A Framework for Applying the Loeb-Turner $\alpha$-Slope Test to Archival Photometry of Trans-Neptunian Objects

Abstract

Reflected sunlight from a solar-system body produces a flux at Earth that scales as the heliocentric distance to the negative fourth power, whereas self-luminous emission scales as the negative second power. This difference defines the Loeb--Turner $\alpha$-slope test, a photometric technosignature diagnostic applicable to any solar-system body observed at multiple heliocentric distances. Of 22 (observatory $\times$ band) analysis bins for Pluto in the Minor Planet Center (MPC) archive, none recovers the reflected-sunlight flux--distance slope predicted when photometry is restricted to a single instrument and band. The archive cannot cleanly execute the $\alpha$-slope test on the brightest, most-observed trans-Neptunian object. We formalize a six-criterion eligibility pipeline (Q1--Q6) for the Loeb \& Turner technosignature test and apply it to every numbered TNO. Of 8,606 candidate bins (KBO $\times$ observatory $\times$ band), 1,089 pass Q1--Q3 and 186 additionally pass Q4--Q6, splitting into 53 consistent with reflected sunlight ($\alpha =-4$), 24 with self-luminous emission ($\alpha =-2$), and 109 anomalous. The anomalous bins exhibit slopes steeper than $\alpha =-4$ or shallower than $-2$, consistent with uncorrected per-instrument calibration offsets rather than any single physical mechanism. All 24 self-luminous-like bins originate from Pan-STARRS PS1/PS2; no other observatory contributes any. This indicates a per-instrument calibration systematic. The Rubin Observatory's ten-year survey will deliver uniform single-instrument calibration on a roughly threefold larger sample and either resolve the test at $>10\sigma$ on hundreds of TNOs or, by reproducing the same clustering, falsify the calibration-systematic interpretation.

8 pages, 3 figures, 5 tables. v2: corrected Eq. (2); pipeline re-run with updated counts (8,606 candidate bins, revised Tables 2-5); revised Lempo analysis. Submitted to the Open Journal of Astrophysics