Erratum: “The Pure Rotational Line Emission of Ortho‐Water Vapor in Comets. I. Radiative Transfer Model” (ApJ, 615, 531 [2004])

Abstract

The comet model presented in the paper is based on the radiation transfer code ratran (M. R. Hogerheijde & F. F. S. van der Tak, ApJ, 615, 531 [2004]), an accelerated Monte Carlo code to calculate the line excitation and the emerging line intensities. For a given density profile, ratran determines the level population and, in a second step, calculates the spectral line emission for a given telescope beam, source distance, and velocity resolution. The numerical simulations for water-line emission in cometary coma show that the line excitation varies considerably on radii smaller than the projected telescope beam at the source distance for the models and telescope parameter considered in the paper. Thus, in our calculation, the water excitation in the second step was incorrectly sampled and the emission predictions were inexact, particularly for weak, optically thin lines.4 This problem also resulted from a limitation of the ratran version with respect to the spatial sampling of the intensity distribution for a convolution with a telescope beam. The relevant part of the ratran code was corrected by the authors with the May 2003 release of their software (F. F. S. van der Tak 2006, private communication). To correct this issue, we redid the numerical models presented in the original paper using the May 2003 release of the ratran software and made tests to ensure that the spatial intensity distribution used to calculate the emission detected by a given telescope beam is sampled with a sufficient spatial resolution. The corrected version of the radiation transfer model does not affect the first step, where the level population is calculated; however, the beam-averaged line intensities calculated from the level populations are generally lower than quoted in the original paper. The impact is moderate for the ground-state transitions and for the models with a water production rate of Q29=1 (M1, M6, M7), but can be substantial for the emission in weak comets and the H218O transitions, as detailed below. For a given (measured) line intensity, the corrected model gives a water production rate that is larger than quoted in the original paper. Corrected versions of Figures 5 to 9 and Tables 4, 5, and 6 are given here, and the implications for the relevant sections in the paper are discussed (� 4, Model for the SWAS Observations of C/1999 T1 McNaught-Hartley � 5, Line Predictions for Future Observatories; � 7, Summary). Along with the model results, we correct a typo in Table 4 (Q29=QH2O/1029 s-1 for models M3 and M5 is 0.01). For the SWAS observations of comet C/1999 T1 (McNaught-Hartley) made on 2001 February 2, the corrected model gives a water production rate of QH2O=(5.72+/-0.85)�1028 s-1 for xne=1.0 and QH2O=(7.36+/-1.15)�1028 s-1 for xne=0.2, where xne is the scaling factor for the electron abundance (see � 2.4 of the original paper). For the average of the data observed between 2001 March 1 and 8, the corrected water production rate is QH2O=(1.69+/-0.45)�1028 s-1 (xne=1.0) and QH2O=(1.99+/-0.55)�1028 s-1 (xne=0.2), respectively. This is larger by 10%-57% than the results quoted in the original paper, but is still within 20%-40% of the water-production rates published in F. Bensch et al. ApJ, 615, 531 [2004], where the model by D. Bockel�e-Morvan (ApJ, 615, 531 [2004]) is used. The difference of 20%-40% is of the order of the model accuracy due to the uncertainties in the electron abundance (compare the results for xne=1.0 and xne=0.2). However, this residual discrepancy possibly reflects the different numerical codes used to calculate the line excitation and radiation transfer, an accelerated Monte Carlo in ratran vs. an escape probability formalism in the model by D. Bockel�e-Morvan (ApJ, 615, 531 [2004]). The low ratio of the expansion velocity over the local line-width, of a factor of 3, is close to the limit where an escape probability formalism can be applied. Systematic differences are therefore expected for the water-rotational transitions of the most abundant isotopologue, H216O, where optical depths can be large. The simulations made for a comet with Q29=0.3, rh=1.15 AU and Delta=0.88 AU show that the line-integrated intensities of both models agree within 5%-15% for the optically thin ortho-H218O emission lines. The corrected models M1, M6, and M7 have line intensities that are lower by typically 10%-30%. Both ground-state transitions 110-->101 and 121-->110 are affected to a lesser degree, while a larger difference is noted for the 221-->221 and 312-->221 transition. A significantly larger impact is noted for models with Q29 1 AU. Typically, the line emission is 30%-50% smaller than presented in the original paper (model M2); 50%-80% for model M3. Even larger differences of a factor of 2-10 are found for models M4 and M5, as well as for the H218O models (M1-18 through M3-18). The corrected line intensities are lower by more than an order of magnitude in a few individual cases; for example, the 212-->101 transition in model M5 and the 221-->212,312-->221 transitions in M3, M4, M5, M2-18, and M3-18. With the line intensities in the corrected models being lower than in the original paper, the integration time estimated for a detection with Herschel HIFI and SOFIA CASIMIR is underestimated. The impact on the time estimate is large, since the required integration time varies with the inverse square of the anticipated line intensity. The integration time estimated for a detection of the ground-state transition 110-->101 is still relatively short for the corrected models M1-M3, being of the order of 1 minute or less. For example, a 5 sigma detection of this emission line with Herschel HIFI in a comet with Q29=0.01 and rh,Delta=1 (model M3) requires ton~57 s (on-source integration time). For model M4, ton=34 s gives a S/N = 10 for the same emission line, and ton=106 minutes are required for a 3 sigma detection in the extreme case of model M5. Even with the integration for the 110-->101 transition being significantly larger than previously estimated (a factor of 10 for M4 and as much as a factor of 240 in M5), a detection of this emission line is still easily feasible with Herschel HIFI. Some of the transitions in the models M3, M4, and M5 which were predicted to be easily detectable in the original paper now turn out to be difficult or even impossible to detect with a reasonable investment of observing time. An on-source integration time of as much as 7.5 hr is required for a 3 sigma detection of the 221-->212 transition in model M3, compared to ton=190 s in the original paper. This gives an S/N of 34 for the simultaneously detected 212-->101 emission line. In M4, ton=5.3 minutes is required to achieve a S/N of 10 for latter emission line. This is insufficient for a simultaneous detection of the 221-->212 transition in the same band. Despite these limitations, multiline observations still provide a promising method to constrain the electron density and thus the contribution of the electron-impact excitation in the cometary coma. The corrected models for H218O indicate that ton=81 minutes is required for a 4 sigma detection of the 110-->101 transition of model M1-18 with SOFIA CASIMIR. Even though this is a factor of 9 larger than previously estimated, it still appears to be feasible with a single SOFIA observing flight. Observations of in particular higher H218O rotational transitions with SOFIA CASIMIR are probably limited to strong comets with Q29>1 or comets that make a close Earth approach (Delta<<1 AU), however.