Improved V II log( gf ) Values, Hyperfine Structure Constants, and Abundance Determinations in the Photospheres of the Sun and Metal-poor Star HD 84937
M. P. Wood, J. E. Lawler, E. A. Den Hartog, C. Sneden, J. J. Cowan
IIMPROVED V II log(gf) VALUES, HYPERFINE STRUCTURE CONSTANTS, AND ABUNDANCE DETERMINATIONS IN THE PHOTOSPHERES OF THE SUN AND METAL-POOR STAR HD 84937 M. P. Wood , J. E. Lawler , E. A. Den Hartog , C. Sneden , and J. J. Cowan Department of Physics, University of Wisconsin, Madison, WI 53706; [email protected], [email protected], [email protected] Department of Astronomy and McDonald Observatory, University of Texas, Austin, TX 78712; [email protected] Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019; [email protected] BSTRACT New experimental absolute atomic transition probabilities are reported for 203 lines of V II . Branching fractions are measured from spectra recorded using a Fourier transform spectrometer and an echelle spectrometer. The branching fractions are normalized with radiative lifetime measurements to determine the new transition probabilities. Generally good agreement is found between this work and previously reported V II transition probabilities. Use of two spectrometers, independent radiometric calibration methods, and independent data analysis routines enables a reduction in systematic uncertainties, in particular those due to optical depth errors. In addition, new hyperfine structure constants are measured for selected levels by least squares fitting line profiles in the FTS spectra. The new V II data are applied to high resolution visible and UV spectra of the Sun and metal-poor star HD 84937 to determine new, more accurate V abundances. Lines covering a range of wavelength and excitation potential are used to search for non-LTE effects. Very good agreement is found between our new solar photospheric V abundance, log ε (V) = 3.95 from 15 V II lines, and the solar-system meteoritic value. In HD 84937, we derive [V/H] = -2.08 from 68 lines, leading to a value of [V/Fe] = 0.24. . INTRODUCTION Stellar abundances, particularly their trends as a function of metallicity, are tests for models of nucelosynthesis and provide valuable information regarding the evolution of chemical elements in the Galaxy. Abundances in old, metal-poor stars are especially valuable since they represent the “fossil-record” of nucleosynthesis in the earliest generations of stars. Studies of metal-poor stars have found large and unexpected iron (Fe)-group abundance trends (McWilliam et al. 1995a, 1995b, McWilliam 1997, Westin et al. 2000, Cowan et al. 2002, Sneden et al. 2003, Cayrel et al. 2004, Barklem et al. 2005, Lai et al. 2008, Bonifacio et al. 2009, Roederer 2009, Suda et al. 2011, Yong et al. 2013) which have thus far refused explanation using current models of early Galactic supernova yields. These relative Fe-group abundance trends can cover ±1 dex for metallicities ranging from solar ([Fe/H] ≡
0) to -4 (e.g. Figure 12 of McWilliam 1997) . It may be that these unexpected trends represent a failure for models for nucleosynthesis in the early Galaxy. However, these trends may also indicate the breakdown of standard abundance derivation techniques in low metallicity stars, or they may result from inaccurate laboratory atomic data. Fairly comprehensive databases of atomic transition probabilities exist (e.g. NIST Atomic Spectra Database and Vienna Atomic Line Database ). These are of utmost importance for stellar abundance determinations. To obtain the most accurate abundances it is crucial to use lines that are unsaturated in the photosphere of the star being investigated. For studies covering a wide metallicity range, this requirement necessitates the use of many lines covering a range of excitation potential (E.P.) and log( gf ) values, which introduces the possibility that inaccurate laboratory atomic data are affecting the measured abundances. In the We adopt standard spectroscopic notations. For elements X and Y, the relative abundances are written [X/Y] = log (N X /N Y ) star – log (N X /N Y ) ⊙ . For element X, the “absolute” abundance is written log ε (X) = log (N X /N H ) + 12. Metallicity is defined as the [Fe/H] value. hotospheres of stars of interest, neutral atoms (first spectra) are a minor ionization stage while singly ionized atoms (second spectra) represent the dominant ionization stage. Therefore, in order to avoid saturation in higher metallicity stars, one makes use of weak first spectra lines that arise from high E.P. levels. In lower metallicity stars, however, one must change to stronger lines with lower E.P. values, and assuming suitable second spectra lines exist in the observed spectra, singly ionized lines become important as well. The strength of these high and low E.P. lines can vary by orders of magnitude, making it rather difficult to measure both with small uncertainties in the same laboratory spectra. If the laboratory atomic data are not at fault, the unexpected Fe-group abundance trends might result from the failure of 1D/LTE (one-dimensional/local thermodynamic equilibrium) approximations traditionally incorporated into photospheric models used for abundance determinations in metal-poor stars of interest (e.g. Asplund 2005). Giant stars are favored in studies of metal-poor stars to provide large photon fluxes for high signal-to-noise (S/N), high-resolution spectra. The combination of low-density atmospheres and reduced electron pressure from a lower metal content leads to lower collision rates in metal-poor giant stars, which may result in departures from LTE. The two possible explanations described above for the unexpected trends can be investigated with expanded and more accurate experimental Fe-group transition probabilities. One approach to determine if the trends result from 3D/non-LTE effects is to search for anomalous abundance measurements from various lines covering a range of E.P., log( gf ), and wavelength for a wide range of stellar types. If improved atomic data and targeted searches for 3D/non-LTE effects fail to eliminate the observed Fe-group abundance trends, it would provide evidence that nucleosynthetic models for the early Galaxy are incomplete and need to be reexamined. ur group has an effort underway to expand sets of transition probabilities and reduce transition probability uncertainties for Fe-group lines. Den Hartog et al. (2011) focuses on selected multiplets in Mn I and Mn II that cover small wavelength ranges and/or are Russell Saunders (LS) multiplets. Given these benefits, it is possible to reduce the Mn transition probability uncertainties to 0.02 dex with 2 σ confidence. Such small uncertainties are practical only under favorable conditions and in general and difficult to achieve. A broader approach is taken in the recent work on Ti I (Lawler et al. 2013), Ti II (Wood et al. 2013), and Ni I (Wood et al. 2014) by attempting measurements on every possible line connecting to upper levels with previously reported radiative lifetimes. This results in a larger set of transition probability measurements, though often with higher uncertainties (0.02 to ~0.10 dex). However, small (~0.02 dex) uncertainties, such as those reported by Den Hartog et al. (2011), are not necessary for the detection of non-LTE effects in metal-poor stars. Mn I resonance lines connected to the ground level show non-LTE effects of 0.5 to 1 dex (Sobeck et al. 2014, in preparation). The V II study reported herein follows the broad approach previously used for Ti I , Ti II , and Ni I by attempting transition probability measurements for all lines connected to the 31 odd-parity upper levels with laser induced fluorescence (LIF) lifetime measurements by Den Hartog et al. (2014), plus an additional odd-parity upper level with a previously reported lifetime (Biémont et al. 1989, Xu et al 2006). The result is a set of 203 transition probabilities covering a wide range of E.P., log( gf ), and wavelength. Uncertainties range from 0.02 dex for dominant branches, primarily determined by the LIF lifetime uncertainties, to ~0.12 dex for weak branches widely separated in wavelength from the dominant branch(es). The uncertainties on weak branches, which are often the most important for accurate abundance measurements, primarily result from S/N effects, uncertainty in the radiometric calibration, or both. The use of both a ourier transform spectrometer (FTS) and an echelle spectrometer, with independent radiometric calibrations, serves to reduce systematic uncertainties on weak line measurements. In Section 2 and Section 3 we describe the spectra recorded using the FTS and echelle spectrometer, and in Section 4 we discuss the determination of V II branching fractions from these spectra. In Section 5 we present new absolute transition probabilities with comparisons to previous results in the literature. In Section 6 new hyperfine structure (HFS) constants and component patterns derived from our FTS spectra are introduce. We apply the new V II data to determine the photospheric V abundance of the Sun in Section 7 and metal-poor star HD 84937 in Section 8. 2. FOURIER TRANSFORM SPECTROMETER DATA This V II transition probability study makes use of archived FTS data from the 1.0 m FTS previously at the National Solar Observatory (NSO) on Kitt Peak. The NSO 1.0 m FTS has a large etendue (like all interferometric spectrometers), a resolution limit as small as 0.01 cm -1 , wavenumber accuracy to 1 part in 10 , broad spectral coverage from the near ultraviolet (UV) to infrared (IR), and a high data collection rate (Brault 1976). Unfortunately the NSO FTS has been dismantled, and while there are plans to restore it to full operational status at a university laboratory, it is currently unavailable to guest observers. Table 1 lists the 13 FTS spectra used in this V II branching fraction study. All spectra, raw interferograms, and header files are available in the NSO electronic archives. Multiple FTS spectra are needed to determine high-quality branching fractions. Optimum sensitivity is achieved for different spectral ranges using various beam splitter, filter, and detector combinations. Although branching fractions are determined mainly from spectra Available at http://nsokp.nso.edu/. btained with lamps having an Ar gas fill, additional spectra are needed from lamps with a Ne buffer gas to allow for the correction of blends between V and Ar lines. In addition, spectra are needed with the lamp operating over a range of current. Overlapping visible-UV and IR spectra of the lamps operating at high current are needed for high S/N measurements on very weak branches to all known lower levels. Conversely, one also needs visible-UV spectra of the lamps operating at low currents in which the dominant branches are optically thin. Optical depth errors can still be present even for the lowest current FTS spectra used in this study, and these concerns are addressed using the echelle spectrometer as described in Section 3. A relative radiometric calibration of the FTS spectra is essential for the measurement of accurate emission branching fractions. As in our past branching fraction studies we make use of the Ar I and Ar II line calibration technique. Sets of well-known branching ratios for Ar I and Ar II lines have been established for this purpose in the 4300 - 35000 cm -1 range by Adams & Whaling (1981), Danzmann & Kock (1982), Hashiguchi & Hasikuni (1985), and Whaling et al. (1993). Intensities for these lines are measured and compared to known branching ratios in order to construct a relative radiometric calibration. This technique is internal to the HCD lamp and captures the wavelength-dependent response of the detectors, spectrometer optics, lamp windows, and any reflections which contribute to the measured signal. As described in the next Section, the use of an echelle spectrometer allows us to extend the branching fraction measurements beyond 35000 cm -1 . 3. ECHELLE SPECTROMETER DATA As mentioned in the previous section, one motivation for the construction of an echelle spectrometer at the University of Wisconsin is the closure of the NSO 1.0 m FTS. A further otivation is the need to reduce optical depth errors as a source of systematic uncertainty in branching fraction measurements, especially on weak lines. FTS instruments suffer from inherent multiplex noise, in which quantum statistical (Poisson) noise from all spectral features, particularly strong visible and near-IR branches, is smoothly redistributed throughout the entire spectrum. This can be a hindrance when measuring the weak UV transitions that are typically the most important for accurate Fe-group abundance determinations. Often, as the lamp current is reduced, the weak lines become comparable to the multiplex noise before the dominant branch(es) from the common upper level are optically thin. The dispersive echelle spectrometer is free from multiplex noise and provides adequate S/N on these astrophysically important weak lines even at very low lamp current, reducing the possibility of optical depth errors. The new spectrometer incorporates a 3.0 m focal length grating spectrograph with a large (128 × 254 mm ruled area), coarse (23.2 grooves mm -1 ) echelle grating with a 63.5° blaze angle. Attached to the spectrograph is a custom 0.5 m focal length orthogonal order separator, which generates and images a 2D spectrum onto a large UV-sensitive CCD array while also serving to compensate aberrations in the spectrograph. The echelle spectrometer has a resolving power of 250,000, broad wavelength coverage, and superb UV sensitivity. While the echelle spectrometer has lower resolution and wavenumber precision compared to a FTS, it has the main advantage of being free from multiplex noise. This allows us to record spectra of commercial sealed hollow cathode discharge (HCD) lamps operating at very low currents, in order to eliminate optical depth errors, while still being able to detect weak lines with adequate S/N. Two HCD lamps are used, one each with Ar and Ne buffer gases, to check for and eliminate possible blends. A more detailed description of the echelle spectrometer, including a thorough aberration analysis, is presented by Wood & Lawler (2012). In addition to the 13 FTS spectra listed in Table 1, the 75 CCD frames of echelle spectrometer spectra listed in Table 2 are also part of this V II transition probability study. These spectra are radiometrically calibrated using the UV continuum from a NIST-traceable D standard lamp. This lamp is periodically checked against a NIST-calibrated Ar mini-arc to ensure an accurate UV calibration. The use of standard lamps to calibrate a FTS is often difficult due to ghosts, and we instead rely upon the calibration method described in Section 2, but it is our preferred method for calibrating the echelle spectrometer. The use of a D standard lamp also enables branching fraction measurements to wavelengths shorter than that allowed using the Ar I and Ar II branching ratio technique since the standard lamp is calibrated to 2000 Å. 4. V II BRANCHING FRACTIONS All possible transitions wavenumbers between known energy levels of V II from Thorne et al. (2013) that satisfy both the parity change and | Δ J| ≤ and are unimportant for stellar abundance studies. These two selection rules are obeyed throughout the periodic table whereas many important Fe-group transitions violate the Δ S = 0 and | Δ L| ≤ -1 , which has previously reported lifetime measurements from Biémont et al. (1989) and Xu et al. (2006). As in our previous ork, thousands of possible spectral line observations are analyzed in both FTS and echelle spectra to calculate the branching fractions. Integration limits and non-zero baselines are set “interactively” during data analysis. Non-zero baselines are necessary for the echelle spectra, which are not background corrected, and are occasionally needed for the FTS spectra when a line falls on the wing of a dominant feature. A simple numerical integration technique is used to determine un-calibrated V II line intensities. This method is preferred since the majority of V II lines have unresolved hyperfine structure that leads to variations in the observed line width. For consistency, this method is also applied to lines with partially resolved hyperfine structure. This same integration technique is also used on selected Ar I and Ar II lines to establish a relative radiometric calibration of the FTS spectra. Branching fraction uncertainties depend on the S/N of the data, the line strengths, and the wavelength separation of lines from a common upper level. Branching fraction uncertainty always migrates to the weakest lines because branching fractions sum to 1.0 by definition. Uncertainties on weak lines near the dominant branch(es) from the common upper level tend to be limited by S/N. For lines that are widely separated in wavelength from the dominant branch(es), systematic errors in the radiometric calibration tend to be the dominant source of uncertainty. The systematic uncertainty in the calibration is estimated using the product of 0.001%/cm -1 and the wavenumber difference between the line of interest and the dominant branch from the common upper level, as presented and tested by Wickliffe et al. (2000). The calibration uncertainty is combined with the standard deviation of measurements from multiple spectra to determine the total branching fraction uncertainty. The final uncertainty, especially for lines widely separated from the dominant branch(es) from a common upper level, is primarily systematic and it is therefore impractical to state whether it represents 1 σ or 2 σ error bars. The ombination of data from both the FTS and echelle spectrometer, which make use of independent radiometric calibration methods, is important in assessing and controlling systematic uncertainties. 5. V II TRANSITION PROBABILITIES AND COMPARISON TO EARLIER MEASUREMENTS Absolute transition probability measurements are given for 203 lines of V II in Table 3. Branching fraction measurements from a combination of FTS and echelle data are normalized with published LIF radiative lifetimes (Den Hartog et al. 2014) to determine the transition probabilities. Air wavelengths in the table are computed from V II energy levels (Thorne et al. 2013) using the standard index of air (Peck & Reeder 1972). Often lines must be omitted if they are too weak to have reliable S/N, have uncertain classifications, or are too seriously blended to be separated. The effect of these problem lines can be seen by summing all transition probabilities for a given upper level in Table 3 and comparing the sum to the inverse upper level lifetime (Den Hartog et al. 2014). The sum is typically > 90% of the inverse level lifetime. While these problem lines have large fractional uncertainty in their branching fractions, this does not have a significant effect on the uncertainties of the lines kept in Table 3. The transition probability uncertainties quoted in Table 3 are found by combining branching fraction uncertainties and radiative lifetime uncertainties in quadrature. Figures 1-3 compare our new V II transition probability data to the NIST Atomic Spectra Database as of 2014 June 11 (Kramida et al. 2013; see footnote 2). The figures are distinguished by the accuracy ratings assigned to each value in the database. Figure 1 is a comparison of 62 og( gf ) values in common to this work and to NIST database values with a “B” ( ≤ gf ) value reported in this study in the lower panel (b). Individual error bars on the log( gf ) differences represent the uncertainties on measurements from this work. The central solid line represents perfect agreement at a logarithmic difference of zero, while the grey dotted lines represent ±10% differences in f -values. Figure 2 is a comparison of 19 lines in common between this work and the NIST database having accuracy grades of “C+” ( ≤ ≤ gf ) value reported in this study in the lower panel (b). The error bars and central solid line have the same meaning as in Figure 1, while the grey dotted lines represent ±25% differences in f -values. Karamatskos et al. (1986) are cited as the source of the “B”, “C+”, and “C” rated data in the NIST database. Similarly to this work, those authors used a combination of LIF lifetimes and emission branching fractions to determine their transition probabilities. Aside from a few outliers, the majority of lines agree within combined uncertainties. The slight dip in Figure 1a for lines near 3550 Å was observed previously by Biémont et al. (1989), who suggested it results from an incorrect calibration of the FTS spectra used by Karamatskos et al. A comparison of 15 log( gf ) values in common to this work and the NIST database with accuracy grades of “D” ( ≤ gf ) value measured in this work in the lower panel (b). The error bars and central solid line have the same meaning as in Figure 1, whereas the grey dotted lines represent ±50% differences in f -values. Both the work of Wujec & Musielok (1986) and the earlier work of Roberts et al. (1973) are cited as the sources of the “D” rated values in the NIST database. Roberts et al. determined their log( gf ) values from a combination of lifetimes measured using the eam-foil technique with branching fractions measured from an arc discharge. Wujec & Musielok (1986) also performed branching fraction measurements using an arc discharge, with some log( gf ) values determined using the Roberts et al. lifetimes, while other values were determined using a Boltzmann analysis to set relative log( gf ) values on an absolute scale. The agreement between this work and previous measurements is not as good as in Figures 1-2. The overall trend of higher log( gf ) values in this work can be explained by our use of the new LIF lifetime measurements of Den Hartog et al. (2014), which in many cases are lower than the lifetimes of Roberts et al. Biémont et al. (1989) noted that the beam-foil lifetimes of Roberts et al. are long by as much as a factor of two, which they attribute to the possibility of cascading transitions in the beam-foil excitation. In addition, the tendency for stronger lines to be enhanced compared to weaker lines, as seen in Figure 3b, is evidence for optical depth errors in the earlier measurements. This current work makes use of a new echelle spectrometer which was specifically developed to address optical depth concerns in transition probability measurements. Figure 4 is a comparison of log( gf ) values for 137 lines in common to this work and the work of Biémont et al. (1989), plotted as a function of wavelength in the upper panel (a) and the log( gf ) value measured in this work in the lower panel (b). The solid line represents perfect agreement at a logarithmic difference of 0, while the error bars represent the uncertainty reported by Biémont et al. (1989) and the uncertainty reported herein combined in quadrature. Similarly to this work, Biémont et al. used a combination of LIF radiative lifetimes and emission branching fractions from FTS spectra to determine the majority of their transition probabilities. Transition probabilities for two additional levels were measured by interpolating upper level populations in an inductively-coupled plasma source. While six of the LIF lifetimes were new measurements (including the lifetime value utilized in this study for the 39403.787 cm -1 upper evel), Biémont et al. also utilized earlier lifetime measurements from Karamatskos et al. (1986). As in this work, spectra were recording using the NSO 1.0 m FTS, and as such there is some overlap in the FTS spectra used by Biémont et al. and in this work (e.g., Index II HYPERFINE STRUCUTRE CONSTANTS Vanadium is essentially monoisotopic, with V being the only naturally occurring stable isotope, and therefore isotope shifts are unimportant for this study. However, since V has a non-zero nuclear spin (I = 7/2), hyperfine structure (HFS) leads to a broadening of many V II transitions observed in this study. Several V II levels have previously reported experimental HFS A constants. Arvidsson (2003) measured 26 A constants using least squares fitting of HFS patterns in two FTS spectra, one recorded using the NSO 1.0 m FTS (likely V is nearly stable, with a half-life of ~10 years. However, its solar-system abundance is only 0.25%, entirely negligible for this study. nd an additional FTS spectrum, recorded at Lund University, to capture the deep UV. More recently, Armstrong et al. (2011) published a set of 55 high accuracy HFS A constants from LIF measurements made using a single-frequency laser on a beam of V II atoms. Similarly to Arvidsson (2003), in this work we use least squares fitting of V II line profiles in order to determine new HFS A constants. We make use of the Casimir formula, as presented in the text by Woodgate (1980), )12()12( )1()1(4)1(382 −− ++−++=Δ JJII JJIIKKBKAE , where Δ E is the wavenumber shift of an HFS sublevel ( F , J ) from the center of gravity of the fine-structure level ( J ), )1()1()1( +−+−+= IIJJFFK , F is the total atomic angular momentum, J is the total electronic angular momentum, and I is the nuclear spin. Unfortunately the FTS spectra we utilize do not have adequate resolution or S/N, or both, in order to determine any HFS B constants, and therefore we neglect the electric quadrupole interaction term in determining the energy shifts. For this same reason, rather than taking a broad approach and measuring as many new HFS A constants as possible, we instead target transitions which are used in either the abundance analyses of the Sun (Section 7) or HD 84937 (Section 8). We choose to focus on lines that are broadened and/or show HFS in our FTS spectra and cause a non-negligible amount of broadening in the solar and stellar spectra, as we are able to obtain the most reliable results for these lines. For these transitions, we start by using the LIF measurements of Armstrong et al. (2011) to fix either the upper or lower level HFS A constant, and then nonlinear least-squares fit the observed HFS pattern in order to determine the HFS A constant for the other level. By fixing these newly measured HFS A constants, we can then proceed to fit HFS patterns for transitions which have neither an upper or lower LIF HFS onstant measurement. In addition to the HFS A constants of the upper or lower level, the fitting parameters include the center of gravity wavenumber, the total intensity of the line, and one line-profile parameter which represents the convolution of the instrumental sinc function with a variable-temperature Doppler-broadened Gaussian function. Table 4 lists 21 new magnetic dipole HFS A constants measured in this study. These values are determined from a S/N weighted mean of HFS pattern fits in four FTS spectra ( A constants from Armstrong et al. are not listed in Table 4, they did serve as reference values in our study due to the high spectral resolution and S/N of their single frequency laser measurements. For the level at 2605.040 cm -1 , the agreement is significantly worse, with our new result having almost equal magnitude but opposite sign to that reported by Arvidsson (2003). However, the value presented here is reinforced by new theoretical relativistic configuration interaction calculations from Beck & Abdalmoneam (2014). Using the LIF HFS measurements of Armstrong et al. (2011) in combination with the new HFS A constants from Table 4, HFS component patterns for selected lines used in the solar and/or HD 84973 V II abundance determinations are listed in Table 5. Several patterns listed in Table 5 connect to the ground term, even though these levels have no previously reported HFS A constants and are not included in Table 4. While we are unable to reliably measure the HFS constants for these levels, we conclude from the FTS spectra that they are small, and for the purposes of Table 5 the HFS A onstants for levels in the ground term have been set to zero. Individual energy shifts are calculated using the Casimir formula quoted above and the component strengths are normalized to sum to unity. Given the relatively large error bars on some of the newly measured HFS A constants listed in Table 4, we choose not to attempt HFS pattern determinations on lines which are not needed in the abundance analyses presented in Section 7 and Section 8. Therefore we caution that Table 5 is not meant to be an exhaustive list of lines with measurable HFS in V II , and there may be other lines with detectable HFS broadening. 7. THE VANADIUM ABUNDANCE IN THE SOLAR PHOTOSPHERE We apply our new V II transition probability and HFS data to produce a new V abundance for the solar photosphere. We follow the techniques described in our previous studies of Fe-group species: Ti I (Lawler et al. 2013), Ti II (Wood et al. 2013), and Ni I (Wood et al. 2014). Since we employ synthetic spectrum analyses for each feature, substitution of full sets of HFS components for individual lines is straightforward; see Lawler et al. (2001a, 2001b) for previous examples of this procedure. In our Ni I study (Wood et al. 2014) we included the effects of isotopic wavelength shifts in our solar abundance determinations, but with only one naturally-occurring stable isotope ( V), isotopic shifts are irrelevant here. However, whereas HFS was unimportant in our Ni I study, it must be incorporated into our abundance analysis here. To begin, as in our previous papers, we estimate approximate V II absorption transition strengths with the simple formula, STR ≡ log( gf ) − θχ with the log( gf ) values given in Table 3, excitation energies χ (eV), and inverse temperature θ = 5040/T (we assume θ = 1.0 for this rough calculation). The STR values are plotted as a function f wavelength in Figure 5. Red circles call attention to those lines that we use in the solar abundance computations (see below). These relative strengths apply only to V II because they include neither Saha ionization factors (which could allow comparison to other vanadium species) nor the vanadium solar abundance (which could allow comparison to other elements). They do, however, indicate the relative line strengths for V II lines. In Figure 5, the horizontal line at STR = –4.1 indicates the strengths of V II lines that lie at the approximate weak-line limit of features that are useful in a solar abundance analysis. Expressing the line equivalent width EW as log of the reduced width log( RW ) = log( EW / λ ), the weak-line limit is approximately log( RW ) ~ –6. For Figure 5 the corresponding weak-line strength of –4.1 is determined empirically, by measuring the EW s of the weakest V II lines of Table 3. All of the lines in our study are stronger than log( RW ) ~ –6 in the solar center-of-disk spectrum (Delbouille et al. 1973) . Thus if unblended they are potentially useful photospheric vanadium abundance indicators. Table 3 lists nearly 110 V II lines with wavelengths longer than the atmospheric cutoff (3000 Å, indicated with the blue vertical line in Figure 5). However, almost all of these lines arise at wavelengths λ < 4100 Å, in the crowded near-UV spectral region. Therefore the main impediment to their use is contamination by transitions of other atomic and molecular species. We follow the procedures of our previous papers to determine which V II lines can be employed. We inspect each line in the Delbouille et al. (1973) photospheric spectrum, and then use the Moore et al. (1966) solar line identification compendium and the Kurucz (2011) atomic/molecular line database to identify those V II lines that are too blended to yield http://bass2000.obspm.fr/solar_spect.php http://kurucz.harvard.edu/linelists.html rustworthy vanadium abundances. Unfortunately, this procedure eliminates the vast majority of V II lines in Table 3, and we are left with only 25 V II lines meriting further investigation. We compute synthetic spectra for these surviving transitions with the current version of the LTE line analysis code MOOG (Sneden 1973). Line list assembly is described in detail by Lawler et al. (2013). Briefly, we begin with the Kurucz (2011) line database, gathering atomic and CN, CH, NH, and OH molecular lines in a typically 4 Å interval centered on each V II line, but modify transition probabilities and account for isotopic/hyperfine substructure as needed from recent lab studies on these species: second spectra rare earth atoms (Sneden et al. 2009 and references therein), Cr I (Sobeck et al. 2007), Ti I (Lawler et al. 2013), Ti II (Wood et al. 2014), and Ni I (Wood et al. 2014). To be consistent with our previous work beginning with Lawler et al. (2001), we adopt the Holweger & Müller (1974) empirical model photosphere. The line lists and solar model are used as inputs in MOOG, and the output raw synthetic spectra are then convolved with Gaussian smoothing functions to empirically match the broadening effects of the spectrograph instrument profile (a negligible effect for the Delbouille et al. 1973 solar spectral atlas) and solar macroturbulence. For V II lines and for the lines with lab transition data named above, the lab data are accepted without alteration. For other contaminants (the majority of features in most near-UV spectral windows), adjustments are made to their log( gf ) values to best reproduce the observed solar photospheric spectrum. The comparisons of observed and synthetic solar spectra result in the elimination of more V II lines, due either to unacceptably large contamination by other species or because they are simply too strong to be sensitive to abundance changes. In the end we are left with only 15 lines that are appropriate for a solar vanadium abundance determination. In Figure 6 we show observed and synthetic spectra for representative V II lines at 3530.78 and 4564.58 Å. This igure also shows the positions and fractional strengths of the HFS components for each line. Inclusion of HFS always serves to broaden and desaturate a transition, resulting in a derived abundance which, compared to single-line assumptions, ranges from slightly smaller (a few percent) for weak lines to factors approaching five times smaller for strong (saturated) lines. The abundances from individual lines are listed in Table 6, in which we also include columns for line wavelengths, excitation energies, oscillator strengths, and whether HFS is included in the synthetic spectrum computations. While the majority of lines listed with a “no” in Table 6 have negligible HFS, there are some for which HFS patterns could not be determined. This may be due to a lack of resolved structure, a lack of S/N, or both in the available FTS spectra. However, the majority of lines for which HFS has a detectable effect on derived abundances have HFS patterns reported in Table 5. Inclusion of the missing HFS patterns for lines listed “no” in Table 6 would likely have a negligibly small effect on the abundance determinations. The line abundances are plotted as functions of wavelengths in the top panel of Figure 7. With this small data set we do not find any obvious trends of abundance with line wavelength, excitation energy, transition probability, or overall line strength. From these 15 lines we derive a new solar photospheric vanadium abundance:
HST/STIS
UV high-resolution spectrum . Lawler et al. (2013) describe these spectra in detail. The availability of a UV spectrum for this star causes us to repeat the transition candidate selection process from the beginning, which results in nearly 75 possible V II lines for analysis. Line-by-line abundance derivation via spectrum syntheses is done as described in Lawler et al. (2013). This yields a mean abundance in HD 84937 of
1 1984 Dec. 9 3 Ar-Ne 600 7764 - 49105 0.057 12 UV Mid Range Si Diode 2 1984 Dec. 9 4 Ar-Ne 300 7764 - 49105 0.057 8 UV Mid Range Si Diode 3 1984 Dec. 9 5 Ar-Ne 150 7764 - 49105 0.057 8 UV Mid Range Si Diode 4 1986 July 30 9 Ar 500 14924 - 37018 0.048 4 UV CuSO Large UV Si Diode 5 1986 July 30 10 Ar 500 14924 - 37018 0.048 4 UV CuSO Large UV Si Diode 6 1981 June 16 7 Ar 332 6924 - 37564 0.043 8 UV WG295 UV Mid Range Si Diode 7 1981 June 15 3 Ar 250 14878 - 36533 0.043 8 UV CuSO WG295 UV Mid Range Si Diode 8 1979 Dec. 12 9 Ar 300 12422 - 31054 0.042 10 UV TC+ 4-97 Mid Range Si Diode G345 9 1979 Dec. 12 8 Ar 300 7716 - 22421 0.030 8 UV GG945 Super Blue Si Diode 10 1980 Sept. 4 1 Ar 110 0 - 17837 0.023 5 UV RG610 InSb 11 1983 Nov. 30 3 Ar 460 2799 - 9518 0.011 17 CaF Si InSb 12 1983 Apr. 17 4 Ne-Ar 370 1534 - 5769 0.011 80 CaF Ge InSb 13 1984 July 25 5 Ne 1000 12948 - 45407 0.054 8 UV CuSO R166 photomultiplier Mid Range Si Diode a Detector types include the Super Blue silicon (Si) photodiode, Large UV Si photodiode, Mid Range Si photodiode, UV Mid Range Si photodiode, a solar blind R166 photomulitplier, and InSb detectors for the IR. The UV beam splitter is fused silica.
Table 2. Echelle spectra of commercial V HCD lamps. Index Date Serial Numbers a Buffer Gas Lamp Current(mA) Wavelength Range (Å) Resolving Power Coadds Exposure Time (s) 47-51 2013 May 24 1, 3, 5, 7, 9 Ne 3 2200-3900 250,000 60 90 52-56 2013 May 21 1, 3, 5, 7, 9 Ne 5 2200-3900 250,000 90 60 57-61 2013 May 22 1, 3, 5, 7, 9 Ne 10 2200-3900 250,000 90 60 62-66 2013 May 23 1, 3, 5, 7, 9 Ne 15 2200-3900 250,000 60 90 67-71 2013 May 20 1, 3, 5, 7, 9 Ar 3 2200-3900 250,000 6 900 72-76 2013 May 15 1, 3, 5, 7, 9 Ar 5 2200-3900 250,000 18 300 77-81 2013 May 16 1, 3, 5, 7, 9 Ar 10 2200-3900 250,000 88 60 82-86 2013 May 17 1, 3, 5, 7, 9 Ar 12 2200-3900 250,000 60 90 87-91 2014 Jan. 30 1, 3, 5, 7, 9 Ne 5 2000-2800 250,000 18 300 92-96 2014 Jan. 31 1, 3, 5, 7, 9 Ne 10 2000-2800 250,000 36 150 7-101 2014 Feb. 3 1, 3, 5, 7, 9 Ne 15 2000-2800 250,000 72 75 102-106 2014 Feb. 5 1, 3, 5, 7, 9 Ar 15 2000-2800 250,000 45 120 127-131 2014 May 13 1, 3, 5, 7, 9 Ar 10 2100-3200 250,000 40 180 132-136 2014 May 9 1, 3, 5, 7, 9 Ar 15 2100-3200 250,000 90 60 137-141 2014 May 14 1, 3, 5, 7, 9 Ne 15 2100-3200 250,000 120 45 a At least 3 CCD frames are needed to capture a complete echelle grating order in the UV. In the above data 5 CCD frames are used to provide redundancy and a check for lamp drift. able 3. Experimental atomic transition probabilities for 203 lines of V II from upper odd parity levels organized by increasing wavelength in air. Wavelength Upper Level b Lower Level b Transition log ( gf ) in air a (Å) Energy (cm -1 ) J Energy (cm -1 ) J Probability (10 s -1 ) 2123.3231 47420.230 4 339.125 4 5.8 ± 1.0 -1.45 2126.9227 47108.079 1 106.643 1 5.8 ± 0.9 -1.93 2129.4687 47051.889 3 106.643 1 5.9 ± 1.1 -1.55 2131.8351 47101.932 2 208.790 3 9.1 ± 1.3 -1.51 2134.0805 46879.911 2 36.102 1 13.3 ± 2.1 -1.34 Note –Table 3 is available in its entirety via the link to the machine-readable version online. a Wavelength values computed from energy levels using the standard index of air from Peck & Reeder (1972). b Energy levels, parities, and J values are from Thorne et al. (2013). itle: Improved V II log(gf) Values, Hyperfine Structure Constants, and Abundance Determinations in the Photospheres of the Sun and Metal-poor Star HD 84937 Authors: Wood M.P., Lawler J.E., Den Hartog E.A., Sneden C., & Cowan J.J. Table: Experimental atomic transition probabilities for 203 lines of V II from upper odd-parity levels organized by increasing wavelength in air. ========================================================================= Byte-by-byte Description of file: Table3mr.txt ------------------------------------------------------------------------- Bytes Format Units Label Explanations ------------------------------------------------------------------------- 1- 9 F9.4 0.1nm WaveAir Wavelength in air; Angstroms (1) 11- 19 F9.3 cm-1 UpLev Upper level (2) 21 I1 --- UpJ Upper level J value (2) 23- 31 F9.3 cm-1 LowLev Lower level (2) 33 I1 --- LowJ Lower level J value (2) 35- 41 F7.3 10+6/s TranP Transition probability 43- 48 F6.3 10+6/s e_TranP Total uncertainty in TranP 50- 54 F5.2 --- log(gf) Log of degeneracy times oscillator strength ------------------------------------------------------------------------- Note (1): Computed from energy levels using the standard index of air from Peck & Reeder (1972). Note (2): From Thorne er al. (2013). ------------------------------------------------------------------------- 2123.3231 47420.230 4 339.125 4 5.8 1.0 -1.45 2126.9227 47108.079 1 106.643 2 5.8 0.9 -1.93 2129.4687 47051.889 3 106.643 2 5.9 1.1 -1.55 2131.8351 47101.932 2 208.790 3 9.1 1.3 -1.51 2134.0805 46879.911 2 36.102 1 13.3 2.1 -1.34 2134.1128 47051.889 3 208.790 3 30. 5. -0.85 2137.2994 46879.911 2 106.643 2 44. 6. -0.82 2138.1559 46754.533 1 0.000 0 25. 4. -1.29 2139.8084 46754.533 1 36.102 1 46. 7. -1.02 2140.0680 47051.889 3 339.125 4 86. 12. -0.38 2141.9777 46879.911 2 208.790 3 46. 7. -0.80 2143.0445 46754.533 1 106.643 2 34. 5. -1.16 2145.9909 46690.495 1 106.643 2 8.7 1.4 -1.74 2148.4186 46740.008 2 208.790 3 7.8 1.2 -1.57 2672.0004 37520.665 3 106.643 2 21.7 1.4 -0.79 2677.7959 37369.154 2 36.102 1 32.2 2.2 -0.76 2678.5644 37531.132 4 208.790 3 12.2 0.9 -0.93 2679.3159 37520.665 3 208.790 3 31.4 2.0 -0.63 2682.8655 37369.154 2 106.643 2 17.8 1.4 -1.02 2683.0803 37259.529 1 0.000 0 32.9 2.5 -0.97 2685.6826 37259.529 1 36.102 1 6.2 0.5 -1.70 2687.9517 37531.132 4 339.125 4 85. 6. -0.08 2688.7084 37520.665 3 339.125 4 13.9 0.9 -0.98 2689.8735 37201.538 0 36.102 1 97. 6. -0.98 2690.2406 37369.154 2 208.790 3 32.2 2.1 -0.76 2690.7822 37259.529 1 106.643 2 52. 4. -0.77 2694.7359 37205.021 3 106.643 2 0.188 0.022 -2.84 700.9275 37352.464 5 339.125 4 35.4 2.0 -0.37 2702.1765 37205.021 3 208.790 3 26.8 1.6 -0.69 2705.2145 36954.686 1 0.000 0 4.5 0.4 -1.83 2706.1564 37150.615 4 208.790 3 33.2 1.9 -0.48 2706.6904 37041.179 2 106.643 2 16.8 1.1 -1.03 2707.8600 36954.686 1 36.102 1 12.3 0.8 -1.39 2711.7303 37205.021 3 339.125 4 8.5 0.7 -1.18 2713.0442 36954.686 1 106.643 2 6.4 0.4 -1.67 2714.1973 37041.179 2 208.790 3 7.6 0.5 -1.38 2715.6547 36919.266 3 106.643 2 30.3 1.8 -0.63 2715.7383 37150.615 4 339.125 4 2.42 0.18 -1.62 2723.2115 36919.266 3 208.790 3 2.33 0.16 -1.74 2728.6373 36673.584 2 36.102 1 20.1 1.2 -0.95 2733.9014 36673.584 2 106.643 2 2.40 0.16 -1.87 2742.4220 36489.437 1 36.102 1 7.9 0.8 -1.57 2742.6731 39612.964 5 3162.966 5 1.92 0.17 -1.62 2743.7721 39403.787 4 2968.389 4 0.84 0.08 -2.07 2808.6905 47108.079 1 11514.784 1 3.20 0.25 -1.94 2824.4280 46690.495 1 11295.513 0 2.91 0.27 -1.98 2840.0887 47108.079 1 11908.261 2 6.0 0.4 -1.67 2840.5848 47101.932 2 11908.261 2 4.7 0.4 -1.55 2869.9608 37520.665 3 2687.208 2 1.89 0.13 -1.79 2875.6857 37369.154 2 2605.040 1 3.30 0.22 -1.69 2879.1594 37531.132 4 2808.959 3 4.3 0.3 -1.32 2880.0276 37520.665 3 2808.959 3 26.1 1.6 -0.64 2882.4990 37369.154 2 2687.208 2 45.5 2.8 -0.55 2884.7830 37259.529 1 2605.040 1 61. 4. -0.64 2889.6187 37201.538 0 2605.040 1 216. 14. -0.57 2891.6396 37259.529 1 2687.208 2 154. 10. -0.24 2892.4409 37531.132 4 2968.389 4 41.4 2.8 -0.33 2892.6542 37369.154 2 2808.959 3 147. 9. -0.03 2893.3172 37520.665 3 2968.389 4 123. 7. +0.03 2896.2060 37205.021 3 2687.208 2 21.7 1.2 -0.72 2903.0754 37041.179 2 2605.040 1 31.6 1.7 -0.70 2906.4581 37205.021 3 2808.959 3 80. 4. -0.15 2907.4714 37352.464 5 2968.389 4 25.4 1.5 -0.45 2908.8174 37531.132 4 3162.966 5 177. 12. +0.31 2910.0193 37041.179 2 2687.208 2 95. 5. -0.22 2910.3858 36954.686 1 2605.040 1 119. 6. -0.34 2911.0629 37150.615 4 2808.959 3 38.7 2.1 -0.35 2917.3647 36954.686 1 2687.208 2 18.4 1.2 -1.15 2919.9933 37205.021 3 2968.389 4 13.6 0.8 -0.92 2920.3835 36919.266 3 2687.208 2 33.1 1.8 -0.53 2924.0190 37352.464 5 3162.966 5 188. 9. +0.42 2924.6411 37150.615 4 2968.389 4 130. 7. +0.18 2930.8078 36919.266 3 2808.959 3 61. 3. -0.26 2934.4007 36673.584 2 2605.040 1 17.4 1.0 -0.95 2941.3852 37150.615 4 3162.966 5 41.7 2.2 -0.31 2941.4954 36673.584 2 2687.208 2 29.7 1.7 -0.71 2944.5712 36919.266 3 2968.389 4 82. 4. -0.13 2950.3486 36489.437 1 2605.040 1 41. 3. -0.80 2952.0712 36673.584 2 2808.959 3 72. 4. -0.33 2957.5207 36489.437 1 2687.208 2 51. 4. -0.70 2968.3787 47420.230 4 13741.640 3 212. 11. +0.40 975.6514 47108.079 1 13511.799 1 93. 5. -0.43 2976.1960 47101.932 2 13511.799 1 97. 5. -0.19 2983.5619 47101.932 2 13594.723 2 53.7 2.9 -0.45 2988.0247 47051.889 3 13594.723 2 40. 3. -0.43 2995.9995 46879.911 2 13511.799 1 48. 4. -0.49 3001.2041 47051.889 3 13741.640 3 223. 19. +0.32 3003.4639 46879.911 2 13594.723 2 69. 6. -0.33 3007.2997 46754.533 1 13511.799 1 15.8 1.7 -1.19 3008.6143 46740.008 2 13511.799 1 31.9 1.8 -0.66 3013.1043 46690.495 1 13511.799 1 105. 6. -0.37 3014.8205 46754.533 1 13594.723 2 237. 18. -0.01 3016.1417 46740.008 2 13594.723 2 23.1 1.4 -0.80 3016.7801 46879.911 2 13741.640 3 130. 10. -0.05 3093.1002 35483.606 6 3162.966 5 200. 10. +0.57 3102.3005 35193.182 5 2968.389 4 178. 9. +0.45 3110.7101 34946.637 4 2808.959 3 157. 8. +0.31 3118.3816 34745.828 3 2687.208 2 147. 7. +0.18 3121.1470 35193.182 5 3162.966 5 21.8 1.1 -0.46 3125.2856 34592.843 2 2605.040 1 149. 7. +0.04 3126.2194 34946.637 4 2968.389 4 37.1 1.9 -0.31 3130.2701 34745.828 3 2808.959 3 46.6 2.3 -0.32 3133.3346 34592.843 2 2687.208 2 43.1 2.3 -0.50 3145.3375 34592.843 2 2808.959 3 3.09 0.22 -1.64 3145.3586 34946.637 4 3162.966 5 1.18 0.19 -1.80 3145.9755 34745.828 3 2968.389 4 2.60 0.20 -1.57 3164.8395 40430.087 4 8842.050 3 4.42 0.25 -1.22 3168.1325 40195.567 3 8640.362 2 7.2 0.8 -1.12 3187.7122 40001.754 2 8640.362 2 112. 6. -0.07 3188.5129 40195.567 3 8842.050 3 108. 6. +0.06 3190.6825 40430.087 4 9097.889 4 125. 6. +0.24 3208.3461 40001.754 2 8842.050 3 18.2 1.0 -0.85 3214.7456 40195.567 3 9097.889 4 14.3 0.8 -0.81 3267.7022 39234.086 3 8640.362 2 157. 8. +0.25 3271.1225 39403.787 4 8842.050 3 160. 8. +0.36 3276.1247 39612.964 5 9097.889 4 170. 9. +0.48 3289.3882 39234.086 3 8842.050 3 10.5 0.6 -0.92 3298.7378 39403.787 4 9097.889 4 7.4 0.4 -0.97 3469.5166 47108.079 1 18293.871 2 9.0 1.0 -1.31 3477.4946 47101.932 2 18353.827 3 5.6 0.8 -1.30 3479.8324 37369.154 2 8640.362 2 2.50 0.26 -1.64 3485.9210 37520.665 3 8842.050 3 4.0 0.4 -1.29 3493.1622 37259.529 1 8640.362 2 7.0 0.8 -1.42 3499.8282 37205.021 3 8640.362 2 0.49 0.07 -2.20 3504.4357 37369.154 2 8842.050 3 18.6 1.8 -0.77 3514.4108 46740.008 2 18293.871 2 4.2 0.7 -1.41 3517.2994 37520.665 3 9097.889 4 44. 4. -0.24 3517.5215 46690.495 1 18269.514 1 3.7 0.6 -1.69 3520.0190 37041.179 2 8640.362 2 8.1 0.8 -1.13 3520.5388 46690.495 1 18293.871 2 7.9 0.9 -1.36 3521.8340 46740.008 2 18353.827 3 14.3 1.1 -0.88 3524.7160 37205.021 3 8842.050 3 7.9 0.7 -0.99 3530.7720 36954.686 1 8640.362 2 53. 4. -0.53 3531.4904 37150.615 4 8842.050 3 0.36 0.04 -2.21 3538.2387 37352.464 5 9097.889 4 1.13 0.11 -1.63 545.1959 37041.179 2 8842.050 3 51. 4. -0.32 3556.7999 37205.021 3 9097.889 4 64. 5. -0.07 3560.5897 36919.266 3 8842.050 3 3.0 0.3 -1.40 3566.1777 36673.584 2 8640.362 2 8.8 0.8 -1.08 3574.3485 47101.932 2 19132.791 2 12.3 1.4 -0.93 3589.7591 36489.437 1 8640.362 2 78. 4. -0.35 3592.0216 36673.584 2 8842.050 3 52. 4. -0.30 3593.3330 36919.266 3 9097.889 4 20.9 1.7 -0.55 3621.2087 46740.008 2 19132.791 2 25.9 1.9 -0.59 3625.6113 46740.008 2 19166.314 1 6.1 0.6 -1.22 3627.7151 46690.495 1 19132.791 2 11.0 1.3 -1.19 3632.1336 46690.495 1 19166.314 1 4.2 0.8 -1.61 3674.6849 47108.079 1 19902.608 0 8.9 0.8 -1.27 3700.1245 47108.079 1 20089.650 1 12.7 1.2 -1.11 3700.9665 47101.932 2 20089.650 1 4.5 0.5 -1.33 3703.8190 39612.964 5 12621.485 5 0.54 0.06 -1.91 3709.3258 47108.079 1 20156.670 0 6.1 0.7 -1.42 3715.4638 39612.964 5 12706.078 6 26.3 1.7 -0.22 3718.1508 40430.087 4 13542.645 3 2.36 0.18 -1.36 3722.1315 39403.787 4 12545.100 4 0.58 0.08 -1.97 3727.3412 40430.087 4 13608.939 4 31.7 2.2 -0.23 3731.9693 46690.495 1 19902.608 0 9.2 0.9 -1.24 3732.7476 39403.787 4 12621.485 5 25.7 1.6 -0.32 3735.1560 47108.079 1 20343.046 2 12.9 1.2 -1.09 3736.0141 47101.932 2 20343.046 2 9.2 0.8 -1.01 3743.5972 40195.567 3 13490.883 2 2.77 0.27 -1.39 3745.7992 39234.086 3 12545.100 4 26.6 1.8 -0.41 3750.8677 40195.567 3 13542.645 3 26.8 2.0 -0.40 3760.2208 40195.567 3 13608.939 4 4.8 0.4 -1.15 3767.7039 46690.495 1 20156.670 0 7.0 0.7 -1.35 3770.9662 40001.754 2 13490.883 2 31.5 2.5 -0.47 3774.6699 47101.932 2 20617.073 2 2.7 0.6 -1.55 3778.3435 40001.754 2 13542.645 3 6.3 0.5 -1.17 3787.2392 46740.008 2 20343.046 2 24.1 2.0 -0.59 3794.3565 46690.495 1 20343.046 2 11.2 1.1 -1.14 3826.9679 46740.008 2 20617.073 2 7.5 0.8 -1.08 3863.7854 40430.087 4 14556.068 4 3.15 0.27 -1.20 3865.7093 39403.787 4 13542.645 3 0.30 0.04 -2.21 3866.7219 37369.154 2 11514.784 1 2.8 0.3 -1.50 3875.6446 39403.787 4 13608.939 4 0.62 0.12 -1.90 3878.7074 40430.087 4 14655.607 5 13.4 1.1 -0.57 3884.8361 40195.567 3 14461.748 3 2.64 0.23 -1.38 3896.1379 36954.686 1 11295.513 0 5.6 0.6 -1.42 3899.1276 40195.567 3 14556.068 4 10.6 0.9 -0.77 3903.2525 37520.665 3 11908.261 2 7.8 0.9 -0.91 3916.4045 37041.179 2 11514.784 1 7.3 0.8 -1.07 3926.4802 37369.154 2 11908.261 2 0.94 0.13 -1.96 3929.7201 36954.686 1 11514.784 1 3.7 0.5 -1.59 3951.9570 37205.021 3 11908.261 2 11.3 1.2 -0.73 3968.0884 36489.437 1 11295.513 0 7.2 0.5 -1.29 3973.6283 36673.584 2 11514.784 1 7.4 0.8 -1.06 3977.7204 37041.179 2 11908.261 2 2.30 0.26 -1.56 3989.7890 39612.964 5 14556.068 4 0.47 0.06 -1.90 3997.1098 36919.266 3 11908.261 2 3.7 0.4 -1.20 002.9279 36489.437 1 11514.784 1 5.0 0.4 -1.44 4005.7021 39612.964 5 14655.607 5 13.5 1.1 -0.45 4008.1622 39403.787 4 14461.748 3 0.67 0.08 -1.83 4023.3772 39403.787 4 14556.068 4 11.1 0.9 -0.61 4035.6204 39234.086 3 14461.748 3 11.0 0.9 -0.72 4036.7636 36673.584 2 11908.261 2 2.21 0.24 -1.57 4051.0450 39234.086 3 14556.068 4 0.62 0.10 -1.97 4183.4285 40430.087 4 16532.983 5 3.7 0.4 -1.06 4202.3526 37531.132 4 13741.640 3 1.7 0.3 -1.38 4205.0842 40195.567 3 16421.528 4 3.5 0.4 -1.19 4225.2146 40001.754 2 16340.981 3 3.6 0.4 -1.32 4528.4829 40430.087 4 18353.827 3 3.2 0.3 -1.06 4564.5771 40195.567 3 18293.871 2 2.8 0.4 -1.22 4600.1697 40001.754 2 18269.514 1 2.7 0.3 -1.37 l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y Wavelength (Å) (a) −0.20−0.15−0.10−0.050.000.050.100.15−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y log( gf ) this study (b) l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y Wavelength (Å) (a) −0.25−0.20−0.15−0.10−0.050.000.050.100.15−2.4 −2.2 −2.0 −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y log( gf ) this study (b) l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y Wavelength (Å) (a) −0.60−0.50−0.40−0.30−0.20−0.100.000.100.20−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 l og ( g f ) N I S T − l og ( g f ) t h i s s t ud y log( gf ) this study (b) l og ( g f ) B i e m on t − l og ( g f ) t h i s s t ud y Wavelength (Å) (a) −0.60−0.50−0.40−0.30−0.20−0.100.000.100.200.30−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 l og ( g f ) B i e m on t − l og ( g f ) t h i s s t ud y log( gf ) this study (b) Table 4. New V II magnetic dipole hyperfine structure constants from FTS spectra. Configuration a Term a J a Parity a Level Energy a Hyperfine Structure Constant A (10 -3 cm -1 ) (cm -1 ) This Work Arvidsson b d ( F)4 s a F 1 ev 2605.040 -13.7 ± 1.0 17.0 ± 5.7 3 d ( F)4 s a F 2 ev 2687.208 13.5 ± 3.0 11.1 ± 1.9 3 d ( F)4 s a F 3 ev 2808.959 18.4 ± 1.0 19.8 ± 2.0 3 d ( F)4 s a F 4 ev 2968.389 20.5 ± 1.0 27.6 ± 1.9 3 d ( F)4 s a F 5 ev 3162.966 21.8 ± 1.0 24.4 ± 1.5 3 d ( F)4 s a F 2 ev 8640.362 30.5 ± 1.0 31.3 ± 0.2 3 d ( F)4 s a F 3 ev 8842.050 6.0 ± 1.0 3 d ( F)4 s a F 4 ev 9097.889 -2.9 ± 1.0 3 d a P 1 ev 11514.784 0.0 ± 2.0 3 d a P 2 ev 11908.261 0.0 ± 2.0 3 d a G 3 ev 14461.748 5.0 ± 1.0 d ( F)4 p z G 2 od 34592.843 26.0 ± 1.5 3 d ( F)4 p z G 3 od 34745.828 14.4 ± 1.5 3 d ( F)4 p z G 4 od 34946.637 9.0 ± 1.5 3 d ( F)4 p z G 5 od 35193.182 6.7 ± 1.5 3 d ( F)4 p z G 6 od 35483.606 5.2 ± 2.0 3 d ( F)4 p z F 3 od 36919.266 4.9 ± 1.5 3 d ( F)4 p z F 4 od 37150.615 4.9 ± 1.5 3 d ( F)4 p z D 3 od 37520.665 2.5 ± 1.5 3 d ( F)4 p z P 2 od 46879.911 -4.2 ± 1.5 3 d ( F)4 p z P 3 od 47051.889 1.1 ± 1.5 a Level energies and classifications are from Thorne et al. (2013). b Arvidsson (2003) master’s thesis at Lund University, Lund, Sweden. able 5. Hyperfine structure line component patterns for V II . Center of gravity wavenumber a (cm -1 ) Center of gravity air wavelength b (Å) F uppera F lowera Component offset from center of gravity wavenumber(cm -1 ) Component offset from center of gravity wavelength (Å) Component strength c a Energy levels and total angular momentum F values are from Thorne et al. (2013). b Wavelength values computed from energy levels using the standard index of air from Peck & Reeder (1972). c Component strengths are normalized to sum to unity. itle: Improved V II log(gf) Values, Hyperfine Structure Constants, and Abundance Determinations in the Photospheres of the Sun and Metal-poor Star HD 84937 Authors: Wood M.P., Lawler J.E., Den Hartog E.A., Sneden C., & Cowan J.J. Table: Hyperfine structure line component patterns for V II. ========================================================================= Byte-by-byte Description of file: Table5mr.txt ------------------------------------------------------------------------- Bytes Format Units Label Explanations ------------------------------------------------------------------------- 1- 9 F9.3 cm-1 WaveNum Center-of-Gravity Wavenumber 11- 19 F9.4 0.1nm WaveAir Center-of-Gravity Air Wavelength in Angstroms 21- 23 F3.1 --- Fupp Component upper level F or total angular momentum 25- 27 F3.1 --- Flow Component lower level F or total angular momentum 29- 36 F8.5 cm-1 CWaveR Component offset Wavenumber with respect to Center-of-gravity Wavenumber 38- 46 F9.6 0.1nm CWave Component offset Wavelength with respect to Center-of-gravity Wavelength 48- 54 F7.5 --- Str Component strength (1) ------------------------------------------------------------------------- Note (1): Normalized to sum to one. ------------------------------------------------------------------------- 37414.022 2672.0004 6.5 5.5 0.02625 -0.001875 0.25000 37414.022 2672.0004 5.5 5.5 0.01000 -0.000714 0.04545 37414.022 2672.0004 5.5 4.5 0.01000 -0.000714 0.16883 37414.022 2672.0004 4.5 5.5 -0.00375 0.000268 0.00455 37414.022 2672.0004 4.5 4.5 -0.00375 0.000268 0.06926 37414.022 2672.0004 4.5 3.5 -0.00375 0.000268 0.10476 37414.022 2672.0004 3.5 4.5 -0.01500 0.001071 0.01190 37414.022 2672.0004 3.5 3.5 -0.01500 0.001071 0.07483 37414.022 2672.0004 3.5 2.5 -0.01500 0.001071 0.05612 37414.022 2672.0004 2.5 3.5 -0.02375 0.001696 0.02041 37414.022 2672.0004 2.5 2.5 -0.02375 0.001696 0.06531 37414.022 2672.0004 2.5 1.5 -0.02375 0.001696 0.02143 37414.022 2672.0004 1.5 2.5 -0.03000 0.002143 0.02857 37414.022 2672.0004 1.5 1.5 -0.03000 0.002143 0.04286 37414.022 2672.0004 0.5 1.5 -0.03375 0.002410 0.03571 37311.875 2679.3159 6.5 6.5 0.02625 -0.001885 0.21635 37311.875 2679.3159 6.5 5.5 0.02625 -0.001885 0.03365 37311.875 2679.3159 5.5 6.5 0.01000 -0.000718 0.03365 37311.875 2679.3159 5.5 5.5 0.01000 -0.000718 0.12787 37311.875 2679.3159 5.5 4.5 0.01000 -0.000718 0.05276 37311.875 2679.3159 4.5 5.5 -0.00375 0.000269 0.05276 37311.875 2679.3159 4.5 4.5 -0.00375 0.000269 0.06629 37311.875 2679.3159 4.5 3.5 -0.00375 0.000269 0.05952 37311.875 2679.3159 3.5 4.5 -0.01500 0.001077 0.05952 37311.875 2679.3159 3.5 3.5 -0.01500 0.001077 0.02721 37311.875 2679.3159 3.5 2.5 -0.01500 0.001077 0.05612 37311.875 2679.3159 2.5 3.5 -0.02375 0.001706 0.05612 37311.875 2679.3159 2.5 2.5 -0.02375 0.001706 0.00638 7311.875 2679.3159 2.5 1.5 -0.02375 0.001706 0.04464 37311.875 2679.3159 1.5 2.5 -0.03000 0.002154 0.04464 37311.875 2679.3159 1.5 1.5 -0.03000 0.002154 0.00000 37311.875 2679.3159 1.5 0.5 -0.03000 0.002154 0.02679 37311.875 2679.3159 0.5 1.5 -0.03375 0.002424 0.02679 37311.875 2679.3159 0.5 0.5 -0.03375 0.002424 0.00893 37192.007 2687.9517 7.5 7.5 0.03997 -0.002889 0.20148 37192.007 2687.9517 7.5 6.5 0.03997 -0.002889 0.02074 37192.007 2687.9517 6.5 7.5 0.01856 -0.001341 0.02074 37192.007 2687.9517 6.5 6.5 0.01856 -0.001341 0.14005 37192.007 2687.9517 6.5 5.5 0.01856 -0.001341 0.03365 37192.007 2687.9517 5.5 6.5 0.00000 0.000000 0.03365 37192.007 2687.9517 5.5 5.5 0.00000 0.000000 0.09324 37192.007 2687.9517 5.5 4.5 0.00000 0.000000 0.03977 37192.007 2687.9517 4.5 5.5 -0.01570 0.001135 0.03977 37192.007 2687.9517 4.5 4.5 -0.01570 0.001135 0.05899 37192.007 2687.9517 4.5 3.5 -0.01570 0.001135 0.04012 37192.007 2687.9517 3.5 4.5 -0.02855 0.002064 0.04012 37192.007 2687.9517 3.5 3.5 -0.02855 0.002064 0.03527 37192.007 2687.9517 3.5 2.5 -0.02855 0.002064 0.03571 37192.007 2687.9517 2.5 3.5 -0.03855 0.002786 0.03571 37192.007 2687.9517 2.5 2.5 -0.03855 0.002786 0.02012 37192.007 2687.9517 2.5 1.5 -0.03855 0.002786 0.02750 37192.007 2687.9517 1.5 2.5 -0.04568 0.003302 0.02750 37192.007 2687.9517 1.5 1.5 -0.04568 0.003302 0.01185 37192.007 2687.9517 1.5 0.5 -0.04568 0.003302 0.01620 37192.007 2687.9517 0.5 1.5 -0.04997 0.003612 0.01620 37192.007 2687.9517 0.5 0.5 -0.04997 0.003612 0.01157 37181.540 2688.7084 6.5 7.5 0.02625 -0.001898 0.22222 37181.540 2688.7084 6.5 6.5 0.02625 -0.001898 0.02618 37181.540 2688.7084 6.5 5.5 0.02625 -0.001898 0.00160 37181.540 2688.7084 5.5 6.5 0.01000 -0.000723 0.16827 37181.540 2688.7084 5.5 5.5 0.01000 -0.000723 0.04196 37181.540 2688.7084 5.5 4.5 0.01000 -0.000723 0.00406 37181.540 2688.7084 4.5 5.5 -0.00375 0.000271 0.12311 37181.540 2688.7084 4.5 4.5 -0.00375 0.000271 0.04885 37181.540 2688.7084 4.5 3.5 -0.00375 0.000271 0.00661 37181.540 2688.7084 3.5 4.5 -0.01500 0.001085 0.08598 37181.540 2688.7084 3.5 3.5 -0.01500 0.001085 0.04837 37181.540 2688.7084 3.5 2.5 -0.01500 0.001085 0.00850 37181.540 2688.7084 2.5 3.5 -0.02375 0.001718 0.05612 37181.540 2688.7084 2.5 2.5 -0.02375 0.001718 0.04209 37181.540 2688.7084 2.5 1.5 -0.02375 0.001718 0.00893 37181.540 2688.7084 1.5 2.5 -0.03000 0.002170 0.03274 37181.540 2688.7084 1.5 1.5 -0.03000 0.002170 0.03175 37181.540 2688.7084 1.5 0.5 -0.03000 0.002170 0.00694 37181.540 2688.7084 0.5 1.5 -0.03375 0.002441 0.01488 37181.540 2688.7084 0.5 0.5 -0.03375 0.002441 0.02083 37013.339 2700.9275 8.5 7.5 0.09399 -0.006859 0.20455 37013.339 2700.9275 7.5 7.5 0.04834 -0.003528 0.01697 37013.339 2700.9275 7.5 6.5 0.04834 -0.003528 0.16485 37013.339 2700.9275 6.5 7.5 0.00806 -0.000588 0.00071 37013.339 2700.9275 6.5 6.5 0.00806 -0.000588 0.02785 37013.339 2700.9275 6.5 5.5 0.00806 -0.000588 0.13054 7013.339 2700.9275 5.5 6.5 -0.02686 0.001960 0.00175 37013.339 2700.9275 5.5 5.5 -0.02686 0.001960 0.03338 37013.339 2700.9275 5.5 4.5 -0.02686 0.001960 0.10124 37013.339 2700.9275 4.5 5.5 -0.05640 0.004116 0.00275 37013.339 2700.9275 4.5 4.5 -0.05640 0.004116 0.03428 37013.339 2700.9275 4.5 3.5 -0.05640 0.004116 0.07660 37013.339 2700.9275 3.5 4.5 -0.08057 0.005879 0.00337 37013.339 2700.9275 3.5 3.5 -0.08057 0.005879 0.03127 37013.339 2700.9275 3.5 2.5 -0.08057 0.005879 0.05628 37013.339 2700.9275 2.5 3.5 -0.09936 0.007251 0.00325 37013.339 2700.9275 2.5 2.5 -0.09936 0.007251 0.02494 37013.339 2700.9275 2.5 1.5 -0.09936 0.007251 0.04000 37013.339 2700.9275 1.5 2.5 -0.11279 0.008231 0.00212 37013.339 2700.9275 1.5 1.5 -0.11279 0.008231 0.01556 37013.339 2700.9275 1.5 0.5 -0.11279 0.008231 0.02778 36996.231 2702.1765 6.5 6.5 0.05612 -0.004099 0.21635 36996.231 2702.1765 6.5 5.5 0.05612 -0.004099 0.03365 36996.231 2702.1765 5.5 6.5 0.02138 -0.001561 0.03365 36996.231 2702.1765 5.5 5.5 0.02138 -0.001561 0.12787 36996.231 2702.1765 5.5 4.5 0.02138 -0.001561 0.05276 36996.231 2702.1765 4.5 5.5 -0.00802 0.000586 0.05276 36996.231 2702.1765 4.5 4.5 -0.00802 0.000586 0.06629 36996.231 2702.1765 4.5 3.5 -0.00802 0.000586 0.05952 36996.231 2702.1765 3.5 4.5 -0.03207 0.002342 0.05952 36996.231 2702.1765 3.5 3.5 -0.03207 0.002342 0.02721 36996.231 2702.1765 3.5 2.5 -0.03207 0.002342 0.05612 36996.231 2702.1765 2.5 3.5 -0.05077 0.003709 0.05612 36996.231 2702.1765 2.5 2.5 -0.05077 0.003709 0.00638 36996.231 2702.1765 2.5 1.5 -0.05077 0.003709 0.04464 36996.231 2702.1765 1.5 2.5 -0.06413 0.004684 0.04464 36996.231 2702.1765 1.5 1.5 -0.06413 0.004684 0.00000 36996.231 2702.1765 1.5 0.5 -0.06413 0.004684 0.02679 36996.231 2702.1765 0.5 1.5 -0.07215 0.005270 0.02679 36996.231 2702.1765 0.5 0.5 -0.07215 0.005270 0.00893 36918.584 2707.8600 4.5 4.5 0.09660 -0.007085 0.25463 36918.584 2707.8600 4.5 3.5 0.09660 -0.007085 0.16204 36918.584 2707.8600 3.5 4.5 -0.02760 0.002024 0.16204 36918.584 2707.8600 3.5 3.5 -0.02760 0.002024 0.01058 36918.584 2707.8600 3.5 2.5 -0.02760 0.002024 0.16071 36918.584 2707.8600 2.5 3.5 -0.12419 0.009110 0.16071 36918.584 2707.8600 2.5 2.5 -0.12419 0.009110 0.08929 36848.043 2713.0442 4.5 5.5 0.09660 -0.007113 0.30000 36848.043 2713.0442 4.5 4.5 0.09660 -0.007113 0.09722 36848.043 2713.0442 4.5 3.5 0.09660 -0.007113 0.01944 36848.043 2713.0442 3.5 4.5 -0.02760 0.002032 0.15278 36848.043 2713.0442 3.5 3.5 -0.02760 0.002032 0.12698 36848.043 2713.0442 3.5 2.5 -0.02760 0.002032 0.05357 36848.043 2713.0442 2.5 3.5 -0.12419 0.009145 0.05357 36848.043 2713.0442 2.5 2.5 -0.12419 0.009145 0.09643 36848.043 2713.0442 2.5 1.5 -0.12419 0.009145 0.10000 36812.623 2715.6547 6.5 5.5 0.05145 -0.003796 0.25000 36812.623 2715.6547 5.5 5.5 0.01960 -0.001446 0.04545 36812.623 2715.6547 5.5 4.5 0.01960 -0.001446 0.16883 36812.623 2715.6547 4.5 5.5 -0.00735 0.000542 0.00455 6812.623 2715.6547 4.5 4.5 -0.00735 0.000542 0.06926 36812.623 2715.6547 4.5 3.5 -0.00735 0.000542 0.10476 36812.623 2715.6547 3.5 4.5 -0.02940 0.002169 0.01190 36812.623 2715.6547 3.5 3.5 -0.02940 0.002169 0.07483 36812.623 2715.6547 3.5 2.5 -0.02940 0.002169 0.05612 36812.623 2715.6547 2.5 3.5 -0.04655 0.003434 0.02041 36812.623 2715.6547 2.5 2.5 -0.04655 0.003434 0.06531 36812.623 2715.6547 2.5 1.5 -0.04655 0.003434 0.02143 36812.623 2715.6547 1.5 2.5 -0.05880 0.004338 0.02857 36812.623 2715.6547 1.5 1.5 -0.05880 0.004338 0.04286 36812.623 2715.6547 0.5 1.5 -0.06615 0.004880 0.03571 36811.490 2715.7383 7.5 7.5 0.06860 -0.005061 0.20148 36811.490 2715.7383 7.5 6.5 0.06860 -0.005061 0.02074 36811.490 2715.7383 6.5 7.5 0.03185 -0.002350 0.02074 36811.490 2715.7383 6.5 6.5 0.03185 -0.002350 0.14005 36811.490 2715.7383 6.5 5.5 0.03185 -0.002350 0.03365 36811.490 2715.7383 5.5 6.5 0.00000 0.000000 0.03365 36811.490 2715.7383 5.5 5.5 0.00000 0.000000 0.09324 36811.490 2715.7383 5.5 4.5 0.00000 0.000000 0.03977 36811.490 2715.7383 4.5 5.5 -0.02695 0.001988 0.03977 36811.490 2715.7383 4.5 4.5 -0.02695 0.001988 0.05899 36811.490 2715.7383 4.5 3.5 -0.02695 0.001988 0.04012 36811.490 2715.7383 3.5 4.5 -0.04900 0.003615 0.04012 36811.490 2715.7383 3.5 3.5 -0.04900 0.003615 0.03527 36811.490 2715.7383 3.5 2.5 -0.04900 0.003615 0.03571 36811.490 2715.7383 2.5 3.5 -0.06615 0.004880 0.03571 36811.490 2715.7383 2.5 2.5 -0.06615 0.004880 0.02012 36811.490 2715.7383 2.5 1.5 -0.06615 0.004880 0.02750 36811.490 2715.7383 1.5 2.5 -0.07840 0.005784 0.02750 36811.490 2715.7383 1.5 1.5 -0.07840 0.005784 0.01185 36811.490 2715.7383 1.5 0.5 -0.07840 0.005784 0.01620 36811.490 2715.7383 0.5 1.5 -0.08575 0.006326 0.01620 36811.490 2715.7383 0.5 0.5 -0.08575 0.006326 0.01157 36637.482 2728.6373 5.5 4.5 0.05593 -0.004165 0.30000 36637.482 2728.6373 4.5 4.5 0.01198 -0.000893 0.09722 36637.482 2728.6373 4.5 3.5 0.01198 -0.000893 0.15278 36637.482 2728.6373 3.5 4.5 -0.02397 0.001785 0.01944 36637.482 2728.6373 3.5 3.5 -0.02397 0.001785 0.12698 36637.482 2728.6373 3.5 2.5 -0.02397 0.001785 0.05357 36637.482 2728.6373 2.5 3.5 -0.05193 0.003868 0.05357 36637.482 2728.6373 2.5 2.5 -0.05193 0.003868 0.09643 36637.482 2728.6373 1.5 2.5 -0.07191 0.005356 0.10000 34711.706 2880.0276 6.5 6.5 -0.16695 0.013853 0.21635 34711.706 2880.0276 6.5 5.5 -0.04735 0.003929 0.03365 34711.706 2880.0276 5.5 6.5 -0.18320 0.015201 0.03365 34711.706 2880.0276 5.5 5.5 -0.06360 0.005277 0.12787 34711.706 2880.0276 5.5 4.5 0.03760 -0.003120 0.05276 34711.706 2880.0276 4.5 5.5 -0.07735 0.006418 0.05276 34711.706 2880.0276 4.5 4.5 0.02385 -0.001979 0.06629 34711.706 2880.0276 4.5 3.5 0.10665 -0.008849 0.05952 34711.706 2880.0276 3.5 4.5 0.01260 -0.001045 0.05952 34711.706 2880.0276 3.5 3.5 0.09540 -0.007916 0.02721 34711.706 2880.0276 3.5 2.5 0.15980 -0.013259 0.05612 34711.706 2880.0276 2.5 3.5 0.08665 -0.007190 0.05612 4711.706 2880.0276 2.5 2.5 0.15105 -0.012533 0.00638 34711.706 2880.0276 2.5 1.5 0.19705 -0.016350 0.04464 34711.706 2880.0276 1.5 2.5 0.14480 -0.012015 0.04464 34711.706 2880.0276 1.5 1.5 0.19080 -0.015831 0.00000 34711.706 2880.0276 1.5 0.5 0.21840 -0.018121 0.02679 34711.706 2880.0276 0.5 1.5 0.18705 -0.015520 0.02679 34711.706 2880.0276 0.5 0.5 0.21465 -0.017810 0.00893 34562.743 2892.4409 7.5 7.5 -0.24703 0.020674 0.20148 34562.743 2892.4409 7.5 6.5 -0.09328 0.007806 0.02074 34562.743 2892.4409 6.5 7.5 -0.26844 0.022466 0.02074 34562.743 2892.4409 6.5 6.5 -0.11469 0.009599 0.14005 34562.743 2892.4409 6.5 5.5 0.01856 -0.001553 0.03365 34562.743 2892.4409 5.5 6.5 -0.13325 0.011152 0.03365 34562.743 2892.4409 5.5 5.5 0.00000 0.000000 0.09324 34562.743 2892.4409 5.5 4.5 0.11275 -0.009436 0.03977 34562.743 2892.4409 4.5 5.5 -0.01570 0.001314 0.03977 34562.743 2892.4409 4.5 4.5 0.09705 -0.008122 0.05899 34562.743 2892.4409 4.5 3.5 0.18930 -0.015842 0.04012 34562.743 2892.4409 3.5 4.5 0.08420 -0.007046 0.04012 34562.743 2892.4409 3.5 3.5 0.17645 -0.014767 0.03527 34562.743 2892.4409 3.5 2.5 0.24820 -0.020772 0.03571 34562.743 2892.4409 2.5 3.5 0.16645 -0.013931 0.03571 34562.743 2892.4409 2.5 2.5 0.23820 -0.019935 0.02012 34562.743 2892.4409 2.5 1.5 0.28945 -0.024224 0.02750 34562.743 2892.4409 1.5 2.5 0.23107 -0.019338 0.02750 34562.743 2892.4409 1.5 1.5 0.28232 -0.023627 0.01185 34562.743 2892.4409 1.5 0.5 0.31307 -0.026200 0.01620 34562.743 2892.4409 0.5 1.5 0.27803 -0.023268 0.01620 34562.743 2892.4409 0.5 0.5 0.30878 -0.025842 0.01157 34552.276 2893.3172 6.5 7.5 -0.26075 0.021836 0.22222 34552.276 2893.3172 6.5 6.5 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