Since H2S was detected in Comets Austin (1989cl) and Levy (1990c) in the microwave range, there has been increasing interest in searching for SH, which is the prime dissociative product of H2S. We present g-factors for the A-X (0-0) band of SH as a function of heliocentric velocity at r = 1.0 AU. We derive an upper limit production rate, Q(SH)/Q(H2O) less than 0.017, for Comet Brorsen-Metcalf (1989o) and calculate a dissociative lifetime of 105 sec at a heliocentric distance, r = 1.0 AU, and at a heliocentric velocity, v(r) = -28.5 km/sec

AHearn, Michael F.

Kim, Sang J.

English

NASA Technical Reports Server

ICARUS 97,, 303-306 (1992)
NOTE
g-Factors of the 8H (0-0) Band and SH Upper Limit
P/Brorsen-Metcalf (19890)
SANG J. KIM AND MtCHAEL F. A'HEARN
A._'tronomy Department, University qf Ma_3'hmd. College Park, Mao'land 20742
Received October 8, 1991; revised March 20, 1992
in Comet
Since H2S was detected in Comets Austin (1989cl) and Levy
(1990c) in the microwave range, there has been increasing interest
in searching for SH, which is the prime dissociative product of
H2S. We present g-factors for the A-X (0-0) band of SH as a
function of heliocentric velocity at r = 1.0 AU. We derive an
upper limit production rate, Q(SH)/Q(H20 ) < 0.017, for Comet
Brorsen-Metcalf (19890) and calculate a dissociative lifetime of
105 sec at a heliocentric distance, r = 1.0 AU, and at a heliocentric
velocity, v(r) = - 28.5 km sec- 1.... ,1992 Academic P..... Inc.
been thought to predissociate significantly. They found that the predis-
sociative and radiative lifetimes are 3 and 820 nsec, respectively. Sene-
kowitsch et al. (19851 subsequently revised the radiative lifetime to be
704 nsec. Since most of the radicals predissociate subsequent to their
first excitation to the A state, fluorescent equilibrium will not be estab-
lished and the emission spectrum will be controlled by the Swings effect
operating on a ground-slate population. The general formula for the
g-factor Is II for a transition undergoing predissociation can be ex-
pressed by
gp , = y_,, _ .%..Bt.,:;p;.:_ . ill
/,-
Introduction. Colom et al. (1990) recently reported the first detection
of H._S in the millimeter-wavelength range of Comet Austin (1989cl).
Subsequently Crovisier et al. (1991} presented production rates of H,S
for Comets Austin and Levy ( 1990c1 derived from their microwave data.
Marconi eta/. (1990) first identified H3S" in a mass spectrum of Comet
Halley obtained with the heavy ion analyzer (PICCA) on board the
Giotto spacecraft and attributed its existence to protonation of H_,S. It
is, therefore, of interest to search for SH, which is the prime dissociative
product of H_S. Krishna Swamy and Wallis (1986) and Wallis and
Krishna Swamy ( 19871 tentatively identified the B-X bands of SH in the
1670-1920 A range in the IUE spectra of faint comets and of Comet
Halley, respectively. The suspected features in those spectra are, how-
ever, hampered by the typical IUE noise (e.g., Kim and A'Hearn 1991).
The recent availability of good, high-resolution, groundbased spectra
covering the spectral range including the SH A-X transitions (()'Dell et
a/. 1990) provides additional stimulus for estimating the expected
strength of the emission by SH.
g-factors tt['the SH A-X (0-0) hand. The individual lines of the SH
A-X (0-0) band have been observed in absorption, and their line posi-
tions were presented by Ramsay (1952). We used his line positions
in our g-factor calculations because the line posilions are sufficiently
accurate for calculation of the Swings effect, and they are the best
available in the literature.
The A-X system is the same type of electronic transition as is the OH
A-X system. For the HOnI-London (H-L) factors of this band, we
adopted an updated list of the H-L factors for the 2E" -'I1 system of
the OH A-X band presented in Appendix B of Schleicher and A'Hearn
(1982).
Friedl et al. (1983) found experimentally that predissociation of SH
occurs throughout the rotational levels of the (I-0 band of the A-X
system, although previously only the v' -> 1 levels of the A state had
where the summation is restricted by the selection rule for the rotational
transitions, x0;, is the fractional population of the j"' rotational level in
the ground state, Yi_" is the branching ratio for radiative decay from the
j' rotational level of the excited state to the f' rotational level of the
ground state. B_.:i is the Einstein B coefficient, and pi_:i, is the solar
radiation density. There is major uncertainly as to what should be used
for the populations of the ground-state rotational levels, .%,,. The follow-
ing is a discussion of the possible population of the ground state and
corresponding temperalure of SH.
Hawkins and Houston (1980) conducted laboratory experiments on
the photodissociation of H.,S and measured the rotational temperatures
of SH. They found that the SH radicals are formed a little warmer
(about 40 K greater) than their parents when their parents are at room
temperature. Hawkins and Houston (1982) performed the same experi-
ment for HzS at 3 K and found that the rotational temperature of the
nascent SH is about 150 K. This indicates that if the parents are very
cold, the nascent SH becomes much warmer (150 K) than the parents.
From the results of Hawkins and Houston. the rotational temperature
of the nascent SH seems to be greater than 150 K regardless of the H_,S
temperature.
Crovisier et al. {1991) measured a rotational temperature of 40 K for
H_S in Comet Austin at about I AU heliocentric distance. Although the
rotational temperature was not measured, we expect a low rotational
temperature for this molecule in Comet B-M because rotationally ex-
cited H.,S relaxes rapidly (D. Bockelee-Morvan, private communication,
1991). From these arguments, we can say that the temperature of the
nascent SH is greater than 150 K and is likely to be less than 400 K
because of the probably low excitation temperature of H,S.
In order to estimate the changes in the rotational populations of SH
expected after formation but prior to fluorescence, we roughly calculated
rotational transition probabilities of SH as follows. The OH and SH
303
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304 KIM AND A'HEARN
ground slates have the same transition types, and therefore the only
major differences are the frequency and dipole moment. The radiative
transition probability is proportional to the square of the dipole moment
and the cube of the frequency. The dipole moments of SH and OH are
0.7580 and 1.6676 D, respectively, and the rotational B constants are
9.46 and 18.5 cm i, respectively. Burdyuzha and Varshalovich (1973)
presented Einstein A coefficients for the hyperfine transitions of OH.
We scale down these values using the ratios of the dipole moments and
the frequencies of SH and OH. The resultant radiative lifetimes for the
lowest lines in the R branch are about 200 sec, which are greater than
the SH lifetime of- 100 sec as discussed in the next section. The radiative
lifetime decreases as rotational quantum number J increases, and it
approaches I sec at around J = 25. The radiative lifetimes for lines in
other satellite branches are much greater than the SH lifetime. We
conclude that the lower rotational levels of the SH radicals do not
undergo significant rotational deexcitation (or cooling) before they are
destroyed by photodissociation.
Since the SH is formed where densities in the coma are moderately
high, collisions can also affect the distribution of populations. The recent
mode[ of Crifo (1991) predicts kinetic temperatures near 200 K at a
distance of 4000 km from the nucleus, the mean distance at which H,S
photodissociates to produce the SH. Thus collisions, which would tend
to produce rotational distributions in equilibrium with the kinetic temper-
ature, will tend to produce a rotational excitation characterized by a
temperature near 200 K. We therefore will assume that the rotational
distribution in the ground state can be characterized by temperatures
between 150 and 400 K. This range leads to about a 15% variation in the
g-factor for the entire 0-0 band and about a 50% variation for the R I +
RQ21 branch lines clustered near 3238 A. These variations tire still smaller
than the variation caused by the Swings effect. The variation for individ-
ual lines within the band, however, is greater than that caused by the
Swings effect.
The other parameters needed to solve Eq. (I) are much better deter-
mined. The branching ratio, "YiT", can be expressed in terms of the Ein-
stein A coefficients for the downward transitions coupled with the disso-
ciative lifetime of the upper state as follows:
Ai?,,
Ys'/.... tilt d) + A;;, + Ajj,,+I + AiT I"
Here Ajf, is the Einstein A coefficient and "rd is the dissociative lifetime
of the v' = 0 state in the A state. The equation is written for a Q-branch
line, and the subscripts in the denominator differ for P and R branches.
In all cases, the branching ratio can be approximated as A/;.rj because
1/r a dominates the term in the denominator.
Bi._i, is the Einstein coefficient for radiative absorption in a given
transition and can be expressed in terms of At0-0), the Einstein coeffi-
cient for spontaneous emission in the entire band, as follows:
A[0-0) H-L
Bi"J = 87rh_o__li(2j'" + I)'
where h is Planck's constant, _o0_0 is the frequency of the band bead in
units of cm i, and H-L is the H6nI-London factor for the transition
taken, as noted above, from Schleicfier and A'Hearn II982).
The radiation density at each transition, pj..7., is taken directly from
A'Hearn et al. (1983) with allowance for the Swings effect.
Using the above equations, g-factors for Comet B-M (19890) have
been calculated for a heliocentric distance, r = 1.0 AU, and for a
heliocentric velocity, v(r) = -28.5 km sec _. A model spectrum made
from these g-factors with a I-A spectral resolution is presented in Fig.
I. The R I + RQ21 branch occurs at 3238 ._l, consisting of about 15
individual lines. In Fig. 2 we present g-factors for this branch as a
function of heliocentric velocity at r = 1 AU. The g-factor for this
branch is 6.2 × 10 -6 sec -I for v(r) = 0 km sec -_ and 7.8 × 10 _ sec -1
for v(r) = - 28.5 km sec- L The g-factor of the entire 0-0 band ranges
from2.5 × 10-5to4.1 × 10 Ssec _fortheheliocentricvelocitybetween
- 80 and 80 km sec- _ at a constant temperature of 200 K. The total g-
factor also varies between 3.4 x 10 5 and 4.4 × 10 -5 sec-1 for the
temperature range of 50-400 K at a heliocentric velocity of 0.0 km sec i.
Our values are significantly lower than the value (2.32 × 10 _ sec i)
derived by Krishna Swamy and Wallis (1988), who apparently did not
consider predissociation in the A-X band.
Krishna Swamy and Wallis (1986) and Wallis and Krishna Swamy
(1987) tentatively identified the B-X band of SH in the 1670-1920 ,_
range in the IUE spectra of certain comets. Krishna Swamy and Wallis
11988) derived the g-factors of the B-X bands to be less than 5 × 10 -s
sec -I, which is so low that the presence of the band in the noisy IUE
spectra is doubtful. They also did not consider possible predissociation
in the B-X band. According to the absorption spectrum of the B-X band
presented in Fig. 1 of Morrow (1966), the absorption linewidths (_0.8
cm t) are wider than the uncertainty (_+0. I cm-t) in the line positions.
This suggests that predissociation occurs through these lines, and the
predissociation will lower the derived g-factors even more, rendering
the tentative detection even more doubtful.
Upper limits _4f SH in Comet PIBrorsen-Metealf and li['etimes of
SH. In order to calculate the upper limits of SH in comets, the lifetimes
of H2S and SH are required. Crovisier et al. (1991) estimated an H2S
lifetime of 4000 sec at 1 AU using an absorption spectrum of Lee et al.
(1987).
The dissociation rate of SH through the 0-0 transitions can be easily
derived from Eq. (1) and is given by
D,(0-0) = _ xo;,,B;;o;,,;.
f,,
(4)
Here we have used the lifetimes given previously to assume that the
branching ratio for dissociation is nearly unity. The total dissociation
rate through the 0-0, 1-0, and 2-0 bands is the sum of De(0-0), D_ (1-0),
121 andD,.(2-O).l),tO-O)allAUis8.20× 10 3sec Iforv(r) = -28.5km
sec -I and 5.78 × 10 _ sec -I for vIr) = 0 km sec-L According to
Franck-Condon (F-C) factor calculations by Nicholls et al. (1960),
which, although old, is the only available source, the F-C factors of the
0-0, 1-0, and 2-0 transitions are 0.74, 0.20, and 0.04, respectively.The
0-0, 1-0, and 2-0 bands occur at approximately 3250, 3070, and 2923
,_, where the solar radiation densities are about 1.2 × 10- 2o 6.0 × 10 -21,
and 5.2 × 10 -21 erg cm -3 Hz -t, respectively. Considering the F-C
factors and the radiation densities, we obtain a total dissociation rate of
9.50 × 10 3 sec-i at I AU for v(r) = -28.5 km sec -1. The SH lifetime
is, therefore, about 105 sec at 1 AU for v(r) = -28.5 km sec -z.
O'Dell et al. ( 1991 ) presented a spectrum of Comet P/Brorsen-Metcalf
covering the 3000-3600 _, range with 1-_, spectral resolution. From Fig.
4 of O'Dell et al., we obtain an upper limit flux of 5 × 10 17 erg cm -2
(3) sec i pixel i for the 3238-,_t band of SH. Since this flux is an average
over the entrance slit, 1.28 by 139 arcsec (I.28 arcsec per pixel), the
total flux, F, within the slit is 5.4 × 10 _5 erg cm -2 sec -t. At the time
of the observations, the average heliocentric distance was 1.0 AU, the
average geocentric distance was 0.645 AU, and the average heliocentric
velocity was -28.5 km sec-L Using the formula
47r dl2F
N(SH per slit) < -- (5)
ghv
we obtain N (SH per slit) < 1.3 x 10:9 for the slit area of 600 × 32,600
km. Here, _ is the geocentric distance, g is the g-factor, and v is the
NOTE 305
FIG.1.
r= IAU.
m
_6
8
E-7
6
E--7
4
E-7
2
E-7
i i I _ I
3200 3220 3240 3260 3280 3300 3320
Wovelength (A)
A model spectrum of the 0-0 band of the A-X system with a 1-,_ slitwidth for a heliocentric velocity, t,(r) = - 28.5 km sec i, at
frequency. Using the H,S lifetime of 4000 sec and the SH lifetime of 105
sec, and a Haser model {Haser 1957) with u I km sec _ for SH and
H,S, we obtain a production rate of SH, Q [SH), which is less than
6.7 × l0 -'7 sec i. Using the OH (0-0) observations of Comet B-M by
O'Dell eta/., we determined Q (H20) to be about 4.0 × 10 > sec i using
a Haser model with u - I km sec i. We derive that Q (SH)/Q (H_,O) is
about <1).017.
Crovisier et al. 11991) reported a production rate of HeS, Q(HeS)/
Q{H2OI = 2 x l0 _, for both Comets Austin and Levy{1990c) using
their microwave observations. Our upper limit for Comet B-M is thus
consistent with the results of Crovisier et al. for Comets Austin and
Levy. Detection of SH, which should require an order of magnitude
12
E 5
1
E-5
%-
8
\ E 6
6
E-6
- v T
4
_L_m _ . i i ___
E 6100 50 0 50 1 O0
He'docentric Velocity (kin/see)
FIG. 2. g-Factors as a function of heliocentric velocity at r = I AU
for the R I + '_Q,.I branch which produces the sharp feature at 3238 a,
and which consists of about 15 individual lines.
greater sensitivity, would be valuable in testing the models used to
interpret the observations of H:S.
ACKNOWLEDGMENTS
We thank J. Crovisier for giving us encouragement to publish this
paper. We also thank W. D. Cochran for his discussions on the signal-
to-noise ratios of the Comet B-M data. We are grateful to D. Bockelee-
Morvan for her detailed and critical comments on this paper as a referee.
This work was supported by NASA Grant NAGW-902.
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g-Factors of the SH (0-0) Band and SH Upper Limit in Comet P/Brorsen-Metcalf (1980o)

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