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, $D_{\rm frac}^{\rm N_2H^+} \equiv
[\rm N_2D^+]/[N_2H^+]$, with values of $D_{\rm frac}^{\rm N_2H^+} \simeq
0.2$--$0.7$, 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 $\rm H_2$, 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, $\alpha_{\rm ff}$. In order to reach the high level of observed
deuteration of $\rm N_2H^+$, we find that the most likely evolutionary history
of the cores involves collapse at a relatively slow rate, $\lesssim1/10$th of
free-fall.
