${{\rm{C}}}_{60}^{+}$ IN DIFFUSE CLOUDS: LABORATORY AND ASTRONOMICAL COMPARISON

In 2010 neutral C₆₀ was detected in a young planetary (Cami et al. 2010) and reflection (Sellgren et al. 2010) nebula by observation of its four characteristic infrared bands in emission. Cami et al. (2010) also identified the infrared spectral signatures of the larger fullerene C₇₀. Since then there have been reports of C₆₀ in a variety of stellar environments (for example, Roberts et al. 2012 and references therein). Recently, the presence of the singly charged cation ${{\rm{C}}}_{60}^{+}$ was confirmed in the diffuse medium (Campbell et al. 2015), as had been first predicted by Kroto (1987).

In 1994 Foing & Ehrenfreund (1994) observed two diffuse interstellar bands (DIBs) near 9577 and 9632 Å and proposed that they are due to ${{\rm{C}}}_{60}^{+}$ based on the absorption spectrum recorded in a neon matrix (Fulara et al. 1993). Confirmation of the presence of ${{\rm{C}}}_{60}^{+}$ in diffuse clouds came as a result of laboratory measurements obtained by photofragmentation of ${{\rm{C}}}_{60}^{+}-{\rm{He}}$ at an internal temperature of around 6 K in a cryogenic radiofrequency ion trap (Campbell et al. 2015). In addition to the wavelengths, the astronomical data are consistent with both the widths of the laboratory bands which are broadened by the lifetime (ps) of the excited electronic state and their relative intensities.

The spectral region covered by the ${{\rm{C}}}_{60}^{+}$ absorptions is dominated by strong telluric water lines leading to variations in the DIB wavelengths, FWHM, and equivalent widths (EWs). Their characteristics are also affected by the accuracy of the stellar corrections, the number of clouds sampled along a particular line of sight, and the environmental conditions (e.g., temperature) in the interstellar clouds themselves. Combined, all of these factors contribute to some uncertainty in the astronomical data, for which the systematic errors are larger than for the laboratory results (see, for example, Figure 1 in Walker et al. 2015).

The laboratory data are an approximation to the electronic spectrum of ${{\rm{C}}}_{60}^{+}$ because the wavelengths are to a small extent perturbed by the presence of the weakly bound helium atom. Due to the importance of ${{\rm{C}}}_{60}^{+}$ identification, further laboratory results are presented here which allow more accurate limits to be placed on the wavelengths of the ${{\rm{C}}}_{60}^{+}$ absorption bands. These have been obtained following improvements to the experimental apparatus. Concurrently, the complete set of astronomical data published hitherto for the DIBs near 9577 and 9632 Å are compared. The scatter in the wavelengths, FWHM, and EWs in the astronomical spectra is found to be much larger than the uncertainty in the laboratory results; however, the agreement between the two sets of data is convincing.

Laboratory experiments used the same cryogenic ion trap apparatus and methodology described by Campbell et al. (2016). The ${{\rm{C}}}_{60}^{+}$ ions are produced by electron bombardment of the neutral gas and subsequently confined in a linear quadrupole trap that is mounted onto the second stage of a closed cycle helium cryostat (temperature of trap walls, T_nom = 3.7 K). In the trap the ions interact with high number density helium buffer gas (10¹⁵ cm⁻³), which serves the purpose of cooling the internal degrees of freedom of ${{\rm{C}}}_{60}^{+}$ and also gives rise to the formation of weakly bound ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ complexes. After pumping out the helium buffer gas for several hundred milliseconds the ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ ions are exposed to continuous wave laser radiation. The trap contents are subsequently analyzed using a quadrupole mass spectrometer and a Daly detector. Fragmentation spectra are recorded by monitoring the decrease in the number of ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ ions as a function of the laser wavelength.

The conversion of ${{\rm{C}}}_{60}^{+}$ ions into complexes is significantly more efficient at 3.7 K than at the higher trap wall temperature of 5 K used earlier by Campbell et al. (2015). Conversion efficiencies (${N}_{{{\rm{C}}}_{60}^{+}-{\rm{He}}}/{N}_{{{\rm{C}}}_{60}^{+}}$) of more than 50% have been achieved while in the previous study only a few percent was possible. The present observations suggest a different mechanism of ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ formation occurs at this lower temperature.

Typical measurements of the two strongest absorption bands in the electronic spectra of ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}\;(n=1\mbox{--}3)$ are presented in Figure 1. The experimental data for each band have been obtained using two laser fluences. Due to the finite number of confined ions, measurements recorded with ≥20% attenuation show a saturation broadening. An example of this effect was reported by Campbell et al. (2015).

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The laboratory spectra shown in the bottom panel of Figure 1 are homogeneously broadened as a result of the picosecond lifetime of the excited electronic state and are thus well represented by a Lorentzian function. These fits lead to central wavelengths which lie within 0.1–0.2 Å of the results obtained using a Gaussian. Small deviations from either a Gaussian or Lorentzian profile also result in differences of 0.1–0.2 Å depending on the laser fluence used, with this effect slightly more pronounced for the 9632 Å band. The astronomical data (Section 4) are typically evaluated using a Gaussian function.

The central wavelengths obtained from Gaussian and Lorentzian fits to the ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}\;(n=1\mbox{--}3)$ spectra recorded with different fluence are plotted in Figure 2. The data for both bands show a linear behavior as a function of n and this allows extrapolation to the corresponding values of bare ${{\rm{C}}}_{60}^{+}$.

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The experimental data recorded at 3.7 K (Figure 2) imply a shift of ∼0.7 Å per adsorbed helium atom, similar to the value recently reported after the formation of ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}\;(n=5\mbox{--}22)$ in a helium nanodroplet and measurement in the region of the 9577 Å absorption (Kuhn et al. 2016). Electronic structure calculations indicate that the binding energy for helium adsorbed on ${{\rm{C}}}_{60}^{+}$ is largest above the center of a hexagon, with that above a pentagon only 1.3 meV smaller. The vertex sites as well as those located above the carbon bonds are less favorable (Leidlmair et al. 2012). Molecular dynamics simulations performed by these authors show that for ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ with n ≤ 32 the adsorbed helium atoms occupy the hexagonal and pentagonal sites. As there are many equivalent sites one might anticipate that the perturbation caused to the electronic transition of ${{\rm{C}}}_{60}^{+}$ is additive with n.

The central wavelengths in the ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{2}$ spectrum are rather sensitive to the experimental conditions used. For example, measurements recorded at T_nom = 4.7 K yield 9577.8 Å whereas a value of 9578.4 Å is obtained at 3.7 K. The former result lies within the uncertainty of the corresponding band for ${{\rm{C}}}_{60}^{+}-{\rm{He}}$, in accordance with the 22-pole ion trap measurements reported by Campbell et al. (2015). The mechanism of formation of helium complexes may be different at the two temperatures leading to changes in the distribution of ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}$ isomers produced in the trap. One possibility is that at the lowest trap temperatures the complexes are not formed via sequential ternary association but rather through bimolecular collisions with (possibly doped) He_n clusters. These neutral species may be formed on special regions of the cold surface and sublimate into the gas phase. Subtle changes to the n ≥ 2 spectra could arise, for example, if the helium atoms are localized and their relative position is influenced by the formation mechanism.

Whatever the reason for the difference, the low temperature n = 1–3 data reported here allow a better estimate of the corresponding wavelengths for ${{\rm{C}}}_{60}^{+}\;(n=0)$. This gives values of 9577.0 ± 0.2 Å and 9632.1 ± 0.2 Å, where the uncertainties from the fits are the 2σ level.

To our knowledge eight astronomical studies of the two DIBs near 9577 and 9632 Å have been published. Table 1 summarizes the reported wavelengths, FWHMs, and EWs. The majority of studies give wavelengths without any error bars and several report only integer values. In addition, it appears to be common practise to list "average" values of the wavelengths following observations toward several different stars but "individual" values of the other parameters.

Table 1 highlights the spread in the reported wavelengths of the two DIBs. The difference between the longest and shortest values are 1.9 and 1.3 Å for the 9632 and 9577 DIBs, respectively. The laboratory results for ${{\rm{C}}}_{60}^{+}-{\rm{He}}$ and the inferred values of bare ${{\rm{C}}}_{60}^{+}$ lie within this spread for both absorption bands. The extraction of an accurate wavelength for the 9632 DIB appears more complicated because of the overlap of the interstellar absorption with a Mg ii stellar line, in addition to the necessary telluric corrections and continuum level setting.

Only Jenniskens et al. (1997) and Cox et al. (2014) provide uncertainties with the reported wavelengths. They give 9577.4 ± 0.2 Å and 9577.1 ± 0.2 Å for the 9577 DIB and 9632.6 ± 0.2 Å and 9632.1 ± 0.2 Å for the 9632 DIB, respectively. The study by Walker et al. (2015) reported 9577.4 and 9577.2 Å for the 9577 DIB and stressed the difficulty in providing, with confidence, an estimation of the systematic errors. The mean values of the wavelengths from all eight studies are 9632.2 ± 0.5 Å and 9577.0 ± 0.3 Å, where the errors are merely the standard deviations. These are close to both the results from Cox et al. (2014) and the experimental wavelengths of 9632.1 and 9577.0 Å for ${{\rm{C}}}_{60}^{+}$ inferred in this article from the ${{\rm{C}}}_{60}^{+}-{{\rm{He}}}_{n}(n=1\mbox{--}3$) data.

The FWHM reported for the 9577 DIB ranges from 2.3 to 5.4 Å, with 2.0–4.5 Å for the DIB at 9632 Å. The FWHM provides information on the rotational temperature of ${{\rm{C}}}_{60}^{+}$ in the absence of broadening due to other effects such as several interstellar clouds viewed along the line of sight. At temperatures below 30 K the ∼2.5 Å width is determined by the lifetime of the excited electronic state. An increase in the FWHM from this value indicates temperatures higher than 30 K in the local environment. The mean values for the 9632 and 9577 DIBs are 3.2 ± 1.0 Å and 3.6 ± 1.0 Å, respectively, and these are close to those obtained in laboratory spectrum of ${{\rm{C}}}_{60}^{+}-{\rm{He}}$ (Campbell et al. 2015).

Comparison of the EWs for the two bands provides information on the relative intensities of the 9632 and 9577 Å absorptions. As shown in Table 1 the ratio of the EWs has a rather large scatter, and spans the range from 0.8 to 1.6. The ratio also appears to be strongly dependent on the reference star used for the telluric corrections. Herbig (2000) has stated that the EWs obtained in his study are "not entitled to high weight." The mean ratio given in Table 1 is 1.0 ± 0.2. It should be emphasized that while this is consistent with the value of 0.8 reported in the laboratory study, the latter value also has an estimated uncertainty of around 20% as has been stated in Campbell et al. (2015).

4.1. Weaker DIBs Assigned to ${{\rm{C}}}_{60}^{+}$

Three DIBs matching the characteristics of weaker absorption bands in the laboratory spectrum of ${{\rm{C}}}_{60}^{+}-{\rm{He}}$ have also been reported (Walker et al. 2015; Campbell et al. 2016). The wavelengths obtained from Gaussian fits to the astronomical spectra are given in Table 2 along with the corresponding laboratory values for ${{\rm{C}}}_{60}^{+}$ estimated assuming a shift of 0.7 Å due to the helium atom, as determined from the data presented in Figure 2.

Table 2.  Extrapolated ${{\rm{C}}}_{60}^{+}$ Wavelengths (Å) and Weak DIBs

Laboratorya	Objectb
${{\rm{C}}}_{60}^{+}$	HD 183143	HD 169454
9427.8	⋯	9428.4
9365.2	9365.7	9365.6
9348.4	9348.5	⋯

Notes.

^aEstimated using the data shown in Figure 2 and the previously reported n = 1 wavelengths at 9428.5, 9365.9, and 9349.1 Å. Uncertainties in the inferred wavelengths are ±0.2 Å at the 2σ level. ^bIt should be emphasized that the values are from Gaussian fits to the interstellar bands. Due to the weakness of the DIBs and the necessary corrections, the uncertainties in these astronomical data are likely to be larger than for the laboratory absorptions. See Section 4.1 for a discussion of this.

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Walker et al. (2015) emphasized that it is difficult to estimate the uncertainties in the wavelengths of these DIBs given their weakness in comparison with the two strong bands near 9577 and 9632 Å as well as the necessary telluric corrections and continuum line setting. As a result only formal fitting errors were provided. Walker et al. (2015) state that the reported HD 183143 wavelengths were determined under the assumption that one of the two clouds sampled along the line of sight makes a dominant contribution to the DIBs. In addition, the astronomical bands near 9365 and 9348 Å are partially overlapped by DIBs of similar intensity, further complicating an accurate determination of their wavelengths. Given these uncertainties, the values from the laboratory spectrum of ${{\rm{C}}}_{60}^{+}-{\rm{He}}$ and those extrapolated to ${{\rm{C}}}_{60}^{+}$ (Table 2) are in satisfactory agreement with the reported astronomical data.

The authors thank Professor D. Gerlich (TU Chemnitz) for discussions.