Water ice: temperature-dependent refractive indexes and their astrophysical implications

Interstellar ices are largely composed of frozen water. It is important to derive fundamental parameters for H$_2$O ice such as absorption and scattering opacities for which accurate complex refractive indexes are needed. The primary goal of this work is to derive ice-grain opacities based on accurate H$_2$O ice complex refractive indexes and to assess their impact on the derivation of ice column densities and porosity in space. We use the \texttt{optool} code to derive ice-grain opacities values based on new mid-IR complex refractive index measurements of H$_2$O ice. Next, we use those opacities in the \texttt{RADMC-3D} code to run a radiative transfer simulation of a protostellar envelope containing H$_2$O ice. This is used to calculate water ice column densities. We find that the real refractive index in the mid-IR of H$_2$O ice at 30~K is $\sim$14\% lower than previously reported in the literature. This has a direct impact on the ice column densities derived from the simulations of embedded protostars. We find that ice porosity plays a significant role in the opacity of icy grains and that the H$_2$O libration mode can be used as a diagnostic tool to constrain the porosity level. Finally, the refractive indexes presented here allow us to estimate a grain size detection limit of 18~$\mu$m based on the 3~$\mu$m band whereas the 6~$\mu$m band allows tracing grain sizes larger than 20~$\mu$m. Based on radiative transfer simulations using new mid-IR refractive indexes, we conclude that H$_2$O ice leads to more absorption of infrared light than previously estimated. This implies that the 3 and 6~$\mu$m bands remain detectable in icy grains with sizes larger than 10~$\mu$m. Finally, we propose that also the H$_2$O ice libration band can be a diagnostic tool to constrain the porosity level of the interstellar ice, in addition to the OH dangling bond, which is routinely used for this purpose.