FTS measurements with Blackwell-Whitehead et al. (2005c) or Blackwell-Whitehead & Bergemann (2007) FTS measurements. We note that the latter two of these are pure LS multiplets. We recommend using unweighted averages of our FTS measurements with Kling & Griesmann (2000) FTS measurements on the z⁵P decaying to the a⁵D and a⁵S multiplets of Mn ii. As mentioned above we are also using Kling & Griesmann FTS branching fractions for the z⁷P decaying to the a⁷S resonance multiplet of Mn ii, but the branching fractions are scarcely different from 1.000 for these resonance lines.

Our log₁₀(gf) values, as well as recommended log₁₀(gf) values, are presented in machine-readable form in Table 3. The recommended values are calculated from the recommended lifetimes of Table 1 and recommended branching fractions of Table 2. Table 3 also contains a comparison to the log₁₀(gf) values of Blackwell-Whitehead et al. (2005c). In that work, they reported both radiative lifetimes and branching fractions, to produce log₁₀(gf)'s completely independent of other sources. The other works referenced in Table 2 normalized to radiative lifetimes from other sources and are not compared in Table 3. The weak and very weak branches from the z⁴F term and one blended line from the z⁶D_3/2 level are omitted from the log₁₀(gf) list. The branching fractions for these lines have large uncertainties and there are significant differences between Blackwell-Whitehead & Bergemann's (2007) and our measurements. The remaining values are accurate to ±0.02 dex with high or "2σ" confidence. It is always difficult to distinguish between "1σ" and "2σ" uncertainties for measurements dominated by systematic errors. Nevertheless, we argue that it is quite unlikely that any of the listed log₁₀(gf) values are in error by more than 0.02 dex.