Lattice dynamical system modelling of molecular clouds

Because a comprehensive microscopic treatment of interstellar molecular clouds is out of reach, an alternative approach is proposed in which most of the crucial ingredients of the problem are considered, but at some 'minimal' level of modelling. This leads to the elaboration of a lattice dynamical system , i.e. a time-dependent, spatially extended, deterministic system of macroscopic cells coupled through radiative transfer. Each cell is characterized by a small set of variables and supports a caricatural chemistry possessing the essential dynamical features of more realistic reaction schemes.   This approach naturally precludes quantitative results, but allows heretofore unavailable insights into some of the basic mechanisms at play. We focus on the response of the transfer process and the chemistry to a frozen 'turbulent' velocity field. It is shown that the system settles generically into a state where the effective coupling between cells is neither local nor global, and for which no single length-scale exists.   The spectral lines reconstructed from the spatiotemporal evolution of our model may, depending on the velocity field, exhibit profiles ranging from Gaussian to bimodal with strong realization effects. In the bimodal case, the model intrinsically displays an energy cascade transport mechanism to the cells that cool most efficiently: the feedback of chemistry on radiative transfer cannot be neglected.   Finally, extensions of this work are discussed and future developments are outlined.