HIGH-RESOLUTION OSCILLATOR STRENGTH MEASUREMENTS OF THE v' = 0,1 BANDS OF THE B–X, C–X, AND E–X SYSTEMS IN FIVE ISOTOPOLOGUES OF CARBON MONOXIDE

The photochemistry of carbon monoxide affects the structure and evolution of many astronomical environments, including interstellar clouds, circumstellar disks around newly formed stars, and the envelopes surrounding highly evolved stars. When in the presence of a strong ultraviolet field, the primary destruction mechanism for interstellar and circumstellar CO and its isotopologues is photodissociation, which is entirely governed by discrete line absorption into predissociating levels in the wavelength range 91.2–111.8 nm. Because the CO spectrum consists primarily of resolved line features, self-shielding effects in high-column density environments (e.g., diffuse clouds: Federman et al. 2003; Sheffer et al. 2007; circumstellar disks: Smith et al. 2009) can lead to strong isotopic fractionation signatures in both CO and elemental oxygen and carbon (e.g., Bally & Langer 1982; Sheffer et al. 2002; Sonnentrucker et al. 2007).

CO self-shielding in the solar nebula has been invoked (Clayton 2002; Yurimoto & Kuramoto 2004; Lyons & Young 2005) to explain the unusual oxygen isotope ratios observed in the earliest solar system condensates, viz. calcium–aluminum inclusions (CAIs) in primitive meteorites. Analysis of solar wind collected by the NASA Genesis mission (McKeegan et al. 2011) showed that the Sun has an oxygen isotope anomaly similar to that of the isotopically lightest CAIs, a result that is consistent with CO self-shielding in the early solar nebula or parent cloud. Astronomical observations of CO isotopologue ratios (Sheffer et al. 2002; Smith et al. 2009) although valuable, are of insufficient precision to quantitatively address the hypothesis that CO self-shielding is responsible for the oxygen isotope ratios seen in CAIs in primitive meteorites. A comprehensive database of line positions, oscillator strengths (f-values), and linewidths for all relevant CO isotopologues is needed to assess this hypothesis and for the development of models of astrophysical environments. For example, the solar system meteoritic oxygen isotope measurements are extremely precise, but the existing CO photoabsorption data are inadequate for accurate photodissociation calculations needed to quantitatively evaluate the nebular CO self-shielding theory. Despite considerable experimental and theoretical efforts, significant uncertainties and gaps remain in the CO isotopologue spectroscopic database.

In 1988, van Dishoeck and Black developed a detailed CO photodissociation model that includes depth-dependent and isotope-selective photodissociation rates. Visser et al. (2009) updated and extended that widely used model, incorporating results from the subsequent 20 years of laboratory measurements. The detailed surveys of high-resolution line positions (¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, ¹³C¹⁸O) and medium- and low-resolution band f-values (¹²C¹⁶O, ¹³C¹⁶O) between 91 and 101 nm by Eidelsberg & Rostas (1990) and Eidelsberg et al. (1991) served as one primary database, supplemented by measured f-values for selected bands from the work of Federman et al. (2001) and Eidelsberg et al. (2004b, 2006). Visser et al. (2009) also incorporated the results of a suite of laser-based measurements by the Ubachs group at Vrije Universiteit Amsterdam (Ubachs et al. 1994, 2000; Cacciani et al. 1995, 1998, 2001, 2002; Cacciani & Ubachs 2004; Eikema et al. 1994). These measurements established linewidths, line positions, and term values for low-J rotational lines in the relatively sharp transitions to low-lying Rydberg states and in selected bands at higher energies; the work included measurements of the isotopologues ¹²C¹⁶O, ¹²C¹⁷O, ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O.

Notwithstanding the progress represented by the spectroscopic compilation of Visser et al. (2009), the current laboratory database is insufficient for a comprehensive understanding of CO photodissociation in astrophysical environments. As Visser et al. point out, line positions for the minor isotopologues ¹²C¹⁷O, ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O are only tabulated for a subset of the CO bands between 91.2 and 118.8 nm. Very few isotopologue f-values have been measured, and those that have been reported in the literature are inconsistent—for example, Eidelsberg et al. (2006) report ¹²C¹⁶O and ¹³C¹⁶O f-values for the E(v = 1)–X(v = 0) band that differ by 16%, while Stark et al. (1992) report a 3% difference. Discrepancies of this size can have substantial effects on CO isotopic fractionation models (e.g., Lyons & Young 2005), wherein quite small differences in isotopologue absorption strengths can produce large fractionation signatures. At the time of the Visser et al. (2009) work, there were no published laboratory data on departures from standard Hönl–London intensity profiles (e.g., Morton & Noreau 1994) in any CO bands, so single f-values were reported for all bands. Yet, in the isoelectronic molecule N₂, such departures are quite common (e.g., Stark et al. 2005, 2008; Heays et al. 2009). J-dependent effects are expected to be widespread throughout the CO spectrum, just as they are in N₂; these nonstandard intensity distributions affect line-by-line self-shielding calculations, and they translate into temperature-dependent band f-values.

This report is part of a larger effort to catalog, interpret, and model the photoabsorption spectra of the isotopologues ¹²C¹⁶O, ¹²C¹⁷O, ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O throughout the 91.2–111.8 nm region. The spectrum of CO in this region is characterized by a complex array of bands that display a wide range of strengths, linewidths, and rotational contours. At the longest wavelengths, transitions to the low-v vibrational levels of the first three Rydberg states (B¹Σ⁺, C¹Σ⁺, E¹Π) in the series converging to the CO⁺ X²Σ⁺ ground state are prominent. Shortward of 100 nm, the spectrum becomes progressively more congested and complex as additional excited electronic states are accessed; the strongest transitions involve higher Rydberg states converging to the CO⁺ ground state and the CO⁺ A²Π state. Overviews and discussions of the spectroscopy of the 91.2–111.8 nm region are found in Huber (1997), Eidelsberg et al. (2004a), Lefebvre-Brion & Lewis (2007), Vázquez et al. (2009), and Lefebvre-Brion et al. (2010).

Here, we report line and band f-values for the six strong vibrational bands between 105.0 and 115.2 nm, associated with transitions from X(v'' = 0) to the v' = 0 and 1 levels of the B¹Σ⁺, C¹Σ⁺, and E¹Π Rydberg states, in five CO isotopologues. We compute revised dissociation branching ratios for the C(v' = 0,1) and E(v' = 0,1) levels based on these f-values. This work complements our recent reports on f-values and dissociation rates of a number of bands in the 92.5–97.5 nm region in ¹²C¹⁶O (Eidelsberg et al. 2012) and ¹³C¹⁶O and ¹²C¹⁸O (Eidelsberg et al. 2014) as well as on term values of the A(v' = 0–9)–X(0) bands in ¹³C¹⁶O (Gavilan et al. 2013).

Direct astronomical observations of interstellar CO absorption into the low-v' levels of the B, C, and E states include those of the Copernicus satellite (e.g., Morton 1975; Snow 1975; Federman et al. 1980) and the FUSE satellite (e.g., Sheffer et al. 2003; Pan et al. 2005). Martian and Venusian atmospheric emissions originating from the B(0), B(1), C(0), and E(0) vibrational levels were recorded with the Hopkins Ultraviolet Telescope (Feldman et al. 2000), the FUSE satellite (Krasnopolsky & Feldman 2002) and the Cassini UVIS instrument (Gérard et al. 2011), and cometary B(0) and C(0) emissions were recorded with FUSE (Feldman et al. 2002).

Perhaps of broader significance than the direct astronomical observations, some of the bands studied in this report play central roles in CO photodissociation models. In particular, the E(0)–X(0) band, the strongest vibrational band in the entire CO spectrum after C(0)–X(0), is identified by van Dishoeck & Black (1988) and Visser et al. (2009) as being the most important contributor to the CO photodissociation rate in the outer regions of interstellar clouds, and the E(1)–X(0) band is a major contributor to isotopic fractionation effects (van Dishoeck & Black 1988). The theoretical understanding of the VUV absorption spectrum of CO is progressing, but it is not yet developed to the point where a predictive interpretation of the relevant predissociation mechanisms exists. The ab initio calculations of Cooper & Kirby (1987) and Kirby & Cooper (1989) established the importance of the D' ¹Σ⁺ valence state (Wolk & Rich 1983) in the predissociation of levels in the ¹Σ⁺ manifold. Tchang-Brillet et al. (1992) and Baker et al. (1995) developed a semi-empirical close-coupling model of the B¹Σ⁺ and D' ¹Σ⁺ states that reproduces trends in band positions and in predissociation linewidths for the low-v' levels of the B state, and Li et al. (1998) used ab initio potential curves and nonadiabatic couplings to study predissociation in both the B and C¹Σ⁺ states. Recent work by Vázquez et al. (2009) Lefebvre-Brion et al. (2010), and Lefebvre-Brion & Eidelsberg (2012) has begun to extend the CO spectroscopic model to include the ¹Π states. However, there is no model of the excited states of CO that is comparable to the comprehensive treatment of the Rydberg–Rydberg and Rydberg–valence interactions in N₂ (Stahel et al. 1983; Spelsberg & Meyer 2001; Lewis et al. 2005a, 2005b, 2008) that successfully reproduces the predissociation and absorption strength patterns within the vibrational progressions of that molecule.

Laboratory studies of the low-v' B–X, C–X, and E–X bands are extensive. The principal spectroscopic results, including line positions, upper-state term values, and linewidths and upper-state lifetimes are reviewed and summarized in Visser et al. (2009). Two experimental approaches have been used in the determination of band f-values: optical absorption measurements (Letzelter et al. 1987; Eidelsberg & Rostas 1990; Eidelsberg et al. 2006; Stark et al. 1992, 1999; Federman et al. 2001; Sheffer et al. 2003) and inelastic electron-scattering measurements (Chan et al. 1993; Zhong et al. 1997). Optical absorption measurements provide, in principle, a direct determination of f-values. However, insufficient instrumental resolution can lead to optical depth effects, which, if not minimized or properly accounted for, result in significant systematic errors. The full-width at half-maximum (FWHM) Doppler width of ¹²C¹⁶O rotational lines at 295 K is 0.21 cm⁻¹ at 110 nm. The majority of previous optical f-value measurements were of low or moderate resolution (ranging from ∼12 to ∼2 cm⁻¹), with the exceptions of Stark et al. (1992, 1999), in which the E(0, 1)–X(0) and B(0, 1)–X(0) bands were measured with resolutions of 0.6 cm⁻¹ and 0.14 cm⁻¹, respectively. The measurements reported in this paper were carried out at the third-generation SOLEIL synchrotron facility in Saint Aubin, France. The vacuum ultraviolet Fourier transform spectrometer (VUV-FTS) on the DESIRS beam line, combining high spectral resolution (0.32 cm⁻¹ or 0.22 cm⁻¹ for the majority of the measurements) and a high signal-to-noise ratio (S/N), has allowed us to improve upon the accuracy and consistency of earlier results and to extend CO absorption measurements to include individual line strengths.

The VUV-FTS is a permanent end-station of the high-resolution absorption spectroscopy branch of the DESIRS beamline (Nahon et al. 2012) at Synchrotron SOLEIL. The beamline undulator provides a continuum background with a 7% bandwidth (6400 cm⁻¹ FWHM, or 7.7 nm, at 110 nm). After a gas-filter chamber removes the unwanted high harmonics emitted by the undulator source, the continuum light passes through a gas-sample chamber before entering the VUV-FTS. Figure 1 displays a typical transmission spectrum.

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High-purity gases [¹²C¹⁶O (Alphagaz, 99.997%), ¹³C¹⁶O (Messer, ¹³C 99.1%; ¹⁶O 99.95%), ¹²C¹⁸O (ICON Isotopes, ¹⁸O 99%), ¹³C¹⁸O (Cambridge Isotopes, ¹³C 99%, ¹⁸O 95%), and a mixed ¹²C¹⁶O/¹²C¹⁷O/¹²C¹⁸O sample (ICON Isotopes, ¹²C¹⁶O 41.5%, ¹²C¹⁷O 48.5%, ¹²C¹⁸O 9.9%)] continuously flowed through a 10 cm long, 1.2 cm diameter, windowless absorption cell equipped with two 15 cm × 28 mm² external capillaries. Two stages of differential pumping maintain the ultrahigh vacuum in the VUV-FTS and in the DESIRS beamline. The absorption cell pressure cannot be directly measured, nor is that pressure constant with position in the cell and capillaries. Pressures in the cell are estimated to have ranged from about 3 × 10⁻⁴ mbar to 5 × 10⁻³ mbar. A 0.1 mbar full-scale capacitance gauge monitored the CO pressure in the external gas-handling system. Small drifts in this pressure (⩽5%) were electronically monitored during absorption scans.

The VUV-FTS is described in detail in de Oliveira et al. (2009, 2011). It is a wave-front division interferometer and relies on a modified Fresnel bi-mirror configuration requiring only flat mirrors. The path difference is scanned through the translation of one reflector. This translation is measured by means of an external frequency-stabilized He–Ne laser, providing a very sensitive interferometric determination of the optical path difference variation. A post-recording computation performs a standard FTS phase correction and corrects for residual sampling errors. Owing to strict linearity in the wavenumber scale, the spectra can be put on an absolute scale using a single reference wavelength in the source. While the maximum resolution of the VUV-FTS is 0.08 cm⁻¹, S/N considerations dictated a resolution of 0.32 cm⁻¹ for most scans; a resolution of 0.22 cm⁻¹ was employed for a subset of the measurements. Over the course of about 30 minutes of data collection, 50 co-added scans typically resulted in an S/N at the peak of the undulator bandpass of 150.

The broad and adjustable continuum bandpass of the DESIRS beamline allowed for the simultaneous recording of room-temperature absorption in pairs of CO bands, facilitating the determination of precise ratios of band strengths. For each isotopologue, three separate undulator settings were used to record: (1) the B(0)–X(0) and B(1)–X(0) bands (hereafter, for brevity, the B(0) and B(1) bands); (2) the C(0), E(0), and C(1) bands; and (3) the C(1) and E(1) bands. For each undulator setting, spectra were recorded with a range of column densities; care was taken to avoid optically thick features, and data analyses were generally restricted to features with peak optical depths less than ∼1.5 (absorption depths less than 77%). For a subset of the recorded spectra, external pressure readings were converted to absolute column densities by measuring absorption in the B(0) band. This required recording comparison spectra with different undulator bandpasses and identical gas pressures. The B(0) band f-value has been well-characterized by high-resolution (0.14 cm⁻¹) laser-based measurements (Stark et al. 1999) and by the synchrotron-based measurements of Federman et al. (2001), and was adopted as a calibration standard with a band f-value of 0.0065(5). Calibrated column densities in the windowless cell ranged from 7.3 × 10¹³ to 2.5 × 10¹⁵ cm⁻². Additional scans of the strong E(0) and C(0) bands were recorded at lower external pressures without calibration.

With the exception of the E(1) band, all of the bands in this study are free of significant perturbations, and line assignments are straightforward. Initial line positions for the ¹²C¹⁶O, ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O isotopologues were taken from the atlas of Eidelsberg et al. (1991). For the ¹²C¹⁷O isotopologue, line positions and molecular constants for the C(0) and C(1) bands were taken from Ubachs et al. (1995) and Cacciani et al. (2001), respectively, and E(0) molecular constants were taken from Cacciani et al. (1995). The strongly blended and perturbed Q branches of the E(1) band in all five isotopologues were spectroscopically analyzed by Ubachs et al. (2000), and their assignments were relied on in the initial assignment of line positions.

In the data reduction, the transmitted intensity, I(ν), where ν is the wavenumber, is related to the measured absorption cross section, σ_exp(ν), through application of the Beer–Lambert law,

$$\begin{equation} I(\nu) = I_0 (\nu)e^{ - N\sigma _{\exp } (\nu)}, \end{equation} \tag{ 1 }$$

where σ_exp(ν) includes the effects of the finite instrument resolution, N is the column density of CO molecules, and I₀(ν) is the background continuum level. For each line within a band, a least-squares fitting routine that accounts for the effect of the finite instrumental resolution was used to determine a value for the line's corrected integrated cross section. All rotational lines were modeled with Voigt profiles. The Gaussian component, calculated separately for each isotopologue and band, is the room-temperature Doppler width of ∼0.21 cm⁻¹ FWHM. The onset of predissociation was established at J > 37 for the B(0) vibrational level of ¹²C¹⁶O and at J > 17 for the B(1) level (Eidelsberg et al. 1987). For the range of upper-state rotational levels sampled in our room temperature spectra, typically J ⩽ 25, there are no reports of measured line broadening in either vibrational level, and the Lorenztian component was set to zero for lines in the B(0) and B(1) bands for all isotopologues. Predissociation is known to occur for all rotational levels in the E(0), E(1), and C(1) states, but the associated line broadening is too small to be directly observed in our measurements. Published values of linewidths and lifetimes from laser-based measurements (Cacciani et al. 1998, 2001; Ubachs et al. 2000) were used to establish the Lorenztian components of lines in bands terminating in these states as well as in the C(0) band. The Lorentzian components ranged from 0.003 cm⁻¹ FWHM for lines in the C(0) band of all isotopologues (Cacciani et al. 2001) to 0.036 cm⁻¹ FWHM for the E(1) band of ¹³C¹⁸O (Ubachs et al. 2000).

The instrument function is described by a sinc function (0.32 cm⁻¹ FWHM for most spectra), which results from the finite path difference in the recorded interferogram. In their study of the ¹⁴N¹⁵N spectrum with the DESIRS VUV-FTS, Heays et al. (2011) report the necessity of including an additional Gaussian component in the instrument function to account for fitted linewidths that were ∼0.05 cm⁻¹ broader than expected. They attributed this to the nonideal collimation of the synchrotron beam entering the VUV-FTS. This correction was not adopted in the present study, as it has a much smaller effect on measured line strengths than on measured linewidths.

By varying the position and integrated cross section for each line, the least-squares fitting routine minimized the difference between a model transmission spectrum (calculated by a convolution of the line's Voigt profile in absorption with the instrumental sinc function) and the measured transmission spectrum. Figure 2 illustrates the quality of a fit to the B(0) band in ¹²C¹⁶O. Fitting uncertainties in the integrated cross sections for each line were assessed by the least-squares routine; they varied according to the S/N of each spectrum and the strength of the absorption, and were typically about 3% (one standard error). Uncertainties in the adopted literature values of linewidths produced very small additional uncertainties in the line cross sections, typically less than 1%.

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Uncertainties in the column densities of individual spectra were significantly larger than the statistical uncertainties of the fitting procedure. Because all absolute column densities were determined by absorption in the B(0) band (at the same external pressure settings), the 7% uncertainty in the B(0) f-value, adopted from combining the results of Stark et al. (1999) and Federman et al. (2001), applies to the derived column densities. Small variations in the external pressure during each 30 minute scan resulted in additional column density uncertainties, estimated to be less than 5%. Heays et al. (2011) discuss a further source of f-value uncertainty associated with the apparent effect of mechanical vibrations on the recorded spectrum—there is a small, but noticeable, variation in the center energy of the synchrotron-beam bandpass during sequential scans of the VUV-FTS scanning mirror. When multiple scans are summed (typically, 50 scans were summed to produce each spectrum), there are small distortions in line shapes and systematic errors can be introduced in line strengths. The line strength uncertainties are not yet well characterized, but they can be minimized by avoiding the analysis of deeply absorbed lines and the analysis of lines near the low-intensity wings of the synchrotron-beam bandpass. Importantly, mechanical vibration issues only negligibly affect the ratios of f-values of features appearing in the same spectrum.

The integrated cross sections of individual rotational lines, determined from the fitting procedure, were converted into line oscillator strengths according to (Morton & Noreau 1994)

$$\begin{equation} f_{J^{\prime},J^{\prime\prime}} = \left({\frac{{4\varepsilon _0 m_e c^2 }}{{e^2 }}} \right)\frac{{\int {\sigma (\nu)d\nu } }}{{\alpha _{J^{\prime\prime}} }} = (1.1296 \times 10^{ - 4})\frac{{\int {\sigma (\nu)d\nu } }}{{\alpha _{J^{\prime\prime}} }}, \end{equation} \tag{ 2 }$$

where the integrated cross section is in units of cm, and $\alpha _{J^{\prime \prime} }$ is the fractional population of CO molecules in the J'' rotational level as determined from a normalized Boltzmann factor based on CO isotopologue ground state term values (Guelachvili et al. 1983). For transitions to unperturbed upper vibronic states, the rotational line f-values follow simple patterns described by Hönl–London factors (e.g., Morton & Noreau 1994), and the band f-value is related to the rotational line f-values by

$$\begin{equation} {}^1{ \sum} \hbox{--} {}^1{ \sum} {:\quad } f = \frac{{(2J^{\prime\prime} + 1)f_{J^{\prime}J^{\prime\prime}} }}{{S_{J^{\prime},J^{\prime\prime}} }} \end{equation} \tag{ 3 }$$

$$\begin{equation} {}^1{ \prod} \hbox{--} {}^1{ \sum} {:\quad } f = \frac{{2(2J^{\prime\prime} + 1)f_{J^{\prime}J^{\prime\prime}} }}{{S_{J^{\prime},J^{\prime\prime}} }}, \end{equation} \tag{ 4 }$$

where the $S_{J^{\prime},J^{\prime \prime }}$ are Hönl–London factors.

For unperturbed bands, the band f-values derived from the application of Equations (3) and (4) to measured line f-values are independent of the rotational quantum number J. The B(0) and B(1) bands follow this description, and, hence, it is only necessary to specify a single band f-value to categorize the distribution of strengths among rotational lines. To simplify the least-squares fitting procedure for these bands, a single band f-value was varied and optimized, and Equations (3) and (4) were used to fix the ratios of line strengths in the fits.

The C(0), C(1), E(0), and E(1) bands in all isotopologues display weakly anomalous P-, Q-, and R-branch intensity patterns and are characterized by a J dependence of band f-values derived from Equations (3) and (4). For transitions from the ground state of CO, it is the upper-state wave function that is responsible for all departures from the standard line strength formulas. Accordingly, the band f-values derived from Equations (3) and (4) are considered as functions of J'. It was often sufficient to represent the J'-dependence of the derived band f-values as a linear function in J'(J' + 1); in such cases the P-, Q-, and R-branch intensity patterns were fit by varying and optimizing the J' = 0 intercept and the slope of the linear function. The J-dependent f-value patterns associated with specific bands are presented below.

4.1. B(0) and B(1) Bands

4.2. C(0), C(1), E(0), and E(1) Bands

The C¹Σ⁺ and E¹Π states are the σ and π members of the 3p Rydberg complex associated with the CO⁺ X²Σ⁺ core. The C(0) and E(0) bands, at 108.8 and 107.6 nm in ¹²C¹⁶O, respectively, are the two strongest band features in the CO absorption spectrum; the C(1) and E(1) bands are located at 106.3 and 105.2 nm. Representative absorption spectra in ¹²C¹⁶O are displayed in Figure 3. As with the B(0) and B(1) bands, the DESIRS undulator bandwidth allowed for the determination in each isotopologue of ratios of the C(0) and E(0) f-values and, separately, the C(1) and E(1) f-values, without reference to absolute absorption column densities.

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All four bands display some level of J-dependence in their rotational branch intensity patterns; the J-dependences within each branch were modeled as linear functions in J'(J' + 1) with a common J' = 0 intercept. Because of the deep absorption present in the highly blended Q-branches of the E(0) and E(1) bands, the Q-branch line strengths were sometimes fit independently of the P- and R-branch patterns. The band f-values, determined by summing all of the individual line contributions, were generally insensitive to the particulars of the fitting procedure. A fit to a portion of the ¹²C¹⁶O E(0) band, including the congested Q-branch, is shown in Figure 4. The quality-of-fit of the assumed linear dependence with J'(J' + 1) of the measured f-values is imperfect. A more complex parameterization is not justified by the S/N of the measured spectra.

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The J-dependences of the band f-values derived from Equation (4) for the P- and R-branch lines in the E(0) band of ¹²C¹⁶O are displayed in Figure 5, along with linear fits to a J'(J' + 1) dependence. The figure shows the P-branch lines increasing in strength and the R-branch lines decreasing in strength with J'(J' + 1). The opposite behavior is seen in the P- and R-branches of the C(0) band. This mutual line-intensity pattern in the two bands is expected as the result of an L-uncoupling interaction between the two components of the 3p Rydberg complex (Lefebvre-Brion & Field 2004, p. 394). That interaction, which is also responsible for the Λ-doubling in the E(0) level, has been evaluated by Hines et al. (1990) and by Haridass et al. (1994). Similar branch intensity patterns are seen in the E(1) and C(1) P- and R-branches in all isotopologues.

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Our measured f-value ratios for the two pairs of bands are listed in Table 1. We have assigned 5% uncertainties to these ratios. Within our estimated experimental uncertainties, there is no discernible dependence on the nuclear reduced mass in either ratio. In the absence of more definitive evidence, in the rest of this paper we adopt isotopologue-independent average values for the C(0)/E(0) and C(1)/E(1) ratios of 1.85(9) and 0.99(5), respectively.

All rotational levels in the E(1) vibrational state are predissociated by a currently unidentified mechanism, and there is an additional localized interaction with the rotational levels of the k³Π(v = 6) state (Ubachs et al. 2000) that causes line shifts and line broadening. Ubachs et al. (2000) measured line positions and linewidths in six CO isotopologues with a high-resolution laser system. They spectroscopically analyzed the highly blended Q-branches, identified multiple additional lines stemming from the E(1)–k(6) interaction, and modeled the interaction via a single J-independent spin–orbit coupling parameter. To successfully fit the Q-branch features in our spectra, wherein almost no individual lines are resolved, we adopted the spectroscopic parameters derived by Ubachs et al. (2000). A fit to a portion of the ¹³C¹⁶O E(1)–X(0) SOLEIL spectrum is shown in Figure 6. In our absorption spectra, we are able to identify and characterize a small number of perturbed lines not presented in the spectroscopic study of Ubachs et al. (2000). Level widths and term values for the upper states (when not reported by Ubachs et al.) of these lines are compiled in Table 2. For lines observed by Ubachs et al. (2000), our measured widths tend to be somewhat larger, though the results are consistent within the stated uncertainty ranges.

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Table 2. Measured Widths and Term Values (T) of Perturbed E(1) Levels^a,b

	12C16O	13C16O	12C18O	13C18O
	this work c	this work c	this work	this work
E(1) Je = 7d	0.13(3) 0.10(1)	0.15(3) 0.12	0.10(2)
k(6) Je = 7	0.22(15)	0.20(3) 0.15	0.22(15)
E(1) Jf = 7		0.16(2)
k(6) Jf = 7		0.14(18)	0.29(6)
			T = 95131.95e
k(6) Jf = 1				0.22(26)
				T = 94985.14e

Notes. ^aUncertainties (in parentheses; 1 standard error) are in units of the last-quoted decimal place. ^bAll results are FWHM in cm⁻¹. ^cUbachs et al. (2000). ^dThe subscripts e and f designate the parities of rotational levels. ^eReferenced to J = 0 level of X(0); X(0) term values from Ubachs et al. (2000).

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4.3. Isotopologue Dependence of f-values

The extent of any isotopologue dependence of the C(v) and E(v) band f-values is of significance in the modeling of isotopic fractionation processes (see Section 1). Our most direct measures of these dependences come from the analyses of absorption spectra of mixed samples of CO isotopologues. For this purpose, we used a commercially prepared sample of ¹²C¹⁶O/¹²C¹⁷O/¹²C¹⁸O and a sample of ¹²C¹⁶O/¹²C¹⁸O prepared in the laboratory. The isotopologue concentrations in the samples were determined by a comparison of B(0) band absorption strengths. Under the assumption that the B(0) band f-value is independent of isotopologue (see our earlier discussion of this point), the sample concentrations were found to be ¹²C¹⁶O/¹²C¹⁷O/¹²C¹⁸O = 0.415(4)/0.485(5)/0.099(3) and ¹²C¹⁶O/¹²C¹⁸O = 0.293(6)/0.707(14), with uncertainties, based on fitting statistics, in units of the last-quoted decimal place. Ratios of f-values for the C(0), C(1), E(0), and E(1) bands in ¹²C¹⁶O and ¹²C¹⁷O, and in ¹²C¹⁶O and ¹²C¹⁸O, were determined from absorption spectra of the two mixed sample bottles at a resolution of 0.22 cm⁻¹. The concentration ratio of ∼3:7 for the ¹²C¹⁶O/¹²C¹⁸O sample led to an optically thick Q-branch in the ¹²C¹⁸O E(0) band; the ratio of f-values for this band was determined from analysis of the P- and R-branches only. The ¹²C¹⁶O/¹²C¹⁸O E(1) f-value ratio was not determined because of excessive optical depth in the Q-branch of ¹²C¹⁸O and blending of lines in the P- and R-branches of the two isotopologues. Figure 7 shows a representative spectrum of the C(1) bands of the mixed ¹²C¹⁶O/¹²C¹⁷O/¹²C¹⁸O sample.

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The measured ratios of band f-values from the mixed-gas samples are summarized in Table 3. The results support isotopologue-independent f-values for the C(v = 0,1) and E(v = 0,1) bands. Establishing isotopologue-specific band f-values to accuracies significantly better than 4% will require a more thorough experimental study of a full complement of mixed gas samples. In what follows, we provisionally adopt isotopologue-independent f-values for the C(v = 0,1) and E(v = 0,1) bands.

Table 3. Measured Ratios of Isotopologue-specific f-values^a

	C(0)b	C(1)	E(0)	E(1)
12C17O/12C16O	1.00(4)	1.01(4)	1.01(4)	1.05(4)
12C18O/12C16O		1.01(4)	1.00(4)

Notes. ^aUncertainties (in parentheses; 1 standard error) are in units of the last-quoted decimal place. ^bX(0) is the lower state of all listed bands.

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4.4. Absolute f-values

4.5. Photodissociation Branching Ratios

Table 6 lists calculated photodissociation branching ratios (also referred to as predissociation probabilities) for the C(v = 0,1) and E(v = 0,1) vibrational levels. The branching ratios are derived from lifetime (Cacciani et al. 1998, 2001) and linewidth (Ubachs et al. 2000) measurements combined with our reported f-values. The methodology of the calculation is fully described in Cacciani et al. (1998). Briefly, the dissociation branching ratio, η, is determined by the lifetime, τ, and the radiative decay rate, A_rad, via

$$\begin{equation} \eta = 1 - A_{\rm rad} \tau. \end{equation} \tag{ 5 }$$

Table 6. Dissociation Branching Ratios^a

	12C16O	12C17O	12C18O	13C16O	13C18O
C(0)
this workb,c	−0.07(17)			−0.07(17)	0.10(15)
Cacciani et al 2001	0			0	0.17
C(1)
this work	0.62(8)	0.83(3)	0.87(2)	0.82(3)	0.91(2)
Cacciani et al 2001	0.65	0.84	0.88	0.83	0.91
E(0)
this work	0.83(3)			0.75(5)	0.77(5)
Cacciani et al 1998	0.78–0.85			0.69–0.84	0.69–0.84
E(1)
this work	0.971(5)	0.960(9)	0.960(7)	0.963(7)	0.945(12)
Cacciani et al 1998	0.972–0.986			0.953–0.976	0.936–0.956
& Ubachs et al 2000

Notes. ^aCalculated from band f-values combined with lifetime and linewidth measurements (see the text). ^bUncertainties (in parentheses; 1 standard error) are in units of the last-quoted decimal place. ^cBlank entries indicate that no lifetime or linewidth data are available.

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Measured linewidths (Ubachs et al. 2000) are converted to lifetimes by

$$\begin{equation} \tau = \frac{1}{{2\pi \Gamma c}}, \end{equation} \tag{ 6 }$$

where Γ is the natural linewidth (FWHM) and c is the speed of light. A_rad is the sum of Einstein-A coefficients for all radiative transitions from the upper state. An Einstein-A coefficient for a single vibrational band, e.g., E(0)–X(0), is directly determined from the band f-value (Morton & Noreau 1994), and in each of the cases considered here, dominates the sum. Using radiative branching ratios estimated from band f-values within the E–X system and from calculated branching into the E–A and E–B systems (Kirby & Cooper 1989), Cacciani et al. (1998) estimate that A_rad is 16% larger than the A coefficient for the E(0) band. Cacciani et al. (1998) identified the f-values of the E(0) and E(1) bands as the major contributors to the uncertainty in the dissociation branching ratios for E(0) and E(1), and they presented ranges of branching ratios based on the existing f-value literature (Eidelsberg & Rostas 1990; Stark et al. 1992; Chan et al. 1993). In Table 6, we adopted the relevant estimates of Cacciani et al. (1998) along with our newly measured E(0) and E(1) band f-values to derive a set of branching ratios. For the ¹²C¹⁷O and ¹²C¹⁸O isotopologues, we used the E(1)–X(0) linewidth measurements of Ubachs et al. (2000) to establish the upper state lifetimes. Fractionation effects should be small due to any differences in isotopologue branching ratios for the E(1) level, as all of the branching ratios are very close to unity. This is not the case for the E(0) level, and either linewidth or lifetime measurements are needed to establish the E(0) branching ratios for the ¹²C¹⁷O and ¹²C¹⁸O isotopologues.

There is presently no experimental evidence for predissociation in the C(0) vibrational level of ¹²C¹⁶O. Cacciani et al. (2001) assumed that their measured lifetime for the C(0) level in ¹²C¹⁶O and ¹³C¹⁶O, 1.78 ns, represents a purely radiative decay, and they attributed the shorter lifetime for the ¹³C¹⁸O isotopologue (1.50 ns) to a dissociative contribution to the decay (branching ratio of 17%). We did not make these assumptions, but rather used our measured band f-values and the lifetime measurements of Cacciani et al. (2001) to derive the dissociation branching ratios. Our results in Table 6 corroborate the conclusion that there is no predissociation in the ¹²C¹⁶O and ¹³C¹⁶O C(0) levels, and they are in good agreement with earlier determinations for the E(0), E(1), and C(1) levels.

The work presented here is part of a larger effort to establish a reliable high-resolution database for CO isotopologue absorption features in the 91.2–111.8 nm region (Eidelsberg et al. 2012, 2014). Our ¹²C¹⁶O f-values for the B–X, C–X, and E–X bands are directly applicable to the determination of column densities in diffuse molecular clouds (e.g., Sheffer et al. 2003; Crenny & Federman 2004). In this context, the moderate branch-dependences and J-dependences in the C–X and E–X bands (and the absence of any such dependences in the B–X bands) allow for the determination of temperature-dependent band f-values that can be applied to the interpretation of astrophysical observations. The resulting temperature dependences are, in fact, very modest. We calculate that the T = 50 K ¹²C¹⁶O C(0) and C(1) band f-values are 1.4% and 0.8% smaller, respectively, than the room-temperature f-values, and T = 10 K f-values are 1.6% and 1.1% smaller than the respective room-temperature f-values. For the E(0) and E(1) bands, the percentage changes are +3.0% and −1.7% at T = 50 K, and +3.7% and −4.2% at T = 10 K. We caution against extrapolating our results to temperatures above 300 K, as branch-dependences and J-dependences can change radically due to perturbations of high-J levels.

In addition to providing improved f-values for the interpretation of astronomical observations, our measurements will inform ongoing efforts to develop comprehensive treatments of the dissociation mechanisms in CO (e.g., Lefebvre-Brion et al. 2010; Lefebvre-Brion & Eidelsberg 2012). Any successful quantitative model of CO dissociation mechanisms must reproduce the isotopologue-specific patterns of absorption strengths and line widths (or the isotopologue independence of these patterns). Our most precise measurements come from analyses of absorption in mixed gas samples of ¹²C¹⁶O/¹²C¹⁷O and ¹²C¹⁶O/¹²C¹⁸O. These measurements show minimal or no isotopologue dependence in the C(v = 0,1) and E(v = 0,1) band f-values at the ∼5% uncertainty level. The absence of measureable isotopologue dependence in our band f-values, as well constraining CO dissociation models, is an important factor in establishing more reliable photodissociation branching ratios.

Recent CO photolysis experiments performed at the Advanced Light Source (ALS) synchrotron (Chakraborty et al. 2008, 2012) reported unexpectedly large enrichments in ¹⁷O in the CO₂ product for the synchrotron beam centered at 105.17 and 107.6 nm. Chakraborty et al. concluded that the wavelength dependence of the relative enrichments in ¹⁷O and ¹⁸O do not support the CO self-shielding theory for the origin of the nearly equal depletions seen in ¹⁷O and ¹⁸O in CAIs (Clayton 2002; Yurimoto & Kuramoto 2004; Lyons & Young 2005), which would have implications for the UV environment experienced by the solar system. Understanding the full significance of the distribution of oxygen isotopes in CAIs for solar system formation requires an accurate assessment of isotope fractionation in all of the astrochemically relevant dissociation bands of CO, including the long-wavelength bands reported in this manuscript.

CO absorption in the ALS bandpasses at 105.17 and 107.6 nm is dominated by the C–X and E–X bands presently reported. Chakraborty et al. attributed the ¹⁷O enrichment to "accidental predissociation" in the E(1) band, due to interaction with the k³Π(v = 6) excited state, where an isotopologue-dependent alignment of several rotational levels occurs. Such near-resonance spin–orbit coupling between triplet and singlet states is known to produce strong isotope effects in some molecules (see discussion in Chakraborty et al. 2008), but in this case the interaction is very weak (Ubachs et al. 2000) and is unlikely to be the source of the measured ¹⁷O enrichment (Lyons et al. 2009; Federman & Young 2009; Yin et al. 2009). The minimal isotopologue dependence of our reported C–X and E–X f-values places a further strong constraint on the interpretation of the large ¹⁷O enrichments in the photolysis experiments: f-value variations can be ruled out as being responsible for the large ¹⁷O enrichments.

Self-shielding by C¹⁸O is a more likely explanation. Using our measured band f-values and J-dependent line strengths along with line widths reported by Ubachs et al. (2000), we developed synthetic room-temperature cross section profiles for the E(1) band for each isotopologue. At the lowest photocell column density reported by Chakraborty et al. (2012) for the ALS bandpass centered on the E(1) band at 105.17 nm–2.6 × 10¹⁷ cm⁻²—the peak optical depths of the strong Q-branches in ¹²C¹⁶O, ¹²C¹⁷O, and ¹²C¹⁸O are ∼570, 0.22, and 1.2, respectively. With these peak optical depths, absorption in the ¹²C¹⁸O Q-branch, which normally accounts for ∼50% of the E(1) band absorption, will be significantly reduced by self-shielding while absorption in the ¹²C¹⁷O Q-branch will be only moderately affected by self-shielding. Hence, the ¹⁷O/¹⁸O ratio in the photolysis products should be enhanced. For the ALS measurements centered on the E(0) band at 107.61 nm, the peak E(0) Q-branch optical depths for the lowest photocell column density (1.3 × 10¹⁷ cm⁻²) are ∼1200, 0.46, and 2.5 for ¹²C¹⁶O, ¹²C¹⁷O, and ¹²C¹⁸O. Again, significant self-shielding should be expected in ¹²C¹⁸O relative to ¹²C¹⁷O. Aside from self-shielding effects, there remains the possibility that isotope-dependent dissociation probabilities for C¹⁷O and C¹⁸O could account for the ¹⁷O enhancement in the photolysis products (Lyons 2014). The dissociation branching ratios derived from our f-value measurements and literature line widths (Table 6) should help clarify this possible contribution. In the future, we plan to use the f-values reported in this paper to more quantitatively evaluate the effects of self-shielding on the fractionation results of Chakraborty et al.

This research was supported by funds from NASA (grants NNX09AC5GG to Wellesley College and NNG 06-GG70G and NNX10AD80G to the Univ. of Toledo), CNRS (France), and Programme National Physico-Chimie du Milieu Interstellaire (PCMI). ANH was supported by grant number 648.000.002 by the Netherlands Organization for Scientific Research (NWO) via the Dutch Astrochemistry Network. L.G. and J.L.L. acknowledge the financial support of the European Community 7th Framework Programme (FP7/2007–2013) Marie Curie ITN under grant agreement # 238258 ("LASSIE" contract).