Statistical Reevaluation of the Ultra-short-period Planet Classification Boundary: Smaller Planets within 1 Day, Larger Period Ratios below 2 Days

Abstract Terrestrial worlds with P &lt; 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 multiplanet 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 multiplanet 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">P</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> ; p &lt; 10 −4 ) when compared to non-USP short-period (1 &lt; P /days &lt; 5) worlds, and that these discrepancies rapidly transition toward statistical insignificance ( p &gt; 0.05) at respective orbital periods of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.9</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.19</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> day and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">P</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.0</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.22</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.16</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> days (see Figure 3). 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 ≲ 2 days via eccentric migration, while a subset of these objects near P ∼ 1 day experience subsequent orbital decay and refractory mass loss to become USPs. These results lend evidence toward 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.