The Astrophysical Journal, 737:20 (6pp), 2011 August 10 C 2011.
doi:10.1088/0004-637X/737/1/20
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
THE COMPLETE, TEMPERATURE-RESOLVED EXPERIMENTAL SPECTRUM OF VINYL CYANIDE (H2 CCHCN) BETWEEN 210 AND 270 GHz Sarah M. Fortman1 , Ivan R. Medvedev2 , Christopher F. Neese1 , and Frank C. De Lucia1,3 1 Department of Physics, Ohio State University, Columbus, OH 43210, USA 2 Department of Physics, Wright State University, Dayton, OH 45435, USA
Received 2011 April 5; accepted 2011 June 9; published 2011 July 26
ABSTRACT The results of an experimental approach to the identification and characterization of the astrophysical weed vinyl cyanide in the 210–270 GHz region are reported. This approach is based on spectrally complete, intensity-calibrated spectra taken at more than 400 different temperatures in the 210–270 GHz region and is used to produce catalogs in the usual astrophysical format: line frequency, line strength, and lower state energy. As in our earlier study of ethyl cyanide, we also include the results of a frequency point-by-point analysis, which is especially well suited for characterizing weak lines and blended lines in crowded spectra. This study shows substantial incompleteness in the quantum-mechanical (QM) models used to calculate astrophysical catalogs, primarily due to their omission of many low-lying vibrational states of vinyl cyanide, but also due to the exclusion of perturbed rotational transitions. Unlike ethyl cyanide, the QM catalogs for vinyl cyanide include analyses of perturbed excited vibrational states, whose modeling is more challenging. Accordingly, we include an empirical study of the frequency accuracy of these QM models. We observe modest frequency differences for some vibrationally excited lines. Key words: astrochemistry – astronomical databases: miscellaneous – ISM: molecules – methods: laboratory – molecular data Online-only material: color figures, machine-readable tables, supplementary data
the inclusiveness of astrophysical catalogs in the millimeter and submillimeter spectral region (Fortman et al. 2010a, 2010b; Medvedev & De Lucia 2007). This method is much simpler because it requires neither spectral assignment nor model building for these complex perturbed spectra. In this paper, we describe an analysis of vinyl cyanide in the 210–270 GHz region. In this region, only 618 of the 2895 strongest lines in the experimental spectrum are in the catalogs, while 1337 of the lines in the catalogs are not among the 2895 strongest experimental lines. Figure 1 shows this comparison in a graphical format. We have also carried out similar experimental work for seven other astrophysical weeds: methyl formate, acetaldehyde, dimethyl ether, methanol, sulfur dioxide, methyl cyanide, and vinyl cyanide (Fortman et al. 2010b). Preliminary analyses show similar results for all species except SO2 , which has a significantly simpler spectrum. The spectroscopy of vinyl cyanide is a particularly interesting example of the challenges (Kisiel et al. 2009) of the spectroscopy of low-lying vibrational states. While it is ordinarily assumed that the rotational spectra of ground vibrational states are unperturbed, vinyl cyanide has significant perturbations even in the ground state, in this case with the ν 11 vibrational state. As a result a combined analysis of the ground and ν 11 states was required. However, the ν 11 state is more strongly mixed with the ν 15 state, but an analysis of the ν 15 would require an analysis that included the 2ν 11 state (457 cm−1 ), and so forth. In the end, the current analysis adopts the practical approach of simply iteratively excluding from the combined ground state and ν 11 analysis lines whose residuals in the fits exceed 10σ (Kisiel et al. 2009). This vibrational state structure explains the divergence of the two distributions plotted in Figure 1. The lowest vibrational state that is not included in the astrophysical catalogs is 2v 11 near 457 cm−1 . Vinyl cyanide is a semi-rigid molecule and the rotational structure in these excited states will be similar
1. INTRODUCTION There is growing recognition that the increase in both sensitivity and resolving power of modern millimeter and submillimeter telescopes has resulted in the capabilities of these facilities outpacing the laboratory data on which they depend. Major new facilities such as the Herschel Space Observatory, the Atacama Large Millimeter Array (ALMA), and the Stratospheric Observatory for Infrared Astronomy will accelerate this pace (Becklin 2005; Clery 2009; Turner & Wooten 2006). There is a general understanding that low-lying vibrational states, which are often challenging to analyze because of perturbations, are the major contributors to the many unidentified lines in these astrophysical spectra, especially in the spectra of hot molecular cores (Goldsmith et al. 2006). Vinyl cyanide has been observed in a wide variety of interstellar sources in the ground, ν 11 (242 cm−1 ), and ν 15 (362 cm−1 ) vibrational states (Gardner & Winnewisser 1975; Schilke et al. 1997). Its 13 C and 15 N isotopologues have also been observed (Muller et al. 2008). Quantum-mechanical (QM) analyses (Cazzoli & Kisiel 1988; Kisiel et al. 2009), which are the basis of these observations and the foundation of catalogs in the millimeter and submillimeter, rapidly become more challenging as analyses are extended from ground vibrational states (which are largely unperturbed) to excited vibrational states (which are often perturbed). It is the resulting incompleteness of the catalogs (Muller et al. 2005; Pickett et al. 1998) that accounts for the large majority of these unassignable astrophysical lines. We have recently shown that an alternative to the QM analysis method, based on analyses of complete, intensity-calibrated spectra taken at many temperatures, can dramatically increase 3 Author to whom any correspondence should be addressed;
[email protected].
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Fortman et al.
Figure 2. Boltzmann population factors for the 2v 11 near 460 cm−1 of vinyl cyanide, along with the Boltzmann factors for the first missing states for other astrophysical weeds (Fortman et al. 2010b). (A color version of this figure is available in the online journal.)
Figure 1. Absorbance of the 2895 strongest experimentally observed lines (upper black trace) and of the 1200 strongest catalog lines (lower red trace) for the vinyl cyanide spectrum between 210 and 270 GHz, both sorted by strength. The points plotted are so dense as to make each family of points appear as a continuous line. (A color version of this figure is available in the online journal.)
fit their measured peak absorbance, Apeak = Lαpeak (T )
to that of the ground state. With this assumption, it would be expected that the strongest lines not included in the catalog would be reduced from the strongest lines in the spectrum by the vibrational Boltzmann factor for these vibrational states, ∼10 at 300 K. Figure 1 shows that this expectation is realized. We have recently shown experimentally that this expectation is also realized for seven other astrophysical weeds: methyl formate, methanol, dimethyl ether, acetaldehyde, sulfur dioxide, methyl cyanide, and ethyl cyanide (Fortman et al. 2010b). For molecules with internal rotation somewhat more complex, considerations are required to account for degeneracies. The location of this divergence as a function of temperature is an important astrophysical question. Although much of the interstellar medium is at low temperature, the ability of telescope arrays to resolve smaller hot cores has resulted in the observation of much higher temperatures. For example, it has been shown with the Submillimeter Array (SMA) and using methyl cyanide as a probe that the temperature measured for the Orion KL hot core has continually increased with increasing telescope angular resolution, with temperatures over 600 K observed in the latest study (Wang et al. 2010). In another example, using the SMA in G19.61–0.23 a rotational temperature of 578 ± 134 K has been measured for ethyl cyanide and of 609 ± 77 K for methyl cyanide (Qin et al. 2010). With the high angular resolving power of ALMA, even smaller and hotter cores should be observed. Accordingly, Figure 2 shows these intensity factors over the 100–500 K range for the excited state of vinyl cyanide near 460 cm−1 , as well as for a number of other astrophysical weeds. Unlike the case of ethyl cyanide, for which only an analysis of the unperturbed ground vibrational is included in the catalogs, the inclusion of even the truncated analyses of the excited states of vinyl cyanide significantly reduces the intensities of the lines that are not included in the catalogs.
nL 8π 3 (1 − e−hν0 /kT )Sij μ2 e−El /kT = Q 3ch
ln(2) ν0 , π δνD
(1)
to obtain the spectroscopic temperature T and nL/Q. Here, n is the number density, L is the effective path length, and Q is the partition function. This fit is performed for each of the spectra recorded over the temperature range 237–386 K. To account for the impact of the small pressure broadening contribution to the peak absorbance, we have introduced a factor of 1 + νk into Equation (1) (Fortman et al. 2010c). With ν in MHz, the fit yielded k = −60,583 MHz. Because we use this equation not only for the fit of T and nL/Q but also inversely for the calculation of the simulated spectrum, errors associated with linewidths and other systematic experimental errors cancel. This spectroscopic fitting procedure also eliminates difficulties associated with high absolute accuracy pressure measurements, spatial and temporal temperature variations, and cell length measurements. While Q calculations can be problematic, because we use as reference the standard astrophysical catalogs, this means that we are making the same assumptions about Q and any subsequent refinements in the Q calculations will impact both our calculations and the catalog calculations the same. Furthermore, because we use Equation (1) for both fitting and spectral simulation, the fit errors provide a measure of the accuracy of the simulated lines since exactly the same procedure is used to calculate the intensities of the calibration lines for the fit as for the unassigned lines in the simulated spectrum. 2.1. The Line List Catalog To produce the experimental line list catalog, for each temperature scan the lines are identified with a peak finder and fit to Gaussian lineshape functions to make a list of frequencies, strengths, and widths. This information is used to calculate Sij μ2 and El via least squares for each of the 2895 lines above our intensity cutoff. The software also provides figures of merit to inform the user of spectral features whose origins may be from more than a single transition. Because a number of cataloged lines are overlapped by significantly stronger lines that are not included in the catalogs, these blends are an issue not only for our experimental method, but for the QM catalog as well.
2. ANALYSIS We have previously described the spectroscopic system and the procedures used in our approach (Fortman et al. 2010a, 2010c; Medvedev & De Lucia 2007). For this study, we selected 192 assigned lines (Muller et al. 2005; Pickett et al. 1998) to use as intensity references. Using the known strengths Sij μ2 and lower state energy levels El (from the QM analyses), and Doppler widths δν D and line frequencies ν 0 (from the temperatures and measured frequencies of our experiment), we 2
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to the line strength. Off of line center, the meanings of S˜ ij μ2 and E˜ are less physical, but Equation (4) is still a valid fitting function for describing the spectral intensity. Because at 77 K most lines of significant intensity are included in the QM catalog, we include in our analysis a spectrum calculated from the QM analysis at this temperature to improve the predictions at low temperature. This significantly reduces extrapolation errors that might occur if only the higher temperature experimental data were used.
Table 1 Example of the Results of This Work in Catalog Format Frequency (MHz) 227820.916 227821.777 227826.268 227827.710 227834.675 227838.149 227850.297 227857.065 227858.221 227866.026 227870.968 227872.144 227892.603 227897.612 227906.700
Sij μ2 (D2 )
Energy (cm−1 )
Figures of Merit
197 600 335 315 630 9 703 429 310 532 304 415 485 635 694
1056 1196 1106 1093 1257 395 1244 1146 637 825 654 1145 1229 157 150
W, G, T W W W, T W, G, T W, G, T W W ... ... ... W W, G, T ... ...
3. RESULTS Figure 3 shows a small portion of the spectrum of vinyl cyanide and compares the catalog predictions with a single scan at 300 K, a simulation based on the experimental catalog parameters convolved with a Doppler linewidth, and the simulation based on the frequency point-by-point fits of the more than 400 different temperature scans. We note the following:
(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)
1. All of the experimentally based simulations contain considerably more lines than the QM catalog at comparable absorbance. 2. In addition to the point-by-point simulation having much greater S/N than the individual scans, its baseline is better as well, due to the averaging of the baseline that moves as a function of temperature. 3. The point-by-point simulation includes many more lines than the experimental catalog. This is because the catalog fit begins with identification and analyses of lines in individual spectral scans. 4. Near 227.86 GHz is an example of an experimental line that is close to the frequency of a QM catalog line, but clearly is due to the overlap with a stronger non-catalog line. It is coincidences such as these that cause many of the outerliers in our analysis of experimental intensity accuracy. 5. With the exception of cases where non-catalog lines overlap weaker QM catalog lines, the agreement of intensities among the catalog, the single scan, the catalog simulation, and the point-by-point simulation is excellent. 6. In the point-by-point fit, lines whose cross sections are ∼5000 times weaker than the strongest lines are observable. If terrestrial abundances are assumed, these weaker lines will include those due to 13 C (1/90) and 15 N (1/273). If their non-terrestrial abundances become of astrophysical significance, their identification via QM analyses of the ground states of the isotopic species is a considerably smaller task than the QM analyses of any of the perturbed excited states. Indeed, such analyses of 13 C and 15 N species have been carried out and interstellar identifications have been made (Muller et al. 2008; Schilke et al. 1997).
2.2. A Spectral Point-by-point Catalog A second method does not identify individual lines but rather predicts the spectra as a function of temperature on a frequency point-by-point basis. Collectively, the 444 spectral scans contain considerably more information than is contained in the catalog of 2895 lines of Table 1, and this information will become important as the sensitivity of astronomical systems continues to improve. Although temperature dependent, each of the spectral scans contains ∼4000 lines of signal-to-noise ratio (S/N) > 2. Moreover, the catalog processing of Section 2.1 is limited by the noise of each of the individual scans. In this section, we will describe a process that takes advantage of averaging over these scans not only to reduce random noise, but also to effectively deal with the blends that begin to occur at deeper levels of sensitivity. With the Doppler width (half-width at half-maximum) given by √ 2Na k ln(2) √ δνD = T ν0 = W T ν0 , (2) 2 Mc the absorbance as a function of frequency can be rewritten as
hν0 ν−ν0 2 E ln(2) nL ν0 1 − e− kT 2 − kTl − ln(2) δνD Sij μ e e , π Q δνD (3) where Na is Avogadro’s number and M is the molecular mass. The absorbance normalized by the nL/Q factor becomes 8π 3 A(ν) = 3ch
hν0 2 El − ln(2) 1− ν 8π 3 ln(2) 1 1 − e− kT A(ν) ν0 = Sij μ2 e− kT e W 2 T √ nL/Q 3ch π W T hν − kT0 1−e ˜ E(ν) =K (4) S˜ij μ2 e− kT , √ T with
ν 2 ln(2) ˜ . E(ν) = EL + k 2 1 − W ν0
In our earlier work on ethyl cyanide (Fortman et al. 2010c), we noted that in some cases the simulation based on the experimental catalog produced lines that were too narrow (or alternately had too small of an integrated intensity). This is a much less common effect in vinyl cyanide because its spectrum is less crowded. Examples of the measured spectroscopic temperatures and nL/Q parameters for 10 of the 444 spectral scans are shown in Table 2. The entire set is included in the online archives along with the experimental data at each temperature. Each spectral file includes 2.4 million absorbances, starting at 210 GHz and incrementing in 25 kHz steps. These intensity-calibrated data make possible additional future analyses of these data and
(5)
In Equation (4) every frequency slice of the data (2.4 × ˜ On 106 points) is represented by two parameters S˜ ij μ2 and E. line center E˜ is the lower state energy and S˜ ij μ2 corresponds 3
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Figure 3. Vinyl cyanide spectrum between 227.82 and 227.91 GHz at 300 K. The green trace is a single scan at 300 K, the blue scan is a simulation based on the 2895 catalog lines, and the black trace is a simulation based on the point-by-point analysis of the 444 temperature scans. The red stick spectra represent the lines that are included in the QM catalogs. (A color version of this figure is available in the online journal.) Table 2 Experimental Temperatures and nL/Q Parameters for 10 of the 437 Spectral Scans Index 50 51 52 53 54 55 56 57 58 59
T (K)
nL/Q (nm−2 )
247.688 248.106 248.541 248.916 249.137 249.298 249.812 250.143 250.629 251.168
.0024353 .0024217 .0024087 .0023940 .0023791 .0023651 .0023535 .0023395 .0023236 .0023086
Figure 4. Number of tagged lines as a function of intensity at 300 K (red) in comparison to the total number of lines (black). (A color version of this figure is available in the online journal.)
(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)
Forty-seven percent of the lines are tagged in Table 1, often indicating either a blend or a line whose intensity varies rapidly with temperature, thereby reducing the number of temperature points available to calculate the catalog parameters. Many of the lines in Table 1 have lower state energies above 1000 cm−1 . In single spectral scans at low temperature these lines have small absorptions, which reduce the accuracy of the linewidth measurements and result in a “W” tag. Figure 4 confirms that the vast majority of the tagged lines are relatively weak lines, typically those whose intensities are 1% or less of the strongest line. Thus, for the simulation of spectra down to the 1% level, the tagged lines are of little consequence except for a few warnings associated with overlaps of relatively strong lines. Because the catalog uses information from many temperatures to calculate its parameters, simulations based on the
provide useful input for future QM analyses. They may be of particular utility in addressing some of the frequency accuracy issues discussed in Section 4. 3.1. The Catalog Results The results for 15 of the 2895 lines analyzed in the catalog format described in Section 2.1 are shown in Table 1. This table includes a column that tags problematic results according to “W” (a line that is too wide in comparison to its expected Doppler width), “G” (a line whose Gaussian fits did not converge), and “T” (a line whose temperature dependence is unphysical) (Fortman et al. 2010c). The full table is available in the online archives of this journal. 4
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Table 3 Parameters of the Point-by-point Fit S˜ ij μ2 (D2 )
E˜ (cm−1 )
101.137 69.179 45.740 53.829 31.549 61.748 64.887 33.014 27.589
953.694 899.490 805.606 844.410 750.237 879.462 905.260 801.159 756.390
Figure 5. Frequency difference between catalog calculation and experimental value sorted by lower state energy. The black squares are due to the ground vibrational state, the red squares are due to first excited vibrational state (v 11 ), and the blue squares are due to the second excited vibrational state (v 15 ). Those circled in green indicate lines whose QM predicted intensities did not match the experimental observations. (A color version of this figure is available in the online journal.)
(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)
that were smaller than this number. In regions without lines, this prevents the negative-going noise from causing numerical problems in the fit to Equation (4). The net effect of this is that in areas of no spectral absorption the noise did not average to zero. Thus, in the evaluation of any line strengths in the point-bypoint spectra they should be referenced to zero, not the apparent baseline near 0.1 nm2 .
catalog parameters are typically quite good, even for tagged lines. Inspection of the spectra at the expansion scale of Figure 3 confirms this. However, the point-by-point analysis of Sections 2.2 and 3.2 efficiently deals with blends and extends the analysis not only to the strength floor of the 2895 lines (∼0.1% of the strongest lines), but considerably deeper because of the averaging over the 444 spectral scans. As in our earlier work on ethyl cyanide, we compared the lower state energies obtained from the experimental intensity fits with QM results to provide a measure of the physical basis of this approach. We found for the lines whose intensities are >10% of the strongest line that the rms difference between the QM and the experimental results is 10 cm−1 (with two outliers excluded from the analyses). The overall distribution of these differences is slightly smaller than that of ethyl cyanide, most likely due to the somewhat less crowded spectrum of vinyl cyanide.
4. LINE FREQUENCIES A new analysis of the ground and first excited states of vinyl cyanide has recently been published and included in the catalogs (Kisiel et al. 2009) along with results from an earlier analysis of the two lowest vibrational states (Cazzoli & Kisiel 1988). An interesting feature of the new analysis is that it was found that the data set was comprehensive enough to show perturbation between the ground vibrational state and the first excited vibrational state ν 11 , as well as between the first excited state and the second excited vibrational state ν 15 . A second interesting feature of this analysis is that even with this extensive data set it was not possible to accurately model many of the perturbed levels, and it was necessary to impose an iterative 10σ cutoff in the analysis. While it might be assumed that this would have little impact on the calculated frequencies in the well-studied 210–270 region, Figure 5 shows systematic deviations. This is probably a by-product of including lines in the analysis that are perturbed by ∼10σ , which in turn pull the fit away from fitting the unperturbed lines in the analysis. A third interesting feature shown in Figure 5 is that in regions for which the QM analysis is not perturbed, the agreement between the calculated and experimental frequencies is very good (∼0.005 MHz). In the case of the QM analysis, the statistical redundancy of fitting more than 5000 lines plays a major factor and it is for this reason that it is ordinarily assumed that calculated line positions are more accurate than the individual measured frequencies. Because in the recording of our experimental data we took no special care in the measurement of frequencies, their quality is a bit more surprising. Apparently, the statistical redundancy obtained from the 444 spectral scans is also effective, at least in part due to the randomization of baseline effects due to the temperature-dependent standing waves.
3.2. The Point-by-point Results Table 3 shows a few of the 2.4 million pairs of S˜ ij μ2 and E˜ coefficients. The complete set is available in the online archives. The S˜ ij μ2 are reported in units of D2 (Debye squared) and the E˜ in units of cm−1 . For use of these data, Equation (4) can be written as √ 1 − e−C2 ×ν/T A(ν) ˜ = C1 · M (6) S˜ij μ2 e−C3 ×E/T , √ nL/Q T with nm2 K1/2 , amu1/2 D2 K C3 = 1.43877506 −1 , cm C1 = 54.5953
C2 = 4.799237 × 10−5
K , MHz
and M the molecular weight in amu, T the temperature in K, and ν the frequency in MHz. We have previously noted that this approach more effectively deals with blends than does an experimental catalog line approach. Additionally, Figure 3 shows how the averaging associated with the more than 400 distinct spectral scans reveals many weaker lines. Careful inspection of Figure 3 shows that the baseline of this fit is above zero. This results from our setting to a small positive number all points in our experimental spectra
5. SUMMARY The complete, intensity-calibrated spectrum of vinyl cyanide in the 210–270 GHz window and the analysis and archiving 5
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of these data in an astrophysically convenient format were described. As in our earlier work on ethyl cyanide, we found that the completeness of QM catalogs is a strong function of temperature. Because the stronger rotational lines of the two lowest lying vibrational states of vinyl cyanide have been analyzed, the QM catalog of vinyl cyanide is complete to higher temperature than that of ethyl cyanide. However, an analysis of the QM catalog frequencies showed that the inclusion of perturbed lines in these analyses impacted the calculated frequencies. This work also shows the challenges, even in the low-lying states of relatively rigid and well-behaved species, of analyses in which all vibrational states, including the ground state, are coupled together via perturbations.
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We thank the National Science Foundation and NASA for their support of this work. This work was also supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program grant NNX09AP10H. REFERENCES Becklin, E. E. 2005, Adv. Space Res., 36, 1087 Cazzoli, G., & Kisiel, Z. 1988, J. Mol. Spectrosc., 130, 303
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