Ionisation in turbulent magnetic molecular clouds - I. Effect on density and mass-to-flux ratio structures

Context. Previous studies show that the physical structures and kinematics of a region depend significantly on the ionisation fraction. These studies have only considered these effects in non-ideal magnetohydrodynamic simulations with microturbulence. The next logical step is to explore the effects of turbulence on ionised magnetic molecular clouds and then compare model predictions with observations to assess the importance of turbulence in the dynamical evolution of molecular clouds.Aims. In this paper, we extend our previous studies of the effect of ionisation fractions on star formation to clouds that include both non-ideal magnetohydrodynamics and turbulence. We aim to quantify the importance of a treatment of the ionisation fraction in turbulent magnetised media and investigate the effect of the turbulence on shaping the clouds and filaments before star formation sets in. In particular, here we investigate how the structure, mass and width of filamentary structures depend on the amount of turbulence in ionised media and the initial mass-to-flux ratio.Methods. To determine the effects of turbulence and mass-to-flux ratio on the evolution of non-ideal magnetised clouds with varying ionisation profiles, we have run two sets of simulations. The first set assumes different initial turbulent Mach values for a fixed initial mass-to-flux ratio. The second set assumes different initial mass-to-flux ratio values for a fixed initial turbulent Mach number. Both sets explore the effect of using one of two ionisation profiles: step-like (SL) or cosmic ray only (CR-only). We compare the resulting density and mass-to-flux ratio structures both qualitatively and quantitatively via filament and core masses and filament fitting techniques (Gaussian and Plummer profiles). Results. We find that even with almost no turbulence, filamentary structure still exists although at lower density contours. Comparison of simulations shows that for turbulent Mach numbers above 2, there is little structural difference between the SL and CR-only models, while below this threshold the ionisation structure significantly affects the formation of filaments. This holds true for both sets of models. Analysis of the mass within cores and filaments shows that the mass decreases as the degree of turbulence increases. Finally, observed filaments within the Taurus L1495/B213 complex are best reproduced by models with supercritical mass-to-flux ratios and/or at least mildly supersonic turbulence, however, our models show that the sterile fibres observed within Taurus may occur in highly ionised, subcritical environments. Conclusions. From the analysis of the simulations, we conclude that in the presence of low turbulent velocities, the ionisation structure of the medium still plays a role in shaping the structure of the cloud, however, above Mach 2, the differences between the two profiles become indistinguishable. However, differences may be present in the underlying velocity structure. Kinematics studies will be the focus of the next paper in this series. Regions with fertile fibres likely indicate a trans- or supercritical mass-to-flux ratio within the region while sterile fibres are likely subcritical and transient.