An equivalent observation, however, was made in comet Kohoutek by Wehinger et al. (2), who identified H₂O⁺ and attributed the phenomenon to fluorescence excitation of molecules at temperatures below 50 K. The reason for the missing vibrational bands can be found in the electronic structure of H₂O⁺ and NH₂ (3, 4) that gives rise to optical transitions involving a lower state bent asymmetric rotor with quantum numbers J", N", K_a", and K_c" and an upper state linear symmetric rotor with quantum numbers J, N, and K, the latter quantum number being equivalent to K_a. While there is no vibrational level-dependent constraint on K_a" values in the ground electronic state, odd K vibronic sublevels of the linear excited state are restricted to even bending vibrational states, while even K sublevels are associated with odd bender states.

Given the K_a = ±1 selection rule of the H₂O⁺ and NH₂ òA₁  ²B₁ transitions, absorption to the unobserved odd bender states can only occur from odd K_a" levels of the lower state. Population of K_a" = 1 states requires a minimum rotational excitation of 37 cm¹ for H₂O⁺ (4) [32 cm¹ for NH₂ (3)], corresponding to a temperature of 53 K. We calculated (Fig. 1) the temperature dependence of H₂O⁺ fluorescence excitation spectra for the same spectral range in which H₂O⁺ emissions were observed by Rauer et al. (1). The calculations use term values, frequencies, line strengths given by Lew (4), and the methodology described by Dressler et al. (5, 6). The H₂O⁺ à state bending vibrational assignment adopted by Rauer et al. has recently been revised (7, 8). The (0,9,0)-(0,0,0) band becomes apparent between 15 and ~25 K, suggesting that odd bands should be visible closer to perihelion. This was indeed the case for Kohoutek (2) and was also observed by Rauer et al. in Hale-Bopp for NH₂ at r_h < 3 AU (1).

Rainer A. Dressler
Phillips Laboratory,
Optical Effects Division,
Hanscom Air Force Base,
MA 01731-3010, USA

REFERENCES

1. H. Rauer et al., Science 275, 1909 (1997) [Abstract/Full Text].
2. P. A. Wehinger, S. Wyckoff, G. H. Herbig, G. Herzberg, H. Lew, Astrophys. J. 190, L43 (1974).
3. K. Dressler and D. A. Ramsay, Philos. Trans. R. Soc. London Ser. A 251, 553 (1959).
4. H. Lew, Can. J. Phys. 54, 2028 (1976).
5. R. A. Dressler, J. A. Gardner, R. H. Salter, E. Murad, J. Chem. Phys. 96, 1062 (1992) .
6. R. A. Dressler, S. T. Arnold, E. Murad, ibid. 103, 9989 (1995) .
7. M. Brommer et al., ibid. 98, 5222 (1993).
8. R. A. Dressler and S. T. Arnold, ibid. 102, 3481 (1995).

Response: We thank Dressler for his interesting comment to our observation of the excitation of NH₂ and H₂O⁺ in comet Hale-Bopp. His calculation shows that odd vibrational bands should become visible at temperatures larger than 25 K and might therefore be visible closer to perihelion as the temperature in the coma increases. However, we would like to point out in more detail than we could in our short report (1) that a straightforward interpretation of the observations is not possible and a more detailed model of the excitation in a cometary coma is required.

The calculation by Dressler assumes thermal populations of the lower rotational levels and determines relative line intensities under fluorescence excited by an unspecified source. In such a case, the input kinetic temperature, T_k, is equivalent to the rotational excitation temperature, T_exc, in the computed spectrum. However, in nonthermal equilibrium conditions as they are found throughout most of the cometary coma, T_exc, determined by the relative population of the rotational or vibrational levels, is not generally equivalent to T_k. While the absence of the odd bands in a comet at large heliocentric distance is indicative of a low rotational T_exc as we pointed out [page 1911, column 3, paragraph 3 in our report (1)], it does not allow any conclusion to be drawn as to a thermal excitation at a corresponding T_k.

In comets, a temperature-dependent excitation should play a role only in the innermost, collisionally dominated coma. In comet Hale-Bopp, this collisionally dominated region is larger than that in other comets at the same heliocentric distance range as a result of its higher gas production rate. However, throughout most of the coma and in the ion tail, the populations of all the levels--and therefore the NH₂ and H₂O⁺ emissions--are governed by purely radiative processes; they depend on the incoming solar radiation as well as on the molecular characteristics, notably the strength of pure rotational transitions within the ground state (2). Existing resonance fluorescence models (3) are unable to reproduce the observed visibility of even and odd bands, mainly because they do not account for the rotational structure of the molecule or ion.

A realistic excitation model of NH₂ and H₂O⁺ in a cometary coma and ion tail must take into account that thermal rotational equilibrium does not hold in such low density environments. The temporal evolution of the population of rotational levels with increasing nucleocentric distance must be taken into account, in addition to the pumping by solar flux as a result of resonance fluorescence processes and the rotational de-excitation processes mentioned above. The latter are important in the species in hand because they are in the hydride radicals OH, NH, and CH. The spectra modeled by Dressler show the effect of temperature-dependent excitation in thermal equilibrium conditions for NH₂ and H₂O⁺. However, only a detailed investigation including all significant excitation processes, considering the spatial distribution of the emissions, and covering a range of heliocentric distances will provide a full explanation of the observations.

A correct treatment of the populations of even and odd levels for NH₂ and H₂O⁺ is important. Neglecting to account for the appropriate selection rules leads to production rates that are underestimated by a factor of about 2 near 1 AU from the sun (4). For H₂O⁺ it was shown (5) that the large discrepancy of the ion production rates in comparison to its parent, water, is most likely caused by incorrect g-factors for the emission bands observed. Furthermore, the observations of comet Kohoutek (6), quoted by Dressler, showed that odd bands of H₂O⁺ were weak in a comet still at heliocentric distances of about 1.4 AU. Some other spectra of the same comet and of comet West at the same r_h, however, showed these bands (also those of NH₂) with comparable intensities to the even bands (7). A similar remark can be made regarding comet West near 1.6 AU (8).

Finally, we would like to thank Dressler for making us aware of the changed assignments of vibrational levels for H₂O⁺.

H. Rauer
Observatoire de Paris-Meudon,
5, Place Jules Janssen,
F-92190 Meudon, France
C. Arpigny
Institute d'Astrophysique,
Université de Liège, B-4000 Liège, Belgium
H. Boehnhardt
Institut für Astronomie und Astrophysik,
Ludwig-Maximilian-Universität München,
D-81679 München, Germany
F. Colas
Bureau des Longitudes,
F-75014 Paris, France
J. Crovisier
Observatoire de Paris-Meudon
L. Jorda
M. Küppers
Max-Planck-Institut für Aeronomie,
D-37191 Katlenburg-Lindau, Germany
J. Manfroid
Institute d'Astrophysique, Belgium
K. Rembor
N. Thomas
Max-Planck-Institut für Aeronomie

REFERENCES

1. H. Rauer et al., Science 275, 1909 (1997) [Abstract/Full Text].
2. C. Arpigny, Annu. Rev. Astron. Astrophys. 3, 351 (1965).
3. B. Lutz, Astrophys. J. 315, L147 (1987); S. Tegler and S. Wyckoff, ibid. 343, 445 (1989).
4. C. Arpigny, AIP Conf. Proc. 312, 205 (1994).
5. M. A. DiSanti et al., Icarus 86, 152 (1990); H. Rauer et al., Astron. Astrophys. 325, 839 (1997).
6. P. A. Wehinger, S. Wyckoff, G. H. Herbig, G. Herzberg, H. Lew, Astrophys. J. 190, L43 (1974).
7. C. Arpigny et al., Atlas of Cometary Spectra (Kluwer, Dordrecht, Netherlands, 1997).
8. M. F. A'Hearn, R. J. Hanisch, C. H. Thurber, Astron. J. 85, 74 (1980).