  Absolute photoionization cross sections for the Rb$^{2+}$ ion were recently
measured at high resolution over the energy range 37.31 eV -- 44.08~eV, with
autoionizing Rydberg resonance series identified, using the photon-ion
merged-beam setup at the Advanced Light Source (\textsc{als}) in Berkeley
{(Macaluso D A et. al. J. Phys. B: At. Mol. Opt. Phys. {\bf 49} (2016) 235002;
{\bf 50} (2017) 119501)}. Detailed photon-energy scans taken at 13.5 $\pm$ 2.5
meV bandwidth illustrated multiple Rydberg resonance series associated with the
ground and metastable states. Here we present theoretical cross section results
obtained using the Dirac-Coulomb $R$-matrix approximation with a detailed
analysis of the resonances. The calculations were performed for the
$3d^{10}4s^2 4p^5 \; {^2}{\rm P^o}_{J}$, $J=\frac{3}{2}$ ground state and the
corresponding $3d^{10}4s^2 4p^5 \; {^2}{\rm P^o}_{J}$, $J=\frac{1}{2}$
metastable level. Results from the large-scale calculations are benchmarked
against the \textsc{als} high-resolution measurements and reproduce the
dominant resonance features in the spectra, providing confidence in the
theoretical work for astrophysical applications.
