The Deuterium Fractionation Timescale in Dense Cloud Cores: A Parameter Space Exploration

The deuterium fraction [N$_2$D$^+$]/[N$_2$H$^+$], may provide information about the ages of dense, cold gas structures, important to compare with dynamical models of cloud core formation and evolution. Here we introduce a complete chemical network with species containing up to three atoms, with the exception of the Oxygen chemistry, where reactions involving H$_3$O$^+$ and its deuterated forms have been added, significantly improving the consistency with comprehensive chemical networks. Deuterium chemistry and spin states of H$_2$ and H$_3^+$ isotopologues are included in this primarily gas-phase chemical model. We investigate dependence of deuterium chemistry on model parameters: density ($n_{\rm H}$), temperature, cosmic ray ionization rate, and gas-phase depletion factor of heavy elements ($f_{\rm D}$). We also explore the effects of time-dependent freeze-out of gas-phase species and dynamical evolution of density at various rates relative to free-fall collapse. For a broad range of model parameters, the timescales to reach large values of $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$, observed in some low- and high-mass starless cores, are relatively long compared to the local free-fall timescale. These conclusions are unaffected by introducing time-dependent freeze-out and considering models with evolving density, unless the initial $f_{\rm D} \gtrsim$ 10. For fiducial model parameters, achieving $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$ requires collapse to be proceeding at rates at least several times slower than that of free-fall collapse, perhaps indicating a dynamically important role for magnetic fields in the support of starless cores and thus the regulation of star formation.