The Deuteration Clock for Massive Starless Cores

To understand massive star formation requires study of its initial conditions. Two massive starless core candidates, C1-N & C1-S, have been detected in IRDC G028.37+00.07 in ${\mathrm{N}}_2{\mathrm{D}}^{+}$(3-2) with $ALMA$. From their line widths, either the cores are subvirial and are thus young structures on the verge of near free-fall collapse, or they are threaded by $\sim 1$ mG $B$-fields that help support them in near virial equilibrium and potentially have older ages. We modeled the deuteration rate of ${\mathrm{N}}_2{\mathrm{H}}^{+}$ to constrain collapse rates of the cores. First, to measure their current deuterium fraction, $D_{\rm frac}^{\rm N_2H^+}$ $\equiv [{\mathrm{N}}_2{\mathrm{D}}^{+}]\mathrm{/}[{\mathrm{N}}_2{\mathrm{H}}^{+}]$, we observed multiple transitions of ${\mathrm{N}}_2{\mathrm{H}}^{+}$ and ${\mathrm{N}}_2{\mathrm{D}}^{+}$ with $CARMA$, $SMA$, $JCMT$, $NRO45m$ and $IRAM30m$, to complement the $ALMA$ data. For both cores we derived $D_{\rm frac}^{\rm N_2H^+}\sim0.3$, several orders of magnitude above the cosmic [D]/[H] ratio. We then carried out chemodynamical modeling, exploring how collapse rate relative to free-fall, ${\alpha }_{\mathrm{f}\mathrm{f}}$, affects the level of $D_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{c}}^{{\mathrm{N}}_2{\mathrm{H}}^{+}}$ that is achieved from a given initial condition. To reach the observed $D_{\rm frac}^{\rm N_2H^+}$,mostmodelsrequireslowcollapsewith$\alpha_{\rm ff}\sim0.1$,i\mathrm{.}e\mathrm{.},$\sim1/10$th of free-fall. This makes it more likely that the cores have been able to reach a near virial equilibrium state and we predict that strong $B$-fields will eventually be detected. The methods developed here will be useful for measurement of the pre-stellar core mass function.