The Astrophysical Journal, 669: L113–L116, 2007 November 10 䉷 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.
IMPROVED REST FREQUENCIES OF HCO⫹ AT 1 THz F. Tinti, L. Bizzocchi, C. Degli Esposti, and L. Dore Dipartimento di Chimica “G. Ciamician,” Universita` di Bologna, via Selmi 2, 40126 Bologna, Italy;
[email protected],
[email protected],
[email protected],
[email protected] Received 2007 July 30; accepted 2007 September 22; published 2007 October 9
ABSTRACT The ground-state rotational spectrum of HCO⫹ , produced in a negative-glow discharge cell, has been recorded up to 892 GHz. The sources of systematic error have been carefully accounted for, thus obtaining accurate rotational and centrifugal distortion constants. The present measurements have allowed us to determine a value of the sextic distortion constant, HJ , which, unlike the recent determination of Lattanzi et al., is consistent with the values determined for DCO⫹ and for the isoelectronic molecule HCN. The new set of spectroscopic constants allows us to predict the rotational spectrum of the formyl ion with an accuracy of 1 part in 108 near 1 THz. Such an accuracy is important for kinematic studies of dense cores in molecular clouds and for future far-infrared observations. Subject headings: ISM: molecules — methods: laboratory — molecular data Savage & Ziurys 2005), but no accurate high-frequency data were available for comparison purposes, as in the case of DCO⫹ and D13CO⫹, since the far-infrared measurements carried out with tunable laser sideband spectrometers (van den Heuvel & Dymanus 1982; Blake et al. 1987) suffer from the inaccuracy of the FIR-laser frequency. In spite of the efforts made to minimize systematic errors, the values of the spectroscopic constants determined by Lattanzi et al. (2007) include a very anomalous value for the sextic centrifugal distortion constant (⫺0.341 Hz), which disagrees in sign and order of magnitude with the value determined by Maiwald et al. (2000) for the isoelectronic species HCN (0.0891 Hz); conversely, the value of this constant determined by Lattanzi et al. (2007) for DCO⫹ (0.0522 Hz) compares well to that of DCN (0.07326 Hz; Bru¨nken et al. 2004). This was a clue to some inaccuracy in the data or in their treatment, and led us to reinvestigate the rotational spectrum of the formyl ion in its ground state up to nearly 900 GHz, in order to compare to the data of Lattanzi et al. (2007) and to derive accurate spectroscopic constants. In addition, relying on previously published data about the pressure shift of the rotational transition of HCO⫹ perturbed by Ar gas (Buffa et al. 1994, 2006), another possible source of systematic error is discussed.
1. INTRODUCTION
The identification of the more than 130 molecules observed in space by radioastronomy is based on laboratory data: the agreement between laboratory and astronomical frequencies is typically within 3 ppm (Gottlieb et al. 2003). Even better precision is needed to investigate the physics and chemistry of interstellar clouds and star-forming regions. For instance, to detect inward motions in star-forming molecular cloud cores, the velocity difference between lines of a thin and of a thick tracer has to be determined, and this requires a frequency precision of 3 parts in 108 (Caselli & Dore 2005 and references therein). In addition, a new perspective in astrophysical spectroscopy is provided by the approaching launch of the Herschel Space Observatory, which will open the far-infrared (FIR) region to high-resolution observations with the HIFI spectrometer mounted on it (de Graauw & Helmich 2001). For species of astrophysical interest, therefore, there is a need for very accurate laboratory measurements of rotational frequencies extending up to the THz region. Recently, Lattanzi et al. (2007) have addressed this issue for the formyl ion, HCO⫹, probably the most abundant molecular ion in dense sources (see Herbst 2005). The ground-state spectra of HCO⫹ and of its rare isotopologues (DCO⫹, H13CO⫹, and D13CO⫹) have been measured up to 1.159 THz, and rotational transitions in excited vibrational states have also been detected for HCO⫹ up to 1.164 THz. The authors discussed the problem of the systematic errors which may bias the measured transition frequencies and lead to inaccurate predictions at higher frequency: they cite, for instance, (1) the Doppler shift, which may affect the transition frequency of molecular ions produced in a DC discharge; and (2), in general, a bad calibration of a reference oscillator of the experimental setup. They conclude that comparison of data sets from different experimental groups is the only way to mitigate systematic errors, and they support the accuracy of their measurements by reporting the good agreement with the measurements of DCO⫹ and D13CO⫹ carried out in this laboratory up to nearly 800 GHz (Caselli & Dore 2005). As far as the ground state of the main isotopologue HCO⫹ is concerned, Lattanzi et al. (2007) compared their line frequencies with those measured in several different laboratories (Woods et al. 1981; Bogey et al. 1981; Sastry et al. 1981;
2. EXPERIMENTAL DETAILS AND DATA ANALYSIS
Rotational lines of HCO⫹ from J p 6 to J p 9, in the range 624.2–891.6 GHz, were observed with a frequency-modulated millimeter-wave spectrometer (Cazzoli & Dore 1990) equipped with a negative glow discharge cell made of a Pyrex tube, 3.25 m long and 5 cm in diameter, with two cylindrical hollow electrodes 25 cm in length at either end. The radiation source was a Gunn oscillator, working in the region 85–105 GHz (J. E. Carlstrom Co.), driving a frequency multiplier, built by a doubler in cascade with a multiplier (RPG-Radiometer Physics GmbH). Two phase-lock loops allow the stabilization of the Gunn oscillator with respect to a frequency synthesizer, which is driven by a 5 MHz rubidium frequency standard. The frequency modulation of the radiation source is obtained by sinewave modulating at 1.666 or 16.66 kHz, the reference signal of the wide-band Gunn synchronizer (total harmonic distortion less than 0.01%). The signal, detected by a liquid-heliumL113
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Vol. 669 TABLE 1 Measured Rotational Transition Frequencies of HCO⫹
Transition J⬘
J
Frequency (MHz)
Residual (MHz)
Uncertainty (MHz)
1 2 4 5 6 7 8 9 10
0 1 3 4 5 6 7 8 9
89,188.5247a 178,375.0563a 356,734.2230b 445,902.8721b 535,061.5810b 624,208.3606c 713,341.2278c 802,458.1995c 891,557.2903c
⫺0.0014 ⫺0.0079 ⫺0.0016 0.0008 0.0019 ⫺0.0003 ⫺0.0019 0.0001 0.0063
0.0041 0.0081 0.0015 0.0015 0.0015 0.0015 0.0020 0.0020 0.0079
a
From spectra of Buffa et al. (1994); see text. From spectra of Buffa et al. (2006); see text. c This work. b
Fig. 1.—Spectra of the J p 8 R 7 transition of HCO⫹ recorded in singleand double-pass configurations. Their profile has been fit to a model speeddependent Voigt profile with the inclusion of a dispersion term to recover an accurate line frequency (Dore 2003). Fit residuals are shown at the bottom of each plot.
cooled InSb hot electron bolometer (QMC Instruments Ltd. type QFI/2), is demodulated at 2-f by a lock-in amplifier. The molecular ion was produced by flowing a 1 : 1 mixture of CO and H2 (about 1 mtorr) in Ar buffer gas with a total pressure of about 7 mtorr and DC discharging with a current of a few mA. The Pyrex cell was cooled by liquid nitrogen circulation in an external plastic pipe tightly wound around it, and an axial magnetic field up to about 165 G was applied throughout the length of the discharge. With the longitudinal magnetic field applied, ions are produced and observed in the negative glow (De Lucia et al. 1983), which is a nearly fieldfree region where they are expected to show negligible Doppler shift due to the drift velocity occurring, instead, in the positive column (Sastry et al. 1981), where a low axial electric field is present. All the transition frequencies were measured in a single-pass configuration, except for the J p 8 R 7 frequency, which, to verify the absence of Doppler shift, was measured both in a single- and in a double-pass arrangement, and it was found to be equal within the uncertainty of the line measurement (see spectra of Fig. 1). Also Hirao et al. (2007) have very recently shown, by comparing their rotational frequencies of DCO⫹ with those of Caselli & Dore (2005), that “the drift velocity shift of ions is negligibly small” in negative-glow discharges.
The experimental procedure employed to measure line frequencies has already been discussed in previous work concerning DCO⫹ (Caselli & Dore 2005): a typical spectrum is recorded by sweeping the frequency up and down several times for signal averaging and using scan parameters as those reported in Figure 1. The systematic errors should have been minimized, but it is also worth considering the pressure shift induced by collision with the buffer gas. This topic was the subject of two papers (Buffa et al. 1994, 2006), which reported the pressure broadening and pressure shift parameters of several transitions of HCO⫹ perturbed by Ar. The spectra of these two studies, recorded at increasing Ar pressure, were analyzed employing the proFFiT code (Dore 2003) to fit the full line profile, and the recovered transition frequencies at zero Ar pressure are reported in Table 1. In this work, the J p 7 R 6 line was treated in the same way to give a pressure shift parameter of ⫺0.33 kHz mtorr⫺1, which implies an offset of about ⫺2 kHz in the line frequency determined from the spectra recorded in the standard condition of 6 mtorr of Ar gas flowing through the cell. Table 1 lists the rotational transition frequencies along with their uncertainties: the latter were derived as the rms error of the distribution of the line frequencies recovered from several recordings of each transition. When this “statistical” error was lower than 1.5 kHz, for transitions with the pressure shift accounted for, or lower than 2 kHz in the other cases, the uncertainty was assumed to be 1.5 and 2 kHz, respectively. The experimental data were fitted, in a weighted-leastsquares procedure, to the standard frequency expression of the rotational transition J ⫹ 1 R J: n0 p 2B 0 (J ⫹ 1) ⫺ 4DJ (J ⫹ 1) 3 ⫹ HJ (J ⫹ 1) 3[(J ⫹ 2) 3 ⫺ J 3 ], (1) where B 0 is the rotational constant and DJ and HJ are the quartic and sextic centrifugal distortion constants, respectively; the weights were the inverse-square of the uncertainties. The values of the spectroscopic constant derived from the fit are reported in Table 2. 3. CONCLUSION
This work provides very accurate rest frequencies for the formyl ion up to nearly 900 GHz, from which improved values of the rotational and centrifugal distortion constants have been obtained. In particular, the new measurements allow us to cor-
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HCO⫹ SUBMILLIMETER-WAVE FREQUENCIES
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TABLE 2 Spectroscopic Constants of HCO⫹ Constants
Lattanzi et al. (2007)
This Worka
B0 /MHz . . . . . . . . DJ /kHz . . . . . . . . . HJ /Hz . . . . . . . . . . . rmsresb/kHz . . . . . . j c ...............
44594.4230(44) 82.724(49) ⫺0.341(156)
44594.42873(28) 82.8351(59) 0.083(36)
Correlation Matrix 1.000 0.953 0.885
1.000 0.980
1.000
3.6 0.967
a Errors, as listed in the output of the SPFIT program (Pickett 1991), are reported in parentheses in units of the last quoted digits; standard errors of the fit parameters are obtained multiplying by j. b rms error of residuals: [( residual2)/(N observations)]1/2. c Fit standard deviation: {[ (residual/uncertainty)2]/(degrees of freedom)}1/2.
冘 冘
rect the anomalous value of the sextic centrifugal distortion constant, HJ, previously determined by Lattanzi et al. (2007); the present value of HJ is comparable to that of HCN in sign and order of magnitude, as is the case for the deuterated pair DCO⫹/DCN. A comparison with the frequencies measured in other laboratories is presented in Figure 2, which is analogous to Figure 2 of Lattanzi et al. (2007); it confirms the conclusion drawn by these authors about the accuracy of previous papers, but it also shows that their high-frequency measurements are considerably scattered around the present best-fit predictions, thus suggesting that the frequencies of the transitions J p 10 R 9 and J p 13 R 12, even if not affected by systematic errors, have an uncertainty higher than the assumed value of 50 kHz. This high uncertainty prevented a reliable determination of the higher order distortion constant HJ. Accurate spectroscopic constants for the ground state of HCO⫹ are now available, and they can be used to update databases such as CDMS (Mu¨ller et al. 2005) and JPL (Pickett et al. 1998). As an example, Table 3 presents a portion of the catalog file obtained by running the SPCAT program (Pickett 1991), where predictions along with their uncertainties are listed up to J p 12. Considering the J p 13 R 12 transition at 1.159 THz, it now has a frequency precision of 3 parts in 108, corresponding to 0.01 km s⫺1 in radial velocity, while the same transition measured by Lattanzi et al. (2007) was ⫺150 kHz off, corresponding to a precision of 0.04 km s⫺1. The
normalized velocity difference, dV p (Vthick ⫺ Vthin )/DVthin (Mardones et al. 1997), between the peaks of optically thick and thin lines is used to detect infall motions in dense cores of the molecular clouds; for the condition dV/jdV 1 3 to hold, the required error on V (jV) should be no greater than 0.01 km s⫺1 (Caselli & Dore 2005), and this is the case of the present improved rest frequency. Lee et al. (1999) as well, in their survey of infall motions toward starless cores, have shown that “it is necessary to use accurate and consistent frequencies for the different molecular lines”: two choices of the frequency of the J p 2 R 1 thick line of CS differing by 0.055 km s⫺1 led to a significant excess of blueshifted sources in one case with respect to the other, as shown in Figure 6 of that paper. Finally, it may be worth reporting that similar studies on protostellarcollapse candidates were carried out by Gregersen et al. (1997) by detecting also the J p 4 R 3 transition of HCO⫹ as thick line: they used a frequency of 356,734.288 GHz, which is 63 kHz (0.05 km s⫺1) higher than the value of the presently suggested rest frequency; thus we wonder whether this discrepancy may have been reflected in their analysis. Financial support from MIUR (Cofin 2005) and the University of Bologna (RFO funds) is gratefully acknowledged. TABLE 3 Predicted Rotational Transition Frequencies of HCO⫹ Transition
Fig. 2.—Residuals of transition frequencies from different papers calculated with respect to the predicted frequencies of Table 3. Residuals marked with a plus sign (⫹) are from Warner (1988).
J⬘
J
Frequency MHz
Uncertainty MHz
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
89,188.5261 178,375.0642 267,557.6263 356,734.2246 445,902.8713 535,061.5791 624,208.3609 713,341.2297 802,458.1994 891,557.2840 980,636.4982 1,069,693.8571 1,158,727.3769 1,247,735.0739 1,336,714.9657 1,425,665.0705 1,514,583.4074 1,603,467.9965 1,692,316.8589 1,781,128.0167 1,869,899.4933 1,958,629.3132
0.0005 0.0010 0.0012 0.0011 0.0009 0.0008 0.0010 0.0011 0.0017 0.0045 0.0106 0.0211 0.0375 0.0616 0.0958 0.1427 0.2051 0.2867 0.3911 0.5228 0.6865 0.8877
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REFERENCES Blake, G. A., Laughlin, K. B., Cohen, R. C., Busarow, K. L., & Saykally, R. J. 1987, ApJ, 316, L45 Bogey, M., Demuynck, C., & Destombes, J. L. 1981, Mol. Phys., 43, 1043 Bru¨nken, S., Fuchs, U., Lewen, F., Urban, Sˇ., Giesen, T., & Winnewisser, G. 2004, J. Mol. Spectrosc., 225, 152 Buffa, G., Dore, L., Tinti, F., & Meuwly, M. 2006, ChemPhysChem, 7, 1764 Buffa, G., Tarrini, O., Cazzoli, G., & Dore, L. 1994, Phys. Rev. A, 49, 3557 Caselli, P., & Dore, L. 2005, A&A, 433, 1145 Cazzoli, G., & Dore, L. 1990, J. Mol. Spectrosc., 141, 49 de Graauw, Th., & Helmich, F. P. 2001, in The Promise of the Herschel Space Observatory, ed. G. L. Pilbratt et al. (ESA SP-460; Noordwijk: ESA), 45 De Lucia, F. C., Herbst, E., Plummer, G. M., & Blake, G. A. 1983, J. Chem. Phys., 78, 2312 Dore, L. 2003, J. Mol. Spectrosc., 221, 93 Gottlieb, C. A., Myers, P. C., & Thaddeus, P. 2003, ApJ, 588, 655 Gregersen, E. M., Evans, N. J., II, Zhou, S., & Choi, M. 1997, ApJ, 484, 256 Herbst, E. 2005, J. Phys. Conf. Ser., 4, 17 Hirao, T., Yu, S., & Amano, T. 2007, J. Chem. Phys., 127, 074301
Lattanzi, V., Walters, A., Drouin, B. J., & Pearson, J. C. 2007, ApJ, 662, 771 Lee, C. W., Myers, P. C., & Tafalla, M. 1999, ApJ, 526, 788 Maiwald, F., et al. 2000, J. Mol. Spectrosc., 202, 166 Mardones, D., Myers, P. C., Tafalla, M., Wilner, D. J., Bachiller, R., & Garai, G. 1997, ApJ, 489, 719 Mu¨ller, H. S. P., Schlo¨der, F., Stutzki, J., & Winnewisser, G. 2005, J. Mol. Struct., 742, 215 Pickett, H. M. 1991, J. Mol. Spectrosc., 148, 371 Pickett, H. M., Poynter, R. L., Cohen, E. A., Delitsky, M. L., Pearson, J. C., & Mu¨ller, H. S. P. 1998, J. Quant. Spectrosc. Radiat. Transfer, 60, 883 Sastry, K. V. L. N., Herbst, E., & De Lucia, F. C. 1981, J. Chem. Phys., 75, 4169 Savage, C., & Ziurys, L. M. 2005, Rev. Sci. Instrum., 76, 043106 van den Heuvel, F. C., & Dymanus, A. 1982, Chem. Phys. Lett., 92, 219 Warner, H. W. 1988, Ph.D. thesis, Univ. Wisconsin, Madison Woods, R. C., Saykally, R. J., Anderson, T. G., Dixon, T. A., & Szanto, P. G. 1981, J. Chem. Phys., 75, 4256
