Formation of $\mathrm{H}{}_3{}^{-}$ by radiative association of ${\mathrm{H}}_2$ and ${\mathrm{H}}^{-}$ in the interstellar medium

We develop the theory of radiative association of an atom and a diatomic molecule within a close-coupling framework. We apply it to the formation of $\mathrm{H}{}_3{}^{-}$ after the low-energy collision (below 0.5 eV) of ${\mathrm{H}}_2$ with ${\mathrm{H}}^{-}$. Using recently obtained potential energy and permanent dipole moment surfaces of $\mathrm{H}{}_3{}^{-}$, we calculate the lowest rovibrational levels of the $\mathrm{H}{}_3{}^{-}$ electronic ground state and the cross section for the formation of $\mathrm{H}{}_3{}^{-}$ by radiative association between ${\mathrm{H}}^{-}$ and ortho- and para-H${}_2$. We discuss the possibility for the $\mathrm{H}{}_3{}^{-}$ ion to be formed and observed in the cold and dense interstellar medium in an environment with a high ionization rate. Such an observation could be a probe for the presence of ${\mathrm{H}}^{-}$ in the interstellar medium.

Figure 1

Adiabatic curves of $\mathrm{H}{}_3{}^{-}$ as functions of the Jacobi coordinate $R$ (on a logarithmic scale), and the scheme for radiative association at a low collisional energy $E$. Horizontal lines indicate positions of several bound states (reported in Table ) and resonances.

Figure 2

RA cross section (in atomic units) starting from para-H${}_2$ ($v_0=0,\hspace{0.5em}{j}_0=0$) (solid line) and from ortho-H${}_2$ ($v_0=0,\hspace{0.5em}{j}_0=1$) (dashed line) as a function of collision energy $E$ above the corresponding thresholds. Inset: Enlargement of the region of Feshbach resonances induced by the bound states of the closed-channel para-H${}_2$ $(v=0,\hspace{0.5em}j=2)+{\mathrm{H}}^{-}$ (see Fig. 1).

Figure 3

Rate coefficient $k_{\mathrm{RA}}$ as a function of temperature for RA of ${\mathrm{H}}^{-}$ with para-H${}_2$ ($v_0=0,\hspace{0.5em}{j}_0=0$) (solid line) and with ortho-H${}_2$ ($v_0=0,\hspace{0.5em}{j}_0=1$) (dashed line).