Electron Abundance in Protostellar Cores
  The determination of the fractional electron abundance, Xe, in protostellar cores relies on observations of molecules, such as DCO+, H13CO+ and CO, and on chemical models to interpret their abundance. Studies of protostellar cores have revealed significant variations of Xe from core to core within a range 10^-8<Xe<10^-6. The physical origin of these large variations in Xe is not well understood, unless unlikely variations in the cosmic ray ionization rate or ad hoc values of metal depletion are assumed. In this work we explore other potential causes of these variations in Xe, including core age, extinction and density. We compute numerically the intensity of the radiation field within a density distribution generated by supersonic turbulence. Taking into account the lines of sight in all directions, the effective visual extinction in dense regions is found to be always much lower than the extinction derived from the column density along a fixed line of sight. Dense cores with volume and column densities comparable to observed protostellar cores have relatively low mass-averaged visual extinction, 2mag <= A_V <= 5mag, such that photo-ionization can sometimes be as important as cosmic ray ionization. Chemical models, including gas-grain chemistry and time dependent gas depletion and desorption, are computed for values of visual extinction in the range 2mag <= A_V <= 6mag, and for a hydrogen gas density of 10^4cm^-3$, typical of protostellar cores. The models presented here can reproduce some of the observed variations of ion abundance from core to core as the combined effect of visual extinction and age variations. The range of electron abundances predicted by the models is relatively insenstive to density over 10^4 to 10^6 cm^{-3}. 
Paolo Padoan, Karen Willacy, William Langer, Mika Juvela