REASSESSMENT OF THE DISSOCIATIVE RECOMBINATION OF N₂H⁺ AT CRYRING

Protonated nitrogen, N₂H⁺, is an important interstellar ion. It has been detected in a variety of interstellar environments including dark clouds (Turner 1974), translucent clouds (Turner 1995), protostellar cores (Caselli et al. 2002), and photodissociation regions (Fuente et al. 1993). In Titan's N₂-dominated ionosphere, N₂H⁺ is formed from the reaction between N⁺₂ and H₂, but is quickly lost via proton transfer to CH₄ (e.g., Vuitton et al. 2007). In dark clouds N₂H⁺ is an important tracer for N₂, which lacks a permanent dipole moment and therefore does not possess a radiofrequency spectrum. To predict the abundance of N₂ based on N₂H⁺ measurements it is necessary to have an insight into the production and destruction mechanisms of N₂H⁺. The proton affinity of N₂ is in between that of the two most abundant interstellar molecules, H₂ and CO. Therefore N₂H⁺ is mainly produced by the proton transfer to N₂ from the important interstellar ion H⁺₃,

$$\begin{equation} {\rm H}_3 ^ + + {\rm N}_2 \to {\rm N}_2 {\rm H}^ + + {\rm H}_2, \end{equation} \tag{ 1 }$$

and lost mainly via proton transfer to CO

$$\begin{equation} {\rm N}_2 {\rm H}^ + + {\rm CO} \to {\rm HCO}^ + + {\rm N}_2 \end{equation} \tag{ 2 }$$

and through the dissociative recombination (DR) with free electrons

$$\begin{equation} {\rm N}_2 {\rm H}^ + + e^ - \to {\rm N}_2 + {\rm H} \end{equation} \tag{ 3a }$$

$$\begin{equation} \to {\rm NH} + {\rm N}. \end{equation} \tag{ 3b }$$

The DR of N₂H⁺ has been experimentally studied before. Based on a Flowing Afterglow Langmuir Probe (FALP) experiment Smith & Adams (1984) reported thermal rate coefficients of the reaction equal to 1.7 × 10⁻⁷ cm³ s⁻¹ at room temperature and 4.9 × 10⁻⁷ cm³ s⁻¹ at 95 K, suggesting a (T/300 K)^−0.92 dependence on the rate coefficient. More recent FALP experiments, by Poterya et al. (2005) and Lawson et al. (2011), indicate a nearly constant rate coefficient of about 2.8 × 10⁻⁷ cm³ s⁻¹ over the temperature range from 200 to 500 K (near 100 K, Poterya et al. 2005 found a rate coefficient of about 4 × 10⁻⁷ cm³ s⁻¹). By using vacuum ultraviolet absorption of the Lα line of produced H atoms Adams et al. (1991) argued that the DR of N₂H⁺ is very much dominated by Channel (3a). In contrast to these findings, Geppert et al. (2004) reported, from a CRYRING experiment, a T_e^−0.51 dependence on the rate coefficient (with T_e being the electron temperature) and branching fractions implying that as much as 64% of the DR reactions proceeds via Channel (3b). Molek et al. (2007) performed a new flowing afterglow measurement of the branching ratios by employing electron impact to ionize DR products prior to detection in a quadrupole mass analyzer. Again channel (3a) was observed to dominate the reaction and an upper limit of 5% for Channel (3b) was reported. The authors raised the question (prior to publishing their results) whether strong contamination by ¹⁵N¹⁴N⁺ could have been present in the experiment at CRYRING. Although a later test of the ion source under the experimental conditions did not suggest such a possibility, this served as a motivation for us to re-measure the DR of N₂H⁺ at CRYRING and the results from these new measurements are presented in this paper.

The experimental approach and the data analysis procedure to determine the absolute cross section, thermal rate coefficient, and branching fractions were essentially similar to other recent DR investigations at CRYRING (see, e.g., Vigren et al. 2010). We will therefore, in this section, only mention details relevant to the present experiment. The N₂H⁺ ions were created in a hollow cathode discharge ion source (Peterson et al. 1998) with N₂ and H₂ as precursor gases. The source was mounted on a high-voltage platform (40 kV) and mass selection by a bending magnet was applied prior to the injection of the ions into the ring. Within the ring the ions were accelerated to 3.3 MeV during 1.0 s and then stored for an additional 4.0 s before measurements from DR reactions started. The ions reacted with electrons in a section of the ring equipped with an electron cooler and the neutral products formed in DR events were unaffected by a bending magnet located after the interaction region and left the ring tangentially for detection. During the storage time the velocity of the electrons was set to match the ion beam velocity. The absolute DR cross section was determined based on electron and ion current measurements and count rates from DR reactions recorded during 1.0 s long electron-velocity scans, covering interaction energies between ∼0 and 1 eV twice. The branching fractions were determined at velocity-matched conditions by employing the grid technique conventionally used at CRYRING (see, e.g., Neau et al. 2000).

Figure 1 shows the retrieved absolute cross section for the DR of N₂H⁺ as a function of the relative kinetic energy. The data have been corrected for (1) reactions between the ions and the residual gas in the ring (Hellberg et al. 2005), (2) space charge effects (DeWitt et al. 1996), (3) the increase of relative kinetic energy of the reactants in the regions in which the electron beam is bent into and out of the ion beam by toroidal magnets (Lampert et al. 1996), and (4) the transverse energy spread of the electrons in the interaction region, k_BT_⊥ ∼ 2 meV (Danared et al. 2000; Mowat et al. 1995).

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The absolute cross section (cm²) of the title reaction is best fitted by

$$\begin{equation} \sigma (E/{\rm eV}) = 1.07 \times 10^{ - 16} (E/{\rm eV})^{ - 1.42} \end{equation} \tag{ 4 }$$

for relative kinetic energies, E, exceeding 3 meV. By folding the cross section over Maxwellian electron speed distributions corresponding to particular electron temperatures, T_e, we obtain thermal rate coefficients (cm³ s⁻¹) according to

$$\begin{equation} k(T_e) = 2.98 \times 10^{ - 7} (T_e /300\ {\rm K})^{ - 0.74}\quad \;{\rm for}\;10 < T_e < 150\;{\rm K} \end{equation} \tag{ 5 }$$

and

$$\begin{eqnarray} &&k(T_e) = 2.74 \times 10^{ - 7} (T_e /300\ {\rm K})^{ - 0.84}\quad \;{\rm for}\;150 < T_e < 1000\;{\rm K}{\rm.}\nonumber\\ \end{eqnarray} \tag{ 6 }$$

Systematic uncertainties in the DR cross section include, e.g., the electron beam radius, the length of the interaction region, and the ion beam circumference. Statistical uncertainties include, e.g., uncertainties in counts from DR events. The estimated overall uncertainty for the DR cross section below 0.1 eV (where the count rate was high) is ∼20%. A similar uncertainty is to be considered for the thermal rate coefficients for T_e < 1000 K.

The background-subtracted energy spectrum from the DR of N₂H⁺ recorded at velocity-matched conditions with the grid inserted in front of the energy-sensitive ion-implanted silicon detector is displayed in Figure 2.

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The peak intensities I_N, I_N+H, and I_2N+xH relate to the transmission probability P of the grid (P ∼ 0.297 ± 0.015; Neau et al. 2000) and the number of reactions that occurred leading to the products N₂ + H and NH + N, respectively. A reaction forming the products N₂ + H contributed to the peak labeled "2N + xH" with a probability of P (x being 0 or 1). A reaction forming the products NH + N contributed to one of the peaks labeled "N" or "N+H" with a probability given by 2P(1 − P) (it required that one of the fragments was stopped by the grid while the other one passed through it and hit the detector). Finally, a reaction producing NH + N contributed to the peak labeled "2N + xH" only if both fragments passed the grid, which had a probability of P². This gives rise to an equation system in which the two unknowns are the number of DR reactions leading to N₂ + H (X_3a) and NH + N (X_3b)

$$\begin{equation} \left[\begin{array}{@{}c@{}} {I_{\rm N} + I_{\rm{N + H} }} \\ {I_{\rm{2N + {\it x}H} }}\end{array} \right] = \left[\begin{array}{@{}cc@{}} 0& 2P(1 - P)\\ {P}& {P^2 }\end{array} \right] \times \left[\begin{array}{@{}c@{}} X_{3{\rm a}}\\ {X_{3{\rm b}}}\end{array} \right]. \end{equation} \tag{ 7 }$$

The system was solved and normalization of the results shows that 93⁺⁴_{− 2}% of the DR reactions of N₂H⁺ lead to N₂ + H with the rest, 7⁺²_{− 4}%, leading to NH + N. The error bars are mainly from the uncertainty in the transmission probability of the grid, but take also into account the possibility for a small ion beam contamination by ¹⁵N¹⁴N⁺. In the present experiment the ion source parameters were optimized to generate currents at m/z = 28 and 29 of ∼150 nA and ∼100 nA, respectively. The natural abundance of ¹⁵N is 0.36%, so from a rough estimate the initial level of contamination of ¹⁵N¹⁴N⁺ to the N₂H⁺ beam injected into the ring should have been around 1%.

The obtained branching fractions are in good agreement with the results reported by Molek et al. (2007) and significantly different from those reported by Geppert et al. (2004). It is clear that strong contamination by ¹⁵N¹⁴N⁺ (probably over 80%) was present in the previous experiment at CRYRING (this affected also the cross section measurements). The reason for this cannot be clearly established, since a mass spectrum of the ion source output was taken under the conditions present in the previous experiment and the ¹⁵N¹⁴N⁺ contamination was found to amount to only 8% of the ion signal at the mass-to-charge ratio of 29 Da. Since N₂H⁺ reacts faster than ¹⁵N¹⁴N⁺ with electrons, and perhaps also more readily with rest gas molecules, we have studied the possibility that an initial contamination of 8% could have been significantly increased during the storage time prior to the measurements in the previous CRYRING experiment. We found that a storage time of only a few seconds is very unlikely to bring about such a drastic change in the contamination level. We believe instead that the strong contamination was mainly due to dramatic changes of ion source parameters at some point during the experiment. One such possibility is an accidental (and maybe intermediate) decrease of the H₂ supply flow to the ion source.

As for the thermal rate coefficient for the DR of N₂H⁺ we focus the discussion on a comparison with the most recent results from FALP experiments (Poterya et al. 2005; Lawson et al. 2011) and we mention only that our rate coefficients at T_e = 95 K and 300 K (see Equations (5) and (6)) are about 61% and 42% higher, respectively, than the values reported by Smith & Adams (1984). Our rate coefficient at 300 K is in excellent agreement with the values reported by Poterya et al. (2005) and Lawson et al. (2011). Their observation of a nearly constant rate coefficient over the temperature range from 200 to 500 K is not, however, in line with the present results. One can speculate that the difference in temperature dependence (above 200 K) comparing the present result with the studies by Lawson et al. (2011) and Poterya et al. (2005) may be related to the fact that the electron temperature is expected to be equal to the internal ion temperature in the FALP measurement, while in our study only the T_e dependence could be studied. The ions studied in our experiment were most probably in their vibrational ground state because of the employed ion source, the relatively long storage time of >4 s, and the short radiative lifetime of vibrationally excited N₂H⁺ ions reported by Heninger et al. (2003; see also Keim et al. 1990). Therefore, the discrepancy between the temperature dependencies cannot be assigned to different degrees of vibrational excitations in the ion populations. N₂H⁺ has a rather high dipole moment of ∼3.4 D (Havenith et al. 1990) and we believe, therefore, that the storage time was sufficient to give the ion population a rotational temperature of about ∼300 K, though we cannot be absolutely certain about this temperature (e.g., Buhr et al. 2010). Assuming that the rate coefficient for the DR of N₂H⁺ has power-law dependencies on both the electron temperature and the rotational temperature of the ions implies a rotational temperature dependence of approximately T^0.84_rot for T_rot > 200 K in order to reach consistency between the present results and those reported by Poterya et al. (2005) and Lawson et al. (2011). At this stage we can only encourage further theoretical calculations and experimental efforts (note, e.g., that an electrostatic Cryogenic Storage Ring, CSR, at present is under construction at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany) to investigate the rotational temperature dependence in the DR of N₂H⁺. Talbi (2007, 2009) has reported theoretical calculations on the DR of N₂H⁺ along both the N₂ + H and the NH + N reaction paths. She showed that the lowest repulsive state of N₂H (intermediate neutral complex in the DR of N₂H⁺) leading to NH and N in their ground electronic states is likely to cross the N₂H⁺ ionic curve well above the v = 0 energy level and argued that this may indicate that formation of NH + N via the DR of N₂H⁺ is improbable under the cold conditions prevailing in interstellar clouds. In addition, she showed that the DR of linear N₂H⁺ can involve the direct mechanism as the second repulsive state of N₂H (leading to N₂ + H) crosses the ionic curve, though at the turning point of the v = 0 energy level.

It is interesting to use the obtained DR rate coefficient to assess the most important destruction mechanism of N₂H⁺ in a standard dark interstellar cloud with T ∼ 10 K, a fractional ionization of 10⁻⁸–10⁻⁷ and a fractional abundance of CO equal to 10⁻⁴ with respect to H₂ molecules (e.g., Herbst 2001). If we denote by n_e and n_CO number densities of free thermal electrons and CO molecules, respectively, it then follows that n_e/n_CO ∼ 10⁻⁴–10⁻³. We use k_PT to denote the rate coefficient for the proton transfer reaction from N₂H⁺ to CO and we use k_DR to represent the rate coefficient for the DR of N₂H⁺ at an electron temperature of 10 K (we consider here only the electron temperature dependence of the title reaction). If the ratio k_DRn_e/n_CO exceeds k_PT it implies that DR is a more important destruction mechanism of N₂H⁺ than proton transfer to CO. Using Equation (5) with T_e = 10 K we obtain a k_DR value of 3.7 × 10⁻⁶ cm³ s⁻¹. For our standard dark cloud k_DRn_e/n_CO is then about 3.7 × 10⁻¹⁰ to 3.7 × 10⁻⁹ cm³ s⁻¹. According to Bohme et al. (1980) k_PT is approximately 8.8 × 10⁻¹⁰ cm³ s⁻¹ (the reaction has been studied at room temperature but is not likely to have a pronounced temperature dependence due to the low dipole moment of CO). Thus, we may state that free electrons are expected to play an almost equally important role as CO for the destruction of N₂H⁺ in dark clouds. A deeper insight into the contributions from the two mechanisms relies on a more precise knowledge of the fractional ionization in dark clouds and the influence of the ions' rotational temperature in the DR of N₂H⁺.

The DR of N₂H⁺, a reaction of astrochemical relevance, has been reinvestigated at CRYRING. It has been shown that at ∼0 eV relative kinetic energy the reaction leads predominantly (in 93⁺⁴_{− 2}%) to the formation of N₂ + H. This is in agreement with results reported from Flowing Afterglow studies (Adams et al. 1991; Molek et al. 2007) and in disagreement with an earlier experiment at CRYRING (Geppert et al. 2004). It is clear that strong contamination of ¹⁵N¹⁴N⁺ was present in the previous experiment at CRYRING. The reason for this is unclear, but it could be related to an accidental change of a critical ion source parameter (such as the input of H₂ gas) at some point during the experiment. Rate constants obtained in the present and previous experiments suggest that free electrons probably play an approximately equally important role as CO for the destruction of N₂H⁺ in dark interstellar clouds. It is noted that a deeper knowledge of the influence of the ions' rotational temperature in the DR of N₂H⁺ would be helpful to set further constraints on the relative importance of the different destruction mechanisms for N₂H⁺ in dark interstellar clouds.

We thank the staff at the Manne Siegbahn Laboratory for excellent technical support. W.D.G. thanks the Swedish Research Council for his Senior Researcher grant (contract number 2006-427) and the Swedish Space Board (grant number 76/06). M.K. thanks the Swedish Institute for financial support and also acknowledges support from the Ministry of Science and Higher Education, Poland, under contract N202 111 31/1194.