Limits on Stellar Flybys in the Solar Birth Cluster

The orbits of small bodies in the outer solar system are particularly sensitive to gravitational perturbations, including stellar flybys. Stellar clusters, with low velocity dispersions and high number densities, can be the source of strong and frequent flybys. As a result, we can infer what properties of the solar birth environment would be incompatible with the structure of the outer solar system observed today. Here, we explore with $n-$body simulations the implications of the low inclinations ($i < 20^{\circ}$) of the distant sednoids (objects with perihelia $q > 40 \mathrm{\; AU}$ and semimajor axes $a > 400 \mathrm{\; AU}$) for the properties of the solar birth cluster. We find that the existence of these orbits, if they were in place in the Sun's birth cluster phase, would limit the product of the stellar number density and the Sun's residence time in the birth cluster to $\lesssim 5 \times 10^3 \mathrm{\; Myr \; pc^{-3}}$, as compared to the weaker limit $\lesssim 5 \times 10^4 \mathrm{\; Myr \; pc^{-3}}$ implied by the low inclinations of the cold classical Kuiper belt.