Statistical Reevaluation of the USP Classification Boundary: Smaller Planets Within 1 Day, Larger Period Ratios Below 2 Days

Abstract: Terrestrial worlds with $P < 1$ day, known as ultra-short period planets (USPs), comprise a physically distinct population whose origins may be attributed to various possible formation channels within multi-planet systems. However, the conventional 1 day boundary adopted for USPs is an arbitrary prescription, and it has yet to be evaluated whether this specific cutoff, or any alternatives, may emerge from the data with minimal assumptions. We accordingly present a statistical evaluation of the USP classification boundary for 376 multi-planet systems across Kepler, K2, and TESS. We find that USPs are smaller in size ($p = 0.004$) and exhibit larger period ratios with their immediate neighbors ($\mathcal{P} = P_{2}/P_{1}$; $p < 10^{-4}$) when compared to non-USP short-period ($1 < P/\text{days} < 5$) worlds, and that these discrepancies rapidly transition towards statistical insignificance ($p > 0.05$) at respective orbital periods of $P_{R} = 0.97^{+0.25}_{-0.19}$ days and $P_{\mathcal{P}} = 2.09^{+0.16}_{-0.22}$ days (see Figure 1). We verify that these results are not driven by imprecise planetary parameters, giant companions, low-mass host stars, or detection biases. Our findings provide qualitative support for pathways in which proto-USPs are detached from companions and delivered to $P \lesssim 2$ days via eccentric migration, while a subset of these objects near $P \sim 1$ day experience subsequent orbital decay and refractory mass loss to become USPs. These results lend evidence towards an astrophysical basis for the 1 day USP cutoff and encourage consideration of an additional 2 day boundary within future investigations of USP architectures and evolutionary dynamics.