A COUPLED CHEMISTRY-EMISSION MODEL FOR ATOMIC OXYGEN GREEN AND RED-DOUBLET EMISSIONS IN THE COMET C/1996 B2 HYAKUTAKE

3.1.1. H₂O and OH

The dissociation of H₂O molecule starts at wavelengths less than 2424 Å and the primary products are H and OH. But the pre-dissociation process mainly starts from 1860 Å (Watanabe & Zelikoff 1953). The threshold wavelength for the photoionization of H₂O is 984 Å. Hence, solar UV photons in the wavelength region 1860–984 Å can dissociate H₂O and produce different daughter products. The threshold wavelengths for the dissociation of H₂O resulting in the production of O(¹S) and O(¹D) are 1390 Å and 1770 Å, respectively. Till now, the photoyield value for the production of O(¹D) from H₂O has been measured in only two experiments. Slanger & Black (1982) measured the O(¹D) yield in the photodissociation of H₂O at 1216 Å, and found its value to be 10%. McNesby et al. (1962) reported a 25% yield for the production of O(¹D) or O(¹S) at 1236 Å from H₂O.

Huebner et al. (1992) calculated photoproduction rates for different excited species produced from H₂O using absorption and ionization cross sections compiled from different experimental measurements. In our model the cross sections for the production of O(¹D) in the photodissociation of H₂O are taken from Huebner et al. (1992), which were determined based on experiments of Slanger & Black (1982) and McNesby et al. (1962). Huebner et al. (1992) assumed that in the 1770–1300 Å wavelength region around 25% of H₂O molecules photodissociate into H₂ and O(¹D), while between 1300 and 984 Å about 10% of H₂O dissociation produces O(¹D) (cf. Figure 4). Below 984 Å, Huebner et al. (1992) assumed that 33% of the dissociation of H₂O leads to the formation of O(¹D). Festou (1981) discussed various dissociation channels for H₂O in the wavelength region less than 1860 Å. Solar photons in the wavelength region 1357–1860 Å dissociates around 72% of H₂O molecules into ground states of H and OH. But, according to Stief et al. (1975) approximately 1% of H₂O molecules are dissociated into H₂ and O(¹D) in this wavelength region. The calculated rates for the O(¹D) production from the photodissociative excitation of H₂O by Huebner et al. (1992) are 5.97 × 10⁻⁷ s⁻¹ and 1.48 × 10⁻⁶ s⁻¹ for solar quiet and active conditions, respectively. Using the S2K solar EUV–UV flux on 1996 March 30 and cross sections from Huebner et al. (1992; see Figure 4), our calculated value is 8 × 10⁻⁷ s⁻¹ (cf. Table 2), which is a factor of ∼1.5 higher than that of Huebner et al. (1992) for solar minimum condition at 1 AU. This difference in calculated values is mainly due to the higher (a factor of 1.24) value of solar flux at 1216 Å in the S2K model than that used by Huebner et al. (1992; cf. Figure 2).

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No experimentally determined cross sections for the production of O(¹S) in the photodissociation of H₂O are available. The solar flux at H Lyα (cf. Figure 2) is more than an order of magnitude larger than the flux at wavelengths below 1390 Å, which is the threshold for the O(¹S) production in the dissociation of H₂O. To account for the production of O(¹S) in the photodissociation of H₂O, we assumed a yield of 0.5% at solar H Lyα (1216 Å). However, to assess the impact of this assumption on the green and red line emissions we varied the yield between 0% and 1%. The calculated photorate for the production of O(¹S) from H₂O is 6.4 × 10⁻⁸ s⁻¹ at 1 AU assuming 1% yield at 1216 Å (cf. Table 1).

The primary dissociative product of H₂O is OH. The important destruction mechanisms of OH molecule are pre-dissociation through fluorescence process and direct photodissociation. The solar radiation shortward of 928 Å can ionize the OH molecule. The threshold wavelengths for the production of O(¹D) and O(¹S) in the photodissociation of OH are 1940 and 1477 Å, respectively. The dissociation channels of OH have been discussed by Budzien et al. (1994) and van Dishoeck & Dalgarno (1984). We have used the photorates given by Huebner et al. (1992) for the production of O(¹D) and O(¹S) from an OH molecule whose values are 6.4 × 10⁻⁷ and 6.7 × 10⁻⁸ s⁻¹, respectively. These rates are based on the dissociation cross sections of van Dishoeck & Dalgarno (1984), which are consistent with the red line observation made by the wide-field spectrometer (Morgenthaler et al. 2007).

3.1.2. CO₂

3.1.3. CO

In our literature survey we could not find any reported cross section for the production of O(¹D) due to the electron impact dissociation of H₂O. Jackman et al. (1977) have assembled the experimental and theoretical cross sections for electron impact on important atmospheric gases in a workable analytical form. The cross sections for electron impact on atomic oxygen given by Jackman et al. (1977) have been used to estimate emissions which leave the O atom in the metastable (¹D) state. The obtained ratios of 85% in the ground state and 15% in the metastable state are used for the atomic states of C and O produced in the electron impact dissociation of H₂O, CO₂, and CO. It may be noted that the ground state to metastable state production ratio of 89:11 is observed for atomic carbon and atomic oxygen produced from the photodissociation of CO (Singh et al. 1991). However, as shown later, the contributions of these electron impact processes to the total production of O(¹D) are very small (<5%).

Kedzierski et al. (1998) measured the cross section for the electron impact dissociative excitation of H₂O producing O(¹S), with an overall uncertainty of 30%. LeClair & McConkey (1994) measured cross section for the production of O(¹S) in the dissociation of CO₂ by electron impact; they claimed an uncertainty of 12% in their experimental cross section measurements. The cross section for fragmentation of CO into the metastable O(¹S) atom by electron impact is measured by LeClair et al. (1994). These electron impact cross sections are also recommended by McConkey et al. (2008), and are used in our model for calculating the production rate of O(¹S) from H₂O, CO₂, and CO.

Since the ¹D and ¹S are metastable states, the direct excitation of atomic oxygen by solar radiation is not an effective excitation mechanism. However the electron impact excitation of atomic oxygen can populate these excited metastable states, which is a major source of airglow emissions in the upper atmospheres of Venus, Earth, and Mars. We calculated the excitation rates for these processes using electron impact cross sections from Jackman et al. (1977). In calculating the photoelectron impact ionization rates of metastable oxygen states, we calculated the cross sections by changing the threshold energy parameter for ionization of neutral atomic oxygen in the analytical expression given by Jackman et al. (1977). The above-mentioned electron impact cross sections for the production of O(¹S) from H₂O, CO₂, CO, and O, used in the current model, are presented in Figure 5 along with the calculated photoelectron flux energy spectrum at a cometocentric distance of 1000 km.

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The total dissociative recombination rate for H₂O⁺ reported by Rosen et al. (2000) is 4.3 × 10⁻⁷ cm⁻³ s⁻¹ at 300 K. The channels of dissociative recombination have also been studied by this group. It was found that the dissociation process is dominated by three-body breakup (H + H + O) that occurs with a branching ratio of 0.71, while the fraction of two-body breakup (O + H₂) is 0.09, and the branching ratio for the formation of OH + H is 0.2. The maximum kinetic energy of the dissociative products forming atomic oxygen produced in ground state is 3.1 eV and 7.6 eV for the three- and two-body dissociation, respectively. Since the excitation energy required for the formation of metastable O(¹S) is 4.19 eV, the three-body dissociation cannot produce oxygen atoms in the ¹S state. However, the O(¹D) atom can be produced in both, the three-body and the two-body, breakup dissociation processes. To incorporate the contribution of H₂O⁺ dissociative recombination in the production of O(¹D) and O(¹S), we assumed that 50% of branching fraction of the total recombination in three-body and two-body breakups lead to the formation of O(¹D) and O(¹S) atoms, respectively. For dissociative recombination of CO⁺₂, CO⁺, and OH⁺ ions, we assumed that the recombination rates are the same for the production of both O(¹D) and O(¹S). We will show that these assumptions affect the calculated O(¹S) and O(¹D) densities only at larger (⩾10⁴ km) cometocentric distances, but not in the inner coma. Tables 1 and 2 list the rates, along with the source reference, for these recombination reactions.

The calculated O(¹S) production rate profiles for different processes in the comet C/1996 B2 Hyakutake are presented in Figure 6. These calculations are made under the assumption of 0.5% yield of O(¹S) from H₂O at 1216 Å solar H Lyα line and 1% CO₂ relative abundance. The major production source of O(¹S) is the photodissociative excitation of H₂O throughout the cometary coma. However, very close to the nucleus, the photodissociative excitation of CO₂ is also an equally important process for the O(¹S) production. Above 100 km, the photodissociative excitation of CO₂ and CO makes an equal contribution in the production of O(¹S). Since the cross section for the electron impact dissociative excitation of H₂O, CO₂, and CO is small (see Figure 5), the contributions from electron impact dissociation to O(¹S) production are smaller by an order of magnitude or more than that due to photodissociative excitation. At larger cometocentric distances (>2 × 10³ km), the dissociative recombination of H₂O⁺ ion is a significant production mechanism for O(¹S), whose contribution is higher than those from the photodissociative excitation of CO₂ and CO. The dissociative recombination of other ions do not make any significant contribution to the production of O(¹S).

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In the inner coma, the calculated production rates of O(¹S) via photodissociative excitation is CO₂ at various wavelengths are presented in Figure 7. The major production of O(¹S) occurs in the wavelength region 955–1165 Å where the average cross section is ∼2 × 10⁻¹⁷ cm⁻² (cf. Figure 4) and the average solar flux is ∼1 × 10⁹ photons cm⁻² s⁻¹ (cf. Figure 2). The calculated loss rate profiles of O(¹S) for major processes are presented in Figure 8. Close to the nucleus (<50 km), quenching by H₂O is the main loss mechanism for metastable O(¹S). Above 100 km, the radiative decay of O(¹S) becomes the dominant loss process. The contributions from other loss processes are orders of magnitude smaller and hence are not shown in Figure 8.

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The production rates as a function of cometocentric distance for various excitation mechanisms of the O(¹D) are shown in Figure 9. The major source of O(¹D) production in the inner coma is the photodissociation of H₂O. The wavelength-dependent production rates of O(¹D) from H₂O are presented in Figure 10. The O(¹D) production in the photodissociation of H₂O is governed by solar radiation at H Lyα (1216 Å) wavelength. However, very close to the nucleus, the production of O(¹D) is largely due to photons in the wavelength region 1165–1375 Å. Since the average absorption cross section of H₂O decreases in this wavelength region by an order of magnitude, the optical depth at wavelengths greater than 1165 Å is quite small (see Figure 3). Hence, these photons are able to travel deeper into the coma unattenuated, thereby reaching close to the nucleus where they dissociate H₂O producing O(¹D). Thus, at the surface of cometary nucleus the production of O(¹D) is controlled by the solar radiation in this wavelength band. In high production rate comets, the production of O(¹D) near nucleus would be governed by solar photons in this wavelength region. The production of O(¹D) from H₂O by solar photons from other wavelength regions is smaller by more than an order of magnitude.

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After the photodissociative excitation of H₂O, the next significant O(¹D) production process at radial distances below 50 km is the photodissociative excitation of CO₂. Above 50 km to about 1000 km, the radiative decay of O(¹S) and at radial distances above 1000 km the dissociative recombination of H₂O⁺ are the next potential sources of the O(¹D) (see Figure 9). The calculated wavelength-dependent production rates of O(¹D) for the photodissociation of CO₂ are shown in Figure 11. Solar radiation in the wavelength region 1165–955 Å dominates the O(¹D) production. Since the cross section for the production of O(¹D) due to the photodissociation of CO₂ is more than an order of magnitude higher in this wavelength region compared to the cross section at other wavelengths (see Figure 4), the solar radiation in this wavelength band mainly controls the formation of O(¹D) from CO₂. Other potential contributions are made by solar photons in the wavelength band 1585–1375 Å at distances <50 km, and 955–745 Å at radial distances >100 km. Since the CO₂ absorption cross section around 1216 Å is smaller by more than two orders of magnitude compared to its maximum value, the solar radiation at H Lyα is not an efficient source of O(¹D) atoms.

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Zipf (1969) measured the total rate coefficient for the quenching of O(¹S) by H₂O as 3 × 10⁻¹⁰ cm³ s⁻¹. The primary channel in quenching mechanism is the production of two OH atoms. The production of O(¹D) is also a possible channel whose rate coefficient is not reported in the literature. Hence, we assumed that 1% of the total rate coefficient can lead to the formation of O(¹D) in this quenching mechanism. However, this assumption has no implications on the O(¹D) production since the total contribution due to O(¹S) is about three orders of magnitude smaller than the major production process of O(¹D).

The calculated loss rate profiles of O(¹D) are presented in Figure 12. Below 1000 km, the O(¹D) can be quenched by various cometary species. The quenching by H₂O is the major loss mechanism for O(¹D) below 500 km. Above 2 × 10³ km radiative decay is the dominant loss process for O(¹D).

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Using the calculated production and loss rates due to various processes mentioned above, and assuming photochemical equilibrium, we computed the number density of O(¹S) and O(¹D) metastable atoms. The calculated number densities are presented in Figure 13. The O(¹D) density profile shows a broad peak around 200–600 km. But, in the case of O(¹S), the density peaks at much lower radial distances of ∼60 km. The number densities of O(¹D) and O(¹S) are converted into emission rate profiles for the red-doublet and green line emissions, respectively, by multiplying with Einstein transition probabilities as

$$\begin{eqnarray} V_{(6300+ 6364)}(r) &=&A_{(6300+ 6364)} \times [{\rm O}^1D(r)]\nonumber\\ &=& A_{(6300+ 6364)} \frac{\sum _{i=1}^k P_i(r)}{\sum _{i=1}^k L_i(r) + A(^1D) } \end{eqnarray} \tag{ 7 }$$

and

$$\begin{eqnarray} &&V_{(5577)}(r) = A_{(5577)} \times [{\rm O}^1S(r)] = A_{(5577)} \frac{\sum _{i=1}^k P_i(r)}{\sum _{i=1}^k L_i(r) + A(^1S) },\nonumber\\ \end{eqnarray} \tag{ 8 }$$

where [O¹S(r)] and [O¹D(r)] are the calculated number density for the corresponding production rates P_i(r) and loss frequencies L_i(r) for O(¹S) and O(¹D), respectively. A(¹D) and A(¹S) are the total Einstein spontaneous emission coefficients for red-doublet and green line emissions. Using the emission rate profiles, the line-of-sight intensity of green and red-doublet emissions along the projected distance z is calculated as

$$\begin{equation} I(z) = 2 \int _{z}^{R}V_{(5577,\ 6300+6364)} (s)ds, \end{equation} \tag{ 9 }$$

where s is the abscissa along the line of sight and V_{(5577, 6300 + 6364)}(s) is the emission rate for the green or red-doublet emission. The maximum limit of integration R is taken as 10⁵ km. The calculated brightness profiles of 5577 and 6300 Å emissions are presented in Figure 14. These brightness profiles are then averaged over the projected area corresponding to the slit dimension 12 × 82 centered on the nucleus of the comet C/1996 B2 Hyakutake for the observation on 1986 March 30 (Cochran 2008). The G/R ratio averaged over the slit is also calculated.

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Morrison et al. (1997) observed the green and red-doublet emissions on the comet C/1996 B2 Hyakutake in the high-resolution optical spectra obtained on 1996 March 23 and 27 and found the G/R ratio in the range 0.12–0.16. Cochran (2008) observed the 5577 and 6300 Å line emissions on this comet on 1996 March 9 and 30, with the G/R ratio as 0.09 for March 9 observation. We calculated the G/R ratio by varying the yield for O(¹S) production in the photodissociation of H₂O at 1216 Å (henceforth referred to as the O(¹S) yield). Since CO₂ is not observed in this comet, we assumed that a minimum of 1% CO₂ is present in the coma. However, we also carried out calculations for 0%, 3%, and 5% CO₂ abundances in the comet. We calculated the contributions of different production processes in the formation of O(¹S) and O(¹D) at three different projected distances of 10², 10³, and 10⁴ km from the nucleus for the above-mentioned CO₂ abundances and the O(¹S) yield values varying from 0% to 1%. These calculations are presented in Table 3. The percentage contribution of major production processes in the projected field of view for the green and red-doublet emissions is also calculated. The G/R ratio is calculated after averaging the intensity over the projected area 165 × 1129 km, which corresponds to the dimension of the slit used in the observation made by Cochran (2008) on 1996 March 30. These calculated values are presented in Table 4.

Taking 1% CO₂ abundance and 0% O(¹S) yield, the calculated percentage contributions of major production processes of the O(¹S) and O(¹D) atoms are presented in Table 3. Around 60%–90% of the O(¹D) is produced from the photodissociation of H₂O. Contributions of the photodissociative excitation of CO₂ and CO in the production of O(¹S) and O(¹D) are 15%–40% and 1%, respectively. Around 10⁴ km projected distance, the photodissociative excitation of OH (∼20%) and the dissociative recombination of H₂O⁺ (∼30%) are also significant production processes for the O(¹S) atoms. However, the contributions from these processes in O(¹D) production is only around 10%.

For CO₂ abundance of 1% and O(¹S) yield of 0.2%, the calculations presented in Table 3 show that the photodissociation of H₂O contributes around 20%–40% in the production of O(¹S) and 60%–90% in the production of O(¹D) atom. The next major source of O(¹S) production is the photodissociation of CO₂ and CO with each contributing ∼10%–25%. The relative contributions from the photodissociation of parent species H₂O, CO₂, and CO to O(¹S) and O(¹D) production decreases with an increase in projected distance from the nucleus. At 10⁴ km projected distance, the photodissociation of OH contributes 15% and 8% to the production of O(¹S) and O(¹D) atoms, respectively. Above 1000 km projected distance, the contribution of H₂O⁺ dissociative recombination to O(¹S) production is around 20%. The production of the O(¹D) atom is mainly via the photodissociation of H₂O, but around 10⁴ km the dissociative recombination of H₂O⁺ ion is also a significant production process contributing around 12%. At 10⁴ km, the dissociative recombination of OH⁺ also contributes around 10% to the total O(¹D) production, which is not shown in Table 3, and this value is independent of the O(¹S) yield or CO₂ abundance. Radiative decay of O(¹S) is a minor (⩽5%) production process in the formation of O(¹D).

We also calculated the relative contributions of different processes in the formation of green and red line emissions in the slit projected field of view, which are presented in Table 4. For the above case, the photodissociation of H₂O contributes around 35%, while the photodissociation of CO₂ and CO contributes 23% and 22%, respectively, to the production of green line emission. The contribution of dissociative recombination of H₂O⁺ ions is around 10%. The major production process of red lines is the photodissociation of H₂O (90%); the dissociative recombination of H₂O⁺ and radiative decay of the O(¹S) atom are minor (⩽5%) production processes. With the O(¹S) yield of 0.2% and 1% CO₂ abundance, the slit-averaged G/R ratio is found to be 0.11.

When the O(¹S) yield is increased to 0.5% with 1% CO₂ abundance (see Table 3), the contribution from the photodissociative excitation of H₂O to the O(¹S) production is increased, with values varying from 35% to 60%, while the contribution to O(¹D) production is not changed. In this case, the contribution from the photodissociation of CO₂ and CO to the O(¹S) production is reduced (values between 10% and 15%). The contributions from other processes are not changed significantly. Table 4 shows that in this case of around 60% of green line in the slit projected field of view is produced via the photodissociation of H₂O, while the contributions from the photodissociation of CO₂ and CO are around 15% each. The main (90%) production of red-doublet emission is through the photodissociation of H₂O. The slit-averaged G/R ratio is 0.17.

On further increasing the O(¹S) yield to 1% with CO₂ abundances of 1%, the contribution of photodissociation of H₂O to O(¹S) atom production is further increased (values between 50% and 75%), while the contribution from photodissociation of CO₂ and CO is decreased to around 10% each (cf. Table 3). The contributions from other processes are not affected compared to the previous case. As seen from Table 4, in this case the contribution of photodissociation of H₂O to green line is around 75% in the slit projected field of view, while contributions from the photodissociation of CO₂ and CO are decreased to 10% each. The calculated G/R ratio is 0.27 (Table 4).

We also evaluated the effect of CO₂ on the red-doublet and green line emissions by varying its abundance to 0%, 3%, and 5%. The calculated percentage contribution of major processes along the projected distances and in the slit projected field of view are presented in Tables 3 and 4, respectively. In the absence of CO₂, the contributions from H₂O, H₂O⁺, and CO in O(¹S) production are increased by ∼10% (cf. Tables 3 and 4). Taking 0% O(¹S) yield and by increasing CO₂ relative abundance from 1% to 3%, the percentage contributions for O(¹S) from the photodissociative excitation of CO₂ (CO) are increased (decreased) by 50%. The contribution from H₂O to O(¹D) production is not changed.

The calculations presented in Tables 3 and 4 depict that the contributions of various processes are significant in the production of O(¹S) atom, whereas the photodissociative excitation of H₂O is the main production process for the O(¹D) atom. Since the comet C/1996 B2 Hyakutake is rich in CO (abundance ∼22%) compared to other comets, the contribution from CO photodissociation to O(¹S) production is significant (10%–25%). In the case of a comet having CO abundance less than 20%, the major production source of the metastable O(¹S) atom would be the photodissociation of H₂O and CO₂.

In 1996 March, the green and red-doublet emissions were observed in the comet C/1996 B2 Hyakutake from two ground-based observatories (Morrison et al. 1997; Cochran 2008). Each observatory determined the G/R ratio using a different slit size. Using a circular slit, the projected radial distance over the comet for the Morrison et al. (1997) observation on March 23 and 27 varied from 640 to 653 km, while for the Cochran (2008) observation, using a rectangular slit, the projected area was 480 × 3720 km on March 9 and 165 × 1129 km on March 30. The clear detection of both green and red-doublet emissions and determination of the G/R ratio could be done for March 9 and 23 observations only (Cochran 2008; Morrison et al. 1997). The observed G/R ratio was 0.09 and 0.12–0.16 for the observation on March 9 and 23, respectively.

Performing a very high resolution (R = 200,000) observation of the comet C/1996 B2 Hyakutake on 1996 March 30, Cochran (2008) obtained radial profiles of 5577 and 6300 Å lines. In Figure 14, we have compared the model-calculated intensity profiles of 6300 and 5577 Å lines at different projected cometocentric distances with the observation of Cochran (2008). The calculated G/R ratio along the projected distance is shown in Figure 15. The 6300 Å emission shows a flat profile up to ∼500 km, whereas the 5577 Å green line starts falling off beyond 100 km. This is due to the quenching of O(¹S) and O(¹D) by H₂O in the innermost coma (cf. Figures 8 and 12), thereby making both the production and loss mechanisms controlled by H₂O. Above these distances, the emissions are mainly controlled by the radiative decay of ¹S and ¹D states of oxygen atoms.

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Similar to the calculations presented in Tables 3 and 4, in Figures 14 and 15 we present the red and green line intensity profiles and the G/R ratios, respectively, for different contributions of O(¹S) yield and CO₂ abundances. Since the photodissociative excitation of H₂O is the main production process for the O(¹D) atom, the red line intensity is almost independent of the variation in O(¹S) yield and CO₂ abundance. In the case of 0% CO₂ abundance, the best fit to the observed green line profile is obtained when the O(¹S) yield is ∼0.5% (±0.1%), where the G/R ratio varies from 0.06 to 0.26 (cf. Figure 15) and the slit-averaged G/R ratio for March 30 observation is 0.15 (cf. Table 4). The shape of green line profile cannot be explained with 1% or 0% O(¹S) yield, while the case for 0.2% O(¹S) yield can be considered as somewhat consistent with the observation. For this case, the value of G/R ratio shown in Figure 15 is found to vary over a large range from 0.54 to 0.02.

When we consider 1% CO₂ in the comet, the best-fit green profile is obtained when the O(¹S) yield is ∼0.2%. The case for 0.5% O(¹S) yield also provides the green line profile consistent with the observation. In both these cases the G/R ratio varies between 0.32 and 0.04 over the cometocentric projected distances of 10 to 10⁴ km. The calculated 5577 Å profiles for the O(¹S) yield of 0% and 1% are inconsistent with the observed profile.

In Figure 14 we also show a calculated profile for a case when the CO₂ abundance is 3% while the O(¹S) yield is 0% (i.e., no O(¹S) is produced in the photodissociation of H₂O). The calculated 5577 Å green line profile shows a good fit to the observed profile: suggesting that even a small abundance of CO₂ is enough to produce the required O(¹S). This is because the CO₂ is about an order of magnitude more efficient in producing the O(¹S) atom than H₂O in the photodissociation process (see Table 1). However, since O(¹S) would definitely be produced in the photodissociation of H₂O, and that the CO₂ would surely be present in the comet (though in smaller abundance), the most consistent value for the O(¹S) yield would be around 0.5%. Assuming 5% CO₂ and 0.5% O(¹S) yield, the calculated green line emission profile is inconsistent with the observation (cf. Figure 15). In this case, the calculated G/R ratio shown in Figure 15 is found to vary between 0.24 and 0.05.

From the above calculations, it is clear that the slit projected area on to the comet also plays an important role in deciding the G/R ratio. This point can be better understood from Table 5 where the G/R ratio is presented for a projected square slit on the comet at different geocentric distances. It is clear from this table that for a given physical condition of a comet and at a given heliocentric distance, the observed G/R ratio for a given slit size can vary according to the geocentric distance of the comet. For example, for an O(¹S) yield of 0.2% (0.5%) and CO₂ abundance of 1%, the G/R ratio can be 0.17 (0.26) if the comet is very close to the Earth (0.1 AU), whereas the G/R ratio can be 0.07 (0.1), 0.06 (0.08), or 0.06 (0.07), if the comet, at the time of observation, is at a larger distance of 0.5, 1, and 2 AU from the Earth, respectively. Furthermore, a G/R ratio of ∼0.1 can be obtained even for the O(¹S) yield of 0%. This suggests that the value of 0.1 for the G/R ratio is in no way a definitive benchmark value to conclude that H₂O is the parent of atomic oxygen atom in the comet, since smaller (∼5% relative to H₂O) amounts of CO₂ and CO itself can produce enough O(¹S) compared to that from H₂O. This table also shows that for observations made around a geocentric distance of 1 AU, the G/R ratio would be generally closer to 0.1. The G/R ratio observed in different comets ranges from 0.02 to 0.3 (e.g., Cochran 2008; Capria et al. 2010).

Thus, we can conclude that the G/R ratio not only depends on the production and loss mechanisms of the O(¹S) atom, but also depends on the nucleocentric slit projected area over the comet. Moreover, the CO₂ plays an important role in the production of O(¹S), and thus the green line emission, in comets. With the present model calculations and based on the literature survey of dissociation channels of H₂O, we suggest that the O(¹S) yield from the photodissociation of H₂O cannot be more than 1% of the total absorption cross section of H₂O at solar Lyα radiation. The best-fit value of the O(¹S) yield derived from Figure 14 for a smaller (1%) CO₂ abundance in the comet C/1996 B2 Hyakutake is 0.4% (±0.1)%. As per Tables 1 and 2, this means that the ratio of rates of O(¹S) to O(¹D) production in the H₂O photodissociation should be 0.03 (±0.01), which is much smaller than the value of 0.1 generally used in the literature based on Festou & Feldman (1981). Furthermore, if the source of red and green lines is CO₂ (CO), the ratio of photorates for O(¹S) to O(¹D) would be around 0.6 (0.8) (see Tables 1 and 2).

To verify whether the O(¹S) yield of 0.5% (for the CO₂ abundance of 1%) derived from Figure 14, based on the comparison between model and observed red and green line radial profiles in the comet Hyakutake on 1996 March 30, is consistent with the G/R ratio observed on other days on this comet, we present in Table 6 the G/R ratio calculated for observations made on 1996 March 9, 23, 27, and 30, along with the observed value of G/R ratio from Morrison et al. (1997) and Cochran (2008). These calculations are made by taking the solar flux on the day of observation using the Tobiska (2004) SOLAR2000 model and scaled according to the heliocentric distance of the comet on that date. The CO abundance is 22%, the same as in all the calculations presented in the paper.

Table 6. Calculated Intensities of Green and Red-doublet Emissions and the G/R Ratio in the Comet C/1996 B2 Hyakutake on Different Days of Observation in 1996 March

Date of	r	Δ	$Q_{{\rm H_2O}}$	Slit	Projected	Calculated	Calculated
Observation				Dimension	Distance	5577 Å	(6300 + 6364 Å)
(1996 March)						Intensity	Intensity	G/R Ratio
	(AU)	(AU)	(s−1)	(arcsec)	(km)	(kR)	(kR)	Calculated	Observed
9a	1.37	0.55	5 × 1028	12 × 82	470 × 3720	0.06	0.62	0.09	0.09a
23b	1.08	0.12	1.8 × 1029	75 (circular)c	640	0.69	5.88	0.12	0.12–0.16b
27b	1.00	0.11	2 × 1029	75 (circular)	653	0.89	7.12	0.12	⋅⋅⋅
30a	0.94	0.19	2.2 × 1029	12 × 82	165 × 1129	0.90	7.97	0.17	⋅⋅⋅

Notes. Calculations are made for O(¹S) yield of 0.5%, and CO₂ and CO relative abundances of 1% and 22%, respectively. ^aCochran (2008). ^bMorrison et al. (1997). ^c75 is the diameter of the circular slit.

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The calculated G/R ratio on March 9, when the geocentric distance was 0.55 AU and the H₂O production rate was 5 × 10²⁸ s⁻¹, is 0.09 (see Table 6) which is the same as the observed ratio obtained by Cochran (2008). On March 23 and 27, the comet is closer to both the Sun and Earth (geocentric distance ∼0.1 AU) and its H₂O production rate was four times higher than the value on March 9. The calculated G/R ratio on March 23 is 0.12, which is in agreement with the observed ratio obtained by Morrison et al. (1997).