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Accurate rest frequencies for the submillimetre-wave lines of the ¹⁵N-containing isotopologues of N₂H⁺ and N₂D⁺

L. Dore - L. Bizzocchi - C. Degli Esposti - F. Tinti

Dipartimento di Chimica ``G. Ciamician'', via F. Selmi 2, 40126 Bologna, Italy

Received 27 October 2008 / Accepted 13 January 2009

Abstract
The submillimetre-wave spectrum of the molecular ions N¹⁵NH⁺, ¹⁵NNH⁺, N¹⁵ND⁺, and ¹⁵NND⁺ have been investigated in the laboratory using a source-modulation microwave spectrometer equipped with a negative glow discharge cell. The diazenylium ion was produced in a Ar/N₂/H₂(D₂) discharge plasma and the ¹⁵N-containing isotopologues were observed in natural abundance. Six new rotational transitions for the protonated species and seven for the deuterated ones were accurately measured in the frequency range 270-760 GHz. These new laboratory measurements of the rare isotopologues of N₂H⁺ provide very precise rest frequencies at millimetre and submillimetre wavelengths useful for the radioastronomical identification of their rotational lines in the ISM.

Key words: molecular data - methods: laboratory - techniques: spectroscopic - radio lines: ISM

1 Introduction

Samples of primitive solar system materials, such as meteorites that reached the Earth's surface and the interplanetary dust particles (IDPs) returned by the Stardust mission, have shown anomalies and enhancements in various elemental isotopic ratios (e.g. Ehrenfreund & Charnley 2000; Clayton & Nittler 2004; McKeegan et al. 2006). In particular, the laboratory analyses have provided evidences of large D/H and ¹⁵N/¹⁴N ratios, which have been attributed to the survival of D- and ¹⁵N-enriched material from the interstellar medium (ISM; Messenger 2000; Maret et al. 2006).

It has long been established that low-temperature gas-phase ion-molecule reactions and catalysis on the surface of cold interstellar dust grains lead to large D fractionation. In contrast, for nitrogen the situation is less clear due the scarcity of observational data and also because models of the ¹⁵N fractionation in typical dense clouds predict only modest enhancements (Terzieva & Herbst 2000). Charnley & Rodgers (2002) has suggested that a significant increase of the ¹⁵N-fractionation can occur if CO is depleted onto dust grains; the key fractionation process involves diazenylium ion via the exotermic reactions:

which preferentially drive ¹⁵N into molecular nitrogen through the main dissociative recombination channel N₂H N₂ + H (Molek et al. 2007) at the expense of atomic N⁰which becomes isotopically light. Under normal interstellar conditions the degree of fractionation is limited by chemical reactions which exchange ¹⁴N and ¹⁵N between atomic and molecular forms:

However, if CO is frozen out, OH is unavailable, the cycle (2) is broken, and the processes (1) produce a larger ¹⁵N-enhancement, which might explain the high ¹⁵N/¹⁴N ratio of the IDPs and meteoritic data (Rodgers & Charnley 2008). This picture, also predicts enhanced abundances of ¹⁵N-bearing diazenylium in CO-depleted cores, thus the observation of N₂H⁺, N¹⁵NH⁺, and ¹⁵NNH⁺, and the determination of their isotopic ratio provides a very effective test for the reliability of the model (Charnley & Rodgers 2002)

Previous searches of N¹⁵NH⁺ and ¹⁵NNH⁺ have been carried out long time ago (Womack et al. 1992; Linke et al. 1983) and the detection has been successful only toward massive star forming region, owing to the low sensitivity achieved and also because of the selection of sources, which did not focuse on cold, centrally concentrated cores showing heavy CO depletion, which were not known at that time. In CO-depleted regions, also deuterium fractionation increases, therefore N₂D⁺ can be easily detected (see Dore et al. 2004), however its ¹⁵N-containing isotopologues have not been observed until now, owing also to the lack of any accurate spectral data.

As for the laboratory spectroscopy of N¹⁵NH⁺ and ¹⁵NNH⁺ is concerned, Gudeman (1982) reported the transitions; the spectrum of the former species was split into three components due to the quadrupole coupling of the external ¹⁴N nucleus, while for the other species no hyperfine structure could be resolved. The only other transition detected in laboratory was the (Havenith et al. 1990), but with a 1 MHz accuracy. No spectra, instead, are reported for the deuterated species N¹⁵ND⁺ and ¹⁵NND⁺.

In order to provide reliable spectroscopic information for these species, we measured, in the region 270-760 GHz, transitions from to of N¹⁵NH⁺and ¹⁵NNH⁺, and from to of N¹⁵ND⁺ and ¹⁵NND⁺. The newly obtained laboratory data, together with the previously determined ¹⁴N-hyperfine constants (Caselli et al. 1995; Dore et al. 2004) allowed for the calculation of very accurate rest frequencies for all four ¹⁵N-containing variants of N₂H⁺ and N₂D⁺at millimetre and submillimetre wavelengths, the predicted uncertainties being less that 0.005 kms^-1 up to 1 THz.

2 Experimental details and data analysis

Table 1:   Rotational transition frequencies and spectroscopic constants of N¹⁵NH⁺.

Table 2:   Rotational transition frequencies and spectroscopic constants of ¹⁵NNH⁺.

Table 3:   Rotational transition frequencies and spectroscopic constants of N¹⁵ND⁺.

Table 4:   Rotational transition frequencies and spectroscopic constants of ¹⁵NND⁺.

Table 5:   Predicted rest-frequencies, estimated uncertainties, and line strengths for N¹⁵NH⁺.

Table 6:   Predicted rest-frequencies, estimated uncertainties, and line strengths for ¹⁵NNH⁺.

Table 7:   Predicted rest-frequencies, estimated uncertainties, and line strengths for N¹⁵ND⁺.

Table 8:   Predicted rest-frequencies, estimated uncertainties, and line strengths for ¹⁵NND⁺.

The rotational spectra of the four isotopologues of N₂H⁺ and N₂D⁺ containing ¹⁵N were observed with a frequency-modulated millimetre-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 frequency multiplier, built by a doubler in cascade with a multiplier (RPG - Radiometer Physics GmbH), which was driven by Gunn oscillators working in the region 67-105 GHz (Farran Technology Limited, RPG - Radiometer Physics GmbH). Two phase-lock loops allow the stabilisation 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 is obtained by sine-wave modulating at 16.66 kHz the reference signal of the wide-band Gunn-synchronizer (total harmonic distortion less than ). The signal, detected by a liquid-helium-cooled InSb hot electron bolometer (QMC Instr. Ltd. type QFI/2), is demodulated at 2f by a lock-in amplifier.

N₂H⁺ (or N₂D⁺) was produced in a DC discharge by flowing a 1:1 mixture of N₂ and H₂ (D₂) (3 mTorr, 0.4 Pa) with addition of Ar buffer gas for a total pressure of about 10 mTorr (1.3 Pa). The ¹⁵N-containing species were observed in natural abundance. The discharge current was a few mA, the Pyrex cell was cooled at about 80 K by liquid nitrogen circulation in an external plastic pipe tightly wound around it, and an axial magnetic field up to about 110 G was applied throughout the length of the discharge. It is well established (see Tinti et al. 2007) that, with this magnetic confinement, the ions are produced and observed in a nearly field free region, the negative glow, thus they do not show any Doppler shift due to the drift velocity.

The spectra were recorded by sweeping the frequency up and down (several times if signal averaging is needed) in steps of 5 or 10 kHz with an acquisition time of 8-18 ms per step: the lock-in amplifier time constant was set at 10 ms.

It has to be pointed out that low-J rotational lines of ¹⁴N¹⁵NH⁺ and ¹⁴N¹⁵ND⁺, with the quadrupolar ¹⁴N nucleus in the external position, are split by hyperfine interactions; however, the transitions recorded in the present work appear as a main blended peak, produced by the collapsed triplet, with two very weak features at its both sides apparent only with a high signal to noise ratio. Therefore, the unperturbed line frequency was recovered by a line shape analysis of the spectral profile modeled as a sum of hyperfine components with their frequency shift and intensity fixed at the values accurately predicted using the hyperfine constants known from literature (Caselli et al. 1995; Dore et al. 2004). Figure 1 illustrates a recording of the transition of the N¹⁵ND⁺ isotopologue analyzed in this way. The same procedure, which also accounts for the frequency modulation and the line asymmetry due to etalon effects in the cell (see Dore 2003), was used to analyze the spectra of ¹⁵N¹⁴NH⁺ and ¹⁵N¹⁴ND⁺ as well.

Since each transition was recorded several times, its frequency was derived as the mean of the determined unperturbed line centers, with an uncertainty estimated from the root mean square error of their distribution. When such uncertainty resulted to be less than 5 kHz, it was given a 5 kHz value, to account for a possible tiny pressure shift, whose value and sign are difficult to estimate, which, for instance for HCO⁺ broadened by Argon, has an absolute value less than 1 kHz/mTorr (Buffa et al. 2006).

The determined experimental transition frequencies were fitted, in a weighted-least-squares procedure, to the standard frequency expression of the rotational transition :

where B₀ and D_J are the ground-state rotational and quartic centrifugal distortion constants, respectively; the weights were the inverse-square of the uncertainties. The values of the spectroscopic constants of N¹⁵NH⁺, ¹⁵NNH⁺, N¹⁵ND⁺, and ¹⁵NND⁺ derived from the fits are reported in Tables 1-4.

3 Discussion

This paper reports new laboratory measurements of the the rotational spectra of ¹⁵N-containing variants of diazenylium ion at millimetre and submillimetre wavelengths (270-760 GHz). Six and seven rotational transitions were accurately determined for the H- and D-containing pairs of isotopic species, respectively. Efforts were made in order to minimize the significance of the the most common sources of systematic error in the determination of the line positions. The precision of the data is also excellent: only in few instances the least-squares residuals exceed 5 kHz, which is a very low value for Doppler limited measurements.

The accuracy of the determined spectroscopic constants is even higher than that attained by Amano et al. (2005) in their paper concerning the main isotopologues ¹⁴N₂H⁺ and ¹⁴N₂D⁺. Thus, the present rotational, B₀, and quartic centrifugal distortion, D_J, constants allow the calculation of a very reliable set of rest frequencies for the four isotopologues N¹⁵NH⁺, ¹⁵NNH⁺, N¹⁵ND⁺, and ¹⁵NND⁺at millimetre and submillimetre wavelengths. The predicted uncertainties at 1 THz are, even in the less favourable case, less than 0.01 km s^-1, whereas they are only few thousandths of km s^-1 for the 3 mm band J = 1-0 transition of all species.

Tables 5-8 collect a list of rest frequencies up to 1 THz calculated from the spectroscopic constants of Tables 1-4 and include also the estimated uncertainty at level obtained by propagation of the standard errors of spectroscopic and hyperfine constants. The hyperfine structure of each transition has been predicted, assuming the hyperfine constants of Caselli et al. (1995) and Dore et al. (2004), by means of the SPCAT prediction program (Pickett 1991), and the hyperfine components included in each multiplet collect at least the 90% of the total intensity of the relevant J+1 - J rotational transition. The line strength value, S_ij, is defined as the square of the reduced matrix element of the rotation matrix (Brown & Carrington 2003)

The intensity of a line in absorption can be obtained by multiplying the line strength S_ijby the square of the dipole moment , by the transition frequency and by the population factor of the lower level. The Einstein A-coefficients for spontaneous emission from state i to j can also be calculated from the line strengths by use of

Acknowledgements

This work has been supported by MIUR (PRIN 2007 funds, project ``Trasferimenti di energia, carica e molecole in sistemi complessi'') and by University of Bologna (RFO funds).

References

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All Tables

Table 1:   Rotational transition frequencies and spectroscopic constants of N¹⁵NH⁺.

Table 2:   Rotational transition frequencies and spectroscopic constants of ¹⁵NNH⁺.

Table 3:   Rotational transition frequencies and spectroscopic constants of N¹⁵ND⁺.

Table 4:   Rotational transition frequencies and spectroscopic constants of ¹⁵NND⁺.

Table 5:   Predicted rest-frequencies, estimated uncertainties, and line strengths for N¹⁵NH⁺.

Table 6:   Predicted rest-frequencies, estimated uncertainties, and line strengths for ¹⁵NNH⁺.

Table 7:   Predicted rest-frequencies, estimated uncertainties, and line strengths for N¹⁵ND⁺.

Table 8:   Predicted rest-frequencies, estimated uncertainties, and line strengths for ¹⁵NND⁺.

All Figures

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