The Deuterium Fraction in Massive Starless Cores and Dynamical Implications

We study deuterium fractionation in two massive starless/early-stage cores C1-N and C1-S in Infrared Dark Cloud (IRDC) G028.37+00.07, first identified by Tan et al. (2013) with ALMA. Line emission from multiple transitions of $\rm N_2H^+$and$\rm N_2D^+$ were observed with the ALMA, CARMA, SMA, JCMT, NRO 45m and IRAM 30m telescopes. By simultaneously fitting the spectra, we estimate the excitation conditions and deuterium fraction, $D_{\rm frac}^{\rm N_2H^+} \equiv [\rm N_2D^+]/[N_2H^+]$,withvaluesof$D_{\rm frac}^{\rm N_2H^+} \simeq 0.2$--$0.7$, several orders of magnitude above the cosmic [D]/[H] ratio. Additional observations of o-H${}_2$D${}^{+}$ are also presented that help constrain the ortho-to-para ratio of ${\mathrm{H}}_2$, which is a key quantity affecting the degree of deuteration. We then present chemodynamical modeling of the two cores, exploring especially the implications for the collapse rate relative to free-fall, ${\alpha }_{\mathrm{f}\mathrm{f}}$. In order to reach the high level of observed deuteration of ${\mathrm{N}}_2{\mathrm{H}}^{+}$, we find that the most likely evolutionary history of the cores involves collapse at a relatively slow rate, $\lesssim 1\mathrm{/}10$th of free-fall.