Radiative association of H$_2$ and H$^-$ at low temperature: can we observe H$_3^-$ 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 H$_3^-$ after the low energy collision (below 0.5~eV) of H$_2$ with H$^-$. Using recently obtained potential energy and permanent dipole moment surfaces of H$_3^-$, we calculate the lowest rovibrational levels of the H$_3^-$ electronic ground state, and the cross section for the formation of H$_3^-$ by radiative association between H$^-$ and ortho- and para-H$_2$. We discuss the possibility for the H$_3^-$ ion to be formed and observed in the cold and dense interstellar medium in an environment with a high ionization rate and thus suggest a way to detect the H$_3^-$ ion in the interstellar medium. Such an observation would be a probe for the presence of H$^-$ in the interstellar medium.