Nitrogen hydrides and the H{}_{2} ortho-to-para ratio in dark clouds

Nitrogen hydrides and the H ortho-to-para ratio in dark clouds

V. Dislaire Université Joseph Fourier and CNRS, Institut de Planétologie et d’Astrophysique, Grenoble, France
Université Paris-Orsay and CNRS, Institut d’Astrophysique Spatiale, Orsay, France
   P. Hily-Blant Université Joseph Fourier and CNRS, Institut de Planétologie et d’Astrophysique, Grenoble, France
Université Paris-Orsay and CNRS, Institut d’Astrophysique Spatiale, Orsay, France
   A. Faure Université Joseph Fourier and CNRS, Institut de Planétologie et d’Astrophysique, Grenoble, France
Université Paris-Orsay and CNRS, Institut d’Astrophysique Spatiale, Orsay, France
   S. Maret Université Joseph Fourier and CNRS, Institut de Planétologie et d’Astrophysique, Grenoble, France
Université Paris-Orsay and CNRS, Institut d’Astrophysique Spatiale, Orsay, France
   A. Bacmann Université Joseph Fourier and CNRS, Institut de Planétologie et d’Astrophysique, Grenoble, France
Université Paris-Orsay and CNRS, Institut d’Astrophysique Spatiale, Orsay, France
   G. Pineau des Forêts
Key Words.:
ISM: Astrochemistry, abundances, ISM individual objects: IRAS 16293-2422

Nitrogen bearing species are common tracers of the physical conditions in a wide variety of objects, and most remarkably in dark clouds. The reservoir of gaseous nitrogen is expected to be atomic or molecular, but none of the two species are observable in the dark gas. Their abundances therefore derive indirectly from those of N-bearing species through chemical modelling. The recent years have accumulated data which stress our incomplete understanding of the nitrogen chemistry in dark cloud conditions. To tackle this problem of the nitrogen chemistry in cold gas, we have revised the formation of nitrogen hydrides, which is initiated by the key reaction . We propose a new rate for this reaction which depends on the ortho-to-para ratio of . This new rate allows to reproduce the abundance ratios of the three nitrogen hydrides, NH, , and , observed towards IRAS16293-2422, provided that the channel leading to NH from the dissociative recombination of is not closed at low temperature. The ortho-to-para ratio of  is constrained to by the abundance ratio NH:, which provides a new method to measure . This work stresses the need for reaction rates at the low temperatures of dark clouds, and for branching ratios of critical dissociative recombination reactions.

1 Introduction

Chemistry in an astrophysical context is not only a matter in itself but also provides invaluable tools to determine physical conditions such as volume density and kinetic temperature (bergin2007). Astrochemistry relies on chemical networks which depend on the type of environment (e.g. diffuse vs dense gas). The kinetic rates of the reactions are, in the best cases, based on thermodynamical and quantum mechanical calculations and experiments, which make the setup of such chemical networks an extremely demanding process. Various such networks of reactions are publicly available (KIDA, UMIST, OSU111http://kida.obs.u-bordeaux1.fr, http://www.udfa.net/, http://www.physics.ohio-state.edu/~eric, Flower & Pineau des Forêts222http://massey.dur.ac.uk/drf/protostellar/), with various degrees of complexity and/or completeness regarding specific aspects of the chemistry (e.g. deuteration, cations…).

The nitrogen element is among the 5th or 6th most abundant in the Solar neighbourhood, after H, He, C, O, and probably Ne (asplund2009; nieva2011). In the cold neutral medium, nitrogen is expected to be predominantly atomic or molecular, but direct observations of N or are not possible. The amount of gaseous nitrogen thus relies on the abundances of N-bearing molecules via chemical models. Nitrogen bearing molecules are observed in a wide variety of physical conditions. Molecules such as CN, HCN, and HNC, with large permanent dipole moments, are detected towards diffuse clouds (liszt2001), dense cores (tafalla2004), protoplanetary disks (kastner2008b) and high-z galaxies (guelin2007). N-bearing species, such as (and its deuterated isotopologues), are also efficient tracers of the dense and cold gas where CO has already frozen-out (crapsi2007; hilyblant2008cn; hilyblant2010n). The cyanide radical CN is also a precious molecule which serves as a tracer of the magnetic fields through Zeeman splitting (crutcher2010). Understanding the chemistry of nitrogen is thus crucial in many astrophysical areas.

Ammonia and are daughter molecules of , which forms from atomic N through neutral-neutral reactions mediated by CN and NO (pineau1990). The formation of CN and the related HCN and HNC molecules, and in particular their abundance ratio CN:HCN, are however not fully understood (hilyblant2010n). The formation of ammonia in dark and dense gas is thought to take place in the gas phase. Once exists in the gas phase, it reacts with ions formed by cosmic-ray ionization, to form which by subsequent hydrogen abstractions lead to and finally by dissociative recombination. lebourlot1991 (LB91 in the remainder of the paper) was the first to investigate the influence of the ortho-to-para ratio (noted ) on the formation rate of . LB91 considered the conversion between  and  through proton exchange in the gas phase. He concluded that when , the formation of ammonia no longer depends on the value of . However, a better test of the nitrogen chemistry is provided by the simultaneous observations of all three nitrogen hydrides, NH, , and (e.g., persson2010). The Herschel/HIFI instrument has opened the THz window which contains the fundamental rotational transitions of light molecules with large electric dipole moments such as hydrides. hilyblant2010nh have detected NH, , and in the cold envelope of the Class 0 protostar IRAS16293-2422. The hyperfine structures of the transitions of NH and are seen for the first time, in absorption, and allow a precise determination of their excitation temperature () and line centre opacity. Four lines of ammonia are also detected in absorption, plus the fundamental rotational transition at 572 GHz which evidences a self-absorbed line profile, likely tracing both warm and cold gas. For all three molecules, excitation temperatures were found in the range 8–10 K (Paper I). The derived column density ratios are . Whilst abundances are generally delicate to derive because the column density of is uncertain, the column density ratios above provide a stringent test for the first steps of the nitrogen chemistry and for the ammonia synthesis in particular. Indeed, the current nitrogen networks available all produce more than NH under dark cloud conditions (Paper I), at odds with the observations.

In this Letter, we investigate the NH: problem in dark gas, by revisiting the kinetic rate for the reaction

(1)

We derive separate rates for reaction with p- and  for which the nuclear spin and respectively. In Section 2 we describe the new rates which are compared to experimental measurements and derive the abundances of nitrogen hydrides in typical dark cloud conditions. The results are discussed in Section 3 and we propose conclusion remarks in Section 4.

2 Chemical modelling

Figure 1: Comparison of the rate coefficient as given by Eq. 3 to experimental data for the reaction of with  and  with different  admixtures: 13%, 3%, 0.8%, and 0% (blue line). The small symbols are taken from gerlich1993 while the large triangles are CRESU results from marquette1988. The solid lines correspond to Eq. 3 of the present paper.
Figure 2: Comparison of the rate coefficient for reaction (1) as given by Eq. 3 to the rates from LB91 (dashed) and the OSU database (dot-dashed). The rates are computed for temperatures in the range 8–150 K and , , 0.01, 0.1, and 3 (black lines). The symbols show the fits from marquette1988 for normal  (red circles, =3) and p- (blue triangles).

2.1 Rate of reaction

Reaction (1) has a small activation energy in the range 130-380 K (gerlich1993), with a consensus now tending towards a value below 200 K (e.g.gerlich2008). This reaction has been studied experimentally by marquette1988 who considered pure para- and a 3:1 mixture of o- and , refered to as normal  (). These authors fitted the two rates with normal and  as and . The rate with p- was used by LB91, who assumed that the reaction with  proceeds with no endothermicity, on the basis that the 170.51 K internal energy of the level of  is used to overcome the endothermicity. Accordingly, the rate of reaction (1) was written as , where is the fraction of . Actually, the expressions for and allow to derive a simple expression for , the reaction rate of with , namely (gerlich1989). For =3:1 and at temperatures less than  K, the rate is essentially , and is thus a good approximation of at the low temperatures ( K) of dark clouds. Alternatively, a single-exponential fit to leads to (see Fig. 5)

(2)

The rate for reaction (1) with an  admixture of arbitrary  is then obtained as

(3)

In Figure 1, the rate from Eq. 3 is compared to the experimental data of marquette1988 for the reaction with n- and p- down to 8 K and 45 K respectively. gerlich1993 performed experiments with  and with  containing admixtures of  (13%, 8%, and 0.8%), at temperatures down to 14 K. The agreement between our Eq. 3 and the three sets of  data of gerlich1993 is excellent at temperatures below 20 K, and to within a factor of 2 up to 100 K. This suggests that Eq. 3 should be accurate to within a factor of 2-3 down to 10 K. On the other hand, this rate should not be employed above  K.

We compare, in Fig. 2, the rate given by Eq. 3 to and to the rate given by the OSU database  cm. The rate is computed for several values of . As expected, it converges towards the n- and p- rates for large (=3) and small (=) values respectively. It is evident that LB91 overestimated the rate of reaction (1) by several orders of magnitude at temperatures smaller than 20 K. In warmer gas ( K), and agree to within a factor of 10 or less, whilst the OSU rate approaches the =3 curve. The OSU rate thus amounts to assume  ratios larger than 0.01, whereas LB91 provides acceptable rates only at temperatures larger than 20 K.

2.2 Abundance of nitrogen hydrides

Species Flower 2003 Wakelam 2008
H 0.50 0.50
He 0.10 0.14
N 6.39(-5) 2.14(-5)
O 1.24(-4) 1.76(-4)
C 8.27(-5) 7.30(-5)
S 1.47(-5) 8.00(-8)
Si 8.00(-9) 8.00(-9)
Fe 3.00(-9) 3.00(-9)
Mg 7.00(-9) 7.00(-9)
Table 1: Initial gas phase fractional abundances () from flower2003 with . For comparison, the fractional abundances from the low-metal model of wakelam2008 are also given. Numbers in parentheses are powers of 10.

In this work, we wish to reproduce the ratios NH:: observed in the cold envelope of IRAS16293-2422 (Paper I). The fundamental hyperfine transitions of NH, and several transitions of have been detected in absorption. Absorption is interpreted as resulting from the low temperature of the gas in the envelope seen against the warmer continuum emitted by the dust closer to the protostar. The gas density is low (-) as compared to the critical density of the detected transitions () which ensures that collisions do not govern the (de)excitation processes. The transitions are therefore thermalized with the dust emission temperature which, in the THz domain, correspond to excitation temperatures close to a kinetic temperature of 10 K. The lines are Gaussian and do not show signatures of strong dynamical effects such as infall. Dynamical timescales are then expected to be large with respect to the free-fall time. The observed lines therefore trace a cold gas, moderately dense, free of dissociating photons, and where the ionization is driven by cosmic rays.

The main point raised by Paper I is that the observed ratios NH::=5:1:300 could not be reproduced by chemical networks updated regarding the rates of the dissociative recombination (DR) reactions leading to NH, , and ammonia. Paper I considered three models, with varying branching ratios for some DR reactions. Whilst the NH:NH abundance ratio could be reproduced in all three cases, no model was able to produce333Hereafter, the fractional abundance of species X is noted and equals . . These models used the OSU rate for reaction (1) which was shown in Sec. 2.1 to depart from the measured rate by several orders of magnitude in cold gas and  smaller than 0.01. The next Section explores the consequence of the new rate given by Eq. 3 on the abundances of the nitrogen hydrides, in typical dark cloud conditions.

We have performed chemical calculations in a gas at  K, with density . The gas is screened by 10 mag of visual extinction, such that the ionization is primarily due to cosmic rays at an adopted rate . Gas-phase abundances are computed as a function of time by solving the chemical network until steady-state is reached. Freeze-out of gas-phase species onto dust grains are ignored in this work. In what follows, the quoted abundances correspond to the steady-state. The initial fractional elemental abundances () are the gas phase abundances taken from flower2003 who considered the depletion of metals in grain mantles, grain cores, and PAHs (see Table 1). These abundances differ from those adopted in Paper I (wakelam2008). The rates for the dissociative recombination reactions are those of the model 1 of Paper I. From the above, the rate for the key reaction (1) depends on the  which is not known, but which might strongly differ from the thermodynamical equilibrium value (maret2007; pagani2009; troscompt2009) which is at 10 K. The steady-state abundances of NH, , and have thus been computed for various values of  in the range to 3.

In this work, the DR of has three output channels, , , and (ojekull2004). However, another channel may be (adams1991), but to our knowledge, no branching ratio is available in the litterature. Values up to 10% may be considered in a future work.

We first consider the case where the DR of produces only (adams2009). The resulting abundances are the dashed lines in Fig. 3. It appears that the  controls the abundances of NH, , and but the ratios NH: and : are insensitive to . In a second series of calculations, the channel is given a 10% branching ratio for the DR of . In this case, the abundance of NH is nearly independent of , while the abundances of and remain unaffected (full lines in Fig. 3. As a consequence, it is found that for , . In Paper I though, opening this channel did not solve the NH: problem, which contrasts with the above result. This may be understood as follows. When the channel of the dissociative recombination of is opened with a 10% braching ratio, the corresponding rate is , several orders of magnitude larger than (see Fig. 2). Hence this channel, which is insensitive to , dominates the formation of NH over . In contrast, the other hydrides and are daughter molecules of which is formed from whose rate does explicitely depend on  in the present work. Hence the abundances of and do also depend on . On the other hand, at the temperature of 10 K and , the revised rate (Eq. 3) is at least an order of magnitude smaller than the OSU rate used in Paper I. For larger , the rate is similar or even larger up to a factor of 10. These two effects, namely the drop of for low , and the -independant formation of NH, makes it possible to produce a NH: ratio with values greater than unity. In the following we keep the channel opened to 10% and explore some consequences of this result.

Figure 3: Steady-state abundances (with respect to H nuclei) of nitrogen hydrides as a function of , in a 10 K gas with =, and  . The rate of reaction (1) is given by Eq. 3. Two branching ratios for the channel are considered: 0% (dashed lines) and 10% (full lines). The observed abundances from Paper I are also indicated (filled rectangles).

3 Discussion

3.1 The   ratio in dark clouds

Computing the abundance ratios NH: and : for different  ratios leads to the left panel of Fig. 4. The initial fractional abundances are kept fixed, while the rate of reaction (1) is calculated for values of  from (close to the Boltzmann value at 10 K) to 3. The calculated ratios are compared with the observational constraints. As expected, the : ratio is insensitive to  variations. It is equal to 10, not consistent with the observed value of 300. On the contrary, the NH: ratio shows two regimes: for , , and for , . The observed ratio of 5 is intermediate, and indeed well constrains the  to . From Fig. 4, we conclude that there is a range of  for which and simultaneously. In our case, this range is . The  ratio appears as a control parameter for the NH: ratio, and allows for the first time to produce more NH than . Conversely, the measure of NH: tightly constrains the  ratio. We note that the fractional abundance of of 1.9, measured by crapsi2007 towards the starless core L 1544, corresponds to an . This ratio is a factor of 10 larger than the corresponding ratio from the model of LB91. It is thus found that reaction (1) regulates the formation of and whilst the formation of NH is controlled by the dissociative recombination of provided the branching ratio towards NH is 10%. The value of this branching ratio is uncertain but is likely non-zero (adams2009).

3.2 Dependence on the initial abundances

The : ratio is in the above models, a factor 30 below the observed values towards IRAS16293-2422. However, models computed in Paper I with the initial abundances of wakelam2008 lead to a ratio close to the observed value, hence suggesting that the initial elemental abundances influence this ratio. The gas phase elemental abundances of C, N, and O in dark clouds are poorly known because the amount of these elements incorporated into the dust (core or mantles) is loosely constrained. The elemental abundance of oxygen in the gas phase is not known accurately, and variations by an order of magnitude are fully conceivable (jenkins2009), whilst that of carbon is better known. Accordingly, we have considered variations of the initial elemental abundances of oxygen, to vary the ratio C:O, encompassing the value of 0.41 from wakelam2008.

The resulting abundance ratios, computed for an  ratio of , are shown in Fig. 4 (right panel). As C:O decreases below the 0.66 value of FPdF03, the ratio : increases. In the process, NH: remains constant. When C:O is now increased above 0.66, both ratios decrease, by at most a factor 2 to 5. It is thus apparent that, when is increased, the C:O ratio controls the : ratio. On chemical grounds, the C:O ratio is expected to influence the abundance of , for which the main destruction routes involve oxygen to form NO, NH, and HNO. Similarly, NH is mostly removed by reaction with oxygen to form principally NO. However, when oxygen is significantly depleted from the gas phase (C:O ), another destruction route of NH, involving sulfur, becomes important. As a result, the NH: ratio is mostly insensitive to C:O, until C:O when it starts to decrease by small factors.

The situation is different for which is destroyed by charge transfer reactions with and and by proton exchange reactions with and , forming notably , which dissociates back into , and . A fraction of will lead to and NH which are the true destruction channels of ammonia. The abundance of is thus only marginally affected by the change in C:O, unless the ionization fraction is modified, which is the case for low C:O ratios. An increase of the oxygen abundance (i.e. a decrease of C:O) is accompanied by a deacrease of , or equivalently – the dominant ion – which makes the abundance of to increase. Consequently, as C:O decreases below 0.66, NH: keeps constant and : increases by more than one order of magnitude. Whereas when C:O increases, NH: decreases by less than a factor 10, whilst : is approximately constant.

Figure 4: Abundance ratios calculated when a 10% branching ratio is considered for the reaction . The hashed bands show the observed ratios with their uncertainties. Left panel: varying , with the initial abundances of flower2003 (=1.24(-4) and =8.27(-5).). Right panel: varying while keeping constant, at constant =. The low-metal abundances of wakelam2008 are =1.76(-4) and =7.30(-5), or C:O=0.41.

4 Conclusions

Using an updated rate for reaction (1) with an explicit dependence on the  ratio, we have shown that the  of  controls the ratio NH: in dark clouds without affecting the : ratio. A value of  close to leads to and as observed. Interestingly, this value of  is close to the predictions of flower2006a under similar conditions. In addition, measuring the NH: ratio may be a new method to constrain the  ratio of  in dark clouds. We have also shown that decreasing the C:O ratio by increasing controls the : ratio. Finally, acceptable parameters are found that lead to abundance ratios in agreement with the observations towards IRAS16293-2422, namely and C:O. It is to be noted, however, that in this range of parameters, the absolute abundances predicted by the models are a factor of 10 below those derived in Paper I.

In this work, the influence of  on the ratios NH:: has been explored only through the rate of reaction (1). A better study would be to self-consistently compute the  ratio from a model of conversion of  into , as was first considered by LB91, and more recently by e.g. pagani2009. Including proton exchange reactions, in the gas phase, between  and (honvault2011), (crabtree2011), and (hugo2009), would reprocess the 3:1 mixture of  formed on grains to a different . An even more self-consistent approach would be that of flower2006a who separate reactions with the ortho- and para- forms of all concerned N-bearing molecules. Another obvious continuation would be to explore these findings in different physical conditions (, cosmic-ray ionization rate, etc).

Branching ratios of dissociative recombination reactions are crucial to the formation of nitrogen hydrides. In this work, the dissociative recombination of has three output channels , , and (ojekull2004). However, another channel may be (adams1991), but to our knowledge, no branching ratio is available in the litterature. Values up to 10% may be considered in a future work. Critical too are the values of rates at low temperatures, especially for reaction (1) with  for which measurements at temperatures lower than 14 K are not available.

Acknowledgements.
We thank Pr. D. Gerlich for stimulating discussions and an anonymous referee for useful comments which improved the manuscript. We acknowledge financial support from the CNRS national program “Physique et Chimie du Milieu Interstellaire”.

References

Appendix A Reaction rate

For the purpose of implementing the rate of the reaction (1) with ortho- in chemical networks, Figure 5 shows the result of a single-exponential fit. The filled squares are based on the fitted reaction rates from marquette1988. A weighting in the form was adopted, which is accurate to better than 6% for  K.

Figure 5: Rate for reaction (1) with  and fit result (see Eq. 2). Bottom panel: filled squares are the values derived from marquette1988, and the fitted curve (full line). Top panel: relative error.
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