Broadband spectroscopy of astrophysical ice analogues: III. Scattering properties and porosity of CO and CO$_2$ ices

$Context.$ The quantification of the terahertz (THz) and IR optical properties of astrophysical ice analogs, which have different molecular compositions, phases, and structural properties, is required to model both the continuum emission by the dust grains covered with thick icy mantles and the radiative transfer in the dense cold regions of the interstellar medium. $Aims.$ We developed a model to define a relationship between the THz$-$IR response and the ice porosity. It includes the reduced effective optical properties of porous ices and the additional wave extinction due to scattering on pores. The model is applied to analyze the measured THz$-$IR response of CO and CO$_2$ laboratory ices and to estimate their scattering properties and porosity. $Methods.$ Our model combines the Bruggeman effective medium theory, the Lorentz-Mie and Rayleigh scattering theories, and the radiative transfer theory to analyze the measured THz$-$IR optical properties of laboratory ices. $Results.$ We apply this model to show that the electromagnetic-wave scattering in studied laboratory ices occurs mainly in the Rayleigh regime at frequencies below 32 THz. We conclude that pores of different shapes and dimensions can be approximated by spheres of effective radius. By comparing the measured broadband response of our laboratory ices with those of reportedly compact ices from earlier studies, we quantify the scattering properties of our CO and CO$_2$ ice samples. Their porosity is shown to be as high as 15% and 22%, respectively. Underestimating the ice porosity in the data analysis leads to a proportional relative underestimate of the THz$-$IR optical constants. $Conclusions.$ The scattering properties and porosity of ices have to be quantified along with their THz$-$IR response in order to adequately interpret astrophysical observations.