Properties of non-interacting BH-star systems in the fiducial model. Here, we only show stars in the giant phase, that is, outside the main sequence and that have not started the core helium burning phase yet. Also, we do not show systems that undergo a Roche-lobe overflow episode. From top to bottom and from left to right: Orbital period versus companion star mass; BH mass versus companion star mass; eccentricity versus orbital period; eccentricity versus companion star mass. The colour map shows the integrated time spent by the systems in a given bin; thus, it is a proxy of the likelihood of observing a system with such properties. The map does not include information about the stellar luminosity, which is also important for detectability. We assumed a metallicity of Z = 4.1 × 10⁻⁵. The star indicates the properties of Gaia BH3, while the light blue boxes show the criteria used to select Gaia BH3-like systems. The colour maps saturate at 98% of the maximum value.