Testing the Isotropy of the Dark Energy Survey's Extreme Trans-Neptunian Objects

We test whether the population of extreme trans-Neptunian objects (eTNOs) detected in the first four years of the Dark Energy Survey (DES Y4) data exhibit azimuthal asymmetries that might be evidence of gravitational perturbations from an unseen super-Earth in a distant orbit. By rotating the orbits of the detected eTNOs, we construct a synthetic population that, when subject to the DES selection function, reproduces the detected distribution of eTNOs in the orbital elements a, e, and i as well as absolute magnitude H, but has uniform distributions in mean anomaly M, longitude of ascending node Omega, and argument of perihelion omega. We then compare the detected distributions in each of Omega, omega, and the longitude of perihelion (omega) over bar equivalent to Omega + omega to those expected from the isotropic population, using Kuiper's variant of the Kolmogorov-Smirnov test. The three angles are tested for each of four definitions of the eTNO population, choosing among a > (150, 250) au and perihelion q > (30, 37) au. These choices yield 3-7 eTNOs in the DES Y4 sample. Among the 12 total tests, two have the likelihood of drawing the observed angles from the isotropic population at p < 0.03. The three detections at a > 250 and q > 37 au and the four detections at a > 250 and q > 30 au have a omega distribution with p asymptotic to 0.03 coming from the isotropic construction, but this is not strong evidence of anisotropy given the 12 different tests. The DES data taken on their own are thus consistent with azimuthal isotropy and do not require a Planet 9 hypothesis. The limited sky coverage and object count mean, however, that the DES data by no means falsify this hypothesis.