Mon. Not. R. Astron. Soc. 317, 563±568 (2000)
The possibility of nitrogen isotopic fractionation in interstellar clouds
R. Terzieva1 and Eric Herbst2w
1
2
Department of Physics and Chemical Physics Program, The Ohio State University, Columbus, OH 43210, USA
Departments of Physics and Astronomy, The Ohio State University, Columbus, OH 43210, USA
Accepted 2000 April 18. Received 2000 April 11; in original form 2000 February 16
A B S T R AC T
The possibility of nitrogen isotopic fractionation owing to ion±molecule exchange reactions
involving the most abundant N-containing species in dense interstellar clouds has been
explored. We find that exchange reactions between N atoms and N-containing ions have
most influence on the fractionation, although the extent of fractionation is too small to be
readily detectable.
Key words: molecular processes ± ISM: abundances ± ISM: clouds ± ISM: molecules.
1
INTRODUCTION
The element nitrogen has two stable isotopes: 14N (14NˆN
throughout this paper) and 15N, which is less abundant. In the
terrestrial atmosphere, the N=15 N isotopic ratio is 272. Variations
from this value in other selected objects of the Solar system have
been summarized by Kallenbach et al. (1998); the ratio ranges
from 125 to 325 (or slightly more) depending on the source for the
measurement. The solar wind N=15 N isotopic ratio of 200 ^ 55 is
probably the best approximation to the protosolar value (Kallenbach et al. 1998). A cometary measurement of 323 ^ 46 has been
obtained from molecular spectra of HCN isotopes (Jewitt et al.
1997). Large excesses in 15N and deuterium relative to terrestrial
values have been found in some meteorites and interplanetary dust
particles (IDPs), with the largest 15N excess of 50 per cent
observed in an IDP known as `Dragonfly' (Messenger et al. 1996).
The variation in Solar system values is doubtless caused by a
variety of effects, one of which might be differing degrees of
chemical fractionation in different nitrogen-containing molecules
during the interstellar and protosolar periods (Owen, private
communication). For example, if during these early stages the
N=15 N isotopic ratio in NH3 and HCN differed from that in N2,
and different molecules were responsible for bringing nitrogen to,
say, the Earth and the Sun, then the current N=15 N isotopic ratios
pertaining to the Earth and to the Sun might reflect this history.
Astronomical measurements appear to show an even wider
variation of the N=15 N isotopic ratio, which can range from <200
to 600. The largest astronomical surveys use the H13CN and
HC15N isotopomers (Wannier, Linke & Penzias 1981; Dahmen,
Wilson & Matteucci 1995), but the analysis must also account for
the spatial variation of the C=13 C ratio. GuÈsten & Ungerechts
(1985) have used hyperfine structure to help to determine the
NH3 =15 NH3 ratio in assorted warm interstellar sources, while the
detection of H15NN1 and HN15N1, which have nearly equal
abundances, has been reported in one interstellar cloud ±
w
E-mail: [email protected]
q 2000 RAS
DR21(OH) ± by Linke, GueÂlin & Langer (1983). A discussion
of the dependence of N=15 N upon distance from the Galactic
Centre, DGC, has been given by Wilson & Rood (1994) and by
Dahmen et al. (1995). Within a large degree of scatter, the local
interstellar value (400) appears to be somewhat larger than the
solar wind value (which approximately reflects the N=15 N isotopic
ratio 5 109 yr ago). The N=15 N isotopic ratio versus DGC (kpc)
is given by the expression …19:7 ^ 8:9†DGC 1 …288:6 ^ 65:1†
(Dahmen et al. 1995). Interestingly, extrapolation of this result to
the Galactic Centre does not agree with the value of .600
reported for Sgr A by Wannier (1980).
In most of the astronomical studies, the assumption was made
either implicitly or explicitly that the molecular ratios represent
the elemental isotopic ratio directly. This assumption may not
pertain to cold interstellar clouds, where chemical fractionation
occurring via ion±molecule reactions can be important. The
fractionation is not caused by a so-called `kinetic isotope effect',
in which the rates of analogous reactions involving different
isotopomers are different. Instead, fractionation is caused by a
thermodynamic effect in which the exchange of isotopic atoms
between molecules in pairs of forward and reverse reactions has a
preferred direction owing to exothermicity. The best-known
example consists of the reactions
1
H1
3 1 HD O H2 D 1 H2
…1†
involving the abundant `reservoir' molecules H2 and HD. In this
system, the left-to-right reaction is exothermic by 230 K owing to
zero-point energy differences and (for the case of H1
3 † the Pauli
exclusion principle (Herbst 1982). In a low-temperature cloud, the
right-to-left reaction occurs slowly and the abundance of the ion
H2D1 is strongly enhanced. Deuterium fractionation, which can
lead to the enrichment of D in molecules by factors of thousands,
occurs via a variety of exchange reactions in addition to (1) and
subsequent chemical reactions. It has been a subject of interest
from the earliest days of astrochemistry (e.g. Watson 1973; GueÂlin
et al. 1977) and has been explored in large model calculations
(Millar, Bennett & Herbst 1989). The dominant exchange
564
R. Terzieva and E. Herbst
processes in carbon and oxygen isotopic fractionation in dense
interstellar clouds have also been studied (Graedel, Langer &
Frerking 1982; Langer et al. 1984), although the effects for these
elements are much smaller since the energy changes for exchange
reactions are nowhere near as large as for deuterium fractionation.
Carbon isotopic fractionation is noticeable for CO in diffuse
interstellar clouds, where the enhancement in 13CO competes with
the self-shielding of 12CO against photodissociation (Federman
et al. 1999). Despite this past work on carbon and oxygen fractionation, the likelihood for nitrogen isotopic fractionation via
exchange reactions in the interstellar medium has not been
explored in great detail.
Some previous work concerning the likely nitrogen fractionation reactions
15
15
1
HN1
2 1 N N O H NN 1 N2
…2†
has been undertaken. Laboratory studies on the system have been
reported by Adams & Smith (1981). It appears that the reactions
go by a simple proton jumping mechanism, presumably via a
linear transition structure with the proton in the middle. The leftto-right reaction is the exothermic direction, but the exothermicity
is small and is expected to lead to only a small amount of
fractionation even in clouds at 10 K (GueÂlin & Lequeux 1980).
Unfortunately, the previous work on this reaction is not free of
uncertainties, such as the lack of a distinction between H15NN1
and HN15N1. In addition, to our knowledge, no other system of
reactions has been suggested as a possible mechanism for nitrogen
fractionation. For this reason we report a study of a variety of ion±
molecule exchange reactions involving abundant N-containing
species likely to lead to isotopic fractionation in dense interstellar
clouds. We then include these reactions in a gas-phase model
calculation of cloud chemistry.
Section 2 of this paper discusses the statistical mechanical
approach that we use for the calculation of rate coefficients, and
presents the specific reactions that we have considered. Section 3
contains our model results and a discussion.
2
F R AC T I O N AT I O N R E A C T I O N S
For a reaction system with forward and reverse reactions, the
equilibrium coefficient K(T), where T is temperature (K), is
defined by the relation
K…T† ˆ kf =kr ;
…3†
where kf and kr are the forward and reverse rate coefficients,
respectively. For a system in thermal equilibrium, the equilibrium
coefficient can be calculated by the methods of statistical
mechanics. The individual rate coefficients in both directions
can then be obtained with an additional assumption. When the
forward rate coefficient is much larger than the reverse one, this
additional assumption should be to equate kf with the collisional
rate coefficient, while if the forward and reverse coefficients are
nearly equal, one can assume that, in the absence of complications, the sum of kf and kr is equal to the collision rate coefficient.
This latter assumption derives from the view that the reaction
intermediate, or complex, can dissociate into either reactants or
products.
Consider a system of the type:
kf
A1 1 B O C1 1 D;
kr
…4†
where A1 and C1 are isotopic species (or isotopomers: e.g. H1
3
and H2D1) as are B and D (e.g. HD and H2). The equilibrium
coefficient K(T) is given by the equation (McQuarrie 1976)
3=2
kf
m…C1 †m…D†
q…C1 †q…D†
K…T† ˆ ˆ
exp…DE0 =kT†;
…5†
1
kr
m…A †m…B†
q…A1 †q…B†
where the m(¼) are masses, the q(¼) are the internal molecular
partition functions and DE0, the zero-point vibrational energy
difference between the `reactants' and the `products', is defined to
be positive for exothermic reactions. The partition functions are
given by
X
q…T† ˆ
gi exp…2Ei =kT†;
…6†
i
where gi is the electronic, vibrational, and rotational±nuclear spin
degeneracy, Ei is the energy of the ith state above the lowest state,
k is the Boltzmann constant, and T is the temperature. In the
absence of coupling, the partition functions can be factored into
electronic, vibrational and rotational±nuclear spin terms. The
translational energy has already been taken account of in the mass
factors. Because the internuclear potential energy surfaces for
each pair of isotopomers are the same, the electronic partition
functions are the same in the Born±Oppenheimer approximation.
In any case, at low temperatures only the ground electronic states
are populated. The vibrational partition functions for the isotopic
pairs are different, but at low temperatures they need not be considered since excited vibrational states are generally not populated. Some care has to be taken when evaluating the rotational±
nuclear spin partition functions of homonuclear diatomic
molecules.
Since N and N2 are the main reservoirs of nitrogen atoms in
interstellar clouds (Womack, Ziurys & Wyckoff 1992), we
naturally have looked for some exchange reactions that involve
either 15N or N15N. It is worth pointing out that N has a nuclear
spin I ˆ 1 and is a boson, while 15N has I ˆ 12 and is a fermion.
The rotational partition function for a homonuclear diatomic
molecule in a symmetric electronic state, such as N2 in its ground
state, which has nuclei with integral spin, can be formulated as
(McQuarrie 1976)
X
qrot;nuc …T† ˆ …I 1 1†…2I 1 1† …2J 1 1† exp‰2BJ…J 1 1†=kTŠ
J even
X
1 I…2I 1 1† …2J 1 1† exp‰2BJ…J 1 1†=kTŠ;
…7†
J odd
where J is the rotational quantum number and B is the rotational
constant for the molecule.
It should be noted that this expression assumes the spin states of
the homonuclear diatomic molecules to be in equilibrium. A more
common situation in the laboratory is the `normal' one, in which
two classes of spin states, designated `ortho' and `para', do not
communicate with one another and maintain a temperatureindependent concentration ratio with respect to each other. In
interstellar clouds, the equilibrium ratio should prevail given
enough time for ion±molecule reactions to scramble spins, but the
time-scale for complete conversion may be too long (Flower &
Watt 1984). For N2, the ortho states consist of those with even J
and the para states those with odd J. In normal N2, the ortho-topara ratio is 2, reflecting the ratio of nuclear spin states. In
equilibrium N2, the ortho-to-para ratio is given by the ratio of the
first term on the right-hand-side of equation (7) to the second
term; at 10 K this is 2.01. Only at temperatures considerably under
q 2000 RAS, MNRAS 317, 563±568
Nitrogen isotopic fractionation
565
Table 1. Calculated molecular parameters.
Molecule
Scaled vibrational frequencies (cm21)
HN1
2
HN15N1
15
H NN1
CNC1
C15NC1
HCNH1
HC15NH1
670 (p); 2068, 3294 (s )
669 (p); 2033, 3293 (s )
666 (p); 2041, 3280 (s )
179 (pu); 1259 (s g); 2024 (s u)
175 (pu); 1259 (s g); 1981 (s u)
624, 789 (p); 2091, 3286, 3557 (s )
620, 789 (p); 2064, 3286, 3543 (s )
Scaled E0 (kJ mol21)
B (GHz)
40.08
39.85
39.78
21.78
21.48
70.35
70.05
44.53
43.14
43.59
13.38
13.38
36.24
35.53
Notes: some of the results have been published before but are listed here for completeness.
Calculated frequencies and zero-point energies (E0) have been scaled by a factor of 0.969.
10 K does the equilibrium ortho-to-para ratio differ substantially
from the normal value. In the calculations here, equation (7) may
be used to determine equilibrium coefficients.
When B ! kT; which is approximately
for N2 even
Pthe caseP
P at
1
<
<
low interstellar temperatures, the sums
J even
J odd
J
2
in equation (7) can be replaced by an integral and easily evaluated
(McQuarrie 1976). For I ˆ 1; one gets
qrot;nuc …T† <
9 kT
;
2 BN2
…8†
which is one-half of the value of the partition function in the
absence of the Pauli exclusion principle. If equation (8) is
insufficiently accurate, the direct sum can be computed numerically. The partition function for the heteronuclear N15N is
qrot;nuc …T† ˆ …2I N 1 1†…2I 15 N 1 1†
X
kT
…2J 1 1† exp‰2BJ…J 1 1†=kTŠ < 6
: …9†
B
N15 N
J
Partition functions similar to these can be written for polyatomic
linear species. No non-linear species have been included in our
analyses. A simplified expression for K(T) equivalent to (5) is
K…T† ˆ f …B; m† exp…DE0 =kT†;
…10†
in which the `symmetry' factor f …B; m† depends on the rotational
constants, masses and symmetries of the reactants and products. It
is near unity for the reactions studied here unless N2 appears, in
which case it is near 2.0 if N2 is a reactant and near 0.5 if N2 is a
product. When direct sums are computed, f …B; m† also has a slight
dependence on temperature, which affects our results only
marginally.
Unless experimental values are available, ab initio calculations
with gaussian 981 (Frisch et al. 1998) at the second-order
MoÈller±Plesset perturbation theory level (MP2/6-31G*) were used
to determine the zero-point vibrational energies and the rotational
constants B for the molecules of interest. Rotational constants
calculated at the MP2 level are known to differ from the
experimental constants, but are sufficiently accurate for our
study. The vibrational frequencies, acquired at the optimized
geometry for each species, were scaled by 0.969 ± an MP2 scaling
factor used for similar molecules by Talbi, Ellinger & Herbst
(1996). The resulting parameters are listed in Table 1.
2.1
Specific fractionation reactions
We have studied eight exchange reaction systems. These are listed
1
Gaussian, Inc., Carnegie Office Park, Building 6, Pittsburgh, PA 15106,
USA.
q 2000 RAS, MNRAS 317, 563±568
Table 2. Fractionation reactions.
Reaction
15
1
N15 N 1 HN1
2 O N2 1 H NN
1
15
15 1
N N 1 HN2 O N2 1 HN N
15 1
N 1 N2 O N1 1 N15 N
15 1
N 1 NO O N1 1 15 NO
15
N 1 CNC1 O N 1 C15 NC1
15
15
1
N 1 HN1
2 O N 1 H NN
15
15 1
N 1 HN1
O
N
1
HN
N
2
15
N 1 HCNH1 O N 1 HC15 NH1
f …B; m†
(10 K)
DE0/k
(K)
K
(10 K)
0.494
0.499
1.959
0.979
0.938
0.968
0.977
0.968
10.7
2.25
28.3
24.3
36.4
36.1
27.7
35.9
1.44
0.63
33.2
11.1
35.7
35.8
15.6
35.1
Note: the equilibrium coefficient K(T) for each reaction is given
by K…T† ˆ f …B; m† exp…DE0 =kT†:
in Table 2 along with f …B; m†; the pre-exponential factor for the
equilibrium coefficients at 10 K, DE0 =k (K), the left-to-right
reaction exothermicity in K, and the equilibrium coefficient K(T)
at 10 K. The exothermicities range from 2 to 36 K, which is far
below the exothermicity for reaction (1) but, taken together with
the calculated equilibrium coefficients, suggests that some
nitrogen fractionation might be possible via the exchange
mechanism at low temperatures if the exchange reactions are
competitive with other reactions in our model network.
Let us first consider reaction (2) and the similar reaction system
15
15 1
HN1
2 1 N N O HN N 1 N2 :
…11†
The calculated DE0 =k is 10.7 K for reaction (2) and 2.25 K for
reaction (11), which suggests that, if any fractionation occurs at
all, HN15N1 will be slightly less abundant than H15NN1 in
interstellar clouds. A previous unpublished value of 10 ^ 1 K
exists for reaction (2) (Henning, Kraemer & Diercksen 1977). At
10 K, the equilibrium coefficient for reaction (11) is 0.63, showing
that, for this reaction, the symmetry factor of 0.5 drives the
equilibrium coefficient to less than unity. Direct comparison
between our theoretical results for reactions (2) and (11) and the
experimental study of the proton exchange reaction between HN1
2
and N15N by Adams & Smith (1981) can be undertaken. This
comparison is not fully quantitative, however, because Adams &
Smith (1981) did not distinguish between the products H15NN1 and
HN15N1, used `normal' N2, and apparently did not include nuclear
spin statistics in their determination of DE0 =k from the measured
equilibrium coefficient. These factors tend to cancel each other out
to an extent. Their determination of 9 ^ 3 K is in reasonable
agreement with theory for reaction (2) if not for reaction (11).
For modelling purposes we have assumed that each of the
forward reactions (2) and (11) occurs with a rate coefficient equal
to one-half the Langevin collisional rate …kL ˆ 8:1 10210
cm3 s21). This value is an upper limit, since the experimental
rate coefficient reported for the combined forward reactions (2)
566
R. Terzieva and E. Herbst
and (11) without distinction between H15NN1 and HN15N1 is
4:6 10210 cm3 s21 at 80 K (Adams & Smith 1981).
In addition to fractionation from molecular nitrogen, we have
also considered exchange reactions involving neutral and ionized
atomic nitrogen. The abundance of ionized atomic nitrogen is
uncertain in models because of the still uncertain rate of its
reaction with molecular hydrogen at low temperature (e.g. Le
Bourlot 1991). One of the exchange reaction systems studied
involving the atomic nitrogen ion is that between N1 and N2:
15
N1 1 N2 O N1 1 N15 N:
…12†
15
1
The alternative charge-exchange reaction leading to N N and N
is endothermic by 2.8 eV (Freysinger et al. 1994). Accounting for
the symmetry of the homonuclear N2 molecule in comparison with
N15N, and using experimental frequency data (Huber & Herzberg
1998), we have calculated DE0 =k ˆ 28:3 K and an equilibrium
coefficient K 12 …T† ˆ 1:96 exp…28:3=T†: The rate coefficient kf has
been set to one-third of the Langevin collision rate based on ion
cyclotron resonance studies of the N1 1 15 N15 N ion-exchange
reaction (Anicich, Huntress & Futrell 1977).
Another reaction system involving 15N1, which may lead to
fractionation, is
15
1
1
N 1 NO O N 1
15
NO:
…13†
15
Using the highly accurate rotational constants for NO and NO
measured by Varberg, Stroh & Evenson (1999) and experimental
frequency data (Huber & Herzberg 1998), we have calculated
DE0 =k ˆ 24:3 K and an equilibrium coefficient K 13 …T† ˆ
0:98 exp…24:3=T†: The reaction between nitrogen ions and NO
has been studied experimentally at room temperature (Huntress &
Anicich 1976; Adams, Smith & Paulson 1980), and found to
produce two sets of products: NO1 1 N and N1
2 1 O: We have
estimated the rate coefficient kf for the exchange reaction (13) as
the difference between the theoretical Langevin rate coefficient
for reaction of 15N1 with NO and the sum of the rate coefficients
for the two non-exchange channels.
We have also looked into the fractionation caused by reactions
between neutral atomic 15N and some N-containing ions which do
not react rapidly with H2 and are therefore relatively abundant in
interstellar conditions. In particular, we have chosen three such
1
ions ± HN1
and CNC1 ± which, according to our
2 ; HCNH
models, reach fractional abundances greater than 1 10210 in
1
1
dense interstellar clouds. Contrary to HN1
2 ; HCNH and CNC
have their peak abundances at so-called `early time' in our dense
cloud model (<5 104 yr†; and may be fractionated at times
before HN1
2 : Unfortunately, there is very little experimental
information concerning N-atom reactions, and no common
mechanistic path has been found to allow us to generalize as to
whether the exchange reactions can occur without barriers (Scott
et al. 1998). In order to evaluate the possible importance of the
exchange reactions
15
N 1 CNC1 O N 1 C15 NC1 ;
HN1
2
15
…14†
15
N1
1
…15†
15
15 1
N 1 HN1
2 O N 1 HN N
…16†
O N 1 H NN ;
and
15
N 1 HCNH1 O N 1 HC15 NH1 ;
…17†
we assume that they occur without activation energy barriers and
do not result in additional products. Scott et al. (1998) find no
reaction between N atoms and HCNH1, which supports the
assumption of no additional products but does not rule out the
likelihood of an exchange reaction. In order to derive an upper
limit to the possible fractionation, the forward reactions have been
set to occur at the Langevin rate [except for reactions (15) and
(16), for which the sum of the rate coefficients equals the
Langevin value]. We expect rates lower than the collisional limit
to be more realistic, however, because of the available experimental data for similar reactions (Anicich et al. 1977; Scott et al.
1998) and the necessity for bond rearrangement in the reactions of
15
N with HCNH1 and with CNC1.
It is worth pointing out that we have limited our study to
possible fractionation owing to ion±molecule chemical reactions.
Phenomena such as mass-independent isotope effects (Thiemens
1999) and symmetry-induced kinetic isotope effects (Yoo &
Gellene 1996) seen in some association processes have not been
considered. These may well have been important in the solar
nebula, but are not associated specifically with low-temperature
interstellar chemistry.
3
M O D E L R E S U LT S A N D C O N C L U S I O N S
Starting with the current version of the gas-phase `new standard
model' (Bettens, Lee & Herbst 1995; Herbst, Terzieva & Talbi
2000), with updated chemistry for CNC1 and C2N1 (Knight et al.
1988), we have added 113 new species derived by replacement of
one N atom in each N-containing species in the initial network
with a 15N atom. Reactions, equivalent to the already existing
reactions involving N-containing species, have been added in a
statistical fashion (Millar et al. 1989). Finally, the fractionation
reactions listed in Table 2 have been included in the model. The
resulting network contains 531 species connected through 5536
reactions. A constant hydrogen number density nH of 2 104 cm23 ; a cosmic ray ionization rate z for H2 of 1:3 10217 s21 ; a visual extinction of 20 mag, and `low metal' gasphase elemental abundances (Lee, Bettens & Herbst 1996) have
been used to represent a quiescent dense cloud core. A variety of
15
N elemental abundances have been observed towards different
astronomical objects (Wilson & Rood 1994), and we have utilized
15
N=N ratios between 1=600 and 1=200 for our calculations. The
initial form of nitrogen is assumed to be the neutral atom. The
degree of fractionation has been compared for temperatures of 10,
20 and 40 K.
Selected results from a model calculation at T ˆ 10 K are listed
in Table 3. Only relatively small species, containing four or fewer
carbon atoms and having a fractional abundance relative to H2
greater than 1 10213 ; have been included. The degree of
fractionation is given relative to the 15 N=N ratio, and is essentially
independent of the exact value of 15 N=N in the range between
1=600 and 1=200:
A value of 1.00 in Table 3 signifies that the calculated ratio is
exactly equal to the elemental isotopic ratio 15 N=N used for the
calculation, while a value greater than 1.00 suggests enrichment in
15
N owing to fractionation reactions. The case of N15N is the only
exception because the value of <2 derives from symmetry, or
from the equivalence between N15N and 15NN, and not from
fractionation reactions.
A glance at the results in Table 3 shows that fractionation is
small for all species, especially when the chemistry reaches steady
state, which occurs by 107±8 yr. There are three reasons for the
generally small fractionation. First, some of the exchange
q 2000 RAS, MNRAS 317, 563±568
Nitrogen isotopic fractionation
Table 3. Isotopic fractionation relative to
Ratio
15
N/N
C15N/CN
15
N N/N2
15
NH/NH
15
NO/NO
C215N/C2N
HC15N/HCN
H15NC/HNC
H15NO/HNO
N15NO/N2O
15
NNO/N2O
15
NH2/NH2
15
NO2/NO2
OC15N/OCN
C315N/C3N
H2C15N/H2CN
15
NH3/NH3
C2H215N/C2H2N
CH315N/CH3N
HC215NC/HC2NC
HC315N/HC3N
H15NC3/HNC3
NH2C15N/NH2CN
15
NH2CN/NH2CN
C2H315N/C2H3N
CH515N/CH5N
CH3C315N/CH3C3N
15 1 1
N /N
C15NC1/CNC1
H15NN1/HN21
HN15N1/HN21
HC15NH1/HCNH1
1
15
NH1
4 =NH4
15
567
N=N:
Fractionation at time of
105 yr
106 yr
108 yr
104 yr
1.00
1.03
1.99
1.01
1.00
1.00
1.05
1.07
1.01
1.00
1.00
1.03
1.01
1.00
1.00
1.00
1.02
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.04
1.01
1.01
1.03
1.31
1.04
1.04
1.14
1.03
1.00
1.23
2.00
1.05
1.00
1.03
1.27
1.35
1.24
1.09
1.09
1.24
1.24
1.03
1.01
1.00
1.25
1.11
1.22
1.11
1.10
1.08
1.22
1.22
1.26
1.22
1.04
1.20
1.72
1.05
1.05
1.46
1.26
1.00
1.31
2.03
1.01
1.00
1.00
1.30
1.39
1.01
1.02
1.02
1.01
1.02
1.30
1.00
1.00
1.01
1.00
1.01
1.10
1.11
1.10
1.16
1.16
1.30
1.01
1.02
1.00
1.63
1.05
1.05
1.41
1.01
0.93
1.11
2.03
0.99
0.95
0.94
1.10
1.11
0.99
0.97
0.97
0.99
0.99
1.11
0.94
0.93
0.99
0.96
1.00
1.08
1.08
1.08
1.05
1.05
1.10
0.99
1.00
0.99
1.17
1.05
1.03
1.11
0.99
Note: a fractionation ratio of 1.00 means that the
calculated ratio is exactly equal to the elemental isotopic
ratio 15N/N used for the calculation. A fractionation
greater than 1.00 suggests enrichment in 15N.
reactions (e.g. those involving molecular nitrogen) do not have
equilibrium coefficients seriously different from unity. Secondly,
and more importantly, the exchange reaction systems cannot reach
equilibrium because competitive ion±molecule reactions are far
more rapid. Thirdly, even if some fractionation occurs as a result
of the exchange reactions, this fractionation is not generally
passed on efficiently to other species because the fractionated
species are themselves not extremely abundant.
What fractionation does occur is due mainly to those exchange
reactions involving neutral atomic nitrogen. This conclusion has
been reached by running models with assorted exchange
reactions removed. The reaction in our model that causes the
most N-isotope fractionation is the exchange reaction between 15N
atoms and the HCNH1 ion, which is relatively abundant at early
times (104±5 yr). The small excess of HC15NH1 leads to limited
fractionation in a large number of species, as schematically
presented in Fig. 1. The isotopic fractionations listed in Table 3,
small as they may be, can be regarded as upper limits since
collisional rate coefficients were chosen for the forward fractionation reactions involving nitrogen atoms although no experimental
information is available.
As can be expected, the N-isotope fractionation depends on
the temperature and is, in general, more discernible the lower the
temperature. We have compared the results for 73 species (the
15
N-containing species with four or fewer carbon atoms in our
q 2000 RAS, MNRAS 317, 563±568
Figure 1. Propagation of the fractionation from HC15NH+ to other species.
model) at temperatures of 10, 20 and 40 K, and we find that the
trend for increase in fractionation with decrease in temperature
holds for 95 per cent of the species at the early time of 1 105 yr:
Thus young, cold interstellar clouds are potentially the best places
for investigating nitrogen fractionation even though small factors
of less than 2 would be hard to detect given current uncertainties
in observation. In the one possible comparison with observation,
we cannot reproduce at any time the result of Linke et al. (1983)
that H15NN1 may be a factor of 1.25 as abundant as HN15N1;
indeed, these isotopomers appear to have nearly equal abundances
and are only minutely fractionated at all temperatures studied. We
do note that Linke et al. (1983) felt their value of 1.25 to be of `the
order of the uncertainties.'
Finally, our results do not rule out the possibility that some of
the nitrogen fractionation detected in the Solar system is the result
of exchange reactions that occurred in the pre-natal interstellar
cloud. The large excess in 15N observed in the IDP known as
`Dragonfly' would seem, however, to be incompatible with our
results. Testing our approach by simulation of 15N fractionation in
cold laboratory discharges might be useful.
AC K N O W L E D G M E N T S
We are grateful to Tobias Owen and William Irvine for bringing
the question of N-isotope fractionation to our attention, and to the
referee for a careful reading of the manuscript. RT thanks George
McBane for a helpful discussion. EH acknowledges the support of
the National Science Foundation for his research in astrochemistry. We thank the Ohio Supercomputer Center for time on their
T90 computer.
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