Chemical sensitivity to the ratio of the cosmic-ray ionization rates of   He and H2 in dense clouds
  Aim: To determine whether or not gas-phase chemical models with homogeneous and time-independent physical conditions explain the many observed molecular abundances in astrophysical sources, it is crucial to estimate the uncertainties in the calculated abundances and compare them with the observed abundances and their uncertainties. Non linear amplification of the error and bifurcation may limit the applicability of chemical models. Here we study such effects on dense cloud chemistry. Method: Using a previously studied approach to uncertainties based on the representation of rate coefficient errors as log normal distributions, we attempted to apply our approach using as input a variety of different elemental abundances from those studied previously. In this approach, all rate coefficients are varied randomly within their log normal (Gaussian) distribution, and the time-dependent chemistry calculated anew many times so as to obtain good statistics for the uncertainties in the calculated abundances. Results: Starting with so-called ``high-metal'' elemental abundances, we found bimodal rather than Gaussian like distributions for the abundances of many species and traced these strange distributions to an extreme sensitivity of the system to changes in the ratio of the cosmic ray ionization rate zeta\_He for He and that for molecular hydrogen zeta\_H2. The sensitivity can be so extreme as to cause a region of bistability, which was subsequently found to be more extensive for another choice of elemental abundances. To the best of our knowledge, the bistable solutions found in this way are the same as found previously by other authors, but it is best to think of the ratio zeta\_He/zeta\_H2 as a control parameter perpendicular to the ''standard'' control parameter zeta/n\_H. 
Valentine Wakelam (OSU, L3AB), Eric Herbst (OSU), Franck Selsis   (CRAL), G\'erard Massacrier (CRAL)