The Astrophysical Journal, 730:107 (6pp), 2011 April 1
C 2011.
doi:10.1088/0004-637X/730/2/107
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
MILLIMETER AND SUBMILLIMETER REST FREQUENCIES FOR NaCN (X̃1 A ): A REMARKABLY
ABUNDANT CIRCUMSTELLAR MOLECULE
D. T. Halfen and L. M. Ziurys
Departments of Chemistry and Astronomy, Arizona Radio Observatory and Steward Observatory, University of Arizona,
933 North Cherry Avenue, Tucson, AZ 85721, USA
Received 2010 October 13; accepted 2011 January 25; published 2011 March 10
ABSTRACT
The pure rotational spectrum of NaCN has been recorded in the millimeter/submillimeter region using direct
absorption techniques, the first experimental study of this molecule at frequencies above 40 GHz. The species was
produced in the gas phase in an AC discharge by the reaction of sodium vapor with cyanogen. Twelve rotational
transitions of NaCN have been measured in the range of 180–530 GHz, extending the previous microwave data
to millimeter/submillimeter frequencies. Multiple Ka asymmetry components were recorded in each rotational
transition up to Ka = 5 or 6, a total of 131 individual lines. These data have been analyzed with a standard
asymmetric top Hamiltonian, combined with prior microwave measurements. Higher-order centrifugal distortion
terms were clearly needed to model the millimeter-wave transitions of this floppy molecule. From this revised
set of spectroscopic constants, accurate frequency predictions can now be made up to 600 GHz for NaCN for
the lower-value Ka components (Ka 4). Based on the new laboratory data and past spectral surveys, a revised
abundance for NaCN in IRC+10216 has been estimated. For a 5 source, the fractional abundance for this molecule
was found to be f (NaCN/H2 ) ∼ 1 × 10−8 , comparable to that of c-C3 H2 . These new frequency measurements
should aid in line identification in surveys in the 0.8 mm band and at shorter wavelengths.
Key words: astrochemistry – ISM: molecules – line: identification – methods: laboratory – molecular data – stars:
AGB and post-AGB
frequency discrepancies found by Tenenbaum et al. (2010) for
many astronomical lines of NaCN, particularly of the higher Ka
components, it is clear that additional laboratory measurements
at wavelengths of 1 mm and shorter are necessary. This need is
particularly growing as new facilities such as Herschel, SOFIA,
and ALMA become operational, as they probe the submillimeter regime. Here the frequency uncertainties for NaCN must
be substantial due to lack of higher-order centrifugal distortion
constants, coupled with its floppy structure.
In order to improve the spectroscopic database available
for NaCN, we have conducted new measurements of the
millimeter/submillimeter spectrum of this molecule in the range
180–530 GHz. These new data, combined with the previous
work, have considerably improved the spectroscopic constants
for this species, as well as providing measured rest frequencies. In addition, recently reported spectral lines of NaCN in
IRC+10216 from surveys at 2 and 1 mm have been analyzed to
establish a more accurate abundance for this molecule in this
object. Here we report our laboratory data, improved spectral
constants, and our best estimate of the NaCN abundance in
IRC+10216.
1. INTRODUCTION
Since its original discovery in the circumstellar shell of
IRC+10216 (Turner et al. 1994), NaCN has proven to be a rather
common contributor to millimeter emission from asymptotic
giant branch (AGB) envelopes. This molecule was initially
detected via its 2 and 3 mm rotational transitions in the Ka = 0
asymmetry component, but appears to be prominent in spectral
surveys of IRC+10216 ranging from 7 mm up to 0.8 mm
(Kawaguchi et al. 1995; Cernicharo et al. 2000; He et al. 2008;
Tenenbaum et al. 2010; Patel et al. 2009). In the very recent
Arizona Radio Observatory (ARO) 1 mm spectral survey of
IRC+10216 (Tenenbaum et al. 2010), for example, this molecule
exhibited the fourth highest number of spectral lines, after SiS,
SiC2 , and C4 H, with asymmetry components present as high
as Ka = 7. Tenenbaum et al. (2010) also noted that a large
fraction of the observed features for NaCN had frequencies that
deviated significantly from predictions in common databases,
with errors as large as 15 MHz. NaCN has also been observed
in the envelope of the post-AGB star CRL 2688 at 1 and 2 mm
(Highberger et al. 2001, 2003).
Laboratory spectroscopic studies of sodium cyanide, on the
other hand, have been very limited. The only study to date has
been that of van Vaals et al. (1984), who measured the microwave spectrum of this molecule from 9.7 to 39.4 GHz. These
authors concluded that NaCN was a very floppy molecule. More
recently, He et al. (2008) reanalyzed the microwave data of van
Vaals et al. (1984), including millimeter transitions observed in
their 1–2 mm survey of IRC+10216. They found that the inclusion of the astronomical data did not affect the analysis because
of its larger frequency uncertainty relative to the laboratory
data, and thus these lines were excluded in the final fit. Predictions of the rest frequencies from this study were given in the
CDMS database (Müller et al. 2005; http://cdms.de), a source
also used by Tenenbaum et al (2010). Given the rather large
2. EXPERIMENTAL DETAILS
Rotational transitions of NaCN in its X̃1 A ground state were
recorded using one of the millimeter/submillimeter spectrometers of the Ziurys group (Savage & Ziurys 2005). Briefly, the
instrument consists of a radiation source (Gunn oscillators/
Schottky diode multipliers) that covers a range of 65–850 GHz,
a free-space gas cell about 1 m in length, cooled to −65◦ C
with methanol, and a helium-cooled hot electron bolometer
detector. The cell contains two ring electrodes for creating a
longitudinal AC discharge. The radiation is propagated through
the system using a series of Teflon lenses, two of which seal
the ends of the gas cell. The radiation is frequency modulated
1
The Astrophysical Journal, 730:107 (6pp), 2011 April 1
Halfen & Ziurys
(FM) and the signals are detected at 2f to give second derivative
spectra.
NaCN was created in the spectrometer cell in an AC discharge
by the reaction of gas-phase sodium with cyanogen. Metal
vapor was produced by placing solid sodium in a glass oven
attached to the bottom of the cell, and heating it to ∼230◦ C
(450 F). The reaction mixture was composed of <1 mtorr of Na
vapor and approximately 1 mtorr of (CN)2 , as well as 20 mtorr
of Ar to help sustain the discharge. The AC discharge was
operated at 200 W at an impedance of 600 Ω, which created an
orange-colored plasma in the cell, arising from atomic sodium
emission. NaCN was also created in a DC discharge of sodium
vapor and cyanogen. In this case, the metal vapor was generated
in a Broida-type oven, and the discharge required 200 mA at
300 V.
Transition frequencies were determined by measuring pairs of
scans 5 MHz in width, each recorded in 30 s, one in increasing
frequency, followed by another in decreasing frequency. One
to two such scan pairs were necessary to achieve an adequate
signal-to-noise ratio for the NaCN spectra. A Gaussian function
was then used to fit the line profile to determine the center
frequency and line width, which ranged from 600 to 1300 kHz
from 180 to 530 GHz. The experimental error is estimated to be
±50 kHz.
Table 1
Measured Rotational Transitions (in MHz) of NaCN (X̃1 A )
3. RESULTS AND ANALYSIS
NaCN is a floppy, T-shaped asymmetric top species characterized by the quantum numbers J, Ka , and Kc , with a large a-dipole
moment calculated to be μa = 8.85 D (http://cdms.de; He et al.
2008). A previous calculation by Klein et al. (1981) suggested
a dipole moment of μa = 9.05 D, in good agreement. For the
strong a-type rotational transitions that were measured in this
study, the selection rules are ΔJ = ±1, ΔKa = 0, and ΔKc =
±1. The previous study by van Vaals et al. (1984) recorded
a-type, as well as b-type transitions. The latter follow the selection rules of ΔJ = ±1, ΔKa = ±1, and ΔKc = ∓1, but the
b-dipole moment is considerably weaker: μb ∼ 0.2 D (He et al.
2008).
The initial investigation began with the measurement of the
JKa,Kc = 190,19 ← 180,18 transition of NaCN near 284.2 GHz as
a test line for another molecule, based on the predictions given
in the CDMS database (Müller et al. 2005). It was immediately
evident that the predicted frequencies were not accurate, as
the observed line differed by ∼8 MHz from the calculated
value. Coincidently, Tenenbaum et al. (2010) were also finding
similar frequency discrepancies in their astronomical data.
Consequently, an effort was launched to record transitions of
NaCN at 2 mm and shorter wavelengths.
The transition frequencies recorded for NaCN are listed
in Table 1, along with the data of van Vaals et al. (1984).
These authors measured 20 a-type and b-type transitions in the
frequency range of 9.7–39.4 GHz. The new data presented in this
work include 12 rotational transitions spanning the frequency
range of 180–530 GHz (J = 12 ← 11 up to J = 33 ← 32)
and an energy range of El = 34–317 cm−1 , with Ka ranging
from Ka = 0 to 6, a total of 131 spectral features. (Sensitivity
limited the measurements to Ka < 7.) At frequencies above
400 GHz, the molecule’s spectrum begins to deviate from the
simple asymmetric top, rigid-rotor model. For example, the
Ka = 6 lines at the highest transitions (J = 26 ← 25, J =
32 ← 31, and J = 33 ← 32) could not be positively identified,
as the predictions did not match any given feature. Moreover,
the Ka = 4 components in this frequency range were noticeably
2
J
Ka
Kc
↔
J Ka
Kc
ν obs
ν obs –ν calc
13
4
15
11
9
4
1
5
12
1
13
6
6
12
7
2
5
16
10
8
12
12
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
3
1
2
2
1
0
0
1
2
1
2
1
2
3
1
0
0
2
1
1
1
0
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
11
3
13
9
8
4
1
4
10
1
11
5
5
10
6
2
5
14
9
7
12
12
14
14
13
8
9
9
10
11
10
12
11
13
12
15
15
14
9
10
11
10
12
11
13
12
14
13
16
16
15
11
10
12
11
13
12
14
13
15
14
17
17
16
12
11
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
→
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
14
4
14
11
8
3
0
5
12
2
13
6
7
13
7
1
4
15
9
8
11
11
13
13
13
13
13
13
13
13
13
13
13
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
2
1
3
2
2
1
0
1
2
0
2
1
1
2
1
0
1
3
2
1
1
0
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
4
3
3
1
2
1
0
2
6
6
12
4
12
10
7
3
0
5
11
2
12
6
6
11
7
1
4
13
8
8
11
11
13
13
12
7
8
8
9
10
9
11
10
12
11
14
14
13
8
9
10
9
11
10
12
11
13
12
15
15
14
10
9
11
10
12
11
13
12
14
13
16
16
15
11
10
9783.5098a
10962.9463a
11402.5098a
12153.1380a
14251.7157a
15497.1375a
15640.3280a
16439.8314a
16691.9700a
18289.3222a
22246.5130a
23005.2519a
25796.2003a
30238.9880a
30652.1941a
31262.3341a
33010.2203a
33303.6225a
34919.1656a
39369.7637a
179921.922
183024.642
209495.657
212124.021
217447.550
218290.814c
218290.814c
218642.686c
218642.686c
219036.678
219065.793
219321.073
220086.260
224030.639
224082.604
224232.271
226581.108
232748.150
233895.452c
233895.452c
234290.371c
234290.371c
234738.219
234785.898
235008.455
236078.931
239546.374
240507.222
238936.974
241000.315
248003.174
249502.733c
249502.733c
249943.262
249944.902
250449.035
250524.134
250685.210
252143.791
254945.207
256909.373
253611.375
255396.367
263210.438
265112.792c
265112.792c
−0.0036
0.0015
b
−0.0058
0.0044
0.0028
0.0023
0.0040
−0.0006
0.0065
0.0101
0.0005
−0.0041
−0.0054
−0.0037
0.0019
0.0080
−0.0067
−0.0069
−0.0028
−0.035
−0.021
−0.059
−0.087
−0.025
−0.437
−0.431
−0.463
0.083
0.044
−0.056
0.067
−0.167
−0.045
0.001
−0.049
−0.110
0.031
−0.101
−0.088
0.519
−0.517
−0.018
0.011
0.069
0.055
−0.073
0.018
−0.046
−0.078
0.028
0.249
0.222
0.001
−0.242
−0.059
−0.096
0.061
0.060
−0.014
0.042
−0.045
−0.087
−0.300
0.466
0.411
The Astrophysical Journal, 730:107 (6pp), 2011 April 1
Halfen & Ziurys
Table 1
(Continued)
Table 1
(Continued)
J
Ka
Kc
↔
J Ka
Kc
ν obs
ν obs –ν calc
J
Ka
Kc
↔
J Ka
Kc
17
17
17
17
17
17
17
17
18
18
18
18
18
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
20
20
20
20
21
21
26
26
26
26
26
26
26
26
26
26
26
32
32
32
32
32
32
32
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
3
4
3
1
2
1
0
2
6
6
5
5
3
4
4
1
3
2
1
0
2
6
6
5
5
3
4
4
1
3
1
0
1
0
2
1
3
5
5
4
4
2
3
1
0
2
1
3
5
4
13
12
14
13
15
14
16
15
18
18
17
12
13
14
13
15
16
14
15
17
16
19
19
18
14
13
15
14
17
16
15
18
16
17
20
20
19
15
14
16
15
18
17
16
19
17
21
21
26
26
25
25
24
22
21
23
22
24
23
32
32
31
31
30
28
29
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
17
17
17
17
18
18
18
18
18
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
19
19
19
20
20
25
25
25
25
25
25
25
25
25
25
25
31
31
31
31
31
31
31
5
5
4
4
3
3
1
2
1
0
2
6
6
5
5
4
3
4
3
1
2
1
0
2
6
6
5
5
3
4
4
1
3
2
1
0
2
6
6
5
5
3
4
4
1
3
1
0
1
0
2
1
3
5
5
4
4
2
3
1
0
2
1
3
5
4
12
11
13
12
14
13
15
14
17
17
16
11
12
13
12
14
15
13
14
16
15
18
18
17
13
12
14
13
16
15
14
17
15
16
19
19
18
14
13
15
14
17
16
15
18
16
20
20
25
25
24
24
23
21
20
22
21
23
22
31
31
30
30
29
27
28
265603.271
265606.467
266168.621
266283.634
266346.972
268287.569
270217.359
273268.597
268257.243
269780.824
278369.355
280725.826c
280725.826c
281270.168
281275.578
281896.071
281989.140
282067.491
284514.732
285355.271
289567.192
282876.641
284161.701
293477.697
296342.014c
296342.014c
296944.168
296953.211
297607.077
297630.203
297879.798
300354.336
300826.641
305790.354
297471.417
298544.252
308535.016
311961.563c
311961.563c
312625.573
312640.040
313196.092
313369.377
313724.989
315213.839
317220.570
312043.585
312931.205
384625.025
384936.059
397815.974
401981.839
405885.339
406870.048
407023.694
407765.217
409815.715
416335.423
416554.283
471263.135
471339.561
485502.495
487175.595
496644.944
501283.267
501491.254
0.071
−0.022
−0.081
−0.078
0.070
0.053
−0.014
0.091
−0.088
−0.053
0.046
0.377
0.481
0.161
0.016
−0.150
0.067
−0.184
0.040
0.005
0.106
−0.046
−0.070
0.049
0.170
−0.021
0.190
0.129
0.070
−0.236
−0.242
0.060
0.019
0.148
−0.046
−0.030
0.071
−0.598
−0.941
0.221
0.164
0.030
−0.358
−0.362
0.074
−0.002
−0.020
0.010
0.099
0.103
0.118
0.200
−0.219
0.146
0.018
32
32
32
32
33
33
33
33
33
33
33
33
33
33
33
5
2
4
3
1
0
2
1
3
4
5
5
2
4
3
27
30
28
29
33
33
32
32
31
30
29
28
31
29
30
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
31
31
31
31
32
32
32
32
32
32
32
32
32
32
32
5
2
4
3
1
0
2
1
3
4
5
5
2
4
3
26
29
27
28
32
32
31
31
30
29
28
27
30
28
29
ν obs
ν obs –ν calc
502221.039
505510.267
508448.135
514262.137
485663.112
485722.952
499996.091
501390.766
511560.286
516978.209
517010.911
518226.337
519855.907
525108.524
530119.371
−0.011
0.013
b
−0.053
−0.038
−0.069
−0.181
0.104
0.288
b
0.025
0.017
−0.381
b
0.025
Notes.
a From van Vaals et al. (1984).
b Not included in fit.
c Unresolved lines.
~
NaCN (X 1A')
J = 19 18
J = 20
Ka = 3
J = 19
Ka = 5
18
19
Ka = 6
J = 21
20
Ka = 1
Ka = 4
Ka = 5
*
296.933
296.963
297.605
297.635
311.961
312.041
Frequency (GHz)
Figure 1. Laboratory spectrum of NaCN (X̃1 A ) showing several Ka components
of the J = 19 ← 18 (Ka = 3, 4, and 5), J = 20 ← 19 (Ka = 6), and J = 21 ←
20 (Ka = 1) transitions in the range 297–312 GHz. There are three frequency
breaks in the spectrum to display all of these lines, which are plotted on the
same relative intensity scale. There is an unknown line marked by an asterisk
next to the J = 19 ← 18, Ka = 3 line. Note that the Ka = 5 asymmetry doublets
lie close in frequency so that they appear in the same 50 MHz wide region. The
other component of the Ka = 1, 3, and 4 doublets lie at much higher frequency.
Each spectrum was obtained in a single, 110 MHz wide scan, recorded in 70 s,
and then cropped to display either a 25 or 50 MHz wide range.
shifted from their expected frequencies by typically 10 MHz,
although the Ka = 5 lines appeared unperturbed. Such behavior
is expected in a floppy molecule such as NaCN.
Representative spectra of NaCN are presented in Figure 1.
Here one component of the Ka = 3 and 4 asymmetry doublets
and both doublets for Ka = 5 lines of the J = 19 ← 18 transition
near 297 GHz are displayed. In addition, the collapsed Ka = 6
components of the J = 20 ← 19 transition, as well as one
asymmetry line of the Ka = 1 doublet of the J = 21 ← 20
transition near 312 GHz, are shown. There are three frequency
breaks in the spectrum to show the different spectral features.
An unknown line is marked with an asterisk.
A stick spectrum covering the frequency range of
280–310 GHz is shown in Figure 2. Here the full pattern
b
b
0.530
−0.026
0.054
0.035
−0.092
0.120
−0.022
−0.043
b
3
The Astrophysical Journal, 730:107 (6pp), 2011 April 1
Halfen & Ziurys
Table 2
Spectroscopic Constants (in MHz) for NaCN (X̃1 A )
MW, MMW
MWa
57921.926(11)
8368.4941(12)
7271.8848(13)
0.0132949(29)
0.79862(29)
0.1969(37)
−0.0023429(24)
−0.00140603(62)
−3.23(19) × 10−8
−3.524(89) × 10−5
0.000168(45)
0.00045(40)
−4.78(51) × 10−8
−3.62(33) × 10−8
2.149(47) × 10−8
6.8(1.2) × 10−9
6.35(65) × 10−7
6.7(1.1) × 10−6
6.1(2.6) × 10−12
1.44(22) × 10−11
−2.56(26) × 10−12
−1.04(52) × 10−12
−2.18(15) × 10−8
0.151
57921.9378(50)
8368.4953(13)
7271.8852(13)
0.013336(48)
0.8002(10)
0.1965(51)
−0.0023491(10)
−0.0014090(55)
5.4(1.5) × 10−7
−3.5(3.6) × 10−6
0.000156(55)
0.00143(66)
Parameter
A
B
C
DJ
DJK
DK
d1
d2
HJ
HJK
HKJ
HK
h1
h2
h3
LJJK
LJK
LKKJ
l1
l2
l4
PJK
PJKK
rms
MWb
57921.951(12)
8368.4918(15)
7271.8816(14)
0.012909(65)
0.7917(14)
0.2262(56)
−0.0023496(28)
−0.0014050(10)
−2.56(10) × 10−5
0.000269(21)
4.0(2.1) × 10−8
Notes. Errors are 3σ in the last quoted digits.
a From He et al. (2008).
b From van Vaals et al. (1984); converted from the planar reduction.
components, reflected in the expression (B – C)J. For NaCN,
(B + C) = 15.6 GHz, while for the J = 19 ← 18 transition,
(B – C)J = 20.8 GHz. This situation starts to occur at the J =
15 → 14 transition (see Table 2), as (B – C)J becomes greater
than (B + C), and continues at higher frequency.
The millimeter and previous microwave laboratory data for
NaCN were analyzed in a combined fit using a Watson S-reduced
effective Hamiltonian that included rotation and centrifugal
distortion:
Stick Spectrum of NaCN (X 1A')
J = 19
Ka
18
J = 18
Ka
Ka
Ka
Ka = 4
+
Ka = 3
Ka
J = 20
19
Ka
Ka
Ka
17
Ka
Ka
Ka
Ka
Ka
Ka
Ka
Ka
Ĥeff = Ĥrot + Ĥcd .
280
285
290
295
300
305
(1)
The lines were fitted with the nonlinear least-squares routine
SPFIT (Pickett 1991). The resulting spectroscopic parameters
are given in Table 2. Many higher-order centrifugal distortion
constants were needed to achieve an adequate fit, including the
fourth-order terms HJ , HJK , HKJ , HK , h1 , h2 , and h3 , the sixthorder constants LJJK , LJK , LKKJ , l1 , l2 , and l4 , as well as the
eighth-order parameters PJK and PJKK . The values of LJ , LK ,
and l3 could not be determined within the 3σ error limit and
were excluded from the analysis. The rms of the fit is 151 kHz.
The analyses of van Vaals et al. (1984) and He et al. (2008)
are also given in Table 2. The rotational and second-order
centrifugal distortion constants are similar between our fit and
the previous works, as expected, except here DJ and DJK are
better determined. Differences between the analyses arise in
the fourth-order centrifugal distortion parameters, HJK and HK .
These terms are significantly larger in our analysis than in that
of He et al. (2008). Furthermore, the higher-order constants
were found necessary in the combined fit, as mentioned. These
differences occur because of the inclusion of higher energy
transitions.
310
Frequency (GHz)
Figure 2. Stick spectrum of NaCN displayed over the frequency range of
280–310 GHz based on observed relative intensities. The J = 19 ← 18 transition
(solid black line) is present in this region for Ka = 0 up to Ka = 6. In addition,
there are multiple Ka components from the J = 18 ← 17 (Ka = 1–6: dashed
line) and J = 20 ← 19 (Ka = 0–2: dotted line) transitions interspersed among
the J = 19 ← 18 features. This complex pattern arises from the high asymmetry
of this molecule.
measured for the J = 19 ← 18 transition (solid black lines)
is presented. However, due to the highly asymmetric nature
of this T-shaped molecule (κ = −0.957; Townes & Schawlow
1975), lines from both the J = 18 ← 17 (gray dashed lines)
and J = 20 ← 19 (gray dotted lines) transitions are interspersed
with the J = 19 ← 18 features. The overlap between transitions
occurs because the spacing between two rotational transitions
(B + C), i.e., 2Beff , is smaller than the overall splitting of the Ka
4
The Astrophysical Journal, 730:107 (6pp), 2011 April 1
Halfen & Ziurys
Table 3
Astronomical Observations of NaCN (X̃1 A )a
Source
IRC+10216
CRL 2688
J
Ka
Frequency Range (GHz)
Telescope
ηmb
θ b ( )
Ref.
3
5–9
8–11
9, 10
14–18
>18
9, 10
9–11, 15
0, 1
0
0–7
0–4
0–7
...
0, 2, 3
1, 2, 4–6
45.3–48.5
77.8–138.6
129.1–171.7
135.3–153.5
218.6–281.3
300–355
138.6–158.6
140.3–234.3
Nobeyama 45 m
NRAO 12 m
IRAM 30 m
ARO 12 m
ARO SMT
SMA
ARO 12 m
ARO 12 m, IRAM 30 m
0.71–0.79
0.56–0.65
0.55–0.65
0.75
0.74
...
0.73–0.78
0.50–0.78
35–42
45–81
15–19
41–46
27–35
...
40–45
11–45
Kawaguchi et al. 1995
Turner et al. 1994
Cernicharo et al. 2000
He et al. 2008
Tenenbaum et al. 2010
Patel et al. 2009
Highberger et al. 2001
Highberger et al. 2003
Note. a For J (Ka , Kc ) → J (Ka , Kc ), ΔKa = 0.
4. DISCUSSION
(Turner et al. 1994; Guélin et al. 1997; Highberger et al.
2003). Turner et al. (1994) observed flat-top profiles for this
molecule, using the former NRAO 12 m with a beam of
θ b 45 , indicating that they did not resolve its emission. They
assumed a source size in the range 12 –72 , allowing for an
extended source distribution. However, there is no evidence of
U-shaped profiles in the 2 mm survey of Cernicharo et al. (2000),
conducted with the IRAM 30 m with θ b = 15 –19 , nor in the
He et al. (2008) and Tenenbaum et al. (2010) data, measured
with the SMT (θ b ∼ 30 ). A U-shaped profile would indicate
optically thin, resolved shell emission. Moreover, a flat-topped
profile was observed for the JKa,Kc = 151,14 → 141,13 transition
of NaCN at 239.5 GHz measured at the 30 m, with θ b ∼ 10
(Agúndez et al. 2007). Finally, Plateau de Bure interferometer
maps suggest θ s ∼ 5 in IRC+10216 for NaCN (Guélin et al.
1997). Hence, it is most likely that the source size of NaCN in
IRC+10216 is less than 10 .
Assuming a source size of θ s ∼ 5 , the transitions of NaCN
measured by Cernicharo et al. (2000, Table 6), He et al. (2008,
Table 8), and Tenenbaum et al. (2010, Table 1) in IRC+10216
were analyzed using the rotational diagram method with the
following equation (Turner 1991):
The need for the higher-order centrifugal distortion parameters to model NaCN indicates that it is a relatively floppy
molecule, as originally suggested by van Vaals et al. (1984).
The inertial defect, Δ0 , certainly is evidence for the non-rigid
structure. This parameter can be calculated from the moments
of inertia Ia , Ib , and Ic for NaCN and is found to be Δ0 =
0.382 amu Å2 . This value is positive, but relatively large for
a planar molecule. For example, the inertial defect of HNO is
Δ0 = 0.078 amu Å2 (Sastry et al. 1984). For a planar, closedshell molecule, the inertial defect has contributions from both
harmonic and Coriolis terms of vibration–rotation interactions
(Watson 1993). The Coriolis interaction is usually negligible
for small molecules and can be neglected. The harmonic term
can be estimated from the rotational and centrifugal distortion
constants from the following equation (Watson 1993):
1
1
1
1
harm
Δ0 ≈ 3K
,
(2)
+
+
−
ωA ωB ωAB
ωC
where K = 505379.07 amu Å2 MHz. The ωi values are related
to the centrifugal distortion constants DJ , DJK , DK , d1 , and d2
(see Gordy & Cook 1984). For example,
16A3e
ωA = −
.
(3)
4 (−DJ − DJ K − DK )
log
3kW
Eu log e
Ntot
−
,
= log
ζrot
k Trot
8π 3 νμ20 S
(4)
where ν is the frequency of the transition, μ0 is the permanent
dipole moment (μa = 8.85 D; He et al. 2008), S is the line
strength, Eu is the energy of the upper level, W is the integrated
line intensity, Trot is the rotational temperature, and ζ rot is
the partition function. This formula assumes that the lines are
optically thin. The integrated line intensities were taken from
Cernicharo et al. (2000, Table 6), He et al. (2008, Table 8),
and Tenenbaum et al. (2010, Table 1). The Tenenbaum et al.
(2010) data were corrected by the main beam efficiency, given in
Table 3, and all of the data were adjusted for the source size. The
partition function was calculated using SPCAT (Pickett 1991)
from the rotational and centrifugal distortion constants. The
rotational diagram derived for NaCN is given in Figure 3. From
the diagram, the total column density of NaCN was determined
to be Ntot = 7.1 ± 1.6 × 1013 cm−2 in IRC+10216 with a
rotational temperature of Trot = 41 ± 2 K. If the source size
is varied from 3 and 10 , the column densities fall in the
range 0.21–1.9 × 1014 cm−2 , roughly a factor of three different
from the 5 value, with rotational temperatures of 40–41 K. A
corresponding H2 column density for a 5 source was directly
calculated from the mass loss rate, 3 ×10−5 M yr−1 , assuming
an expansion velocity of Vexp = 14.5 km s−1 (e.g., Agúndez &
Cernicharo 2006; Men’shchikov et al. 2002), and a distance for
From these expressions and the constants in Table 3, the inertial
defect was calculated to be Δ0 ∼ 0.331 amu Å2 , in relatively
good agreement with the value determined from the moments
of inertia. It is assumed in this calculation that the equilibrium
rotational constants are approximately equal to the experimental
ones, i.e., Ae = A0 . Therefore, the spectroscopic constants are
internally consistent.
NaCN has been observed in circumstellar gas over a wide
frequency range, as shown in Table 3. For example, the J = 3
→ 2 transition near 45 GHz has been detected in IRC+10216
using the Nobeyama 45 m (Kawaguchi et al. 1995), and several
lines have been observed in this source at 0.8 mm by Patel et al.
(2009) with the Submillimeter Array (SMA). Numerous sodium
cyanide lines have also been identified in recent spectra surveys
of IRC+10216 at 2 and 1.2 mm by Cernicharo et al. (2000),
He et al. (2008), and Tenenbaum et al. (2010), using the IRAM
30 m, the ARO 12 m and the ARO Submillimeter Telescope
(SMT). Given the new laboratory measurements and the broader
range of observed astronomical lines, a better estimate of the
abundance of NaCN is now possible.
There has been some discussion in the literature about the
physical extent of NaCN in the circumstellar shell of IRC+10216
5
The Astrophysical Journal, 730:107 (6pp), 2011 April 1
Halfen & Ziurys
rapidly deteriorates. This result is consistent with the floppy
structure of the molecule. Additional laboratory measurements
are needed above 600 GHz for this molecule if secure line
identifications are to be made at these higher frequencies.
NaCN: Rotational Diagram in IRC+10216
11
This research is supported by NSF grant AST 09-06534.
logg (3kW/8
3
S 2)
Trot = 41 ± 2 K
Ntot = 7.4 ± 1.6 x 1013 cm-2
REFERENCES
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9
0
50
100
150
200
Figure 3. Rotational temperature diagram of NaCN toward IRC+10216,
constructed using the observed transitions of He et al. (2008), Tenenbaum et al.
(2010), and Cernicharo et al. (2000). The data exhibit some scatter about the
fitted line, which gives Trot ∼ 41 K and Ntot ∼ 7 × 1013 cm−2 .
IRC+10216 of 150 pc, resulting in a fractional abundance of
NaCN of f = 10−8 , relative to H2 .
In comparison, Turner et al. (1984) found an abundance of
f = 6 × 10−9 for this molecule, assuming a 72 source, while
Highberger et al. (2003) calculated f = 2.3 × 10−8 for a 5
distribution. The abundance determined here is probably the best
estimate thus far for this species in IRC+10216. With f ∼ 10−8 ,
NaCN is the most abundant metal-containing cyanide species
observed in this source. MgNC is only slightly less abundant
at f = 9 × 10−9 (Highberger et al. 2003), while MgCN, AlNC,
and KCN are at least an order of magnitude less prevalent with
f = 7 × 10−10 , f = 3 × 10−10 , and f = 6 × 10−10 , respectively
(Ziurys et al. 1995, 2002; Pulliam et al. 2010).
With this new set of spectroscopic parameters, the rest
frequencies for NaCN can be predicted at frequencies above
530 GHz. Up to 600 GHz, the estimated uncertainties for the
low Ka components (Ka = 0–4) are less than 1 MHz, based on
the constants and propagating their 3σ errors from Table 3.
Above 600 GHz, the accuracy of the frequency predictions
6