PASJ: Publ. Astron. Soc. Japan 52, 925-930 (2000)
Moderate Dispersion Spectra of NH 2 in Comet Hale—Bopp:
Analysis of Population Distribution
in X 2 B X (0,0,0) State of NH 2
Hideyo KAWAKITA
Gunma Astronomical Observatory, 6860-86 Nakayama, Takayama, Agatsuma, Gunma 377-0702
E-mail (UK): [email protected]
Kazuya AYANI and Tetsuya KAWABATA
Bisei Astronomical Observatory, 1723-70 Ohkura, Bisei, Oda, Okayama 714-1411
(Received 2000 January 31; accepted 2000 May 24)
Abstract
We carried out moderate-dispersion spectroscopic observations of comet Hale-Bopp (C/199501) on
1997 February 25, in order to study the fine structure of two NH 2 emission bands, A(0,9,0)-X(0,0,0) and
A(0,8,0)-X(0,0,0), which was resolved in our spectra. We compared the observed fine structure with that
of the modeled spectra, which were computed based on the transition probabilities of NH2 between the
A(0,i?2,0) and X(0,0,0) states determined by ourselves. Prom a comparison between the observation and
the calculations we concluded that the population distribution of the NH2 in the X(0,0,0) ground state can
be approximated by the Boltzmann distribution at a temperature of 60 K.
Key words: comets: general — comets: individual (C/199501: Hale-Bopp) — molecular processes
1.
Introduction
The emission bands of NH2 are generally seen in the
optical spectra of cometary comae from 4000 A to 9000 A.
These emission bands are assigned to the transition between the upper state, A(0,v 2 ,0), and the ground state,
X(0,0,0), of NH 2 (Dressier, Ramsay 1959). In these transitions the even-v2 levels are connected only with evenKa" rotational levels in the ground state, while the oddv2 levels are connected only with odd-Ka" levels. Therefore, the total population in the ground state can not
be derived by measuring only the even-i?2 band (Arpigny
1995).
The chemical abundance in the coma among NH3, N2,
and CO is important for studying the formation region of
the comet in protoplanetary nebula. The production rate
of NH3 was directly measured from the radio observations
only for the two bright comets, namely comet C/1996B2
(Hyakutake) and comet C/199501 (Hale-Bopp). For
other comets that were not so bright, the production
rate of NH3 was usually estimated from the production
rate of NH2, which is a photo-dissociation product of
NH3. Usually, the production rate of NH2 was estimated
from the A(0,8,0) or A(0,10,0) band, because these bands
were relatively free from other strong molecular or atomic
emissions. Because these two bands have even-t^ values, the population of the even-Ka" rotational levels in
the ground state was derived from these bands. Based
on the assumption that the populations of the groundstate levels follow a unique thermal distribution, the total
abundance of NH2 should be two-times larger than that
derived from an even-Ka" only (Arpigny 1995). This assumption is usually used in studies of the NH2 production
rate (Cochran et al. 1992; Fink, Hicks 1996; Hicks, Fink
1997; Fink et al. 1999).
The fine structure of the A(0,8,0) band was analyzed
for comet Halley by Combi and McCrosky (1991). They
reported that the population in the ground state could
be approximated to obey a Boltzmann distribution at a
rotational temperature of about 60 K for comet Halley.
However, there are no reports on an analysis of the oddv2 band. A comparison between the odd-v 2 band and the
even-t^ band is important for the present NH2 study.
The objective of this study is as follows:
1. To obtain both the spectra of the even-t^ and odd-v 2
bands of NH2 in comet Hale-Bopp during the same
night.
2. To clarify whether the populations of the levels related to even-Ka" and odd-Ka" can be expressed by
a single Boltzmann distribution or not.
If we can say "yes" for this question, we can determine
the production rate of NH2 from an even-v2 band [e.g.,
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
H. Kawakita, K. Ayani, and T. Kawabata
926
Table 1. Observational log.
Date (UT)
1997
1997
1997
1997
1997
1997
February
February
February
February
February
February
Exposure
time
25.82
25.84
25.86
25.87
25.88
25.89
600
600
600
300
600
300
s
s
s
s
s
s
Object
HR 7504
HR 7504
Hale-Bopp
HR 7596
Hale-Bopp
HR 7596
Remarks
for
for
for
for
for
for
NH 2
NH 2
NH 2
NH 2
NH 2
NH 2
(0,9,0)
(0,8,0)
(0,8,0)
(0,8,0)
(0,9,0)
(0,9,0)
A(0,8,0)] only according to Arpigny (1995).
2.
Observation
Moderate dispersion spectra of NH2 in comet HaleBopp were obtained on 1997 February 25.8 (UT) using
the long-slit spectrograph mounted on the lm telescope
at Bisei Astronomical Observatory. The resolving power
of the spectrograph (R) is ~ 10000 . The direction of the
slit was fixed along the south-to-north direction, and the
slit was put on the optical center of comet Hale-Bopp.
Two spectra were taken during the same night. One is
the NH2 A(0,8,0) band and [O i] emissions; The other is
for the sodium D-doublet with the NH 2 A(0,9,0) band.
The background sky spectra, the solar analogue star
(HR 7504), and the spectrophotometric standard star
(HR 7596) were also observed. The observational log is
shown in table 1. Data reduction was performed by using
the astronomical data reduction software package IRAF,
version 2.11 (NOAO). We subtracted the bias frame from
all images, and then divided them by the flat-field image. After the 1-dimensional spectra were extracted from
the object frames (the spectrum was summed along the
slit length of 3.'9), the sky spectra were subtracted from
them. The wavelength calibration was performed by
comparing the observed spectra with the spectrum of a
Fe-Ne lamp. The sensitivity calibration of the observed
spectra was performed by comparing them with the spectrum of the spectral/photometric standard star. Then,
the properly scaled solar spectrum was subtracted from
the wavelength- and flux-calibrated spectrum of comet
Hale-Bopp to obtain only NH2 emissions.
Figures 1 and 2 show the NH 2 A(0,9,0) and A(0,8,0)
band spectra, respectively. In figure 2 the forbidden lines
of the cometary oxygen atoms are also shown at 6300 A
and 6364 A. The line identification was based on the report by Brown et al. (1996) and our model calculations
given in section 5. We can find the wavelength window
where there are no significant emission lines in these spectra. We consider the variation within the region as resultant noise. Thus, the estimated 3a errors are 0.12 and
[Vol. 52,
0.06 for figures 1 and 2, respectively. This noise component may be due to the photometric error of the used
spectra, which stems from the photon statistics and from
the calibration process.
Here, we must consider contamination by the C 2 Swan
band emission. The C 2 (Av = - 2 ) Swan band is present
in the wavelength region shown in figure 1. These lines
can not be resolved in our spectrum. The C 2 (Av = — 2)
Swan band emission lines were resolved in the highdispersion (R ~ 42000) spectrum of comet Swift-Tuttle
reported by Brown et al. (1996). According to their spectrum, the Swan band emission lines were close together
and showed a nearly uniform distribution in the wavelength region between 5900 and 6100 A. The intensities
of the C 2 emission lines were of almost equal strength.
Furthermore, if we assume that the ratio of NH 2 to C 2 of
comet Hale-Bopp is equal to that of comet Swift-Tuttle,
the intensities of the C 2 (Av = - 2 ) Swan band emission
lines were smaller than 15% of 1(01)-2(11) line of the
NH 2 A(0,9,0) band. When we subtracted the continuum
component from the cometary spectrum in our calibration process, the unresolved C 2 emission flux could not
be distinguished from the reflected solar light. As a result, the C 2 emissions were subtracted as if being the
continuum component. Therefore, the subtraction of the
continuum component from the cometary spectrum using the solar spectrum was incomplete. The error caused
by this incompleteness is also included in the error estimation shown above.
3.
Transition Probabilities of N H 2 A - X System
The Einstein M " coefficient can be given as
64TT 4
121
1/42 1
3 ^ " "21IM2
(1)
where h denotes Planck's constant, c the speed of light,
1/21 the frequency of the emission between the transition
from the upper state "2" to the lower state " 1 " , and /JL2I
a matrix element of the transition moment. The /x2i
can be easily calculated for a diatomic or a linear polyatomic molecule, e.g., HCN, C 0 2 , CO, C 2 , CN (Rohlfs,
Wilson 1996). The NH 2 molecule is a bent, asymmetric
top molecule. Therefore, we calculated the matrix elements of the transition moment in the following manner.
The matrix element of the transition moment can be
expressed as the product between the vibronic ( "vibrational and electronic" ) part and the rotational part. The
vibronic part was taken from the table 7 in Jungen et
al. (1980). The rotational part was calculated using the
ASYROT program code (Birss, Ramsay 1984). The relative intensities of the rotational lines can be calculated
by the ASYROT program under the assumption that all
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
No. 5]
NH2 Spectra in Comet Hale-Bopp
927
1(01)-1(11)
2(02)-2(12)
.3(03) -3(13)
1(01)-2(11)
06
j
j
'
Relative Intensity
2(21)- 1(11)
0(00)- 1(10)
02
0
1
2(02) - 3(12)
I
2(20) - 2(12)
J v>I
J vWp\fJ VWVyv
lv\J\AfM
"
5970
.
5960
3000
6010
6020
Wavelength (Angstroms]
2(21)-2(11)
6040
J
6050
6300
6310
6320
6330
6340
Wavelength (Angstroms]
6350
6360
6370
Fig. 1. NH2 A(0,9,0) band spectrum in comet HaleBopp on 1997 February 25.8(UT) using the moderate dispersion (R ~ 10000) spectrograph mounted
on the l m telescope. The several NH2 lines belong
to the NH2 A(0,9,0) band. The relative intensity is
scaled such that the strongest line peak is unity, and
the 3cr error is about 0.12 on this scale.
Fig. 2. NH2 A(0,8,0) band spectrum in comet HaleBopp. The observational date and the instrument
are the same as in figure 1. Except for the forbidden
oxygen lines at 6300 A and 6364 A, most lines belong
to the NH2 A(0,8,0) band. The relative intensity is
scaled such that the strongest line peak is unity, and
the 3cr error is about 0.06 on this scale.
rotational lines belong to the same vibronic transition.
The relative intensity is calculated by
states in the same electronic state, or between the rotational states in the same vibronic state are given for the
NH2 molecule. We thus use the following assumptions as
a first step for simulating the NH2 spectra:
^ASYROT
= 0iexp(-£?i/A:r)|/i ro t|
(2)
where gi is a statistical weight, exp(—Ei/kT)
is a
1. The population of the rotational levels in the vibraBoltzmann factor, and firot is a rotational part of the mational ground state follows a Boltzmann distribution
trix element of the transition moment. We can determine
at a temperature of Trot •
/iTOt from /ASYROT calculated using the ASYROT pro2. The ground state is always the dominant populagram. We used the molecular constants of the upper election reservoir and the upper state population is contronic state, A(0,^2,0), and the ground state, X(0,0,0),
trolled by the ground-state population.
reported by Dressier and Ramsay (1959), Johns et al.
(1976), and Ross et al. (1988) for the ASYROT calculation. The correctness of the ASYROT calculation was Under these assumption, we used the single-fluorescence
checked in the case of H 2 0 + (Lew 1976) as well as that model (Kim et al. 1990) to calculate the emission spectra
of pure rotational transitions (Townes, Schawlow 1975). of NH2. In the single-fluorescence model, the population
Please note that the calculation by ASYROT does not of the upper state, x<i, is derived from
take into account the electron spin structure. Regarding
the line splitting caused by unpaired electron (5 = 1/2)
(3)
x2
E(A 2 i)
'
of NH 2 (the hyperfine splitting caused by the N nucleus
couldn't be resolved with our spectrograph), we calcu- where x\ denotes the population in the lower state, B12
lated the relative intensities between the spin doublet denotes the Einstein B coefficient from the lower-tolines by a conventional expression (Sears 1984).
'upper states, and p\2 denotes the solar radiation density. Here, we use the solar radiation density at 1.1 AU
from the Sun, because the heliocentric distance of comet
4.
Single-Fluorescence Model of N H 2
Hale-Bopp at the observation was 1.1 AU. The Swings
One may think that the fluorescence equilibrium model effect is considered in the calculation of P12. For the
(A'Hearn 1978) is useful to calculate the population dis- high-dispersion solar spectrum we referred to Kurucz et
tribution and the emission spectra of the NH2 molecule. al. (1984). The summations were performed for all of
The Einstein A and B coefficients are necessary to calcu- lower energy states. Thus, the intensity for the downlate the fluorescence equilibrium spectrum of NH2. Un- ward transition per molecule, 7, was calculated using
fortunately, the authors don't know of any literature
where the transition probabilities between the vibrational
I —
x2hv2iA2i.
(4)
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
[Vol. 52,
H. Kawakita, K. Ayani, and T. Kawabata
928
T ro ,=60K
0 8 [•
1
1
0.6 [•
0.4 I
02 [•
I
1I
1
L
JLAJJ
LAiLJ
6040
6050
LJULJ
5970
5980
5990
6000
6010
60K
Wavelength (Angstroms]
6040
T^-IOOK
6050
1
1
0.8
f
Relative in
!
06
|
1
02
5970
5980
5990
1
\
L_jy^J
J l AA Jill
3000
6010
eax
Wavelength (Angstroms]
6040
6050
Fig. 3.
NH2 A(0,9,0) band spectrum based on the
single-fluorescence model. The rotational temperature of the X(0,0,0) ground state is 40, 60, 80,
and 100 K for each figure (from top to bottom),
respectively. The relative intensity is scaled for the
strongest line peak being unity.
6310
6320
6330
6340
Wavelength (Angstroms]
6350
6360
6370
Fig. 4.
NH2 A(0,8,0) band spectrum based on the
single-fluorescence model. The rotational temperature of the X(0,0,0) ground state is 40, 60, 80,
and 100 K for each figure (from top to bottom),
respectively. The relative intensity is scaled for the
strongest line peak being unity. Note that forbidden
oxygen lines are not included in these model spectra.
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
NH2 Spectra in Comet Hale-Bopp
No. 5]
929
we need to compare the relative intensities between the
A(0,9,0) and A(0,8,0) bands. However, since the sky
condition was temporarily variable at the observation,
Calculated spectrum for T =60K
and the spectra of the A(0,8,0) and A(0,9,0) bands were
not taken simultaneously (one was taken slightly after
the other), it is difficult to derive the relative intensities
between the A(0,9,0) and A(0,8,0) bands. If we know
iilLdli
LIHUIL . I L
the cometary continuum emission between 5900 A and
6300 A , we can determine the relative intensity between
Observed spectra
the A(0,9,0) and A(0,8,0) spectra based on the intensity
of the cometary continuum emission in each observation.
The cometary continuum emission is the scattered sunUklLLLUlu
JWHW.
light by cometary dust particles. Furusho et al. (1999) re•TV I ' MPNJf
ported on the dust color map in the inner coma of comet
5800
5900
6000
6100
6200
6300
6400
Hale-Bopp on 1997 March 17. Furusho (1999) also reWavelength [Angstroms]
ported a mean color of 1.6%/1000 A in the inner coma.
Because the comet Hale-Bopp is extremely dust-rich [the
Fig. 5.
Calculated NH2 spectrum based on t h e
dust-to-gas ratio of comet Hale-Bopp is about 10 times
Boltzmaim distribution at a temperature of 60 K
(shown with a vertical offset of + 2 in a relative inlarger than that of comet Halley, as reported by Farnham
tensity) and t h e observed spectra. The calculated
et al. (1997) ], we assume that the flux of the C2 Swan
spectrum is scaled t o fit the emission-line intensity
band (Av — — 2), which was regarded as being equivalent
at 6334 A with t h e observed spectrum. The scale
to the continuum emission (as described in section 2), was
of the relative intensity of the observed spectra is
calibrated using the cometary continuous spectrum
negligible with respect to the flux of scattered sun-light
(see text).
by dust particles. We estimated the contamination by
the C2 Swan band (Av = —2) to be about 6% of the
dust continuum emission. Figure 5 shows the calibrated
spectra of A(0,9,0) and A(0,8,0). The modeled spectra
5.
M o d e l R e s u l t s a n d Discussion
at Trot = 60 K are also shown in this figure, which are in
Figure 3 shows the calculated spectra of the A(0,9,0) good agreement with the observations.
band of NH2 based on the single-fluorescence model. The
The ratio of the population between even- and oddlower ground-state population is assumed to follow the Ka" in the X(0,0,0) ground state is about 1.1 in this case.
Boltzmann distribution at T rot of 40, 60, 80 and 100 K. Thus, the even- and odd-Ka" rotational levels in the viFigure 4 shows the calculated spectra of the A(0,8,0) brational ground state are equally populated. Therefore,
band of NH 2 , assuming T rot of 40, 60, 80 and 100 K. Note the population determined from the even-i?2 band only
that the forbidden lines of the oxygen atom at 6300 A and should be multiplied by 2 to determine the total popu6364 A are not shown in figure 4.
lation in the X(0,0,0) ground state. This conclusion is
For the A(0,8,0) band, the result at Trot = 60 K is consistent with Arpigny (1995).
in good agreement with the observation. The observed
It is an important future work to include the transiA(0,9,0) band spectrum is also in good agreement with tions of the X(0,t?2,0)-X(0,0,0) system and the rotational
the model calculation. However, it is difficult to find an transitions in the X(0,0,0) vibrational ground state in the
optimum solution of TTOt by fitting the observation of the excitation model. Then, the synthesized spectra of NH2
NH2 A(0,9,0) band because the relative intensities of the could be compared with other spectra (the low- and highcalculated lines do not change much with respect to Trot dispersion spectra). For example, the flux ratio between
(see figures 3a-d). As a matter of fact the observation er- the even- and odd-f 2 NH 2 bands showed different values
ror is comparable to the difference between the calculated at 3 AU in Comet Hale-Bopp from the ratio that comets
spectra at Trot = 20 K and 100 K. In any case, since the usually show at about 1 AU (Rauer et al. 1997). The exrotational temperature of 60 K, which was derived from citation model of NH2 will be a powerful tool to research
an observation of A(0,8,0) band, is not inconsistent with the physics of the NH2 gas coma, not only near 1 AU,
the observed A(0,9,0) band spectrum, it may be a rea- but also further than 3 AU from the Sun.
sonable choice also for the T rot of the X(0,0,0) ground
state related to the A(0,9,0) band.
The authors would like to thank Dr. S. J. Kim for his
Then, the question is whether the Boltzmann distri- comments and suggestions concerning the single fluoresbution with a single rotational temperature of 60 K can cent model of NH2, and also thank Dr. S. Saito for fruitful
be applied to the entire population of the vibrational discussions on the calculation of the transition probabilground state or not. In order to answer this question, ities of NH2. We also thank an anonymous referee for
rot
1
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System
930
H. Kawakita, K. Ayani, and T. K a w a b a t a
comments t o improve this manuscript. T h e N S O / K i t t
Peak F T S d a t a used here were produced by N S F / N O A O .
References
A'Hearn M.F. 1978, ApJ 219, 768
Arpigny C. 1995, ASP Conf. Ser. 312, 205
Birss F.W., Ramsay D A . 1984, Comp. Phys. Comm. 38, 83
Brown M.E., Bouchez A.H., Spinrad H., Johns-Krull C M .
1996, AJ 112, 1197
Cochran A.L., Barker E.S., Ramseyer T.F., Storrs A.D. 1992,
Icarus 98, 151
Combi M.R., McCrosky R.E. 1991, Icarus 91, 270
Dressier K., Ramsay D A . 1959, Phil. Trans. Royal Soc. London A251, 553
Farnham T., Schleicher D., Lederer S. 1997, IAU Circ. 6589
Fink U., Hicks M.D. 1996, ApJ 459, 729
Fink U., Hicks M . P , Fevig R.A. 1999, Icarus 141, 331
Furusho R. 1999, PhD Thesis, Kobe University
Furusho R., Suzuki B., Yamamoto N., Kawakita H., Sasaki
T., Shimizu Y., Kurakami T. 1999, PASJ 51, 367
Hicks M.D., Fink U. 1997, Icarus 127, 307
Johns J.W.C., Ramsay D.A., Ross S.C. 1976, Can. J. Phys.
54, 1804
Jungen C.H., Hallin K.-E.J., Merer A.J. 1980, Mol. Phys. 40,
25
Kim S.J., A'Hearn M.F., Larson S.M. 1990, Icarus 87, 440
Kurucz R.L., Furenlid I., Brault J., Testerman L. 1984, National Solar Observatory Atlas, No. 1 (National Solar Observatory, Sunspot NM)
Lew H. 1976, Can. J. Phys. 54, 2028
Rauer H., Arpigny C , Boehnhardt H., Colas F., Crovisier J.,
Jorda L., Kiippers M., Manfroid J., Rembor K., Thomas
N. 1997, Science 275, 1909
Rohlfs K., Wilson T.L. 1996, Tools of Radio Astronomy, 2nd
ed (Springer-Verlag, Berlin, Heidelberg )
Ross S.C, Birss F.W., Vervloet M., Ramsay D.A. 1988, J.
Mol. Spectr. 129, 436
Sears T.J. 1984, Computer Phys. Rep. 2, 1
Townes C.H., Schawlow A.L. 1975, Microwave Spectroscopy
(Dover Pub. Inc., New York) appendix V
© Astronomical Society of Japan • Provided by the NASA Astrophysics Data System