Radiative transfer simulation of water rotational excitation in comets Comparison of the Monte Carlo and escape probability methods

Context. The recent advent of space-based detectors at far-infrared and submillimetre wavelengths opened up the possibility of observing cometary water from its rotational transitions. The 110−101 fundamental line of ortho H2O at 557 GHz was detected in several comets by the Submillimeter Wave Astronomical Satellite and Odin. This line as well as other water and H 18 O lines will be observed by the three instruments of the ESA Herschel Space Observatory. In order to prepare or interpret these observations, excitation models including H2O self-absorption are required. Aims. For treating radiation transfer of water in comets, Bockelee-Morvan (1987, A&A, 181, 169) used the local approximation with the escape probability method (EP). Bensch & Bergin (2004, ApJ, 615, 531) used the Monte-Carlo method (MC), which is more exact from a physical point of view, but is much more CPU time-demanding. The aim of this study is to compare the results of the two methods and to investigate the extent to which the EP method provides acceptable results for synthesizing line profiles and analysing observations. Methods. We developed two 1D numerical codes. The MC code is based on the accelerated Monte Carlo algorithm proposed by Hogerheijde & van der Tak (2000, A&A, 362, 697). The EP code is based on the algorithm proposed by Bockelee-Morvan (1987). They include the seven lowest rotational levels of ortho-water, which are the primarily populated levels in the rotationally cold coma. A spherically symmetric density distribution with constant expansion velocity is assumed. Collisions with water and electrons, and infrared pumping, are taken into account. Synthetic line profiles pertaining to Odin and future Herschel observations with the Heterodyne Instrument for Far-Infrared are computed for water production rates ranging from 10 28 to 10 30 s −1 . Results. We show that the EP method has sufficient accuracy to predict rotational excitation, line intensities and line shapes. Differences in level populations do not exceed 20%, except in the narrow region where a strong gradient in electron temperature and density is present. Line shapes are in excellent agreement and line areas differ by less than 7%.