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Structure, Dynamics and Deuterium Fractionation of Massive Pre-Stellar Cores

High levels of deuterium fraction in N$_2$H$^+$ are observed in some pre-stellar cores. Single-zone chemical models find that the timescale required to reach observed values ($D_{\rm frac}^{{\rm N}_2{\rm H}^+} \equiv {\rm N}_2{\rm D}^+/{\rm N}_2{\rm H}^+ \gtrsim 0.1$) is longer than the free-fall time, possibly ten times longer. Here, we explore the deuteration of turbulent, magnetized cores with 3D magnetohydrodynamics simulations. We use an approximate chemical model to follow the growth in abundances of N$_2$H$^+$ and N$_2$D$^+$. We then examine the dynamics of the core using each tracer for comparison to observations. We find that the velocity dispersion of the core as traced by N$_2$D$^+$ appears slightly sub-virial compared to predictions of the Turbulent Core Model of McKee & Tan, except at late times just before the onset of protostar formation. By varying the initial mass surface density, the magnetic energy, the chemical age, and the ortho-to-para ratio of H$_2$, we also determine the physical and temporal properties required for high deuteration. We find that low initial ortho-to-para ratios ($\lesssim 0.01$) and/or multiple free-fall times ($\gtrsim 3$) of prior chemical evolution are necessary to reach the observed values of deuterium fraction in pre-stellar cores.