Astron. Astrophys. 353, 1101-1114 (2000)

3. Molecular production rates and abundances

To first approximation, the molecular column density within the beam N is related to the line intensity integrated over velocity by:

where is the Einstein A-coefficient of the transition, is the rest frequency, and is the average fractional population of the upper level within the beam. Eq. (1) assumes that the emission is optically thin. Molecular production rates can be then derived from the inferred column densities, knowing the spatial distribution of the molecules in the coma. As discussed later in this section, we used the classical formulae of the Haser's model to describe local densities of parent and daughter species. Integration over the field of view is made assuming gaussian beams described by their FWHM at the observed frequencies (Sect. 2), and taking into account the geocentric distance of the comet.

For the newly detected species, except HC₃N, we use the local thermal equilibrium (LTE) approximation to compute the fractional population , and Eq. (1) to derive the column density. The rotational temperature is taken equal to the gas kinetic temperature derived from the relative intensities of methanol lines, which varied from 95 to 125 K in the February-April period (Paper I). Production rates of HCN, HNC, CO, CS, H₂CO, CH₃OH, CH₃CN, H₂S, HC₃N, and OCS are derived from a more complete modelling which includes radiative excitation of the vibrational bands by the Sun, excitation by collisions with neutrals and electrons, and radiative transfer (Paper I; Biver et al. 1999b; see also, e.g., Crovisier 1987and Bockelée-Morvan et al. 1994for details on the excitation of parent molecules in comets and its modelling). The inferred production rates do not differ much from those calculated under the LTE assumption because of the large size of the collisional region near perihelion. The rotational lines listed in Table 1 are optically thin. Therefore, for molecules for which detailed modelling is not yet completed, we expect this simplistic LTE approach to be a good approximation in most cases.

We tried to take advantage of the observations of some species (namely SO, SO₂, HC₃N and HNCO) through several transitions at about the same date to check this working hypothesis. We performed a rotational diagram analysis (Fig. 2), using the measured line intensities, to derive the rotational temperature. In this analysis, we corrected for the different fields of view from line to line, which results in different molecular column densities. In the case of SO, we have investigated two extreme photodissociation lifetimes published in the literature and assumed that it is produced by SO₂ (see below). To take into account the time variability of the comet, we used our measurements of the HCN production rate (Table 1). In February 1997 at the CSO, observations of HCN were made within one hour before the observations of the HNCO, HC₃N and SO lines started. No corrections were made in the analysis of the PdB observations of March, as daily observations of HCN were not available to us. For this study, as well as for deriving molecular production rates, the spectroscopic parameters (energy levels, line frequencies and strengths) were taken from the JPL molecular data base (Pickett et al. 1998). The rotation diagram analysis includes a 10% uncertainty in the line intensity calibration.

Fig. 2. LTE rotation diagrams for SO (215.2, 251.8 and 261.8 GHz lines observed on Feb. 20-23), SO2 (221.96 and 236.2 GHz lines on March 18-22), HC3N (218.3, 254.7 and 263.8 lines on Feb. 19-21) and HNCO (241.8, 263.7 and 351.6 GHz lines on Feb. 17-18). and are the energy and the statistical weight of the upper level, respectively. The observed line area have been divided by Q(HCN) at the date of the observation and corrected from the different fields of view which result in different column densities N. The dashed lines show the best fits obtained for SO ( = 56 K), SO2 ( = 497 K), HC3N ( = 103 K) and HNCO ( = 162 K)

The rotational temperature derived from the three HC₃N lines observed on 19 to 21 February is 103 40 K, in agreement with the kinetic temperature of 95 K derived from the methanol lines at that time. In this calculation, we have multiplied the intensity of the line (February 19) given in Table 1 by a factor of 1.8: indeed, the intensity of the - E CH₃OH line at 266.838 GHz observed at the same time in the upper sideband of the receiver leads to a CH₃OH production rate 1.8 times lower than that inferred on February 18 from observations of the 241 GHz CH₃OH multiplet, which suggests that the observations made on February 19 with the 263/266 GHz setup were possibly affected by some instrumental problems. The rotational temperature derived from only the and lines is 70 23 K. As can be seen in Table 1, the three different lines give HC₃N production rates in relatively good agreement.

The relative intensities of the three HNCO lines detected from February 17 to 19 poorly constrain the rotational temperature of HNCO to the range 104-362 K. As for HC₃N, the intensity of the 263.7 GHz line detected on February 19 has been multiplied by 1.8 in this rotation diagram analysis. The inferred rotational temperature is = 125 56 K, when not including the 263.7 GHz line. The three lines give consistent production rates (Table 1). The two HNCO lines observed on March 12 and 13 at 219.8 and 241.7 GHz provide also consistent production rates (Table 1).

To correct the intensities of the various SO lines for the different fields of view, we assumed that SO is produced from the dissociation of SO₂, using the photodissociation rate (SO₂) = 2.1 10^-4 s^-1 at 1 AU from the Sun of Kim & A'Hearn (1991) (Table 2). Indeed, radio interferometric observations show that SO does not have a parent density distribution and is produced by a short-lived species (Wink et al. 1999); see also Fig. 7 in Despois 1999).

Table 2. Photodissociation rates at 1 AU from the Sun

The line intensities of the three SO lines detected in February 20, 21, and 23 indicate a rotational temperature in the range 34-150 K, when the SO photodissociation rate at 1 AU (SO) is taken to 1.5 10^-4 s^-1 (Kim & A'Hearn 1991), and in the range 31-101 K when (SO) = 4.9 10^-4 s^-1 (Summers & Strobel 1996). The production rates inferred from these three lines are in good agreement (Table 1). The two SO₂ lines detected in March poorly constrain the rotational temperature, due to the low signal-to-noise ratio of the 236 GHz line. The inferred = is, however, higher than the rotational temperatures derived for the other species (Fig. 2). In contrast to most other species, SO₂ undergoes strong solar UV pumping of its electronic bands with an excitation rate of 10^-2 s^-1 at = 1 AU (Kim & A'Hearn 1991), so that this process overtakes collisional excitation at distances exceeding a few thousand kilometres from the nucleus, comparable to the field of view (10 000 to 20 000 km). Since the time scale for UV pumping and subsequent decay is shorter than the average rotational radiative lifetime, we expect the rotational population within the ground vibrational state to spread over many levels and the rotational temperature to be higher than the kinetic temperature. This is in agreement with our measurement. In addition, following fluorescence calculations made for SO (Kim & A'Hearn 1991), we can expect several vibrational states of the fundamental electronic state to be significantly populated, to the detriment of the ground vibrational state (under LTE at the low temperatures encountered in cometary atmospheres, this fractional population is very close to 1). In Tables 1, 3 and 4, we thus likely underestimate the SO₂ production rate and abundance by a factor whose evaluation requires a more detailed modelling. A rotational temperature of 300 K would lead to SO₂ production rates 2-3 times higher.

The excitation of SO has been investigated by Kim & A'Hearn (1991). However, the solar UV pumping rate, equal to 1.2 10^-2 s^-1, has been overestimated by 2 orders of magnitude, due to the use of an erroneous radiative lifetime for the band (Kim et al. 1999; S.J. Kim, personal communication ). Our inferred rotational temperature suggests that the SO molecules within the field of view are primarily collisionally excited, in agreement with expectations.

In summary, our observations do not provide strong constraints on the rotational temperature of the newly detected cometary species. As the molecules within the beam might deviate from LTE as a result of spontaneous decay (this was observed for methanol, paper I) and since there are, anyway, some uncertainties on the kinetic temperature of the coma (Paper I), we have investigated to which extent the inferred column densities (and thus the production rates) are sensitive to the assumed rotational temperature. The effect varies from line to line, but is relatively small: 15-20 % for most lines when varying the temperature by 20 K.

We used the Haser model (i.e., isotropic outflow at constant velocity) to describe the molecular densities and to infer molecular production rates. The gas expansion velocities determined by Biver et al. (Paper I) (1.1 to 1.2 km s^-1 for the range of heliocentric distances covered here) were used. There is observational evidence (including radio line asymmetries) that the outgassing of Hale-Bopp was anisotropic, but this has little influence on the derived production rates ( 15 % at most). In contrast, the production rates may be more sensitive to the adopted photodissociation rates which are not always precisely known (see Crovisier 1994and references therein). For example, published SO photodissociation rates range from 1.5 10^-4 (Kim & A'Hearn 1991; Kumar 1982) to 5 - 6.2 10^-4 s^-1 (Summers & Strobel 1996; Huebner et al. 1992). Table 2 gives the photorates used to compute the molecular production rates given in Table 1. For NH₂CHO, no reliable determination is available, due to the lack of laboratory data. A photodissociation rate in the range of 1 - 10 10^-5 s^-1 was postulated for this species. For the species considered here other than SO, SO₂, OCS and NH₂CHO, the photodissociation rates correspond to scalelengths larger than the field of view radii (10 000 to 20 000 km). The photodissociation rate is thus not a very critical parameter for the determination of their production rates.

The SO production rates are computed assuming that SO is produced by the photodissociation of SO₂. Other molecules listed in Table 1 are assumed to be released from the nucleus. For OCS there is evidence from infrared observations that a significant amount is produced by an extended source in the coma (Dello Russo et al. 1998). Distributed sources of CO and H₂CO are also found in comet Hale-Bopp (DiSanti et al. 1999; Weaver et al. 1999; Wink et al. 1999). Since the field of view of our observations is large, resulting production rates refer to the release of both nuclear and extended sources, if any. Because our models assume a nuclear source, they might underestimate the total production rate, if the extended source region is comparable to or larger than the field of view. The effect is small for OCS since the size of its extended source is less than 3500 km in radius (Dello Russo et al. 1998), smaller than the radius ( 14 000 km) of the radio field of view.

The resulting molecular production rates are given in Table 1. When approaching perihelion, comet Hale-Bopp displayed increasing activity. The production rates of the main species evolved as in the February-April period (Paper I). Although the water production rate was monitored with various techniques during that period, a better reference for more precise abundance determinations is the HCN production rate derived from our radio measurements at the same or close dates (Table 1). This eliminates several other sources of uncertainties in abundance determinations, such as those resulting from different fields of view and model parameters. Table 4 gives average molecular abundances with respect to HCN for the February-April period. They were calculated by computing the Q/Q(HCN) relative abundances for each date and line, and then calculating the average. Some species show abundances varying with time by as much as a factor of 2 (OCS, SO). A more detailed modeling is required to understand these variations. In Table 4, average abundances relative to water are based on an average [HCN]/[H₂O] abundance ratio of 2.5 10^-3. This average abundance ratio is derived from the HCN production rates measured at 2 AU by Biver et al. (Paper I; see also Table 1), and the water production rates determined by Colom et al. (1999) for the same range of from radio observations of the OH radical. As detailed by Combi et al. (1999), these water production rates are in good agreement with most other determinations such as those obtained from H₂O IR observations (Dello Russo et al. 1998a) and hydrogen Lyman- observations (Combi et al. 1999).

© European Southern Observatory (ESO) 2000

Online publication: January 18, 2000
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