  It has been recently claimed that bulk crystals of transition metal
dichalcogenide (TMD) ReS$_2$ are direct band gap semiconductors, which would
make this material an ideal candidate, among all TMDs, for the realization of
efficient opto-electronic devices. The situation is however unclear, because
even more recently an indirect transition in the photoluminescence spectra of
this material has been detected, whose energy is smaller than the supposed
direct gap. To address this issue we exploit the properties of ionic liquid
gated field-effect transistors (FETs) to investigate the gap structure of bulk
ReS$_2$. Using these devices, whose high quality is demonstrated by a record
high electron FET mobility of 1,100 cm$^2$/Vs at 4K, we can induce hole
transport at the surface of the material and determine quantitatively the
smallest band gap present in the material, irrespective of its direct or
indirect nature. The value of the band gap is found to be 1.41 eV, smaller than
the 1.5 eV direct optical transition but in good agreement with the energy of
the indirect optical transition, providing an independent confirmation that
bulk ReS$_2$ is an indirect band gap semiconductor. Nevertheless, contrary to
the case of more commonly studied semiconducting TMDs (e.g., MoS$_2$, WS$_2$,
etc.) in their bulk form, we also find that ReS$_2$ FETs fabricated on bulk
crystals do exhibit electroluminescence when driven in the ambipolar injection
regime, likely because the difference between the direct and indirect gap is
only 100 meV. We conclude that ReS$_2$ does deserve more in-depth
investigations in relation to possible opto-electronic applications.
