We assess how many ISO discoveries are required to constrain parameters of the intrinsic Galactic ISO population, particularly the population's size-frequency distribution (SFD). Modern models of the Galactic ISO population are developing in theoretical richness, but remain poorly constrained, with only two objects discovered so far. Upcoming deeper wide-field surveys such as the Legacy Survey of Space and Time (LSST) are expected to discover a substantially larger sample, but the scale yet has order-of-magnitude uncertainties.

The SFD of ISOs has important implications for our understanding of the evolution of planetesimals. Modelling in the literature suggests the majority of ISOs are ejected from their origin systems via planetary migration or stellar flybys in the birth cluster; they may follow a streaming instability-like SFD. However, ISOs are primarily sourced from the equivalent parts of their disks to outer Solar System objects like TNOs. Evaluating whether ISOs share the SFD of TNOs will observationally constrain the contribution of exo-TNOs to the ISO population, and help constrain the departure point of ISOs within the early or late formation stages of their origin system.

We use a probabilistic approach to synthesise a sample of ISOs on trajectories through the Solar System, given an ISO velocity distribution inferred from the Gaia stellar sample (Hopkins et al. 2024). We calculate the probability that the sample would be detected by LSST, given observational effects such as trailing loss and phase effects. Comparing the “detected” ISOs to a variety of synthesised ISO populations using statistical power analysis techniques, we determine the minimum number of ISOs required to distinguish between potential ISO SFDs.