A new modified-rate approach for gas-grain chemical simulations

Context. Understanding grain-surface processes is crucial to interpreting the chemistry in many regions of the interstellar medium. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. Aims. A new modified-rate method for solving grain-surface chemical systems is presented. The purpose of the method is to trade a small amount of accuracy, and certain excessive detail, for the ability to accurately model highly complex systems that can otherwise only be treated using the sometimes inadequate rate-equation approach. Methods. In contrast to previous rate-modification techniques, the functional form of the surface production rates was modified, and not simply the rate coefficient. This form is appropriate to the extreme "small-grain" limit, and can be verified using an analytical master-equation approach. Various further modifications were made to this basic form, to account for competition between processes, to improve estimates of surface occupation probabilities, and to allow a switch-over to the normal rate equations where these are applicable. Results. The new method was tested against a number of systems solved previously using master-equation and Monte Carlo techniques. It is found that even the simplest method is quite accurate, and a great improvement over rate equations. Further modifications allow the master-equation results to be reproduced exactly for the methanol-producing system, within computational accuracy. Small discrepancies arise when non-zero activation energies are assumed for the methanol system, which result from complex reaction-competition processes that cannot be resolved easily without using exact methods. Inaccuracies in computed abundances are never greater than a few tens of percent, and typically of the order of one percent, in the most complex systems tested. Conclusions. The new modified-rate approach presented here is robust to a range of grain-surface parameters, and accurately reproduces the results of exact methods. Furthermore, it may be derived from basic approximations, making the behaviour of the system understandable in terms of physical processes rather than time-dependent probabilities or other more abstract quantities. The method is simple enough to be easily incorporated into a full gas-grain chemical code. Implementation of the method in simple networks, including hydrogen-only systems, is trivial, whilst the results are highly accurate.